Evaluate 7m + 2n - 8p/n for m = –4, n = 2, and p = 1.5.

Answer:

56

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{35+20}{20}[/tex] = [tex]\frac{32+?}{32}[/tex] ( cross- multiply )

20(32 + ?) = 1760 ( divide both sides by 20 )

32 + ? = 88 ( subtract 32 from both sides )

? = 56

Answer:

[tex]\boxed{56}[/tex]

Step-by-step explanation:

We can use ratios to solve since the triangles are similar.

[tex]\frac{20}{32} =\frac{35}{x}[/tex]

Cross multiplication.

[tex]20x=35 \times 32[/tex]

Divide both sides by 20.

[tex]\frac{20x}{20} = \frac{35 \times 32}{20}[/tex]

[tex]x=56[/tex]

Answer:

160°

Step-by-step explanation:

The way I am doing it may not be the correct way but it works. What I did was take 90° away from 120° to make it 30° as if there is a line. I did this so I could make a triangle. Using the triangle addition postulate, I Added 30 to 80  to get 110 than subtracted that from 180 to get 70. Lastly, i added 90°  to 70°  to get 160°

Hope this helped you get the answer :)

The measure of angle B in Parallel lines will be 160°.

What are parallel lines?

Parallel lines are those lines that never intersect at any point and always maintain a constant distance.

We have,

Lines L and K are parallel to each other.

And,

The measure of angle A = 120°

The measure of angle C = 80°

Now,

Draw a straight line from A to B,

So, that ∠BAl = 90° and

∠ABk = 90°

We get,

ΔABC,

Now in ΔABC,

∠C = 80°

∠A = 120 - 90 = 30°

So, Using Tringle angle sum property,

80° + 30° + ∠ABC = 180°

⇒

∠ABC = 180° - 110°

∠ABC = 70°,

Now,

Adding  ∠ABC and ∠ABk, to get  ∠CBk,

i.e.

∠CBk = ∠ABC + ∠ABk = 70° + 90°

∠CBk = 160°

Hence we can say that the measure of angle B will be 160°.

To learn more about Parallel lines click here,

https://brainly.com/question/16701300

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Answer:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

Hence, for continuous probability distribution: probability = area.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

Hence, it cannot be computed.

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

Hence, it can be computed.

Answer: 4^3

(Four cubed or Four to the power of 3)

Step-by-step explanation:

Answer:

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Step-by-step explanation:

As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.

Given:

Height of cylinder, [tex]h_1[/tex] = 15 cm

Diameter of cylinder/ cone, D = 26 cm

Slant height of cone, l = 20 cm

Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]

Here,

[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]

To find the Height of Cylinder, we can use the following formula:

[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]

Now, putting the values to find the volume of container:

[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]

Converting [tex]cm^{3 }[/tex] to litres:

[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer: C) Plane: 235 km/h, Wind: 24 km/h

Step-by-step explanation:

Given that :

Average Speed while flying with a tailwind = 259km/hr

Return trip = 211km/hr

Let the speed of airplane = a, and wind speed = w

Therefore ;

Average Speed while flying with a tailwind = 259km/hr

a + w = 259 - - - (1)

Return trip = 211km/hr

a - w = 211 - - - (2)

From (2)

a = 211 + w

Substitute the value of a into (1)

a + w = 259

211 + w + w = 259

211 + 2w = 259

2w = 259 - 211

2w = 48

w = 48/2

w = 24km = windspeed

Substituting w = 24 into (2)

a - 24 = 211

a = 211 + 24

a = 235km = speed of airplane

Answer:

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Step-by-step explanation:

b=7x

sum of straight angle :=180

isoceles traingle = 2 sides are equal, and two angles are equal

b+a=180

7x+a=180

sum of traingle =180

2a+c=180

2a+2x=180  first equation

7x+a=180    second equation

solve by elimination ( multiply second equation by 2)

2a+2x=180

2a+14x=360 ( subtract)

2a+2x-2a-14x=180-360

-12x=-180

x=-180/12=

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Answer:

(B), in which the first two values are 2 and 10.

Step-by-step explanation:

We can tell that this is a proportional relationship because we can examine the numbers in there.

(2,10)

(4,20)

and (6,30).

If you notice, the x value times 5 gets us the y value for every single point there.

Therefore, B is proportional and it's equation is y = 5x.

Hope this helped!

Answer:

B.

