In a geometry class,the girl to boy ratio is 10 to 2.if there are a total of 24 students,how many girls are there?

To fill a rectangular prism with dimensions 9in. by 4in. by 1.5in. using half-inch cubes, you need to divide the volume of the prism (54in.^3) by the volume of a cube (0.125in.^3), resulting in 432 cubes needed.

To determine how many half-inch cubes are needed to fill the rectangular prism, we must first calculate the volume of the prism and then the volume of a single cube. Next, we divide the volume of the prism by the volume of a cube to find the number of cubes needed.

Calculating the Volume of the Rectangular Prism

The volume of a rectangular prism is found by multiplying its length by its width by its height. Volume of the prism = length × width × height = 9in. × 4in. × 1.5in. = 54in.3.

Calculating the Volume of a Cube

The volume of a cube is found by raising the length of an edge to the third power. Volume of a cube = edge length3 = (0.5in.)3 = 0.125in.3.

Number of Cubes Needed

To find the number of cubes needed to fill the prism, divide the volume of the prism by the volume of a cube. Number of cubes needed = Volume of the prism / Volume of a cube = 54in.3 / 0.125in.3 = 432.

Therefore, 432 half-inch cubes are needed to fill the rectangular prism.

To determine if a set of measurements could be the side lengths of a right triangle, we need to check if the Pythagorean theorem holds true. Option D, with side lengths 54 in, 72 in, and 90 in, satisfies the theorem and represents a right triangle.

In a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem: a^2 + b^2 = c^2.

So, to determine if a set of measurements could be the side lengths of a right triangle, we need to check if the Pythagorean theorem holds true. Let's check each option:

Therefore, the correct answer is option D: 54 in, 72 in, 90 in.

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Answer:

Option A. 2

Step-by-step explanation:

To solve this problem we can write equations for each shirt color.

Let's call:

b = black shirts

g = gray shirts

w = white shirts

B = brown shirts

If you have 3 times more black shirts than gray shirts and buy 3 more black shirts then:

[tex]b = 3g +3[/tex]     (i)

If you have 5 times more white shirts than gray shirts and gave a white shirt then:

[tex]w = 5g -1[/tex]      (ii)

It has 2 times more gray shirts than brown camsas, then:

[tex]g = 2B[/tex]         (iii)

It has the same amount of black and white shirts

[tex]b = w[/tex]            (iv)

We want to find the number of gray shirts.

Then replace (iv) in (ii)

[tex]b = 5g -1[/tex]        (v)

Now substitute (v) into (i) and clear g.

[tex]5g -1 = 3g +3\\\\5g -3g = 3 +1\\\\2g = 4\\\\g = 2[/tex]

Joan has 2 gray shirts

Joanie has 2 gray shirts, option A.

To determine the number of gray shirts Joanie has, we'll set up and solve a system of equations. Let G represent the number of gray shirts and let B, W, and R represent the number of black, white, and brown shirts, respectively.

Given the information:

1. Set the equations for black and white shirts equal:

3G + 3 = 5G - 1

2. Simplify and solve for G:

3 + 1 = 5G - 3G

4 = 2G

G = 2

Thus, Joanie has 2 gray shirts.

Answer:

The initial temperature is 80 °F.

The final termperature is 20°F.

During this period, fell 60 °F which represents a percentage of

[tex]\frac{60}{80} \times 100= 75\%[/tex]

We repeat the process for the rest.

From -13 °F to 9 °F, the temperature arose 22 °F, which is equivalent to

[tex]\frac{22}{13} \times 100= 169.23 \%[/tex]

From -5 °F to 8 °F, the temperature fell 13 °F, which is equivalent to

[tex]\frac{13}{5} \times 100= 260 \%[/tex]

Hey there!

Answer:

A. -4

Explanation:

All you do is evaluate:

[tex]-(-(-4))\\= -4[/tex]

= A. -4

Therefore, that is how you got your answer.

Hope this Helps!

Answer:

A. -4

Explanation:

All you do is evaluate:

= A. -4

Therefore, that is how you got your answer.

Hope this Helps

Answer:

7

Step-by-step explanation:

Since these two points are straight left and right from each other it's really easy.  Think of it as just moving so many spaces left or right on the x axis.  We are moving from point (-5,5) along the line y=5 to the point (2,5), which is moving 7 units.

