Решить систему методом сложения:{4x-6y=2
2x-y=5

Answers

Answer 1

Answer:

[tex]x=\frac{7}{2} =3.5\\\\y=2[/tex]

Step-by-step explanation:

The addition method (elimination method) allows us to combine two equations in such a way that the resulting equation has only one variable. Then we can use simple algebraic methods to solve that variable

Let:

[tex]4x-6y=2\hspace{10}(1)\\\\and\\\\2x-y=5\hspace{15}(2)[/tex]

Let's multiply (2) by -2:

[tex]-2*(2):\\\\2x(-2)-y(-2)=5(-2)\\\\-4x+2y=-10\hspace{12}(-2*(2))[/tex]

Now, add (1) and (-2*(2)):

[tex](1)+(-2*(2)):\\\\4x+(-4x)-6y+(2y)=2+(-10)\\\\-4y=-8[/tex]

Hence, solving for y:

[tex]y=\frac{-8}{-4} =2[/tex]

Replacing y into (2):

[tex]2x-(2)=5[/tex]

Solving for x:

[tex]2x=5+2\\\\2x=7\\\\x=\frac{7}{2} =3.5[/tex]

Therefore:

[tex]x=\frac{7}{2} =3.5\\\\y=2[/tex]


Related Questions

I need help so, please help

Answers

Answer:

4.2

Step-by-step explanation:

In a 45°45°90° triangle, the ratios of the sides to the hypotenuse is x : x√2

So if x√2 = 6, x = 3√2

3√2 is approximately 4.2

Hope this helps.

find the odd one in the series.835,734,842,761,853,981,532?

Answers

Answer:

835,761,853,981

Step-by-step explanation:

To find how long numbers are odd you look at the last number for example 835,5 is an odd number making the rest of the numbers odd.

Hope my explanation helped

In ΔGHI, the measure of ∠I=90°, IG = 3.9 feet, and GH = 6.3 feet. Find the measure of ∠H to the nearest tenth of a degree.

Answers

Answer:

IG=28.9 ft

Step-by-step explanation:

we know that

In the right triangle GHI

----> by CAH )adjacent side divided by the hypotenuse)

substitute the given values

solve for IG

see the attached figure to better understand the problem

Answer:

H=38.2466≈38.2

Step-by-step explanation:

We suspect the overall mean monthly rent of apartments in Shadyside is higher than in Oakland, so we survey a random sample of Oakland apartments, and a random sample of Shadyside apartments.
1. Which of the following is the most appropriate statistical test to use to determine if the overall mean monthly rent of apartments in Shadyside is higher than in Oakland?
a. Chi-squared test for independence
b. Inference for regression
c. Matched pairs t-test
d. ANOVA
e. Two-sample t-test

Answers

Answer:

e. Two-sample t-test.

Step-by-step explanation:

This is simply because you only have interval level of measure and you are comparing two populations.

Moreso, this hypothesis test is used to determine questions related to the mean in situations where data is collected from two random data samples. The two sample T-test is often used for evaluating the means of two variables or distinct groups, providing information as to whether the means between the two populations differs. It also can be used to compare the responses of males and females who have each received different treatment within an experiment.

Simplify the expression 12k-2+6k

A. 16k2
B. 10k+6
C. 18k-2
D. 16k

Answers

12k-2+6k

find like terms and put them next to each other

12k+6k-2

combine like terms

18k-2

C

Answer:

16k so it is D

Step-by-step explanation:

Help please

The best answer gets brainliest.

Answers

Elon musk is confused too. I need more detail what amount of what

Renting a trailer for 4 days costs $84. Renting the trailer for 5 days costs $100. Using the
linear equation above that represents the (days, cost) which of the following choices
would be the cost for renting the trailer for 10 days?

