What segment is the projection of ST on QT?

UT
QU
QT

Answer: -3/2x + 7/2

Step-by-step explanation:

for parallel lines; m₁ = m₂

the gradient of the given line is -3/2

2y= -3x + 4

y = -3/2x + 2

therefore the gradient of the parallel line is -3/2

hence the equation is y-y₁ = m(x-x₁)

y-5 = -3/2(x+1)

y - 5 =-3/2x - 3/2

y = -3/2x -3/2 + 5

y = -3/2x + 7/2

Answer:

1. x=2, y=3

2. n=7, m=-6.8

3. x=6, y=3

4. q=-2, p=-1

5. c=2, d=0

Step-by-step explanation:

4x + 3y = 17

5x – 3y = 1

first make it so either x or y can cancel out in both equations, then combine the equations, giving you 9x=18. solve for x, x=2. substitute 2 for x in either equation, 4(2) + 3y = 17. solve for y, 8+3y=17, 3y=9, y=3

–5m + 6n = –8

–5m + 8n = 6

first make it so either m or n can cancel out in both equations, multiply –5m + 6n = –8 by -1, 5m - 6n = 8, then combine the equations, giving you 2n=14. solve for n, n=7. substitute 7 for n in either equation, 5m - 6(7) = 8. solve for m, 5m - 42 = 8, 5m = -34, m = -6.8

2x – 7y = –9

6x + 7y = 57

first make it so either x or y can cancel out in both equations, then combine the equations, giving you 8x=48. solve for x, x=6. substitute 6 for x in either equation, 2(6) – 7y = –9. solve for y, 12 – 7y = –9, –7y = –21, y = 3

5p – 4q = 3

–5p – 4q = 13

first make it so either p or q can cancel out in both equations, then combine the equations, giving you -8q=16. solve for q, q=-2. substitute -2 for q in either equation, 5p – 4(-2) = 3. solve for p, 5p + 8 = 3, 5p = -5, p = -1

6c + d = 12

c – d = 2

first make it so either c or d can cancel out in both equations, then combine the equations, giving you 7c=14. solve for c, c=2. substitute 2 for c in either equation, 6(2) + d = 12. solve for d, 12 + d = 12, d = 0

[EDIT] question 2 is impossible.

D.(18.8) is the answer because the explanatory variable is the x-axis while the response variable is the y-axis.

Answer:  The correct option is (D) (18, 8).

Step-by-step explanation:  Given that the value of an explanatory variable is 18, while the corresponding value of the response variable is 8.

We are to find the co-ordinates of this data plot when plotted on a scatter plot.

Let y = f(x) be a function, where x is the independent variable and y is the dependent variable.

On a scatter plot, we plot any point satisfying this function as (x, y).

Explanatory variable = independent variable, x = 18

and

Response variable = dependent variable, y= 8

Therefore, the required coordinates of this data point when plotted on a scatter plot are (18, 8)

Option (D) is CORRECT.

ANSWER

$16,384

EXPLANATION

From the question we have that,

Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.

This forms a geometric sequence,

[tex]1,2,4,...[/tex]

The first term of this sequence is

[tex]a = 1[/tex]

The common ratio is

[tex]r = \frac{2}{1} = \frac{4}{2} = 2[/tex]

The general term of a geometric sequence is given by the formula:

[tex]f(n) = a {r}^{n - 1} [/tex]

To find the 15th term, we plug in a=1, r=2 and n=15.

[tex]f(15) = 1 {(2)}^{15 - 1} [/tex]

[tex]f(15) = {2}^{14} [/tex]

[tex]f(15) = 16384[/tex]

The amount he will save on the 15th day is $16,384

Answer:

$6,524.96

Step-by-step explanation:

Take the commission total which is $1631.24 divide it by 25% or .25.

$1,631.24 ÷ .25=$6,524.96 cost of the used car

Check your answer by taking your answer and multiple it by 25%.

