CRITICAL THINKING For what angle measure(s) is the tangent of an acute angle in a right triangle equal to 17 greater than 1? less than 17The tangent of an acute angle in a right triangle is equal to 1 for angle measures of:The tangent of an acute angle in a right triangle is greater than 1 for angle measures that are:than:The tangent of an acute angle in a right triangle is less than 1 for angle measures that arethan:
Answers
1. The tangent of an acute angle in a right triangle equal to 17 greater than 1 that measure angle is 57.29 degrees.
2. The tangent of an acute angle in a right triangle equal to 17 less than 1 that measure angle is 45 degrees.
3. The tangent of an acute angle in a right triangle equal to 17 equal to 1 that measure angle is 45 degrees.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite to the angle to the length of the adjacent side. Let us denote the acute angle by θ, the length of the side opposite to the angle by a, and the length of the adjacent side by b. Then we have:
tan(θ) = a/b
Since the angle θ is acute, we have a > 0 and b > 0. We can use the Pythagorean theorem to relate the lengths of the two sides to the length of the hypotenuse c:
a^2 + b^2 = c^2
Solving for b, we get:
\(b = \sqrt{c^2 - a^2}\)
Substituting this into the expression for tangent, we get:
tan(θ) = a/ \(\sqrt{c^2 - a^2}\)
Now, we can use the given conditions to find the possible values of the angle θ.
1. If tan(θ) is 17 greater than 1, we have:
tan(θ) > 1 and tan(θ) = 17 + 1 = 18
Using the expression for tangent above, we get:
a/sqrt(c^2 - a^2) > 1 and a/√(c^2 - a^2) = 18
Squaring both sides of the inequality and simplifying, we get:
a^2 < (c^2 - a^2) and a^2 = 324(c^2 - a^2)
Solving for a/c, we get:
a/c = √(324/325)
Since a/c is the sine of the angle θ, we have:
sin(θ) = a/c = √(324/325)
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.9999 radians or 57.29 degrees satisfies the given condition.
2. If tan(θ) is less than 1, we have:
tan(θ) < 1
Using the expression for tangent above, we get:
a/√(c^2 - a^2) < 1
Squaring both sides and simplifying, we get:
a^2 > (c^2 - a^2)
Solving for a/c, we get:
a/c > √(2)/2
Since a/c is the sine of the angle θ, we have:
sin(θ) > √(2)/2
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition.
3. If tan(θ) is equal to 1, we have:
tan(θ) = 1
Using the expression for tangent above, we get:
a/√(c^2 - a^2) = 1
Squaring both sides and simplifying, we get:
a^2 = c^2 - a^2
Solving for a/c, we get:
a/c = √(2)/2
Since a/c is the sine of the angle θ, we have:
sin(θ) = a/c = √(2)/2
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition. Alternatively, we can note that the angle whose tangent is equal to 1 is 45 degrees.
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Related Questions
What is the multiplicity of the zero x=1 for the function f(x)=x^(2)(x-1)^(4)(x+5)
Answers
The multiplicity of the zero \(x=1\) for the function \(f(x)=x^2(x-1)^(4)(x+5)\) is 4.
In a polynomial function, the multiplicity of a zero is the number of times that zero appears as a factor in the function. In other words, it is the exponent of the factor corresponding to that zero.
In the given function \(f(x)=x^2(x-1)^4(x+5)\), we can see that the zero x=1 corresponds to the factor (x-1)^(4). This means that the multiplicity of the zero x=1 is 4, as it appears as a factor 4 times in the function.
Therefore, the multiplicity of the zero \(x=1\) for the function \(f(x)=x^2(x-1)^(4)(x+5)\) is 4.
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Find the angel between the two vectors (4,1) and (-8,3)
Answers
The angle between the two vectors (4,1) and (-8,3) will be 145.4°.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is possible to calculate the angle () between two vectors using the formula
\(\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}\)
Calculate dot product:
=a · b
= ax · bx + ay · by
= 4 · (-8) + 1 · 3
= - 32 + 3
= -29
=|a|
= √ax² + ay²
= √4² + 1²
= √16 + 1
= √17
=|b|
=√ bx² + by²
= √(-8)² + 3²
= √64 + 9
= √73
\(\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}\)
α = 145.40771131249005°
Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.
