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2 years ago

Which represents where f(x) = g(x)?

Mathematics

2 answers:

Lostsunrise [7]2 years ago

6 0

function f(x), when x = 0 then f(0) = 4
function g(x), when x = -4 then g(-4) = 4
so f(0) = g(–4) = 4

and

function f(x), when x = 4 then f(0) = 4
function g(x), when x = -2 then g(-2) = 4
so f(4) = g(–2) = 4

answer is

d. f(0) = g(–4) and f(4) = g(–2)

djverab [1.8K]2 years ago

3 0

Answer: b. f(–4) = g(–4) and f(0) = g(0)

Step-by-step explanation: We are given function f(x) as a line.

Function g(x) as a parabola.

The line of f(x) function and parabola g(x) cut graph at (0,4) and (-4,4) coordinates.

Therefore, at x=0, f(x) and g(x) has same values.

Also at x=-4, f(x) and g(x) has same values.

Therefore, f(–4) = g(–4) = 4 and f(0) = g(0) =4.

<h3>Therefore, correct option is b. f(–4) = g(–4) and f(0) = g(0).</h3>

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Subtract 5x2 - 7x - 6 from 9x2 + 3x – 4.

andrezito [222]

-7x+4 i’m not sure if it’s correct but i hope it is. sorry if it’s not

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1 year ago

Please answer all of them need this

VikaD [51]

First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in $\Delta BCQ$ , we can easily find the values of CQ and BQ.

Since, $Sin(75^0)=\frac{CQ}{8}$

$\therefore CQ=8\times Sin(75^0)\approx 7.73$ ft

In a similar manner we can find BQ as:

$Cos(75^0)=\frac{BQ}{8}$

$BQ\approx2.07$ ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

$PQ=22-(AP+QB)=22-(2.07+2.07)=17.86$

Let us now consider $\Delta AQC$

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of $\Delta AQC$ .

$AC=\sqrt{(AQ)^2+(QC)^2}=\sqrt{(AP+PQ)^2+(QC)^2}=\sqrt{(2.07+17.86)^2+(7.73)^2}\approx21.38$ feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area= $\frac{1}{2}$ (First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

Area= $\frac{1}{2}\times 218.5\times 224.5\times sin(58.2^0)\approx20845$ $m^2$

Therefore, Option D is the correct option.

Third Question

For this question we will apply the Sine Rule to the $\Delta ABC$ given to us.

Thus, from the triangle we will have:

$\frac{AB}{Sin(\angle C)}=\frac{BC}{Sin(\angle A)}$

$\frac{c}{Sin(\angle C)}=\frac{a}{Sin(\angle A)}$

$\frac{17}{Sin(25^0)}=\frac{a}{Sin(45^0)}$

This gives $a$ to be:

$a\approx28.44$

Which is not close to any of the given options.

Fourth Question

Please find the second attachment for a better understanding of the solution provided her.

As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.

$AC=\sqrt{(AB)^2+(BC)^2-2(AB)(BC)\times Cos(\angle B)}$

$\therefore AC=\sqrt{(172.20)^2+(111.64)^2-2(172.20)(111.64)\times Cos(177.29^0)}\approx283.8$ miles.

Thus, Option D is the answer.

8 0

2 years ago

Read 2 more answers

Kristen is 64 inches tall, and she stands 12 feet away from a streetlight. If she casts an 82-inch-long shadow, how tall is the

o-na [289]

Answer:

176.39 inches or

14.70 feet

Step-by-step explanation:

Consider the right triangle made by Kristen, ground and shadow.

This triangle has one leg as 64 inches.

Next consider the right triangle formed by street light, ground upto shadow tip.

The two triangles have common angle of elevation and also another angle as 90 degrees.

Hence the two triangles would be similar

Also if A is the angle made by hypotenuse of both triangles with the ground we have

$tanx=\frac{64}{82}$

This value also equals by bigger triangle as

$tanx=\frac{h}{82+12(12)}=\frac{h}{226}$

From these two we get

h = height of street light = $\frac{226(64)}{82} =176.39$

6 0

1 year ago

What does it mean in context of the example that Alyssa’s rate of change is greater than Sarah’s?

faltersainse [42]

Answer:

Part 1) The rate of change is the amount of money saved by week

Part 2) The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.

Part 3) see the explanation

Step-by-step explanation:

see the attached figure to better understand the problem

The complete question is

Part 1) What does the rate of change in the example represent?

Part 2) What does it mean in context of the example that Alyssa’s rate of change is greater than Sarah’s?

Part 3) Write ordered pairs for the initial values of each function. Tell what the initial values represent

Part 1) we know that

The rate of change is the slope or unit rate of the linear equation

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this context the rate of change is the amount of money saved by week

Part 2) we know that

Alyssa’s rate of change is equal to $8 per week

Sarah’s rate of change is equal to $6 per week

That means ----> The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.

Part 3) we know that

The initial value or y-intercept is the value of y when the value of x is equal to zero

In this context , the initial value is the amount of money available at the time of beginning to save

Sarah's Savings

Looking at the graph

The initial value is the point (0,8)

That means ----> At the beginning (x=0), Sarah already had $8 saved.

Alyssa's Savings

Looking at the graph

The initial value is the point (0,0)

That means ----> At the begin (x=0), Alyssa had nothing saved.

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2 years ago

Consider two people where one person is 20% taller than the other but proportioned in exactly the same way. (That is, the tall

Masja [62]

Answer:

43.2in

Step-by-step explanation:

If the two people are equally proportional, then knowing the size of the waist of one of them, we gonna we be able to know the other's wais size, by the relation.

36in*(1*20%) = 36in*1.2 = 43.2in

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1 year ago

Read 2 more answers