Step-by-step explanation:

B. Is the only one that proportional because,

(2,10)

(4,20)

(6,30)

All these x values multiply by 5 to get the y value.

So the equation is y = 5x meaning it is linear and it goes through the origin which makes it proportional.

Thus,

answer choice B is correct.

Hope this helps :)

Answer:

O B. 17 units

Step-by-step explanation:

The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:

[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]

The length of the chord is 17 units.

Answer:

The answer is 17 units :D

Step-by-step explanation:

Answer:

Probability of (one club and one heart) = 0.1275 (Approx)

Step-by-step explanation:

Given:

Total number of cards = 52

Each suits = 13

FInd:

Probability of (one club and one heart)

Computation:

Probability of one club = 13 / 52

Probability of one heart = 13 / 51

Probability of (one club and one heart) = 2 [(13/52)(13/51)]

Probability of (one club and one heart) = 0.1275 (Approx)

Answer:

D. 0.1275

Step-by-step explanation:

Justo took the Pre-Test on Edg (2020-2021)!!

Answer:

130

Step-by-step explanation:

just did test on plato/edmentum..it was correct

84 (the answer above) is incorrect

Answer:

Hi sorry for late respond but the answer in 130!!

Step-by-step explanation:

Answer:

  80°

Step-by-step explanation:

The sum of the measures of the acute angles in a right triangle is 90°. The sum of ratio measures in the ratio 8 : 1 is (8+1) = 9. Thus, each of those measures stands for 90°/9 = 10°. Then the angle ratio is ...

  80° : 10° = 8 : 1

The measure of the largest acute angle in the triangle is ...

  10° × 8 = 80°

Answer: sample space

Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.

Answer:

divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125

Answer:

Step-by-step explanation:

It depends on how it is written. By definition

[tex]\csc(x) = (\sin(x))^{-1} = \frac{1}{\sin(x)}[/tex]

[tex]\sec(x) = (\cos(x))^{-1} = \frac{1}{\cos(x)}[/tex]

[tex]\cot(x) = (\tan(x))^{-1} = \frac{1}{\tan(x)}[/tex]

however the functions

[tex]\sin^{-1}(x), \cos^{-1}(x), \tan^{-1}(x)[/tex] are the inverse functions of sine, cosine and tangent respectively. So, they are not equivalent functions

Answer:

Step-by-step explanation:

Hello,

For any function f which has an inverse function we can write

[tex]x=(f^{-1}of)(x)=(fof^{-1})(x)=f(f^{-1}(x))[/tex]

This is why, in practice, to find the inverse of f we will consider f(x) = y and we will look for x as a function of y, so we switch x and y and solve for y. Let's do it.

Step 1 - The function f(x) can be written as a variable.  [tex]\boxed{y}=f(x)[/tex]

f(x) = y = 5x + 2

Step 2 - switch the variables x <-> y

x = 5y + 2

subtract 2 to both parts of the equation

<=> x - 2 =  5y + 2 - 2 = 5y

divide by 5 both parts of the equation

[tex]<=> y=\dfrac{x-2}{5}[/tex]

It means that the inverse of f is as below.

[tex]\boxed{ \ f^{-1}(x)=\dfrac{x-2}{5}\ }[/tex]

Step 3 - Find the inverse of g(x)

We already found that the inverse of f is g, so the inverse of g is f.

Let's do it again.

[tex]g(x)=y=\dfrac{x-2}{5} \ \ \text{ switch x and y } \\ \\ x= \dfrac{y-2}{5} \ \ \text{ solve for y }\\ \\ y-2=5x \ \ \text{ mulitply by 5 both parts of the equation } \\ \\ y = 5x+2 \ \ \text{ add 2 to both parts of the equation }[/tex]

And we found what we already known, meaning f is the inverse of g.

[tex](gof)(x)=(fog)(x)=x[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answers and Step-by-step explanation:

Step 1:

We want to find the variable that ff(x) represents. Well, we know it can't be x because we already have x on the other side of the equation: ff(x) = 5x + 2.

So, ff(x) must equal y.