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Joseph’s lunch at a restaurant costs $13.00, with out tax, he leaves the walter a tip of 17% of the cost of the lunch, with out tax, what is the total cost of the lunch, including the tip, with out tax
Answers
the answer is $15.21
Answer:
The total cost of the lunch, including the tip and without tax, is $15.21.
Step-by-step explanation:
We know that the tip is calculated as 17% of the cost of the lunch, without tax.
1. convert percentage into a decimal
17% = 0.17 because 17/100 = 0.17
2. calculate the tip amount
tip = 0.17 * 13
tip = $2.21
3. find the total cost of the lunch
total cost = cost of lunch + tip
total cost = $13 + $2.21
total cost = $15.21
Therefore, the total cost of the lunch, including tip and without tax is $15.21.
for each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by:
Answers
For each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by the slope of the line.
Slope is the amount of change in the y-axis that occurs as a result of a one-unit change in the x-axis. It is also known as the rise over run.
A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. If the slope is zero, the line is horizontal.
If the line slopes up from left to right, it has a positive slope. As the value of x increases by one, the value of y also increases by the slope. If the line slopes downward from left to right, it has a negative slope. As the value of x increases by one, the value of y decreases by the slope.The slope of a horizontal line is zero, and the slope of a vertical line is undefined because the x or y coordinate does not change as the other changes.
Therefore, the slope of a line represents the amount by which the value on the y-axis increases for every increase of one unit on the x-axis
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Use trigonometric identities to simplify \(sec^2(\pi /2-(x))[sin^2(x) -sin^4(x)]\)
Answers
Answer:
Step-by-step explanation:
I am using trig identities and the formula for the difference of the cos of 2 angles to solve this. I'll do the steps one at a time. It's super tricky. First I'm just going to work on simplifying the sec² part and then I'll introduce the sin²(x) - sin⁴(x) when I need it. Beginning with the identity for the difference of the cos of 2 angles, knowing that sec²(x) = \(\frac{1}{cos^2(x)}\):
\(sec^2(\frac{\pi}{2}-x)=\frac{1}{cos^2(\frac{\pi}{2}-x )}\) and expand that using the formula for the difference:
\(\frac{1}{cos(\frac{\pi}{2}-x)cos(\frac{\pi}{2}-x) }=\) \(\frac{1}{(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x))(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x)) }\) and all of that simplifies down to
\(\frac{1}{(0cos(x)+1sin(x))(0cos(x)+1sin(x))}\) which simplifies further to
\(\frac{1}{(sin(x))(sin(x))}=\frac{1}{sin^2(x)}\) Now we'll bring in the other term. This is what we have now:
\(\frac{1}{sin^2(x)}(\frac{sin^2(x)-sin^4(x)}{1})\) and distribute in to get:
\(\frac{sin^2(x)}{sin^2(x)}-\frac{sin^4(x)}{sin^2(x)}\) which simplifies to
\(1-sin^2(x)\) and that, finally, simplifies down to a simple
\(cos^2(x)\)
The perimeter of square is 96cm .Find the area and the length of the diagonal
Answers
Answer:
length is 32
formula of finding the length of square is 92 divided by 3
32
area is 1024
the formula of finding area is Lenght multiply by length
so 32 multiply by 32
1024
mark my answer brainliest
1. The graph shows the height of a plant after a certain amount of time measured in days. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. The graph shows how much snow fell after a certain amount of time measured in hours. 2. Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning.
Answers
Due to different rates of change in each case, neither graph shows a proportional relationship.
When does a graph represents a proportional relationship?A graph represents a proportional relationship if the output variable y in the y-axis can be written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
Item 1Between days 0 and 10, the plant grew by 4 centimeters.Between days 30 and 40, the plant grew by 8 centimeters.For the first case, the rate of change is of:
k = 4/10 = 0.4.
