The two prisms below are similar. What is the value of x?

A. 30
B. 1
C. 9
D. 3

The answer is the third one.

The first two are easy, you can see that the radius of S is 4 and the radius of T is 5-4=1.

The point of intersection is where the two circles touch each other, and is is (4, 1), because you have to put the x value first.

The equation of the tangent line is just y=4, because it is a straight vertical line.

Answer:

Step-by-step explanation:

Formula

a^2 + b^2 = c^2

Givens

a = x

b = 20.2

c = 14.7 + x

Solution

x^2 + 20.2^2 = (14.7 + x)^2                       Expand the brackets

x^2 + 408.04 = 14.7^2 + 29.4x + x^2       Cancel the x^2

408.04 = 216.9 + 29.4x                            Subtract 216.9 from both sides.

191.98 = 29.4x                                           Divide by 29.4

6.52993 = x                                               Answer.

6.5 to the nearest tenth.

Answer:

x = 6.5 cm

Step-by-step explanation:

The tangent to the circle forms a right angle with the radius x

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides

The hypotenuse is (x + 14.7) ← opposite the right angle, hence

(x + 14.7)² = x² + 20.2² ← expand parenthesis on left side

x² + 29.4x + 216.09 = x² + 408.04 ( subtract x² from both sides )

29.4x + 216.09 = 408.04 ( subtract 216.09 from both sides )

29.4x = 191.95 ( divide both sides by 29.4 )

x ≈ 6.5 cm

Answer:

x = 2[tex]\sqrt{34}[/tex]

Step-by-step explanation:

Using  Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² = 6² + 10² = 36 + 100 = 136

Take the square root of both sides

x = [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{34}[/tex] = 2[tex]\sqrt{34}[/tex]

Answer: [tex]3\sqrt{2}\ m[/tex]

Step-by-step explanation:

The perimeter of a square is:

[tex]P=4s[/tex]

Where "s" is the lenght of a side of the square.

Then, if the perimeter of this square is 12 m, you can solve for "s" and find its value:

[tex]s=\frac{P}{4}\\\\s=\frac{12\ m}{4}\\\\s=3\ m[/tex]

You can calculate the length of the diagonal with this formual:

[tex]d=s\sqrt{2}[/tex]

Where "s" is the lenght of a side of the square.

Substituting the value of "s" into the formula  [tex]d=s\sqrt{2}[/tex], you get that the lenght of the diagonal of this square is:

[tex]d=3\sqrt{2}\ m[/tex]

Answer:

6 people would be in each row // It isn't possible for there to be 7 equal rows

Step-by-step explanation:

36 members/6 rows= 6 people per row // 36 members/7 rows= 5.14..... people per row (just doesn't work!)

Answer:

x  = 3

Step-by-step explanation:

Given in the question an equation,

[tex]2lne^{ln5x}=2ln15[/tex]

Step 1

[tex]e^{lnx}=x[/tex]

so,

[tex]2ln(5x)=2ln15[/tex]

Step 2

cancel 2 on both sides of the equation

[tex]ln{5x}=ln15[/tex]

Step 3

[tex]ln{5x}-ln15=0[/tex]

[tex]ln\frac{5x}{15}=0[/tex]

Step 4

[tex]ln\frac{x}{3}=0[/tex]

Step 5

[tex]e^{ln\frac{x}{3}}=e^{0}[/tex]

Step 6

x/3 = 1

x = 3(1)

x = 3

Answer:

True

Step-by-step explanation:

A plane is a flat, infinite 2D surface, so when we say two things are coplanar, they can all fit on a single plane. In this case, all three lines a, b, c, and d lie on the same 2D surface, so we'd consider them coplanar. True.

