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3 years ago

Combine the like terms to create an equivalent expression: -5+(-5r) + 10

Mathematics

2 answers:

Serjik [45]3 years ago

5 0

Answer:

-5r+5

Step-by-step explanation:

-5+(-5r)+10

-5-5r+10

-5r-5+10

-5r+5

ira [324]3 years ago

5 0

Answer:

-5r + 5

1. When there is a + in front of an expression in parenthesses, the expression remains the same.

2. Calcuate the sum

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I needs help with it please

arlik [135]

Answer:

(i) (0, -32)

(ii) (-4, 0) and (8, 0)

(iii) x = 2

(iv) (2, -36)

(v) (2, -36) minimum

Step-by-step explanation:

Given quadratic equation:

$y=x^2-4x-32$

Part (i)

The y-intercept is the point at which the curve crosses the y-axis.

To find the y-intercept, substitute x = 0 into the given equation:

$\implies (0)^2-4(0)-32=-32$

Therefore, the y-intercept is at (0, -32)

Part (ii)

The zeros are the points at which the curve crosses the x-axis.

To find the zeros, substitute y = 0 into the given equation and factor:

$\implies x^2-4x-32=0$

$\implies x^2-8x+4x-32=0$

$\implies x(x-8)+4(x-8)=0$

$\implies (x+4)(x-8)=0$

Therefore:

$(x+4)=0 \implies x=-4$

$(x-8)=0 \implies x=8$

So the zeros are (-4, 0) and (8, 0)

Part (iii)

The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts. The axis of symmetry is the x-value of the mid-point of the zeros.

$\sf \implies midpoint=\dfrac{8+(-4)}{2}=2$

Therefore, the axis of symmetry is: x = 2

Part (iv)

The vertex is the turning point of the parabola.

If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.

If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.

The axis of symmetry is the x-value of the vertex.

To find the y-value, substitute x = 2 into the equation:

$\implies (2)^2-4(2)-32=-36$

Therefore, the vertex is (2, -36)

Part (v)

The optimal value is also known as the vertex.

Therefore, the optimal value is (2, -36).

As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.

4 0

2 years ago

Help I AM STUCKKK I WILL GIVE BRAINLIST

juin [17]

Answer:

Sorry I have tried it lot but I am not able to find the answer...

I'm Really Sowwy...

8 0

3 years ago

Two positive numbers have a sum of 8 and their product is equal to the larger number plus 10

IRISSAK [1]

Answer:

There are 2 sets of numbers that work...

x = 3, y = 5

and

x = 6, y = 2

Step-by-step explanation:

Let x be one number, and let y be the other number. We have 2 equations...

x + y = 8 (two positive numbers have a sum of 8)

xy = y + 10 (their product is equal to the larger number plus 10)

solve the first equation for y, and substitute that into the second equation...

y = 8 - x

x(8 - x) = 8 - x + 10

now solve for x...

8x - x² = 18 - x

This is a quadratic, so get everything to one side so it's equal to zero...

-x² + 9x - 18 = 0 (add x and subtract 18 from both sides)

Now solve for x...

x² - 9x + 18 = 0 (divide both sides by -1)

(x - 6)(x - 3) = 0 (factor)

x - 6 = 0 becomes x = 6 (add 6 to both sides)

and

x - 3 = 0 becomes x = 3 (add 3 to both sides

If x is 3, then y = 5 (3 + 5 is 8, and 3(5) = 5 + 10, both equations hold up)

If x is 6, then y = 2 (6 + 2 is 8, and 6(2) = 2 + 10, both equation hold up)

5 0

3 years ago

Help please help please

Nat2105 [25]

The answer would be $712

4 0

3 years ago

The difference between half a number and 11 is -25

kenny6666 [7]

Answer:

1/2n - 11 = -25

Hope this helps you! Have a good night!

Also, n = -28

1/2n - 11 = -25

1/2n - 11 + 11 = -25 + 11

1/2n = -14

1/2n / 1/2 = -14 / 1/2

n = -28

Check:

1/2(-28) - 11 = -25

-14 - 11 = -25

-25 = -25

6 0

3 years ago

Combine the like terms to create an equivalent expression: -5+(-5r) + 10​

Combine the like terms to create an equivalent expression: -5+(-5r) + 10