$6,524.96 (cost of the car) × .25 =$1,631.24 commission

Answer:

$6,524.96

Step-by-step explanation:

Step One: Because the amount she is paid is the 25% commission, multiply the 1,631.24 by 4 ( 4 because she is paid 1 out of 4 parts of the total selling price)

Step Two: the answer is 6,524.96

Answer:

The quotient is [tex]2x^2-5x+2[/tex]

Step-by-step explanation:

We want to simplify:

[tex]\frac{6x^4-15x^3+10x^2-10x+4}{3x^2+2}[/tex]

We factor the numerator to get:

[tex]\frac{(x-2)(2x-1)(3x^2+2)}{3x^2+2}[/tex]

We cancel out the common factors to get:

[tex](x-2)(2x-1)[/tex]

Therefore the quotient is [tex]2x^2-5x+2[/tex]

-40*.15 + 150*(1-.15)= 121.50

Given the probabilities of sunny and rainy days and the respective profits, the Sudsy car wash's expected net profit per day, considering the rain probability, is $121.5.

The subject of the question is about Expected Value, a concept in Probability Theory. Considering the Sudsy car wash's situation, we know that it loses $40 on rainy days and gains $150 on sunny days. The probability of having a rainy day is given as 15%, which means the probability of having a sunny day is 85% (100% - 15%).

The expected value of the net profit can be calculated by the formula for Expected Value: E[X] = ∑[x*P(X=x)]. In the context of this problem, we can write out the expected value E[N] of the net profit N as E[N] = (-$40 * 0.15) + ($150 * 0.85) = -$6 + $127.5 = $121.5. So, it is expected that the Sudsy car wash will have a net profit of $121.5 per day, on average.

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Answer:

slope = -0.5

Step-by-step explanation:

Answer:

slope = change in y / change in x

slope = 0 -3.5 / 7 -0

slope = -3.5 / 7

slope = -.5

Step-by-step explanation:

Answer:

  A. product 1

Step-by-step explanation:

An exponential function (with a base larger than 1) will eventually exceed the value of any polynomial function. Product 1 has a price described by an exponential function, so its price will exceed all others. (One only need to compute the values for x=4 to see this.)

_____

The attachment extends the table and plots the functions up to the point where Product 1 exceeds the others.

Answer:

w = 54°

Step-by-step explanation:

w is the inscribed angle subtended on the same arc with measure of 108°

w is half the size of the central angle, that is

w = 0.5 × 108° = 54°

Answer:

[tex][g\circ f](x)=-2[/tex]

Step-by-step explanation:

By the definition

[tex][g\circ f](x)=g(f(x))[/tex]

You are given

[tex]f(x)=2x-1\\ \\g(x)=-2[/tex]

So,

[tex][g\circ f](x)=g(f(x))=g(2x-1)=-2[/tex]

Answer:

Step-by-step explanation:

No, you're not an idiot.  You are just misunderstanding pi.  Pi is an irrational number, meaning it goes on forever.  Literally, forever, with no end.  Some weird guy actually memorized the first 100,000 places of it or something crazy like that.  Anyway, if you use 3.14 you have rounded so incredibly, that you lose a lot of your precision.  Your calculator uses the first 9 places of the decimal or something like that.

Answer:

  27,409.308

Step-by-step explanation:

Compute the given sum. If you're really stuck, your calculator can help you.

Answer:

False

Step-by-step explanation:

Let's list all the odd numbers less than 15.

13, 11, 9, 7, 5, 3, 1

Prime numbers are numbers that can only be multiplied by 1 and themselves. But, we can see, that 9 can be multiplied by 3 and 3, making it a not-prime number (sorry I don't remember the exact name for that, I'm blanking out).

The number 9 makes that statement false.

Hope I helped! ouo.

~Potato.

Copyright Potato 2019.

Answer:

False

Step-by-step explanation:

Consider the odd numbers less than 15

1, 3, 5, 7, 9, 11, 13

A prime number has only 2 factors, namely 1 and itself

9 has factors : 1, 3, 9 ← not Prime

The statement is therefore False

Answer:

y = 13

Step-by-step explanation:

If it's a parallelogram then its consecutive angles are supplementary (add up to 180°).

