The solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct
The given equation is 1/(x-3) + 1/(x+5) = 1/3
Take LCM on left hand side
(x+5)+(x-3)/(x-3)(x+5)= 1/3
2x+2/(x-3)(x+5) = 1/3
2(x+1)/(x-3)(x+5) = 1/3
6(x+1)=(x-3)(x+5)
6x+6 = x²+5x-3x-15
6x+6 = x²+2x-15
x²+2x-6x-15-6=0
x²-4x-21=0
x² -7x+3x-21=0
x(x-7)+3(x-7)
(x+3)(x-7)
The solutions are x=-3, x=7
Hence, the solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct
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In an attempt to improve brand recognition, the marketing department of AC Sports is
creating conical paper water cups with their brand printed around the surface of the
cup. The cups will be sent to athletic departments for free. About how much space do
the graphic artists working on the design have to work with if the cup will have a
diameter of 2.5 inches and a height of 3.5 inches?
Answer:
about 37.31 inches of space
Step-by-step explanation:
In this case, you would need to find the area of a cylinder with these dimensions.
Formula: 2πrh+2πr²
The r is the radius, and since the diameter in this situation would be 2.5, the radius would be 1.25.
2π(1.25)(3.5)+2π(1.25)²
2π4.375+2π1.5625
8.75π+3.125π
37.3064128
about 37.31 inches of space
Find the surface area of a cylinder pls
The total surface area of the cylinder is 157 square feet.
Given the radius of the cylinder = 4 inches
height of the cylinder = 9 inches
Total surface area is calculated by the formula:
A = 2πr² + 2πh
A = 2 × 3.14 × 4² + 2 × 3.14 × 9
or, A = 157 square feet.
Therefore the total surface area of the cylinder is 157 square feet.
The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves.
The definition of surface area for polyhedral (i.e., particles with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated.
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There are 6 arms for every 4 eyes.
If there are 3 arms, how many eyes
are there?
8
7
2
3
Answer:
2 eyes
Explanation:
I just did this lol.
Solve for the value of 'x' given:5.25 = -log(x)This question will require an answer in scientific notation. For example, 0.0435 would be input as 4.35e-2Answer:
Solution
Solve for the value of 'x' given:
5.25 = -log(x)
\(5.25=-logx\)\(\begin{gathered} x=\frac{1}{10^{5.25}} \\ x=5.62341...e-6 \end{gathered}\)Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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What is the name of each labeled part?
A:dentrite
B: cell body
C:axon terminal
D:axon
E: nucleus
Trinagle ABC has vertices at A(0,5), B(-3,3), and C(0,-5) Classify the triangle according to the side lengths
The classification of the triangle according to its side lengths and vertices would be scalene triangle.
How to classify the triangle?To classify the triangle, you first need to find the lengths of the sides of the triangle. You can do this by finding the distance between the vertices given.
To find the vertices, the formula is:
= √ ( ( x₂ - x₁ ) ² + ( y ₂ - y ₁) ² )
The length of AB is therefore 3.61 units
The length of BC is 8.54 units
The length of AC is 10 units.
None of the side lengths of this triangle are the same so it is a scalene triangle.
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Juan has $72, which is 6 times as much money as Kayla has. How much
money does Kayla have? Select the correct solution method, using x to
represent Kayla's money.
Answer:
12
Step-by-step explanation:
because 6x=72 so you could do 72/6 which 72/6 is 12 so the answer is 12
3 1/8 divided by (x - 4 7/28) = 17/18 + 1 5/6
(Key on how to write the mixed numbers: Three is a whole number and then the fraction is 1/8, 4 is the whole number and 7/28 is the fraction, 1 is the whole number and 5/6 is the fraction)
Please provide the work and the answer! :)
x = 301/56
Algebraic expressionsAlgebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expression
Given the algebraic expression,
\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)
Step 1:
Simplify the expression by converting the mixed numbers into improper fractions:
25/8 ÷ ( x - 119/28) = 17/18 + 11/6
Step 2: Simplify the right side of the equation
25/8 ÷( x - 119/28) = 17/18 + 33/18
25/8 ÷( x - 119/28) = 50/18
Step 3: Multiply both sides of the equation by (x - 119/28)
25/8 = 50/18 × (x - 119/28)
Step 4: Multiply both sides of the equation by (18/50)
25/8 × (18/50) = (x - 119/28)
Step 5: Simplify the left side of the equation
9/8 = (x - 119/28)
Step 6: Add 119/28 to both sides of the equation
9/8 + 119/28 = x
Step 7: Calculate the value of x:
x = 9/8 + 119/28
= 63/56 + 238/56
= 301/56
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A rectangular garden has a length of 57 m and a width of 42 m. How many m2 will decrease the area of a garden, if the ornamental fence with a width of 60 cm will be planted inside its perimeter?