For the second case, the rate of change is of:
k = 8/10 = 0.8.
Different rates, hence cannot be written as proportional relationship.
Item 2Between hours 0 and 2, the amount of snow grew by 2 inches.Between days 2 and 4, the amount of snow remained constant at 2 inches.Hence the rates for each interval are given as follows:
Hours 0 - 2: 2/2 = 1 inch a hour.Hours 2 - 4: 0/2 = 0 inches a hour.Different rates, hence it is not a proportional relationship.
What is the missing information?The graphs are missing and are given by the image inserted at the end of the answer.
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Find the values of x
when y = 1
Answers
Step-by-step explanation:
when y=1 then,
y=1+X
X=1-y .
I'm assuming the equations are o that you solve in your own:
x = y + 1 = 1+1 = 2
x = y -1 = 1-1 = 0
x = 1*y = 1*1 = 1
x = y*1 = 1*1 = 1
x = y/1 = 1/1 = 1
x = 1/y = 1/1 = 1
What is an Equation?
An equality relationship between two expressions written on both sides of the equal to sign.
How Equations are Used in Real Life?There are many situations in which equations can be used. Whenever an unknown quantity has to be found, an equation can be formed and solved.
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find the smallest positive integer $n$ with the property that the polynomial $x^4 - nx 63$ can be written as a product of two nonconstant polynomials with integer coefficients.
Answers
The smallest positive integer n for which the polynomial x^4 - nx - 63 can be factored as a product of two nonconstant polynomials with integer coefficients is 97.
To find the smallest positive integer n that satisfies the given condition, we need to consider the factors of the constant term -63 and check if any combination can be used to factorize the polynomial x^4 - nx - 63.
The constant term -63 can be factored as (-1) * 3^2 * 7, giving us several possible combinations of factors to consider: {-1, 1, -3, 3, -7, 7, -9, 9, -21, 21, -63, 63}.
We try each combination and check if it is possible to factorize the polynomial with those factors. After testing these combinations, it is found that n = 97 is the smallest positive integer for which the given polynomial can be factored as a product of two nonconstant polynomials with integer coefficients.
Thus, the polynomial x^4 - 97x - 63 can be written as a product of two nonconstant polynomials with integer coefficients, and 97 is the smallest positive integer that satisfies this condition.
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What is the length of a segment in the complex plane with endpoints at 4 2i and 7 – 2i?
Answers
The length of the segment in the complex plane is 5.
The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:
Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.
Plugging these values into the formula, we have:
Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
= sqrt(3^2 + (-4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
Therefore, the length of the segment in the complex plane is 5.
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Find the cosine of the angle between the vectors i + 6j and 10j + 7k. (Use symbolic notation and fractions where needed.) cos(0) =
Answers
The cosine of the angle between the two vectors is:
cosθ = 60 / √5501
The numerator and denominator do not share any factors, we cannot simplify the fraction any further.
To find the cosine of the angle between two vectors, we first need to find the dot product of the two vectors and then divide it by the product of their magnitudes. Let's start by finding the dot product:
(i + 6j) · (10j + 7k) = 0 + 60 + 0 = 60
Next, we need to find the magnitudes of the two vectors:
|i + 6j| = √(1² + 6²) = √37
|10j + 7k| = √(0² + 10² + 7²) = √149
Now we can plug in the values into the cosine formula:
cosθ = (i + 6j) · (10j + 7k) / |i + 6j| |10j + 7k|
= 60 / (√37)(√149)
= 60 / √5501
Finally, we can see that cosθ is equal to 1 when the angle between the two vectors is 0. This makes sense since i + 6j and 10j + 7k are not perpendicular to each other.
