5. Evaluate each expression if x is 1, y is 2, and z is 3. (Lesson 6-15) a. 77² – Z b. (x+4)3 - y c. y(x+3) d. 07- y + z)? i need help ​

Given:

The vertex of a quadratic function is (-5,-1) and it passes through the point (-2,2).

To find:

The vertex and standard form of the quadratic function.

Solution:

The vertex form of a quadratic function is:

[tex]f(x)=a(x-h)^2+k[/tex]

Where, a is a constant, (h,k) is vertex.

The vertex of a quadratic function is (-5,-1). It means [tex]h=-5,k=-1[/tex].

[tex]f(x)=a(x-(-5))^2+(-1)[/tex]

[tex]f(x)=a(x+5)^2-1[/tex]             ...(i)

The quadratic function passes through the point (-2,2). Putting [tex]x=-2,f(x)=2[/tex] in (i), we get

[tex]2=a(-2+5)^2-1[/tex]

[tex]2+1=a(3)^2[/tex]

[tex]3=9a[/tex]

[tex]\dfrac{1}{3}=a[/tex]

Putting [tex]a=\dfrac{1}{3}[/tex] in (i), we get

[tex]f(x)=\dfrac{1}{3}(x+5)^2-1[/tex]

Therefore, the vertex for of the quadratic function is [tex]f(x)=\dfrac{1}{3}(x+5)^2-1[/tex].

The standard form of a quadratic function is:

[tex]f(x)=Ax^2+Bx+C[/tex]

We have,

[tex]f(x)=\dfrac{1}{3}(x+5)^2-1[/tex]

[tex]f(x)=\dfrac{1}{3}(x^2+10x+25)-1[/tex]

[tex]f(x)=\dfrac{1}{3}x^2+\dfrac{10}{3}x+\dfrac{25}{3}-1[/tex]

[tex]f(x)=\dfrac{1}{3}x^2+\dfrac{10}{3}x+\dfrac{22}{3}[/tex]

Therefore, the standard form of a quadratic function is [tex]f(x)=\dfrac{1}{3}x^2+\dfrac{10}{3}x+\dfrac{22}{3}[/tex].

Answer:

[tex]2\sqrt{51}[/tex]

Step-by-step explanation:

first, you have to look pythagoras theorem (in picture)

then; x² + 14² = 20²

x² + 196 = 400

x² = 204

x = [tex]\sqrt{204}[/tex] = [tex]2\sqrt{51}[/tex]

Hope this helps ^-^

The length of the unknown side ( x )

We'll have to use pythagoras Theorem.

[tex]\huge\boxed{\sf{Formula: {a}^{2} + {b}^{2} = {c}^{2} }}[/tex]

In this question hypotenuse is given so we'll have to subtract.

Let the unknown be "x"

[tex] {c}^{2} = {a}^{2} - {b}^{2} [/tex]

[tex] {x}^{2} = {20}^{2} - {14}^{2} [/tex]

[tex]x = 204[/tex]

[tex] {x}^{2} = \sqrt{204} [/tex]

[tex]x = 14.28285686[/tex]

[tex]\large\boxed{\sf{x = 14.3 \: (nearest \: tenth)}}[/tex]

Hence, the unknown side of the given triangle is 14.3

Answer:

C

Step-by-step explanation:

5 - 1 = 4

5 - 5 = 0

5 - -1 = 6

I hope this helps but the answer most likely is C

Answer:

I think it's letter C ..........

Answer:

Y=1.50

Step-by-step explanation:

For the graph chart the x as the table says and the y as 1.50 for one then keep adding 1.50 for the others

1) 4x1.50= 6.00

2)5.00/1.50= 3 and 1/3

Answer:c

Step-by-step explanation:

Answer:

a + [tex]11^{3}[/tex]

or

a + 1331

Step-by-step explanation:

The sum of 11 cubed and a

[tex]11^{3}[/tex] + a

or

1331 + a

Answer:

both ansers are 2.7

Step-by-step explanation:

This is an 45˚, 45˚, 90˚ so the two smaller sides are equal so x=5.4.

the hypotenuse is always sqrt2 times bigger than the smaller sizes so y=[tex]5.4\sqrt{2}[/tex]

Answer:

7040 yards

Step-by-step explanation:

Because 1 mile = 1760 yards.  So 4 x 1760 = 7040.

