Henry divided his socks into five equal groups. Let s represent the total number of socks. Which expression and solution represent the number of socks in each group if s = 20?

Answer:

x = [tex]\frac{12}{17}[/tex] or 0.706

[tex]y = \frac{59}{34}[/tex] or 1.735

Step-by-step explanation:

5x + 2y=7    ----->(eq 1)

- 2x + 6y=9 ----->(eq 2)

Multiply (eq 1) with 3

3×(5x + 2y) = 3×7  

15x + 6y = 21  ----->(eq 3)

substract (eq 3) from (eq 2)

- 2x + 6y - (15x + 6y) = 9-21

- 2x + 6y - 15x - 6y = 9-21

- 2x - 15x + 6y - 6y = 9-21

-17x = -12

x = -12 ÷ -17

x = [tex]\frac{12}{17}[/tex]

put x = [tex]\frac{12}{17}[/tex] in (eq 1)

[tex]5*\frac{12}{17} + 2y = 7[/tex]

[tex]2y = 7- 5*\frac{12}{17}[/tex]

[tex]2y = \frac{7*17 - 60}{17}[/tex]

[tex]2y = \frac{119- 60}{17}[/tex]

[tex]2y = \frac{59}{17}[/tex]

[tex]y = \frac{59}{17*2}[/tex]

[tex]y = \frac{59}{34}[/tex]

[tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .

Step-by-step explanation:

Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.

The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.

We know that 1 radian = 180°/[tex]\pi[/tex] . So [tex]\frac{9\pi }{5}[/tex] radians is equal to :

⇒ [tex]\frac{9\pi }{5}(\frac{180}{\pi } )[/tex]

⇒ [tex]\frac{9(180) }{5}[/tex]

⇒ [tex]9(36)[/tex]

⇒ [tex]324[/tex]°

Therefore , [tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .

To convert 9pi/5 radians to degrees, multiply by the conversion factor of 180°/π, resulting in 324 degrees.

To convert the angle 0 = 9pi/5 radians to degrees, we need to use the relationship between radians and degrees. Recall that 360° = 2π radians. Consequently, to convert radians to degrees, we can multiply by a conversion factor of 180°/π. Using this conversion factor, the computed angle in degrees is:

9π/5 radians × (180°/π) = 9/5 × 180° = 9 × 36° = 324°

Therefore, the angle of 9π/5 radians is equivalent to 324 degrees.

Answer:

Slope = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Slope = [tex]\frac{2 - 12}{-8 - 4}[/tex]

Slope = [tex]\frac{-10}{-12}[/tex]

Slope = [tex]\frac{5}{6}[/tex]

Answer:  Slope = [tex]\frac{5}{6}[/tex]

Answer:

(-4, -1)

Step-by-step explanation:

x = 4y

-4x - y = 17

Plug in 4y for x in the second equation:

-4(4y) - y = 17

Simplify. Remember to follow PEMDAS. Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.

First, multiply 4y with -4:

-4(4y) = -16y

-16y - y = 17

Simplify. Combine like terms:

-16y - y = 17

-17y = 17

Isolate the variable, y. Divide -17 from both sides:

(-17y)/-17 = (17)/-17

y = 17/-17

y = -1

Plug in -1 for y in the first equation:

x = 4y

x = 4(-1)

x = -4

x = -4, y = -1

Answer: (-4, -1)

~

The number of trays she needs is 94 trays.

Step-by-step explanation:

Number of trays she needs :

Number of trays needed = Remaining seashells / 8

⇒ 746/8

⇒ 93 trays and remaining 2 seashells is arranged in another tray

⇒ 93+1 = 94 trays.

[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-6)}}}\implies \cfrac{-15}{3+6}\implies \cfrac{-15}{9}\implies -\cfrac{5}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-\cfrac{5}{3}}[x-\stackrel{x_1}{(-6)}]\implies y-8=-\cfrac{5}{3}(x+6) \\\\\\ y-8=-\cfrac{5}{3}x-10\implies y = -\cfrac{5}{3}x-2[/tex]

Answer:

[tex]m=\frac{-5}{3}[/tex]

Step-by-step explanation:

Step 1: Let's find the slope between your two points.

[tex](-6,8); (3,-7)\\\\(x_{1} ,y_{1} )=(-6,8)\\\\(x_{2} ,y_{2} )=(3,-7)[/tex]

Step 2: Use the slope formula

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\\\\=\frac{(-7) - 8}{3- (-6)} \\\\=\frac{-15}{9}\\\\= \frac{-5}{3}[/tex]

Therefore, the equation is [tex]\frac{-5}{3}[/tex]

Answer:

D) Each additional day is associated with an additional 17.5 grams of mass.

Step-by-step explanation:

Slope = 17.5

= change in mass/change in day

Which is 17.5 g increase in 1 day

Answer:

its d!