Answers

Answer:

$210

Step-by-step explanation:

do 84/4 to find out money per day which is 21. 21 x 10 = 210

therefore 210 is the answer

The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with a 99% confidence interval and a margin of error within plus or minus $6. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is ________.
A) 313 B) 284 C) 210 D) 239

Answers

Answer:

D) 239

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Required sample size:

Is n

n is found when [tex]M = 6[/tex]

We have that [tex]\sigma = 36[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]6 = 2.575*\frac{36}{\sqrt{n}}[/tex]

[tex]6\sqrt{n} = 36*2.575[/tex]

Simplifying by 6

[tex]\sqrt{n} = 6*2.575[/tex]

[tex](\sqrt{n})^{2} = (6*2.575)^{2}[/tex]

[tex]n = 238.7[/tex]

We round up, and the answer is 239.

$5000 was invested into an account that earns an annual rate of 4.75%. If money is compounded monthly, how much will the account be worth after 3 years?

Answers

Answer:

  $5764.14

Step-by-step explanation:

The future value formula is useful here.

  FV = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

  FV = $5000(1 +.0475/12)^(12·3) = $5764.14

The account will be worth $5764.14 after 3 years.

Evaluate 8j-k+14 when j=0.25 and k=1

Answers

Hey Mate

Substitute

8(.25)-1+14

2-1+14

1+14

15

Hope it helps

So the right answer is 15.

Look at the attached picture

Hope it will help you

please answer fast im having trouble please help

Answers

Answer:

For the first question the answer is B

For the second question the answer is 15

Step-by-step explanation:

In the picture we can see that 45 is equal to 3 z's, which can also be written as 45 = 3z. Now that we know that 45 = 3z, we can divide both sides by 3 so that we know what z equals.

45 (/3) = 3z (/3)

15 = z

Now we can see that z is equal to 15

Answer:

The answer is B

Step-by-step explanation: 45 is =3z because it shows three triangles in the expression and three z variables so when you add all the variable together you get 3z, hence 45=3z. And the value of z is 1 because like all variables unless the expression accounts for the number of variable they all start out to have only one.

Two lines intersect to form 4 angles. Angles 2 and 4 are vertical angles with angle 2 = 4x + 12 and angle 4 = 7x - 6. a) Find x. b) What is the measure of angle 2 ?

Answers

Answer:

Does this help?

Step-by-step explanation:

2 = 4x + 12 and angle 4 = 7x - 6

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0

y-intercept: 4

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0

y-intercept: 2

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0

y-intercept: 4

Graph 2= 4x + 12

Slope: Undefined

y-intercept: No y-intercept

Plot each graph on the same coordinate system.

4=

2=

4=

2= 4x + 12

4= 7x − 6

How is 5,328 represented in expanded notation

Answers

Answer:

5000

300

20

8

would be your answer :)

why
do we use
quartz clock

Answers

Answer:

because see a time

Step-by-step explanation:

Ryan earned money babysitting. He earned $40, $40, $51, $32 and $22. Find the mean amount he earned.

Answers

Answer:

37

Step-by-step explanation:

add all and divide

Answer:

$37

Step-by-step explanation:

Add the values in the data set:

40 + 40 + 51 + 32 + 22 = 185

There are 5 values in the data set.

Divide 185 by 5:

185 ÷ 5 = 37

The mean amount that Ryan earned should be $37 dollars.

Angles R and S are complementary if m <R=65.3 what is the measure of <S?​

Answers

Answer:

Step-by-step explanation:

if angles are complementary, that means they add up to 90º

if one is 65.3, then the other is just 90 - 65.3

<S = 90º - <R

<S = 90º - 65.3º

<S = 24.7º

Volume of a rectangular prism is 15.75 in.³ the base has an area 10.5 in.² what is the height of the prism?

Answers

Answer:

Volume of a rectangular prism is 15.75 in.³ the base has an area 10.5 in.²

We also have:

Volume of a rectangular prism (V) = base area x height

=> height  = V/base area = 15.75/10.5 = 1.5 in

Hope this helps!

:)

Which statement about a sphere is true?

Answers

Answer:

it is 3D

Step-by-step explanation:

Answer:

Its 3 dimensional

Step-by-step explanation:

I took the test

need some assistance on this question.

