Which of these strategies would eliminate a variable in the system of equations?

( 6x + 5y = 1

16x - 5y = 7

Choose all answers that apply:

Answers

Answer 1

Answer:

B) Subtract the bottom equation from the top equation.

C) Add the equations.

Step-by-step explanation:

Let us analyze each of the options to see which one of them work.

A) Multiply the top equation by 7, then subtract the bottom equation from the top equation.

Multiplying the top equation by 7 gives:

7 * (16x + 5y) = (1 * 7)

112x + 35y = 7

Then, subtracting the bottom equation from this:

 112x + 35y = 7

-  (16x - 5y = 7)

=> 112x + 35y - 16x + 5y = 7 - 7

112x - 16x + 35y + 5y = 0

96x + 40y = 0

This method didn't eliminate any variable, so it didn't work for us.

B) Subtract the bottom equation from the top equation

This will yield:

  16x + 5y = 1

- (16x - 5y = 7)

=> 16x + 5y - 16x + 5y = 1 - 7

16x - 16x + 5y + 5y = -6

0x + 10y = -6

10y = -6

y = -6 / 10

Hence, one variable has been eliminated. It works.

C) Add the equations

This yields:

  16x + 5y = 1

+ 16x - 5y = 7

  32x + 0y = 8

  32x = 8

=>x = 8 / 32 = 1 / 4

This method works since one variable has been eliminated.


Related Questions

Adrianna ran 10 miles , which was twice as far as Ady ran. How far did Ady run

Answers

Answer:

5 miles

Step-by-step explanation:

5*2=10

Answer:

5 miles

Step-by-step explanation:

Adrianna (a) ran 10 miles.

She ran twice as much as Ady:

Ady = a/2

a = 10

Plug in 10 for a:

Ady = 10/2 = 5

Ady ran 5 miles.

~


Subtract (5y3 + 6y + 3y4) from (4y4 - 8y3).

A) y4 - 13y3 - 6y
B) y4 - 13y3 + 6y
C) 9y4 -13y3 - 6y
D) y4 + 13y 3 - 6y

Answers

Answer:

a

Step-by-step explanation:

Answer:

A) y ^4 −  13 y^ 3  −  6 y

Step-by-step explanation:

     4y^4 - 8y^3

-    5y^3 + 6y + 3y^4

----------------------------

flip the equations around

  -8y^3 + 4y^4

-   5y^3 + 6y + 3y^4

------------------------

-13y^3 - 6y + y^4

Rearrange to get:

y^4 - 13y^3 - 6y

I hope this helps you out!!!

Nine bean plants were grown in varying amounts of light. Mark thinks that, if the light is too intense, a bean plant will not grow as
high.
Is Mark's prediction correct?
Yes; the tallest plants were the ones that got the weakest light.
No; some plants grew just as well while getting very strong light.
Yes, when the light was too strong the plants did not grow as well.
No: plants that got the strongest light were also the ones that grew best.

Answers

Answer: C) Yes, when the light was too strong the plants did not grow well

Step-by-step explanation:

The equation y= ax describes the graph of a line. If the value of a is positive,
What direction does the line go?

Answers

Answer:

Step-by-step explanation:

If the value a is positive in the linear equation y = a x ( for example: y = 2 x ) then the line ( from the left to the right ) must go up and to the right. It also passes through the origin ( 0, 0 ).           For x = 1: y = 2 * 1 = 2, so that point is ( 1, 2 ),  x2 > x1,  and y2 > y1.Answer:A. goes up and to the right.

 

Final answer:

The line described by the equation y = ax slopes upward to the right when the value of a is positive, illustrating a positive relationship between x and y.

Explanation:

The equation y = ax describes a linear relationship between x and y. When the value of a is positive, the line slopes upward to the right on a graph. This behavior is because a positive slope indicates that as the x-value increases, the y-value also increases, leading to an upward trajectory on the graph.

