Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas for a total of 152 slices. Let c represent the number of cheese pizzas and let v represent the number of vegetable pizzas. Which equation represents the relationship between the number of cheese pizzas and the number of vegetable pizzas? Which equation represents the total number of pizza slices?

Answer:

[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]

Step-by-step explanation:

Given that:

r < 5

To simplify:

|3r−15|

Solution:

First of all, let us learn about Modulus function:

[tex]f(x) =|x| =\left \{ {x, \ if\ {x>0} \atop -x\ if\ {x<0}} \right.[/tex]

In other words, we can say:

Modulus function has a role to make its contents positive.

If the contents are positive, the result will be equal to its contents only.

If the contents are negative, it will add a negative sign to the contents to make it positive.

Now, let us consider the given condition:

[tex]r < 5[/tex]

Multiply both sides with 3. (As 3 is a positive number, the equality sign will not change.)

[tex]3r < 15[/tex]

Subtracting 15 from both sides:

[tex]3r-15<15-15\\\Rightarrow 3r-15<0[/tex]

Now, we know that [tex]3r-15<0[/tex], let us use the definition of Modulus function.

Add a negative sign to the contents because the contents are already negative.

[tex]\\\Rightarrow |3r-15| = -(3r-15)\\\Rightarrow -3r+15[/tex]

So, the answer is:

[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]

Answer:

(-4^9)^2 = -4^18

(4^6)^-3 = 1/4^18

(4^0)^-9 = 4^0

(4^-3)^-3 = 4^9

Step-by-step explanation:

Here, we want to match what we have on the left with the expressions on the right.

(-4^9)^2

= -4^18

(4^6)^-3

= 4^-18 = 1/4^18 according to laws of indices

(4^0)^-9 = 4^0

(4^-3)^-3

= 4^9

Answer:

(-4^9)^2 = -4^18

(4^6)^-3 = 1/4^18

(4^0)^-9 = 4^0

(4^-3)^-3 = 4^9

Step-by-step explanation:

Answer: 2n+2

Step-by-step explanation:

1. Remove the parentheses

-n-3+3n+5

2. Collect like terms

2n-3+5

3. Calculate the sum

2n+2

Answer: 1035 cm^2

Step-by-step explanation:

Given that the shape s is exactly one quarter of solid sphere.

Where the volume of the shape s is 1994πcm^3.

The formula for volume of a sphere is

V = 4/3πr^3

The volume will be divided by 4 since the given solid is exactly quarter of solid sphere. Then equate it to the given value

1994π = 4/3πr^3 × 1/4

The π will cancel out

1994 = r^3/3

Cross multiply

5982 = r^3

r = cube root of 5982

r = 18.2 cm

The surface area of a sphere is

A = 4πr^2

Substitute r in the formula

A = 4× π × 18.2^2

A = 4141

Since the shape is exactly one quarter of solid sphere. Divide the answer by 4

A = 4141/4

A = 1035.3 cm^2

The surface area of s is therefore 1035.3 cm^2

The surface area of the shape s is approximately 329.53 cm².

Important information:

Volume of a sphere is:

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

The volume of one-quarter of a solid sphere is 1994π cm².

[tex]1994\pi=\dfrac{1}{4}\times \dfrac{4}{3}\pi r^3[/tex]

[tex]1994\pi=\dfrac{1}{3}\pi r^3[/tex]

[tex]\dfrac{1994\pi\times 3}{\pi}=r^3[/tex]

[tex]5982=r^3[/tex]

Taking cube root on both sides, we get

[tex]\sqrt[3]{5982}=r[/tex]

[tex]r\approx 18.153[/tex]

Surface area of a sphere is:

[tex]S=4\pi r^2[/tex]

Surface area of one quarter of solid sphere is:

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

[tex]S=\pi (18.153)^2[/tex]

[tex]S=329.5314\pi[/tex]

[tex]S\approx 329.53\pi[/tex]

Therefore, the surface area of the shape s is 329.53 cm².

Find out more about 'Sphere' here:

https://brainly.com/question/16415229

Answer:

78/4=19.5, 68/7=9.71, 98/6=16.3

Step-by-step explanation:

Answer: 3/4 cups per cake.

