Mathematics College

Solve the system of equations using the substitution method.

{y=−3x+7
x=−2y−16



Enter your answers in the boxes.

x=



y=

Answers

Answer 1

ANSWER

[tex]x = 6[/tex]

[tex]y = - 11[/tex]

EXPLANATION

The given system of equations is

[tex]y = - 3x + 7...(1)[/tex]

and

[tex]x = - 2y - 16...(2)[/tex]

We substitute equation (1) into equation (2) to get;

[tex]x = - 2( - 3x + 7) - 16[/tex]

[tex]x = 6x - 14- 16[/tex]

We group similar terms

[tex]x - 6x = - 14 - 16[/tex]

[tex] - 5x = - 30[/tex]

Divide both sides by -5.

[tex]x =6[/tex]

Put x=6 into equation (1).

[tex]y = - 3(6) + 7[/tex]

[tex]y = - 18 + 7[/tex]

[tex]y = - 11[/tex]

Answer 2

Answer:

x = 6 and y = -11  

Step-by-step explanation:

Given : System of linear equation

y=−3x+7

x=−2y−16

We have to solve the system of equations using the substitution method.

In substitution method, we substitute the value of one variable in term of other and solve for it.

Consider the given system of linear equation

y = −3x + 7  ...(1)

x = −2y − 16 .....(2)

Substitute, (2) in (1), we get,

y = -3(-2y - 16) + 7

Simplify , we get,

y = 6y + 48 + 7

6y - y = - 55

5y = -55

y = -11

Substitute y = -11 in (2), we get,

x = −2(-11) − 16 = 22 - 16 =  6

thus, x = 6

Thus , x = 6 and y = -11  

Related Questions

simplify x + 2/ x^2 - 6x - 16 divided by 1/9x

Answers

Hello there!

Simplify the expression
9/x(x - 8)

Hope this helps! :)
~Zain

What number would you add to both sides of x2 + 7x = 4 to complete the square? 22 72

Answers

x^2 + 2*x*(7/2) + (7/2)^2  = (x + 7/2)^2

answer is (7/2)^2
the answer is D (7/2)^2 

Your typical markup for merchandise is 40%. Your cost on an item is $8.00. Calculate the selling price.

Answers

To calculate the selling price of the item, you must apply the following formula:
 
 Selling price=(Markup/Product costx100%)+Product cost
 
 You have that:
 
 Markup=40%
 Product cost=$8.00
 
 Given these values, you only have to substitute them into the formula of Selling price:
 
 Selling price=(Markup/Product costx100%)+Product cost
 Selling price=(40%/$8.00x100%)+$8.00
 Selling price=$3.20+$8.00
 Selling price=$11.20

Mr. Jacobs is going to make a histogram of the test scores from the last math test he gave. He plans to first organize the data into a stem-and-leaf plot and then make the histogram from the stem-and-leaf plot. The test scores are listed below. 79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87, 85 What is the mode interval of the data?60-69 70-79 80-89 90-99

Answers

The modal interval would be the range of numbers that include the most number of data points.  So, looking at your information, there would be 3 numbers in the 60-69 range, 4 numbers that fall in the 70-79 range, 6 numbers that fall in the 80-89 range, and 5 numbers that fall in the 90-99 range.  The interval with more data than any other is the 80-89 range therefore making it the mode interval.

Answer:4

Step-by-step explanation:  just mark me brainlest

the area of a circle is 78.5 square meters. what is the radius ?

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ ------\\\ A=78.5 \end{cases}\implies 78.5=\pi r^2\implies \cfrac{78.5}{\pi }=r^2 \\\\\\ \sqrt{\cfrac{78.5}{\pi }}=r[/tex]
The radius will be = 5

Explain how to compare 43 and 35

Answers

Final answer:

The element with 35 protons is bromine (Br). Its isotopes with 44 and 46 neutrons have the symbols ^79Br and ^81Br, respectively, with the mass numbers derived from adding the number of neutrons to the atomic number 35.

Explanation:

To address Exercise 1.8.2, we first need to identify the element with 35 protons. In the periodic table, the element with 35 protons is bromine (Br). This element is defined by the number of protons in its nucleus, which is also known as its atomic number. Therefore, bromine is the element we are looking for.

