Two lines. C and D. are represented by the equations given below:
Line C. y = x + 12
Line D. y = 3X + 2
Which of the following shows the solution to the system of equations and explains why?

For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.

As given in the question,

Two triangles ΔTRS and ΔQRP,

It is given that :

Line segment SR ≅ Line segment PR

Line segment SP bisects Line segment TQ

⇒ line segment TR ≅ line segment RQ

∠TRS ≅ ∠PRQ ( by vertically opposite angle )

By Side angle side theorem we have ,

ΔTRS ≅ ΔPRQ

Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.

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Answer:333

Step-by-step explanation:

Since this is a scalene triangle, two sides will equal the same, meaning two angles will equal the same. So 70 has an equal on the other side, meaning 70+70=140, and x will equal the remainder, meaning x=40.

Hope that helps.

Step-by-step explanation:

2.

it is a square !

what do we know about squares ?

first of all, they are a special rectangle, where length = width, and therefore all 4 sides are equally long.

and secondly, as they are a form of rectangle, every inner angle is 90°.

so,

6x - 12 = 90

6x = 102

x = 102/6 = 17

therefore,

CD = x + 15 = 17 + 15 = 32

many greetings to your teacher, CD is a side, a length, and NOT an angle, so it is NOT measured in degrees (°).

since it is a square and all sides are equally long,

AD = CD = 32

3.

it is a rectangle.

so, it has 4 sides consisting of 2 pairs of equally long sides. that means there are 2 equally long side we call length, and 2 equally long sides we call width.

these equally long sides are always opposite of each other.

that means

2x - 52 = x - 2

x - 52 = -2

x = -2 + 52 = 50

The different ways that are there for the students to be ordered in the list so that Ed is higher on the list than Ned is 19,958,400

In the order, if Ned comes first on the list then Ed will not be on the list before Ned. (remember for Ed to be higher than Ned on the list, it should come after Ned on the list).

So if Ned is first on the list, then all the remaining (including Ed) can occur anywhere in the remaining list. Hence the total permutations will be 10!

Ned's corresponding choices: 1 109 8 7 6 5 4 3 -2 1

If Ned comes in the second position, then Ed can't come in the first position. Hence in the first position, there are only 9 choices.

*(excluding Ed) Ned * corresponding choices:

= 9*9!

*(including Ed (including Ed) Ned corresponding choices: *k

= 9*8*8!

Total combinations will be:

10! + 9*9! + 9*8*8! + 9*8*7*7! + 9*8*7*6*6! + 9*8*7*6*5*5! + 9*8*7*6*5*4*4! + 9*8*7*6*5*4*3*3! +9*8*7*6*5*4*3*2*2! + 9*8*7*6*5*4*3*2*1*1! .

= 19,958,400

We can directly compute it. Since there will be a total of 11! combinations in which 11!/2 times Ed comes after Ned and 11!/2 times Ed comes before Ned.

and 11!/2 = 39,916,800/2 = 19,958,400

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Using the angle of elevation, the height of the tower is 9.2 ft.

He is  5 ft tall. The angle of elevation of the tower is 23 degree.

He is standing 10 feet away from the base of the tower.

The height of the tower can be found as follows;

The situation forms a right angle triangle.

The height of the tower can be found using trigonometric ratios.

Hence,

tan ∅ = opposite / adjacent

where

tan 23° = h / 10

cross multiply

h = 10 tan 23°

h = 4.2447481621

h = 4.2 ft

Therefore,

height of the tower = 4.2 + 5 = 9.2 ft

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Answer:

x=7

Step-by-step explanation:

2(2x - 7) = 14

Solve for x

Divide each side by 2

2/2(2x - 7) = 14/2

2x-7 = 7

Add 7 to each side

2x-7+7 = 7+7

2x = 14

Divide each side by 2

2x/2 = 14/2

x = 7

Answer:

b) x = 7

Step-by-step explanation:

Given equation,

→ 2(2x - 7) = 14

Now the value of x will be,

→ 2(2x - 7) = 14

→ 4x - 14 = 14

→ 4x = 14 + 14

→ x = 28/4

→ [ x = 7 ]

Hence, the value of x is 7.

26.2% is the total percent of discount offered by the merchant.

