Find the value of y.

Answer:

Step-by-step explanation:

Equation of the line has been given as,

[tex]y=\frac{3}{2}x-5[/tex]

By comparing this equation with the y-intercept form of the equation,

y = mx + b

Slope of the line 'm' = [tex]\frac{3}{2}[/tex]

and y-intercept 'b' = -5

Table for the points to be plotted on a graph will be,

x              y

-4           -11

-2           -6

0            -5

2            -4

4            -3

By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.

Answer: actually the answer to this question is (0, -5) and ( 2, -2)

Step-by-step explanation: I just took the test on Plato and got it right :)

Answer:

Larger force= 66.28 pounds

Step-by-step explanation:

The angle of the resultant force 80 pounds = 180-(52+20)

The angle of the resultant force 80 pounds = 180-72

The angle of the resultant force 80 pounds = 108°

The larger force is the force with 52°

Let the larger force be x

Magnitude of the larger force

x/sin52 = 80/sin108

X= sin52 *(80/sin 108)

X= 0.7880*(80/0.9511)

X = 0.7780*(84.1131)

X = 66.28 pounds

There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.

Now, sin51°/20=sinN/14

0.7771/20=sinN/14

0.038855=sinN/14

sinN=14×0.038855

sinN=0.54397

N=33°

Therefore, option B is the correct answer.

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Answer:-8

Step-by-step explanation:

Answer:

x = -4/3 and x = 5/2.

Step-by-step explanation:

6x² - 7x = 20

6x² - 7x - 20 = 0

To solve this, we can use the quadratic formula to solve this.

[please ignore the A-hat; that is a bug]

[tex]\frac{-b±\sqrt{b^2 - 4ac} }{2a}[/tex]

In this case, a = 6, b = -7, and c = -20.

[tex]\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}[/tex]

= [tex]\frac{7±\sqrt{49 + 80 * 6} }{12}[/tex]

= [tex]\frac{7±\sqrt{49 + 480} }{12}[/tex]

= [tex]\frac{7±\sqrt{529} }{12}[/tex]

= [tex]\frac{7±23 }{12}[/tex]

[tex]\frac{7 - 23 }{12}[/tex] = [tex]\frac{-16 }{12}[/tex] = -8 / 6 = -4 / 3

[tex]\frac{7 + 23 }{12}[/tex] = [tex]\frac{30}{12}[/tex] = 15 / 6 = 5 / 2

So, x = -4/3 and x = 5/2.

Hope this helps!  

Answer:

Step-by-step explanation:

[tex]6 {x}^{2} - 7x = 20[/tex]

Move constant to the left and change its sign

[tex] {6x}^{2} - 7x - 20 = 0[/tex]

Write -7x as a difference

[tex]6 {x}^{2} + 8x - 15x - 20 = 0[/tex]

Factor out 2x from the expression

[tex]2x(3x + 4) - 15x - 20 = 0[/tex]

Factor out -5 from the expression

[tex]2x(3x + 4) - 5(3x + 4) = 0[/tex]

Factor out 3x + 4 from the expression

[tex](3x + 4)(2x - 5) = 0[/tex]

When the product of factors equals 0 , at least one factor is 0

[tex]3x + 4 = 0[/tex]

[tex]2x - 5 = 0[/tex]

Solve the equation for X1

[tex]3x + 4 = 0[/tex]

Move constant to right side and change its sign

[tex] 3x = 0 - 4[/tex]

Calculate the difference

[tex]3x = - 4[/tex]

Divide both sides of the equation by 3

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

Calculate

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

Again,

Solve for x2

[tex]2x - 5 = 0[/tex]

Move constant to right side and change its sign

[tex]2x = 0 + 5[/tex]

Calculate the sum

[tex]2x = 5[/tex]

Divide both sides of the equation by 2

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

Calculate

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

[tex]x1 = - \frac{4}{3} [/tex]

[tex]x2 = \frac{5}{2} [/tex]

Hope this helps...

Best regards!!

Answer:

11% of the Total the entire voting population

Step-by-step explanation:

Let's bear in mind that the total number of sample candidates is equal to 600.

But out of 600 only 66 preffered candidate A.

