To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?



First equation:

Second equation:

The first equation should be multiplied by 3 and the second equation by -5.
The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 7 and the second equation by -6.
The first equation should be multiplied by 7 and the second equation by 6.

The equation written when r is the subject is:

[tex]\displaystyle{r=\dfrac{5p}{m}-n}[/tex]

To make the term r as the subject of equation means to isolate r-term. In order to do that, we will apply properties of equality.

Properties of equality are properties regarding equations/equality where states that when either sides are done by something (addition, subtraction, multiplication, division, etc.) then the other sides will also act the same as the acted side.

Example

Suppose we are given an equation of x = y. In this case, x and y are equal to each other. If x = 1 then y = 1. If we decide to add +2 to x we’d have to add it to y too so the result will be x + 2 = y + 2.

Same also applies to other equations!

Isolating r-term, first, we will apply division property where we divide both sides by m-term:

[tex]\displaystyle{\dfrac{m(n+r)}{m}=\dfrac{5p}{m}}\\\\\displaystyle{n+r=\dfrac{5p}{m}}[/tex]

Next, we use subtraction property to subtract both sides by n:

[tex]\displaystyle{n+r-n=\dfrac{5p}{m}-n}\\\\\displaystyle{r=\dfrac{5p}{m}-n}[/tex]

Please let me know if you have any questions!

Answer:

x = 11,2 inchs

Step-by-step explanation:

I infer that the units are in inches.

8-3 = 5

Then:

By the Pythagorean Teorem:

x² = 10² + 5²

x² = 100 + 25

x² = 125

√x² = √125

x = 11.18

to the nearest tenth:

x = 11.2 inches

The measure that would most correctly answer this question is standard deviation.

What is standard deviation?

The standard deviation is measure of how spread out data from mean.

Step-by-step explanation:

Average age of respondents in a survey is [tex]49[/tex] years. Researcher interested in finding out if most respondents are close to [tex]49[/tex] years or not.

Hence here measures of dispersion fact will be used.

Measures of dispersion are range and standard deviation.

Range is nothing but the difference between maximum and minimum values of the data.

Standard deviation gives proper idea about how far the data values are scattered from the mean point [tex]49[/tex] years.

Therefore the correct option is standard deviation.

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Answer:

Step-by-step explanation:

solve for x

2x+14=-21-5

2x+14=-26

subtract 14 from both sides

2x+(14-14)=-14-26

2x=-14-26

2x=-40

divide both sides of 2x = -40 by 2

[tex]\frac{2x}{2} =\frac{-40}{2}[/tex]

2/2=1

x=[tex]\frac{-40}{2}[/tex]

x= -20

Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

The following investments were done:

In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:

Metal: x

Glass: 2 · x

Paper: 8,000 - 3 · x

And the yield function is equal to:

280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)

280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x

120 =  0.08 · x

x = 1500

The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.

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After solving the given equation using quadratic formula we gat solutions as 0.83 and 0.169

What is quadratic formula?

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b±√(b²-4ac))/(2a).

On simplifying the given equation we get,

(2x-3)²=4x

4x²+9-12x = 4x

4x²-16x+9 = 0

Comparing with ax²+bx+c = 0

a = 4, b = -16, c = 9

Quadratic formula is:

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

putting the values from question we get,

[tex]\frac{16 +- \sqrt{16^2-4(4)(9)} }{216}[/tex]

[tex]\frac{16 +- \sqrt{256-144} }{32}[/tex]

[tex]\frac{16 +- \sqrt{112} }{32}[/tex]

[tex]Solution 1 = \frac{ 16+ 10.58 }{32} = 0.83[/tex]

[tex]Solution 2 = \frac{16 - 10.58}{32} = 0.169[/tex]

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Complete question

(2x-3)²=4x solve using quadratic formula

[tex]0.744\div6[/tex]

Simplify:

[tex]\frac{0.744}{6}[/tex]

[tex]=0.124[/tex]

The number of pounds when company A and B have same amount is 16 pounds.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.

