Given the above graph of y=-a(x+2)(x-6), where a>0,
(a) write down the equation of the line of symmetry,
(b) find the value of a. ​

Answer:

[tex] \frac{25}{16} \: \: or \: \: 1\frac{9}{16} [/tex]

Step-by-step explanation:

[tex]( \frac{5}{4} )^{3} = \frac{ {5}^{3} }{ {4}^{3} } = \frac{5 \times 5 \times 5}{4 \times 4 \times 4} = \frac{5 \times 25}{20 \times 4} = \frac{25}{4 \times 4} = \frac{25}{16} = 1 \frac{9}{16} [/tex]

Answer:

[tex]\frac{7}{3} =2\frac{1}{3}[/tex]

Step-by-step explanation:

For the problem:

[tex]\frac{5}{3} +\frac{4}{6} = ?[/tex]

The Least Common Multiple (LCM) of 3 and 6 is 6. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM:

[tex]\frac{5}{3} +\frac{4}{6} =\frac{5*2}{3*2} +\frac{4}{6} =\frac{10}{6} +\frac{4}{6}[/tex]

Now that the fractions have like denominators, add the numerators:

[tex]\frac{10}{6} +\frac{4}{6} =\frac{10+4}{6} =\frac{14}{6}[/tex]

The Greatest Common Factor (GCF) of 14 and 6 is 2. The result can be simplified by dividing both the numerator and denominator by 2.

[tex]\frac{14}{6} =\frac{14/2}{6/2} =\frac{7}{3}[/tex]

7 ÷ 3 = 2R1, therefore:

[tex]\frac{7}{3} =2\frac{1}{3}[/tex]

The Length of the fence in the example doubles as the perimeter of the circular garden. Hence the largest whole number of the radius is 8 feet

Given Data

Length of Fence = 50 feet

Largest Whole number Radius = ??

In this exercise, the Length of the fence is the same as the perimeter of the circular vegetable garden.

We know that the expression for the perimeter of a circle is given as

Perimeter of Circle = 2πr

From here we can solve for the Radius r

50 = 2*3.142*r

50 = 6.284r

divide both sides by 6.284

r = 50/6.284

r = 7.956 feet

r = 8 feet

Learn more about circle here:

https://brainly.com/question/24375372

Answer:

62°

Step-by-step explanation:

Angle KPO = 90°. If you add angles KPN and NPO together, you will get 90°. Set up an equation and solve for x.

2x + x - 3 = 90

3x - 3 = 90

3x - 3 + 3 = 90 + 3

3x = 93

3x/3 = 93/3

x = 31

Now solve for the measure of KPN by substituting 31 for x.

KPN = 2x

KPN = 2(31)

KPN = 62°

Answer:

D 62

Step-by-step explanation:

Good luck

Answer:

1. This is a Quadrilateral.

(There're 4 sides)

2. This is a Pentagon.

(There're 5 sides)

The first polygon is a quadrilateral.

The second polygon is a pentagon.

Polygons are  flat or plane, two-dimensional closed shape with straight sides.

Polygons are classified base on the number of side they possess. For example polygon with 4 sides are called quadrilaterals, the ones with 8 sides are referred to as octagons.

Therefore, the  polygons above have 4 sides and 5 sides respectively.

The polygon with 4 sides is know as a quadrilateral.

The polygon with 5 sides is known as a pentagon

learn more on polygons here: https://brainly.com/question/7921826

Answer:

Prime numbers:

11, 61, 43, and 29.

Step-by-step explanation:

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

For example:

13 has only two factors, itself and 1. So, it is a prime number.

4 has three factors, itself, 1, and 2. So, it is not a prime number.

Your other answers are correct.

Hope this helped!

Answer:

Their angles are equal and the sides are the same ratio

Step-by-step explanation:

Hope this helps (doesn't need much explanation)

Answer:

  (b)  16 ft²

Step-by-step explanation:

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h . . . . . where b1, b2 are the base lengths, h is the height

Using the values shown on the diagram, we find the area to be ...

  A = 1/2(3 ft + 5 ft)(4 ft) = (1/2)(8 ft)(4 ft) = 16 ft²

The area of the trapezoid is 16 ft².

