There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?

Answer:

Direct Variation

Step-by-step explanation:

The relationship between two variables such that y = kx if k is a nonzero number. Also, as one quantity increases, the second quantity increases or as one quantity decreases, the second quantity decreases. Therefore ac=5 is a direct variation

The equation that fits this pattern is: [tex]\[ \text{Total Cost} = 3 \times (\text{Number of Days}) + 2 \][/tex]

The table depicts a linear relationship between the number of days a movie is rented and its total cost.

To identify the equation used to create this table, we can observe that each additional day increases the total cost by a constant amount.

Considering the initial cost and the rate of increase, we can formulate the equation. In this case, the initial cost appears to be $2, and for each additional day beyond the first, the cost increases by $3.

Therefore, the equation that fits this pattern is:

[tex]\[ \text{Total Cost} = 3 \times (\text{Number of Days}) + 2 \][/tex]

This equation represents a constant rate of increase of $3 per day, plus the initial cost of $2.

Thus, it accurately models the relationship between the number of days and the total cost.

The probable question may be:

The total cost of renting a movie for different numbers of days is shown in the table.

Which equation was used to create this table?

| Number of Days | Total Cost |

|----------------|------------|

| 1              | $5         |

| 2              | $8         |

| 3              | $11        |

| 4              | $14        |

| 5              | $17        |

Answer:

Yellow of course but it depends on how you look in the colors

Step-by-step explanation:

Answer:

If your day is not feeling good then I would recommend a yellow to brighten it up. If your day is already good but feeling not good where a purple to stand out. Good Luck I hope your day is doing well!!

Step-by-step explanation:

Answer:12.66667

Step-by-step explanation:

Answer:

Average = (sum of numbers) ÷ (the amount of numbers)

a = (12 + 13 + 13) ÷ 3

a = 38/3 = 12.6...

To find the length of the side of a square using area, find the square root of the area.

Side = √206 = 14.35 feet.

Answer:

[tex]\large\boxed{x=\dfrac{-3+\sqrt{40+10\sqrt{10}}}{2}}[/tex]

Step-by-step explanation:

[tex]2\log x=3-2\log(x+3)\\\\Domain:\ x>0\ \wedge\ x+3>0\to x>-3\\\\D:x>0\\============================\\2\log x=3-2\log(x+3)\qquad\text{add}\ 2\log(x+3)\ \text{to both sides}\\\\2\log x+2\log(x+3)=3\qquad\text{divide both sides by 2}\\\\\log x+\log(x+3)=\dfrac{3}{2}\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log\bigg(x(x+3)\bigg)=\dfrac{3}{2}\qquad\text{use the de}\text{finition of a logarithm}\\\\x(x+3)=10^\frac{3}{2}\qquad\text{use the distributive property}[/tex]

[tex]x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D[/tex]

Answer:

it would be 3 because if you list words then just divide 12 by 4 and you get 3

The number of the 4 letter words that can be made from a list of 12 letters will be 495.

Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Then the number of the 4 letter words can be made from a list of 12 letters will be

¹²C₄ = 12! / [(12 - 4)! x 4!]

¹²C₄ = 12 x 11 x 10 x 9 x 8! / 8! x 4 x 3 x 2 x 1

¹²C₄ = 11 x 5 x 9

¹²C₄ = 495

More about the combination link is given below.

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Answer:

309 Cm.

Step-by-step explanation:

Since the dimensions of the Large Jewelry Box is tripled, and all the sides are only added together, the answer of the question is simply the Surface Area of the Small Jewelry Box x 3.

103 x 3 OR 103 + 103 + 103 = 309.

_______________________________________

100 + 100 + 100 = 300

3 + 3 + 3 = 9

300 + 9 = 309.

The formula for area of a circle is:

A = [tex]\pi r^{2}[/tex]

In this case the radius is 7.4 cm so...

pi * 7.4^2

pi * 54.76

172.0033

so...

172.0 cm^2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

huh

Step-by-step explanation:

Answer:

Step-by-step explanation:

= 12.50

12.50

13,5 = 18

To solve the problem, Connie can use the concept of proportion by setting up an equation with the given ratios.

By cross-multiplying and solving for x, the cost of 18 boxes of cereal can be determined.

To solve this problem, Connie can use the concept of proportion.

A proportion is an equation that states that two ratios are equal.

In this case, the ratio of the cost of 5 boxes of cereal to the number of boxes is equal to the ratio of the cost of 18 boxes of cereal to the number of boxes.

Let's set up the proportion:

5 boxes / $12.50 = 18 boxes / x

To solve for x, we can cross-multiply:

5x = 18 * $12.50

Now, divide both sides by 5 to isolate x:

x = (18 * $12.50) / 5

Calculate the value of x to find the cost of 18 boxes of cereal.

