Choose whether each function represents exponential growth or exponential decay.

The diameter , radius and area of the circle is 126cm, 63cm, 12474cm² respectively.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle.

The circumference of a circle is given as;

C = π d

where d is the diameter of the circle

therefore 396 = 22/7 × d

22d = 396× 7

22d = 2772

divide both sides by 22

d = 2772/22

d = 126 cm

the diameter of a circle is 2 times it's radius

d = 2r

126 = 2r

r = 126/2

r = 63cm

The area of the circle is

A = πr²

A = 22/7× 63× 63

A = 22×9× 63

A= 12474cm²

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Jamal and Lin will meet 3.21 miles from Jamal's house.

Meet is a gathering of two or more people for a specific purpose, such as to discuss an issue, make a decision, or socialize. It can take place in person or online, either in a formal or informal setting.

The time it takes for Jamal and Lin to meet is the time it takes for Jamal to travel 2 miles plus the time it takes for Lin to travel 2 miles.
Since Jamal is walking at 3 mi/h, it takes him (2 miles) / (3 mi/h) = 0.67 hours to travel 2 miles.
Since Lin is walking at 5 mi/h, it takes her (2 miles) / (5 mi/h) = 0.4 hours to travel 2 miles.
The total time it takes for Jamal and Lin to meet is 0.67 + 0.4 = 1.07 hours.
Jamal and Lin will meet 1.07 hours after they left their houses.
Since Jamal is walking at 3 mi/h, he will have traveled (1.07 hours) * (3 mi/h) = 3.21 miles when they meet.
Jamal and Lin will meet 3.21 miles from Jamal's house.

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Answer:

R' ( -2,1)

S' (-8,2)

T' ( -4,7)

Step-by-step explanation:

The height of the statue is:

A. 276 inches

If Wally, who is 69 inches tall, catch a shadow that is 41 inch in length.

To determine the height of the statue, you can use the principle of similar triangles. Similar triangles have the same angles, but not necessarily the same side lengths. You can use the ratio of the height of Wally and the length of his shadow to the height of the statue and the length of its shadow to find the height of the statue.

Height of Wally: 69 inches

Length of Wally's shadow: 41 inches

Height of statue: x

Length of statue's shadow: 164 inches

You can set up the proportion as:

69/41 = x/164

Solving for x, you get:

x = (69 × 164)/41

x = 276 inches

Thus the answer is A. 276 inches.

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The perimeter of the horse corral is 600 feet.

The area of Rectangle is length times of width.

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and

p is the perimeter of the polygon.

Given that area of the horse corral is 3000 ft²

Length of the apothem is 10 ft

We need to find the perimeter.

3000=10p/2

6000=10p

Divide both sides by 10

600=perimeter

Hence, the perimeter of the horse corral is 600 feet.

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To find the equation of the axis of symmetry using factored form, we can use the multiply and conversion method which converts it into vertex form.

It can be multiplied and converted to vertex form.

Example: (x-3)(x+2) f(x)

f(x) = x^2 - x - 6

We can now combine the x terms to finish the square.

f(x) = (x^2 - x +1/4 ) - 6 - 1/4

f(x)= (x - 1/2)^2 -25/4

As a result, the vertex is (1/2, -25/4)

Any quadratic given in factored form can be solved this way.

If the parabola contains the equation y=f(x)=a(xr1)(xr2), the zeroes of f(x), i.e., r1 and r2, can be read off right away. The vertex then has coordinates (h,k), where k=f(h) is the result of inserting x=h through the function f(x), and h=(r1+r2)/2 is the average of the two zeroes.

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He ran 194 miles fewer he ran in 3 days than the 16 days run.

the statute mile, which is 5,280 feet long, is one example of a mile (1.609 km). The mille passus, or "thousand paces," was a unit of measurement used in ancient Rome and equaled 5,000 Roman feet.

The "old London" mile, which was eight furlongs, was first established around the year 1500. The mile at that time was equal to 5,000 feet, with the furlong being 625 feet at that time, using the larger northern (German) foot.

A statute from 1593 that confirmed the use of a shorter foot and made the length of the furlong 660 feet increased the mile by 280 feet during the reign of Queen Elizabeth I, bringing it to 5,280 feet.

The Fewer mile he ran = (16 × 14) - (3 × 10)

                                      = 194 miles

Thus, He ran 194 miles fewer he ran in 3 days than the 16 days run.