The proportion of sampled people to that prefer candidate A to the total number of people is 66/600

= 11/100

In percentage

=11/100 *100/1 =1100/100

=11% of the entire voting population

Answer:

1/3

Step-by-step explanation:

Ratios are basically comparisons of multiple numbers that shows their quantity relationship with each other. If we want to find the ratio of x to y, then the ratio is written as x : y or x/y.

Here, we want the ratio of adults to children. There are 3 adults and 9 children, so we have:

adults / children = 3 / 9 = 1/3

The answer is thus 1/3.

~ an aesthetics lover

Answer:

1:3

Step-by-step explanation:

The ratios of two terms is written as x:y.

3 ⇒ adults

9 ⇒ children

The ratio of adults to children:

3:9

Simplify the ratio.

1:3

Answer:

Answer is 24288.

Step-by-step explanation:

Given that there are 18 senior and 22 junior partners.

To find:

Number of ways of selecting at least one junior partner to form a committee of 3 partners.

Solution:

At least junior 1 member means 3 case:

1. Exactly 1 junior member

2. Exactly 2 junior member

3. Exactly 3 junior member

Let us find number of ways for each case and then add them.

Case 1:

Exactly 1 junior member:

Number of ways to select 1 junior member out of 22: 22

Number of ways to select 2 senior members out of 18: 18 [tex]\times[/tex] 17

Total number of ways to select exactly 1 junior member in 3 member committee: 22 [tex]\times[/tex] 18 [tex]\times[/tex] 17 = 6732

Case 2:

Exactly 2 junior member:

Number of ways to select 2 junior members out of 22: 22 [tex]\times[/tex] 21

Number of ways to select 1 senior member out of 18: 18

Total number of ways to select exactly 2 junior members in 3 member committee: 22 [tex]\times[/tex] 21 [tex]\times[/tex] 18 = 8316

Case 3:

Exactly 3 junior member:

Number of ways to select 3 junior members out of 22: 22 [tex]\times[/tex] 21 [tex]\times[/tex] 20 = 9240

So, Total number of ways = 24288

Answer:

Time taken = 6 sec (Approx)

Step-by-step explanation:

Given:

Total distance = 1/12 mi = 0.083333

Speed of train = 50 mph = 50 / 3600 = 0.01388889 mps

Find:

Time taken

Computation:

Time taken = Total distance / Speed

Time taken = Total distance / Speed of train

Time taken = 0.0833333 / 0.01388889

Time taken = 6 sec (Approx)

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph.  When the man  

runs toward point A, the relative speed of the train with respect  

to the man is the train's speed plus the man's speed (45 + M).  

When he runs toward point B, the relative speed of the train is the  

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.  

When he runs in the direction of the train the distance he covers  

is 3 units. We can now write that the ratio of the relative speed  

of the train when he is running toward point A to the relative speed  

of the train when he is running toward point B, is equal to the  

inverse ratio of the two distance units or

              (45 + M)          3

              -----------  =      ---

              (45 - M)          2

          90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

Answer: 9 mph

Step-by-step explanation:

Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .

If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5

The remaining distance = 1 - 4/5 = 1/5

If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be

Speed = distance/time

Time = 1/5d ÷ speed

The time it will take the train to cover the entire distance d will be

Time = d ÷ 45

Equate the two time

1/5d ÷ speed = d ÷ 45

Speed = d/5 × 45/d

Speed = 9 mph

Answer:

The range of T is a subspace of W.

Step-by-step explanation:

we have T:V→W

This is a linear transformation from V to W

we are required to prove that the range of T is a subspace of W

0 is a vector in range , u and v are two vectors in range T

T = T(V) = {T(v)║v∈V}

{w∈W≡v∈V such that T(w) = V}

T(0) = T(0ⁿ)

0 is  Zero in V

0ⁿ  is zero vector in W

T(V) is not an empty subset of W

w₁, w₂   ∈ T(v)

(v₁, v₂ ∈V)

from here we have that

T(v₁) = w₁

T(v₂) = w₂

t(v₁) + t(v₂) = w₁+w₂

v₁,v₂∈V

v₁+v₂∈V

with a scalar ∝

T(∝v) = ∝T(v)

such that

T(∝v) ∈T(v)

so we have that T(v) is a subspace of W. The range of T is a subspace of W.

Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

Answer: the numbers are 3 and -3

Step-by-step explanation:

let the unknown number be x

The first UNKNOWN NUMBER = X

The second unknown number is = 6 + x

Their product = -9

(X)(6 + X) = -9

6x +[tex]x^{2}[/tex]=-9

[tex]x^{2}[/tex] +6x +9=0

we multiply the coefficient of x which is 1 with 9

now, we look for two numbers that when multiplied will give us 9 and when added will give 6 and that is 3 and 3

[tex]x^{2}[/tex] +3x+3x +9 = 0

x(x+3) +3(x+3) = 0

(x +3 ) = 0

or (x +3)=0

x +3 =0

x=0 -3

x =-3

x +3=0

x =0-3

x =-3

since the numbers are the same ,we pick one

therefore,the first number =x =-3

the second number is 6 + x=6 + (-3)

6-3=3

Answer:

Step-by-step explanation:

Given: MN ≅ MA

          ME ≅ MR

Prove: ∠E ≅ ∠R

From the given diagram,

YN ≅ YA

EY ≅ RY

<EMA = <RMN (right angle property)

EA = EY + YA (addition property of a line)

NR = YN + RY (addition property of a line)

EA ≅ NR (congruent property)

ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)

<MNR ≅ MAE (angle property of congruent triangles)

Therefore,

<E ≅ <R (angle property of congruent triangles)

Answer:

[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]

Thanks!!!!

Answer:

$16,750.00

Step-by-step explanation:

Simple interest:

I = Prt

Value of an investment of value P over t years at r interest rate:

F = P + Prt

F = P(1 + rt)

19,513.75 = P(1 + 0.03 * 5.5)

1.165P = 19,513.75

P = 16,750

Answer: $16,750.00

The present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

We have been given data as:

Rate of Interest (R) = 3% = 3/100 = 0.03

Time (T) = 512  years

Value of an investment of value P over t years at r interest rate:

A = P + Prt

A = P(1 + rt)

19,513.75 = P(1 + 0.03 × 5.5)

19,513.75 = 1.165P

1.165P = 19,513.75

P = 19,513.75/1.165

P = 16,750

Thus, the present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.

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Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood

Step-by-step explanations:

Find explanations in the attachment

Answer:

sin(O) = 2/sqrt(5)   or 2sqrt(1/5)

Step-by-step explanation:

using 1+cot^2(x) = csc^2(x)

we have, taking reciprocal on both sides,

sin(x) = 1/sqrt(1+cot^2(x)

= 1/sqrt(1+(-1/2)^2)

= 1/sqrt(5/4)

= 2/sqrt(5)   or 2sqrt(1/5)

Since angle x is in the second quadrant, sin(x) is positive.

Answer:

0.0414 with an upper tailed test

Step-by-step explanation:

Claim: P1P1 = P2P2

The above is a null hypothesis

The alternative hypothesis for a two-tailed test would be:

P1P1 \=/ P2P2

Where "\=/" represents "not equal to".

Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04

With an upper tailed test, the

2 × [probability that z>2.04] = 2[0.0207] = 0.0414

This is the p-value for the test statistic.

Focus is on the alternative hypothesis.

Answer:

Where is the table

Step-by-step explanation:

I cant answer without it

Answer:

Step-by-step explanation:

Given the half like of a material to be 8.3 hours and the amount of iron-52 left after t hours is modeled by the equation [tex]A(t) = A_0 a^{t}[/tex], we can get A(t) as shown;

At t = 8.3 hours, A(8.3) = 1/2

Initially at t = 0; A(0) = 1

Substituting this values into the function we will have;

[tex]\frac{1}{2} = 1 * a^{8.3}\\\\Taking \ the \ log \ of\ both \ sides;\\\\log(\frac{1}{2} ) = log(a^{8.3} )\\\\log(\frac{1}{2} ) = 8.3 log(a)\\\\\fr-0.30103 = 8.3 log(a)\\\Dividing\ both\ sides\ by \ 8.3\\\\\frac{-0.30103}{8.3} = log(a)\\\\log(a) = - 0.03627\\\\a =10^{-0.03627} \\\\a = 0.919878 (to\ 6dp)[/tex]

Answer:

[tex]\boxed{(1, -3)}[/tex]

Step-by-step explanation:

[tex]y+3=2 (x-1)[/tex]

Put equation in slope-intercept form.