Answer:

x = 17

Step-by-step explanation:

Since the triangles are similar then corresponding angles are congruent.

∠ I = ∠P ← substitute values and solve for x

3x + 4 = 72 - x ( add x to both sides )

4x + 4 = 72 ( subtract 4 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Answer:

Part 1)

a) The ratio of the heights of the similar solids is 5/1

b) The ratio of the surface areas of the similar solids is (5/1)²=25/1

c)  The ratio of the volumes of the similar solids is (5/1)³=125/1

Part 2) Two spheres with different radii measurements are always similar

Part 3) The volume of the sphere is greater than the surface area of the sphere

Step-by-step explanation:

Part 1) we know that

The ratio of the corresponding heights of the similar solids is equal to the scale factor

The ratio of the surface areas of the similar solids is equal to the scale factor squared

The ratio of the volumes of the similar solids is equal to the scale factor elevated to the cube

In this problem

The scale factor is 5/1

therefore

a) The ratio of the heights of the similar solids is 5/1

b) The ratio of the surface areas of the similar solids is (5/1)²=25/1

c)  The ratio of the volumes of the similar solids is (5/1)³=125/1

Part 2)

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.  

In this problem to prove that two spheres  are similar, a translation and a scale factor (from a dilation) will be found to map one sphere onto another.

therefore

Two spheres with different radii measurements are always similar

Part 3) The length of the diameter of a sphere is 8 inches

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=8/2=4\ in[/tex] -----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (4)^{3}[/tex]

[tex]V=85.33\pi\ in^{3}[/tex]

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

substitute

[tex]SA=4\pi (4)^{2}[/tex]

[tex]SA=64\pi\ in^{2}[/tex]

therefore

The volume of the sphere is greater than the surface area of the sphere

The scale factor used for the dilation from N to N' is 1/3. The midpoint between the points (-8, 5) and (2, -2) is (-3, 1.5).

To find the scale factor used to dilate point N(6, -3) to N'(2, -1), we compare the coordinates directly since the transformation scales both the x and y components equally.

Using the x-coordinates (6 to 2), the scale factor can be calculated as the ratio of N' to N, which is 2/6 or 1/3.

Similarly, using the y-coordinates (-3 to -1), we would also arrive at a scale factor of 1/3, confirming our result.

To find the midpoint between two points, (-8, 5) and (2, -2), we use the midpoint formula ((x1 + x2)/2, (y1 + y2)/2).

Substituting the relevant coordinates, the midpoint is calculated as ((-8 + 2)/2, (5 + (-2))/2) which simplifies to (-3, 1.5).

Therefore, the midpoint is (-3, 1.5).

To determine the scale factor used for the dilation of point N to N', you must find the ratio of the image coordinates to the pre-image coordinates. Since the dilation is defined by N(6, -3) transforming to N'(2, -1), you calculate the scale factor as follows:
For the x-coordinates:
The pre-image, N, has an x-coordinate of 6, and the image, N', has an x-coordinate of 2. Therefore, the scale factor in the x-direction is:
\[ \text{Scale factor}_x = \frac{N'_{x}}{N_{x}} = \frac{2}{6} = \frac{1}{3} \]
Now for the y-coordinates:
The pre-image, N, has a y-coordinate of -3, and the image, N', has a y-coordinate of -1. So the scale factor in the y-direction is:
\[ \text{Scale factor}_y = \frac{N'_{y}}{N_{y}} = \frac{-1}{-3} = \frac{1}{3} \]
The x and y scale factors are equivalent, which suggests uniform scaling. Thus, the scale factor used in the dilation is \(\frac{1}{3}\).
To find the midpoint between two points, you calculate the average of the x-coordinates and the y-coordinates separately. Let's find this midpoint for the points (-8, 5) and (2, -2):
For the x-coordinates:
The average of the x-coordinates of the two points is:
\[ \text{Midpoint}_x = \frac{(-8) + 2}{2} = \frac{-6}{2} = -3 \]
For the y-coordinates:
The average of the y-coordinates of the two points is:
\[ \text{Midpoint}_y = \frac{5 + (-2)}{2} = \frac{3}{2} = 1.5 \]
So, the midpoint between the points (-8, 5) and (2, -2) is (-3, 1.5).

Answer:

4

Step-by-step explanation:

The first thing you need to do is find the geometric mean between 2 and 6.

That is the ratio that they hypotenuse of the largest triangle is divided into.

altitude^2 = 2* 6

altitude^2 = 12

altitude = sqrt(12)

altitude = 2 sqrt(3)

Now use Pythagorus to find x

x^2 = 2^2 + altitude^2

x^2 = 2^2 + 12

x^2 = 4 + 12

x^2 = 16

x = 4

Answer:

about 13.6

Step-by-step explanation:

Assuming DEF is a right triangle, you use trig functions to solve this problem. Out on sin, cos, and tan, sin would work for this problem. You plug in the numbers and put it into a calculator. This gives you the answer after you round to the nearest tenth. See work for more.

