Need help with a system of equations

Answer:

  24

_______

2r^3 - 12r

Step-by-step explanation:

Let's solve for a.

24 = a(−2r^1)(6 − r^2)

Step 1: Flip the equation.

2ar^3 − 12ar = 24

Step 2: Factor out variable a.

a(2r^3 − 12r) = 24

Step 3: Divide both sides by 2r^3 - 12r.

a(2r^3 − 12r)            24

__________ = ________

   2r^3 - 12r       2r^3 - 12r

Answer:

a²+b²=c²

7.5²+9²=c²

137.25=c²

√137.25=c²

11.72.... = c

The Radius of the circle is approximately 11.72cm

Step-by-step explanation:

Using this data. Create a Triangle with the Chord and Center of the dot. We know the distance between the chord and center which is one length of one of the sides.

We split the chord from the intersecting line from the center to the chord making the second line being 7.5cm

After We draw a line from the center of the circle to where the chord meets to the edge of the circle to create the triangle

We now have 2 measurements and can use Pythagorean Theorem to determine the radius from the missing length of the triangle.

Answer:

A). X is 80 degrees

Step-by-step explanation:

B). We know this because AD and EH are congruent.  Since B and F are also congruent, then x and the angle above B must be congruent. So, the angle an=bove B is 80 degress, which makes line AD 180 degrees, or a straight line. that must mean that x is 80 degrees as well.

I hope this works. Good luck!

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

[tex]\frac{h^{2}-1 }{h+3}[/tex]

[tex]\frac{5^{2} -1}{5+3}[/tex]

[tex]\frac{25-1}{8}[/tex]

[tex]\frac{24}{8}[/tex]

3

Answer:

243 or 3^5

Step-by-step explanation:

You can do the product by multiplying starting from the left.

3 * 3 * 3 * 3 * 3​ =

= 9 * 3 * 3 * 3

= 27 * 3 * 3

= 81 * 3

= 243

You can also change it to an exponential form.

3 * 3 * 3 * 3 * 3​ = 3^5

Answer:

243

Step-by-step explanation:

3x3x3x3x3=243

Answer:

q = ± [tex]\sqrt{\frac{p}{2} }[/tex]

Step-by-step explanation:

Given

p = 2q² ( divide both sides by 2 )

[tex]\frac{p}{2}[/tex] = q² ( take the square root of both sides )

± [tex]\sqrt{\frac{p}{2} }[/tex] = q

Answer:

It is the first one.

Step-by-step explanation:

"I" is for interest.

"P" is for the amount you deposited or your initial amount.

"R" is for the rate of interest (ex. 3.86%)

"T" is for the time passed.

Answer:

C

Step-by-step explanation:

Given

[tex]\sqrt[4]{81y^{12} }[/tex]

= [tex]\sqrt[4]{3^{4} }[/tex][tex](y^3)^{4}[/tex]

= 3y³ → C

Answer: For Ryan to get an average of exactly 91, she needs to get a 90 on her fifth quiz.

Step-by-step explanation:

You can find the average of a set of numbers by adding them together and dividing the sum by the amount of numbers added.

Ryan has five total quizzes. Only four of them are known, so we can represent her fifth quiz as X.

[tex]\frac{87 + 93 + 96 + 89 + x}{5}[/tex], dividing the five quizzes' sum by 5

She wants the average to be exactly 91, so you can set the expression equal to 91 and solve:

[tex]\frac{365 + x}{5} = 91\\\\365 + x = 455\\\\x = 90[/tex]

For Ryan to get an average of exactly 91, she needs to get a 90 on her fifth quiz.

Answer:

(A)A triangle with angles 45 degrees, 45 degrees, and 90 degrees. 2 sides are congruent.

Step-by-step explanation:

If Javier wants to construct a square by drawing two congruent triangles.

Therefore, the triangle which could be used is a triangle with angles 45 degrees, 45 degrees, and 90 degrees.

The correct option is A.