Step-by-step explanation:

He needs 3 cups for 4 cakes.

Then, if you want to know the amount that he needs for each cake, you need to see the quotient between the number of cups and the number of cakes:

S = 3cups/4 cakes = (3/4) cups per cake.

In the number line, 3/4 will be:

0--I--I--(here)--1--I--I--I--2

Answer:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Step-by-step explanation:

Given that:

Initial Investment, P  = $5000

Formula:

[tex]A(t) = P(1.06)t[/tex]

To find: If James invests $5000,

average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20=?

Solution:

First of all, let us find out A(15) and A(20):

Putting t = 15 first,

[tex]A(15) = 5000(1.06)\times 15 ....... (1)[/tex]

Putting t = 20,

[tex]A(20) = 5000(1.06)\times 20 ....... (2)[/tex]

Average rate of change / year is defined as:

[tex]\dfrac{\text{Change in value of A}}{\text{Number of years}}[/tex]

So, required rate of change:

[tex]\dfrac{A(20)-A(15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 20-5000 \times 1.06 \times 15}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times (20-15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 5}{5}\\\Rightarrow 5000 \times 1.06\\\Rightarrow \$5300\ per \ year[/tex]

So, the answer is:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Answer: x=6, y=20

Step-by-step explanation:

Since ΔBCD and ΔTUS are congruent triangles, we can set the sides equal to each other.

y=2y-20                           [subtract both sides by 2y]

-y=-20                              [divide both sides by -1]

y=20

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

3x+32=9x-4                    [add both sides by 4, and subtract both sides by 3x]

36=6x                              [divide both sides by 6]

x=6

Answer:

HL, the two triangles both share a side and have right angles.

Step-by-step explanation:

Congruent Triangles - Hypotenuse and leg of a right triangle. (HL) Definition: Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. If, in two right triangles the hypotenuse and one leg are equal, then the triangles are congruent.

Answer:

x = 20

Step-by-step explanation:

If AE is a bisector then it divides the angle in half

BAE = EAC

x+30 = 3x-10

Subtract x from each side

30 = 2x-10

Add 10 to each side

40 = 2x

Divide by 2

40/2 =2x/2

20 =x

Answer:

The solution is the triplet: (a, b, c) = (-3, 0, 0)

Step-by-step explanation:

Let's start with the second equation, and solving for "a":

a - b = -3

a = b - 3

Now replace this expression for a in the third equation:

2 a + b = -6

2 (b - 3) +b = -6

2 b - 6 +b = -6

3 b = -6 +6

3 b = 0

b = 0

So if b = 0 then a = 0 - 3 = -3

now we can replace a= -3, and b = 0  in the first equation and solve for c:

2 a - b + c = -6

2 ( -3) - 0 + c = -6

-6+ c = -6

c = -6 + 6

c = 0

Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)

Answer:

"descends"

Step-by-step explanation:

(just had the same question).

Answer:

111111 [tex]\times[/tex] 1111110 is the simple expression.

Step-by-step explanation:

The expression to be solved:

[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}[/tex]

First of all, let us solve the first term:

[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111[/tex]

Now, the right term:

[tex]\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111[/tex]

So, the expression to be solved becomes:

[tex]1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110[/tex]

Answer: 1 3/4

Step-by-step explanation:

Step 1: Subtraction

1/4+1 1/2

Step 2: Addition

1 3/4

Hope it helps <3

Answer:

1 3/4

Step-by-step explanation:

Simplify 1/2 -1/4+1 1/2​

1/2 - 1/4 + 1 1/2 =

= 2/4 - 1/4 + 1 2/4

= 1/4 + 1 2/4

= 1 3/4

Answer:May be 12

Step-by-step explanation:

Answer: The surface area of the rectangular prism is 114 cm^2.

