writing linear equations

Answer:

1/6

Step-by-step explanation:

Each roll is independent.  So the probability of rolling a six is 1/6, regardless of the previous rolls.

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]

Answer:

12

Step-by-step explanation:

If you add the ratio you will get 8 and 1 in the ratio number represents

6 people so 5-3=2

Therefore, the no. of girls minus boys= 6×2=12

so you need 12 more boys to make it to be a ratio of 1:1

Answer:

2,666.67 L of water

Step-by-step explanation:

Solve for W:

1) 3200 = 2400 + 0.3w

2) 800 = 0.3w

Divide both sides by 0.3 to get the variable alone

3) (800)/0.3 = (0.3w)/0.3

4) w = 2,666.67 L

Answer:

The explicit formula for the sequence is

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

Hope this helps you

Answer:

[tex]\huge\boxed{a_n=-6n+44}[/tex]

Step-by-step explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

[tex]a_n=a_1+(n-1)(d)[/tex]

Substitute:

[tex]a_1=38;\ d=-6[/tex]

[tex]a_n=38+(n-1)(-6)[/tex]         use the distributive property

[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]

Answer:

m ∠DBC=80−10=70

m ∠ABC=80+30=110

Step-by-step explanation:

m ∠DBC+m ∠ABC=180

( x−10)+(x+30.)=180

2x+20=180

2x=180-20

2x=160

x=80

>>m ∠DBC=80−10=70

>>m ∠ABC=80+30=110

Answer:

[tex]\boxed{<DBC = 70 degrees}\\\boxed{<ABC = 110 degrees}[/tex]

Step-by-step explanation:

∠ABC and ∠DBC are supplementary which means that the sum of these two angles is equal to 180.

∠ABC + ∠DBC = 180

Given that: ∠ABC = x+30 and ∠DBC = x - 10

So,

=> x+30+x-10 = 180

=> 2x+20 = 180

=> 2x = 180-20

=> 2x = 160

Dividing both sides by 2

=> x = 80

Now, Finding measures of the angles.

=> ∠DBC = x-10 = 80-10 = 70 degrees

=> ∠ABC = x+30 =80+30 = 110 degrees

Answer:

Yes, because each x-value corresponds to one y value.

Step-by-step explanation:

If you look at the table, you notice that there is one output (y) for every input (x). This means that it is a function. It would NOT be a function if you had two outputs for an input. For example, there are two x values that are 6. For one coordinate pair, the table says (6,9) and (6,8). Since there are two values for the same input- it wouldn't be a function. In this case, there is an input of 4 and 5 with the same output. That is okay! Even though they have the same y value, those inputs still only have ONE output.

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:

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: 4^3

(Four cubed or Four to the power of 3)

Step-by-step explanation:

Answer:

w²-30w+210=0

Step-by-step explanation:

2w + 2l = 60 , w + l = 30, l = 30 - w

wl = 210

w(30-w) -210 = 0

30w - w²-210 = 0

w²-30w+210=0

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:

  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:

[tex]\dfrac{10}{4} \ hour[/tex]

Step-by-step explanation:

Given that :

Jack had 4 hours of school.

He spent 45 minutes in the library

1/2 hour on a science lecture  and;

had a lunch break of 25 minutes

The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.

In order to do that, we will have to convert the minutes into hours,

we all know that; 60 minutes = 1 hour.

Then,

45 minutes = (45/60)hour = 3/4 hour

25/60 minutes = 1/4 hour

Therefore, the amount of time left  for the school to get over is:

= [tex]4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})[/tex]

=  [tex]\dfrac{16-(3+2+1)}{4}[/tex]

= [tex]\dfrac{16-6}{4}[/tex]

= [tex]\dfrac{10}{4} \ hour[/tex]

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:

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:

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:

(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:

it is c because i took test review

Step-by-step explanation:

Answer:

C The solution should be 6, and the cyclists will need to ride 6 laps before the sprint to the finish.

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]

Step-by-step explanation:

since PQRT is a rhombus,

URQ=TPU

y=180-90-24=66

x=180-32-90-24=34

Answer:

Because the triangle is isosceles, the base angles are congruent, meaning that the angles that are not right angles are x and x. Since the sum of angles in a triangle is 180°, we can write:

90 + x + x = 180

x + x = 90

2x = 90

x = 45°

Answer:

45 degrees

Step-by-step explanation:

This triangle is "isosceles..." two legs are equal.  Thus, the triangle has two 45 degree angles.  The indicated angle is 45 degreees.

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: C

Step-by-step explanation:

The open dot means its not equal to X and the placement is -14.5

Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

There are 15 points on a circle.

We need three points to form a triangle

Therefore the number of triangles = 15 choose 3 ​= 15!/(3!x12!)​ = (15x14x13)/(3x2x1) = 5x7x13 = 455

Hence the number of triangles formed is 455

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:

3

1/5

3/4

3/4

Step-by-step explanation:

Coefficient is a number that is always written in front of a term.

3xy^3=3

xy/5=1/5

3/4xy=3/4

3/4x^2y=3/4

Hope this helps ;) ❤❤❤