What is one of the solutions to the following system of equations? y2 x2 = 53 y − x = 5 (−10, −5) (−7, −2) (7, 2) (5, 10).

Answers

Answer 1

The solution of the system of equation is (-7, -2).

Given

The system of the equations;

[tex]\rm y^2 + x^2 = 53 \\\\y -x = 5[/tex]

From equation 1

[tex]\rm y -x=5\\\\y = 5+x[/tex]

Substitute the value of y in equation 1

[tex]\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2[/tex]

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

[tex]\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2[/tex]

Hence, the solution of the system of equation is (-7, -2).

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Related Questions

6m + 17  is greater then or equal to 77 (HELP WILL GIVE BRAINLIST)

Answers

6m> 60

m>10

m is greater than or equal to 10

Answer:

if 6m+17 is greater than or equal to 77 it means that m≥10

Given the points A(-6, 8) and B(4, -6), find the slope of the line that contains these two points.

Answers

Answer:

m=-7/5

Step-by-step explanation:

y=y2-y1/x2-x1

m=-6-8/4-(-6)

m=-7/5

SOMEONE PLEASE HELP ME

ANYONE WHO HELPS ME GETS ONE HUNDRED POINTS

Answers

Answer:

  80 ft²

Step-by-step explanation:

The carpet area will be the area of the pentagon less the 25 square feet taken up by the tree. The area of the pentagon is found by putting the given numbers into the given formula.

  pentagon area = 5((7 ft)(6 ft))/2 = 105 ft²

  carpet area = 105 ft² -25 ft² = 80 ft²

Peter will need 80 square feet of carpet.

Mason is building a scale model of a truck, using the scale factor 5:64. The actual measurements of the truck are given in this table.

Drag and drop the length of the scale model of the truck.

Measurements are rounded to the nearest tenth of an inch.
Dimension Measurement
Length 230 in.
Width 79 in.
Height 80 in.

Answers

Here are dimensions of the scale model of the truck:

Length = 18 inches

Width =  6.2 inches

Height = 6.3 inches

What are the dimensions?

A scale drawing is a smaller image of a bigger image. The scale drawing is usually reduced at a constant dimension

Length = (5 x 230) / 64 = 18 inches

Width = (5 x 79) / 64 = 6.2 inches

Height = (5 x 80) / 64 = 6.3 inhes

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1. Find the value of x. If your answer is not an integer, leave it in simplest radical form.
Х
32
12

Answers

Answer:

4[tex]\sqrt{73}[/tex] units

Step-by-step explanation:

The given shape is a right triangle and in right triangles the sum of square length of legs is equal to square length of hypotenuse (represented with x in here):

12^2 + 32^2 = x^2

1168 = x^2 find the root for both sides

4[tex]\sqrt{73}[/tex] =x

IM TOO d u m b FOR THIS

Answers

Answer:

x > 12, so the answer is the last one or D

Step-by-step explanation:

2/3x − 5 > 3

Step 1: Add 5 to both sides.

2/3x − 5 + 5 > 3 + 5

2/3x > 8

Step 2: Multiply both sides by 3/2.

2/3x * (3/2) > 8 * (3/2)

x > 12

> = open circle

< = open circle

≤ = closed circle

≥ = closed circle


Suppose you are adding two negative integers. Will the sum be positive or negative?
Show me an example of adding two negative integers and explain how you know what the
answer will be

Answers

Answer: Adding two negative integers will still keep the sum negative.

Step-by-step explanation: An integer is a whole number, it can be either positive or negative. If it’s a fraction that cannot be simplified to a whole number, then it’s not an integer.

An example of the answer would be -4 + -6. This would equal to -10. Positive and negative would remain negative in math.

length of a cube is 13 feet, what is the correct way to write the expression

Answers

take side as a

volume of cube=a×a×a

= 13×13×13

Find the 51st term of the arithmetic sequence -17, -25, -33

Answers

The explicit formula is an = −8n − 9


So plug in 51 as n

-8(51) - 9

-408 - 9

-417


51st term = -417

you have 26 dogs and 69 cats . what is your ratio of dogs to cats?

Answers

Answer:

Ratio is 26:69

Step-by-step explanation:

[tex]{ \tt{dogs : cats = \frac{dogs}{cas} }} \\ [/tex]

dogs → 26cats → 69

[tex]{ \tt{dogs : cats = \frac{26}{69} }} \\ \\ { \underline{ \tt{ \: dogs :cats = 26 : 69 \: }}}[/tex]

Answer:

Step-by-step explanation:

dogs : Cats = 26 : 69

It is in the simplest form as they have no common terms.

                   

True or false:

A closed circle means the number is a part of the solution.