The direction in which the line moves across the graph depends solely on the sign of a, where a positive a signifies an upward slope and a negative a results in a downward slope. Specifically, for a positive a, for every unit increase in x, there is a proportional increase in y, making the graph rise from left to right.

Show some graphing proportional and linear relationships

Answers

I don’t see anything?
I also don’t see anything

Anja simplified the expression
10x9 15
10 to 15. What mistake did Anja make?

Answers

Answer:

10 times 9 is 90 divide 90 bye 15 and there u go

Step-by-step explanation:

She subtracted the coefficients instead of dividing them

Please help me I don’t know how

Answers

Answer:

6 5/6

Step-by-step explanation:

8

- 1 1/6

We need to borrow from the 8

We will borrow 1 from the 8 and make it a 7.  The 1 will be written in the form 6/6

7 6/6

- 1 1/6

-----------------

6  5/6

A cone-shaped container has a height of 9 inches and diameter of 2.5 inches. It is filled with a
liquid that is worth $2 per cubic inch.
What is the total value of the liquid in the container?
Use 3.14 for .
Enter your answer in the box.




*pleaseee help i will mark brainliest if right*!!!!!

ps, thank you ​

Answers

Answer:

the total value of the liquid in the container is $29.4

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

The volume of a cone is expressed as

V=1/3(πr²h)

Given data

Height h= 9 inches

Radius r= diameter/2= 2.5/2= 1.25in

Substituting we have

V= 1/3(3.14)*(1.25)²*9

V= 1/3*(3.14)*14.06

V= 44.156/3

V= 14.7in³

The volume of the cone is 14.7in³

Hence If 1 in³ of liquid costs $2

14.7in³ will cost $x

x= 14.7*2

x= $29.4

plz help asap
I will mark you as BRAINLIEST ​

Answers

Answer:

-86 ≥ x

Step-by-step explanation:

Answer:

-87 ≥ x

Step-by-step explanation:

In this inequality, it states that -87 is greater than and equal to x.

So we know we have to use this sign.

So, -87≥x

Consider the exponential function f(x) = 1 (154). What is the value of the growth factor of the function?

Answers

The value of the growth factor of the function is 15. To add to your answer, exponential growth happens when the rate of the number of the function corresponds with the present value of the function. This then lets its increase together with time be called an exponential function. 

Answer:

15.

Step-by-step explanation:

f(x) = a b^x

The growth factor is  b - in this case 15.

the difference of a number x and 7 *

Answers

Answer:

C

Step-by-step explanation:

x-7 is the answer

Answer:

difference means subtract

x-7

C. is correct because it subtracts and the numbers are in order

Step-by-step explanation:

Girls in science class account for one-third of the total number of students in their 3rd period class. 3 girls are absent today. Find the total number of students in the class if four girls attended class today.

Answers

Answer:

See Explanation

Step-by-step explanation:

The question isn't clear enough. However, I'll solve for the total number of students in science class and I'll.also solve for the total number of students present in class.

Given

Proportion of girls = ⅓

Number of girls absent = 3

Number of girls present = 4

Required

Find the total number of students

If 3 girls were absent and 4 were present, then there are total of 7 girls in science class.

Let the number of students in the class be represented by y.

⅓ of the total number of students are girls;

This means

⅓ of y = 7

⅓ * y = 7

Multiply both sides by 3

3 * ⅓ * y = 3 * 7

y = 3 * 7

y = 21.

Hence, the total number of students in science class is 21

Recall that 3 girls are absent;

This means that 21 - 3 are presently in the class.

21 - 3 = 18.

Hence, 18 students are presently in class.

*25 points* Hailey ran a few laps. D(n), models the duration (in seconds) of the time it took for Hailey to run her n^th lap. When did the lap duration increase faster?