6x - 12 + 132 - x = 180°,

5x + 120 = 180

5x = 60

 x = 12

6x - 12 = 6(12) - 12 = 72 - 12 = 60

Parallelogram, opposite angles are equal

so

6y + 18 = 6x - 12

6y - 18 = 60

6y = 78

  y = 13

ANSWER

[tex]4(x + 6)(x - 2)[/tex]

EXPLANATION

The given rational expression is:

[tex] \frac{1}{ {x}^{2} + 4x - 12} + \frac{3x}{4x - 8} [/tex]

We can factor the denominators to obtain:

[tex] \frac{1}{(x + 6)(x - 2) } + \frac{1}{4(x - 2)} [/tex]

The common denominator is least common multiples of the denominators.

The common denominator is of the given rational expression is

[tex]4(x + 6)(x - 2)[/tex]

Answer:

C

Step-by-step explanation:

As with most problems of this type, you need to draw an actual line that has approximately the same number of data points on each side of it.  If you'll do that you'll see that this line crosses the y-axis at approx. y = 4.  Only Answer C has that y-intercept.

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

The opposite side x is 7

Step-by-step explanation:

Step one

From the given expression in the picture

We can estimate x by applying the

SOH CAH TOA rule on the triangle

Since we have one side and one angle given

step two

From the given picture we have

We have θ and adjacent side given

Hence we need to apply

tan θ= opposite/adjacent =

Tan 35°=x/10

Step three

From 4 figure table or calculator

tan 35° is 0.7

0.7=x/10

x=0.7*10

x= 7

Answer:

(a + b, c )

Step-by-step explanation:

Using the midpoint formula

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[ [tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex] ]

let (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(2a+2b, 2c), then

midpoint = [ [tex]\frac{0+2a+2b}{2}[/tex], [tex]\frac{2c}{2}[/tex] ]

               = [tex]\frac{2(a+b)}{2}[/tex], c ] = (a + b, c )

Answer:

216

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

The probability that a football player has suffered more than 3 broken bones is equal to the probability they suffered 4 or 5.

P(x>3) = P(4 or 5)

P(x>3) = P(4) + P(5)

P(x>3) = 0.10 + 0.15

P(x>3) = 0.25

Answer:

1,352.32

Step-by-step explanation:

If you take 7.6 and multiply it to 16,412.05 (.076)(16,412.05), you get 1,247.32. You then add the overhead cost of 105 to get 1352.32. (Apex verified too)

The drivers insurance premium is:

                $ 1352.3158

The probability of a driver getting into an accident is 7.6%.

The average cost of an accident is $16,412.05.

This means that the expected amount that will be paid to each of the driver by the company on accident will be:  0.076×16412.05

                                                       = $ 1247.3158

Also, the overhead cost for an e company per insured driver is $105.

This means that the insurance premium of driver is:

       =   105+1247.3158

     =    $ 1352.3158

1. Same length.

2.vertically opposite angle.

3.BAC =BDE

4.AC = DE

Hope this helps you ___!!❤

Sorry this is a little late, but I hope it'll still help someone in the near future.

The next larger scale size is 2.827

Hope this helps :)

Answer:

Next larger scale size = 2.827

Step-by-step explanation:

For a certain font scale factor is 1.414 and one of the scale size is 1.999.

so we have to find the next larger scale size.

Since scale factor will be defined as the ratio of larger scale size of the font and smaller font size.

[tex]\text{Scale factor}=\frac{\text{Larger font size}}{\text{smaller font size}}[/tex]

1.414 = [tex]\frac{\text{Larger font size}}{1.999}[/tex]

Larger font size = 1.414 × 1.999 = 2.8266 ≈ 2.827

Next larger scale size = 2.827

ANSWER

[tex]15 {x}^{2} + 22x - 5[/tex]

EXPLANATION

It was given that, the length of the rectangular building is

[tex](3x + 5) \: meters[/tex]

and the width of the is

[tex](5x - 1) \: meters[/tex]

The area of a rectangular building is calculated using the formula for finding the area of a rectangle.

