Find the radius of the circle below. Round your answer to the nearest tenth.

Answer:

42°

Step-by-step explanation:

→ Since this quadrilateral is a parallelogram, ∠S is equal to ∠R. Let's represent the situation in terms of equations

6x + 6 = 3x + 24

→ Minus 3x from both sides to collect the 'x' terms

3x + 6 = 24

→ Minus 6 from both sides isolate 3x

3x = 18

→ Divide by 3 on both sides isolate x

x = 6

⇒ The value of x is 6, but this isn't the measurement of ∠S, we need to substitute in x = 6 into the expression 6x + 6

6 (6) + 6 ⇔ 36 + 6 = 42°

m<S= 42°

Step-by-step explanation:

6x + 6 = 3x + 24

-6 -6

6x= 3x + 18

-3x -3x

3x = 18

[tex] \frac{3x}{3x} = \frac{18}{3x} [/tex]

x= 6

m<S= 6x + 6

m<S= 6(6) + 6

m<S= 42°

Answer:

Option A is the correct option.

Step-by-step explanation:

As PW is the median.

PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )

Plug the values

x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]

Calculate the sum

x = [tex] = \frac{1}{2} \times 17.6[/tex]

Calculate the product

x = [tex] = 8.8[/tex]

Hope this helps...

Best regards!

Answer:

x < 7

Step-by-step explanation:

-6x > -42

Divide each side by -6, remembering to flip the inequality

-6x/-6 < -42/-6

x < 7

Answer:

[tex]\boxed{x<7}[/tex]

Step-by-step explanation:

[tex]-6x > -42[/tex]

Divide both sides by -6 (flip sign).

[tex]\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}[/tex]

[tex]x<7[/tex]

Answer:

The correct option is;

B. It is the ratio of the area of the circle to the area of the square from a cross section.

Step-by-step explanation:

The formula for the volume of a pyramid = 1/3*Area of base*Height

The formula for the volume of a cone = 1/3*Area of base*Height

The area of the base of the square pyramid of side 2r = 2r*2r = 4r²

The area of the base of the cone of base radius r = πr²

The ratio of the volume of the cone to the volume of the square pyramid is given as follows;

[tex]\dfrac{\dfrac{1}{3} \times \pi \times r^2\times h}{\dfrac{1}{3} \times( 2 \times r)^2\times h}[/tex]

Given that the height are equal, h/h = 1, which gives;

[tex]\dfrac{\dfrac{1}{3} \times \pi \times r^2}{\dfrac{1}{3} \times( 2 \times r)^2} = \dfrac{Area \ of \ the \ circle}{Area \ of \ the \ square} =\dfrac{\dfrac{1}{3} \times \pi \times r^2}{\dfrac{1}{3} \times 4 \times r^2} = \dfrac{\pi }{4}[/tex]

Therefore, where the π/4 comes from is that it is the ratio of the area of the circle to the area of the square from a cross section.

Answer:

b

Step-by-step explanation:

Answer:

42 ducks remain in the pond

Step-by-step explanation:

First, find the number of white ducks

28*2=56

Add them to the brown ducks

56+28= 84

Then divide by 2 because half flew away

84/2=42

So 42 ducks remain in the pond. Hope this helps :)

Answer:

Option C. f¯¹(x) = x + 3

Step-by-step explanation:

f(x) = x – 3

To find the inverse, f¯¹(x) of f(x), we simply do the following:

f(x) = x – 3

Replace f(x) with y

y = x – 3

Interchange y and x

x = y – 3

Make y the subject by rearranging

x + 3 = y

y = x + 3

Replace y with f¯¹(x)

f¯¹(x) = x + 3

Therefore, the inverse of f(x) = x – 3 is f¯¹(x) = x + 3

Answer:

s = 25.33m

θ = 60.65°

12.37m

A = 160m^2

Step-by-step explanation:

The pyramid has a side base of 35m and a height of 22m.

side base = b = 35m

height of the pyramid = h = 22m

To calculate the slant edge of the pyramid, you first calculate the diagonal of the squared base of the pyramid.

You use the Pythagoras theorem:

[tex]d=\sqrt{(\frac{35}{2})^2+(\frac{35}{2})^2}=24.74[/tex]

With the half of the diagonal and the height, and by using again the Pythagoras theorem you can calculate the slat edge:

[tex]s=\sqrt{(\frac{24.74}{2})^2+(22)^2}=25.23[/tex]

The slant edge of the pyramid is 25.33m

The angle of the base is given by:

[tex]\theta=sin^{-1}(\frac{h}{s})=sin^{-1}(\frac{22}{25.23})=60.65\°[/tex]

The angle of the base is 60.65°

The distance between the corner of the pyramid and its center of its base is half of the diagonal, which is 24.74/2 = 12.37m

The area of one side of the pyramid is given by the following formula:

[tex]A=\frac{(b/2)l}{2}[/tex]        (1)

l: height of the side of pyramid

then, you first calculate l by using the information about the side base and the slant.