Answer: 6.4

Step-by-step explanation: trust

Answer:

Step-by-step explanation:

0.25

Answer:

Between 2 and 3 scoops

and 10 divided by 4

Step-by-step explanation:

The fourth point would need to be at the top and in line horizontally with The point at (3,4) so the Y value needs to be 4.

The first top red dot is 2 units to the right of the lower dot, so the 4th dot needs to be 2 units to the right on the other lower dot.

The 4th point needs to be at (7,4)

The answer is B.

Answer:

b 7,4

Step-by-step explanation:

Answer:

64 in2

hope it helps (:

Answer:

A

Step-by-step explanation:

it is what it is; you either know it or you don't.

Answer:

B) 511

Step-by-step explanation:

1. How many pennies are in the last square:

Sequence: # of pennies = 2^(box # - 1)

Plug in: # = 2⁸

Solve: # of pennies in box 9 = 256

2. Process of elimination:

Not C or D, since the total must be greater than 256.

So the answer is B, not A, since 2⁰ + 2¹ ... 2⁷ = 2⁸ + 1.

Final answer:

Using the formula for the sum of a geometric sequence, we find that a total of 511 pennies will be placed on the board after the 9 squares are filled, following the sequence where each square has double the pennies of the previous one.

Explanation:

The student is asked to calculate the total number of pennies used when they are placed in each of the 9 squares of a board following a geometric sequence, starting with 1 penny and doubling the amount in each subsequent square. To find the total, we use the formula for the sum of the first n terms of a geometric sequence, which is Sn = a1(1 - [tex]r^{n}[/tex])/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a1 = 1 (first square), r = 2 (doubling each time), and n = 9 (nine squares). Therefore, the sum is:

The correct answer is B: 511 pennies will be used in total when every square is filled.

Answer:

[tex]\large\boxed{\text{The slope}\ m=\dfrac{2}{3}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-4, 2) and (2, 6). Substitute:

[tex]m=\dfrac{6-2}{2-(-4)}=\dfrac{4}{6}=\dfrac{4:2}{6:2}=\dfrac{2}{3}[/tex]

For this case we have the following equations:

[tex]f (x) = \sqrt {6x}\\g (x) = x-3[/tex]

We must find [tex](f_ {o} g) (x):[/tex]

By definition of composition of functions we have to:

[tex](f_ {o} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {o} g) (x) = \sqrt {6 (x-3)}[/tex]

We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined. That is to say:

[tex]6 (x-3) \geq0\\(x-3) \geq0\\x \geq3[/tex]

Then, the domain is given by [3, ∞)

Answer:

The smallest number that is the domain of the composite function is 3

Answer:  on Plato I got it wrong for the answer 3

Step-by-step explanation:

Answer:

The ratio is 15:13 (15 boys to 13 girls).

There are 28 students in all

13/28 of the students are girls.

Step-by-step explanation:

For the ratio, you simply need to put the information on the correct side of the colon [:]. The total amount of students is calculated by adding the numbers together. Finally, the fraction of girls in the class is found by adding the number of girls above the number of total students.

Answer:

Given:

Number of girls in class = 13

Number of boys in class = 15

Ratio of boys to girls,

[tex]\frac{Number\:of\:boys}{Number\:of\:girls}=\frac{15}{13}[/tex]

Ratio = 15 : 13

⇒ Total number of student = 13 + 15 = 28

Fraction of students are girls = [tex]\frac{13}{28}[/tex]

Answer: 830.7 per square mile.

Step-by-step explanation:

The formula for population density is Number of people divided by total area.

11,547 divided by 13.9 is 830.7.

Hope this helps!

The population density of Covington, Georgia is calculated by dividing the total population (11,547 people) by the total area (13.9 square miles). The result is approximately 830.79 people per square mile.

The population density of a place is calculated by dividing the total population by the total area. In this case, Covington, Georgia, has a total population of 11,547 people and a total area of 13.9 square miles. Thus, to determine the population density, we will use the following formula: Population Density = Total Population / Total area.

By substituting our given numbers into this formula, we would get: Population Density = 11,547 / 13.9. This calculation results in a population density of approximately 830.79 people per square mile for Covington, Georgia.

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Answer:

28.25 square units

Step-by-step explanation:

A circumference of the circle is

[tex]C=2\pi r,[/tex]

where r is the radius of the circle.

