5. Mrs. Perkins hosts a birthday party for her son and 7 guests. She orders 2 cookies and a
cupcake for each child. The cost of the cupcake is $2.75, and the total bill is $46.00. What is the
cost of a cookie?

Answer:

B

Step-by-step explanation:

According to the Factor Theorem, if (x - a) is a factor (where a is a zero) of the polynomial P(x), then P(a) must equal zero.

Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.

Testing each choice, we can see that only choice B is true. That is:

[tex]\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0 \end{aligned}[/tex]

In conclusion, our answer is B.

Answer:

B. -9/11

Step-by-step explanation:

(f/g)(-4) = f(-4) / g(-4)

To find f(-4), we plug in -4 everywhere there is an x

f(-4) = 2(-4) - 1 = -8 - 1 = -9

Same idea for g(-4):

4(-4)^2 + 14(-4) + 3

4*16 - 56 + 3 = 11

So (f/g)(-4) = f(-4) / g(-4) =

-9/11

Step-by-step explanation:

let : the pair of jeans = X

a. the equation is :

4(X-3) + 8 = 92

b. 4(X-3) = 92-8

4X -12 = 84

4X = 84+12

4X = 96

X = 96/4

X = 24

so, the price of each pair of jeans = $24

_________

For the solution x = 2.6, the left side of equation

(2x - 6) => would be 2(2.6)-6 = 5.2-6 = -8 ( the negative value),

but on the right side of the equation 4x+8 => 4(2.6) +8 = 18.4 ( the positive value)

this difference indicates that x=2.6 is not the right solution.

Answer:

a)  Let x be the cost of one pair of jeans

    [tex]4(x-3)+8=92[/tex]

b)  $24

Step-by-step explanation:

Given information:

Define the variable:

Let x = the cost of one pair of jeans

Create an equation using the defined variable and the given information:

[tex]4(x-3)+8=92[/tex]

To find the price of each pair of jeans, solve the equation for x:

[tex]\implies 4(x-3)+8=92[/tex]

[tex]\implies 4(x-3)+8-8=92-8[/tex]

[tex]\implies 4(x-3)=84[/tex]

[tex]\implies \dfrac{4(x-3)}{4}=\dfrac{84}{4}[/tex]

[tex]\implies x-3=21[/tex]

[tex]\implies x-3+3=21+3[/tex]

[tex]\implies x=24[/tex]

Therefore, the price of each pair of jeans was $24.

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

Solving  3(2x - 6) = 4x + 8  mentally:

Expand the brackets:

⇒ 16x - 18 = 4x + 8

Subtract 4x from both sides:

⇒ 12x - 18 = 8

Add 18 to both sides:

⇒ 12x = 26

Two times 12 is 24.  As 26 is very close to 24, then x ≈ 2.

(The actual value of x is 2.2 to 2 decimal places).

Assessing the student's solution:

As x = 2.6 rounds to x ≈ 3 then the student's solution is incorrect because:

⇒ 3(2(3) - 6) = 4(3) + 8

⇒ 3(6 - 6) = 12 + 8

⇒ 3(0) = 20

⇒ 0 = 20

Answer:

14

step by step explanation

-7×(-2)

14

Answer:

770

Step-by-step explanation:

12 month ×60 per month

Plus 50 set up fee

=770

Answer:

235.34

Step-by-step explanation:

122×193-12 = 23534

23534/100

23534/100 = 235.34

[tex]\\ \rm\hookrightarrow (x,y)=\left(\dfrac{x_1+x_2}{2}_\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\\ \rm\hookrightarrow (x,y)=\left(\dfrac{6+9}{2},\dfrac{2+4}{2}\right)[/tex]

[tex]\\ \rm\hookrightarrow (x,y)=\left(\dfrac{15}{2},\dfrac{6}{2}\right)[/tex]

[tex]\\ \rm\hookrightarrow (x,y)=(7.5,3)[/tex]

Answer:

8. 5

Step-by-step explanation:

First of all, I converted 3 hours 30 minutes to min. And we have 60 mins in an hour.

Therefore 60 × 3= 180mins +30 mins = 210 mins

So,

If 210=29.75

60=?