Answers

Answer:

True Hope It's Help

#Carryonlearning

classify by number of terms:

Answers

Answer:

c) trinomial

Step-by-step explanation:

terms are separated by '+' or '-' signs

2/7 times a number minus 11.5 is no more than 13.5

Answers

Answer:

x<=87.5

Step-by-step explanation:

2/7x - 11.5 <= 13.5

2/7x <= 25

x <= 87.5

4y=-3-x
7x-4y=43
elimination please help!!

Answers

Answer:

x = 5 y =-2

Step-by-step explanation:

You can substitute the 4y in,
7x - (-3-x) = 43
7x + 3 + x = 43
8x + 3 = 43
8x = 40
x = 5

Then plug the x back into the equation,
4y = -3 - 5
4y = -8
y = -2

Answer:

y= -2 x=5

Step-by-step explanation:

(See attachment below)

Question 10
Find a value of "n" that makes the equation true:
1.5 * n = 10

Answers

Answer:

20/3

Step-by-step explanation:

1.5 * n = 10

We need to "undo" the multiplication by canceling it with division.

1.5 * n / 1.5 = 10 / 1.5

10 / 1.5 is also 20/3

n = 20/3

Someone please help me I don’t understand

Answers

First you need to find the area of the base of the triangle. On the base of the triangle you use the area of a triangle formula which gives you: 1/2(20*21) which is 210. Now you have the area of the base. To find the volume (the storage space) you need to use the formula V=Area of base(height). This would then equal V = 210 (72). Finally that equals 15,120.

Your final answer is 15,120 cubic inches of space.

Four watermelons cost $22. Complete the table.

Answers

Answer:

which table xD

Step-by-step explanation:

:ooo

log1000=3 converted to exponential form​

Answers

The answer to your math equation is 10^3=1000

can someone pleas help with this?? (i really prefer you editing on it but i honestly need this due today!!, please take your time).

Answers

Answer:

She used 5/8 of the seeds.I think the second one is 7/8 but I'm really not sure I understand what they are asking... Its weirdly worded.

Step-by-step explanation:

  1.

1/4 of 2 1/2

(1/4) times 5/2

5/8 of the seeds were used.

 2.

1/2 of 1 3/4

(1/2) times 7/4

7/8

Find the 29th term 29,33,37,41
(arithmetic)

Answers

Answer:

a₂₉ = 141

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 29 and d = a₂ - a₁ = 33 - 29 = 4 , then

a₂₉ = 29 + (28 × 4) = 29 + 112 = 141

Answer:

The 29th term of arithmetic sequence is 141.

Step-by-step explanation:

Here's the required formula to find the arithmetic sequence :

[tex]\longrightarrow{\pmb{\sf{a_n = a_1 + (n - 1)d}}}[/tex]

[tex]\pink\star[/tex] aₙ = nᵗʰ term in the sequence[tex]\pink\star[/tex] a₁ = first term in sequence [tex]\pink\star[/tex] n = number of terms [tex]\pink\star[/tex] d = common difference

Substituting all the given values in the formula to find the 29th term of arithmetic sequence :

[tex]\purple\star[/tex] aₙ = a₂₉[tex]\purple\star[/tex] a₁ = 29[tex]\purple\star[/tex] n = 29 [tex]\purple\star[/tex] d = 4

[tex]\leadsto{\sf{ \: \: a_n = a_1 + (n - 1)d}}[/tex]

[tex]\leadsto{\sf{ \: \: a_{29} = 29 + (29 - 1)4}}[/tex]

[tex]\leadsto{\sf{ \: \: a_{29} = 29 + (28)4}}[/tex]

[tex]\leadsto{\sf{ \: \: a_{29} = 29 + 28 \times 4}}[/tex]

[tex]\leadsto{\sf{ \: \: a_{29} = 29 + 112}}[/tex]

[tex]\leadsto{\sf{ \: \: a_{29} = 141}}[/tex]

[tex]\star \: \: \red{\underline{\boxed{\sf{a_{29} = 141}}}}[/tex]

Hence, the 29th term of arithmetic sequence is 141.

[tex]\rule{300}{2.5}[/tex]

The table represents the height of a ball that is dropped, h(t), after t seconds.

Answers

Answer:

hello. me or anyone else don't have enough information to give you an answer to anything..

Step-by-step explanation:

please show a picture of the question you would like to ask

For what values of x, does the graph's slope equal zero?​

Answers

Answer:

1 < x ≤ 2

Step-by-step explanation:

A graph's slope equals zero when there is a change in the x-value, but there's no change in the y-value.

Here, we can see in the piecewise function that between 1 (not included) and 2 (included), the slope of the graph is 0.