Sphere = 4PiRsquared

Radius = 13

13 x 13 = 169

169 x 4= 676 Pi

5e surface is 676Pi

Answer:

The correct answer is option B.   676π units²

Step-by-step explanation:

Formula:-

The surface area of a sphere = 4πr²

Where r is the radius of sphere

To find the surface area of given sphere

Here r = 13 units

Surface area = 4πr²

 = 4 * π * 13²

 = 4 * π * 169 = 676π units²

Therefore the  correct answer is option A.   676 units²

[tex]V=209.44[/tex] | Formula for the volume of a cone: [tex]V=\pi r^2\frac{h}{3}[/tex]

ANSWER

Option B

EXPLANATION

The equation given to us is;

[tex] {(x - 2)}^{2} = 12(y - 3)[/tex]

Comparing this to the general parabolic equation:

[tex] {(x - h)}^{2} = 4p(y - k)[/tex]

We have h=2 and k=3.

The vertex of this parabola is (h,k) which is (2,3).

This parabola also opens upwards because the value of p is positive.

The correct graph is B.

Answer:

False

Step-by-step explanation:

SA=2πrh+2πr²

SA = 2 · (3.14) · 3.6 · 9.7 + 2 · (3.14) · 3.6²

SA = 6.28 · 34.92 + 6.28 · 12.96

SA = 219.30 + 81.39

SA = 300.69

For this case we have that by definition, the surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

A: It's the radio

h: It's the height

Substituting according to the data we have:

[tex]SA = 2 \pi * 3.6 * 9.7 + 2 \pi * (3.6) ^ 2\\SA = 219.2976 + 81.3888\\SA = 300.6864 \ units ^ 2[/tex]

If we round up we have:

[tex]SA = 300.69 \ units ^ 2[/tex]

Answer:

False

Answer:

  c. intersection of the side and the perpendicular passing through the center

Step-by-step explanation:

The radius of the incircle is the distance from the center of that circle (known) to the nearest point on any side. That point is at the intersection of a perpendicular line through the center of the incircle.

the center is : (-8 , 12)

Answer:

Option A, 7 and Option B, -2

(7,0) and (-2,0)

Step-by-step explanation:

Given in the question a function f(x) = (x+2)(x-7)

Step 1

Expand the function (x+2)(x-7)

x(x-7)+2(x-7)

x² - 7x + 2x - 14

x² - 5x - 14

Step 2

To find the x-intercepts we will substitute y with 0

y = x² - 5x - 14

0 = x² - 5x - 14

(x-7)(x+2) = 0

x = 7

x = -2

Answer:

The x-intercepts would be 7 and -2.

Step-by-step explanation:

Answer:

the perimeter is 46.6 feet

Step-by-step explanation:

The length of Chen’s office is 15.5 feet and the width is 7.8 fee

length =15.5

width = 7.8

Use the formula [tex]P = 2l + 2w[/tex]

where 'l' is the length and 'w' is the perimeter

Plug in the values of length and width in the perimeter formula

[tex]P = 2l + 2w[/tex]

[tex]P = 2(15.5) + 2(7.8)=46.6[/tex]

So the perimeter is 46.6 feet

The perimeter of the office is 46.6 feet

The office is in the shape of a rectangle

A rectangle is a 2-dimensional quadrilateral.

Characteristics of a rectangle

The perimeter of a rectangle = 2(length + width)

2length + 2width

2(15.5) + 2(7.8)

31 + 15.6 = 46.6 feet

To learn more about the perimeter of a rectangle, please check: brainly.com/question/18793958?referrer=searchResults

Answer:

yes

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Draw in <QOS. That's the central angle. It is also 60 degrees.

<R  which has Q and S as its end points, = 1/2 the central angle (always) so <R = 30 degrees.

C

I'd say it's high: both datasets are made of 8 elements, and 6 of those 8 are in common: the only element belonging to dataset 1 but not dataset 2 is 5, and the only element belonging to dataset 2 but not dataset 1 is 10.

The overlap between Data Set 1 and Data Set 2 will be high. Then the correct option is A.

The number of the data will be 8.

If the number of data overlaps is less than 4, then low.