Step-by-step explanation:

Answer:

(3, -2) or (3, 2)

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer:

21.75

Step-by-step explanation:

i hoped this helped.  14.50 divide-by 2 = 7.25 so 14.50 + 7.25= 21.75

Answer:

Part A is Answer C

C=2pi * r

D= 2r

C= 2 * 3.14 * 31.5

C= 197.82

__________________________

Part B is 3115.67 sq cm

A = 3.14 * r*r

A= 3.14 x 31.5x31.5

A=3115.665

Rounded: 3115.67

The circumference of the circle is C = 197.82 cm

The area of the circle is A = 3,115.67 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the diameter of the circle be d = 63 cm

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle and π is the mathematical constant pi, approximately equal to 3.14159.

C = π(63)

C = 197.92 cm

The area of a circle is given by the formula

A = πr²

where r is the radius of the circle. Since we are given the diameter, we can find the radius by dividing the diameter by 2:

r = d/2

r = 63/2

r = 31.5 cm

Substituting the radius r = 31.5 cm into the formula for the area, we get:

A = 3.14159 x 31.5²

A = 3.14159 x 992.25

A = 3,117.15 cm²

Hence , the area of the circle is 3,117.15 cm²

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Answer:

Fourth answer choice.

Step-by-step explanation:

Start by factoring the numerator and the denominator:

(x - 1)(x + 1)

-----------------

(x + 1)(x + 4)

Note that x can be neither -1 nor -4, since either results in an undefined quotient.  These two x-values are critical values because of this.  If we cancel the (x + 1) terms, we obtain the result

(x - 1)

--------- for x ≠ -1 and x ≠ - 4

(x + 4)

The next step is to evaluate the given quotient on the three intervals defined by {-4, -1}:  (-∞, -4), (-4, -1), (-1, ∞ ).  We choose an x-value from within each interval and evaluate the given function at each.  Suitable test values include {-10, -3, 0}:

At x = -10, the reduced given quotient (x - 1) / (x + 4) takes on the value  (-10 - 1) / (-10 + 4) = -11/(-6), which is positive.  Reject this interval, as we want and expect the quotient value to be 0 or less.

At x = -3, we get (-3 - 1) / (-3 + 4), which is negative.  The given inequality is true on the interval (-4, -1) (or -4 < x < -1).

At x = 0, we get (0 - 1) / (0 + 4), which is negative, so the inequality is true on (-1, ∞ ).

So the fourth answer choice is the correct one.

Answer:

Answer D

Step-by-step explanation:

Answer:

the answer is  about 4.243

Step-by-step explanation:

Squares mean all sides would have the same length. So you just need to find the square root of the area (18)  which is about 4.243 and just to check multiply 4.243 by itself and you would get 18.

Final answer:

The length of one side of the table top with an area of 18 square feet is approximately 4.24 feet, as calculated by taking the square root of the area.

Explanation:

To find the length of one side of a table top with an area of 18 square feet, we should understand that a square has all sides of equal length. Therefore, to find the side length of a square, we take the square root of the area. In this case, we have an area of 18 square feet, so the calculation would be √18, which is approximately 4.24 feet. Thus, the length of one side of the table top is approximately 4.24 feet.

Answer:5

Step-by-step explanation:

The volume of the ball is 24,400 cm³

Step-by-step explanation:

Volume of the ball = 4/3 πr³

                               = 4/3 × 3.14 × (18)³

                               = 24,416.64 cm³ ≈ 24,400 cm³ (nearest hundredth)

In physics, work is defined force that causes displacement. So this can be expressed by the following equation:

[tex]W=Fs[/tex]

Where:

[tex]F:Force \\ \\ s:Displacement[/tex]

The force can be found as:

[tex]F=ma \\ \\ F=5(10)=50N[/tex]

And for the displacement:

[tex]s=6-2=4m[/tex]

The force (weight) is down and the displacement is up, then the work must be negative. So:

[tex]W=-(50)(4) \\ \\ \boxed{W=-200J}[/tex]

Answer: The equations are as follows;

5p + 4d = 43.25 ————(1) and

3p + 2d = 24.25 ————(2)

Also a bag of popcorn costs $5.25

Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as

5p + 4d = 43.25 ————(1)

Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as

3p + 2d = 24.25 ————(2)

Now we have a pair of simultaneous equations as follows

5p + 4d = 43.25 ————(1)

3p + 2d = 24.25 ————(2)

We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)

5p + 4d = 43.25 ——— x3

3p + 2d = 24.25 ——— x5

15p + 12d = 129.75 ———(3)

15p + 10d = 121.25 ———(4)

Subtract equation (4) from equation (3) and we have

2d = 8.5

Divide both sides of the equation by 2

d = 4.25.