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The measure of the exterior angle in this case is 60+60 = 120 degrees.

What is exterior angle ?

An exterior angle of a polygon is an angle formed between one side of the polygon and a line extended from the endpoint of the opposite side. An exterior angle can be formed by standing outside of the polygon and looking at it.

In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it. In any convex polygon, the sum of the measures of the exterior angles is always 360 degrees.

The support for a window air-conditioning unit forms a triangle. A triangle is a three-sided polygon, and all the interior angles in a triangle add up to 180 degrees. Therefore, the measure of each interior angle of a triangle is (180/3) = 60 degrees.

An exterior angle of a triangle is the angle formed between one side of the triangle and a line extended from the endpoint of the opposite side. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it.

Therefore, the measure of the exterior angle in this case is 60+60 = 120 degrees.

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The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

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Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

Answer: it's 5000 :)

Step-by-step explanation:

Answer: 5000

Step-by-step explanation:

Answer:

k = 75

Step-by-step explanation:

Let's write down the prime factors of 15 and 375

15 = 3 x 5

375 = 3 x 5 x 5 x 5

So 15 x 375 = 3 x 5 x 3 x 5 x 5 x 5

= (3 x 3) x   (5 x 5 x 5) x 5

This cannot be a perfect cube

However if we multiply this by 3 x 5 x 5 we will get

(3 x 3 x ) x (5 x 5 x 5) x(5 x 5 x 5) which is a perfect cube

Since we are asked to find k such that 15 x 375 x k is a perfect cube

k = 3 x 5 x 5 = 75

ans
k = 75

Two lines that make right angles at their intersection are Perpendicular lines.

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Answer:

x = 14°

Step-by-step explanation:

We know that,

→ Straight line is always 180°.

Forming the equation,

→ 156° + (x + 10°) = 180°

Now the value of x will be,

→ 156° + (x + 10°) = 180°

→ x + 166° = 180°

→ x = 180° - 166°

→ [ x = 14° ]

Hence, the value of x is 14°.

The value of x in the given supplementary angle pair is 14°.

Then,

156 + (x + 10) = 180

166 + x = 180

x = 180 - 166

x = 14°

Thus, the value of x in the given supplementary angle pair is 14°.

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Answer:

see below

Step-by-step explanation:

33ft wire is needed for 6 trees.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Each wire is attached to the trunk 3ft. above the ground,

and then anchored to the ground 2.5 ft. from the base of the tree.

So, for each tree total wire = 3+2.5

                                             =5.5 ft.

So, for 6 trees = 5.5*6

                       =33ft

Hence, 33ft wire is needed for 6 trees.

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Answer:

276.75

Step-by-step explanation:

one gallon lets sara drive 22.5 miles. multiply that by 12.3 and u get 276.75 !

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.

The area of Rectangle is length times of width.

Given that the area of rectangle is 70y⁸+30y⁶

The width of the rectangle is the greatest common factor of 70y⁸ and 30y⁶

70y⁸+30y⁶

10y⁶(y²+3)

10y⁶ is the width of the rectangle.

y²+3 is the length of the rectangle.

Hence, 10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.

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Answer: mean = 55

Step-by-step explanation:

Distance between 64 and 82 = 18

Each standard deviation is worth 9 units.

So 64 - 9 = 55(mean)

Or use m= x-zq

The advantages of having a graphing calculator

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A tudy how that the more exercie people had a day the more they lept at night which catter plot repreent the relationhip The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.

A scatter plot would be used to represent the relationship between the amount of exercise people have per day and the hours of sleep they get at night. The scatter plot would show the number of hours of exercise on the x-axis and the number of hours of sleep on the y-axis. Each point on the scatter plot would represent an individual's exercise and sleep hours. The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.

1. A scatter plot is used to represent the relationship between two variables.

2. In this case, the two variables are the amount of exercise people have per day and the hours of sleep they get at night.

3. The x-axis of the scatter plot would represent the amount of exercise, while the y-axis would represent the hours of sleep.

4. Each point on the scatter plot would represent an individual's exercise and sleep hours.

5. The overall pattern of the scatter plot should show that as the amount of exercise increases, the amount of sleep also increases.

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The graph for the points (-1, 0), (0, 6), (1, 8), (2, 6) and (3, 0) is plotted below.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=-2(x-3)(x+1).