Answers

Answer:

Surface area = [tex]2 \pi r^2 = 2 (12)^2 \pi in^2 = 288 \pi in^2[/tex]

Volume =[tex] 2/3 \pi r^3 = 2/3 (12)^3 \pi in^3 = 1152 \pi in^3[/tex]

Answer:

volume = 2/3πr³

2×π×12×12×12

3

1152π

surface area= 2πr²

2×π×12×12

288π

Evaluate 15 + |-3| - 4

Answers

Those lines on both sides of the number means "absolute value." Those lines tell us that the number is positive no matter what. So:

15 + |-3| - 4 → 15 + 3 - 4

Remember to follow PEMDAS when solving.

(15 + 3) - 4

18 - 4

14

Therefore, the answer is 14.

Best of Luck!

Answer: 14

Step-by-step explanation: The vertical bars around the -3 mean that we take the absolute value of that number which is the positive version of that number.

So the absolute value of -3 would be 3.

So we have 15 + (3) - 4 which simplifies to 18 - 4 or 14.

Notice that I used parentheses when first getting rid of the absolute value signs. I think that this method will help you avoid confusion when simplifying absolute values.

It's a good habit to get into for future problems.

The volume of the cylinder pi cm.^3. What is the volume of a cone with the same base and height as the cylinder

Answers

Radius times pi times height I believe

Which phrase represents the algebraic expression – 0472
the product of one-fourth and a number, plus seven
the product of seven and a number
the product of one-fourth and seven, plus a number
the product of seven and one-fourth

Answers

The product of one-fourth and a number plus 7 - 7.25
The product of 7 and a number - 11
The product of one-fourth and seven, plus a number - 11.25
The product of seven and one-fourth - 7.25

Megan's aquarium has a volume of 4,320 cubic inches.

Which could be the dimensions of the aquarium?

Select all that apply.

A 24 in. by 32 in. by 13 in.
B 18 in. by 24 in. by 10 in.
C 22 in. by 25 in. by 18 in.
D 12 in. by 15 in. by 24 in.


Answers

Answer:

B, and D.

Step-by-step explanation:

To calculate all of the possible dimensions, you multiply all of numbers in each letter to get the volume. If the volume in one of the letters equals 4,320 cubic inches, then that letter is one of your answers. For example, if you multiply for letter A, which includes the dimensions 24 in, 32 in, and 13 in, then you would get 9,984, which is not the same as 4,320.

Una tirolina de 26 m de largo está atada entre dos postes que están separados por 24 m. Si Manuela monta la tirolina desde el primer poste a una altura de 50 m, ¿cuál es la diferencia entre los dos postes?

Answers

Answer:

The difference between the heights of the poles is 10m

Step-by-step explanation:

The distance between poles is 24 m

The length of the cable is 26m

You first use the Pythagoras' theorem to calculate the vertical distance between the end of one pole and the end of the other one.

[tex]c_2=\sqrt{h^2-c_1^2}\\\\c_2=\sqrt{(26m)^2-(24m)^2}=\sqrt{100}m=10m[/tex]

The difference between the heights of the poles is 10m

The higher pole has height of 50m

Then, the lower pole has a height of 50m - 10m = 40m

A triangular prism. The rectangular sides are 5 feet by 4 feet, 5 feet by 5 feet, and 5 feet by 3 feet. The triangular sides have a base of 4 feet and height of 3 feet. [Not drawn to scale] 60 square feet 72 square feet 82 square feet 84 square feet

Answers

Answer:

72ft²

Step-by-step explanation:

Calculate the area of each face and then sum them.

area of base = 4 × 5 = 20 ft²

area of back = 5 × 3 = 15 ft²

area of sloping face = 5 × 5 = 25 ft²

area of 2 triangular faces = 2 ×  × 4 × 3 = 4 × 3 = 12 ft²

Thus

surface area = 20 + 15 + 25 + 12 = 72 ft²

What is the distance between the points 3, 7 and 15, 6 on a coordinate plane

Answers

Answer:

