The solutions of this system:x² + y = -4
y=x²-6
are: (Select)
-5) and ( (Select)
-5).

Answers

Answer 1
Answer:

Therefore , the solution of the given problem of equation comes out to be  the system of equations' answers are (-1, -5) and (1, -5).

What is an equation?

The foundation of a regression model based on linearity is the equation y=mx+b. The inclination is B, and the y-intercept is m. Even though y but also y are separate components, the above line is frequently referred as the "mathematical issues with two variables". Two factors make up bivariate linear equations. There are no simple answers for the applications of linear functions. Y=mx+b .

Here,

We can change the second equation into the first equation to find the solution to the system of equations, which results in:

=> x² + (x²-6) = -4

By condensing and rearrangeing, we obtain:

=> 2x² = 2

=> x² = 1

Consequently, x can either be 1 or -1.

We can determine the appropriate values of y by substituting these values of x into either of the two equations:

When x Equals 1:

=> y = x² - 6 = 1 - 6 = -5

When x Equals -1:

=> y = x² - 6 = 1 - 6 = -5

As a result, the system of equations' answers are (-1, -5) and (1, -5).

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You are going to have a swimming pool put your back yard this summer. The dimensions of the pool are going to be 15 ft by 30 ft. There is going to be a concrete walkway around the outside of the pool, but they are not sure how wide it will be. The design of the pool, including the walkway, is shown below.

Answers

The perimeter of a shape is the sum of the all visible side lengths of the shape. The perimeter of the pool including the walkway is 90 + 8x

Given that:

Length = 15

Width = 30

Let the width of the walkway be x.

The dimension of the pool including the walkway is calculated by adding the dimension of the pool to the width of the walkway (on both sides):

So, we have:

Length = 15 + x + x

Length = 15 + 2x

Width = 30 + x + x

Width = 30 + 2x

The perimeter (P) of the walkway is then calculated using:

P = 2 * (Length + Width)

This gives:

P = 2 * (15 + 2x + 30 + 2x)

Collect like terms

P = 2 * (15 + 30+ 2x + 2x)

P = 2 * (45+ 4x)

Open brackets

P = 2 * 45+ 2 * 4x

P = 90+ 8x

Hence, the perimeter of the pool including the walkway is 90 + 8x (see attachment)

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Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution.

Answers

Answer:  x= 4 is an extraneous solution.

Step-by-step explanation:

Since we have given that

3(√(x+5))=-9

We need to find the extraneous solution.

So, our equation becomes,

√(x+5)=(-9)/(3)\n\n√(x+5)=-3\n\n\text{On squaring both sides}\n\nx+55=(-3)^2\n\nx+5=9\n\nx=9-5\n\nx=4

Now, we will check that x = 4 is an extraneous solution.

3√(4+5)\neq -9\n\n3√(9)\neq -9\n\n3* 3\neq -9\n\n9\neq -9

Hence, x= 4 is an extraneous solution.

The solution is x=4.

What is the y-intercept of the line with the equation 4x 2y = 12?

Answers

Hello,
I suppose it is 4x+2y=12

==>4*0+2y=12
==>y=6 and x=12-4*6=-12

Which equation represents the line that passes through the point (3,4) and is parallel to the x-axis?x = 4
x = 3
y = 4
y = 3

Answers

paralell to x axis means x=something

it is first  2 choices

(x,y)
(3,4)
has to pass through x=3

answer is x=3 (2nd option)

6r+7=13+7r
how do you solve this?

Answers

Simplifying 6r + 7 = 13 + 7r Reorder the terms: 7 + 6r = 13 + 7r Solving 7 + 6r = 13 + 7r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7r' to each side of the equation. 7 + 6r + -7r = 13 + 7r + -7r Combine like terms: 6r + -7r = -1r 7 + -1r = 13 + 7r + -7r Combine like terms: 7r + -7r = 0 7 + -1r = 13 + 0 7 + -1r = 13 Add '-7' to each side of the equation. 7 + -7 + -1r = 13 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 13 + -7 -1r = 13 + -7 Combine like terms: 13 + -7 = 6 -1r = 6 Divide each side by '-1'.

Mr. Atinga shared his cattle among his three children Lordia,Anita,and Richmond. He gave 3/5 of cattles to Anita and shared the remaining between Lordia and Richmond in the ratio 2:3 respectively. In all 80 cattle were shared between Lordia and Richmond. How many cattle were shared among the three children How many cattle did Anita receive than Richmond

Answers

Answer:

a). The total number of cattle shared among the three children=200

b). Anita's share=120 cattle

    Lordia's share=32 cattle

    Richmond's share=48 cattle

Step-by-step explanation:

a)

Step 1

Determine fraction shared between Lordia and Richmond as follows;

Lordia:Richmond=2:3

Let the total cattle be x

Lordia's fraction=2/(2+3)=2/5 of x=(2/5)x

Lordia's fraction=(2/5)x

Richmond's fraction=3/(2+3)=3/5 of x=(3/5) x

but;

x=80 cattle

replacing;

Total number of cattle Lordia got=(2/5)×80=32 cattle

Total number of cattle Richmond got=(3/5)×80=48 cattle

Step 2

Express the total cattle Mr. Atinga had initially as follows;

Let the initial number of cattle be y

The fraction remainder given to Lordia and Richmond=Initial number-fraction of the totat given to Anita

where;

Initial number=y

fraction of the total given to Anita=3/5 y

replacing;

The fraction remainder given to Lordia and Richmond=y-3/5 y=2/5 y

but;

2/5 y=80

y=80×5/2=

y=200

The total number of cattle shared among the three children=200

b).

Anita's share=(3/5)×200=120 cattle

Lordia's share=(2/5)×80=32 cattle

Richmond's share=(3/5)×80=48 cattle