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maple has 4 identical loaves of bread that weigh a total of 6.6 pounds how much does 1 loaf of bread weigh
Answers
Answer:
1.65 pounds
Step-by-step explanation:
6.6 ÷ 4 = 1.65
Answer:
1.65
Step-by-step explanation:
since all together it weighs 6.6 pounds then 1 = x then you cross multiply after cross multiplying you divide 4 by 6.6. Then x = 1.65
find the value of z such that 0.1 of the area lies to the right of z. round your answer to two decimal places.
Answers
The value of z is approximately 1.28 (rounded to two decimal places).
To find the value of z such that 0.1 of the area lies to the right of z, we need to determine the z-value corresponding to the 90th percentile of the standard normal distribution. This can be achieved using a standard normal distribution table or statistical software.
In detail, the standard normal distribution has a mean of 0 and a standard deviation of 1. The area under the curve is standardized, allowing us to use z-scores to find percentiles. Since we want to find the z-value corresponding to the 90th percentile, we are looking for the value that leaves 10% of the area to the right. Using a standard normal distribution table or statistical software, we find that the z-value corresponding to the 90th percentile is approximately 1.28. Therefore, the value of z is approximately 1.28.
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1
Write an algebraic
expression for:
Seven added to five
times a number
Answers
Write an algebraic expression for: seven added to five times a number
Answer:
7 + 5x
The sum of two numbers is 12
and their product is 32.
What are the two numbers ?
Answers
Answer:
8 and 4
Step-by-step explanation:
8 x 4= 32
8+4 = 12
What is the IQR for the following set of data
17, 11, 12, 18, 12, 16, 15, 14, 13
Answers
Answer:
First, we have to set it from least to greatest 11, 12, 12, 13, 14, 15, 16, 17, 18
The interqurtile range is q3 - q1
Q3 is 16.5 and the q1 is 12
16.5 - 12 = 4.5
Step-by-step explanation:
Answer is 4.5
Interquartile range (IQR) :
The interquartile range shows the range in values of the central 50% of the data. To find the interquartile range, subtract the value of the lower quartile ( or 25%) from the value of the upper quartile ( or 75%).
=> IQR = Q3 – Q1
Here,
First Arrange the data in ascending order.
11, 12, 12, 13, 14, 15, 16, 17, 18
Median = 14.
Q1 = 12 and Q3 = 16.5
IQR = Q3 - Q1 => 16.5 - 12 = 4.5
Answer is 4.5
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Suppose $700 is invested for 2 years at a nominal yearly interest rate that is compounded monthly, further suppose it accumulates to 773.45 after 2 years. Find the effective annual interest rate of the investment. Effective annual interest rate =
Answers
The effective annual interest rate of the investment is approximately 5.4%.
To find the effective annual interest rate, we need to consider the compounding frequency and the total accumulated amount after the specified time period. In this case, the investment is compounded monthly, and it accumulates to $773.45 after 2 years.
Convert the nominal interest rate to the monthly rate:
Since the interest is compounded monthly, we need to convert the nominal yearly interest rate to the monthly rate. Assuming a nominal interest rate of \(\(r\)\), the monthly rate can be calculated as \(\(i = \frac{r}{12}\)\).
Calculate the effective annual interest rate:
To find the effective annual interest rate, we can use the formula:
\(\((1 + i)^{12} = (1 + \text{effective annual interest rate})\)\).
Rearranging the formula and solving for the effective annual interest rate, we have:
\(\(\text{effective annual interest rate} = (1 + i)^{12} - 1\)\).
Substitute the values and calculate:
In this case, the accumulated amount is $773.45 after 2 years. By substituting the values into the formula, we have:
\(\(773.45 = 700(1 + \frac{r}{12})^{24}\)\).
Solving for \(\(r\)\), we find:
\(\(\frac{r}{12} \approx 0.0045\)\).
Converting the monthly rate to the effective annual interest rate, we get:
\(\((1 + \frac{r}{12})^{12} - 1 \approx 0.054\),\) which is equivalent to 5.4%.
Therefore, the effective annual interest rate of the investment is approximately 5.4%.