Answer:

3/10

Step-by-step explanation:

total boxes = 100

shaded boxes = 30

fraction =30/100

= 3/10

Answer:

m=7 z=-12

Step-by-step explanation:

expand brackets:

8m+24=5m+45

Change sides:

8m-5m=45-24

3m=21

m=7

z-6    =  3

2z         4

Coss multiply:

4z-24=6z

4z-6z=24

-2z=24

Divide both sides by -2:

z=-12

Answer:

3/9 or 1/3 is the slope

Step-by-step explanation:

yeah

Answer:

isosceles triangle

Step-by-step explanation:

An isosceles triangle has 2 congruent sides

The triangle described here has 2 congruent sides of 8 cm

The triangle is isosceles

Answer:

if 2x-1 is a factor of the polynomial f(x)= 8^3 +4^2+kx+15 where is a constant find the value of k and factorise f(x) completely when k has this value

Answer:

2 6 12

Step-by-step explanation:

there are the only factor of 12 there

Answer:

D, $18,000.00

Step-by-step explanation:

Club A

$3 x is donated where x is the number of donations

Club B

$1.25x  is donated where x is the number of donations

The total of donations is 25500.00

Add the donations  times the dollar amount  for Club A and Club B and you get the total amount donated

$3x +$1.25x = 25500.00

Combine like terms

4.25x = 25500.00

Divide by 4.25 on each side

4.25/4.25x = 25500.00/4.25

x =6000

There were 6000 donations

We want to find Club A donation amount

$3 x is the amount donated

3*6000 = 18000

Answer:

that guys smart

Step-by-step explanation:

Answer:

120/97

Step-by-step explanation:

When you're turning a mixed fraction into an improper fraction, you keep the denominator (bottem number) the same, but you times the numerator (top number) by the whole number (non-fraction number/left number)

6 * 20 = 120

Therefore it should be 120/97

This can not be simplified though (if I recall)

35*75 is

2625

2625/400 is

6.5625

Since you cannot have a decimal amount of a bag, you should purchase

(rounding)

7 bags of fertilizer

Answer:

7 bags

Step-by-step explanation:

First thing you need to do is figure out the area of the garden. Area=length×width, so just put in your numbers, 35×75=2625 square feet. One bag covers 400 feet, so you divide the area by 400, 2625÷400=6.5625. You can't buys 6.5625 bags of fertilizer, so you have to go up to the next whole number which is 7.

Answer:

x = 2, y = -3

Step-by-step explanation:

Add them together and get

9x + 8y - 9x - 9y = -6 + 9

-y = 3

so y = -3.

Sub it into the first equation and get

9x + 8(-3) = -6

9x - 24 = -6

9x = -6 + 24 = 18

x = 18/9 = 2

Answer:

1.5

Step-by-step explanation:

picture

Answer:

1¹/₈ hours

Joelle spent 1¹/₂ hours reading and Rileigh spent 3/4 of that time.

To find out how much time Rileigh spent, multiply the fractions but first convert the improper fraction to a proper fraction:

= 1¹/₂ = 3/2

= 3/2 * 3/4

= 9/8

= 1¹/₈ hours

Step-by-step explanation:

Answer:

30 feet

Step-by-step explanation:

A ratio of 4:3 means that if one part can be represented by x, the original height is equal to 4 * x and the mural height is equal to 3 * x. This is because the ratio of original : mural is 4 : 3, so if one part = x, we have 4 * x : 3 * x. Therefore,

original mast height = 40 feet

4 * x = original mast height = 40 feet

divide both sides by 4 to get x

x = 10 feet

3 * x = mural mast height = 3 * 10 feet = 30 feet

Answer:

480 minutes would be the answer

Step-by-step explanation:

Answer:

480 minutes

Step-by-step explanation:

We can write this relationship as [tex]y=0.11x+18[/tex] and then solve for x when y=70.80:

[tex]y=0.11x+18\\\\70.80=0.11x+18\\\\52.80=0.11x\\\\480=x[/tex]

Therefore, you spent 480 minutes talking.

Answer:

31

Step-by-step explanation:

hope this helps

Answer:

5/8 inch longer

Step-by-step explanation:

Answer:

19.7 inches

Step-by-step explanation:

circumference of a circle = 2πr

62 = 2*22/7 *r

r = 62 * 7 / 44 = 9.86

diameter = 2* r

= 2* 9.86

= 19.7 inches

Answer:

They flipped the wrong fraction it should have been 2/3 as the fraction you divide by is the fraction you flip

Answer:

AX / AB = 6/18 = 1/3

AY / AC = 10/25 = 2/5

They are not similar because the two ratios is not the same.

Step-by-step explanation:

I'm not really sure okay!

Note that [tex]\frac{AX}{AB}=\frac{6}{24} =\frac{1}{4} ,and\frac{AY}{AC}=\frac{10}{35}=\frac{2}{7}.[/tex]

Because the ratio of the lengths of corresponding sides of the triangles are not equal, the triangles are not similar.

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Answer by: Medunno13

https://brainly.com/question/26646936