A. Between the 3rd and 7th lap

B. Between the 7th and 9th lap

C. The lap duration increased at the same rate over both intervals

Answers

Answer:

B

Step-by-step explanation:

4 laps were ran between her 3rd and 7th lap (inclusive) and the duration increased by 14 seconds

But just 2 laps were ran between her 7th and 9th lap and the duration increased by 11 seconds

So obviously the lap duration increased faster between the 7th and 9th lap

Answer:

B

Step-by-step explanation:

I just did the quiz, so you all can trust me :)

How do you do this anyone know how

Answers

Slope is rise over run, or the change in y over the change in x. So, you go up vertically then directly horizontal and whatever the change is is the slope.

For example, the first one is -1/3. It's slope is going down to the right, so it's negative . It goes down 1 (y value) and over to the right 3 (x value). Since it goes down and to the right it is a slope of -1/3.

Answer:

ok so........

Step-by-step explanation:

For example, the first one is -1/3. It's slope is going down to the right, so it's negative . It goes down 1 (y value) and over to the right 3 (x value). Since it goes down and to the right it is a slope of -1/3.

Cards in a deck are numbered 1-4. You pick one card and keeps it. You pick a second card. The tree diagram shows you possible outcomes. What is the probability you picked a 1 and then a 2

Answers

The possibility of you picking a 1 and then a 2 would be 1-4

Helppp plzz!!! Julius is in charge of planting a peach orchard that covers 15 acres. He uses the same amount of ground space for each tree. Julius plants 25 trees in the section of the orchard called the South Hill region that measures 450 feet by 24 feet. Approximately how many trees does Julius plant in the orchard in all? (1 = 43,560 ).

A. 909

B. 1,151

C. 1,513

D. 1,746

Answers

Answer:

C

Step-by-step explanation:

Area of known planted trees: 450ft x 24ft = 10800 sq ft

total area of orchard: 43560 sq ft. x 15 acres = 653400 sq ft

653400 / 10800 = 60.5 "duplicated known areas"

25 trees in each "known area"

60.5 x 25 = 1512.5 trees

round to 1513 trees

C

I worked it out but not sure

Solve the system of equations 3x + y = 3 and 7x + 2y = 1.

1. Solve for the variable y in the first equation:     y = 3 − 3x

2. Substitute the value for y into the second equation:  7x + 2(3 − 3x) = 1

3. Solve for x: x =

Answers

Answer:

(-5, 18)

Step-by-step explanation:

7x + 2(3 − 3x) = 1 simplifies to

7x + 6 - 6x  = 1,   which, in turn, simplifies to:

x = -5

Using y = 3 - 3x (see Step 1), we find that y = 3 - 3(-5) = 3 + 15 = 18.

Thus, the solution is (-5, 18).

Answer:

Step-by-step explanation:

here is the answer

Which expression is equivalent to 5y^-3

Answers

Answer:

Step-by-step explanation:

                5

5y^-3 = ---------

               y^3

PLZZZ HELP ME Sue travels by bus or walks when she visits the shops. The probability that she catches the bus to the shops is 0.4. The probability she catches the bus from the shops is 0.7. complete the tree diagram

Answers

last time i did this i got 1.4

Answer: 0.72

Step-by-step explanation:

0.7x0.4=0.28

1-0.28= 0.72

That is what I did in the box and got the correct answer. Hope you have a good day!

2(x - 5) + 7 = x + 8 what is x represents

Answers

Answer: [tex]x=11[/tex]

Reorder the terms in parentheses

[tex]+(+2x-10)+7=x+8[/tex]

Remove unnecessary parentheses

[tex]+2x-10+7=+x+8[/tex]

Move all terms containing x to the left and all other terms to the right

[tex]+2x-1x=+8+10-7[/tex]

Simplify left and right side of the equation

[tex]+1x=+11[/tex]

divide both sides of the equation by 1 to get x

[tex]x=11[/tex]

Consider a single spin of the spinner. Which events are mutually exclusive? Choose all that apply. a)landing on a shaded sector and landing on a number greater than 3
b)landing on a shaded sector and landing on a 3
c)landing on a shaded sector and landing on an even number
d)landing on an unshaded sector and landing on a number less than 2
e)landing on an unshaded portion and landing on an odd number


Answers

Answer: the correct options are b and d.