Next, we need to write the symbols for bromine's isotopes with 44 and 46 neutrons. The total number of nucleons (protons plus neutrons) gives us the mass number of an isotope. For bromine with 44 neutrons, the mass number is 35 (protons) + 44 (neutrons) = 79. Therefore, the symbol for this isotope of bromine is ^79Br.

For the isotope with 46 neutrons, the mass number is 35 (protons) + 46 (neutrons) = 81. So, the symbol for this isotope of bromine is ^81Br. Each isotope differs in the number of neutrons, and therefore, in the mass number, while the number of protons (the atomic number) remains constant.

Final answer:

The element with 35 protons is bromine (Br). Its isotopes with 44 and 46 neutrons are written as ^79Br and ^81Br, respectively, where the numbers represent the mass numbers of each isotope.

Explanation:

To answer Exercise 1.8.2, we must first identify the element with 35 protons. The element with 35 protons is bromine, which is represented by the chemical symbol Br. To write the symbols for its isotopes with 44 and 46 neutrons, we must add the atomic number (protons) and the number of neutrons to get the mass number for each isotope.

For the isotope with 44 neutrons:

Mass number = Number of protons + Number of neutronsMass number = 35 + 44Mass number = 79Therefore, the symbol for this isotope is ^79Br.

For the isotope with 46 neutrons:

Mass number = 35 + 46Mass number = 81Therefore, the symbol for this isotope is ^81Br.

Isotopes of an element have the same number of protons but different numbers of neutrons, hence different mass numbers. The isotopes of bromine are thus ^79Br and ^81Br, referring to the atomic mass which is composed of the protons and neutrons together.

Suppose that 44% of all Americans approve of the job the president is doing. The most recent Gallup poll consisted of a random sample of 1400 American adults.
A) What is the mean of the sampling distribution?
B) What is the standard deviation of the sampling distribution?
C) Describe the normal approximation for this sampling distribution.
D) What is the probability that the Gallup poll will come up with a proportion within 3 percentage points of the true 44%?

Answers

This is a typical binomial distribution since we are dealing with only two possible outcomes. For this distribution we have:
n = population = 1400
p = probability of positive answer = 0.44 

A) The mean of a binomial distribution is
μ = np
  = 1400 × 0.44
  = 616

Hence, μ = 616

B) The standard deviation of a binomial distribution is
σ = √[np(1 - p)]
   = √[1400×0.44×(1-0.44)]
   = √(1400×0.44×0.56)
   = 18.6

Hence, σ = 18.6

C) A binomial distribution B(n, p) can be approximated by a normal distribution N(μ, σ) only when:
np ≥ 10 (we have 616 > 10)
np(1 - p) ≥ 10 (we have 344.96 > 10)

Hence, the normal approximation is N(616, 18.6)

D) We need to calculate the probability of the sample population to be within 3% of the true mean.

In order to do so, as a first thing, we need to calculate the sample standard deviation, which will be given by the formula:
[tex]\sigma = \sqrt{ \frac{p(1-p)}{n} } [/tex]
= √[0.44 × (1 - 0.44) ÷ 1400]
= √0.000176
= 0.013

Now, we need to calculate the z-score associated with the values we want: since we want 3% from the mean, it means between 41% and 47%.
The z-score can be calculated by the formula:
z = (Y - p) / σ
z₁ = (0.41 - 0.44) / 0.013 = -2.31
z₂ = (0.47 - 0.44) / 0.013 = 2.31

Therefore, we can write
P(0.41 ≤ Y ≤ 0.47) = P(-2.31 ≤ z ≤ 2.31)
                              = P(z ≤ 2.31) - P(z ≤ -2.31)
                              = P(z ≤ 2.31) - [1 - P(z ≤ 2.31)]
                              = 2×P(z ≤ 2.31) - 1

From a standard normal distribution table, we find:
P(z ≤ 2.31) = 0.9896

Therefore:
2×P(z ≤ 2.31) - 1 = 2 × 0.9896 - 1
                            = 0.9792

Hence, the probability to find a proportion within 3% of the real mean is 97.92%

The Orlando eye in Orlando, Florida is a regular polygon with 30 sides. Which of the following is the measure of each interior angle of the polygon?