Let us assume that each item is $100.

As it is given that 18% is off, we have an amount after off is:

Amount after 18% off = 100 × (100 - 18)/ 100

                           = 100 × 0.82

                           = 82

Next, there is 10% off

So the amount become = 82 ×( 100 - 10) / 100

                                        = 82 ×0.9

                                        = 73.8

So the final price of an item is $73.8

The discount = (100 - 73.8) / 100

                      = 26.2%

Therefore the total percent of discount is 26.2%.

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Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

The mean of this sample distribution is

Mean = μₓ = np = 0.61 × 1600 = 976

But the sample mean according to the population mean should have been

Sample mean = population mean = nP

= 0.56 × 1600 = 896.

To find the interval of values where the sample proportion should fall 68%, 95%, and almost all of the time, we obtain confidence intervals for those confidence levels. Because, that's basically what the definition of the confidence interval is; an interval where the true value can be obtained to a certain level. of confidence.

We will be doing the calculations in sample proportions,

We will find the confidence interval for the confidence levels of 68%, 95% and almost all of the time (99.7%).

Basically the empirical rule of 68-95-99.7 for standard deviations 1, 2, and 3 from the mean.

Confidence interval = (Sample mean) ± (Margin of error)

Sample Mean = population mean = 0.56

The margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Standard deviation of the distribution of sample means = [tex]\sqrt{[p(1-p)/n]}[/tex] =

[tex]\sqrt{[(0.56\times0.44)/1600]}[/tex] = 0.0124

The critical value for 68% confidence interval = 0.999 (from the z-tables)

The critical value for 95% confidence interval = 1.960 (also from the z-tables)

Critical values for the 99.7% confidence interval = 3.000 (also from the z-tables)

Confidence interval for 68% confidence level

= 0.56 ± (0.999 × 0.0124)

= 0.56 ± 0.0124

= (0.5476, 0.5724)

Confidence interval for 95% confidence level

= 0.56 ± (1.960 × 0.0124)

= 0.56 ± 0.0243

= (0.5357, 0.5843)

Confidence interval for 99.7% confidence level

= 0.56 ± (3.000 × 0.0124)

= 0.56 ± 0.0372

= (0.5228, 0.5972)

Therefore,

Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

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The graph that shows the x- and y-intercepts to graph the equation. y = 1/3x + 1 is added as an attachment

From the question, we have the following equation that can be used in our computation:

y = 1/3x + 1

We set x = 0 to determine the y-intercept

So, we have

y = 1/3 x 0 + 1

Evaluate

y = 1

So, we have

(x, y) = (0, 1)

We set y = 0 to determine the x-intercept

So, we have

0 = 1/3x + 1

Evaluate

1/3x = -1

This gives

x = -3

So, we have

(x, y) = (-3, 0)

So, the intercepts are (0, 1) and (-3, 0)

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Step-by-step explanation:

in order to be able to decide each case we need the slopes of all involved lines.

and that means we need to bring all of the equating into a "y = ..." form, because then the slope is always the factor of x.

parallel lines have the same slope.

the slopes of perpendicular lines (intercept at a right angle) have the y/x ratio turned upside-down and a flipped sign : -x/y.

"neither" is everything else.

our reference line

x + 2y = 6

2y = -x + 6

y = -1/2 x + 3

so, the reference slope is -1/2.

y = -1/2 x - 5 is parallel (same slope).

-2x + y = -4

y = 2x - 4 perpendicular (2/1 vs. -1/2)

-x + 2y = 2

2y = x + 2

y = 1/2 x + 1 neither

x + 2y = -2 parallel (as the structure except for the constant part is the same as our reference line).

2y = -x - 2

y = -1/2 x - 1

Answer:

Step-by-step explanation:

You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)

Answer:

D) n<-4

Step-by-step explanation:

The required equation for the given condition is 50x + 100y = 1000.

What is an algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

Given, the charge for every birthday party =$50

number of birthday parties = x

So, the total charge for birthday parties = 50x

the charge for every wedding  = $100

the number of weddings = y

So, the total charge for the wedding = 100y

Then,

Total amount achieve = $1000

or, 50x + 100y = 1000

Hence, the required equation is 50x + 100y = 1000.