Step-by-step explanation:

1) Formula:  A = 2wl + 2lh + 2hw

( W=width, l= length, h=height)

2) Plug it in: A=2(3)(8) + 2(8)(3) + 2(3)(3)  

3) A= 2( 24) + 2(24) + 2(9)

4) A= 48+ 48+ 18= 114

Answer:

x= 48

Step-by-step explanation:

x∝ y

x= ky

24= 8k

k= 3

Now solve for x

x= ky

x= 3x 26

x= 48

I hope it helped

Responda:

P (verde) = 8/15

P (vermelho) = 1/3

P (azul)). 2/15

P (verde ou azul) = 2/3

P (não verde) = 7/15

Explicação passo a passo:

Dado o seguinte:

Número de bolas verdes = 8

Número de bolas vermelhas = 5

Número de bolas azuis = 2

N (verde) = 8

N (vermelho) = 5

N (azul) = 2

Portanto, número total de bolas;

N (total) = 8 + 5 + 2 = 15

Probabilidade = número de resultados requeridos / Total de resultados possíveis

1.) Probabilidade de escolher uma bola verde:

P (verde) = número de bolas verdes / número total de bolas

P (verde) = 8/15

2.) Probabilidade de pegar uma bola vermelha: P (vermelho) = número de bolas vermelhas / número total de bolas

P (vermelho) = 5/15 = 1/3

3) Probabilidade de pegar uma bola azul:

P (azul) = número de bolas azuis / número total de bolas

P (azul) = 2/15

4) probabilidade de verde ou azul:

P (verde ou azul) = P (verde) + p (azul)

P (verde ou azul) = 15/8 + 2/15 = 10/15 = 2/3

P (não verde) = 1 - P (verde)

P (não verde) = 1-8/15

P (não verde) = 7/15

Answer:

(0, 4)

Step-by-step explanation:

The y-intercept is where the graph crosses the y-axis when x = 0. Since you are given the graph, you can see that when x = 0, the graph crosses y = 4, so our y-int is (0, 4).

Answer:

Hey there!

We want to change the equation for each line into slope intercept form, or y=mx+b form.

Luckily, the first one is already in slope intercept form.

The second line can be converted to: y=-3/4x-7/4.

The third line can be converted to: -8y=-6x+4, or y=3/4x-1/2

Line one and line two are neither perpendicular or parallel.

Line one and line three are perpendicular.

Lines two and three are neither perpendicular or parallel.

This is because parallel lines have same slope, and perpendicular lines have opposite reciprocal slopes.

Hope this helps :)

Answer:

Line 1 and Line 2: Neither

Line 1 and Line 3: Perpendicular

Line 2 and Line 3: Neither

Step-by-step explanation:

To make the answering process easier, begin by converting each formula into the format y = mx +b:

Line 1: y = -4/3x + 1 (already in format)

Line 2:

-4y = 3x + 7

Divide all terms by -4:

y = -3/4x - 7/4

Line 3:

6x - 8y = 4

Subtract both sides by 6x:

-8y = -6x + 4

Divide all terms by -8:

y = 3/4x - 1/2

We can determine the relationships of the lines:

Line 1 and Line 2: Neither. They do not have the same slope, and they are not opposite reciprocals of each other.

Line 1 and Line 3: Perpendicular. The slopes of each line are opposite reciprocals: (-4/3 and 3/4)

Line 2 and Line 3: Neither. The slopes are the same but one is negative.

Answer:

Square root of 12 is a interfering because it isn’t a perfect square.

Answer:

It is an integer.

Step-by-step explanation:

Integers are all types of numbers may it be negative or positive but rational numbers are positive and negative fractions or decimals. So √12 is an integer.

Hope this helps.

Answer:

1.

a. 5p + 3

b. 26p + 6

2.

a r = (v ÷(pi)h)½

b. r = 3.74 to the nearest hundredth

Step-by-step explanation:

1.

Area of deck = 40p² + 24p

Width of deck = 8p

Area = length × width(breadth)

a. Area = length × width

40p² + 24p = length × 8p

Factorise out 8p from the left hand side

8p(5p + 3) = length × 8p

Divide both sides by 8p

5p + 3 = length

b Perimeter of deck = 2 (length + width)

"" = 2(5p+3 + 8p)

"" = 2 (13p + 3)

"" = 26p + 6

2.

