Find the vertex of f(x)=x2 -6x +8 .

Answer:

x≤11

Step-by-step explanation:

x+5<17, I can subtract 5 on both sides so

x+5<17

 -5  -5

x<12

that's wrong though because my x needs to make my answer less than x to make the statement true since we're looking for a value that is less than 17 not less than or equal to 17. So in conclusion, if x≤11 ( if x is less than or equal to 11), my statement will be true because 11+5<17=16<17, which is true. Even 10 or less is fine because it will still be smaller than 17 and that will keep my statement balanced.

Answer:

68

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part C: (Explanation with steps)

Let the length of the swimming pool = l feet

And width of the pool = w feet

Perimeter of the pool = 2(l + w) feet

Since, perimeter of the pool = 8 feet

2(l + w) = 80

l + w = 40

l = (80 - w) -------(1)

Area of the pool = Length × width

A(w) = l × w

By substituting the value of l from equation (1)

A(w) = (80 - w) × w

A(w) = 80w - w²

To find the maximum area of the pool we will find the derivative of the function with respect to 'w' and equate it to zero.

A'(w) = 80 - 2w

(80 - 2w) = 0

w = [tex]\frac{80}{2}[/tex]

w = 40 feet

Therefore, for width (w) = 40 feet area of the pool will be maximum.

From equation (1),

l = 80 - 40

l = 40 feet

Therefore, maximum area of the pool = l × w

                                                               = 40 × 40

                                                               = 1600 square feet

Part A:

Function representing area of the pool,

A(w) = -w² + 80w

Part B:

Maximum area of the surface of the pool = 1600 square feet

Answer:

6574900

Step-by-step explanation:

Answer:

6,574,900

Step-by-step explanation:

have a good day

Answer:

1 : 2.5

Step-by-step explanation:

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

2(x-y)=3y

divide both sides of the equation by 2

x - y = 3y/2

x - y = 1.5y

combine like terms together

x = 1.5y + y

x = 2.5y

ratio of x : y

1 : 2.5

Answer:

B) & C)

Step-by-step explanation:

___________________

Take a deep breath and try to study right before the exam. Use your time on the exam wisely because it time goes away fast. Study the basics and formulas. Have a good exam your going to do good!!!

Answer:

A= third interior angle

108+24+A=180

A=180-24-108

A=48

Step-by-step explanation:

Step-by-step explanation:

Correct option is

A

x= 4 and y = 5

Let the parallelogram be ABCD Perimeter= 40cm

AB =3x cm BC=2x cm(given)

Perimeter of parallelogram 2(3x+2x)=40

solving equation we get x=4

Also,AB=CD(opposite sides of parallelogram) 3x=2(y+1) (given)

Putting x=4

3(4)=2y+2

12=2y+2

10=2y

Hence y=5 and x=4

Answer:

x+133 =131

x. =131-133

x. =(-2)

Answer: 104 boxes were sold in 1 week.

Step-by-step explanation:

I think I'm right sorry if I'm not, good luck!

Answer: First Week: 104 Second Week:109 Third Week: 218

sorry for being a year late

Answer:

a = 9 / 7

step by step explanation:

9 / - a + 15 = 8

Determined the defined range

9 / ( - a ) + 15 = 8 , a ≠ 0

subtract 15 from each side

9 / - a + 15 - 15 = 8 - 15

calculate the difference

9 / - a = - 7

multiply both side of equation by - a

9 / - a × - a = - 7 × - a

9 = 7 a

divide each side by of equation by -7

9 / 7 = 7 a / 7

9 / 7 = a

swap the side of equation . ( optional )

a = 9 / 7

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex]\huge\underline{\sf{\red{Problem:}}}[/tex]

[tex]\huge\underline{\sf{\red{Solution:}}}[/tex]

[tex] \quad \quad \quad \quad\sf{ ⟶ \frac{9}{ - a} + 15 = 8}[/tex]

[tex]\quad \quad \quad \quad\sf{ ⟶ \frac{9}{ - a} = 8 - 15}[/tex]

[tex]\quad \quad \quad \quad\sf{ ⟶ \frac{9}{ - a} = -7}[/tex]

[tex]\quad \quad \quad \quad\sf{ ⟶ 9 = 7a}[/tex]

[tex]\quad \quad \quad \quad\sf{ ⟶ \frac{9}{a} = \frac{7a}{a} }[/tex]

[tex]\quad \quad \quad \quad\sf{ ⟶ \frac{9}{ 7} = \frac{ \cancel{ \red{7}} a}{ \cancel{ \red{7} }} }[/tex]

[tex]\quad \quad \quad \quad \boxed{\sf{ ⟶ \frac{9}{7} = a } }[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex] \huge \quad \quad \underline{ \boxed{\sf{ \red{ \frac{9}{7} = a }} }}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

#CarryOnLearning

[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]

Answer:

A(-1,1) B(-3,2) C(-3,4) D(-1,5)

Step-by-step explanation:

when the shape is rotated 270° it will be in quadrant 2(top left). the x coordinates will be negative. the y coordinates will still be positive. basically if you move your paper so the shape in in the top left corner, you will find your coordinates.