Since ff(x) = y, we know then that ff(x) = y = 5x + 2. And our equation is:

y = 5x + 2

Step 2:

Let's switch the variables now. This means that what used to be y will be x and what used to be x will be y:

y = 5x + 2  ⇒  x = 5y + 2

Subtract 2 from both sides:

5y = x - 2

Divide by 5 from both sides:

y = (x - 2)/5

Step 3:

Let's find the inverse of g(x) by doing the exact same thing as we did with ff(x):

g(x) = y = (x - 2)/5

Switch the variables:

y = (x - 2)/5  ⇒      x = (y - 2)/5

Multiply by 5 on both sides:

5x = y - 2

Add 2 to both sides:

y = 5x + 2

Notice that this is the exact same as ff(x)! This means that ff(x) and g(x) are inverses.

Answer:

151200 possible combinations

Step-by-step explanation:

There are 10 digits 0 - 9  ( 0,1,2,3,4,5,6,7,8,9)

There are 10 choices for the first digit

10

There are 9 choices for the second digit

9

There are 8 choices for the third digit

8

and so on  since we can only use each digit once

10 *9*8 *7 *6*5

151200 possible combinations

Answer:

$320

Step-by-step explanation:

Let the total sum of money be $x.

Therefore,

12 1/2% of x = 40

25/2% * x = 40

0.125 * x= 40

x = 40/0.125

x = $320

Thus, total sum of money is $320.

Answer:

x = 4 or x = - [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Given

(2x - 8)(7x + 5) = 0

Equate each factor to zero and solve for x

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]

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

If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that

[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]

Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.

---------

So we have,

|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2

As long as a < 7, the result of |a-7| - |a-9| will always be -2.

---------

As an example, let's say a = 0

|a-7| - |a-9| = |0-7| - |0-9|

|a-7| - |a-9| = |-7| - |-9|

|a-7| - |a-9| = 7 - 9

|a-7| - |a-9| = -2

I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.

Area of a triangle is 1/2 x base x height.

The graphed triangle has height of 2 and base of 2.

Area = /2 x 2 x 2 = 2 square units.

The triangle gets enlarged by a scale factor of 2, so the new height would be 2 x 2 = 4 and the new base would be 2 x 2 = 4

Area of enlarged triangle = 1/2 x 4 x 4 = 8 square units.

The answer is C) 8

Answer:

4x:9=7:3 can be written as

[tex] \frac{4x}{9} = \frac{7}{3} [/tex]

Cross multiply

We have

4x(3) = 9 × 7

12x = 63

Divide both sides by 12

[tex]x = \frac{21}{4} \: \: \: \: \: or \: \: \: 5 \frac{1}{4} [/tex]

Hope this helps you

Answer:

[tex]\boxed{x=\frac{21}{4}}[/tex]

Step-by-step explanation:

[tex]4x:9=7:3[/tex]

Turn ratios to fractions.

[tex]\frac{4x}{9} =\frac{7}{3}[/tex]

Cross multiplication.

[tex]4x \times 3 = 9 \times 7[/tex]

Simplify.

[tex]12x=63[/tex]

Divide both sides by 12.

[tex]x=\frac{63}{12}[/tex]

[tex]x=\frac{21}{4}[/tex]

Answer:

Afful is 21 and Naomi is 13.

Step-by-step explanation:

Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.

The sum of their ages is 34. In other words:

[tex]A+N=34[/tex]

In 5 years time, Afful will be two times the age of Naomi now. In other words:

[tex]A+5=2N[/tex]

Solve for the system. Substitute.

[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]

Afful is currently 21 and Noami is currently 13.

Answer:

Naomi=x

Afful=2x

In 5 years time= +5

So Naomi=x+5

and and Afful=2x+5

=x+5+2x+5=34

=3x+10=34

Subtract 10 on both sides

3x=24

Divide 3 on both sides

X=8

Check:

X=8

Naomi=16

In 5 years

=16+5=21

Naomi=8+5=13

13+21=34

Hope this helps

Step-by-step explanation:

Answer:

We could rewrite 7/2 as 7a + 2

Step-by-step explanation:

Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.

k = b + 13

k - 19 = b - 6

k = b + 19 - 6

k = b + 13

Answer:

[tex]\boxed{k=b+13}[/tex]

Step-by-step explanation:

[tex]k-19=b-6[/tex]

Add 19 on both sides.

[tex]k-19+19=b-6+19[/tex]

[tex]k=b+13[/tex]

Answer:

A ( -4, -7)

Step-by-step explanation:

if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )

Answer:

A.

Step-by-step explanation:

Answer:

             [tex]\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}[/tex]

Step-by-step explanation:

m∠Z = 180° - 118° - 28° = 34°

[tex]\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\[/tex]

[tex]\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5[/tex]

Step-by-step explanation:

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