[tex]A = l \times w[/tex]

Since the dimensions are given in terms of x, the area is also a function of x,

[tex]A(x) = (3x +5 )(5x - 1)[/tex]

We expand to get,

[tex]A(x) = 3x(5x - 1) + 5(5x - 1)[/tex]

[tex]A(x) = 15 {x}^{2} - 3x + 25x - 5[/tex]

[tex]A(x) = 15 {x}^{2} + 22x - 5[/tex]

meters square

Answer:

D. 15x^2 + 22x -5

Step-by-step explanation:

I just took the test

Answer:

D. 28 feet

Step-by-step explanation:

a²+b²=c²

45²+b²=53²

2025+b²=2809

b²=784

[tex]\sqrt{784}[/tex]=[tex]\sqrt{b}[/tex]

b=28

Answer:

D. 28 feet

Step-by-step explanation:

Answer:  The correct option is

(A) at the most 10.

Step-by-step explanation:  Given that Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10 on food.

Also, she wishes to buy some books and each book costs $3.

We are to solve the inequality to find the number of number of books that she can buy.

Let the number of books that Mary can buy be n.

Then, according to the given information, we have

[tex]20+10+n\times3\leq 60\\\\\Rightarrow 30+3n\leq 60\\\\\Rightarrow 3n\leq 60-30\\\\\Rightarrow 3n\leq 30\\\\\Rightarrow n\leq \dfrac{30}{3}\\\\\Rightarrow n\leq 10.[/tex]

Thus, Mary can buy at most 10 books.

Option (A) is CORRECT.

Answer:

d

Step-by-step explanation:

30% of 50 is 15 because 30 % means 30out of 100

and if you half 100 you also half 30

Valentina, with a 30% probability, can expect to draw a blue marble 15 times out of 50 draws. This is calculated by multiplying the total number of draws by the probability of drawing a blue marble.

The question revolves around the concept of probability. The probability of an event is the measure of the likelihood that the event will occur. In Valentina's case, she has a 30% chance of drawing a blue marble. Therefore, if she were to draw a marble 50 times, we would expect her to draw a blue marble 30% of those 50 times. Probability is often expressed as a fraction or decimal, and in this case, 30% translates to 0.30 in decimal form.

To calculate how many times we can expect Valentina to draw a blue marble, we multiply the total number of draws (50) by the probability of drawing a blue marble (0.30).

So, 0.30 * 50 = 15.

Therefore, Valentina can expect to draw a blue marble 15 times out of 50 draws.

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Answer:

Step-by-step explanation:

Let s represent the length of the shortest side. Then the other two sides are ...

The perimeter is the sum of the lengths of the three sides, so is ...

  56 ft = s + (s+6) + (2s-6) = 4s . . . . collect terms

  14 ft = s . . . . . . . divide by the coefficient of s

The shortest side is 14 ft; the second side is 20 ft; the third side is 22 ft.

Final answer:

Using the given information about the sides of the triangular deck and its perimeter, we set up an equation to solve for the shortest side and then used that to find the lengths of the other two sides. The three sides of the triangular deck are 14 feet, 20 feet, and 22 feet.

Explanation:

To solve the problem, we need to set up an equation based on the given information. Let's define the shortest side of the triangle as x feet. According to the problem, the second side is x + 6 feet, and the third side is 2x - 6 feet. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 56 feet.

We can set up the following equation:

x + (x + 6) + (2x - 6) = 56

Combining like terms, we get:

4x = 56

Divide both sides by 4:

x = 14

Now we can find the lengths of the sides:

The shortest side: 14 feet

The second side: 14 + 6 = 20 feet

The third side: 2(14) - 6 = 22 feet