1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
artcher [175]
3 years ago
8

Help ! solve the following system of equations -9x+2y=-13 2x-9y=20

Mathematics
1 answer:
Stella [2.4K]3 years ago
5 0

Answer: x = 1, y = -2

Step-by-step explanation:

-9x+2y=-13

x= 13/9 + 2/9y

2x-9y=20

2(13/9+2/9y)-9y=20

<em>Substitute y with -2.</em>

<em />

x= 13/9+2/9(-2)

<em>After solving you'll see that 1 is a possible solution for x.</em>

<em />

Check your answer

-9x+2y=-13

-9x1+2(-2) = -13

2x-9y=20

2x1-9(-2) = 20

-13 = -13

20 = 20

Therefore, x=1 and y=-2

You might be interested in
A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman
Yanka [14]

Answer:

W\approx 8.72 and L\approx 15.57.

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

2L+W+\frac{1}{2}(2\pi r)=38

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

2L+W+\frac{1}{2}(2r\pi)=38

2L+W+\frac{\pi}{2}W=38

Let us find area of window equation as:

\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)

\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)

\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})

\text{Area}=W\cdot L+\frac{\pi}{8}W^2

Now, we will solve for L is terms W from perimeter equation as:

L=38-(W+\frac{\pi }{2}W)

Substitute this value in area equation:

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2

Since we need the area of window to maximize, so we need to optimize area equation.

A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2  

A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2  

Let us find derivative of area equation as:

A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W  

A'=38-2W-\pi W+\frac{\pi}{4}W    

A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W

A'=38-2W-\frac{3\pi W}{4}

To find maxima, we will equate first derivative equal to 0 as:

38-2W-\frac{3\pi W}{4}=0

-2W-\frac{3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}=-38

\frac{-8W-3\pi W}{4}*4=-38*4

-8W-3\pi W=-152

8W+3\pi W=152

W(8+3\pi)=152

W=\frac{152}{8+3\pi}

W=8.723210

W\approx 8.72

Upon substituting W=8.723210 in equation L=38-(W+\frac{\pi }{2}W), we will get:

L=38-(8.723210+\frac{\pi }{2}8.723210)

L=38-(8.723210+\frac{8.723210\pi }{2})

L=38-(8.723210+\frac{27.40477245}{2})

L=38-(8.723210+13.70238622)

L=38-(22.42559622)

L=15.57440378

L\approx 15.57

Therefore, the dimensions of the window that will maximize the area would be W\approx 8.72 and L\approx 15.57.

8 0
3 years ago
A number increased by 7
postnew [5]

Answer:

x+7

Step-by-step explanation:

7 0
3 years ago
2 3 2/15+ 5 2 8/15+ 1 6 1/15=​
allsm [11]

Answer:

91 11/15

Step-by-step explanation:

 23+2/15+52+8/15+16+1/15

=23+52+16+2/15+8/15+1/15

=91+11/15

8 0
3 years ago
Read 2 more answers
A recent study was conducted to explore the relationship between the weight of a car and miles per gallon (gas mileage). A linea
k0ka [10]

Answer: a.  iv. The weight of a car can be used to explain about 79.6% of the variability in gas mileage using a linear relationship.

b. ii. There is a fairly strong, negative relationship between car weight and miles per gallon.

Step-by-step explanation:

  • A coefficient of determination (denoted by R²) is a measure in a regression model that determines proportion of the variance in the dependent quantity that is predictable from the independent quantity.
  • It is square of correlation coefficient (R).

Here,   independent quantity = weight of a car  

dependent quantity = miles per gallon (gas mileage)

The coefficient of determination (R²) was reported to be 79.6%.

That means, The weight of a car can be used to explain about 79.6% of the variability in gas mileage using a linear relationship.

  • A correlation coefficient(R) tells about the strength and direction of relation .
  • It lies between -1 and 1.

For the study, the correlation coefficient R is -0.8921.

There is a fairly strong, negative relationship between car weight and miles per gallon.

7 0
3 years ago
24 inches is equal to how many feet
cupoosta [38]
The answer is 2 feet it is equal to two feet

3 0
3 years ago
Read 2 more answers
Other questions:
  • A network charges $855,000 for a 30-second ad during a major televised sports event. The advertisers must purchase a minimum of
    5·1 answer
  • Someone help me with this
    7·2 answers
  • Lauren is the touring students at the library on Saturday if she is a library for a total of 6 hours and she helps each student
    10·1 answer
  • Kamal's bakery recently spent a total of $700 on new equipment and their average hourly operating costs are $12. Their average h
    13·1 answer
  • (6k^4-k^3-8k)-(5k^4+6k-8k^3)​
    12·2 answers
  • 0401) Which unitrate is equivalent to 17 miles per gallon
    14·1 answer
  • What is the measure of angle x?
    8·1 answer
  • 2. Identify the measure of angle x. (Write your answer in number form only, 1 point
    9·2 answers
  • Help please.... almost done.
    8·2 answers
  • During a period of inflation, the graph of the consumer price index (CPI) will
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!