Solve the following quadratic by completing the square.

Answer:

10 inches by 8 inches

The length and with would be half the perimeter: 36/2 = 18

find 2 numbers when added together equal 18 and when multiplied together equal 80.

8 + 10 = 18

8 x 10 = 80

Answer:

66 degrees

Step-by-step explanation:

All three angles on any given triangle have a sum of 180 degrees.

We know that the measure of angle B is the the same as angle C.

So 57 +57 = 114

180 - 114 = 66

Hope that helps!

Answer:

Center: (2, -11)

Radius: 10

Step-by-step explanation:

(x - 2)² + (y + 11)² = 100

(x - h)² + (y - k)² = r²

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

x - 2 = 0

  +2   +2

x = 2

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

y + 11 = 0

   -11    -11

y = -11

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

r² = 100

r = √100

r = 10

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

Center: (h, k)

Radius: r

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

Center: (2, -11)

Radius: 10

I hope this helps!

We are given the equation of circle (x - 2)² + (y + 11)² = 100 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-2)^{2}+(y+11)^{2}=100}[/tex]

Can be further written as ;

[tex]{:\implies \quad \sf (x-2)^{2}+\{y-(-11)\}^{2}={10}^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

Answer :

⠀

Explanation :

We know,

[tex]{ \longrightarrow \qquad\pmb {\boldsymbol{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}[/tex]

Where,

⠀

Substituting the values in the formula :

⠀

[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times ({4})^{2} \times 6 \: }}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times 16\times 6 \: }}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times 96 \: }}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ \ { \it{ \pmb{ Volume_{(cylinder)} {= 301.44 \: }}}}}}[/tex]

⠀

Therefore,

Answer:

  a.  x = 9

  b.  GH = 30; GK = 20

Step-by-step explanation:

An angle bisector in a triangle divides the sides proportionally.

In this triangle, that means ...

  (3x +3)/18 = (3x -7)/12

  2(3x +3) = 3(3x -7) . . . . . . . multiply by 36

  6x +6 = 9x -21 . . . . . . . . . eliminate parentheses

  27 = 3x . . . . . . . . . . . . . . add 21 -6x

  x = 9 . . . . . . . . . . . . . . . divide by 3

__

The segment lengths are found by substituting the value of 3x in each of the given expressions:

  GH = 3x +3 = 27 +3 = 30

  GK = 3x -7 = 27 -7 = 20

The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2.

Second order polynomials are represented graphically by parabolae and it may have two, one or no x-intercepts. The quantity of x-intercepts can be deducted from the discriminant of the quadratic formula, which is defined below:

For a · x² + b · x + c = 0, the discriminant is defined by:

d = b² - 4 · a · c   (1)

There are three rules to determine the number of possible intercepts:

Then, we have to find a value of b so that (1) has the following form:

b² - 4 · 3 · (-24) = 0

b² - 288 = 0

b = 12√ 2

The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2. [tex]\blacksquare[/tex]

The answer choices do not correspond with the given statement, the phrase "same x-intercepts" may lead to confusion and possible graph cannot be found. A possible corrected statement is shown below:

The graph of g(x) = 3 · x² + b · x - 24 has only one x-intercept. What is the value of b?

To learn more on parabolae, we kindly invite to check this verified question: https://brainly.com/question/10572747

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{2\pi }{3};\frac{4\pi }{3}.[/tex]

Step-by-step explanation:

1) cos(θ)=-0.5;

theta=±2π/3+2πn, where n∈Z;

2) if θ∈[0;360], then

[tex]\theta=\frac{2\pi }{3}; \frac{4\pi }{3}.[/tex]

Answer:

Step-by-step explanation:

the answer is correct  so good job ok

Consider the fraction first ;

[tex]{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}[/tex]

[tex]{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}[/tex]

[tex]{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}[/tex]

Hence, Option B) is required answer

Answer:

81 inches

Step-by-step explanation:

I believe this is it…

The area of the rectangular base is the amount of space on the rectangular base

The area of the rectangular base is 60 square inches

The question is incomplete; as the diagram is not given.

