The measure of angle BAC in Triangle ABC is 45 degrees.
The measure of angle YZX in Triangle XYZ is 60 degrees.
We have,
a)
Let's denote the third angle in Triangle ABC as angle BAC.
Since we know that angle CAB measures 45 degrees and angle BAC is acute, we can subtract the sum of these two angles from 180 degrees to find angle BAC:
BAC = 180 degrees - CAB - BCA
= 180 degrees - 45 degrees - 90 degrees
= 45 degrees
b)
Let's denote the third angle in Triangle XYZ as angle YZX.
Since we know that angle XYZ measures 30 degrees and angle YZX is acute, we can subtract the sum of these two angles from 180 degrees to find angle YZX:
YZX = 180 degrees - XYZ - ZXY
= 180 degrees - 30 degrees - 90 degrees
= 60 degrees
Therefore,
The measure of angle BAC in Triangle ABC is 45 degrees.
The measure of angle YZX in Triangle XYZ is 60 degrees.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ4
The complete question:
Consider two triangles, Triangle ABC and Triangle XYZ.
Triangle ABC:
Side AB has a length of 5 units.
Side BC has a length of 8 units.
Angle CAB (opposite side AB) is acute and measures 45 degrees.
Triangle XYZ:
Side XY has a length of 7 units.
Side YZ has a length of 10 units.
Angle XYZ (opposite side XY) is acute and measures 30 degrees.
In both triangles, angle C in Triangle ABC and angle Z in Triangle XYZ are both acute angles.
Based on this information, you can consider the following questions:
a) Calculate the measure of the third angle in Triangle ABC.
b) Calculate the measure of the third angle in Triangle XYZ.
Working together, Mary and Trevon can
inflate twenty balloons in 7.34 minutes.
Had he done it alone it would have taken
Trevon 14.1 minutes. How long would it
take Mary to do it alone?
20 balloons in 7.34 minutes? lets do the math! \(\frac{20}{7.34\\}\) = 2.73 balloons a minute.
If Trevon took 14.1 minutes, lets do the math, \(\frac{20}{14.1}\) = 1.42 balloons a minute, now if we take 2.73, subtract 1.42 from 2.73. 2.73 - 1.42, we get, Drum roll please...................... 1.31 !!! So, with that fact, we get 1.31, so that means Mary would have to blow 1.31 balloons a minute WITH Trevon, now some more math. we take the amount Mary did, 1.31, and the amount of time it took for both, 7.34, we get this problem, 1.31 x 7.34 which equals (yes I'm doing it again) DRUM ROLL PLEASEEEE....................... 9.60!!!!!!!!
So, in the end, the answer is 9.60
~~Best regards
~Akmp
Cicely and James are working on if-then statements in their geometry class. Their statements for "Right triangles have one right angle" are shown below.
Cicely
If a triangle is a right triangle, then it has one right angle.
James
If a triangle has one right angle, then it is a right triangle.
Which of the two has written a correct if-then statement
James has written a correct if-then statement.
In an if-then statement the part following the "if" should be a hypothesis, and the part following the "then" should be a conclusion statement.
Considering the two of the given statements:
Cicely's statement: "If a triangle is a right triangle, then it has one right angle." is correct since the hypothesis and conclusion are both correct.
James's statement: "If a triangle has one right angle, then it is a right triangle." is also correct since the hypothesis and conclusion are both correct.
Now, comparing both the statements "If a triangle has one right angle" is a perfect hypothesis since it gives a condition which when followed gives the conclusion.
Hence, James has written a correct if-then statement.
Learn more about Conditional Statements:
https://brainly.com/question/18152035
#SPJ1
Out of these numbers which ones are multiples of 7 {−7, −4, 2, 14, 21, 34, 42}
Answer:
-7, 14, 21, and 42
Step-by-step explanation:
7•-1=-7
7•2=14
7•3=21
7•6=42
which of the following statements is true? a high correlation is insufficient to establish causation on its own. if the two variables of a scatterplot are strongly related, this condition implies causation between the two variables. only a correlation equal to 0 implies causation. a correlation of 1 or -1 implies causation.
A high correlation is insufficient to establish causation on its own.