Answer:

[tex]y = \frac{2}{3}x + \frac{23}{3}[/tex]

Step-by-step explanation:

To write the equation of a line with a point and a slope, use the point-slope form of a linear equation. Substitute m = 2/3 and the point (-4,5) into the equation.

[tex]y - y_1 = m(x-x_1)\\y - 5 = \frac{2}{3}(x --4)\\y - 5 = \frac{2}{3}(x+4)[/tex]

Convert to slope intercept form by using the distributive property.

[tex]y - 5 = \frac{2}{3}(x+4)\\y - 5 = \frac{2}{3}x +\frac{8}{3}\\y = \frac{2}{3}x + \frac{8}{3} + 5\\y = \frac{2}{3}x + \frac{23}{3}[/tex]

Answer:  [tex]x=2[/tex]

Step-by-step explanation:

To solve this exercise you must apply the Intersecting secan theorem.

Then, according to this theorem, you can know that:

[tex]EC*ED=EB*EA[/tex]

Therefore, you must substitute the values shown in the figure attached, as following:

[tex](x+4)(x+4+1)=(x+1)(x+1+11)[/tex]

Now you can solve for x, as you can see below:

[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)\\\\\\x^2+5x+4x+20=x^2+12x+x+12\\\\x^2+9x+20=x^2+13x+12\\x^2-x^2+9x-13x=12-20\\-4x=-8\\x=2[/tex]

Answer:

Step-by-step explanation:

y-intercept is for x = 0. Substitute x = 0 to the equation of a function

[tex]y=3\left(\dfrac{8}{9}\right)^x[/tex]

[tex]y=3\left(\dfrac{8}{9}\right)^0=3(1)=3[/tex]

The constant variation is k=-13/2

Answer:

k = - 6.5

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 4 when y = - 26, hence

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-26}{4}[/tex] = - [tex]\frac{13}{2}[/tex] = - 6.5

Answer:

Option B. [tex]R(2,4)[/tex]

Step-by-step explanation:

we know that

If a ordered pair lie on the circle. then the ordered pair must satisfy the equation of the circle

step 1

Find the equation of the circle

we know that

The equation of the circle in center radius form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

r is the radius of the circle

(h,k) is the center of the circle

substitute the values

[tex](x-6)^{2}+(y-1)^{2}=5^{2}[/tex]

[tex](x-6)^{2}+(y-1)^{2}=25[/tex]

step 2

Verify each case

case A) [tex]Q(1, 11)[/tex]

substitute the value of [tex]x=1, y=11[/tex] in the equation of the circle and then compare the results

[tex](1-6)^{2}+(11-1)^{2}=25[/tex]

[tex]25+100=25[/tex] ------> is not true

therefore

the ordered pair Q not lie on the circle

case B) [tex]R(2,4)[/tex]

substitute the value of [tex]x=2, y=4[/tex] in the equation of the circle and then compare the results

[tex](2-6)^{2}+(4-1)^{2}=25[/tex]

[tex]16+9=25[/tex] ------> is true

therefore

the ordered pair R lie on the circle

case C) [tex]S(4,-4)[/tex]

substitute the value of [tex]x=4, y=-4[/tex] in the equation of the circle and then compare the results

[tex](4-6)^{2}+(-4-1)^{2}=25[/tex]

[tex]4+25=25[/tex] ------> is not true

therefore

the ordered pair S not lie on the circle

case D) [tex]T(9,-2)[/tex]

substitute the value of [tex]x=4, y=-4[/tex] in the equation of the circle and then compare the results

[tex](9-6)^{2}+(-2-1)^{2}=25[/tex]

[tex]9+9=25[/tex] ------> is not true

therefore

the ordered pair T not lie on the circle

the answer is going to be C

circumference = pi times the diameter , so i used 3.14 as pi and used the values in the answer choices to determine the diameter

12 is the closest because 12 times 3.14 is 37.68 which is very close to 37.5

pls mark brainliest

Each friend will get 37 water balloons, with 4 remaining.

To divide the 300 water balloons evenly among the 8 friends, we can use division. We divide 300 by 8 to find out how many water balloons each person will get. The quotient is 37 with a remainder of 4. So, each friend will get 37 water balloons, and there will be 4 remaining balloons.