Volume = 200 mm³

Height = 17mm

a. isolate the r in the equation v = (pi)r²h

v = (pi)r²h

Divide both sides by (pi)h

v ÷ (pi)h = r²

Take the square roots of both sides

(v ÷ (pi)h)½ = r

b. find r using your answer in a.

r = (v ÷ (pi)h)½

r = (200 ÷ ( 22/7 × 17))½

r = (200 ÷ 53.4286)

r = 3.7433

r = 3.74 to the nearest hundredth

Answer:

y = G(x) = 6, when x = -4

y = G(x) = -2, when x = 3

Step-by-step explanation:

From the attached graph tracing the first point to the graph and then to x axis.

y = G(x) = 6

as shown on the attachment(by the thick line)

y = G(x) = 6, when x = -4

From the attached graph tracing the second point to the graph and then to x axis.

y = G(x) = -2

as shown on the attachment(by the thin line)

y = G(x) = -2, when x = 3

Step-by-step explanation:

5(2h+8) <60

10h +40< 60

10h + 40-40 < 60-40

10h < 20

10h/10 < 20/10

h < 2

Answer:

see below

Step-by-step explanation:

Alright, geometric probability.

We need to find

To find those, we need to find the areas of:

Let's start off with the easiest figure. The circle.

The circle has a radius of 10. Therefore, its area is is π[tex]r^2[/tex]. 100π is roughly 314.159265.

The circle has an area of around 314.159265.

Half of the diagonal of the square is 10m. That means that the full diagonal of the square is 20 m.

Formula for side of square using diagonal:

a = q / √2

20/√2 = 14.142135623731

The area of a square is a^2

14.142135623731^2= 200

The area of the square is 200 m^2. (28)

Using this, and the area of the circle, we can find the area of the part of the circle that does not include the square.

314.159265 - 200= 114.159265

The area of the part of the circle that does not include the square is 114.159265.

Now, the most important calculation (because it lets us find the total area of the rectangle); the equiangular triangle.

The height of this triangle is 30m. Therefore, the area is 519.6152422706632.

The area of the equiangular triangle is 519.6152422706632.

The side length of the equiangular triangle is 34.64101615137755.

The area of the rectangle= l times w.

l = 34.64101615137755

w= 30

30 times 34.64101615137755= 1039.23048454133

The total area is 1039.23048454133.

Now that we have the denominator of our fraction (total area), lets go back to our questions.

We need to find

The area of the equilateral triangle = 519.6152422706632

519.6152422706632/1039.23048454133 = .5

The geometric probability that a point chosen randomly inside the rectangle is inside the equilateral triangle is .5

The area of the square = 200

200/1039.23048454133 = 0.19245008973

The geometric probability that a point chosen randomly inside the rectangle is inside the square is 0.19245008973

The area of the part of the circle that doesn't include the square: 114.159265

114.159265/1039.23048454133= 0.10984980396

The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle that doesn't include the square is 0.10984980396

The part of the rectangle that doesn't include the square, circle or triangle.

Area of triangle = 519.6152422706632

(The triangle contains the circle and square).

1039.23048454133- 519.6152422706632 = 519.61524227067

519.61524227067 /1039.23048454133 = 0.5

The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle doesn't include the square, circle, or triangle is 0.5

Hope this helped! Let me know if I made an errors, or if my answers are incorrect.

Answer:

to the nearest hundreths or any one

Step-by-step explanation:

Answer:

Angle B =  75 degrees

AC =  35.7

BC =  9.6

Step-by-step explanation:

Angle A = 15 degrees (given)

Angle C = 90 degrees (given)

c = 37 (given)

Angle B = 90-15 = 75 degrees

AC = AB cos(A) = 37 cos(15) = 35.7

BC = AB sin(A) = 37 sin(15) = 9.6

Answer:

58>13>-35>-51, so A is correct.

Step-by-step explanation:

Altitude of Snowvale: 13

Altitude of Highbridge: 58

Altitude of Westsilver: -51

Altitude of Springmoor: -35

Decreasing order means from greatest to least.

Obviously, positive numbers are greater than negative numbers, so we put the positive numbers first. 58>13>-35>-51.

(Note that with negatives, a greater number is a number closer to zero!)

Answer:

A

Step-by-step explanation:

The altitudes have to be arranged in decreasing order.

58 > 13 > -35 > -51