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3 years ago

Given f(x) = –7x + 9 and h(x) = –5(–7x + 9), what are the slope and y-intercept of the graph of function h?

Mathematics

2 answers:

Ierofanga [76]3 years ago

8 0

Answer:

h(x): Slope(m) = 35, Y-intercept(c) = -45

f(x): Slope(m) = -7, Y-intercept(c) = 9

Step-by-step explanation:

We are given the functions in the question:

$f(x) = -7x + 9\\h(x) = -5(-7x + 9)$

We have to find the slope and y-intercept of the graph of function h(x).

First we simplify h(x)

$h(x) = -5(-7x + 9)\\h(x) = -5(-7x) + (-5)(9)\\h(x) = 35x -45$

Comparing the equation to the point slope form of the straight line, we have,

$y = mx + c$

where m is he slope of line and c is the y-intercept that is the value of y when x is zero.

Comparing, we get,

Slope, m = 35

Y-intercept, c = -45

For function f(x), we have

Slope, m = -7

Intercept, c = 9

taurus [48]3 years ago

4 0

The Slope of f(x) = –7x + 9 is (-7)

The slope of h(x) = –5(–7x + 9) is (35)

The y-int of h(x) is (-45).

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3 years ago

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Here, P(A∪B) = 4% = 0.04

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3 years ago

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The distance b between each beam is 9ft.

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$I \to$ I-Beam

$d_I \to$ distance between I beam and the bridge

$b \to$ distance between each I beam

Given that:

$I = \frac 34 ft\\$

$d_I = 3 ft$

$Length = 55ft\ 6in$ --- length of the bridge

From the diagram (see attachment), there are: 6 I-beams.

So, the length of the 6 I-beams is:

$L_1 = 6 \times I$

$L_1 = 6 \times \frac 34$

$L_1 = \frac {18}4$

$L_1 = 4.5ft$

There are 2 I-beams beside the bridge

So, the distance between the 2 I-beams and the bridge is:

$d_1 =2 \times d_I$

$d_1 =2 \times 3ft$

$d_1 =6ft$

There are 5 spaces between the I-beams

So, the length of the total spaces is:

$L_2 = 5 \times b$

$L_2 = 5b$

The total length is:

$Length = L_1 + d_1 + L_2$

So, we have:

$4.5ft + 6ft + 5b = 55ft\ 6in$

Collect like terms

$5b = 55ft\ 6in - 4.5ft - 6ft$

$5b = 44.5ft\ 6in$

Convert inches to feet

$5b = 44.5ft\ + \frac{6}{12}ft$

$5b = 44.5ft\ + 0.5ft$

$5b = 45ft$

Divide both sides by 5

$b = 9ft$

Hence, the distance (b) between each beam is 9ft.