There are six bottles of juice for the same size and we need to make each kid have a 1/3 of a bottle how many kids will there be enough for is this the right story problem for 6÷1/3
Answer:
yes, 6÷1/3, which is 6×3 or 18
Step-by-step explanation:
plot points H I and J on the coordinate plane
In order to plot points H I and J on the coordinate planeIdentify the x-coordinate and y-coordinate of each point (H, I, and J). For example, let's say the coordinates are as follows:
Point H: (xH, yH)
Point I: (xI, yI)
Point J: (xJ, yJ)
How to explain the informationLocate the origin (0, 0) on the coordinate plane. This is the starting point for plotting any point.
Move along the x-axis according to the x-coordinate of each point. If the x-coordinate is positive, move to the right; if it's negative, move to the left. Mark a point on the x-axis at the appropriate location.
Move along the y-axis according to the y-coordinate of each point. If the y-coordinate is positive, move upward; if it's negative, move downward. Mark a point on the y-axis at the appropriate location.
The point where the x and y axes intersect is the location of the point. Mark that point on the coordinate plane.
Learn more about coordinate on
https://brainly.com/question/29765572
#SPJ1
How to Plot points H I and J on the coordinate plane
how to find the area of a quadrilateral with coordinates
To find the area of a quadrilateral with given coordinates, you can use the Shoelace Formula.
The Shoelace Formula, also known as Gauss's area formula, provides a method to calculate the area of any polygon given its coordinates. Here's how it works for a quadrilateral:
Let's say you have the coordinates of the four vertices of the quadrilateral: (x1, y1), (x2, y2), (x3, y3), and (x4, y4).
1. Write down the coordinates in a clockwise order:
(x1, y1), (x2, y2), (x3, y3), (x4, y4), (x1, y1).
2. Multiply each x-coordinate by the y-coordinate of the next vertex.
For example, for the first vertex (x1, y1), multiply x1 by y2, and for the second vertex (x2, y2), multiply x2 by y3, and so on.
3. Multiply each y-coordinate by the x-coordinate of the next vertex.
For example, for the first vertex (x1, y1), multiply y1 by x2, and for the second vertex (x2, y2), multiply y2 by x3, and so on.
4. Add up all the results from Steps 2 and 3.
5. Take the absolute value of the sum calculated in Step 4 and divide it by 2.
By following the steps of the Shoelace Formula, you can calculate the area of a quadrilateral given its coordinates. Remember to ensure that the coordinates are listed in a clockwise or counterclockwise order to obtain the correct result. This method can be applied to any quadrilateral shape and provides an efficient way to find its area without requiring complex calculations or trigonometric functions.
To know more about Area, visit
https://brainly.com/question/25292087
#SPJ11
Given the ordered pairs {(-2,6). (1,0), (-3,10), (5,4), (7,8), (9,-9)], the value 8 is part of the _______________.
a. range
b. domain
In this case, the pair (7,8) is present in the given set. Here, the input or domain is 7, and the output or range is 8. The value 8 is part of the range of the given ordered pairs.
In the given set of ordered pairs {(-2,6), (1,0), (-3,10), (5,4), (7,8), (9,-9)], the first value in each pair represents the input or domain, while the second value represents the output or range. The range consists of all the output values obtained from the given set. By observing the second values of the pairs, we can determine which numbers are part of the range.
In this case, the pair (7,8) is present in the given set. Here, the input or domain is 7, and the output or range is 8. Therefore, the value 8 is part of the range. The range of the given set of ordered pairs is the collection of all the second values, which includes 6, 0, 10, 4, 8, and -9.
To learn more about range visit:
brainly.com/question/31397986
#SPJ11
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. tan(A) = 5/12 , b = 2
I have to find a=?
I have to find c=?
The length of side a is 10/3, and the length of the hypotenuse c is 2√(34)/3.
What are the lengths of the missing sides?To find the length of side a, we can use the tangent of angle A. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, tan(A) = 5/12, which means that the length of side a is 5/12 times the length of the adjacent side. Since we know that side b is 2, we can calculate a = \((5/12) * 2 = 10/3\).