[tex]y=mx+b[/tex]

[tex]y=2(x-1)-3[/tex]

[tex]y=2x-2-3[/tex]

[tex]y=2x-5[/tex]

Let x = 1

[tex]y=2(1)-5[/tex]

[tex]y=2-5[/tex]

[tex]y=-3[/tex]

The point (1, -3) lies on the line.

A - No

B - No

C - Yes

D - Yes

.

C and D are alternate exterior angles

Answer:

Step-by-step explanation:

3x+4y = 17 _______ equation 1

-4x -7y= -18 _______ equation 2

muliply by 4 in equation 1

12x + 16y = 68 ______ equation 3

multiply by 3 in equation 2

-12x - 21y = -54 ________ equation 4

add equation 3 & 4

- 5y = 14

y = - 14/5

substitute y in equation 1

3x + 4 (-14/5) =17

3x = 17+ (56/5)

3x =( 85 + 56) / 5

3x = 141/5

x = 47/5

hence (a,b) = (47/5, -14/5)

Answer:

Henry had the best record for the number of shots made

Step-by-step explanation:

From the given information.

Four friends are on a basketball team.

Henry

Allison

Arthur

Trevor

We are being told that Henry made 0.45  of his shots out of all his attempts

Allison made Arthur made of her shots  of his shots.

i,e Arthur did the work for Allison , so out of Arthur's shot , we have to  figured out Allison shots,

Trevor missed 58% of his shots.

i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot

Then the attempts Trevor made is :

= 1 - 0.58

= 0.42

SO , Trevor made 0.42 shots out of all his attempt

N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.

Therefore; we will focus on only Henry and Trevor shots

So ;

Henry made 0.45  of his shots

Trevor made 0.42 out of his shots

We can thereby conclude that :

Henry had the best record for the number of shots made

Answer:

0, 22, 44, 66

Step-by-step explanation:

Given the equation for the model, [tex] d = 11t [/tex] , you can complete the table above by simply plugging in each value of "t" has given in the table to solve for "d".

*When t (seconds) = 0, distance (feet) would be:

[tex] d = 11(0) [/tex]

[tex] d = 0 [/tex]

*When t (seconds) = 2, distance (feet) would be:

[tex] d = 11(2) [/tex]

[tex] d = 22 [/tex]

*When t (seconds) = 4, distance (feet) would be:

[tex] d = 11(4) [/tex]

[tex] d = 44 [/tex]

*When t (seconds) = 6, distance (feet) would be:

[tex] d = 11(6) [/tex]

[tex] d = 66 [/tex]

Answer:

B. edge 2021

B. is correct for the next one too.

Step-by-step explanation:

B. is the correct answer for the first one
B. is also the correct answer for the second one

Answer:

[tex] Area = 316.6 mi^2 [/tex]

Step-by-step explanation:

Given:

Angle of arc = 300°

Radius of circle = 11 miles

Take π as 3.14

Required:

Area of the major sector

Solution:

Area of sector is given as: angle of arc/360*πr²

Thus,

[tex] Area = \frac{300}{360}*3.14*11^2 [/tex]

[tex] Area = 316.616667 [/tex]

[tex] Area = 316.6 mi^2 [/tex] (rounded to the nearest tenth)

Answer:

Richard will pay $30.

Step-by-step explanation:

Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!

Answer:

2432902008176640000 programs are possible using 20 distinct (different) songs.

Step-by-step explanation:

There are 20 choices for the first song, 19 choices for the second, ...1 song for the last for a total of

N = 20*19*18*...*3*2*1 = 20!= 2432902008176640000  programs

The number 20! is the number of permutations for 20 distinct objects put in order.

20! is pronounced as 20 factorial.

Example: factorial of 5 is 5*4*3*2*1 = 120

Answer:

20*19*18*17*16=1 860 480 different programs

Step-by-step explanation:

So there are 20 pieces total and each of them can be first.

Each of residual 19 can be the second

Each of residual of 18 can be the third

Each of residual 17 can be the fourth

Each of residual 16  can be the fifth

Total amont of possible different programs ( the order of the pieces matters)

is :  20*19*18*17*16=1 860 480 different programs