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4(y-3) + 3(y+4). solve the equation fast and ill mark you brainliest
Answers
Step-by-step explanation:
4(y-3) + 3(y+4)
4y-12+ 3y+12
4y+3y-12+12
7y
I hope it helped U
stay safe stay happy
Answer:
hope it helps you.......
The average and standard deviation of the weights of 350 Indian students are 55 kg and 3 kg respectively. And the average and standard deviation of weights of 450 German students are 60 kg and 4 kg respectively. a. Determine the combined mean weight of all those Indian and German students. b. Find the standard deviation of weight for the combined group of students.
Answers
The combined mean weight of all Indian and German students is 57.81 kg. The combined standard deviation of weight for the group is 3.59 kg.
The combined mean weight is calculated by adding the mean weights of the two groups and dividing by the total number of students. In this case, the mean weight of the Indian students is 55 kg and the mean weight of the German students is 60 kg. There are a total of 350 Indian students and 450 German students, so the combined mean weight is (350 * 55 + 450 * 60) / (350 + 450) = 57.81 kg.
The combined standard deviation is calculated using a formula that takes into account the standard deviations of the two groups and the number of students in each group. In this case, the standard deviation of the Indian students is 3 kg and the standard deviation of the German students is 4 kg. The combined standard deviation is sqrt((350 * 3^2 + 450 * 4^2) / (350 + 450)) = 3.59 kg.
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If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)? m
Answers
Answer:x − x^{2} − 1.
Step-by-step explanation:
.
solve the given initial-value problem. d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0
Answers
The solution to the given initial-value problem is x(t) = c1(e-ωt - eωt) = 2c1 sin ωt
The given initial-value problem is a second-order differential equation: d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0
First, we can solve the homogeneous equation d2x dt2 + ω2x = 0 using the method of characteristic equation. The characteristic equation is r2 + ω2 = 0, which has two solutions r1 = -ω, r2 = ω.
The general solution to the homogeneous equation can be expressed as:
x(t) = c1e-ωt + c2eωt
Next, we can solve the non-homogeneous equation d2x dt2 + ω2x = f0 sin ωt. Since the right-hand side of the non-homogeneous equation has a sinusoidal form, we can use the method of variation of parameters to solve it.
The particular solution can be expressed as:
x(t) = A sin ωt + B cos ωt
By substituting the initial conditions, we can get:
A = 0, B = 0
Therefore, the solution to the given initial-value problem is:
x(t) = c1e-ωt + c2eωt
The constant c1 and c2 can be determined by the initial conditions:
x(0) = c1 + c2 = 0
x'(0) = -ωc1 + ωc2 = 0
Therefore, c1 = -c2 and c1 + c2 = 0.
Hence, the solution to the given initial-value problem is:
x(t) = c1(e-ωt - eωt) = 2c1 sin ωt
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efine the relation ~ on Q as follows: For a, b e Q, a ~ b if and only if a-b e Z. In Progress Check 7.9 of Section 7.2, we showed that the relation ~ is an equivalence relation on Q. Also, see Exercise (9) in Section 7.2. * (a) Prove that [*] = {m+ {mez]. (b) Ifa e Z, then what is the equivalence class of a? (c) Ifa e Z, prove that there is a bijection from
Answers
a. [*] = {m + neZ | z e Z}. b. If a e Z, then the equivalence class of a is [*] = {a + n | n e Z}, which can be written as {n + {a}}. c. f is both injective and surjective, it is a bijection from [*] to Z.
(a) To prove that [] = {m + neZ | z e Z}, we need to show that every element in [] is of the form m + neZ, and every element of the form m + neZ is in [*].
First, let x be an arbitrary element of []. Then x is of the form x = a + b, where a e Z and b e []. Since b e [*], we know that b = m + n, where m e Z and n e Z. Therefore, x = a + m + n, which can be written as x = m + (a + n). Since a + n is an integer, x is of the form m + neZ.
Now, let y be an arbitrary element of the form m + neZ. Then y = m + nz for some integer z. Since n e Z, we know that n = []. Therefore, y = m + []z, which can be written as y = m + b, where b e []. Hence, y e [].
