Given:
The system of equations:
[tex]x-3y=9[/tex]
[tex]\dfrac{1}{5}x-2y=-1[/tex]
To find:
The number that can be multiplied by the second equation to eliminate the x-variable when the equations are added together.
Solution:
We have,
[tex]x-3y=9[/tex] ...(i)
[tex]\dfrac{1}{5}x-2y=-1[/tex] ...(ii)
The coefficient of x in (i) and (ii) are 1 and [tex]\dfrac{1}{5}[/tex] respectively.
To eliminate the variable x by adding the equations, we need the coefficients of x as the additive inverse of each other, i.e, a and -a So, a+(-a)=0.
It means, we have to convert [tex]\dfrac{1}{5}[/tex] into -1. It is possible if we multiply the equation (ii) by -5.
On multiplying equation (ii) by -5, we get
[tex]-x+10y=5[/tex] ...(iii)
On adding (i) and (iii), we get
[tex]7y=14[/tex]
Here, x is eliminated.
Therefore, the number -5 can be multiplied by the second equation to eliminate the x-variable.
Last year the girls basketball team had 12 fifth grade students and 3 sixth grade students what is the ratio of sixth grade students to total students on the team
(Include a answer in paper)
Answer:4:1
Step-by-step explanation: you have to find the unit rate ( how much for 1) so you set 3 to equal 1 and to do that you divide by three so you do that to the 12 also
The answer for your question will be...3:12
Sam earned $154 washing 7 cars. He earned the same amount for washing each car
Select all the equations that show reasonable estimates for the amount Sam eamed washing each car
A $140 = 7 = $20
B. $190 = 9 = $10
C. $160 = 8=320
D. $150 = 5= $10
E $150 = 3= $50
Answer:
the answer is A cause you divide 7 by 140 and the answer is 22 so 20 is the closest
Help me guys, Due now please
Answer:
about 8.3 miles an hour.
Step-by-step explanation:
34/4 is 8.5
90/11 is 8.2
average: 8.3
In the equation y = 2x + 5, what values represent the m (slope) and the b (y-intercept)?
Answer:
m(slope)=2
b(y-intercept)=5
Step-by-step explanation:
Answer:
2x represents the slope and 5 represents the y intercept.
1. What is the 15th partial sum of the geometric sequence (262,144; 32,768; 4,096; 512; ...)? Round to the nearest whole number, if needed.
Answer:
[tex]S_{15} = 299593[/tex]
Step-by-step explanation:
Given
[tex]262144,\ 32768,\ 4096,\ 512; ...[/tex]
Required
Determine the 15th partial sum
The nth partial sum of a geometric series is:
[tex]S_n = a* \frac{1 - r^n}{1 - r}[/tex]
In this case:
[tex]a = 262144[/tex]
[tex]n = 15[/tex]
r is calculated as:
[tex]r = \frac{32768}{262144}[/tex]
[tex]r = 0.125[/tex]
Substitute values for a, r and n in [tex]S_n = a* \frac{1 - r^n}{1 - r}[/tex]
[tex]S_{15} = 262144* \frac{1 - 0.125^{15}}{1 - 0.125}[/tex]
[tex]S_{15} = 262144* \frac{1}{0.875}[/tex]
[tex]S_{15} = \frac{262144* 1}{0.875}[/tex]
[tex]S_{15} = \frac{262144}{0.875}[/tex]
[tex]S_{15} = 299593.142857[/tex]
[tex]S_{15} = 299593[/tex] -- approximated
Studies suggest that people with a high sense of humor tolerate negative events better than people with low sense of humor. Let x represent the intensity of a negative life event. To find the depression level for people
Answer:
explain
Step-by-step explanation:
1. Look at the table.
Х
у
2
0.4
4.
0.8
7
1.4
9
1.8
11 2.2
What is the constant of proportionality?
A. 1.6
B. 5
C. 0.2
D. 2
Answer:
D
Step-by-step explanation:
On the X side they add 2 every time to reach the next number needed. For example if it was to keep going the nect x would be 13
What proportion can be used to find 65% of 90?