Cross multiply

29.75×60/210

=8.5

She's earns 8.5 in an hour

Find total collected by multiplying the amount per person by number of people:

1000 x 0.12 = $120.00

Total collected = $120.00

Divide total collected by number of people:

120.00 / 109 = $1.20

Each person gets $1.20

Answer:

(-4+y)=-7

-4+y=-7

by adding 4 on both sides, we get

-4+4+y=-7+4

y=-3

Step-by-step explanation:

Let 5 consecutive no. be

n, n+1,n+2,n+3,n+4

n+n+1+n+2+n+3+n+4=110

5n+10=110

5n=110-10

5n=100

n=100/5

n=20

4th term is n+3=20+3=23

                                                    Thank You

Answer:

6+x

Step-by-step explanation:

sum means add

6+x

Hey there!

When you see/hear the word “sum” in mathematics.. it usually means “to add”.

So, we are adding 6 from the unknown number (the x-value)

Answer: 6 + x

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

158

Step-by-step explanation:

4+16 = 20

20×8-2= 158

the dot means multiply and u must first find the answer in the bracket

if there is no bracker, then u must start with multiply first

Step-by-step explanation:

4+ 16 is equal to 20

8-2 is equal to 6

20×6 is equal to 120

120 is ans

Step-by-step explanation:

remember : calculations are usually done from left to right, but multiplications and divisions come before + and -.

and exponents come before multiplications and divisions.

and minus a negative number always turns into plus a positive number.

so,

3b²c - 2ad = 3×4²×2 - 2×3×-2 = 96 - -12 = 96 + 12 = 108

and

ac - bd/7 = 3×2 - 4×-2/7 = 6 - -8/7 = 6 + 8/7 = 7 1/7 ≈ 7.143

Answer:

16

Step-by-step explanation:

since -4 is being squared, we can write it out as -4 * -4, to get us the answer 16. this answer is positive because a negative times a negative will cancel out and = a positive.

MACARONI AND AN POT THATS AN WAAAAAPP

Answer:

x = 8

length is 12 meters

width is 9 meters

Step-by-step explanation:

P = 2l + 2w

where l is the length and w is the width.

(There are two sides with the same length, and two sides with the same width.)

Let l = x + 4 and w = 2x - 7

so 2(x+4) + 2(2x-7) = 42

Distribute the 2s

2x + 8 + 4x - 14 = 42

Combine like terms

2x + 4x + 8 - 14 = 42

Group

6x - 6 = 42

Add 6 to both sides

6x = 48

Divide 6 on both sides

x = 8

Plug back in

l = 8 + 4 = 12 meters

and w = 2(8) - 7 = 16 - 7 = 9 meters

Double-check: 2 * 12 + 2 * 9 = 24 + 18 = 42

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bsksbs

DE \\ BC

So ;

[tex] \frac{AD}{AB} = \frac{DE}{BC} [/tex]

AD = 3cm , BC = 14cm , DB = 4cm

AB = AD + DB

AB = 3 + 4 = 7 cm

[tex] \frac{AD}{AB} = \frac{DE}{BC} \\ \frac{3}{7} = \frac{DE}{14} \\ DE = \frac{14 \times 3}{7} = \frac{42}{7} = 6[/tex]

I hope I helped you^_^

Answer:

Below.

Step-by-step explanation:

396,242,002

Answer:

p = -10

Step-by-step explanation:

[tex]\frac{p+1}{2} = \frac{3p+7}{5}[/tex] cross multiply fractions

6p + 14 = 5p + 5

6p - 5p = 5 - 15 subtract like terms

p = - 10

Answer:

8

Step-by-step explanation:

6x+5=53

6x=48

6x/6=48/6

x=8

Answer: D

Step-by-step explanation:

Answer:

(23,500 +14m) miles

Step-by-step explanation:

the mileage on Sari's odometer after her trip =

(23,500 + 14 m) miles

Step-by-step explanation:

x1=6

y1=8

x2=1

y2=6

then ,

distance =

[tex] \sqrt{(6 - 1) {?}^{2} { + (8 - 6)}^{2} } \\ \sqrt{25 + [/tex]

Answer:

3

Step-by-step explanation:

hope it helps have a great day

Answer:

x = 3

Step-by-step explanation:

2x + 5x - 4 = 17      (Given)

7x - 4 = 17              (Simplify)

7x - 4 + 4 = 17 + 4  (Add 4 on both sides)

7x = 21                   (Simplify)

7x/7 = 21/7             (Divide 7 on both sides)

x = 3                      (Simplify)