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12. Answer:  $9.50

Step-by-step explanation:

4 tickets plus 1 popcorn equals 44.25

    4t         +       1(6.25)       =       44.25

4t + 6.25 = 44.25

   -  6.25   -6.25     Subtraction Property of Equality

4t            = 38.00

÷4             ÷4           Division Property of Equality

t             = 9.50  

13. Answer:

Step-by-step explanation:

4.9x - 1.9 = 27.5

       +1.9    +1.9        Addition Property of Equality

4.9x         = 29.4

÷4.9           ÷4.9        Division Property of Equality

     x          =   6

GgAnswer:

Step-by-step explanation:

gg

Answer:

11 days

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex], then

[tex]a^{x^2-5x}[/tex] = [tex]a^{6}[/tex], hence

x² - 5x = 6 ( subtract 6 from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 1

Answer:

Step-by-step explanation:

Using the rule of exponents:

a^{m} ÷ a^{n} = a^{(m-n)} , then

aˣ² ÷ a^{5x}  = a⁶

⇒ a^{x^2 - 5x} = a⁶

⇒ x² - 5x = 6

x² - 5x - 6 = 0

(x - 6)(x + 1) = 0 [middle term splitting]

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6     ║     x + 1 = 0 ⇒ x = -1

The answer is A.

29 + 39 < 69.

Answer:

Step-by-step explanation:

Seems to be a

The only correct statement that identifies the right angle is:

Option A: ∠DEF is a right angle

To identify the true statements of the diagram, we will need to look at each of the options to get:

Option A: ∠DEF is a right angle:

We see that the line FA is a straight line and we also see that the line DE is perpendicular to FA and as such we can say that:

∠DEF = ∠DEA = 90°

Option B: m∠DEA = m∠FEC:

This is not true because we can clearly see that m∠DEA is a right angle while  m∠FEC is an acute angle.

Option C: m∠BEA = m∠BEC:

We can't really say if they are equal because we are not told it ED is a bisector of ∠AEC

Option D: EB bisects  ∠AEF

This is wrong as it is not a bisector

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Answer:   [tex]\bold{x^{\frac{1}{3}}y^{\frac{1}{2}}}[/tex]

Step-by-step explanation:

[tex]\sqrt[6]{x^2y^3} =x^{\frac{2}{6}}y^{\frac{3}{6}}=x^{\frac{1}{3}}y^{\frac{1}{2}}[/tex]

Answer:  F) 7 mph

Step-by-step explanation:

The line you drew is correct but you read the graph wrong.  

The line drawn from 15 hours of training (bottom axis) meets the "line of best fit" at the average running speed (left axis) between 6 and 8, which is 7.

Answer:

The only possible numbers are 6 and 0.

Step-by-step explanation:

We are given the following information in the question:

Let x and y be the two numbers whose difference is 6 and whose sum is also 6.

We can write it in the form of the equation:

[tex]x - y = 6\\x+y =6\\\\\text{Adding the two equations}\\(x-y) + (x+y) = 12\\2x =12\\x = 6\\\\\text{Putting this value of x in one of the equations}\\6 + y = 6\\y = 0[/tex]

Hence, the only possible numbers are 6 and 0.

It is possible as the numbers are 0 and 6.

Let the numbers be a and b.

Based on the question, the equation to solve the question will be:

a - b = 6 ........ i

a + b = 6 ........ ii

From equation i, a = 6 + b

Put the above into equation ii

a + b = 6

(6 + b) + b = 6

6 + 2b = 6

2b = 6 - 6.

2b = 0

b = 0/2

b = 0

Therefore, the value of a will be:

a = 6-0 = 6.

The numbers are 0 and 6.

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Answer:f(x)=x

Step-by-step explanation:

Answer:

r=C

2π

Step-by-step explanation:

1120cm^3+800cm^3

ans

=1920cm^3

Answer:

Volume of the cuboid = 1120cm³

Step-by-step explanation:

The question is incomplete and incorrect. Here is the complete and correct question.

"Find the volume of cuboid measuring 14cm, 10 cm and 8cm"

The volume of a cuboid = Length × breadth × Height.

Given Length = 14cm

Breadth = 10cm

Height = 8cm

Volume of the cuboid = 14cm × 10cm × 8cm

Volume of the cuboid = 1120cm³

Answer:

Explanation:

x = [tex]\frac{105}{5}[/tex] = 21 degree will be the answer.