Answer:
C. 65/100 = x/90
Step-by-step explanation:
65% of 100 is 65/100 as 65% of 90 is x/90.
You can find the correct answer by cross multiplying to see if the part / whole = percent / 100.
Solve for r.
5r - -17r - 4r + -9 = 9
Answer:
r=1
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
5r−−17r−4r−9=9
5r+17r+−4r+−9=9
(5r+17r+−4r)+(−9)=9(Combine Like Terms)
18r+−9=9
18r−9=9
Step 2: Add 9 to both sides.
18r−9+9=9+9
18r=18
Step 3: Divide both sides by 18.
18r/18 = 18/18
r=1
Which of the following units are most commonly used in the United States? Check all that apply
A. Ounces
B. Meters
C. Kilograms
D. Feet
please help I am confused i'll answer one of your questions!! I got it wrong the first time
Answer:
Step-by-step explanation:
22.2
Answer:
22.2
Step-by-step explanation:
What is equal to 3.6 x 0.005
Answer:
0.018
Step-by-step explanation:
basta yan ang sagot
Answer: 0.018
Step-by-step explanation: insta: camryn_boeling
Determine whether or not x = 2 would make the following functions equal. Show your work.
y = 2x + 1 and
y = 4x – 3
Answer:
Yes.
Step-by-step explanation:
Substituting x = 2 into y = 2x + 1,
y = 5
Substituting x = 2 into y = 4x - 3
y = 5
Which equation is equivalent to the given equation?
X^2-14x=-48
Answer:
(x-6)(x-8)=0
Step-by-step explanation:
x^2-14x+48=0
Factorizing
x^2-8x-6x+48=0
(x^2-8x)+(-6x+48)=0
x(x-8)-6(x-8)=0
(x-6)(x-8)=0
In the box, type the number that correctly completes the sentence.
Andrew bought a sandwich for $4.37. If he gives the cashier a $10 bill, he
should receive $
in change.
❌Will mark brainliest answer
Select all the correct answers.
Which equations have one solution?
How much water does Ms. Maryna need to add to 60g of sugar to make a syrup that is 20% concentrated?
Answer:240
Step-by-step explanation:You get 240 because 60X4 is 240. to get the 4, you need to use 100-20, then therer would be 80. 80 divided by 20 is 4, which is the amount of water.
Ms. Maryna needed 240g water to add to 60g of sugar to make a syrup that is 20% concentrated
Given that,
Ms. Maryna need to add to 60g of sugar to make a syrup that is 20% concentrated.
We have to determine,
How much water does she need.
According to the question,
Ms. Maryna need to add to 60g of sugar to make a syrup that is 20% concentrated.
If Maryna need 20% sugar by mass,
Then,
[tex]= \dfrac{20}{100} = \dfrac{1}{5}[/tex]
It is 1/5 of the total mass is sugar,
And ,
Total water needed is,
[tex]= 1-\dfrac{1}{5} \\\\=\dfrac{5-1}{5}\\\\= \dfrac{4}{5}[/tex]
It needed 4\5 times of water.
Then,
Maryna needed times as much water as sugar,
[tex]= \dfrac{4}{5} \times \dfrac{5}{1}\\\\= 4 \ times[/tex]
Maryna needed 4 times as much water as sugar.
Maryna need water to add in syrup = 4 × 60g = 240g.
Hence, Maryna needed 240g of water to add to make a syrup.
To know more about Multiplication click the link given below.
https://brainly.com/question/11921451
Julie’s family took a 4-day trip. Julie’s mother wrote an equation to calculate their gas mileage, m, in miles per gallon. Let d = the number of total miles driven on the trip. Let g = the total number of gallons of gas used for the trip.
=
What was the gas mileage for the 4-day trip?