Thus, we have shown that [*] = {m + neZ | z e Z}.
(b) If a e Z, then the equivalence class of a is [*] = {a + n | n e Z}, which can be written as {n + {a}}.
(c) To prove that there is a bijection from [] to Z, we need to construct a function f: [] -> Z that is both injective and surjective.
Let f(x) = m, where x = m + n for some m e Z and n e [*].
To show that f is well-defined, suppose x = m1 + n1 = m2 + n2 for some m1, m2 e Z and n1, n2 e []. Then m1 - m2 = n2 - n1, which means that m1 - m2 e []. Therefore, f(x) = m1 = m2, and so f is well-defined.
To show that f is injective, suppose f(x1) = f(x2) for some x1, x2 e []. Then f(x1) = m1 = m2 = f(x2), which means that x1 and x2 have the same first coordinate (i.e., the same element of Z). But since x1 and x2 are elements of [], they also have the same second coordinate (i.e., they belong to the same equivalence class). Therefore, x1 = x2, and so f is injective.
To show that f is surjective, let m be an arbitrary element of Z. Then f(m + []) = m, which means that every element of Z is the image of some element of [] under f. Therefore, f is surjective.
Since f is both injective and surjective, it is a bijection from [*] to Z.
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each point of the plane is colored red or blue. show that there is a rectangle whose corners are all the same color
Answers
We can always find a monochromatic rectangle by reducing the problem to finding a monochromatic rectangle in a smaller area by moving the bottom of the rectangle up by one unit method.
What is rectangle?
A rectangle is a quadrilateral (a 2-dimensional shape with four sides) with four right angles. This means that opposite sides of a rectangle are parallel and congruent, and all four angles are equal to 90 degrees.
Let us consider a rectangle with sides parallel to the coordinate axes. Such a rectangle can be uniquely determined by two pairs of points that define its opposite corners. If all four of these points are the same color, then we have found a monochromatic rectangle. Otherwise, there are three cases to consider:
The two points at the top of the rectangle are the same color, and the two points at the bottom are the other color. In this case, we can reduce the problem to finding a monochromatic rectangle in a smaller area by moving the bottom of the rectangle up by one unit.
The two points on the left side of the rectangle are the same color, and the two points on the right side are the other color. In this case, we can reduce the problem to finding a monochromatic rectangle in a smaller area by moving the left side of the rectangle to the right by one unit.
Both pairs of points are of mixed color. In this case, we can reduce the problem to finding a monochromatic rectangle in two smaller areas by dividing the rectangle into four equal parts with a vertical or horizontal line.
By repeating this process on the smaller rectangles obtained in each case, we can eventually find a monochromatic rectangle. Since the rectangles we consider at each step have half the area of the previous ones, this process terminates after at most log_2(A) steps, where A is the area of the original rectangle.
Therefore, we can always find a monochromatic rectangle with this method.
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Complete question:
Each point in the x-y plane colored red or blue. show that there is a rectangle whose corners are all the same color.
a) -20
b) -8
c) 8
d) 48
Answers
Answer:
b. -8
Step-by-step explanation:
Solution Given:
Equation is:
y=8-2x
if x=8
Substitute value of x in above equation
y=8-2*8
y=8-16
y=-7
Answer:
-8
Step-by-step explanation:
This question is asking us what y is equal to when x equals 8. To determine this, we can plug 8 into the equation for x and solve for y. So, let's do just that!
y = 8 - 2x [ Plug in 8 for x ]
y = 8 - 2(8) [ Simplify ]
y = 8 - 16 [ Solve ]
y = -8
So, when x=8, y=-8. Attached is an image of the function graphed that also shows that when x=8, y=-8.