In this case, shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound.

Let each pound be represented by p.

Company A will be 7 + 0.50p

Company B will be 11 + 0.25p

We will equate both equations.

7 + 0.50p = 11 + 0.25p

Collect like terms

0.50p - 0.25p = 11 - 7

0.25p = 4

Divide

p = 4 / 0.25

p = 16

The number of pounds is 16 pounds.

The complete information is given below.

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shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound. How many pounds will give an equal amount?

The dimensions are Width = 7 feets ; length = 20 feets

As given,

Meadow area is 140 square feet.

Height = W (smaller dimension and 2 sides)

Height = L (longer dimension and 1 side)

Fence yards equal 34 feet;

Hence,

L + W = 34

L + 2W = 34

L = 34 - 2W - - - (1)

Recall:

Area = L * W = 140

Substitute value of L

140 = (34 - 2W) * W

140 = 34W - 2W²

2W² - 34W + 140 = 0

W² - 17W + 70 = 0

W² - 10W - 7W + 70 = 0

W(W - 10) - 7(W - 10) = 0

(W - 10) = 0 or (W - 7) =0

W = 10 or W = 7

We choose the shorter width because length should be as long as possible:

W = 7

L + 2W = 34

L = 30 - 14

L = 20 feets

Therefore, The measurements are 7 feet wide and 20 feet long.

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Answer: b=13

Step-by-step explanation:

b=39/3

b=13

Answer:  its 13  

Step-by-step explanation

The age of the radioactive artifact is approximately 19029.6 years old

Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.

To solve this problem, we have to find the disintegration constant and we can use the formula of half-life of the sample to do that.

The half-life of a sample is given as;

[tex]T_\frac{1}{2}=\frac{ln}{\lambda}\\T_\frac{1}{2} =\frac{ln}{5715} \\ T_\frac{1}{2} = 0.000121\\[/tex]

The formula of radioactivity is given as

[tex]N = N_oe^(^-^\lambda ^t)[/tex]

Substituting the values into the equation

[tex]N = N_oe^(^-^\lambda ^t)\\\frac{N}{N_o} = e^-^(^\lambda ^t)\\0.1 = e^-^(^0^.^0^0^0^1^2^1^*^t^)\\t = 19029.6 years[/tex]

The artifact is approximately 19029.6 years.

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

Explanation:

Anything perpendicular to Ax+By = C is of the form Bx-Ay = D

The given equation is x-y = -2 showing that A = 1, B = -1 and C = -2.

So Bx-Ay = D will update to -x-y = D

Plug in the coordinates of (-4,1) to find D.

-x-y = D

D = -x-y

D = -(-4)-1

D = 4-1

D = 3

We go from -x-y = D to -x - y = 3

Then multiply both sides by -1 to end up with x + y = -3

Solution

We will draw a diagram to illustrate the information

Using the concept of SOHCAHTOA

We are given adjacent and we want to find opposite

Therefore, the answer is

Answer:

A. 1/6 would be the answer I think

Answer: y = 15

Step-by-step explanation:

Combine multiplied terms into a single fraction

-6 = -2y/5

Then, multiply both sides by 5 to get:

-30 = -2y

Last, you divide both sides by -2 to get:

15 = y or y = 15

Hope this helps!

Draw of a modelled object

Answer: 2 years

Step-by-step explanation: If Joe was meant to serve 5 years but then his sentence got shortened by 3 years, that means we need to use subtraction. 5 minus 3 equals 2. Therefore, the answer is 2 years.

Answer:

x < 5

Step-by-step explanation:

[tex]2x - 4 < 6[/tex]

[tex]2x < 10[/tex]

[tex]x < 5[/tex]

.........................................................

Answer:

1/x to the -8 power simplified would be x^8

Step-by-step explanation:

When there is a negative exponent you put the fraction under 1

[tex]\frac{1}{\frac{1}{x^{8} } }[/tex]  and its the same as x^8

The simplified expression is [tex]x^8[/tex].