To find the length of the hypotenuse c, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we know that side b is 2 and side a is 10/3. Let's denote the length of c as x. Applying the Pythagorean theorem, we have \((10/3)^2 + 2^2 = x^2\). Simplifying this equation, we get \(100/9 + 4 = x^2\). Combining the terms, we have 100/9 + 36/9 = \(x^2\), which gives us \(136/9 = x^2\). Taking the square root of both sides, we have \(x = \sqrt{(136/9)} = \sqrt{(136)/} \sqrt{(9)} = \sqrt{(136)/3} = 2\sqrt{(34)/3}\).
Therefore, the lengths of the missing sides are a = 10/3 and c = \(2 \sqrt{(34)/3}\).
Learn more about Length
brainly.com/question/8552546
#SPJ11
please help will give brainliest
if is right and has explanation
Answer:
(B) 1 unit cube and 75 smaller cubes of volume fraction 1 over 125 cubic inch each
Step-by-step explanation:
.
A student passes a magnet over 10 grams of a powder. Four grams of the powder stick to the magnet, while 6 grams do not. Which of these identifies the substance?
answer choices
element
compound
mixture
solution
As per the unitary method, mixture identifies the substance
The term unitary method in statistics means mathematical process to calculate the value of a single unit from the value of multiple units and the value of multiple unit rate from the value of a single unit.
Here we have given that A student passes a magnet over 10 grams of a powder. Four grams of the powder stick to the magnet, while 6 grams do not.
And we need to find in which of these identifies the substance
While we looking into the given question , we know that the properties of the components of substance are different.
We also know that one component has magnetic properties, another does not.
Therefore, here we have at least 2 individual substances that were mixed together and we have a mixture.
To know more about unitary method here.
https://brainly.com/question/28276953
#SPJ4
у кого-нибудь есть ответы на рт матем 2022/2023 1 этап 1 вариант?
Answer:
извините, у меня нет ответа
5. Jessie has jogged 30 miles since starting her new exercise program
plans to continue jogging 6 miles every day for the next x days,
Which expression below represents the total amount of miles that she will
have jogged after x days?
A. *(30 + 6)
B. 6(x + 30)
C. 6x + 30
D. 6 + 30x
Answer:
C
Step-by-step explanation:
30 is the b in this equation which represents the number of miles she has already jogged. 6 represents the number of miles she jogs every day for x amount of days. x could be 5, in which case it would be represented as 6*5+30=60. But since we don't know what x is, it is just 6x+30.
Which is the better value? 12 bottles of juice for $15.00, or 18 bottles of juice for $23.04?
Answer: it’s 1.25 for the first and 1.28 for the second so the first of 12 bottles 15$ Is the better value
Step-by-step explanation:
Convert Roman Numeral:
The conversion of CIX from roman numeral to Hindu-arabic form is; 109
How to convert roman numerals?We are given the roman numeral; CIX
Now, in roman numerals we know that;
C = 100
IX = 9
Thus, we can express the given roman numeral as;
CIX = 100 + 9
CIX = 109
Read more about Roman Numerals at; https://brainly.com/question/17380759
#SPJ1
A town has a population of 20000 and grows at 5% every year. To the nearest tenth of a year, how long will it be until the population will reach 41600?
If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .
To find out how long it will take for the town's population to reach 41600, we can use the formula :
⇒ A = P(1 + r)ⁿ
Where:
A = final population of town , P = initial population o town
r = percent increase (as a decimal)
let n = number of years for population to reach 41600 .
We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05 and we have to solve for n.
Substituting the values ,
we get ;
⇒ 41600 = 20000(1 + 0.05)ⁿ ;
⇒ 41600 = 20000(1.05)ⁿ ;
⇒ 41600/20000 = (1.05)ⁿ ;
taking "log" on both sides ,
we get ;
⇒ log(41600/20000) = n × log(1.05) ;
⇒ n = log(41600/20000)/log(1.05) ;
⇒ n = 15.0105 ≈ 15
Therefore , it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.
Learn more about Percent Increase here
https://brainly.com/question/15175015
#SPJ4
Log2 x = -5 Write into exponential equation
\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_2(x)=-5\implies 2^{-5}=x\)
Answer:
y=mx+b
Step-by-step explanation:
An angle in a rectangular coordinate system is in standard position if its vertex is at the_______.
An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.
The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.