Answers

Answer:

The measure of each interior angle of the polygon is [tex]168\°[/tex]

Step-by-step explanation:

we know that

The sum of the internal angles in a polygon is equal to

[tex]S=(n-2)180\°[/tex]

where

n is the number of sides of polygon

In this problem we have

[tex]n=30\ sides[/tex]

substitute

[tex]S=(30-2)180\°=5,040\°[/tex]

To find the measure of each internal angle divide the total sum of internal angles by the number of sides

so

[tex]5,040\°/30=168\°[/tex]

Answer:168

Step-by-step explanation:

N is the number of sides. Formula is (n-2)×180/n. So (30-2)= 28×180=5040÷30= 168

for a stem competition julienne constructed a model rocket the rocket can reach an average height of 545 ft. Find the differences between the average height and the actual Heights reached. Then write them as a positive and negative rational numbers. order the differences from least to greatest

Answers

We have the following table:
 545-534.2 = 10.8
 545-556.4 = -11.4
 545-554.0 = -9
 545-535.3 = 9.7
 write them as a positive and negative rational numbers
 positive:
 9.7 = 9 7/10
 10.8 = 10 4/5
 negative:
 -11.4 = -11 2/5
 -9 = -9
 the differences from least to greatest
 -11 2/5
 -9
 9 7/10
 10 4/5

Steven earns extra money babysitting. He charges $37.50 for 6 hours and $50.00 for 8 hours.

Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.

The equation is y =

Answers

we have that
x------------------> represent the number of hours Steven babysits
y----------------- > represent the amount he charges

for x=6 hours
y=$37.50 ----------------> y/x=37.5/6=6.25
for x=8 hours
y=$50---------------------> y/x=50/8=6.25

therefore
y=6.25x

the answer is 
y=6.25x

What is the following sum? 2(^3√16x^3y)+4(^3√54x^6y^5)

Answers

Option A: 4x(^3√2y)+12x^2y(^3√2y^2)

Answer: the answer is a

Step-by-step explanation:

I just took the test

Find an equation for the plane that contains the line v = (−1, 1, 2) + t(7, 6, 2) and is perpendicular to the plane 8x + 5y − 7z + 8 = 0.

Answers

Final answer:

The equation for the plane that contains the given line and is perpendicular to the provided plane is 8x + 5y - 7z + 17 = 0.

Explanation:

To find an equation for the plane that contains the line given by v = (−1, 1, 2) + t(7, 6, 2) and is perpendicular to the plane described by 8x + 5y − 7z + 8 = 0, we first need to understand that the normal vector of this plane will be parallel to the normal vector (8, 5, -7) of the given plane since both planes are perpendicular to each other.

Knowing that the line lies on the required plane, we can use the point (−1, 1, 2) that the line passes through, along with the parallel normal vector, to write the equation of our plane. The general form of the equation of a plane is Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane. Substituting our point into the equation, we calculate the constant D.

Thus, the equation of our plane will be 8x + 5y − 7z + D = 0. Inserting the point (−1, 1, 2) into this equation gives us 8(-1) + 5(1) - 7(2) + D = 0, which simplifies to -8 + 5 - 14 + D = 0. Solving for D yields D = 17. Hence, the final equation of the plane is 8x + 5y − 7z + 17 = 0.

a collection of nickels and dimes is worth $2.95 there are 47 coins and all how many nickels are there

Answers

12D  and 35N

D= dimes
N=nickels

Regina scored 84% on a test. She answered 63 items correctly. How many items did Regina answer incorrectly?

Answers

84% is equivalent to 63 correct questions.

Divide both sides by 84% to normalize:

84%/84% = 63/84%
1 = 75

This means that 100% would be equivalent to 75 questions correct

From here, subtract 75-63=12
STEP 1:
Find total number of questions on the test. The percent (84%) is out of 100%. So set up a proportion. 84% out of 100% is 63 out of x (total number of questions on the test).

x= total # questions on test

63/x= 84%/100%
cross multiply
(63*100)= (x*84)
6300= 84x
divide both sides by 84
75= x (total # on test)

STEP 2:
Subtract number correct from total number of questions to equal number incorrect.

x= number incorrect on test

x= 75 - 63
x= 12 incorrect answers

ANSWER: 12 incorrect answers

Hope this helps! :)

solve for x in the equation x^2 + 20x + 100 = 36

Answers

The answers are x=(-4), or x=(-16)



Comment the correct answer. 

