MATHEMATICS HIGH SCHOOL

Give all solutions if the nonlinear system of equations, including those with no real complex components.y=x^2+6x
4x-y=-24

Answers

Answer 1
Answer: \left\{\begin{array}{ccc}y=x^2+6x\n4x-y=-24\end{array}\right\n\nsubstitute:\n\n4x-(x^2+6x)=-24\n\n4x-x^2-6x+24=0\n\n-x^2-2x+24=0\n\na=-1;\ b=-2;\ c=24\n\n\Delta=b^2-4ac

\Delta=(-2)^2-4\cdot(-1)\cdot24=4+96=100\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(100)=10\n\nx_1=(2-10)/(2\cdot(-1))=(-8)/(-2)=4;\ x_2=(2+10)/(2\cdot(-1))=(12)/(-2)=-6\n\ny_1=4^2+6\cdot4=16+24=40;\ y_2=(-6)^2+6\cdot(-6)=36-36=0\n\nAnswer:\nx=4\ and\ y=40\ or\ x=-6\ and\ y=0
Answer 2
Answer: y=x^2+6x
Apply the value of y into the equation below:
4x-y=-24
4x-(x^2+6x) = -24
4x-x^2-6x = -24
x^2+2x-24=0
(x+6)(x-4)=0
Therefore x can be -6 or 4
If x = -6
Then y = (-6)^2+6(-6) = 36 -36=0
If x = 4
Then y = (4)^2 + 6(4) = 16 + 24 = 40

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What type of graph is best to use to show changes over time?a. Bar Graph
b. Line Graph
c. Histogram
d. Circle Graphs

Answers

Line Graph because you can judge the quality whether if the line goes up or down

Bar Graph, Histogram, Circle Graphs ( or pie graph) usually use to compare things XD

Answer:

line graph

Step-by-step explanation:

Kevin claims he can draw a trapezoid with three right angles. Is this possible? Explain.

Answers

Using an indirect proof:

Assume that the figure is a trapezoid.
All trapezoids are quadrilaterals.
All quadrilaterals' interior angles add up to 360° because any n-gon's interior angles add up to 180(n-2)°.
We are given that the trapezoid has three right angles.
All right angles are 90°, thus these right angles have a total measure of 270°.
We can conclude fourth angle must be 90°.
If it has four right angles, it is a rectangle.
Rectangles have two sets of parallel sides.
However, trapezoids have exactly one set of parallel sides.
Alas, our figure cannot be a trapezoid.
not possibletrapezoid is a quadrilateral with 4 angles and 4 sideswhich means the interior measure =360if 3 angles are right the 4th angle must be a right anglea trapezoid does not have 4 right angles,it only has onepair of parallel sideshope this helps

Solve the equation. Show your work.

1/a =6/18

Answers

 
1          6                    
---    =  ---   
 a        18

- simplify 6/18, which should be 1/3. therefore, a = 3.

Karina bought a camera with a regular price of $89. It was on sale at a 20% discount. There was a 7% tax on the sale price. How much did Karina spend to buy the camera?

Answers

1) we can calculate the price of this camera with 20% discount.
$89-(20/100)($89)=$89-0.2($89)=$89-$17.8=$71.2

2) now, we apply the tax on the sale price.
$71.2 + (7/100)($71.2)=$71.2+(0.07)($71.2)=$71.2+$4.984=$76.184

Answer: Karina spent to buy the camera $76.184.

Answer:

$17.18

Step-by-step explanation:

you can't have $17.184 it has to be two deci.

only

Which hill described in the table is the steepest and why? Street. Horizontal distance vertical
(ft). Rise of
Street (ft)


Dixie hill. 100. 60
Bell hill. 100. 50
Liberty hill 100. 20

A. Dixie hill; it rises 5 feet for every 3 feet of horizontal travel.
B. Dixie hill; rises 3/5 foot for every 1 foot for every 1 foot of horizontal travel.
C. Bell hill; it rises 2 feet for every 1 foot of horizontal travel.
D. Liberty hill; it rises 1 foot for every 5 feet of horizontal travel.

Answers

Answer:

Option: B

Dixie hill; rises 3/5 foot for every 1 foot for every 1 foot of horizontal travel.

Step-by-step explanation:

A slope with a greater absolute value indicates a steeper line.

so, we will find the slope of each of the hill to check the steepness of the road.

1)

Dixie Hill

Street            Horizontal distance              vertical Distance

Dixie hill          100                                           60            

The slope of the hill is:

Vertical distance/ Horizontal ditance

= 6/10=3/5

2)

Street            Horizontal distance              vertical Distance

Bell hill                   100                                      50  

slope=1/2

3)

Street            Horizontal distance              vertical Distance

Liberty hill              100                                      20  

slope=1/5

As slope of Dixie Hill is greater than the rest two.

Hence, option: B is correct.

B. Dixie hill; rises 3/5 foot for every 1 foot for every 1 foot of horizontal travel.

the answer is dixie hill A because 5 feet every 3 feet is pretty steep compared to 1 foot every 5 feet.

What is the coefficient of x2 in the expansion of (x + 2)3?

Answers

I think 6 is the answer. Hopefully I answered your question
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