If the number of data overlaps is equal to 4, then moderate.

If the number of data overlaps is greater than 4, then high.

The number of data that overlap is 6.

The overlap between Data Set 1 and Data Set 2 will be high.

Then the correct option is A.

More about the overlapping link is given below.

https://brainly.com/question/9034420

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It A because the two mirror each other so you can simplify them to (3x−5)^2.

Answer:

(A) [tex](3x-5)(3x-5)[/tex]

Step-by-step explanation:

Perfect-square trinomials have this form:

[tex]a^2x^2 \± 2ab + b^2[/tex]

And can be expressed as a squared binomial:

[tex](ax \± b)^2[/tex]

Which is the same as: [tex](ax+b)(ax+b)[/tex] or  [tex](ax-b)(ax-b)[/tex]

You can observe that [tex](3x-5)(3x-5)[/tex] (Shown in the option A) matches with the form [tex](ax-b)(ax-b)[/tex], therefore, it will result in a perfect square trinomimal.

You can verify this by applyin Distributive property. Then:

[tex](3x-5)(3x-5)=\\=3^2x^2+(3x)(-5)+(3x)(-5)+5^2\\=9x^2-15x-15x+25\\=9x^2-30x+25[/tex]

The result is a perfect square trinomial.

Answer:21

Step-by-step explanation:

if there are 21 feet of ribbon and we need it in foot long pieces there are 21

Answer:

35

Step-by-step explanation:

Answer:

Find the GCF

Step-by-step explanation:

When multiplying the following polynomials:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5)

1.     First we need to use the distributive property:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 2x^3 * 9x^2  - 2x^3 * 4x  + 2x^3 * 5 + 2x^2 * 9x^2 - 2x^2 * 4x + 2x^2 * 5 - 3x * 9x^2 + 3x * 4x - 3x * 5.

2.   Second, we need to use the multiplication property of exponents:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 - 8x^4 + 10x^3 + 18x^4 - 8x^3 + 10x^2 - 27x^3 + 12x^2 - 15x.

3. We need to combine like terms:

(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 +10x^4 -25x^3 + 22x^2 - 15x.

We don't need to find the GCF.

Answer:

  13.98 in²

Step-by-step explanation:

I don't understand it, either.

Point N is part of a "segment" that above and to the right of chord MO. It is the sum of the areas of 3/4 of the circle and a right triangle with 7-inch sides. The larger segment MO to the upper right of chord MO has an area of about 139.95 in², which is not an answer choice.

__

The remaining segment, to the lower left of chord MO does not seem to have anything to do with point N. However, its area is 13.98 in², which is an answer choice. Therefore, we think the question is about this segment, and we wonder why it is called MNO.

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

  A = (1/2)(θ -sin(θ))r² . . . . . . where θ is the central angle in radians.

Here, we have θ = π/2, r = 7 in, so we can compute the area of the smaller segment MO as ...

  A = (1/2)(π/2 -sin(π/2))(7 in)² = 24.5(π/2 -1) in² ≈ 13.9845 in²

Rounded to hundredths, this is ...

  ≈ 13.98 in²

Answer:

All real numbers

Step-by-step explanation:

They ask us to find the domain of (fg)

f(x) = x+2

g(x) = ( 1 / x + 2 )

Multiplying these two equations, we get:

y = 1. And this equation is a straight line passing through 1 on the y-axis.

This means, the domain is all the real numbers.

Answer:

Domain is all real number except  [tex]-2[/tex]

Step-by-step explanation:

[tex]f(x)= x+2[/tex] and [tex]g(x)= \frac{1}{x+2}[/tex]

now we find fg

[tex]fg= f(x) * g(x)[/tex]

Replace f(x) and g(x)

[tex]f(x) * g(x)= (x+2)*\frac{1}{x+2}[/tex]

[tex]f(x) * g(x)=\frac{x+2}{x+2}[/tex]

We have x+2 at the top and bottom. cancel it out

So we have hole at x+2

set the denominator =0 and solve for x

[tex]x+2=0[/tex]

Subtract 2 on both sides

[tex]x=-2[/tex]

the value of x cannot be [tex]-2[/tex]

Domain is all real number except  [tex]-2[/tex]

The standard of deviation is 4.