[tex]l=\sqrt{s^2-(\frac{b}{2}^2)}=\sqrt{(25.33)^2-(\frac{35}{2})^2}\\\\l=18.31m[/tex]

Next, you replace the values of l and b in the equation (1):

[tex]A=\frac{(35/2)(18.31)}{2}=160m^2[/tex]

The area of one aside of the pyramid is 160m^2

Answer:

[tex] \boxed{\sf b. \ 8(2a + 9)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)[/tex]

Answer:

(x - 10)(x - 5)

Step-by-step explanation:

Well to factor X^2-15x+50

we need to find 2 numbers that multiply to get 50 and add to get -15.

-5 * -10 = 50

-5 + -10

x*x = x^2

Factored (x - 10)(x - 5)

Hope this helps :)

Answer:

(x - 10)(x - 5)

Step-by-step explanation:

Step 1- Find 2 numbers that multiply to be 50.

10 × 5

-10 × -5

25 × 2

-25 × -2

All these multiply to get 50.

But the numbers must also add up to be -15.

Step 2- Find the 2 numbers that also add up to be -15.

10 + 5 = 15

-10 + -5 = -15

25 + 2 = 27

-25 + -2 = -27

The correct equation would be - 10 + -5

The 2 number you would use when you factor would be -10 and -5

Step 3- Write the equation

You can write the equation as (x - 10)(x - 5)

Or you can also write it as (x - 5)(x - 10)

Answer:

Step-by-step explanation:

sin ∅ = opposite / hypotenuse

From the question

the hypotenuse is 37

the opposite is 12

So we have

sin (a) = 12/37

Hope this helps you

===========================

Work Shown:

Plug in f(x) = 37. Solve for x. Use logarithms.

f(x) = 20(1.05)^x

37 = 20(1.05)^x

20(1.05)^x = 37

1.05^x = 37/20

1.05^x = 1.85

log( 1.05^x ) = log( 1.85 )

x*log( 1.05 ) = log( 1.85 )

x = log( 1.85 )/log( 1.05 )

x = 12.6088044498867

Round up to the nearest whole number to get x = 13.

In the year 2013, sales exceed 37 million.

Answer:

-1+2-4+8-10+12-14+16-18+20

=

-47+68

= +21

hope youlike this

stay at home stay safe

keep rocking

Answer:

Step-by-step explanation:

Given,

x = [tex] \frac{5}{2} [/tex]

Now, let's find the value of 2x - 5

[tex]2x - 5[/tex]

plug the value of x

[tex] = 2 \times \frac{5}{2} - 5[/tex]

Reduce the number with Greatest Common Factor 2

[tex] = 5 - 5[/tex]

The sum of two opposites equals 0

[tex] = 0[/tex]

Hope this helps..

best regards!!

Answer:

0

Step-by-step explanation:

x=5/2

therefore

2(5/2)-5=10/2-5

=5-5(since 10/2=5)

=0

Answer:

How many students are in P.E? 90

How many are ONLY in P.E? 62

Step-by-step explanation:

How many students are in P.E?

200 students in 8th grade.

35=drama

75=cooking

200-110=90=PE.

How many are ONLY in P.E?

Within 90 students, 15 is also in drama, with 5 is also in cooking, and 8 is in all of 3. =28.

90-28=62

Hope this helps!

Answer:

m<A = 90° - m<B

(AB)^2 = (AC)^2 + (BC)^2

sin A = cos B

if <A = <B, then m<A = 45°

Answer:

Step-by-step explanation:

∠A+∠B=90 complementary angles ( the sum equal 90°)

∠A=90 degrees-∠B

tan A=sinA/cos A

AB²= AC² +BC² (Pythagorean theorem)

if angle A=angle B then the angles are 45 degrees

cos A=sin(90-A)  

sin (a - b) = sin a.cos b - sin b.cos a

sin(90-A)=sin90.cosA-sinbAcos90 cos 90=0 and sin 90=1

sin(90-A)=1*cosA

sin(90-A)=cosA

the ones are  in bold are right

Answer:

42°

Step-by-step explanation:

AD bisects ∠CAB, which means it splits ∠CAB into two equal parts. ∠CAB equals 84°. 84° ÷ 2 = 42°.

Answer:-12

Step-by-step explanation:

Add 10+14 to get 24 then divide it by a negative 2 to get -12

Answer:

x = ±2

Step-by-step explanation:

x^2 – 14 = –10

Add 14 to each side

x^2 – 14+14 = –10+14

x^2 = 4

Take the square root of each side

sqrt(x^2) = ±sqrt(4)

x = ±2

Answer:

A. Volume = 462 cm³; Surface Area = 458 cm²

B. Volume

C. Surface area

Step-by-step explanation:

A. Given a rectangular box:

[tex] Width (w) = 3 cm [/tex]

[tex] Height (h) = 14 cm [/tex]

[tex] length (l) = 11 cm [/tex]

=>Volume of the juice box

[tex] Volume (V) = whl [/tex]

[tex] Volume (V) = 3*14*11 [/tex]

[tex] = 3*14*11 = 462 [/tex]

Volume of juice box = 462 cm³

=>Surface area (S.A) of juice box:

[tex] S.A = 2(wl + hl + hw) [/tex]

[tex] S.A = 2(3*11 + 14*11 + 14*3) [/tex]

[tex] S.A = 2(33 + 154 + 42) [/tex]

[tex] S.A = 2(229) [/tex]

[tex] S.A = 458 cm^2 [/tex]

Surface area of juice box = 458 cm²

B. Volume would be used to find the amount of juice the box can hold

C. Surface area would be used to know how much wax to buy to use in coating the box.

Rahul ate more tangerines...