Answer:

7040 I think

Step-by-step explanation:

sorry if I'm wrong

Answer:

Check to see if each input value is paired with only one output value. If so, the table represents a function.

Yes. It is a function.

Step-by-step explanation:

Answer:

change the date of 4images and the giant is the quiz on my essay

Step-by-step explanation:

you wanna play 3rd party or something else do it was 4th day

Answer:

C

Show your work:

A perpendicular line has a negative reciprocal slope so 2/3 becomes -3/2, then substitute your point (-6,4) and you get letter C

I used your picture since your Question does not match the picture.

Answer:

Step-by-step explanation:

y = opposite

15 = hypotenuse

θ = 57°

therefore we use sin

sinθ = opposite/hypotenuse

sin57° = y/15

y = 15sin(57°)

y = 12,58 units

_________________

#StayPositive - kexcvi

Answer:

907.46 ft²

Step-by-step explanation:

Area of a full circle = πr²

Area of a quarter circle would therefore = ¼(πr²)

Where,

r = 34 ft

π = 3.14

Area of quarter circle = ¼(3.14 × 34²) = ¼(3,629.84)

Area of quarter circle = 907.46 ft²

Answer:

[tex]27a^6b^8 + 63a^5b^8 - 25a^8b^8[/tex]

Step-by-step explanation:

Given

[tex]9a^3b^6(3a^3b^2+7a^2b^2)-(5a^4b^4)^2[/tex]

Required

Simplify

[tex]9a^3b^6(3a^3b^2+7a^2b^2)-(5a^4b^4)^2[/tex]

Open both brackets

[tex]9a^3b^6*3a^3b^2+9a^3b^6*7a^2b^2-5a^4b^4*5a^4b^4[/tex]

This gives

[tex]27a^6b^8 + 63a^5b^8 - 25a^8b^8[/tex]

Answer:

its SAS

Step-by-step explanation:

segment ST is is one side then PS and RD is another because of the line across both of those and angle S

:)

Answer:

Function A

Step-by-step explanation:

Answer:

Function A?

Step-by-step explanation:

Answer:  79 and 14

X would be -3 because (2 x -3 + 85) is 79 and doing it for (5x + 29) would get 14.

Answer:

It is the 3rd option

Step-by-step explanation:

Answer:

hey,i can answer the question but i cant really see the coordinates

Step-by-step explanation:

Answer:

y < 1

Step-by-step explanation:

the value of y in the whole part is less than or equal to 1.

Answer:

B

Step-by-step explanation:

The formula for area for a circle is [tex]a = \pi[/tex] x r^2

Answer:

B and F are congruent tell me if its wrong

Step-by-step explanation:

Answer:

∠ B and ∠ F

Step-by-step explanation:

Given that

EFGH and ABCD are congruent then corresponding angles are congruent.

Then ∠ B and ∠ F are corresponding and congruent

Answer:

6.25 years

Step-by-step explanation:

Simple interest = principal x time x interest rate

simple interest = $4,000 - $2,500 = $1,500

1500 = $4,000 x 0.06 x n

1500 = 240n

divide both sides by 240

n = 6.25 years

Answer:

hmmmm i saw something about 13?????

Step-by-step explanation:

Answer:

y = 1/2x - 2.5

Step-by-step explanation:

(15, 5) and (42, 18.5)

Slope:

m=(y2-y1)/(x2-x1)

m=(18.5 - 5)/(42 - 15)

m = (13.5)/27

m = 1/2

y - y1 = m(x - x1)

y - 5 = 1/2(x - 15)

y - 5 = 1/2x - 7.5

y = 1/2x - 2.5

Answer:

2   or    1/2

Step-by-step explanation:

change in y over change in x

you didnt define what what x and what was y so ill provide both answers and you can figure which is correct

42-15/18.50-5   =27/13.5   =2

18.50-5/42-15    =13.5/27  =1/2

Answer:

1 ._11

2.11

3._84

4._0.333