That means each drink costs $4.25

We can now substitute for the value of d into equation (2)

3p + 2d = 24.25

When d = 4.25

3p + 2(4.25) = 24.25

3p + 8.5 = 24.25

Subtract 8.5 from both sides of the equation

3p = 15.75

Divide both sides of the equation by 3

p = 5.25. This means a bag of popcorn costs $5.25

Answer:

No, not a solution

Step-by-step explanation:

Step 1:  Check if solution

y = 3x + 5

-1 = 3(4) + 5

-1 = 12 + 5

-1 = 17

DOES NOT EQUAL

Answer: No, not a solution

Answer:

a) 8x

b)2+12y

Step-by-step explanation:

Answer:

5X+3X & 8X For the first one

and 2+12y for the second one i believe those are correct let me know in the comments below

Step-by-step explanation:

hope this helps have a great day

Answer:

-5.46

Step-by-step explanation:

Hope this helps!

Answer:

-5.46

Step-by-step explanation:

Represent 4.2 as 42/10 and -1.3 as -13/10

Multiply 42 by -13 and then divide by 100.

Answer:

b=58

Step-by-step explanation:

b-12=46

b=46+12

b=58

Answer:

21

Step-by-step explanation:

The length of EF in the given triangle is 8.80 m.

Step-by-step explanation:

Step 1:

In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.

The angle given is 90°, this makes the triangle a right-angled triangle.

So first we calculate the angle of E and use that to find x.

Step 2:

As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.

[tex]sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.[/tex]

[tex]E = sin^{-1} (0.8395), E = 57.087.[/tex]

So the angle E of the triangle DEF is 57.087°.

Step 3:

As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.

[tex]cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .[/tex]

[tex]cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.[/tex]

Rounding this off to the nearest hundredth, we get x = 8.80 m.

Answer:

2b + 2c

Step-by-step explanation:

If you distribute the 2 in b and c you will get to separate terms that will be added together. Since they are not like terms they cannot be combined.

The distributive property means you just multiply the outside number by the terms in the parenthesis. So 2 * b and 2 * c

[tex]2(b + c)\\2(b + 2c)[/tex]

Answer:

2b+2c

Step-by-step explanation:

We need to expand this term by multiplying a term and an expression.

The following product distributive property will be used:

A(B+C)=AB+AC

In our example, the resulting expression will consist of 2 terms:

the first term is a product of 2 and b.

the second term is a product of 2 and c.

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984′, 1,063′ to tip.

the ' is feet

The required height of the Eiffel Tower is given as 327.27 meters.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Let the height of the Eiffel tower be x,
According to the question,
The ratio of the height to the base of the Eiffel tower is equal to the ratio of  height to the

base of men,
x / 500 = 1.8 / 2.75
x = 327.27 meters

Thus, the required height of the Eiffel Tower is given as 327.27 meters.

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T = 30

A = 4c

A + c = T

Anna Claire has 6 pencils. Times 4 makes Ally's pencil count. 4 * 6 = 24

24 + 6 = 30. So, you answer is: Ally has 24 pencils.

Answer: $822,000

Step-by-step explanation:

Median of even numbers is the average of two middle most numbers

From the question, median

= $764,000 + $880000 ÷ 2

= $1,644,000÷2

$822,000

Answer: 49.8 is the answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Any ellipse has the following equ

ation:

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

where

(as in the picture)

So it should be like:

[tex] \frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1[/tex]

Since it should be moved to the right and up, the answer would be:

[tex]\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1[/tex]

Option D. (x - 5)²/9 + ( y - 1 )²/4 = 1

An ellipse has the following equation:

x²/a² + y²/ b² = 1

where

2b = vertical axis length

2a = horizontal axis length

So it should be like:

x²/(6÷2)² + y²/ (4÷2)² = 1

x²/9 + y²/4 = 1

Since it should be moved to the right and up, the answer would be:

(x - 5)²/9 + ( y - 1 )²/4 = 1

Please check the attached diagram for more details.

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Since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.

The interquartile range is a measure of variability, which can be used in comparing two data distribution.

Interquartile range = Q3 - Q1.

Interquartile range for gas mileage of cars sold in June = 33 - 21 = 12.

Interquartile range for gas mileage of cars sold in December = 26 - 14 = 12.

Therefore, since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.

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Answer: Its C.

Step-by-step explanation:

Edge 2022

Answer:

339.35

Step-by-step explanation:

The amount of money the credit card customer still owes to pay is $339.35.

We are given that,

The amount the credit card customer owes = $523.85.

The amount the credit card customer paid = $184.50.

We have to find the amount of money the credit card customer still owes to pay.

The amount of money the credit card customer still owes to pay :

= The amount the credit card customer owes - The amount the credit card customer paid

= $523.85 - $184.50

= $339.35

Thus, the amount of money the credit card customer still owes to pay after paying $184.50 is $339.35.

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