Answer:
[tex]m = 26[/tex]
Step-by-step explanation:
Given
See attachment for missing details
Required
Determine the gas mileage for the trip
First, we calculate the miles driven
[tex]Miles = 476 + 439 + 382 + 263[/tex]
[tex]Miles = 1560[/tex] --- d
Next, we calculate the amount of gas used
[tex]Gas = 15.0 + 13.5 + 15.4 + 16.1[/tex]
[tex]Gas = 60.0[/tex] ---- g
The gas mileage is then calculated as:
[tex]m = \frac{d}{g}[/tex]
[tex]m = \frac{1560}{60}[/tex]
[tex]m = 26[/tex]
Hence, the gas mileage is 26 miles per gallon
javier is shopping for school supplies . he is buying 3 of the same notebooks and 2 pens that cost $1.75 each. His total, before tax, is $12.47. which equation below could be used to determine the cost of each notebook.
A. 3(1.75)+2x=12.47
B.3x+2(1.75)=12.47
C. 3(12.47)+2(1.75)+x
D. 3(1.75)+2(12.47)=x
PLEASE HELP
Answer:
3notebooks
2pens
the pens are 1.75 each
total is 12.47
i wouldnt use any of these
12.47-(2x1.75)=? then divide that by three and you get each notebook
but
c...
please help me!
7. Two hours after leaving his home, Nolan traveled a distance of 120 miles. Distance in this scenario is represented by d and time is represented by t.. [2 points]Part A. Assuming that Nolan travels at the same speed during his trip, which of the following statements can be used to describe the distance Nolan may have traveled?
a.Nolan traveled 180 miles after 3 hours.
b.Nolan traveled 60 miles after 2 hours
.c.Nolan traveled 120 miles after 1 hour.
d. Nolan traveled 60 miles after 0 hours.
Part B. Write an equation that represents the distance traveled by the car for an amount of time. Then name the dependent variable
.a.d=120t, d is the dependent variable
b.d=60t, d is the dependent variable
c.d=120t, t is the dependent variable
d.
d=60t, t is the dependent variable
Answer:
bueh
Step-by-step explanation:
I will give the BRAINIEST
Simplify. Write your answer in standard form.
(4x^3+6x-7)+(3x^3-5x^2-5x+9)
Answer:
Step-by-step explanation:
Combine like terms.Like terms have same variable with same exponent
4x³ + 6x - 7 + 3x³ - 5x² - 5x + 9 = 4x³ + 3x³ - 5x² + 6x - 5x - 7 + 9
= 7x³ -5x² + x + 2
Explain the power of products property and give an example.
Answer:
(ab)^n = a
Step-by-step explanation:
It basically says to take the entire equation in the parentheses and multiply by the exponent, sorry for the horrible handwriting
Based on the following scenarios, match the scenario with the correct type of problem. Group of answer choices
a. A local Toyota dealership wants to estimate the average cost of maintenance repairs car owners spend per year. They send out a survey asking locals to report the cost for their vehicle over the past year.
b. The University of Florida wants to estimate what number of students visit Library West multiple times per week. They ask the following question: "Do you visit Library West more than twice a week?"
c. A local Toyota dealership wants learn about customers use of the vending machines in the waiting area lobby. They ask the question: "Do you purchase food or drink from the vending machines?"
d. The University of Florida wants to estimate how long students visit Library West per week. They send out a survey and ask respondents to write down how many hours per week they visit Library West.
Options for each question:
1. One proportion
2. One mean
Answer:
Matching the scenario with the correct type of problem:
a. one mean
b. one proportion
c. one proportion
d. one mean
Step-by-step explanation:
A one-proportion problem is tested using the one-sample proportion test. This estimates the proportion of a population by comparing the proportion to a target or reference value. On the other hand, a one-mean problem is tested using the one-sample t-test. This tests whether a population mean is significantly different from some hypothesized value.
John has two different sugar syrups. Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water. How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Answer:
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
Step-by-step explanation:
Syrup A : 2 parts sugar , 8 parts of water .
Total = 10 parts
Syrup B : 3 parts sugar , 5 parts of water .
Total = 8 parts .
Mixture required 280 quarts , 3 parts sugar , 7 parts water
In 280 quarts , sugar = 280 x 3 / ( 3 + 7 )
sugar = 84 parts
Let volume of syrup A be x , volume of syrup B = 280 - x
sugar A = 2 x / 10 = 0.2 x
sugar B = 3 ( 280 - x ) / 8 = .375 ( 280 - x )
Total sugar = .2 x + .375 ( 280 - x ) = 84 .
