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3 years ago

Find the missing values in the ratio table below.

Mathematics

1 answer:

Nataliya [291]3 years ago

3 0

Answer:

attachment

Step-by-step explanation:

Hi there !

trucks/cars = 2/3 = x/9 = 30/y

x = 2×9/3 = 18/3 = 6

y = 3×30/2 = 90/2 = 45

Good luck !

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3 years ago

If h and j are positive, (h+j)2 = 73 and h2 +j2 = 51, what is hj?

kkurt [141]

Answer:

$hj = 11$

Step-by-step explanation:

$(h+j)^2=73,\:\: and\:\: h^2+j^2 =51$ (Given)

$(h+j)^2 = h^2+j^2 +2hj$

$\implies 73= 51 +2hj$

$\implies 73- 51 =2hj$

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2 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

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3 years ago

Yu-Xi draws a triangle with two angles measuring 79 degrees and 23 degrees. What is the measure, in degrees, of the third angle?

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Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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