Answer:

its a

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=x²+4x-7

=x²+4x+4-4-7

=(x+2)²-11

axis of symmetry is x=-2

vertex is (-2,-11)

x²+4x-7=0

[tex]x=\frac{-4 \pm\sqrt{4^2-4(1)(-7)} }{2(1)} \\=\frac{-4 \pm \sqrt{16+28} }{2} \\=\frac{-4 \pm 2\sqrt{11} }{2} \\=-2 \pm\sqrt{11}[/tex]

Answer:

Axis of symmetry is x = -2

(-2, -11) is the vertex

Roots are

-2 + [tex]\sqrt{11}[/tex], -2 - [tex]\sqrt{11}[/tex]

Step-by-step explanation:

a) Axis of symmetry equation is: x = -b/2a

Original equation: y = [tex]x^2+4x-7[/tex]

So...

x= -4/2(1) = -2

Axis of symmetry is x = -2

b) Vertex Point can be found by plugging into original equation.

[tex]y =x^2+4x-7[/tex]

=> y = [tex](-2)^2+4(-2)-7[/tex]

=> 4 - 8 - 7 = y

=> -11 = y

(-2, -11) is the vertex

c) quadratic formula is  [tex]x = \frac{-b +-\sqrt{b^2-4ac} }{2a}[/tex]

Lets plug in the values.

[tex]\frac{-4 +- \sqrt{4^{2}-4(1)(-7) } }{2(1)}[/tex]

[tex]\frac{-4 +- \sqrt{16+28 } }{2}[/tex]

[tex]\frac{-4 +- \sqrt{44 } }{2}[/tex]

[tex]\sqrt{44} = 2\sqrt{11}[/tex]

-4 +- 2[tex]\sqrt{11}[/tex]

--------------

     2

Here, i will factor out 2, and take out the +- and make it into two equations

2(-2 + [tex]\sqrt{11}[/tex]) / 2 = -2 + [tex]\sqrt{11}[/tex]

2(-2 - [tex]\sqrt{11}[/tex]) / 2  =   -2 - [tex]\sqrt{11}[/tex]

x= -2 + [tex]\sqrt{11}[/tex]

or

x = -2 - [tex]\sqrt{11}[/tex]

Roots are

-2 + [tex]\sqrt{11}[/tex], -2 - [tex]\sqrt{11}[/tex]

Answer:

Step-by-step explanation:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Answer: 95

Step-by-step explanation:

Answer:

the pattern is going by 15.

Step-by-step explanation:

Answer:

MAD mean absolute deviation = 18.9

Step-by-step explanation:

mean: 26 + 34 + 66 + 71 + 76 + 82 + 88 + 95 = 538/8 = 67.25

26 - 67.25 = 41.25

34 - 67.25 = 33.25

66 - 67.25 = 1.25

71 - 67.25 = 3.75

76 - 67.25 = 8.75

82 - 67.25 = 14.75

88 - 67.25 = 20.75

95 - 67.25 = 27.75

(MAD) mean absolute deviation: 41.25 + 33.25 + 1.25 + 3.75 + 8.75 + 14.75 + 20.75 + 27.75 = 151.5/8 = 18.9

Answer:

54

Step-by-step explanation:

The area of the model on the left is 12[tex]cm^{2}[/tex]

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

Scale Up (smaller to larger)         = [tex]\frac{Larger figure measurement }{Smaller figure measurement}[/tex]

Scale Down (larger to smaller)     = [tex]\frac{Smaller figure measurement }{larger figure measurement}[/tex]

According to question

area of right triangle which have (1cm= 2inch) is 108 [tex]cm^{2}[/tex] .

and Left triangle  have (1cm= 6inch)

we will convert cm into inch for right triangle

area of right triangle = 108 [tex]cm^{2}[/tex]

 as 1 cm = 2inch

1 [tex]cm^{2}[/tex] = 4 [tex]inch^{2}[/tex]

therefore,

108 [tex]cm^{2}[/tex] = 4 * 108  [tex]inch^{2}[/tex]

as mentioned that  two different models of the same triangular handkerchief

and left triangle is 1 cm = 6 inch

1 [tex]cm^{2}[/tex] = 36 [tex]inch^{2}[/tex]

now we have to scale down as we have to larger to smaller

Scale Down (larger to smaller)    = [tex]\frac{Smaller figure measurement }{larger figure measurement}[/tex]

= 4*108  / 36

= 12

Hence, the area of the model on the left is 12[tex]cm^{2}[/tex]

To know more about scale factor  here :

https://brainly.com/question/26903822

# SPJ2

Answer:

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer: A, C, D

Step-by-step explanation: The other person accidentally put 49 instead of 42

The equations that are correct are n = 10, CF = 59 and FE = 42

From the attached diagram, we can see that the opposite side of the parallelogram are equal, hence;