To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.
Learn more about the rectangular coordinate system: https://brainly.com/question/4726772
#SPJ11
Can someone PLEASE help me ASAP?? It’s due today!! i will give brainliest if it’s correct!!
Find the slope of the line that passes through (2, 12) and (9, 3).
Simplify your answer and write
as a proper fraction, improper fraction, or integer.
Answer:
The slope of line is \(-\frac{9}{7}\).
Step-by-step explanation:
Given points are;
(2, 12) and (9, 3)
Here,
x1 = 2 and y1 = 12
x2 = 9 and y2 = 3
Slope of a line is given by the following formula;
\(m =\frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{3-12}{9-2}\\\\m=\frac{-9}{7}\)
Therefore,
The slope of line is \(-\frac{9}{7}\).
The z score associated with the highest 10% is closest to
a. .0398
b. .5398
c. 1.28
d. -1.28
The z score associated with the highest 10% is closest to: option (c) 1.28
-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.
- Look up the 0.90 (90%) in a standard normal distribution (z score) table, which will give you the corresponding z score.
-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.
Therefore, the z score associated with the highest 10% is closest to 1.28.
To know more about "standard normal distribution" refer here:
https://brainly.com/question/29509087#
#SPJ11
What number should replace the question mark below?
Step-by-step explanation:
2/3 * 150 = 1/2 * ?
100 = 1/2 * ? Multiply both sides by 2 to get
200 = ?
Find the first four nonzero terms of the Taylor series about 0 for the function t^(2)sin(5t)
The first four nonzero terms of the Taylor series about 0 for the function f(t) = t^2 sin(5t) are:
t^2, (5/3)t^3, ...
To find the first four nonzero terms of the Taylor series about 0 for the function f(t) = t^2 sin(5t), we need to compute the derivatives of f(t) at t = 0 and evaluate them at t = 0.
The first few derivatives of f(t) are:
f'(t) = 2t sin(5t) + t^2 * 5cos(5t)
f''(t) = 2 sin(5t) + 2t * 5cos(5t) + (2t)^2 * (-25sin(5t))
f'''(t) = 10cos(5t) + 10t * (-25sin(5t)) + (2t)^2 * (-125cos(5t)) + (2t)^3 * 125sin(5t)
Evaluating these derivatives at t = 0, we have:
f(0) = 0
f'(0) = 0
f''(0) = 2
f'''(0) = 10
Now, let's write the Taylor series using these derivatives:
f(t) ≈ f(0) + f'(0)t + f''(0)t^2/2! + f'''(0)t^3/3! + ...
Substituting the values we obtained, we get:
f(t) ≈ 0 + 0 + 2t^2/2! + 10t^3/3! + ...
Simplifying the expression, we have:
f(t) ≈ t^2 + (5/3)t^3 + ...
Know more about Taylor series here;
https://brainly.com/question/29733106
#SPJ11
Help plzzzz plzzz plzzzzz plzzzzzzzz
Answer:
1 + X
Step-by-step explanation:
You just write whats there
Answer: I think it might be 1 + x or x = 1
Step-by-step explanation:
Which graph represents the line described by the given point (- 2, 3) and slope 0
The graph of the line parallel to x-axis and passes trough the point (-2,3).
What is slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m = Δy/Δx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be shown as
tan θ = Δy/Δx.
Given that the slope of the line is 0. Thus the angle between the line with the x-axis is 0 degree as tan 0° = 0.
The line is parallels to x-axis.
The equation of the line that is parallel to x-axis is y = a.
Since the line passes through the point (-2,3), thus it will be satisfies the equation line.
Putting x = -2 and y = 3
a = 3
The equation of the line is y = 3
To learn more about equation of line, click on below link:
https://brainly.com/question/25776493
#SPJ1
A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if they are different colors, then you win -$1.00. (That is, you lose $1.00.) Calculate
(a) the expected value of the amount you win;
(b) the variance of the amount you win.
(a) The expected value of the amount you win will be -0.0667.
(b) The variance of the amount you win will be 1.089.
(a) the expected value of the amount you win 2/9 , (b) the variance of the amount you win 5/18 , c) The expected value of the amount you win is -$0.0667 and d)The variance of the amount you win is 1.2898.