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The value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

According to the question,

We have the following expressions:

f(x) = -5x+9/2

Now, we will find the all the values of f(x) by replacing x with the given digits:

f(4) = -5*4+4.5

f(4) = -20+4.5

f(4) = -15.5

The value of f(1/4):

f(1/4) = -5/4+4.5

f(1/4) = -1.25+4.5

f(1/4) = 1.375

The value of x when f(x) = 2:

-5x+4.5 = 2

-5x = 2-4.5

-5x = -2.5

x = 2.5/5

x = 0.5

g(x) = 1.5[tex]x^{2}[/tex]-8

Now, we will find all the values of g(x) by replacing x with the given digits.

The value of g(-2):

g(-2) = 1.5(-2)(-2)-8

g(-2) = 6-8

g(-2) = -2

The value of g(2.5):

g(2.5) = 1.5*2.5*2.5-8

g(2.5) = 9.375-8

g(2.5) = 1.375

The value of x when g(x) = 16:

1.5[tex]x^{2}[/tex]-8 = 16

1.5[tex]x^{2}[/tex] = 16+8

1.5[tex]x^{2}[/tex] = 24

[tex]x^{2}[/tex] = 24/1.5

[tex]x^{2}[/tex] = 16

x = +4 and -4

Hence, the value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

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Answer: 30[tex]\pi \\[/tex] or 94.247

Step-by-step explanation:

Circumference=2[tex]\pi[/tex]r

2·[tex]\pi[/tex]·15=30[tex]\pi[/tex]=94.247

Answer:

94.2in.

Step-by-step explanation:

The formula for circumference is 2radius x π

π≈3.14

So we can say:

30in.x3.14=circumference

30x3.14=94.2

94.2in=circumference

(i.e. I don't know what you mean by using T.)

The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.

The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:

Vertex = (h, k).

Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.

Thus:

(h, k) = (3, 5)

a = 1 (this is because the graph opens upward)

To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:

y = 1|x - 3| + 5

The equation is, y = 1|x - 3| + 5.

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Using the theories of probability, we got that 0.0260 is the probability  of choosing 4 spades and 2 cards that are not spades and 0.1202 is the probability of choosing 2 red face cards  from a well shuffled deck of 52 playing cards..

We know a deck of 52 playing cards has  13 hearts, 13 clubs, 13 spades,

13 diamonds.

∴  The possibility that she chooses 4 spades and 2 cards that are not spades is,

= ([tex]^1^3C_4[/tex]×[tex]^3^9C_2[/tex])/([tex]^5^2C_6[/tex])

As from the 13 spade cards 4 are chosen, so now we are left with (52 - 4) = 48

and 2 cards that are not spades means out of 9 spades that are left after choosing 4 that is 9 will also be subtracted (48 - 9) = 39.

= (13!/(13 - 4)!×4!)×(39!/(39 - 2)!×2!)/52!/(52 - 6)!×6!

= (13!/9!×4!)×(39!/37!×2!)/(52!/46!×6!)

= (13×12×11×10)/(4×3×2)×(39×38)/2)/(52×51×50×49×48×47)/(6×5×4×3×2)

= (529815)/(20358520)

= 0.026.

Similarly, the probability of choosing 2 red face card is given by

=([tex]^6C_2[/tex]×[tex]^4^6C_4[/tex])/([tex]^5^2C_6[/tex])

=[ [(6! / (2!.4!)] × [46! / (4!.42!)] ]/ [52! / (6!.46!)]

=(15×163185)/20358520

=0.1202.

Hence, the probability of choosing 4 spades and 2 cards by carrie that are not spades is 0.026 and the probability of choosing 2 red face cards by carrie is 0.1202.

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Answer:

For the first equation, it is "True for one value of x."

For the second equation, it is "True for no value of x."

For the third equation, it is "True for all values of x."

Step-by-step explanation:

Just solve the equation and check the numbers:

If both numbers are the same, it is "true for all values of x"

If there is a variable and a number, it is "true for one value of x"

If there are two numbers and they are different, it is "true for no values of x"

Hope this helps!

Please give brainliest

We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .

The equations are ,

solve this equation for x ,

[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]

[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]

[tex]\longrightarrow 7.5x =11\\[/tex]

[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]

Hence the equation is true for one value of x .

solve out for x ,

[tex]\longrightarrow 9x +27=9x-12\\ [/tex]

[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]

[tex]\longrightarrow 0 = -39[/tex]

This can never to true , so the equation is true for no values of x .

solve out for x ,

[tex]\longrightarrow 8x+12=12+8x \\[/tex]

[tex]\longrightarrow 12-12=8x-8x\\[/tex]

[tex]\longrightarrow 0=0 [/tex]

Hence this equation is true for all values of x .

And we are done!

[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]

Answer:

A = 13 B = 3 C = -7 D = -12

Step-by-step explanation:

Just insert the x values for a, b, c, and d. for example if we were to find a.

The x value for a is -3 so we would put -3 in place of x in the equation.

-5(-3) - 2

Remember: Two negative numbers multiplied with each other equal a positive.

15 - 2 = 13

The slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a equation of a straight line as -

4x - 1 = 3y + 5

We have the equation as follows -

4x - 1 = 3y + 5

Rearranging the equation -

3y = 4x - 1 - 5

3y = 4x - 6

y = (4/3)x - 2

Refer to the graph attached.

The slope of the line is [m] = 4/3

The [y] intercept is at [c] = -2

Therefore, the slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

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In the given equation, the value of n is (p - k - m).

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, p = n + k + m

Solving for n, we get

n = p - k - m

Hence, In the given equation, n = p - k - m

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The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.

Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.

Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25

So, equation for the cost,

Cost(c) = $7.25P - $3.5

Then, the price of 5 pound of almond = $7.25×5 - $3.5

⇒ $36.25 - $3.5 = $32.75

Thus, the price of 5 pounds of almond is $32.75.

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The image of (5, 8) after a reflection over the line y = - x is (-5, -8 ).

To see the graph.

Given,

In the question:

What is the image of (5,8) after the reflection over the line y= -x?

Now, According to the question:

The image of (-5,8) after a reflection over the y-axis

When a point is reflected over y axis, then the value of x changes to -x.

the value of y remains the same.

But, It is given that  the reflection over the line y= -x

Hence, The image of (5, 8) after a reflection over the line y = - x is

(-5, -8 ).

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The monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1

What is compound interest?

When you earn interest on both the money you've saved and the interest you've earned, this is known as compound interest.

what is the monthly payment?

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.

Here,

We know that the monthly payment is given as

MP = [Pr(1 + r)¹²ⁿ] / [(1 + r)¹²ⁿ - 1]

Where MP monthly payment, P is the initial amount, r is the rate of interest, and n is the number of years.

we have

r = 0.0115

P = $150,000

n = 25 * 12

n = 300

Then we have

MP = $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1

Hence, the monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1

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Answer:

70,000

Step-by-step explanation:

Round up if the next digit is higher than or equal to 5.

edit: accidentally answered twice

Answer:

70,000

Step-by-step explanation:

Round up if the next digit is higher than or equal to 5.

A graph of the given system of linear equations is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would rewrite the first equation in standard form as follows:

y - 2x = 0

Adding 2x to both sides of the equation, we have the following:

y - 2x + 2x = 0 + 2x

y = 0 + 2x

y = 2x

By critically observing the graph (see attachment), a solution to the given system of linear equations are 2.5 and 5.

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Answer:  y  =  160/q   -a

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

The answer is 15ab

Step-by-step explanation:

Since (x + y)² = (x + y)(x + y) = x² + 2xy + y²

(3a + 2.5b)²

9a² + 2(3a)(2.5b) + 6.25b²

9a² + 15ab + 6.25b²

Hence, (3a + 2.5b)² = 9a² + 6.25b² + 15ab

Answer:

15 minutes

Step-by-step explanation:

The 3/4 of an hour is,

→ 60 × (3/4)

→ 180/4 = 45

Now required time spend on rope is,

→ 45 × (1/3)

→ 45/3 = 15 minutes

Hence, he had spend 15 minutes.

The algebraic expression of the mentioned statement will be 5x-3.

According to the question,

An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.

Let the unknown number be taken as x.

If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,

x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).

For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).

Hence, algebraically the final statement will be 5x -3.

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