DE = CF
6n - 1  = 5n + 9'

Find the value f n

6n - 5n = 9 + 1

n = 10

CF = 5n + 9

CF = 5(10) + 9
CF = 59

For the measure of FE
FE = 4n + 2

FE = 4(10) + 2

FE = 42

Hence the equations that are correct are n = 10, CF = 59 and FE = 42

Learn more on parallelogram here: https://brainly.com/question/970600

The answer is 21

Step-by-step explanation:

Answer:

121 cm²

Step-by-step explanation:

The area (A) of a square is calculated as

A = s² ( s is the measure of the side )

Given perimeter = 44 cm , then

s = 44 ÷ 4 = 11cm , thus

A = 11² = 121 cm²

Answer:

Step-by-step explanation:

Answer:

8 dollars per extra person

Step-by-step explanation:

subtract the original 40 dollars from 80 ,you get 40,the probloem tells you that there is 9 people meaning there was 5 extras ,so 40/5=8

Answer:

$8 charge for each additional person

Step-by-step explanation

$40/night for each person

First 4 people already paid.

Leftover are 5 people.

9-4=5

Since first 4 people paid, the rest to be paid is $40.

$80-$40=$40

To find the charge for each person, divide the amount of money left by the amount of people left.

40÷5= 8

$8 is the additional charge for each additional person.

Answer:

B. A (1, −2) → A ′(−4, −1) → A ″(−1, −1)

Step-by-step explanation:

When you see anything in between <> (let's say <a, b> are the numbers), it basically means <x+a, y+b>.

So if you replace a with -5, b with 1, and x and y with (1, -2) you get...

= (1 + (-5), -2 + 1)

= (1-5, -1)

= (-4, -1) ----------> Those are the coordinates of the new point.

But wait, it says that we now have to translate along the vector <3, 0>

So (-4, -2) become the new (x, y) coordinates and <3, 0> become the new a, b

= (-4+3, -1 + 0)

= (-1, -1)

That means that the coordinates of point A'' are (-1, -1)

Another way you could do this is by combining the two translations to just do one translation. It'll skip over the middle step, but will still give you the correct answer.

You would combine them by adding the translations of the x-coordinates together and the y-coordinates together

= <-5 + 3, 1 + 0 >

= <-2, 1>

Now you translate the point by this vector and...

= (1 - 2, -2 + 1)

= (-1, -1)

Tada! It works!

Therefore, the answer is B.

Answer:

3

Step-by-step explanation:

you have to count all the xs past the number 6

Answer:

Waddup bro. For your answer, think of it this way. What 3 digits will make up 9? 1 x 9 is 9. So that would work. find it out by trying out different combination that would make up 9. I'm not gonna write all of 'em but 3 digits would add up to 9. There are no other groups of numbers adding up to 9. 4. Add up the remaining digits, 5 + 5 + 0 + 3 = 13. 5.13 is more than 9, so 1 + 3 = 4.  To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers. So add all up the singe digits and divide it by how much there is.

Answer:

Step-by-step explanation:

numbers are

108,117,126,135,144,153,162,171,180,

207,216,225,234,243,252,261,270,

306,315,324,333,342,351,360,

405,414,423,432,441,450,

504,513,522,531,540,

603,612,621,630,

702,711,720,

801,810,

900

total number of terms=9+8+7+6+5+4+3+2+1=45

median =(45+1)/2=23 rd term

median=351

Answer:

it 2

Step-by-step explanation:

i took the test

Answer:

Step-by-step explanation:

[tex]\frac{x}{3}=\frac{x+2}{5}\\\\x*5=3*(x+2)\\5x =3x+6\\\\5x-3x=6\\\\2x=6\\\\x=\frac{6}{2}\\\\x=3[/tex]

Answer:

uniform i think sorry if im wrong

Answer:

cos60 - cos 72

Step-by-step explanation:

you can have an angle measure between 60 and 72 hence cos 60 - cos 72

hope this helps

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As the area is 12, the length multiplied by the width must equal 12

Therefore, we can eliminate option B and option D as they wouldn't multiply to give 12

Let's test option A to see if it gives a perimeter of 16

2 + 6 + 2 + 6 = 16

As you see, this sums to 16

Thus, your answer is option A

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