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3 years ago

What is the vertex of the function f (x) = x^2 + 16x?

Mathematics

1 answer:

Tju [1.3M]3 years ago

8 0

f(x) = x^2 + 16x

Completing the square.

f(x) = a(x-h)^2 + k

f(x) = (x + 8)^2 - 64

h = -8, k = -64

Vertex = (h,k)

Vertex = (-8, -64)

Not fully explained, just a quick summary.

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Boardman's Department Store sells clothing for children and adults. Last weekend the store sold 5 adult shirt's for every 3 chil

Sladkaya [172]

a = adult shirts sold

c = children shirts sold

we know the store sold for every 5 "a", there were 3 "c" sold, so we can say that the adult to children shirts are on a 5 : 3 ratio.

We also know that whatever "c" is, adult shirts sold last weekend was 30 more than that, or namely "c + 30".

$\stackrel{\textit{\large ratios}}{\cfrac{\stackrel{adult}{a}}{\underset{children}{c}}~~ = ~~\cfrac{5}{3}}\qquad \implies \qquad \stackrel{\textit{we also know that \underline{a = c + 30}}}{\cfrac{c+30}{c}~~ = ~~\cfrac{5}{3}} \\\\\\ 3c+90=5c\implies 90 = 2c\implies \cfrac{90}{2}=c\implies \boxed{45=c}~\hfill \stackrel{c + 30}{\boxed{a=75}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{total~sold}{120}~\hfill$

6 0

2 years ago

How do you work the picture out?

FrozenT [24]

Answer:

24cm²

Step-by-step explanation:

Perimeter of rectangle ABCF = 20 cm

One of the sides AB = 6 cm (AB)(Let it be L)

other side of Rectangle=B.

Perimeter of Rectangle = 2 (Length + width)

20 = 2(L+W) = 2(6 + W)

$\frac{20}{2}$ =6+B

10=6+B

B = 10-6

B = 4 cm

Width of Rectangle, W = 4 cm (BC)

Length of side of trapezium, CD = BD - BC = 9 - 4 = 5 cm

And length of EF = 3 cm

Area of Trapezium = $\frac{1}{2}$ ×(CD+EF)×CF

$\frac{1}{2}$ ×(5+3)×6

$\frac{8}{2}$ ×6

4×6=24

5 0

3 years ago

Lex read 7 fewer books than Leona how many books did Leona read

postnew [5]

Answer:

Lex read 7 but Lena had to have 7 books which yea

8 0

3 years ago

A bakery asks 75 customers to vote for a new bagel flavor. Onion flavor receives 33 votes. Cheddar flavor receives 42 votes. Use

m_a_m_a [10]

Using proportions, it is found that:

The fraction that shows the proportion of customers who voted for cheddar flavor is $\frac{42}{75}$

56% of customers voted for cheddar flavor.

A proportion is the number of desired outcomes divided by the number of total outcomes.

A percentage is the proportion multiplied by 100%.

In this question, 42 out of 75 customers voted for the cheddar flavor, hence:

$p = \frac{42}{75}$

That is, the fraction that shows the proportion of customers who voted for cheddar flavor is $\frac{42}{75}$

The percentage is:

$\frac{42}{75} \times 100\% = 56\%$

56% of customers voted for cheddar flavor.

To learn more about proportions, you can take a look at brainly.com/question/24372153

8 0

2 years ago

Geometry proofs Need help!!

Andrew [12]

Angles ∠MOK and ∠NOL are identical by opposite angle theorem.

∠M = ∠N through given information

∠MKO and ∠NLO are congruent. Since the other two angles of each triangle are equivalent, the last angle must be equivalent to the last angle of the other triangle. (180 - ∠1 -∠2 = ∠3); you could also prove ∠MKO = ∠NLO by stating that the opposite sides of the two angles are congruent.

ΔMKO and ΔNLO by Angle-Angle-Side theorem

since ΔMKO and ΔNLO, all corresponding parts of both triangles are congruent, so therefore MO ≅ NO

8 0

3 years ago