Step-by-step explanation:

Let us first define what mutually exclusive events are. If two events are mutually exclusive, it means that they cannot happen at the same time. For example, getting a head and a tail at the same time are mutually exclusive.

Considering a single spin of the spinner, the events that are mutually exclusive are

b)landing on a shaded sector and landing on a 3. This is because 3 is unshaded. You can either land on 3 or an unshaded sector at a time

d)landing on an unshaded sector and landing on a number less than 2. This is because the numbers in the unshaded sectors are greater than 2.

Which expression is equivalent to
- 5/3?

Answers

Answer:

The first one! :)

Step-by-step explanation:

At the bottom of each question for example the first on it has 1 at the top then at the bottom it says 5/3 with a x.So if it does not say 5/3 it can be excluded.So it says only one 5/3.So one 5/3 is the exact same as 5/3!

And for the last one says -5/3.:)

And no im not saying 1  5/3  :(

(❁´◡`❁)     (●'◡'●)     ╰(*°▽°*)╯     (≧▽≦)     (*/ω\*)     (^///^)       ^_^          (┬┬﹏┬┬)        ಥ_ಥ        ಠ_ಠ    

[tex]$\frac{1}{\sqrt[3]{x^{5}}}$[/tex]  is equivalent to [tex]- 5/3[/tex].

The calculation of the given expression can be defined as

[tex]$\begin{aligned} \rightarrow x^{-\frac{5}{3}} &=\frac{1}{x^{\frac{5}{3}}} \\ &=\frac{1}{\sqrt[3]{x^{5}}} \end{aligned}$[/tex]

So, the final answer is "Option b".[tex]$\frac{1}{\sqrt[3]{x^{5}}}$[/tex]

What are Equivalent Fractions?Equivalent fractions are fractions that represent the same value, even though they look different. A fraction has two parts. The number on the top of the line is called the numerator which tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator and it shows the total number of equal parts the whole is divided into or the total number of equal parts which are there in a collection.

To learn more about equivalent refer to:

https://brainly.com/question/9385401

#SPJ2

What is the relationship between segment RS and segment RU

Answers

Answer:

I would like to answer but where is the picture for the question. Download that to this page and i will answer it. Have a great day

Step-by-step explanation:

On Monday Julio ran 3,000 meters and on Wednesday he ran 4,500 meters how many meters did Julio run in all

Answers

Answer:

3000+4500= 7500

8) There are six boys and seven girls in a
class. The teacher randomly selects one
student to answer a question. Later, the
teacher randomly selects a different
student to answer another
question. The
first student is a boy and the second
student is a girl.
I
Are the events independent or dependent?
What is the probability?

Answers

Answer:

i say dependent. i may be wrong

7/26

Step-by-step explanation:

6/13 times 7/12 which is 42/156 which is 14/52 which is also 7/26

Final answer:

The scenario presents dependent events with the probability of selecting a boy first and then a girl being 7/26.

Explanation:

The events described in the scenario are dependent because the outcome of the first trial (selecting a student) affects the outcome of the second trial (selecting another student). In this situation, for the first student selected to be a boy, the probability is 6/13 (as there are six boys and seven girls, totaling 13 students). Once the first boy is selected and not replaced, the probability that the second student chosen is a girl is 7/12, because only 12 students remain and 7 of them are girls.

Therefore, the probability of first drawing a boy and then a girl, in two successive trials without replacement, is the product of the two individual probabilities: (6/13) * (7/12). This equals 42/156= 0.269 or simplified to 7/26.

What does statement that is not correct to use probability to describe an event.