So, I will apply the concept of similar shapes to determine the area of the rectangular base

To determine the area of the rectangular base, we make use of the following equivalent ratio:

Ratio = Height : Area

This gives

3 : 36 = 5 : Area

Express as fraction

36/3 = Area/5

Evaluate the quotient

12 = Area/5

Multiply both sides by 5

Area = 60

Hence, the area of the rectangular base is 60 square inches

Read more about areas at:

https://brainly.com/question/24487155

Answer:

30 cubic feet

Step-by-step explanation:

The volume of a box is found by multiplying the area of the base by the height.  The area of the base is found by multiplying the length by the width.  (3 x 5)(2) = 15(2) = 30 cubic feet

The deductible is the amount one pays towards the auto insurance

The complete statement is: a lower auto insurance deductible usually means a higher premium

When an insured loss or disaster happens, the amount one pay towards the loss is referred to as the deductible

As a general rule, the more the deductible, the lower the premium; and vice versa.

This means that: a lower auto insurance deductible usually means a higher premium

Hence, the text that completes the statement is premium

Read more about deductible and premium at:

https://brainly.com/question/9696972

Answer:

Step-by-step explanation:

First we need to find the score of the incorrect answers and the questions that were not answered.

Score for the incorrect answers = 4*(-2) = -8

Score for the questions not answered = 6*(-1) = -6

Score for the questions answered correctly = 106 - [ (-8) + (-6) ]

                                                                       = 106 -[-14]

                                                                        = 106 + 14

                                                                        = 120

Number of questions answered correctly = total score for questions that were answered correctly ÷ score of 1 correct answer

= 120 ÷ 4

= 30

30 questions were answered correctly.

The surface area of the rectangular prism is 46m²

Surface area of a rectangular prism = 2(width×length + height×length + height×width)

SA = 2(wl + hl + hw)

= 2(2.5×4 + 2×4 + 2×2.5)

= 2(10 + 8 + 5)

= 2(23)

= 46m²

Therefore, the surface area of a rectangular prism is 46m²

Learn more about surface area:

https://brainly.com/question/16519513

Answer:

6/9 or 1/3

Step-by-step explanation:

There is a total of 9 marbles of both colors in the bag.
(3 red marbles + 6 blue marble = 9 marbles)

This means the denominator of your probability will be 9. There are 6 blue marbles in the bag so, in conclusion, the probability that you will take a blue marble out of the bag is 6/9. Also, 6/9 when simplified, is 1/3.

Have a great rest of your day
#TheWizzer

Step-by-step explanation:

a volume is created (calculated) by multiplying 3 dimensions (e.g. length, width and height).

am area is created by multiplying 2 dimensions (e.g. length and width).

but a scale factor applies only to any length in the model (but then separately for every dimension of the model).

so, when we multiply 2 dimensions, we have to multiply the scale factor with every dimension (2 times) in there too.

and for 3 dimensions 3 times.

so,

1.

the scale factor 1/100 or 0.01 says that every side of the model cube is 1/100 the side length of the real cube.

and so, while the volume of the real cube is

side × side × side = 3,401,244 ft³,

the volume of the model cube is

side × 1/100 × side × 1/100 × side × 1/100 =

= side × side × side × (1/100)³ =

= real volume × 1/1,000,000 =

= 3,401,244 / 1,000,000 = 3.401244 ft³

2.

the scale factor is 3/4.

that means that it applies to length as well as to width of the floor.

so, the area of the first floor is

length × width = 1,260 ft²

and the area of the second floor is then

length × 3/4 × width × 3/4 =

= length × width × (3/4)² =

= area first floor × 9/16 = 1,260 × 9/16 = 708.75 ft²

Answer:

16 triangles I am pretty sure.

Step-by-step explanation:

Answer:

0.78

Step-by-step explanation:

78 / 100

note that 100% = 1

Hello!

To solve this exercise, we must use the formula below:

[tex]\mathrm{C=2\cdot\pi\cdot r}[/tex]

Knowing these values, let's replace them in the formula to obtain r:

[tex]\mathrm{C=2\cdot 3.14 \cdot 14}\\\mathrm{C=6.28 \cdot 14}\\\\\boxed{\mathrm{C=87.92}}[/tex]

So, the circle's circumference is 87.92cm.

Hope this helps!

Answer:

Step-by-step explanation:

To solve this problem, you need to multiply the radius of a circle by the circumference formula.

Circumference formula:

[tex]\sf{C=2\pi r}[/tex]

[tex]\sf{C=2*\pi r}[/tex]

C=?

π= 3.14

r= 14

[tex]\sf{2*3.14*14}[/tex]

Solve.