[tex]D=\sqrt{145 }\\[/tex]

Step-by-step explanation:

We are actually using Pythagorean theorem here but to be simple

we can use the equation:

D(distance)=[tex]\sqrt{(x_{1}- x_{2} )^{2} +( y_{1}-y_{2})^{2}}[/tex]

=

[tex]D=\sqrt{(15-3)^{2}+(6-7)^{2} } =\\D=\sqrt{(12)^{2}+(-1)^{2} } =\\\\D=\sqrt{144+1 } =\\D=\sqrt{145 }\\[/tex]

(If you meant 16 instead of 6 the answer would be 15)

Hope this helps!

Answer:

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)

Step-by-step explanation:

What is 9+10 please help I have 1 minute left, please

Answers

Answer:

21

Step-by-step explanation:

9 = 3*3

10 = 5*2  

5*3 = 15

2*3 = 6

15 + 6 = 21

Write an equation in slope-intercept form of the line shown

Y=
Can someone help with the answer??

Answers

Answer:

y= -1/2 + 1

Step-by-step explanation:

It starts at +1 which is the B in y=mx+b. B is where a point touches the y-axis.

starting at a point: (-2,2), it goes down 1, and right 2. which now the slope is -1/2 because it is going down.

What is the area of the trapezoid? If necessary, round your answer to the nearest tenth. A trapezoid with bottom side length of 8.5 feet, top side length of 5.5 feet, and height of 6.5 feet. 35.8 feet squared 45.5 feet squared 46.8 feet squared 55.3 feet squared

Answers

Answer:

45.5 sq. feet

Step-by-step explanation:

Area of trapezoid is given by 1/2(sum of parallel sides) * height of trapezoid.

In the problem

Parallel sides are  bottom and top sides with  length of 8.5 feet and 5.5 feet

Thus sum of Parallel sides =  8.5 feet + 5.5 feet = 14 feet

Height =  6.5 feet.

Thus,

area of  trapezoid = 1/2*(14)* 6.5 feet = 7*6.5 feet = 45.5 sq. feet

The area of the trapezoid is whose sides are 8.5 feet and 5.5 feet with a height of 6.5 feet is 45.5 feet squared.

What is the area of a trapezoid?

A trapezoid is a quadrilateral with parallel opposite sides and a height.

Mathematically, the area of a trapezoid can be calculated by using the expression:

[tex]\mathbf{Area \ of\ a \ trapezoid = \dfrac{1}{2}(a+b)\times h}[/tex]

where:

a and b =the two parallel sides of the trapezoidh = height

[tex]\mathbf{Area \ of\ a \ trapezoid = \dfrac{1}{2}(8.5+5.5)\times 6.5}[/tex]

[tex]\mathbf{Area \ of\ a \ trapezoid = \dfrac{1}{2}(14)\times 6.5}[/tex]

[tex]\mathbf{Area \ of\ a \ trapezoid = 45.5 \ ft^2}[/tex]

Learn more about calculating the area of a trapezoid here:

https://brainly.com/question/1410008

#SPJ2

which of the following correctly shows the quotient of 75 divided by 5?

Answers

Answer:

15

Step-by-step explanation:

in multiplication we have given form of expression

Dividend(D) = Quotient(Q) x Divisor(d) + Remainder(r)

The number which is getting divided is called dividend

divisor is the number which divides the dividend.

quotient is the No. of times a dividend is divisible by divisor.

if dividend is not completely divisible by divisor then leftover after quotient * divisor is remainder.

value of remainder should be always less than divisor.

In  the problem given

Dividend is 75

divisor is 5

so by the given above expression

Dividend(D) = Quotient(Q) * Divisor(d) + Remainder(r) ----> 1

we know that 15*5 = 75

75 = 15*5 + 0

comparing with the  expression 1

we have q = 15

r = 0

Thus, quotient is 15.

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