The area of the rectangular garden can be calculated as follows: 57 m * 42 m = 2406 m^2.
The ornamental fence with a width of 60 cm has a width of 0.6 m. If the fence is planted inside the perimeter of the garden, the length of the garden will decrease by 2 * 0.6 m = 1.2 m and the width of the garden will decrease by 2 * 0.6 m = 1.2 m.
So, the new length and width of the garden will be 57 m - 1.2 m = 55.8 m and 42 m - 1.2 m = 40.8 m, respectively.
The new area of the garden can be calculated as follows: 55.8 m * 40.8 m = 2270.784 m^2.
Finally, the decrease in area can be calculated as follows: 2406 m^2 - 2270.784 m^2 = 35.216 m^2.
Therefore, the area of the garden will decrease by 35.216 m^2.
Answer:
The width of the ornamental fence is 60 cm, which is equal to 60/100 = 0.6 meters.
The total length of the ornamental fence that will be planted inside the perimeter of the rectangular garden is 2 * (57 m + 42 m) = 2 * 99 m = 198 m.
The decrease in the area of the garden due to the ornamental fence is 0.6 m * 198 m = 118.8 m^2.
11/12 - 5/8 in simplest form
Answer:
7/24
Step-by-step explanation:
11/12 - 5/8
Get a common denominator of 24
11/12 * 2/2 = 22/24
5/8 *3/3 = 15/24
22/24 -15/24 = 7/24
Are the points (12, 11), (2, 7), (5, 9), and (1, 5) part of the same linear function? EXPLAIN
The points (12, 11), (2, 7), (5, 9), and (1, 5) are not part of the same linear function because they do not form a straight line on a graph.
How to Determine if a Point is Part of a Linear Function?A linear function is a straight line graph. All points that are part of a linear function lie on the straight line.
To determine if the set of points, (12, 11), (2, 7), (5, 9), and (1, 5) are part of the same linear function, plot each of the points on a coordinate pane to determine if a straight line runs through the given points.
The graph shows the plotted points. If the points are connected together by a line, the line will not be a straight line.
Therefore, the points are not part of the same linear function.
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Find the value of y.
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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Find the measure of ACD
A - 36 degrees
B - 126 degrees
C - 162 degrees
D - 216 degrees
Answer:
C
Step-by-step explanation:
i assume its
C.
square root of 48
\( \sqrt{48} \)
Answer:
\(\sqrt{48} = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{2 \times 2} \times \sqrt{2 \times 2} \times \sqrt{3} \\ = 2 \times 2 \times \sqrt{3} \: \: \: \: \: \: \\ = 4 \times \sqrt{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 4 \sqrt{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)
Step-by-step explanation:
\(\large\pink{HeavenMistress \: }\)
\(\rule{300pt}{4000pt}\)
Which is an equation of the line with a slope of 2 that passes through ( 3 , 1 )?
\(\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}\)
let the solution be \( ax + by - c = 0 \)
let the solutions be a = 3, b = 1
\( 3x + y = 0 \) is the equation with consistent value.
Answer:
the answer is -1
Step-by-step explanation:
im just tyna get my points thats all
Write the prime factorization of 27. Use exponents when appropriate and order the factors from least to greatest (for example, 2235)
Answer:
Step-by-step explanation:
\(27=3\times 3 \times 3=3^3\)
ordered: \(3^3\)
What is the surface area of the box if it is scaled up by a factor of 10? Surface area = 106
The surface area scaled up by a factor of 10 is \(10^7\)
Surface area and scale factorGiven the following information
Surface area = \(10^6\)Scale factor = 10The surface area if the given surface area is scaled up by 10 is expressed as:
\(10 \times 10^6 = 10^7\)Hence the surface area scaled up by a factor of 10 is \(10^7\)
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You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
The calculation of this can be done by first determining the future value of the monthly payments of $327.50
The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,
which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.
The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35
This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.
Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.
for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).
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The length of a rectangle is four times its width.
If the perimeter of the rectangle is 50in, find its length and width
Answer:
Hajj smart kya tum ham held
The area of the base and total surface area of a square based solid pyramid are 144 sq. cm and 384 sq cm respectively. What will be the volume of the pyramid? Find it
Answer:
384 cubic centimeters
Step-by-step explanation:
We are given the base area and total area of a square pyramid and asked to find the volume. The typical volume formula for a pyramid requires that we know the height of it. We can use the formula for the surface area to find the slant height of a face, and we can use the slant height to find the height perpendicular to the base.
__
face areatotal surface area = base area + area of 4 faces
area of 4 faces = total surface area - base area
area of 4 faces = 384 cm² -144 cm² = 240 cm²
area of 1 face = 240 cm²/4 = 60 cm²
__
slant heightThe side length of the square base is ...
A = a²
a = √A = √(144 cm²) = 12 cm
and the slant height of one face is ...