Let's calculate the expected value and variance of the amount you win step by step:
a) Calculate the probability of drawing two marbles of the same color.
First, calculate the probability of drawing two red marbles:
P(RR) = (5/10) * (4/9) = 20/90 = 2/9
Similarly, calculate the probability of drawing two blue marbles:
P(BB) = (5/10) * (4/9) = 20/90 = 2/9
b) Calculate the probability of drawing two marbles of different colors.
P(RB) = (5/10) * (5/9) = 25/90 = 5/18
P(BR) = (5/10) * (5/9) = 25/90 = 5/18
c) Calculate the expected value.
The expected value (EV) is calculated by multiplying each outcome by its probability and summing them up.
EV = (P(RR) * $1.10) + (P(RB) * -$1.00) + (P(BR) * -$1.00) + (P(BB) * $1.10)
= (2/9 * $1.10) + (5/18 * -$1.00) + (5/18 * -$1.00) + (2/9 * $1.10)
= $0.2444 - $0.2778 - $0.2778 + $0.2444
= -$0.0667
Therefore, the expected value of the amount you win is -$0.0667.
d) Calculate the variance.
The variance is a measure of the dispersion of the outcomes around the expected value. It is calculated as the sum of the squared differences between each outcome and the expected value, weighted by their probabilities.
Variance = (P(RR) * ($1.10 - EV)²) + (P(RB) * (-$1.00 - EV)²) + (P(BR) * (-$1.00 - EV)²) + (P(BB) * ($1.10 - EV)²)
Variance = (2/9 * ($1.10 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (2/9 * ($1.10 - (-$0.0667))²)
= (2/9 * $1.1667²) + (5/18 * -$0.9333²) + (5/18 * -$0.9333²) + (2/9 * $1.1667²)
= 1.2898
Therefore, the variance of the amount you win is 1.2898.
To know more about expected value check the below link:
https://brainly.com/question/30398129
#SPJ4
critical thinking, teamwork, leadership, and professionalism are some of the knowledge competencies needed for career readiness. True or False
Helen told her mom she got 85% on a recent math test. She remembered the test was out of 60. What was her actual mark? *
Answer: 85% out of how many questions.
Step-by-step explanation:
Find the surface area of the composite figure
Answer: SA = 644 cm²
Step-by-step explanation:
STEP ONE: Find the surface area of the smaller rectangle (green)
There are in total 5 sides because one of the sides is not shown on the surface level.
Upper base = 3 × 3 = 9 cm²
4 sides = 3 × 8 × 4 = 96 cm²
Total = 9 + 96 = 105 cm²
STEP TWO: Find the surface area of the larger rectangle (orange)
There are in total 5 whole sides with one side covered by the base of the smaller rectangle (green) which should later be subtracted.
Front and back = 7 × 10 × 2 = 140 cm²
Left and right = 7 × 12 × 2 = 168 cm²
Lower base = 10 × 12 = 120 cm²
Upper base = 10 × 12 - 3 × 3 = 111 cm²
Total = 140 + 168 + 120 + 111 = 539 cm²
STEP THREE: Find the total surface area
SA = Green + Orange = 105 + 539 = 644 cm²
Hope this helps!! :)
Please let me know if you have any questions
a set of x and y scores has b = 4, mx = 12, and my = 51. what is the y-intercept (a) for the regression equation?
The y-intercept for the regression equation is 3, given that b = 4, Mx = 12, and My = 51. So, the correct option is C).
The formula for the y-intercept of the regression equation is
a = My - b(Mx)
where My is the mean of the dependent variable (y), b is the slope, and Mx is the mean of the independent variable (x).
Given that b = 4, Mx = 12, and My = 51, we can substitute these values in the formula to find the y-intercept
a = 51 - 4(12)
a = 51 - 48
a = 3
Therefore, the y-intercept (a) for the regression equation is 3.
The correct Answer is C) 3.
To know more about regression equation:
https://brainly.com/question/30738733
#SPJ4
--The given question is incomplete, the complete question is given
" A set of X and Y scores has b = 4, Mx = 12, and My = 51. What is the y-intercept (a) for the regression equation? O 9.75 17.36 3.00 8.25 "--