Answer:

Step-by-step explanation:

[tex]7 \times -6\frac{1}{8} = 7 \times \frac{-49}{8} = -\frac{343}{8}[/tex]

Answer:

-343/8 or -42 7/8

Step-by-step explanation:

7(-49/8) = -343/8 or -42 7/8

Answer:

cone a is the correct answer

the third choice is the cirrect answer.

the cone with a 4.5 cm height and a 8cm diameter

hope this helps :)

Answer:

Line AC

Step-by-step explanation:

Given

See attachment for triangles

Required

60 degrees clockwise rotation about A

Since [tex]\triangle ABC[/tex] and [tex]\triangle ABD[/tex] are equilateral, then all angles in both triangles are [tex]60^o[/tex]

So, rotating in clockwise direction of A means that a line segment in the right of A will be considered.

The closest is line AC;

Hence, AC is [tex]60^o[/tex] clockwise of point A

Answer:

16 x¹⁰ + 88 x⁵ + 121

step-by-step explanation:-

( 4 x⁵ + 11)²

( 4x ⁵)² +2 ( 4x⁵) ( 11 ) + ( 11 )²

calculate we get

16 x¹⁰ + 88 x⁵ + 121

Answer:

D

Step-by-step explanation:

The statement that is also true is: [tex]\triangle QRS \cong \triangle YZX[/tex]

The congruence statement is given as:

[tex]\triangle QSR \cong \triangle YXZ[/tex]

The above statement means that, we have the following corresponding points

The above highlights mean that:

Triangle QSR corresponds to triangle YXZ

It also means that:

Triangle QRS corresponds to triangle YZX

Hence, the correct congruency statement is: [tex]\triangle QRS \cong \triangle YZX[/tex]

Read more about congruent triangles at:

https://brainly.com/question/1675117

Answer:

m+5=7

Step-by-step explanation:

Answer:

254.47

Step-by-step explanation:

Formula is pi r^2

the radius is 9 which is half of the diameter

pi 9^2

Answer:

see below

Step-by-step explanation:

24 = c + -10

Add 10 to each side

24+10 = c-10+10

34 = c

Check

24 = 34 + -10

24 = 24

This is a true statement so it is a solution

Answer:

Step-by-step explanation:

Corresponding angles are congruent

x² - 72 = 6x

x² - 6x - 72 = 0

Sum = -6

Product = -72

Factor = -12 , 6   {-12*6 = -72  & -12 +6 = -6}

x² + 6x - 12x -72 = 0

x(x + 6) - 12(x + 6) = 0

(x + 6)(x -12)=0   {Ignore x + 6 = 0 because angles won't be in negative}

x - 12 = 0

x = 12

Given:

In triangle ABC, AB = AC, AD is angle bisector and measure of angle C is 49 degrees.

To find:

The value of x and y.

Solution:

In triangle ABC,

[tex]AB=AC[/tex]                    (Given)

So, triangle ABC is an isosceles triangle and by the definition of base angles the base angles of isosceles triangle are congruent.

In isosceles triangle ABC,

[tex]\angle B\cong \angle C[/tex]

[tex]m\angle B\cong m\angle C[/tex]

[tex]m\angle B\cong 49^\circ[/tex]

The angle bisector of an isosceles triangle is the median and altitude of the triangle. So, the angle bisector is perpendicular to the base.

[tex]m\angle ADB=90^\circ[/tex]

[tex]x^\circ=90^\circ[/tex]

In triangle ABD,

[tex]m\angle DAB+m\angle ABD+m\angle ADB=180^\circ[/tex]         [Angle sum property]

[tex]y^\circ+49^\circ+x^\circ=180^\circ[/tex]

[tex]y^\circ+49^\circ+90^\circ=180^\circ[/tex]

[tex]y^\circ=180^\circ-49^\circ-90^\circ[/tex]

[tex]y^\circ=41^\circ[/tex]

Therefore, the correct option is B.

Answer:

6π

Step-by-step explanation:

Formula: C=2πr

C=2π3

C=6π

Answer:

13units

Step-by-step explanation:

Using the distance formula;

D = √(x2-x1)²+(y2-y1)²

Distance from home to the soccer field is expressed as;

Home (0,0) and soccer field (-4,3)

D =√(3-0)²+(-4-0)²

D =√3²+4²

D =√9+16

D = √25

D = 5

Distance from  soccer field to library is expressed as;

Library (4,3) and soccer field (-4,3)

D =√(-4-4)²+(3-3)²

D =√(-8)²+0²

D =√64

D = 8

Hence the total distance = 5 + 8 = 13units

Answer:

O número é 3

Step-by-step explanation:

Este número é 3

Número de base = 3

Potência = 3

Então, 3 ^ 3 = 27

Os valores de base e potência são iguais e o número resultante tem dois dígitos.