So,

[tex]18.84=2\pi r\\ \\r=\dfrac{18.84}{2\pi}=\dfrac{9.42}{\pi}\ cm[/tex]

The area of the circle is

[tex]A=\pi r^2[/tex]

Substitute the value of the radius:

[tex]A=\pi \cdot \left(\dfrac{9.42}{\pi}\right)^2=\dfrac{9.42^2}{\pi}\approx 28.25\ un^2[/tex]

Answer:

Step-by-step explanation:

18.84=2\pi r\\ \\r=\dfrac{18.84}{2\pi}=\dfrac{9.42}{\pi}\ cm

The area of the circle is

Answer:

The ball hits the ground after 7.6 sec.

Step-by-step explanation:

Realize that h = 0 when the rocket hits the ground.  Thus, we set h(t) = y = to 0 and solve for time (t):

y = 0 = h(t) = -16t^2 + 113t + 65.

Application of the quadratic formula is the easiest approach here.  Note that a = -16, b = 113 and c = 65.

The discriminant is b^2-4ac, or, in this case, 113^2 - 4(-16)(65) = 16929.

Because the discriminant is positive, we confirm that this equation has two real, unequal roots.

The time values are as follows:

     -113 ± √16929

t =  --------------------- =  -17.11/ (-32) sec, which we must reject                                  

          -32                    

                                     because time in

                                        this situation may not be (-).

The other root is:

 -113 ± √16929            

t =  --------------------- =  7.6 sec

          -32

The ball hits the ground after 7.6 sec.

Answer:

x = 30517578124/29296875

Step-by-step explanation:

Solve for x:

3125 = 3 x + 1/9765625

Put each term in 3 x + 1/9765625 over the common denominator 9765625: 3 x + 1/9765625 = (29296875 x)/9765625 + 1/9765625:

3125 = (29296875 x)/9765625 + 1/9765625

(29296875 x)/9765625 + 1/9765625 = (29296875 x + 1)/9765625:

3125 = (29296875 x + 1)/9765625

3125 = (29296875 x + 1)/9765625 is equivalent to (29296875 x + 1)/9765625 = 3125:

(29296875 x + 1)/9765625 = 3125

Multiply both sides of (29296875 x + 1)/9765625 = 3125 by 9765625:

(9765625 (29296875 x + 1))/9765625 = 9765625×3125

(9765625 (29296875 x + 1))/9765625 = 9765625/9765625×(29296875 x + 1) = 29296875 x + 1:

29296875 x + 1 = 9765625×3125

9765625×3125 = 30517578125:

29296875 x + 1 = 30517578125

Subtract 1 from both sides:

29296875 x + (1 - 1) = 30517578125 - 1

1 - 1 = 0:

29296875 x = 30517578125 - 1

30517578125 - 1 = 30517578124:

29296875 x = 30517578124

Divide both sides of 29296875 x = 30517578124 by 29296875:

(29296875 x)/29296875 = 30517578124/29296875

29296875/29296875 = 1:

Answer:  x = 30517578124/29296875

For this case:

We rewrite the equation as:

[tex]5 ^ {- 10 + 3x} = 3.125[/tex]

We find ln on both sides of the equation to remove the exponent variable:

[tex]ln (5 ^ {- 10 + 3x}) = ln (3,125)[/tex]

Applying properties of logarithm we have:

[tex](-10 + 3x) ln (5) = ln (3.125)[/tex]

We apply distributive property:

[tex]-10ln (5) + 3xln (5) = ln (3,125)[/tex]

We clear the value of "x":

[tex]3xln (5) = ln (3,125) + 10ln (5)\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10ln (5)} {3ln (5)}\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]

ANswer:

[tex]x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]

Answer: the polygones name is a hexagon i believe

Step-by-step explanation:

hex means six in greek and has an internal angle of 120 so the correct ansewer is a hexagon.

A polygon with six vertices is called a hexagon.

It is a two-dimensional figure with six sides and six angles. Hexagons are common in various real-life patterns and have properties like area and perimeter.

A polygon plotted on a coordinate plane with six vertices is known as a hexagon. A hexagon is a two-dimensional geometric figure with six angles and six sides.

Polygons are closed figures made up of straight line segments. When the polygon has six sides, it has interior regions and exterior regions that divide the plane it lies on. Each vertex connects two sides of the hexagon, forming angles at each vertex.

Answer:

a. 18 cm

Step-by-step explanation:

We are given that a circle has an area of 324π cm2. We are required to determine its radius. The formula for the area of a circle with radius r units is;

[tex]A=pi*r*r[/tex]

We plug in the area given and solve for r;

[tex]324pi=pi*r^{2}\\\\r^{2}=324\\\\r=18[/tex]

The radius of the circle is 18 cm

Answer:

a. 18 cm

Step-by-step explanation:

Area of a circle is given by: A=πr²

where r is the radius and A the area.

therefore we substitute A with the value for the area in the question.

324π=πr²

cancelling the factor π on both sides gives: 324=r²

√324=r

r=18cm

The correct answer is A. Hundreds. I hope this helps : )

A is the correct answer