MATHEMATICS COLLEGE

What is the solution of the system of equations: -2x+8y=-8 and 5x-8y=20 using elimination

Answers

Answer 1

Answer:

Answer:

x = 4 and y = 0

Step-by-step explanation:

Given expression:

-2x + 8y = -8

5x - 8y = 20

Now, to solve this problem by elimination, follow this procedure:

-2x + 8y = -8 --- i

5x - 8y = 20 --- ii

Coefficient of y in both expression have similar values;

Now, add equation i and ii;

(-2x + 5x) + (8y -8y ) = -8 + 20

3x = 12

Divide both sides by 3;

x = $(12)/(3)$ = 4

Now, to find y; put x = 4 into equation i,

-2(4) + 8y = -8

-8 + 8y = -8

Add +8 to both sides of the expression;

-8 + 8 + 8y = -8 + 8

8y = 0

y = 0

Related Questions

The amount of cream sauce on the fettuccine at Al Fred-O's follows a Normal distribution, with a mean of 3.78 ounces and a standard deviation of 0.14 ounce. A random sample of 12 plates of fettuccine is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.81 ounces
Which of the following expressions are equivalent to - -a/b
A pump discharges 278 gallons of water in 3.5 minutes. How long would it take to empty a container with 750 gallons? Round up to the nearest minute
Your grandmother always has a jar of cookies on her counter. One day while you are visiting you eat 5 cookies from the jar. In the equation below, c is the number of cookies remaining in the jar and b is the number of cookies in the jar before your visit. The relationship between these two variables can be expressed by the following equation: c=b-5
What is the slope of the line that contains the points (-1,-1) and (3, 15)?O A.14B. 4O C. -4D. -4

The tree diagram represents anexperiment consisting of two trials.
.4
.5
.6
D
.3
С
.5
.7
D
Þ(B and D) = [?]
ter

Answers

Answer:

0.35

Step-by-step explanation:

.5x.7

Help please! I’ll give brainliest!

Answers

Answer:the last one

Step-by-step explanation:

Which of the following is the equation of the line that is parallel toy= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2

Answers

Answer:

Step-by-step explanation:

We want to write the equation of a line that is parallel to:

$y=(3)/(5)x+8$

And also passes through (-10, 4).

Remember that parallel lines have the same slope.

The slope of our old line is 3/5.

Therefore, the slope of our new line is also 3/5.

We know that it passes through (-10, 4). So, we can use the point-slope form:

$y-y_1=m(x-x_1)$

Where m is the slope and (x₁, y₁) is a point.

So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:

$y-(4)=(3)/(5)(x-(-10))$

Simplify:

$y-(4)=(3)/(5)(x+10)$

Distribute on the right:

$y-4=(3)/(5)x+6$

Add 4 to both sides:

$y=(3)/(5)x+10$

So, our answer is C.

And we're done!

Step-by-step explanation:

Hey there!

The equation of a st.line passing through point (-10,4) is ;

(y-y1)= m1(x-x1) [one point formula]

Put all values.

(y - 4) = m1( x + 10)..........(i)

Another equation is; y = 3/5 + 8.............(ii)

From equation (ii)

Slope (m2) = 3/5 [ By comparing equation with y = mx+c].

As per the condition of parallel lines,

Slope of equation (i) = slope of equation (ii)

(i.e m1 = m2 )

Therefore, the value of m1 is 3/5.

Putting value of slope in equation (i).

$(y - 4) = (3)/(5) (x + 10)$

$(y - 4) = (3)/(5) x + (3)/(5) * 10$

$(y - 4) = (3)/(5) x + 6$

$y = (3)/(5) x + 10$

Therefore the required equation is y = 3/5x + 10.

Hopeit helps...

According to a human modeling project, the distribution of foot lengths of women is approximately Normal with a mean of 23.3 centimeters and a standard deviation of 1.4 centimeters. In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long. What percentage of women in the United States will wear a size 6 or smaller?

Answers

Answer:

26.11% of women in the United States will wear a size 6 or smaller

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 23.3, \sigma = 1.4$

In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long. What percentage of women in the United States will wear a size 6 or smaller?