A) the probability of seeing the Stars night is 0.70
B) the probability of going back to time is 0

C) The probability of having leftovers for dinner tonight is 35 percent

D) The probability of finding my keys is - 1/5

Answers

The incorrect statement is option D) The probability of finding my keys is - 1/5, as probabilities cannot be negative. Probabilities range between 0 and 1, and the calculation for combined probability of independent events involves multiplication, not addition.

The statement that is not correct to use probability to describe is option D) The probability of finding my keys is - 1/5. Probabilities range from 0 to 1 (or 0% to 100%), where 0 indicates impossibility and 1 indicates certainty. A negative probability does not make sense within this framework, so option D reflects a misunderstanding of how probabilities are represented.

The correct way to calculate the combined probability of two independent events is to multiply their individual probabilities. For example, to find P(A AND B) when dealing with independent events, you would calculate P(A) * P(B). Therefore, if P(A) = .2 and P(B) = .3, the correct answer for P(A AND B) would be .06, which corresponds to option D in the exercise provided.

It is also important to clarify misconceptions such as adding probabilities of non-mutually exclusive events. For instance, the fallacy that if there is a 60 percent chance of rain on one day and a 70 percent chance on another, then there is a 130 percent chance of rain over the weekend.

This is incorrect because probabilities cannot exceed 100%. Instead, you would evaluate the chances of rain differently depending on the independence or interdependence of the weather on those days.

A senator wishes to estimate the proportion of United States voters who favor

abolishing the Electoral College. How large a sample is needed in order to be 90%

confident that the sample proportion will not differ from the true proportion by more

than 3%?

Answers

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]  

And rounded up we have that n=748

Step-by-step explanation:

The confidence level is 90% and the significance level would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2 =0.05[/tex] and the critical value for this case is:

[tex] z_{\alpha/2}= 1.64[/tex]

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we want a margin of error of [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

Since we don't hace any prior info for the population proportion we can use [tex]\hat p =0.5[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]  

And rounded up we have that n=748

Using the sample size formula, the required number of sample is 752.

Using the confidence interval relation :

[tex] n = \frac{pq}{(\frac{E}{Z_{crit}})^{2}} [/tex]

p =sample proportion = 0.5 q = 1 - p = 1 - 0.5 = 0.5 Zcrit at 90% = 1.645 E = Error Margin = 3% = 0.03

Substituting the values into the equation :

n = [tex] \frac{0.5 \times 0.5}{(\frac{0.03}{1.645})^{2} }[/tex]

[tex] n = \frac{0.25}{0.0003325}[/tex]

[tex] n = 751.67[/tex]

Therefore, the required number of sample is 752.

Learn more : https://brainly.com/question/25609130

Write an equation to represent the following statement.
10 less than j is 35.
_______
Solve for j.
j =_____

Answers

Answer:

j - 10 = 35

j = 45

Step-by-step explanation:

When it says, "less than" it means subtracting. So 10 less than j is (j - 10)

The part where is says "is" means it is equal to.

So the equation would be = (j - 10) = 35

Answer:

Equation: (j - 10) = 35

j = 45

Step-by-step explanation: Lets translate 10 less than j:

Less than means 10 is being subtracted from j.

So we can write 10 less than j as j - 10.

The word is means equal.

So, we can write is 35 as = 35.

Now lets write the whole equation toghter.

j - 10 = 35

We can also write this as 35 = j - 10.

Now we can solve for j.

Add 10 to both sides of the equation to get j by itself.

j - 10 + 10 = 35 + 10

J=45

The following equation matches this situation:

j - 10 = 35

j = 45

Solve for x: −1 < x + 3 < 5

2 < x < 8
−4 < x < 2
2 > x > 8
−4 > x > 2

Answers

Answer:

-4<x<2

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ÷)

The value of a 7 in the
millions place, is how
many times greater
than the value of a 7
in the ten thousands
place?
-
RESERREIRA
What is the answer to the problem above?*
Type your answer in number form.​

Answers

The answer is 6,930,000. You have to subtract them.
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