Therefore, 1 < x ≤ 2 is correct

PLS HELP ILL GIVE BRAINLIEST

Answers

The answer is y = 1/3x + 4. -3x repricdal = 1/3. 4=1/3(0) + 4

Answer:

y=1/3x+4

Step-by-step explanation:

y=2-3x is equivilent to y=-3x+2

Here were see that the coefficient of x is -3. In order to find a line that is perpendicular to another line, we need to put the opposite sign and make the coefficient the reciprical.

So now we know that y=1/3x will be perpendicular to your line. If the point goes through (0,4) that means when x is zero, y is 4. If we plug that into our expression 4=1/3*0, we see that we need to add 4 to make this true.

So our answer is y=1/3x+4

help and show work plzz

Answers

Answer:

Step-by-step explanation:

1. -20 x + y - 10 = 0, y = 10 (2 x + 1), y= 20x + 10

2. The first row will represent the one-time art supply fee. the art supply fee is $10

3. The linear equation for the cost of a lesson in slope-intercept is

y = 20x + 10
4. I cannot directly graph, but I will give points. After that, connect the points in a line. (0,10), (2,50), (4,90), (6,130).

Question 5 and 6 previously answered on different question.

Hope this helps. :) Cya later.

I have been struggling with this for a while lol​

Answers

Answer:

  f(x) = (3x -2)(2x +1)

Step-by-step explanation:

The procedure for factoring expression of the form ...

  ax² +bx +c

is to look for factors of a·c that have a sum of b.

The product a·c is 6·(-2) = -12. You are looking for factors that have a sum of b = -1. From your familiarity with multiplication tables, you know ...

  -12 = 1(-12) = 2(-6) = 3(-4)

The sums of the factor pairs in this list are -11, -4, -1. So, the last pair of factors, {3, -4} is the one we're looking for.

__

At this point, there are several ways to proceed. Perhaps the simplest is to rewrite the linear term as the sum of terms involving these factors:

  -x = 3x -4x

  f(x) = 6x² +3x -4x -2

Now, the expression can be factored 2 terms at a time:

  f(x) = (6x² +3x) -(4x +2) . . . . . pay attention to signs

  f(x) = 3x(2x +1) -2(2x +1) . . . . factor each pair

  f(x) = (3x -2)(2x +1) . . . . . . . . factor out the common factor of (2x+1)

Can someone please help me with this?

Answers

Answer:

[tex]S_{13}[/tex] = 403

Step-by-step explanation:

the sum to n terms of an arithmetic series is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a + l) ← a is the first term and l the last term

here a = - 5 and l = 67 , then

[tex]S_{13}[/tex] = [tex]\frac{13}{2}[/tex] (- 5 + 67) = 6.5 × 62 = 403

Which expression is equivalent to 2/3−1/4x+1/2x−1/6?

Answers

Answer:

-(1 3/4)x - 5

Step-by-step explnation:

1/2x+(−7)−2 1/4x−(−2)   =>   (1/2)x + (−7) − (2 1/4)x − ( −2)?

Combining the x terms, we get:

-2 1/4 + (1/2)x, or - (1 3/4)x - 7 + 2.

Again combining like terms, we get the final answer

-(1 3/4)x - 5

If answer choices are given (which it seems they are here), please share them.

The expression 2/3 − 1/4x + 1/2x − 1/6 is equivalent to 1/2 + 1/2x.

How to solve an expression?

To simplify the expression 2/3 − 1/4x + 1/2x − 1/6, we first need to combine the terms with the same variable.

The terms -1/4x and 1/2x have the same variable, so we can combine them:

-1/4x + 1/2x = (1/2 - 1/4)x = 1/4x

Now, the expression becomes:

2/3 + 1/4x - 1/6 + 1/4x

To simplify further, we can find a common denominator of 12:

(2/3) + (1/4x) - (1/6) + (1/4x) = (8/12) + (3/12x) - (2/12) + (3/12x)

Now, we can combine like terms:

(8/12) - (2/12) + (3/12x) + (3/12x) = (6/12) + (6/12x)

Simplifying the fraction:

6/12 = 1/2

The expression simplifies to:

1/2 + 1/2x

Therefore, the expression 2/3 − 1/4x + 1/2x − 1/6 is equivalent to 1/2 + 1/2x.

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One root of f (x) = x cubed minus 4 x squared minus 20 x 48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Answers

Answer:

C )  ( x - 2 ) ( x + 4 ) ( x - 6 )

Step-by-step explanation:

.

How do I graph y=1/6x - 1

Answers

Answer:

-1 is on the Y axis (vertical) Slope is 1/6

Step-by-step explanation:

-1 is on the Y axis. Go up 1 a right over 6. <- that is the slope

How do states with no personal income tax raise money for public services?

Answers

Answer:

The funding for those services typically comes from three key areas: property taxes, sales taxes, and income taxes. States without a personal income tax might ask residents and visitors to pay more sales tax on groceries, clothes, and other goods, as is the case in Washington.

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