Answer:

x = -4 or x = -16

Step-by-step explanation:

We have to solve equation x^2 + 20x + 100 = 36 and find the value of x

x² + 20x + 100 = 36

x² + 20x + 100 - 36 = 36 - 36

x² + 20x + 64 = 0

(x + 4 ) ( x + 16 ) = 0

x + 4 = 0 or x + 16 = 0

x = -4 or x = -16

Answer would be x = -4 or x = -16

BRAINLIEST to the one who can asnwer my question and show me the work step by step so that I can understand. I want to understand.

Approximate the arc length of​ one-quarter of the unit circle​ (which is π ​/2) by computing the length of the polygonal approximation with n=4 segments. (As seen in picture)

The length of the line segment on the interval 0≤x≤0.25
The length of the line segment on the interval 0.25≤x≤0.5
The length of the line segment on the interval 0.5≤x≤0.75
The length of the line segment on the interval 0.75≤x≤1

Answers

Edited 2018-03-09 07:49

Given unit circle, so radius=1.

We calculate lengths of vertical segments, with the help of Pythagoras Theorem, based on a right triangle radiating from circle centre O, and hypotenuse from O to a point on the circumference.
AO=1 (given unit circle)
BB'=sqrt(1^2-0.25^2)=0.968246
CC'=sqrt(1^2-0.5^2)=0.866025
DD'=sqrt(1^2-0.75^2)=0.661438
EE'=0

Now we proceed to calculate the segments approximating the arc.  Again, we use a right triangle in which the hypotenuse is the segment joining two points on the circumference.  The height is the difference between the two vertical segments, and the base is 0.25 for all four segments.
AB=sqrt((AO-BB)^2+0.25^2)=0.252009BC=sqrt((BB-CC)^2+0.25^2)=0.270091CD=sqrt((CC-DD)^2+0.25^2)=0.323042DE=sqrt((DD-0)^2+0.25^2)=0.7071068

giving a total estimation of the arc length
approximation of arc=AB+BC+CD+DE=1.55225

Hello,

Please, see the attached files.

Thanks.

Using Cramer’s Rule, what is the value of x in the system of linear equations below? x+3y=16 3x+y=8

Answers

Final answer:

Using Cramer's Rule, the value of x in the given system of linear equations is 1.

Explanation:

We can solve the given system of equations using Cramer's Rule. Cramer's Rule states that in a system of linear equations, if the determinant of the coefficient matrix is non-zero, then the system has a unique solution.

First, let's find the determinant of the coefficient matrix:

| 1   3 |

| 3   1 |

Det = (1*1) - (3*3) = -8

Since the determinant is non-zero (-8 ≠ 0), the system has a unique solution.

Next, let's find the determinant of the x-column matrix:

| 16   3 |

|  8   1 |

Det(x) = (16*1) - (3*8) = -8

Finally, we can find the value of x by dividing the determinant of the x-column matrix by the determinant of the coefficient matrix: x = Det(x) / Det = (-8) / (-8) = 1.

Express the work in terms of l, f, and θ. remember to use radians, not degrees, for any angles that appear in your answer.

Answers

Assuming I see a force F acting on an object at an angle theta with the horizontal pushing it through a rough surface over a distance L such that the horizontal component is just required to overcome friction.

Then work done is
W=FLcos(theta)

(Read assumptions above due to lack of diagram)

y varies directly as x. If y = -2 when x = 4, find x when y = 5.

Answers

x = -10 if im correct
[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=-2\\ x=4 \end{cases}\implies -2=k4\implies \cfrac{-2}{4}=k \\\\\\ -\cfrac{1}{2}=k\qquad therefore\qquad \boxed{y=-\cfrac{1}{2}x} \\\\\\ \textit{now, if y = 5, what is \underline{x}?}\qquad 5=-\cfrac{1}{2}x[/tex]

A bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph. Find the distance from the village to the railroad station, if it’s known that it took 1 more hour for the bicyclist to get back to the village.

Answers

The answer would be exactly 30 Miles

neeeeeed help asp please. thx:)

Answers

First, multiply 7 by 3 to get the pounds, which is 21.
Then multiply 12 by 3 to get the ounces, which is 36.

So A, 21 lbs 36 oz, is the correct answer. 
Hope this helps!

what is the value of log3^81

Answers

Answer:

Third option is correct. The value of given expression is 4.