{The sum of angle of opposite circumscribed quadrilateral in circle is 180°}

Answer:

In a cyclic Quadrilateral , sum of opposite pair of interior angles are Supplementary.

So, ∠A + ∠C=180°

And, ∠B + ∠D=180°

We have to find the value of x.

So, we will use the equation

∠B + ∠D=180°

→5 x +75° =180°

5 x= 180° - 75°

5 x= 105°

Dividing both side by , 5 we get

x=21°

Option C

Answer:

5

Step-by-step explanation:

Final answer:

Using the GCF of 10 and 15, which is 5, we cross-cancel the fractions 5/15 and 5/10 to reduce them to 1/3 and 1/2 respectively. Multiplying these reduced fractions, we obtain the final answer of 1/6.

Explanation:

To solve the fraction 5/15 × 5/10, we first identify the Greatest Common Factor (GCF) of the numerators and denominators. The GCF of 10 and 15 is 5. Using this GCF, we cross-cancel to reduce the fractions before multiplying.

Firstly, we divide both 10 and 15 by the GCF, which gives us:

10 ÷ 5 = 2

15 ÷ 5 = 3

Applying cross-cancellation to the original expression, we get:

(5 ÷ 5) / (15 ÷ 5) × (5 ÷ 5) / (10 ÷ 5)

1/3 × 1/2

Multiplying these reduced fractions gives us:

1/3 × 1/2 = 1/6

Thus, the result of multiplying 5/15 by 5/10, after cross-cancelling the common factors, is 1/6.

Answer:

h(x) =  x - 5

set of all integers except 3

-∞ ≤ x ≤ ∞ and x ≠ 3

Step-by-step explanation:

Given the two equations in the question

Equation 1

f(x) = x² − 8x + 15

Equation 2

g(x) = x − 3

To find equation 3 that is h(x) we need to divide f(x) by g(x)

f(x) / g(x)

x² − 8x + 15 /  x − 3

By using quadratic factorisation  

(x-3)(x-5) / (x-3)

Cancel (x-3) from both numerator and denominator

h(x) = x-5

set of all integers except 3

-∞ ≤ x ≤ ∞ and x≠3

Answer:

first blank is x-5

second blank is -infinity, 3

third blank is 3, infinity

Answer:

A. They are the only values that make both equations true.

Step-by-step explanation:

Equation A: 4y-3x=4

Equarion B: -2x-8y=8

Put x=-2, y=-0.5 in those two equations.

Equation A: 4(-0.5)-3(-2)=4

                     -2+6=4

                         4=4

Equation B: -2(-2)-8(-0.5)=8

                      4+4=8

                          8=8

So it's not B and C.

For D, you can tell that they are didferent lines by put them in to F(x)=kx+b format, and it tell you it's not D.

Answer:A

Step-by-step explanation:A P E X

Final answer:

It will take 72 minutes to fill the pool using only 3 taps.

Explanation:

To find out how many minutes it will take to fill the pool using only 3 taps, we can set up a proportion.

If it takes 120 minutes to fill the pool using 5 taps, then the rate at which water flows from the taps is 1 pool/120 minutes/tap.

Using this rate, we can set up the proportion:

5 taps / 3 taps = 120 minutes / x minutes

Cross-multiplying and solving for x gives us:

x = (3 taps * 120 minutes) / 5 taps = 72 minutes

So, it will take 72 minutes to fill the pool using only 3 taps.

Answer:                                  -7=0 --> Impossible

Step-by-step explanation:  

2x-7+x-11= 3x-11

2x+x-7-11=3x-11

3x-18=3x-11

3x-18+11=3x

3x-7-3x=0

-7=0

Impossible

We combined like terms on both sides to solve 2x - 7 + x - 11 = 3x - 11. However, this led to the false equation -18 = -11, indicating a potential error in the given problem.

The equation to solve is 2x - 7 + x - 11 = 3x - 11. The goal is to find the value of x.

The first step is to combine like terms on the left side of the equation. We combine 2x and x to get 3x and -7 and -11 to get -18. So, the problem becomes 3x - 18 = 3x - 11.

From here, we subtract 3x from both sides to isolate x on one side. This gives us -18 = -11. This equation is, however, incorrect.

This discrepancy could arise from a mistake in the original problem, notably, the content loaded 2x - 7 + x - 11 = 3x - 11.

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