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George spends five-eighths of his salary on food,one- sixth of the remainder on school fees,two-thirdths of what remains on contingencies and saves 6000.Calculate George's monthly salary
Answers
Their monthly income of George is 57,600.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given spends of George from monthly income,
let monthly income be x
spends on food = 5/8 of salary
spends on food = 5x/8
amount left = x - 5x/8 = 3x/8
spends on fees = 1/6 of remainder
spends on fees = 1/6 × 3x/8 = x/16
amount left = 3x/8 - x/16 = 5x/16
spend on contingencies = 2/3 of remainder
spend on contingencies = 2/3 × 5x/16
spend on contingencies = 5x/24
amount left = 5x/16 - 5x/24 = 5x/48
amount left = 6000 = 5x/48
x = (6000×48)/5
x = 57,600.
Hence monthly income is 57,600.
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George's monthly salary is 57600
What are fractions?A fraction represents a numerical value, which defines the parts of a whole. the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.
The basics of fractions explain the top and bottom numbers of a fraction. The top number represents the number of selected or shaded parts of a whole whereas the bottom number represents the total number of parts.
Let monthly salary of George be x.
Given, Money spend on food = 5/8th of salary = 5/8x
Remaining salary = x - 5x/8 = 3x/8
Amount on school fees = 3x/8 × 1/6 = x/16
Remaining amount = 3x/8 - x/16 = 5x/16
Amount on contingencies = 5x/16 × 2/3 = 5x/24
According to the question
5x/8 + x/16 + 5x/24 + 6000 = x
(30x + 3x + 10x) /48 +6000 = x
43x /48 + 6000 = x
x-43x/48 = 6000
48x - 43x = 6000 × 48
5x = 288000
x = 57600
George monthly salary = 57600
Hence, George get a monthly salary of 57600
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The set of ordered pairs in the table below can be described as which of the following
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We have two sets from which we get the coordinates of the ordered pair. We know that a set of ordered pair is called a relation, and that the set from which the first coordinate comes from is the domain while the set where the second coordinate comes from is called the range.
Thus, the given set is a relation.
Also we know that there are special kinds of relations--those whose first coordinate only has one corresponding second coordinate. They are called functions.
In this set, -6 corresponds to 3, 0 corresponds to 7, and 6 corresponds to 5. There is a one-to-one relation.
Therefore, this set is also a function.
The answer is the second option--it is both a function and a relation.
If z(m/s2) = a x(m3) + b cos (y), what are the units of a, b,
and y?
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Given that the formula is given as z(m/s²) = a x(m³) + b cos (y) Wherea, b, and y are the unknown terms.To determine the units of a, b, and y, we need to check the units of each term present in the equation. The unit of displacement or distance is meters (m).The unit of acceleration is meters per second squared (m/s²).Unit of cos(y) is not there, but we know that cos(y) is a unitless term.Therefore, the given equation can be written askg x m/s² = kg/m x m³ + b x 1There we can see that the unit of the term on the left side of the equation is kg x m/s² which is equal to Newton (N).Therefore, the unit of the term on the right side of the equation is also in Newton (N).Hence,The unit of "a" is N/m³The unit of "b" is NThe unit of "y" is unitless.
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please help! i’m stuck
Answers
Answer:
CD = 12.
Step-by-step explanation:
By the tangent-secant theorem:
AB^2 = AC * AD
8^2 = 4 * AD
AD = 64/4 = 16
Finally CD = AD - 4 = 12.
74+(-91)x27=?
answer
Answers
Answer:
\( - 2383\)
Step-by-step explanation:
\(74 + ( - 91) \times 27 \\ 74 + (- 2457) \\ - 2383\)
what is the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each?
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2/221 is the probability that a 2-card hand has two queens, two kings, or one of each.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or the probability that a statement is true.Probability varies between zero and 1, wherein zero approaches are not possible and 1 approach is certain.Now, calculate the probability as follows:
There are 4 kings and 4 queens in a deck of cards.Then, it can be either KK or QQ.
Select 2 kings from 4 king cards that can be done in 4c₂=6 ways.Select 2 queens from 4 queen cards that can be done in c₂ = 6 ways.Total ways = 52c₂ = 1326So required probability = 2king or 2 queen
= 6/1326 + 6/1326= 12/1326= 2/221Therefore, the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each is 2/221.
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