Step-by-step explanation:

The given expression is

[tex]log_381[/tex]

The given expression can be written as

[tex]log_3(3\times 3\times 3\times 3)[/tex]

[tex]log_3(3^4)[/tex]

According to the property of logarithm expression,

[tex]log_a(a^b)=b[/tex]

Using this property of logarithm expression, we get

[tex]log_3(3^4)=4[/tex]

Therefore the value of given expression is 4 and option third is correct.

The value of the expression log₃(81) is 4.

We have,

The value of log base 3 of 81 can be found by asking the question: "To what power must 3 be raised to obtain 81?"

In this case, the answer is 4, because 3 raised to the power of 4 equals 81.

i.e

[tex]3^4[/tex] = 81

Therefore,

The value of the expression log₃(81) is 4.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

At Jim's Juice Box Factory, his machine can fill 300 juice boxed an hour. Each juice box holds 0.8 cups. How many gallons of juice does Jim's factory need per hour?

Answers

(300 box/h) * (0.8 cup/box) * (1 gal)/(16 cup) = 300*0.8/16 gal/h
.. = 15 gal/h

Jim's factory needs 15 gallons of juice per hour.

Choose the correct product of (3x − 8)2.
9x2 − 64
9x2 + 64
9x2 − 48x + 64
9x2 + 48x + 64

Answers

Lets get started :)

(3x - 8)²

(3x - 8)(3x - 8)

(3x)² - 8(3x) - 3x(8) + (8)²

9x² - 24x - 24x + 64

9x² - 48x + 64

Your answer will be the second last option


The third option is the correct answer.

Simplify

(343) 1/3

a)21
b)19
c)49
d)7

Answers

(343) 1/3 = 343 × 1/3

343 × 1/3 = 114 1/3

Hope this helps!

Which of the following are linear factors of p(x) = x 3 - 2x 2 - 5x + 6 ?

Answers

The roots are -2, 1, 3, so the linear factors are
.. (x +2)
.. (x -1)
.. (x -3)

_____
Obviously, you don't mind using "technology" (Brainly) to tell you the answer. You might find it useful in the future to learn to use your graphing calculator. It can make short work of these questions.

Which expressions are polynomials? Select each correct answer. y x2−x√+2 2 + s 4x³ + y

Answers

Answer:

Answers are

Y

2+s

4x^3+y

Step-by-step explanation:

I did the quiz

The first, second, and third are the polynomials.

Polynomial

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable

Given

1.  y

2.  x² - x +√2

3.  2 + s

4.  4x³ + y

To find

Which expressions are polynomials?

How to get Which expressions are polynomials?

1.  y is a polynomial with variable y.

2.  x² - x +√2 is a polynomial with variable x.

3.  2 + s is a polynomial with variable s.

4.  4x³ + y is not a polynomial because the polynomial has only one variable in it.

Thus, the first, second, and third are the polynomials.

More about the polynomial link is given below.

https://brainly.com/question/17822016

Rosa is thinking of a number between 9.04 and 9.15 that has a six in the hundreds place what is the number explain

Answers

The number is 9.06. The only answers are that and 9.16. The second number does not pertain to the set range.
A 6 in the hundredths spot would be 9.06, 9.16, 9.26, 9.36, etc.  Since the number has to be between 9.04 and 9.15, the only option is 9.06.   

Answer: 9.06

Hope this helps!  :)

Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 10 and its height is 6?

Answers

1. First, you must find the constant of variation (k). The problem indicates that the base of each triangle varies inversely with the height. So, this can be represented as below:

 B=k/H

 B is the base of the triangle (B=10).
 H is the height of the triangle (H=6).
 k is the constant of variation.

 2. When you clear "k", you obtain:

 B=k/H
 k=BxH
 k=10x6
 k=60

 3. Now, you have:

 B=60/H

 4. You can give any value to "H" and you will obtain the base of the second triangle.

 5. If H=12, then:

 B=60/H
 B=60/12
 B=5

 6. Therefore, the possible base and height of a second triangle is:

 B=5
 H=12

Answer:

12 and 5

Step-by-step explanation:

residents of a small city voted on whether to allow a developer to build a shopping center.the number of votes favor of the shopping center was 4,400.the number of votes against the shopping center was 17,600.what percent of the voters were in favor of building the shopping center?

Answers

The percent of votes in favor is equal to the amount of votes in favor divided by the total number of votes.

Thus in this case, our percentage would be 4400/22000=20%.
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