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3 years ago

15

Determine the midpoint between the two points x(4,-6) and y(-2,8)

1 answer:

ikadub [295]3 years ago

6 0

Answer:

$p(a, b) = (1, 1)$

Step-by-step explanation:

Midpoint formula is

$p(a, b)=(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )$ ---------------(1)

Here

$(x_1, y_1) = (4, -6) \ \ \ and \ \ \ (x_2, y_2) = (-2, 8)$

Substituting values in equation (1)

$p(a, b)=(\frac{4 - 2}{2}, \frac{-6 + 8}{2} )$

$p(a, b) = (1, 1)$

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Which expression is equivalent to<br> (2^3)^-5

kvasek [131]

Answer:

(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)×-(2×2×2)×(2×2×2)

3 0

3 years ago

A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. Which expression r

zavuch27 [327]

we know that

the volume of a solid oblique pyramid is equal to

$V=\frac{1}{3}*B*h$

where

B is the area of the base

h is the height of the pyramid

in this problem we have that

B is a square

$B=b^{2}$

where

<u> $b=x\ cm$ </u>

so

$B=x^{2}\ cm^{2}$

$h=(x+2)\ cm$

substitute in the formula of volume

$V=\frac{1}{3}*x^{2}*(x+2)\\ \\V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}$

therefore

<u>the answer is</u>

$V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}$

4 0

2 years ago

Read 2 more answers

The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

or

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

or

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

or

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

3 0

2 years ago

Can someone help? it’s 7th grade math and im finishing this project for the end of the year

drek231 [11]

Answer:

c

Step-by-step explanation:

8 0

2 years ago

One base of a trapezoid is five times as long as the other. The height is the average of the two bases. The area is 441 square u

Gelneren [198K]

Answer:

The length of the longer base he 35 units

Step-by-step explanation:

Here, we want to find the length of the longer base of the trapezoid

Mathematically, we can find the area using the formula;

1/2( a + b) h

where a is the shorter base

b is the longer base

h is the height

Let the shorter base be x

The other base is 5 times this length and that makes 5 * x = 5x

Height is the average of both bases;

(x + 5x)/2 = 6x/2 = 3x

Substituting these in the formula, we have ;

1/2(x + 5x)3x = 441

3x(6x) = 882

18x^2 = 882

x^2 = 882/18

x^2 = 49

x^2 = 7^2

x = 7

But the longer base is 5x and that will be 5 * 7 = 35 units

4 0

2 years ago