A = 1/2as
s = (2A)/a = (2×60 cm²)/(12 cm) = 10 cm
__
pyramid heightThe distance from the center of the base to the edge of the base is (12 cm)/2 = 6 cm. That is one leg of the right triangle whose hypotenuse is the slant height of the face. The other leg of the triangle is the height of the pyramid:
H² = s² -(a/2)² . . . . Pythagorean theroem solved for one leg
H = √(10² -6²) = 8 . . . . cm . . . . height of the pyramid
__
volumeNow we know the base area of the pyramid (B), and we know its height (H), so we can use the formula ...
V = 1/3BH
V = 1/3(144 cm²)(8 cm) = 384 cm³
The volume of the pyramid will be 384 cm³.
Of the students in Jill's grade, 41 students have a pet and the other 7 students do not. What is the ratio of the number of students who do not have a pet to the total number of students?
Answer:
The answer is 7 : 48.
Step-by-step explanation:
First, you can to calculate how many students are there in Jill's grade by adding the number of students who have pet with the students without pets :
total = 41 + 7 = 48
Next, you have to find the ratio of students without pets to total students :
7 : 48
Answer:
SoluTion :-Total student = Student who have pet + Student who don't have pet
Total Student = 41 + 7
Total Student = 48
Ratio
\( \tt \:7 \ratio \: 48\)
need help with this asap pls really need the answer
In the diagram, the area of the given shape is 102 cm²
Area of a KiteFrom the question question, we are to determine the area of the given shape
The given shape is a kite
The area of a kite is given by the formula,
\(A =\frac{pq}{2}\)
Where A is the area
p and q are the diagonals
In the given diagram,
p = 6cm + 6 cm = 12 cm
q = 3 cm + 14 cm = 17 cm
Thus,
Area of the kite = \(\frac{12 \times 17}{2}\)
Area of the kite = 6 × 17
Area of the kite = 102 cm²
Hence, the area of the given shape is 102 cm²
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Find the area of the triangle.area triangle 1A. 14.1 km²B. 12.8 km²C. 15.2 km²D. 14.7 km²
Given:
a = 7 km
b = 6 km
c = 5 km
To find the Area of the triangle, we use Heron's formula, as follows:
\(A=\sqrt{s(s-a)(s-b)(s-c)}\)where s:
\(Semi\text{ }Perimeter\text{ }(s)=\frac{a+b+c}{2}=\frac{7+6+5}{2}=9km\)hence:
\(A=\sqrt{9\times(9-7)\times(9-6)\times(9-5)}=14.7km^2\)ANSWER
D. 14.7 km²
Given right triangle � � � ABC with altitude � � ‾ BD drawn to hypotenuse � � ‾ AC . If � � = 22 AD=22 and � � = 15 , DC=15, what is the length of � � ‾ BD in simplest radical form?
The length of BD is 18.5 units.
In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.
Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.
In triangle ABD, we have the following sides:
AB = AD = 22 (given)
BD = ?
Now, let's consider triangle CBD. In this triangle, we have the following sides:
BC = DC = 15 (given)
BD = ?
Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.
The area of triangle ABD can be calculated as:
Area(ABD) = (1/2) * AB * BD
Similarly, the area of triangle CBD can be calculated as:
Area(CBD) = (1/2) * BC * BD
Since the areas of ABD and CBD are equal, we can equate their expressions:
(1/2) * AB * BD = (1/2) * BC * BD
We can cancel out the common factor (1/2) and solve for BD:
AB * BD = BC * BD
Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:
AB = BC
In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.
BD is equal to half of the hypotenuse AC:
BD = (1/2) * AC
Substituting the given values, we have:
BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5
Therefore, the length of BD is 18.5 units.
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solve for x, 11, 31°
The value of x is 21.4.
What is right-angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.
The sine of an angle is the ratio of height to the hypotenuse.
Therefore,
sin 31° = height/hypotenuse
sin 31° = 11/x
Multiply x with both sides:
x sin 31° = 11
Divide sin 31° with both sides:
x = 11/ sin 31°
x = 21.35
x ≈ 21.4 units
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At a cafe, the Bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. The Cortez family pays $14 for two salads and two sandwiches. The Donovan family pays $14 for a salad and three fruit bowls. What is the price of a fruit bowl at the cafe?
$2
$3
$4
$5
Answer:
$3
Step-by-step explanation:
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I need 23 questions answered
The surface area of a rectangular prism is 48 5/6 mi².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]
Surface area of rectangular prism = 2[14 + 15/2 + 35/12]
Surface area of rectangular prism = 48 5/6 mi².
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-4x + 21 > -3
What could x be??
Answer:
x < 6
Step-by-step explanation:
subtract 21 on both sides
-4x > -24
divide both sides by -4 and flip the sign (bc you're dividing by a negative)
x < 6
6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answer:
65/100 that is the answer to this question