Exponent is the power of the variable or constant to which it is raised.

The expression 1 over x is denoted by 1/x.

The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].

The exponents of the denominator change from negative to positive when they move from denominator to numerator.

[tex]\frac{1}{x^{-8}}=x^8[/tex]

Thus, the simplified expression will be x raised to the power 8.

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Answer:

Explanation:

• Loan Amount = $500

• Time = 2 weeks

• The amount paid pack = $520

We want to determine the simple interest rate.

First, find the amount paid as interest:

Given (x+ c) is a common factor of (x^2- ax- b )and (2x^2+b)

x= -c is a root of x^2- ax- b= 0 and x^2+ b= 0

Concept used

Quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-b±√b²-4ac/2a

i) 1- 2a+b= 0

ii) 4+ b^b- 2a= 0

4- 2a+b=0,4+ b- 2a= 0

2a+b= 2c+d

2(c−a)= b−d

(c−a)/ (b−d)​= 2

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An equation for the line of best fit for a men's height, y, based on her shoe size, x is; y = 0.25x + 66.6

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the men's shoe size would be plotted on the x-axis of the scatter plot while her height would be plotted on the y-axis.

By critically observing the scatter plot (see attachment) which models the data, we can reasonably deduce that an equation for the line of best fit is given by:

y = 0.25x + 66.6

Interpret the meaning of the residual from part B is given below.

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We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.

(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.

(c)The domain of the function is [0,2.5] and the range of the function is [0,30].

(d) t is not a function of h.

Therefore a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

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The salesman used 460 order forms in total, when he used three types of order forms: a, b, c.

Given that,

A salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b

A = 50

B = 4A + 0.5C = 200+ 0.5C  .......... (i)

C =  A +  0.5B =  50 + 0.5 B  .......... (ii)

multiply (ii) with 2

B = 2C -50              .......... (iii)

B = 0.5C + 160        ...........(i)

subtract (i) from (iii)

0 = 1.5C -210

C = 420/3 = 140

put in (i)

B = 200 + 0.5(140) = 270

Total forms = A+B+C = 50 + 270 + 140 = 460

Therefore, he used 460 forms altogether.

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The mistake that Dolly have in her conclusion is A. Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.

An experiment is carried out in order to get more information about a particular thing.

In this case, at the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight.

Therefore, this caused the mistake that was noticed.

In conclusion, the correct option is A.

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The linear regression equation that represents this data is given as follows: y = 22x - 518.

Using this equation, when 38 passes are thrown, the expected yardage is of 318 yards.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the input and output are given as follows:

The points to be inserted in the calculator are given as follows:

(39, 360), (35, 235), (35, 262), (37, 249), (40, 338).

Hence the equation is given by:

y = 22x - 518.

With 38 passes, the expected yardage is calculated as follows:

y = 22(38) - 518 = 318 yards.

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Answer:

SSS

Step-by-step explanation:

We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.

On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049

a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %

b) The probability that I am assigned exactly 7 of the tasks that I want

p = 10C7 * 17C5 / 27C12 =  0.0427  = 4.27%

c) The probability that I am assigned at least one of the tasks I want

p = 1 - 17C12 / 27C12    where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.

Thus, p = 1 - (7/19665) = 0.9996

d)Probability that I am assigned at least 7 of the tasks I want

p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12

⇒ p = 17 / 345 = 0.049 = 4.9%

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For the given tables, we have that:

a. The grids are given at the end of the answer.

b. The functions are classified as follows: f(x) exponential, g(x) linear.

c. When x increases by one unit from left to right, we have that:

d. The functions are equal for a value between 1 and 2, as at x = 1 g(x) is greater while at x = 2 f(x) is greater.

The difference between exponential and linear functions is in the rate of change, as:

Hence the functions are classified as follows:

We have one exponential and one linear function, so it is quite difficult to solve an equation to verify where they are equal. We have that:

This means that at one point between x = 1 and x = 2, they intersected, that is, they had the same function values.

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