[tex]\sf{2*3.14=6.28}[/tex]

[tex]\sf{6.28*14=\boxed{\sf{87.92}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

24 cubic inches

Step-by-step explanation:

Volume is side x side x side. You already have done side x side so it is just side x area.

Answer:

Step-by-step explanation:

add all the three.

Answer:

60

Step-by-step explanation:

AD= AB+BC+CD

=22+29+9

=60 cm

Answer:

A 2.41 > 2.37

Step-by-step explanation:

2.41 is greater than 2.37

Answer:

A

Step-by-step explanation:

others arent true

Answer:

3 1/5 = 16 / 5

1 1/2 = 3 / 2

16 / 5 * 3 / 2 = 48 / 10 = 24 / 5

The correct answer is 24 / 5 = 4 4 /5

(You can check on your calculator)

Answer:

y = 1x + 7

Step-by-step explanation:

Let's take 2 points, with x being the month and y being the weight as the month is listed first in the graph.  

(0, 7) = the 1st point

(1, 8) = the 2nd point

In y=mx+b, m is the slope.

Slope = change in y / change in x = (y₂-y₁) /(x₂-x₁) = (y₁-y₂) / (x₁-x₂) = (8-7)/(1-0) = 1 / 1 = 1 = (7-8)/(0-1) = -1/-1 = 1

Our equation is thus

y = mx + b = y = (1) x + b

Plug one point, such as (1, 8) into this equation to obtain b

8 = (1) (1) + b

8 = 1 + b

subtract 1 from both sides to isolate b

7 = b

our equation is thus

y = (1) x + 7 = 1x + 7

Answer:

w = 1m + 7

Step-by-step explanation:

w = weight

m = months

If we look at the chart, as every month goes by, the baby gains another pound.

Hence, the best way to find the weight is to just add 7 to the months, since in the beginning (at 0 months) the weighs 7 pounds, so if it’s 1 month, the baby would just way 1 more pound.

This is why the formula: w = 1m + 7 works

Because 1 times the value of any month will be the same value, and all you have to do is add 7.

Example:

(x = multiply in this equation)

At 2 months: w = 1 x 2 + 7

Solve:

1 x 2 = 2

2 + 7 = 9

As you can see, all you have to do is fill in the month # in the formula, and you will get your  w (weight).

Hope this helps :)

Answer:

35

Step-by-step explanation:

well, you know the angles of a triangle add up to 180 degrees, and you have the other 2 degrees right there, so all you have to do is add both of the other angles 111+34= 145 and then subtract by 180, 180-145=35 so your answer is 35

Answer:

26,620

Step-by-step explanation:

1 year: 20,000 x 0.10 = 2000

2 years: 22,000 x 0.10 = 2200

3 years: 24200 x 0.10 = 2420

2420 + 24200 = 26620

Have an amazing day!!

Please rate and mark brainliest!!!!

Theres a button on the question taht you are wanting to answer. Sometimes it will allow one other times it is 2

Using the z-distribution, as we have the standard deviation for the population, it is found that 215 students must be sampled.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is of M = 0.25, with a population standard deviation of [tex]\sigma = 1.87[/tex], hence we solve for n to find the minimum sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.25 = 1.96\frac{1.87}{\sqrt{n}}[/tex]

[tex]0.25\sqrt{n} = 1.96(1.87)[/tex]

[tex]\sqrt{n} = \frac{1.96(1.87)}{0.25}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96(1.87)}{0.25}\right)^2[/tex]

[tex]n = 214.9[/tex]

Rounding up, 215 students must be sampled.

More can be learned about the z-distribution at https://brainly.com/question/25890103

Answer:median of (298, 196, 248) - 196

median of (379, 319) - 349

median of (276,198, 349) - 198

Step-by-step explanation:

Answer:

298

Step-by-step explanation:

Given:

$298,$196, $248, $379, $319, $276, $198, $349, $319

Solve:

Put in order:

196, 198, 248, 276, 298, 319, 319, 349, 379

Median -

Arrange data values from lowest to highest value

The median is the data value in the middle of the set

If there are 2 data values in the middle the median is the mean of those 2 values.

Solution:

196, 198, 248, 276, 298, 319, 319, 349, 379

196, 198, 248, 276, 298, 319, 319, 349, 379

196, 198, 248, 276, 298, 319, 319, 349, 379

196, 198, 248, 276, 298, 319, 319, 349, 379

 Hence, the median is 298.

~lenvy~