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex: (1,8)

Focus: (1,63/8)

Axis of Symmetry: x=1

Directrix: y=65/8

Plot the points (-1, 0), (0, 6), (1, 8), (2, 6) and (3, 0).

Therefore, graph for the points (-1, 0), (0, 6), (1, 8), (2, 6) and (3, 0) is plotted below.

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To use the sine rule for a triangle, we will need to know at least two side lengths and the measure of the angle opposite one of those sides.

What is triangle ?

A triangle is a geometric shape that has three straight sides and three angles. Triangles are classified based on the measures of their angles and the lengths of their sides.

What is law of sine ?

The law of sines, is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. Specifically, the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

It can be written as

[tex]a/sin(A) = b/sin(B) = c/sin(C) = 2R[/tex]

where R is the circumradius of the triangle.

To use the sine law to solve for an unknown side or angle in a triangle, we will need to know at least two side lengths and the measure of the angle opposite one of those sides. Once we have that information, we  can use the sine law to find the measure of the unknown angle or the length of the unknown side.

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So, your total bill including tip and tax is $11.37

First, calculate the subtotal of the food bill by adding the cost of the taco and burrito dinner:

$1.85 + $7.35 = $9.20

Next, calculate the sales tax by multiplying the subtotal by the tax rate (7.5%):

$9.20 x 0.075 = $0.69

Then add the sales tax to the subtotal to get the total before tip:

$9.20 + $0.69 = $9.89

Then calculate the tip by multiplying the total before tip by the tip rate (15%):

$9.89 x 0.15 = $1.48

Finally, add the tip to the total before tip to get the final total bill including tip and tax:

$9.89 + $1.48 = $11.37

So, your total bill including tip and tax is $11.37

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$1.85 + $7.35 = $9.20

$9.20 x 0.075 = $0.69

$9.20 + $0.69 = $9.89

$9.89 x 0.15 = $1.48

$9.89 + $1.48 = $11.37

So, your total bill including tip and tax is $11.37

The distance formula can be used to prove that a triangle has congruent sides.

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Answer:

Yes

Step-by-step explanation:

As long as the odd numbers are not prime numbers, they can still be in a fraction that can be reduced. Not in all cases of course but in some, for instance 9/27 can be reduced to 1/3

The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.

According to the question, 20 greater than 8x +5 = 8x +5 +20 = 8x +25.

We want this value to be -3(2x +1),

So, solving this equation we get: 8x +25 = -3(2x +1)

=> 8x +25 = -6x -3 (eliminating the parentheses)

Further solving this equation we get,

=> 14x = -28

=> x= -2

Thus, The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.

Complete question: Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+5.

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The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.

According to the question, 20 greater than 8x +5 = 8x +5 +20 = 8x +25.

We want this value to be -3(2x +1),

8x +25 = -3(2x +1)

8x +25 = -6x -3 (eliminating the parentheses)

14x = -28

x= -2

An equation which represents the best model for a line of fit for the data is: y equals negative 2 thirds times x plus 7. The correct option is A.

A scatter plot should be used to determine a linear equation of the line of best fit (trend line) that models the data points described above.

In this scenario, the x-values would be plotted on the scatter plot's x-axis, while the y-values would be plotted on the scatter plot's y-axis.

Right-click on any data point on the scatter plot in Excel, select the format trend line, and then check the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between data points in the table, a linear equation for the line of best fit is given by:

y = -0.33x + 7.

Rewriting the equation as an improper fraction, we have:

y = -2/3(x) + 7

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4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

[tex]p(x)=2x^3-7x^2+2x\\g(x)=2x-3\\dviding. p(x) by g(x),\\ we get2x-3)2x^3-7x^2+2x(x^2-2x2x^3-3x^2- +0 -4x^2+2x-4x^2+6x+ -0 -4xq(x)=x^2-2xand, r(x)=-4x\\Now,\\According to division algorithmp\\(x)=g(x)*q(x)+r(x)2x^3-7x^2+2x=(2x-3)(x^2-2x)+(-4x)\\adding 4x-2 on both side,\\ we get\\2x^3-7x^2+2x+4x-2=(2x-3)(x^2-2x)+(-4x)+4x-22x^3-7x^2+6x-2=(2x-3)(x^2-2x)+(-2)[/tex]

4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

what number must be added to[tex]2x^3-7x^2+2x[/tex] so that the resulting polynomial leaves the remainder -2 when divided by 2x-3​