1. What is the simplified form of the rational expression below?
3.22_10x-8
22-1-12

Step-by-step explanation:

Join C to B to form BC, thereby creating ∆ ABC

OC is the radius of the circle (O is the center of the circle).

AD is the tangent to the circle at point C

When a radius of a circle meets with a tangent of the same circle, the angle between them is 90°

<ACB = <ACO = 90°

<ABC = 180 - (<ACB + <BAC)

= 180-(90+40)

= 50

Look closely,

<ABC = x = 50°

.

.

Do same as Example 7

Join O to B to form OB, which is the radius of the circle.

<ABO= 90°

< BOA = 50°

<OAB= x+25= 180-(90+50)

x+25= 40°

x = 15°

Answer:third option

Step-by-step explanation:

I just did it

Answer:

Step-by-step explanation:

Given that the diameter of the flower bed is 17 m and the width of the side walk is 2 m for a total out side diameter of 21 m.

Total Area is pi *(D/2)^2 = 346.4 m^2

Now subtract the area of the 17 m diameter flower bed for the area of the sidewalk alone. 346.4 - (pi*(17/2)^2 = 346.4 - 227.0 = 119,4 m^2

Answer:  119,4 m^2

Step-by-step explanation:

The equation is area = p times r^2

8 times eight times 3.14 =  119,4 m^2

Answer:

Triple the length, height and width

Step-by-step explanation:

Multiply 3x/Cube length, width, and height! (possibly?)

Answer:9

Step-by-step explanation: 30= 2n + 12

Subtract 1Subtract12 from both sides

Divide both sides by 2

Answer: The correct option is D

Step-by-step explanation:

Correct on edge 2022

Considering the situation described, the p-value for Amy's result is of 0.0203.

At the null hypotheses, it is tested if the mean is not greater than $50,000, that is:

[tex]H_0: \mu \leq 50000[/tex]

At the alternative hypotheses, it is tested if the mean is greater, hence:

[tex]H_1: \mu > \leq 50000[/tex]

We are testing if the mean is greater than a value, hence we have a right-tailed test. Using a right-tailed test with t = 2.06 and 200 - 1 = 199 df, the p-value is of 0.0203.

More can be learned about p-values at https://brainly.com/question/26454209

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The product of 2.5 x 10^2 and 3.7 x 10^5 expressed in scientific notation is 9.25 x 10^7.

It is the way of writing a large number between 1 to 10 with a power of 10.

We have,

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. So, we have:

= (2.5 x 10²) x (3.7 x 10^5)

= (2.5 x 3.7) x 10^(2+5)

= 9.25 x 10^7

Therefore,

The product of 2.5 x 10^2 and 3.7 x 10^5 expressed in scientific notation is 9.25 x 10^7.

Learn more about scientific notation here:

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Answer:

I don't see the equation for the line, but I describe the process.

Step-by-step explanation:

Let's look for a line that has the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

The slope of a perpendicular line is the negative inverse of the slope of the reference line.  In this case the equation for the reference line is missing.  If it is in the form y=mx+b, take the m value, invert it, and then give it a "-" sign.  For example, if the line is y = 2x +1, the negative inverse of the slope of 2 would be -(1/2).

The new line will have this new slope [-(1/m)] to make it y = -(1/m)x + b.

To find b, use the given point of (3,-2) in the equation and solve for b:

y = -(1/m)x + b

-2 = -(1/m)*(3) + b

Then solve for b and you'll have the equation for the solution to the problem.

Answer:

b = 2

Step-by-step explanation:

[tex]\frac{a}{b-2}[/tex]

the denominator cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the value that b cannot be

b - 2 = 0 ( add 2 to both sides )

b = 2 ← excluded value

Answer:

Correct!

Step-by-step explanation:

The solution is x = 1

Answer:

[tex]\frac{7}{26}[/tex]

Step-by-step explanation:

let x be the denominator of the fraction then x - 19 is the numerator , so

[tex]\frac{x-19}{x}[/tex] ← is the original fraction

subtrating 1 from the numerator and adding 1 to the denominator , then

[tex]\frac{x-20}{x+1}[/tex] = [tex]\frac{2}{9}[/tex] ( cross- multiply )

9(x - 20) = 2(x + 1) ← distribute parenthesis on both sides

9x - 180 = 2x + 2 (subtract 2x from both sides )

7x - 180 = 2 ( add 180 to both sides )

7x = 182 ( divide both sides by 7 )

x = 26

Then the original fraction is

[tex]\frac{26-19}{26}[/tex] = [tex]\frac{7}{26}[/tex]

Answer: 32 glasses

Step-by-step explanation: If 1 quart is 4 cups and 8 ounces are in 1 cup, 8x4=32 so there are 32 ounces in a quart. If he has 6 quarts 32x6+192 ounces. if each glass is 6 ounces 192/6=32.