Answer:

4 in

Step-by-step explanation:

as you see from the first rectangle it has been reduced 3 times of length

so the breadth also should be reduced 3 times

Answer:

x = 4

Step-by-step explanation:

the simplest way to do that is to divide

12 / 18 = 2 / 3

then we move to the another square:

x / 6 = 2 / 3

x = 6 x 2 / 3

x = 4

.. ..

Answer:

B since the correlation between the numbers in x raise at a higher rate than any other chart

Answer:

Step-by-step explanation:

ABC is a right angle triangle.

Therefore,

[tex]cos \: (75) = \frac{ab}{ac} [/tex]

Plug the values

[tex]cos \: (75) = \frac{x}{21} [/tex]

Apply cross product property

[tex]x = 21 \times cos(75)[/tex]

Calculate

[tex]x = 5.435[/tex]

After rounding to the nearest tenth, the answer will be:

[tex]x = 5.4[/tex]

Hope this helps...

Best regards!!

Answer:

D.y + 1 = 6(x - 6)

Step-by-step explanation:

The general form of a straightline equation is given as

y = mx + c

where m is the slope and c is the intercept

m = Δy/Δx

from the given points

m = (-7 - -1)/(5 - 6)

= -6/-1

= 6

Considering the points x₁ and y which are  6 and -1

and using the formular

m = (y - y₁)/(x - x₁)

6 = (y - -1)/(x - 6)

y + 1 = 6(x - 6)

Answer:

452.39

Step-by-step explanation:

A=4πr^2

=4·π·6^2

≈452.38934

Answer:

y = 2b/3

Step-by-step explanation:

The x-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2(a+c)}{3}[/tex]. Given that:

[tex]y=\frac{b}{a-2c}x -\frac{2bc}{a-2c} \\\\The\ y\ coordinate\ can\ be \ gotten\ by\ substituting\ the \ value\ of\ x\ and\ simplifying.\\ Substituting\ x:\\\\y=\frac{b}{a-2c}(\frac{2(a+c)}{3} ) -\frac{2bc}{a-2c}[/tex]

[tex]Simplyfing\ the\ parenthesis\\y=\frac{2b(a+c)}{3(a-2c)} -\frac{2bc}{a-2c}\\\\y=\frac{2ab+2bc}{3(a-2c)} -\frac{2bc}{a-2c}\\\\Simplyfying\ using\ LCF\\y=\frac{2ab+2bc-6bc}{3(a-2c)}\\\\y=\frac{2ab-4bc}{3(a-2c)}\\\\Factorizing:\\\\y=\frac{2b(a-2c)}{3(a-2c)}\\\\y=\frac{2b}{3}[/tex]

The y-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2b}{3}[/tex].

Answer:

b

Step-by-step explanation:

After translating the expression I got:

[tex] \frac{3}{4} x < 24[/tex]

Once you cross multiply you should have the following expression:

[tex]x < 32[/tex]

Then when you graph, remember it should be an open circle on the 32 and the direction of the arrow should be towards 0

Answer:

D

Step-by-step explanation:

just took the test

Answer:

The maximum size of the smaller jars is 6 liters

Step-by-step explanation:

Container 1=174 liters of oil

Container 2=258 liters of oil

Same pours the entire content of container one and container 2 into the same number of smaller jars

The maximum size of the smaller jar can be found by finding the highest common factor of 174 and 258

Factors of 174=1,2,3,6,29

Factors of 258=1,2,3,6,43

Common factors of 174 and 258=1,2,3 and 6

Highest common factor=6

Therefore,

The maximum size of the smaller jars is 6 liters

Answer:

588 kilómetros

Step-by-step explanation:

La función con la que estamos trabajando según la pregunta es;

F (x) = 6x ^ 2 -12

Ahora, la pregunta que simplemente nos hace es encontrar el valor de F (x) dado que x = 10

Entonces, lo simple que hacemos aquí es hacer una sustitución de x = 10 Eso sería;

F (10) = 6 (10) ^ 2 - 12 = 600-12 = 588

Answer:

D. 4z^3

Step-by-step explanation:

First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3

Hope this helps, if you want me to explain more, feel free to ask questions.

Have a good day! :)

Answer:

4 z^3

Step-by-step explanation:

( 64 z^9) ^ 1/3

Rewriting 64 as 4^3

( 4^3 z^9) ^ 1/3

We know that ( ab) ^c = a^c  * b^c

4^3 ^ 1/3 z^9  ^ 1/3

We know that a^ b^c = a^ ( b*c)

4^(3 * 1/3) z^ (9  * 1/3)

4 ^ ( 1)  z^ ( 3)

4 z^3