MATHEMATICS MIDDLE SCHOOL

And;Find the slope of the line that goes through the given points.

(-6. - 4) and (-8. - 10)

Answers

Answer 1

Answer:

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 4) and (x₂, y₂ ) = (- 8, - 10)

m = $(-10+4)/(-8+6)$ = $(-6)/(-2)$ = 3

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In which quadrants is the ordinate positive?

Answers

Answer:

Quadrants 1 and 2

Step-by-step explanation:

Answer:The first quadrant is positive

Step-by-step explanation:

5 times a number increasedby 18 is the same as 36 more
than times 4 times the
number. Find the number.

Answers

Answer:

Step-by-step explanation:

Let's make this information into an equation.

We'll use 'x' whenever the problem says "a number".

Equation:

5x + 18 = 36 + 4x

How did I get to this equation?

5 times a number means 5 multiplied by x
increased by 18 means to add 18
is the same as means equals
36 more than means to add 36
4 times the number means 4 multiplied by x

Now, let's solve.

Solve:

5x + 18 = 36 + 4x

Subtract 18 on both sides:

5x + 18 = 36 + 4x

-18 -18

5x = 18 + 4x

Subtract 4x on both sides:

5x = 18 + 4x

-4x -4x

x = 18

Therefore, "the number" is 18.

What are the solutions of this system of equationThe first three steps in determining the solution set of the
system of equations algebraically are shown in the table.
y = -x2 +2x - 9
y = -6x + 6
(5,-24) and (3, -12)
(5,36) and (3, 24)
(-5, -24) and (-3, 12)
(-5, 36) and (-3, 24)
Step
Equation
-x² + 2x -9 = -6x + 6
0 = x2 – 8x+15
0 = (x - 5)(x-3)
2
Mark this and retum
Save and Exit
Sumber
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Answers

Answer:

(3,-12) and (5,-24)

Step-by-step explanation:

Given the system of two equations

$\left\{\begin{array}{l}y=-x^2+2x-9\n y=-6x+6\end{array}\right.$

Equate right sides of these two equations:

$-x^2+2x-9=-6x+6$

Rewrite this equation:

$-x^2+2x-9+6x-6=0\n \n-x^2+8x-15=0\n \nx^2-8x+15=0\n \nx^2-5x-3x+15=0\n \nx(x-5)-3(x-5)=0\n \n(x-3)(x-5)=0\n \nx_1=3\ \text{or}\ x_2=5$

If x=3, then

$y=-6\cdot 3+6=-18+6=-12$

If x=5, then

$y=-6\cdot 5+6=-30+6=-24$

You get two solutions (3,-12) and (5,-24)

The solution set of the system of equation is (5, -24) and (3, -12)

System of equations

The given systen of equation is one linear and one quadratic. Given the syatem of equations

$y = -x^2 +2x - 9\ny = -6x + 6$

Equating bothequations will give

$-x^2 + 2x - 9 = -6x+ 6$

Equate to zero

$-x^2 + 2x - 9 + 6x - 6 =0\nx^2 - 2x +9 - 6x + 6 = 0\nx^2 - 8x + 15 = 0$

Factorize

$x^2 - 3x - 5x + 15 = 0\nx(x-3)-5(x-3) = 0\nx-5 = 0 \ and \ x - 3 = 0\nx = 5 \ and \ 3$

Recall that ;

y = -6x + 6

If x = 5

y = -30 + 6

y = -24

If x = 3

y =-6(3) + 6

y = -12

Hence the solution set of the system of equation is (5, -24) and (3, -12)

Learn more on system of equation here: brainly.com/question/25976025

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Write 210 and 252 as products of prime numbers.

Answers

210 = 21 times 10 = 7 times 3 times 5 times 2
252 = 126 times 2 = 63 times 2 times 2 = 21 times 3 times 2 times 2 = 7 times 3 times 3 times 2 times 2 = 7 times 3^2 times 2^2

Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painting. Calculate the area of the isosceles trapezoid.Isosceles trapezoid with top base 16 feet, bottom base of 24 feet, and height of 10 feet.
A. 140 ft2
B. 160 ft2
C. 180 ft2
D. 200 ft2

Answers

Answer:

Option D is the correct answer.

Step-by-step explanation:

Refer the figure given below

Area of isosceles trapezoid = Area of 2 triangles + Area of rectangle.

$\texttt{Area of isosceles trapezoid =}(1)/(2)* (1)/(2)* (b-a)* h+(1)/(2)* (1)/(2)* (b-a)* h+ah\n\n\texttt{Area of isosceles trapezoid =}(1)/(2)* (b-a)* h+ah$