The mean is 10

20 minutes - 10 ( the mean) = 10 minutes longer than the mean.

10 minutes longer / 4 minutes ( deviation) = 2.5 standard deviations.

2.5 on the Z-table = 0.9938

The probability of being more than 20 minutes = 1 - 0.9938 = 0.0062 (0.62%)

Answer:

±4

Step-by-step explanation:

The margin of error in a confidence interval is half the range:

(84 - 76) / 2 = 4

So the margin of error is ±4.

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The margin of error of the survey will be ±4%.

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations. Therefore, the margin of error can be written as,

Margin of Error = (84%-76%)/2 = 8%/2 = ±4%

Hence, the margin of error of the survey will be ±4%.

Learn more about Margin of Error:

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Answer:

  1.3×10⁻² = 0.013

Step-by-step explanation:

The "E" stands for "×10^", so 1.3E-2 means 1.3×10^-2.

Of course 10^-2 = 1/10^2 = 1/100 = 0.01, so

  1.3E-2 = 1.3×10^-2 = 1.3×0.01 = 0.013

_____

This notation was used by early computers to print results where the character set was limited and superscripts could not be printed.

The dog food was originally 20 dollars

Answer: $20

Step-by-step explanation:

4 x 5 (if you used a chart you would get why I used 5) would equal 20, which means $20 is the cost of the bag of dog food without the coupon

A = 1/2aP

P = number of sides x length of each side

P = 8 x 5.8

P = 46.4

A= 1/2 x 7 x 46.4

A = 162.4

Answer:

the interquartile range is 13.5

minimum 16

maximum 43

medium 29

lower  Q1  24

upper Q3  37.5 or 38

Range 27

To obtain a mixture of 200 liters with an average cost of 0.50, we need to start with approximately 133 liters of the wine with a price of 0.35 and approximately 67 liters of the wine with a price of 0.80.

To solve this problem, we will call "x" the quantity of liters of the wine with a price of 0.35, and "y" the quantity of liters of the wine with a price of 0.80 that we need to obtain the desired mixture.

We know that we want to obtain 200 liters of mixture, and the average cost of the mixture should be 0.50.

We can establish the following equations:

x + y = 200 (equation for the total quantity of mixture)

(0.35 * x + 0.80 * y) / 200 = 0.50 (equation for the average cost of the mixture)

Now  solve this system of equations to find the values of "x" and "y".

From the first equation, we can solve for "x" in terms of "y" as follows:

x = 200 - y

Substitute this expression for "x" in the second equation

(0.35 * (200 - y) + 0.80 * y) / 200 = 0.50

Solving this equation, we can find the value of "y":

(0.35 * 200 - 0.35 * y + 0.80 * y) / 200 = 0.50

(70 - 0.35y + 0.80y) / 200 = 0.50

(0.45y + 70) / 200 = 0.50

0.45y + 70 = 0.50 * 200

0.45y + 70 = 100

0.45y = 100 - 70

0.45y = 30

y = 30 / 0.45

y = 66.67

Now that we have the value of "y,"  find the value of "x" by substituting it into the first equation:

x = 200 - y

x = 200 - 66.67

x = 133.33

However, we cannot have a fractional quantity of liters, so we must round these values to whole numbers.

Therefore, to obtain a mixture of 200 liters with an average cost of 0.50, we need to start with approximately 133 liters of the wine with a price of 0.35 and approximately 67 liters of the wine with a price of 0.80.

We have wine of two different qualities with prices of 0.35 and 0.80. If we want to obtain a mixture of 200 that results in 0.50, how many liters of each class do we need to start with?