This is the pvalue of Z when X = 22.4. So

$Z = (X - \mu)/(\sigma)$

$Z = (22.4 - 23.3)/(1.4)$

$Z = -0.64$

$Z = -0.64$ has a pvalue of 0.2611

26.11% of women in the United States will wear a size 6 or smaller

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is $ 32.68 , and the cost for using 52 HCF is $ 95.38 . What is the cost for using 19 HCF of water?

Answers

Answer:

$40.93

Step-by-step explanation:

Given

Linear function of:

14 HCF = $32.68
52 HCF = $95.38

To find:

19 HCF = ?

Solution

Linear equation in slope-intercept form:

y(x) = mx +b

We have points of: (14, 32.68), (52, 95.38):

y(14) = 14 m + b
y(52) = 52 m +b

Using the points we can find the value of m and b:

m= (y2-y1)/(x2-x1)
m= (95.38 - 32.68)/(52 - 14)
m = 62.7/ 28
m= 1.65

Then finding b:

14*1.65 +b = 32.68
b= 32.68 - 23.1
b= 9.58

So the function is:

y = 1.65 x + 9.58

Then y(19) is found as:

y(19) = 1.65*19 + 9.58
y(19) = 40.93

Answer: Cost of 19 HCF of water is $40.93

Consider the following information about travelers on vacation: 40% check work email, 30% use a cell phone to stay connected to work, 25% bring a laptop with them, 23% both check work email and use a cell phone to stay connected, and 50% neither check work email nor use a cell phone to stay connected nor bring a laptop. In addition, 84 out of every 100 who bring a laptop also check work email, and 70 out of every 100 who use a cell phone to stay connected also bring a laptop. (a) What is the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected? (b) What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected? (c) If the randomly selected traveler checked work email and brought a laptop, what is the probability that he/she uses a cell phone to stay connected? (Round your answer to four decimal places.)

Answers

The probability that a randomly selected traveller who checks work email also uses a cell phone to stay connected is 57.5%.

The probability that someone who brings a laptop on vacation also uses a cell phone to stay connected is 70%.

If the randomly selected traveller checked their work email and brought a laptop, the probability that he/she uses a cell phone to stay connected is 58.8%.

We have,

Let:

C = Check work email

P = Use a cell phone to stay connected

L = Bring a laptop

Given information:

P(C) = 0.40 (Probability of checking work email)

P(P) = 0.30 (Probability of using a cell phone to stay connected)

P(L) = 0.25 (Probability of bringing a laptop)

P(C ∩ P) = 0.23 (Probability of both checking work email and using a cell phone to stay connected)

P(Neither) = 0.50 (Probability of neither checking work email, using a cell phone to stay connected, nor bringing a laptop)

Additional information:

P(C | L) = 0.84 (Probability of checking work email given that a laptop is brought)

P(P | L) = 0.70 (Probability of using a cell phone to stay connected given that a laptop is brought)

a. For the value of P(P | C), use the conditional probability formula:

P(P | C) = P(C ∩ P) / P(C)

P(P | C) = 0.23 / 0.40

P(P | C) = 0.575

b. For the value of P(P | L), use the conditional probability formula:

P(P | L) = P(P ∩ L) / P(L)

P (P | L) = 0.70

c. For the value of P(P | C ∩ L), use the conditional probability formula:

P(P | C ∩ L) = P(C ∩ P ∩ L) / P(C ∩ L)

Since we don't have the direct probability of P(C ∩ P ∩ L), we can use the information provided:

P(C | L) = 0.84

P(P | C ∩ L) = P(C | L) × P(P | L)

P(P | C ∩ L) = 0.84 × 0.70

P(P | C ∩ L) = 0.588

Thus, The probability that a randomly selected traveller who checks work email also uses a cell phone to stay connected is 57.5%.

The probability that someone who brings a laptop on vacation also uses a cell phone to stay connected is 70%.

If the randomly selected traveller checked their work email and brought a laptop, the probability that he/she uses a cell phone to stay connected is 58.8%.

Learn more about probability here:

brainly.com/question/14099682

#SPJ12

Other Questions

Which graph does NOT represent a function?

Find the range of the graphed function.OO A. -4sys 8OB. y2-4OO C. -4 sys 9OD. yis all real numbers.

Which expression is equivalent to 3/ x^5y

One cup of popcorn kernels makes four cups of popped corn. There are eight cups of kernels in a bag. How many cups of popped corn will one bag of kernels make?