Answer:

140°

Step-by-step explanation:

edge just did the assignment

The sector of the circle is bounded by 2 radii, and the measure of the central angle that forms the sector is 120 degrees

The given parameters are:

The area is calculated using

Area = α/360 * πr^2

So, we have:

α/360 * π * 15^2 = 75π

Evaluate the exponent

α/360 * π * 225 = 75π

Divide both sides by 75π

α/360 * 3 = 1

Multiply

α/120  = 1

Multiply both sides by 120

α = 120

Hence, the measure of the central angle that forms the sector is 120 degrees

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Answer:

Divide by 4

In this case one side would be 27.5

Step-by-step explanation:

A square has four sides so 110/4=27.5

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

the question asks us to rationalise the given expression !

so let's start ~

[tex] \frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \\ \\ \implies \: \frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \: \times \: \frac{6 - 4 \sqrt{3} }{6 - 4 \sqrt{3} } = \frac{(6 - 4 \sqrt{3}) {}^{2} }{6 {}^{2} - 4 \sqrt{3} {}^{2} } \\ \\ \implies \frac{\: 6 {}^{2} + 4 \sqrt{3} {}^{2} - (2 \times 6 \times 4 \sqrt{3} )}{36 - 48} \\ \\ \implies \: \frac{36 + 48 - 48 \sqrt{3} }{ - 12} \\ \\ \implies \: \frac{84 + 48 \sqrt{3} }{ - 12} \\ \\ \implies \: \frac{ \cancel{- 12}(7 - 4 \sqrt{3} )}{ \cancel{ - 12} } \\ \\ \implies \: 7 - 4 \sqrt{3} [/tex]

hope helpful :D

Answer:

-7+4√3.

Step-by-step explanation:

6-4√3 / 6+4√3     Multiply top and bottom by  6-4√3:-

=  (6-4√3)( 6-4√3) / (6+4√3)(6- 4√3)

= (36-24√3- 24√3+48) / (36-48)

= (36-48√3+48) / (-12)

= -3 +4√3 - 4

=  -7 + 4√3.

Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

[tex]\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3[/tex]

Answer:

Step-by-step

Let us assume that the third leg is X. So, X^2 + 2^2 = 5^2.X^2 = 25 - 4.X^2 = 21.X = root 21.

a right triangle, hypotenuse=5 cm, one leg=2 cm, the other leg=xApplying the Pythagorean theorem:5^2=2^2+x^2, 25=4+x^2,x^2=25–4=21, x=sqrt(21), x=4,58 cmThe measurement of the other leg is 4,58 cm

Answer:

  400

Step-by-step explanation:

The 20 terms of the sum can be formed into 10 pairs, each with a sum of 40:

  = (1 +39) +(3 +37) +(5 +35) + ... +(19 +21)

  = 40 × 10 = 400

The indicated sum is 400.

Answer:

5 minutes

Step-by-step explanation:

it dives at positive 18 feet in a minute

however in order to dive at -54 feet, it must dive -5 times

18-18-18-18-18= -54

and 1min =18feet

so it needs 5minutes for the 5times

OR

Let x=the time needed to dive at -54 feet's

so 1min=18

x= -54

-54=18x

dividing both sides by 18

-54/18=18x/18

x=-54/18

x=-5

however time cannot be negative

therefore x =5

this implies that the penguin dives at -54 feet in 5 minutes.

Answer:

the secound triangle shows right angle

Step-by-step explanation:

But the question says it is 91 ⁰ so the question may be wrong

Answer:

None.

Step-by-step explanation:

None of the given triangles are right triangles as for a triangle to be a right angled triangle it should have one angle which is equal to 90°.

The closest one will be the second triangle as it has one angle as 91° but it's NOT a right triangle .

________

Hope it helps ⚜

Step-by-step explanation:

Step 1:  Answer question 1

[tex]6(4) = x(3)[/tex]

[tex]\frac{24}{3} = \frac{3x}{3}[/tex]

[tex]8 = x[/tex]

Answer: [tex]x=8[/tex]

Step 2:  Answer question 2

The radius of a circle is equal to the halfway point of a circle and in this example it is 29.5 cm.  To find the diameter of a circle we multiply the radius of the circle by 2.

[tex]29.5\ cm * 2[/tex]

[tex]59\ cm[/tex]

Answer:  [tex]59\ cm[/tex]

Step 3:  Answer question 3

The diameter of a circle is a line across a circle and in this example it is 22 cm.  To find the radius of a circle we divide the diameter of the circle by 2.

[tex]\frac{22\ cm}{2}[/tex]

[tex]11\ cm[/tex]

Answer: [tex]11\ cm[/tex]

Answer:

1. x=8

2. a

3. d

Step-by-step explanation:

Answer:

-13x +8y

Step-by-step explanation:

-5x+2y-8x+6y

rearranging;

-5x-8x+2y+6y

(-5x-8x)+(2y+6y)

(-13x)+(8y)

Answer:

-13X+8Y.

Step-by-step explanation:

Combine like terms, -5x-8x = -13x.

2y+6y = 8y. goodluck.

Answer:

1. No

2. No

3. Yes

4. No

Answer:

a) 17.6 ft

b) 81.8 mm

c) 9 cm

d) 12 in

Step-by-step explanation:

Use the formula: πd = circumference to solve this equation

so you need to double the radius to get the diameter.

a) 5.6π = 17.6 ft

b) 26π = 81.8mm

c) 56.5 / π = 18.0 cm / 2 = 9 cm

d) 75.4/ π = 24.0 cm / 2 = 12 in

Answer:

K=19

Step-by-step explanation:

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