You're having a party, and what party is complete without cupcakes? You decide that you're going to
make your own. You've invited some friends to the party. The recipe for cupcakes calls for 7 cups of
flour and 4 cup of milk. To remember this better, your mom suggests that you use a ratio.
1. What is the ratio of flour to milk? Write it in 3 ways.
2. What is you have more friends come over and your mom gives you 35 cups of flour to make
more cupcakes. How much milk will you need now? Draw a bar diagram to represent and
solve the problem.

Answer:

Part A

The equation of the parabola in standard form is f(x) = 0.5·x² + x - 7.5

Part B

The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)

Step-by-step explanation:

The coordinates of the vertex of the parabola, (h, k) = (-1, -8)

The zeros of the parabola = -5, 3

Part A

The quadratic equation representing the parabola can be written as follows;

y = a·(x - h)² + k

The standard form of the equation is f(x) = a·x² + b·x + c

k = c - b²/(4·a)

h = -b/(2·a)

c = k + a·h² = -8 + a

From the zeros of the parabola, we have;

f(-5) = a × (-5)² + b×(-5) + c = 25·a - 5·b + c = 0

f(3) = a × (3)² + b×(3) + c = 9·a + 3·b + c = 0

Therefore, we have;

25·a - 5·b + c = 0...(1)

9·a + 3·b + c = 0...(2)

From which we have;

25·a - 5·b + c = 25·a - 5·b - 8 + a = 26·a - 5·b - 8 = 0

9·a + 3·b + c = 9·a + 3·b - 8 + a = 10·a + 3·b - 8 = 0

We then have;

26·a - 5·b = 8...(3)

10·a + 3·b = 8...(4)

Making 'b', the subject of both equations (3) and (4), equating the values, we find the value of 'a' as follows;

From equation (3), we have;

26·a - 5·b = 8

∴ b = (26·a - 8)/5

From equation (4), we have;

10·a + 3·b = 8

∴ b = (8 - 10·a)/3

From b = b, by transitive property, we have;

(26·a - 8)/5 = (8 - 10·a)/3

3 × (26·a - 8) = 5 × (8 - 10·a)

78·a - 24 = 40 - 50·a

∴ 128·a = 64

a = 64/128 = 1/2 = 0.5

a = 0.5

∴ b = (26·a - 8)/5 = (26 × 0.5  - 8)/5 = (13 - 8)/5 = 1

b = 1

c = -8 + a

∴ c = -8 + 0.5 = -7.5

c = -7.5

The equation of the parabola in standard form is therefore presented as follows;

f(x) = 0.5·x² + x - 7.5

Part B

The equation of the parabola in factored form is given as follows;

With the aid of a graphing calculator, we have;

f(x) = 0.5·x² + x - 7.5 = 0.5×(x² + 2·x - 15) = 0.5·(x + 5)·(x - 3)

The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)

Answer:

[tex]n < 8[/tex]

Step-by-step explanation:

[tex]3n - 3 < 21 \\ 3n - 3 + 3 < 21 + 3 \\ 3n = 24 \\ \frac{3n}{3} < \frac{24}{3} \\ n < 8[/tex]

Answer:

48/5

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

5 × 9 = 45

Step 2

Add the answer from Step 1 to the numerator

45 + 3 = 48

Step 3

Write answer from Step 2 over the denominator

48/5

Answer:

first option

Step-by-step explanation:

Using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] then

[tex]5^4)^{3}[/tex] = [tex]5^{4(3)}[/tex] = [tex]5^{12}[/tex]

Answer:

growth

Step-by-step explanation:

1.034 < 1 means the number will get larger

Answer:

Step-by-step explanation:

Since the ratio or rate is greater than one this is an exponential growth function

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

320 i think lol

Step-by-step explanation:

Answer:

3.56

Step-by-step explanation:

Answer:

d is correct i think

Step-by-step explanation:

My brain aint working

Answer:

2/4=4/8

Step-by-step explanation:

you do 2×2=4 and 4×2=8. You multiply both denominators by 2.

Answer:

12.96c

Step-by-step explanation:

Given the total cost of an item  written as c+0.08c. To get the total cost of an item that sells for 12, we will write;

1 item = c+0.08c

1 item = 1.08c

For 12items;

12 = x

Divide both expressions

1/12 = 1.08c/x

1 * x = 12 * 1.08c

x= 12.96c

Hence the total cost of 212 items is 12.96c

Answer:

You were correct.

Step-by-step explanation:

If the input to the function y = 4x - 3 is 2 Then

y = 4 * 2 - 3

= 8 - 3

= 5

Hope it helps :)

Answer:

[tex]x = 64 + 45 \\ x = 109[/tex]

Answer:

do you need an equation? if so it would be 2x+40

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:42

Step-by-step explanation:

10 1/2 = 21/2

21/2 divided by 1/4

=21/2 times 4 (keep the first number, change the sign, flip the fraction)

=84/2

=42(patties)

Answer:

42

Step-by-step explanation:

10.5÷0.25=42

42 hamburger patties can be made

Answer:

247.728

Step-by-step explanation:

(3.97)(62.4)

=247.728

Answer:

Richie should add the number 36 to both sides.

Step-by-step explanation:

To complete the square, you need to divide b by 2, square it, then add it to both sides. In this case, you'd do this:

12/2=6

6^2=36

Answer:

13.4

Step-by-step explanation:

it just is

Answer:

13.4

Step-by-step explanation:

there you go 8.04 divided by 0.6= 13.4

Answer:

$1100

Step-by-step explanation:

Let the total budget = b

amount spent on props + amount spent on equipment = total budget

If 37% of the budget was spent on equipment

The percentage spent on props = 100% - 37% = 63%

63% of the total budget is $693

the above sentence presented as an equation gives :

63/100 x b = 693

to find b, divide both sides of the equation by 100/63

b = $1100

Answer:

1100

Step-by-step explanation:

Answer:

the first one is correct

Step-by-step explanation:

Answer:

1/2m - 4

Step-by-step explanation:

Answer: The second one, 10 rolls for $12. 1.29 (Rounded)

Step-by-step explanation:

14/18 is 1.29 (Rounded)

10/12 is 1.20.

The unit rate is cheaper, therefore making it the better buy

Answer:

n is 18

Step-by-step explanation:

Answer:

24 - n = 6

Figure out what plus 6 will give you 24.

Or add 24 and 6 and use the sum as the fill-in for n.

24 + 6 = 30.  

Replace the variable.

30 (n) - 24 = 6.

Step-by-step explanation:

Hope that this helps!! :))>

Answer:

Step-by-step explanation:

Increase by 23%

1.23 is the answer

Answer:

I thinks its D.

Step-by-step explanation:

Answer:

y = 7, x ≈ 9.9

Step-by-step explanation:

The remaining angle has to also be 45° which tells us we're working with an isosceles right triangle, or that y also has to be 7 (the same length).

Use the Pythagorean theorem for x.

a^2 + b^2 = x^2

7^2 + 7^2 = x^2

49 + 49 = x^2

x^2 = 98

x ≈ 9.9

Answer:

830

Step-by-step explanation:

Total plates washed is the sum of small plates washed and big plates washed

total plates washed = small plates + big plates

275 + 555 = 830 plates

a total of 830 plates was washed over the weekend

Answer:

The scale factor from PQR to P'Q'R' is ½