Amy bakes and sells cupcakes out of her home. She uses baking pans that hold 12 cupcakes and 36 cupcakes to fill her orders. Amy needs to fill her biggest order of 504 cupcakes for a special event.
a. Write an equation to represent the number of 12-cup and 36-cup baking pans for her
order.

b. Amy needs to use a combination of the 12-cup and 36-cup baking pans to fill the order. With only eighteen 12-cup baking pans in her shop, how many of the 36-cup baking pans does she need to complete the order?

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Work Shown:

The notation f(4) means we want to find f(x) when x = 4.

If x = 4, then we go for the middle definition since 4 makes [tex]3 \le x \le 10[/tex] to be true (ie, 4 is between 3 and 10)

Therefore,

f(x) = x^2 - 7 when [tex]3 \le x \le 10[/tex]

f(4) = 4^2 - 7

f(4) = 16 - 7

f(4) = 9

Answer:

f(4) = 9

Step-by-step explanation:

4 is between 3 and 10 so we use the middle function

f(4) = x^2 -7

     = 4^2 -7

     = 16 -7

    = 9

Answer:

16

Step-by-step explanation:

using BODMAS rule

6 + 16 - 12 + 9 - 3............step 1

22 - 3 - 3....…...................step 2

16

Answer:

y = 10

Step-by-step explanation:

6y−3=57

6y = 60

y = 10

Answer: Try 2. This is my best guess

Answer:

- [tex]\sqrt{3}[/tex] and 0

Step-by-step explanation:

tan(2x)

= tan(2 × [tex]\frac{\pi }{3}[/tex] ) = tan([tex]\frac{2\pi }{3}[/tex] ) = - tan([tex]\frac{\pi }{3}[/tex] ) = - [tex]\sqrt{3}[/tex]

cos(3x) = cos(3 × [tex]\frac{\pi }{6}[/tex] ) = cos([tex]\frac{\pi }{2}[/tex] ) = 0

Answer:

D. The Scott Wedding

Step-by-step explanation:

Scott: 12 guests on the groom's side and 10 guests on the bride's side

Smith: 18 guests on the the groom's side and 13 guests on the bride's side

Answer:

Number of chickens = 8

Number of pigs = 16

Step-by-step explanation:

Let the pigs = p

Let the number of chickens = c

Number of heads = 24

p + c = 24 ----------------(I)

p= 24 - c

Number of feet = 80

Chicken has 2 legs and pig has 4 legs

4p + 2c = 80 --------------(II)

Substitute p = 24 - c in equation (II)

4*(24 - c) + 2c = 80

4*24 - 4*c + 2c = 80

96 - 4c + 2c = 80          {Combine like terms}

     96 - 2c = 80        {subtract 96 from both sides}

          -2c = 80 - 96

         -2c = -16          {Divide both sides by (-2)}

           c = -16/-2

          c = 8

Plugin c = 8 in equation (I)

p + 8 = 24

    p = 24 - 8

  p = 16

Answer:

sinA= 5/13; cosB= 5/13

Step-by-step explanation:

sine is opposite over hypotenuse so 5/13. cosine is adjacent over hypotenuse so 5/13

Answer:

4. 3, 4, and 5​

Step-by-step explanation:

1 ≤ 2x − 5

Add 5 to each side

1+5 ≤ 2x − 5+5

6 ≤ 2x

Divide by 2

6/2  ≤ 2x/2

3 ≤ x

x must be greater than or equal to 3

Answer:

[tex] \frac{3}{2} + 2(x - 1) = 3 - 2x \\ \frac{3}{2} + 2x - 2 = 3 - 2x \\ 2x + 2x = 3 - \frac{3}{2} + 2 \\ 4x = 3 - \frac{3}{2} + 2 \\ 4x = \frac{6 - 3 + 4}{2} \\ 4x = \frac{7}{2} \\ x = \frac{7}{2} \div 4 \\ x = \frac{7}{8} [/tex]

Step-by-step explanation:

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The determinant is C. -541.