.2 x + 105 - .375 x = 84
105 - 84 = .375 x - .2 x = .175 x
.175 x = 21
x = 21 / .175 = 120
Volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts .
John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
Given that,
John has two different sugar syrups.
Syrup A is 2 parts of sugar and 8 parts of water, and Syrup B is 3 parts of sugar and 5 parts of water.
We have to determine,
How much of each should john mix together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
According to the question,
Syrup A: 2 parts sugar, 8 parts of water.
Total number of parts = 10 parts
Syrup B : 3 parts sugar, 5 parts of water.
The total number of parts = 8 parts.
The mixture required 280 quarts, 3 parts sugar, 7 parts water,
In 280 quarts, parts of sugar are,
[tex]= \dfrac{280 \times 3 }{ ( 3 + 7 )}\\\\= \dfrac{280 \times 3}{10}\\\\= 84[/tex]
Let the volume of syrup A be x,
And the volume of syrup B be 280 - x
[tex]Sugar\ A = \dfrac{2x}{10} \\\\Sugar \ A = 0.2 x[/tex]
[tex]Sugar \ B = \dfrac{3 ( 280 - x ) }{8 }\\\\Sugar \ B= .375 ( 280 - x )[/tex]
The total amount of sugar is,
[tex]0.2 x + 0.375 ( 280 - x ) = 84 \\\\0.2 x + 105 -0 .375 x = 84\\\\105 - 84 = 0.375 x - 0.2 x = 0.175 x\\\\ 0.175 x = 21\\\\x = \dfrac{21}{0.175}\\\\x = 120[/tex]
Therefore,
The volume of syrup A = 120 quarts
Volume of syrup B = 280 - 120 = 160 quarts
Hence, John mixes 120 quarts of syrup A and 160 quarts of syrup of B together to get 280 quarts of syrup that is 3 parts sugar and 7 parts water.
For more details, refer to the link.
https://brainly.com/question/11921451
Help
Subtract 2/9 - 2/15 fractions in Lowest terms
20points. Find an equation for the linear graph.
Use the two endpoints to find the slope:
(0,2) and ( 5,5.5)
Slope = change in y over change in x:
Slope = (5.5-2)/(5-0) = 3.5/5 = 0.7
The y intercept is the y value when x is 0, which is 2
Equation: c = 0.7x + 2
What is 83% as a decimal SHOW WORK IF U CAN HELP ASAP!!
0.83Answer:
Step-by-step explanation:
83% means 83 per 100 or 83/100 if you divide 83 by 100 you get 0.83
Answer:
.83
Step-by-step explanation:
to turn a percentage into a number you have to divide by 100, meaning you need to move the decimal point to the left 2 times so you get:
.83
hope this helps!!
If 8% of a number is 40, find 2% of that number.
Answer:
10%
Step-by-step explanation:
0.08×anumber=40,then 0.02x=?
x=40/0.08=500
0.02×500=10
An equation is shown.
1/12(14.4+18)+2.75.
Part A
Rakim starts to evaluate the expression.
Step 1: 1.2 + 18+ 2.75.
The expression Rakim wrote for step 1 is incorrect. Explain how to correct the error in step one.
Enter your explination in the box provided
Answer:
Step 1 should be (14.4+18)...PEMDAS
Step-by-step explanation:
The expression Rakim wrote for step 1 is incorrect therefore the correct solution will give 5.45.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given an expression as;
1/12(14.4+18)+2.75.
Part A;
Rakim starts to evaluate the expression.
Step 1: first solve the bracket;
1/12(14.4+18)+2.75.
1/12(32.4) + 2.75.
2.7+ 2.75.
= 5.45
The expression Rakim wrote for step 1 is incorrect therefore the correct solution will give 5.45.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
What is the process of 8q+6=4q-14
Answer:
Step-by-step explanation:
8q+6=4q-14
minus 4q from both sides to get
4q+6=-14
-6 from both sides
4q=-20
divide by 4
q=-5
we can check if this is right by implementing -5 as a substitute for q
-40+6=-20-14
-34=-34