Using a cofactor expansion along the first row:

[tex]\begin{vmatrix}-8&-4&-1\\1&7&-3\\8&9&9\end{vmatrix} = -8\begin{vmatrix}7&-3\\9&9\end{vmatrix} + 4\begin{vmatrix}1&-3\\8&9\end{vmatrix} - \begin{vmatrix}1&7\\8&9\end{vmatrix} \\\\= -8(7\times9-(-3)\times9) + 4(1\times9-(-3)\times8) - (1\times9-7\times8) \\\\ = -8(63+27) + 4(9+24) - (9-56)\\\\= \boxed{-541}[/tex]

Answer:

See below.

Step-by-step explanation:

When Brian passes Alex they both have travelled the same distance.

Call this distance d.

Let the speed that Brian passes = x miles/hour.

Distance = speed * time  so:

For Alex:

d = (x - 5) * 1.5        ( Alex cycles for 1 + 30 minutes =  1.5 hours)

For Brian:

d = x * 1

So substituting d = x in Alex's equation:

x = 1.5(x - 5)

x = 1.5x - 7.5

7.5 = 0.5x

7/5 / 0.5 = x

15 = x.

ANSWER:

Brian's speed is 15 miles/hour.

Alex's speed is 15 - 5 = 10 miles/hour.

Answer:

62

Step-by-step explanation:

Of means multiply and is means equals

.03 * n = 1.86

Divide each side by .03

.03n/.03 = 1.86/.03

n =62

[tex]\\ \sf\longmapsto 2x+y=2[/tex]

[tex]\\ \sf\longmapsto 2x=2-y[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}\dots(1)[/tex]

And

[tex]\\ \sf\longmapsto x+1=y+2[/tex]

[tex]\\ \sf\longmapsto x=y+2-1[/tex]

[tex]\\ \sf\longmapsto x=y+1[/tex]

[tex]\\ \sf\longmapsto \dfrac{2-y}{2}=y+1[/tex]

[tex]\\ \sf\longmapsto 2-y=2(y+1)[/tex]

[tex]\\ \sf\longmapsto 2-y=2y+2[/tex]

[tex]\\ \sf\longmapsto 2-2=2y+y[/tex]

[tex]\\ \sf\longmapsto 3y=0[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{0}{3}[/tex]

[tex]\\ \sf\longmapsto y=\infty[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-\infty}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Answer:

x=1 , y=0

Step-by-step explanation:

2x+y=2.......1

x+1=y+2

x-y=2-1

x-y=1...... 2

from equation 2 we get ,

x-y=1

x=1+y

putting the value of x in equation 1 we get,

2*(1+y) +y=2

2+2y+y=2

2+3y=2

3y=2-2

3y=0

y=0/3

y=0

putting the value of y in equation 2 we get,

x-0=1

x=1+0

x=1

hence x=1 , y=0

Answer:

w = 70 cm

A = 5600cm^2

Step-by-step explanation:

P = 2(l+w) where l is the length and w is the width

300 = 2(l+w)

We know the length is 10 longer than the width

l = w+10

300 = 2(w+10+w)

Divide each side by 2

300/2 = (w+10+w)

150 = (2w+10)

Subtract 10 from each side

150-10 = 2w

140 = 2w

Divide by 2

140/2 = w

70 = w

Now find the area

A = l*w

A = (w+10) * w

   = (70+10) *70

   = 80*70

5600

Answer:

1209

Step-by-step explanation:

| - 403 | × | - 3 |

= | 403 | × | 3 |

= 403 × 3

= 1209

Answer:

33

Step-by-step explanation:

HJ = HI + IJ

HJ = 3x - 9, HI = x and IJ = x + 5

So 3x - 9 = x + x + 5

Solve for x

Combine like terms

3x - 9 = 2x + 5

Add 9 to both sides

3x = 2x + 14

Subtract 2x from both sides

x = 14

Find HJ

HJ = 3x - 9

We have found that x = 14

HJ = 3(14) - 9

Multiply 3 and 14

HJ = 42 - 9

Subtract

HJ = 33

Answer:

x = 64°, y = 32°

Step-by-step explanation:

The sum of the angles on a straight line = 180° , then angles on PS are

2x + y + 20 = 180 ( subtract 20 from both sides )

2x + y = 160 → (1)

Angles on QT are

x + 3y + 20 = 180 ( subtract 20 from both sides )

x + 3y = 160 → (2)

Solve (1) and (2) simultaneously

Rearrange (1) expressing y in terms of x by subtracting 2x from both sides

y = 160 - 2x → (3)

Substitute y = 160 - 2x into (2)

x + 3(160 - 2x) = 160 ← distribute and simplify left side

x + 480 - 6x = 160

- 5x + 480 = 160 ( subtract 480 from both sides )

- 5x = - 320 ( divide both sides by - 5 )

x = 64

Substitute x = 64 into (3)

y = 160 - 2(64) = 160 - 128 = 32

Then

x = 64°, y = 32°

The relative frequency for football is the number of people who like football divided by total people:

4/28 = 0.14

Answer: 0.14

Its a triangle

[tex]\\ \sf\longmapsto Perimeter=31+18+25[/tex]

[tex]\\ \sf\longmapsto Perimeter=48+25[/tex]

[tex]\\ \sf\longmapsto Perimeter=73cm[/tex]

Its rectangle

[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]

[tex]\\ \sf\longmapsto Perimeter=2(15+10)[/tex]

[tex]\\ \sf\longmapsto Perimeter=2(25)[/tex]

[tex]\\ \sf\longmapsto Perimeter=50ft[/tex]

Answer:

a and c

Step-by-step explanation:

The perimeter is the sum of the 3 sides, that is

perimeter = 25 + 18 + 31 = 74 cm → a

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

The opposite sides of a rectangle are equal, so

perimeter = (2 × 10) + (2× 15) = 20 + 30 = 50 ft → c

Answer:

6

Step-by-step explanation:

5

Answer:

k = 10

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

2x(2x + kx) = 3x(3x + 5x)

4x² + 2kx² = 3x × 8x = 24x² ( subtract 4x² from both sides )

2kx² = 20x² ( divide both sides by 2x² )

k = 10

Answer:

C(x)=40x+14, 6 days

Step-by-step explanation:

C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.

C(x)=254=40x+14, 40x=240, x=6

Answer:

Step-by-step explanation:

Let n = abc is the 3-digit number

b = 0 - 9, total 10 options

Total good 3-digit numbers:

Answer:

2 real solutions

Step-by-step explanation:

Get all the terms to one side

10n^2 = 10 - 8n

10n^2 +8n -10 =0

ax^2 +bx+c =0

The discriminant is

b^2 -4ac

8^2 - 4(10)(-10)

64 +400

464

If the discriminant is greater than 0 we have 2 real solutions

Answer:

[tex]\sqrt{100^2 + 420^2}[/tex]

[tex]\sqrt{100^2+420^2}=20\sqrt{466}\quad \left(\mathrm{Decimal:\quad }\:431.74066\dots \right)[/tex]

Step-by-step explanation:

Answer:

a: x=90 b: x=45 y=45 c: y=68 x=68

Answer:

g(x) = 4 - x^2

at x-intercept, y=0

0=4-x^2

x^2=4

x = ± 2

=> two x- intercepts, (-2,0) and (2,0)

at y-intercept, x = 0

g(x) = y = 4 - 0 = 4

y-intercept = (0,4)

The x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

g(x) = 4 - x²

At x-intercept, y = 0

0=4-x²

x² = 4

x = ± 2

Two x- intercepts, (-2,0) and (2,0)

at y-intercept, x = 0

g(x) = y = 4 - 0 = 4

y-intercept = (0,4)

Therefore, the x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).

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