f(x) = 2x + 4 and g(x) = -8f(x). = What equation shows the correct rule for the function g? O g(x) = -4x O g(x) = -4x + 4 = g(x) = -8x - 32 O g(x) = -4x - 32 – -

Answer:

One piece is 26 inches long while the other is 52 inches long.

We let:

x = one piece of the thread

2x = the other piece of the thread

Since the thread is 78 inches long,

2x + x = 78

Solve for x:

Since one piece of the thread is 26 inches long, the other piece would be:

The other piece would be 52 inches long.

In general, the slope-intercept form of a linear equation is

Thus, in our case,

From the information provided, observe that the three terms are connected by a common ratio.

The first term is multiplied by a value denoted as letter r (common ratio) to derive the second term. The second term is also multiplied by r to derive the third term, and so on.

Therefore;

From the above calculation, the common ratio is 4/5. Therefore, the 10th term in the sequence shall be;

The 10th term is as shown above. To round this figure to the nearest thousandth, we need to convert this fraction into a decimal.

Hence we would have;

Perimeter is formed by 4 side lengths.

Divide perimeter in 4 parts

x= side length

P = 6x = x + x + 4x

then length of the other sides lengths is= 2x

So then ANSWER IS

P= x + x + 2x + 2x

We get the following from the given table.

The percentage of college graduates who believes their education was helping them grow personally and intellectually =62 % + 31 %= 93 %

The percentage of college graduates who believes their education was useful for helping them develop specific skills and knowledge for the workplace = 49%+25%= 84 %

The percentage of college graduates who does not believe their education was useful for helping them develop specific skills and knowledge for the workplace=100-84=16%

The percentage of college graduates believes their education was helping them grow personally and intellectually and does not believe useful for helping them develop specific skills and knowledge for the workplace=the least value of 93 and 16 is 16 %.

Hence the required percentage is 16%.

Radius r:

r = 8 miles

Area of a circle:

A = π * r²

The area of a 180° arc is the half of the area of the entire circle:

A_arc = (π * r²)/2

Solving:

A_arc = 32π square miles

the sum of two supplementary angles is 180 degrees

7x+10+7x-26 = 180

14x = 180 + 16

x = 196/14

x = 14

so the value of m7x+10

= 7(14) + 10

= 98 + 10

= 108

m

It's important to observe that the number that multiples the x is 1/2, that is, it's less than zero.

Since the volume of water depends on the floor area, the floor area is the independent variable while the minimum water volume is the dependent variable.

Let x represents the floor area

Let y represent the miminum volume of water

The rate of change is the ration of the change in y to the change in x

Let the rate of change be represented by dy/dx

Considering the first two rows of the table, since the rate of change does not differ despite the rows picked

Given that Billy used four colours to divide 4.20 by 4

To Determine: The model that shows this division

Solution:

It can be observed that 1 represents 100 small boxes

Dividing 4.20 by 4 would give

1.05 would be represented by small boxes

If we used colours, then each of the colours would have 105 boxes

From the above explanation, the model that shows 4.20/4 is OPTION D

√8 + 3 ? 8 + √3

√8 is between √4 (= 2) and √9 (= 3), then

√8 + 3 < 3 + 3 = 6

Therefore,

√8 + 3 < 8 + √3

GIven:-

An graph with two parallel lines.

To find:-

The given condition which sutis it.

Now we find two points form the line.

The points from the line AB is,

The points from the line CD is,

Now the slope of AB is,

Now the slope of CD is,

The both slopes are equal so we have,

They are parallel because the slopes are equal.

To solve this question, we need to use integers to express different altitudes. We can sketch each situation as follows:

To find the depth at which each person rested, we need to algebraically sum all these altitudes.

Jim:

-8 -18 + 5 - 9 = -30. He rested at 30 feet below the surface.

Carla:

-16 + 5 - 18 = -29. She rested at 29 feet below the surface.

Therefore, Jim rested at a greater depth (30 feet below the surface).

A) 68 mph. B) 3h

1) Gathering the data

time: 5 hours

Space= 340 miles

A) To find the rate, we can calculate it by simply writing a quotient between the Space and the time, (since Nolan is constantly moving

So Nolan was at 68 mph

B) We can find out by setting a proportion since it's been said that the speed is constant. 340 miles have already been driven there are 204 miles to go.

340------5 hours

204 ---- x

340x = 204 *5 Divide both sides by 340

x=3

So it will take more 3 hours so that Nolan can finish his trip.

Given

The perpendicular bisector of the triangle are concurrent. Their common point is the .........

Find

Complete the statement

Explanation

The three angle bisector of triangel are concurrent in a point equidistant from the sides of the triangle.

The point of concurrency of the angle bisectors of a triangle is known as

circumcenter.

Final Answer

Hence , the correct option is C

SOLUTION

Let the smaller number be x

Let the larger number be y

Since the larger number is 31 more than 5 times the smaller number, it folllows:

The sum of the two integers is 463, it follows

Substitute y=5x+31 into the equation

Solve for x

Substitute x=72 into y=5x+31

Therefore the two integers are 72 and 391

The value of 65 km/hr in meter/second will be 18.05 m/sec by the method of "To convert km/hr to m/s ,multiply the quantity by 5/18."

A derived unit for both speed and velocity, kilometers per hour is a measurement that takes length in kilometers and time in hours. Although kph or kmph are also occasionally used, km/h is the correct abbreviation for this unit.

a. 65 KM/hour to metre/second

=65*5/18

=18.05 m/second

b. To convert km/hr to m/s ,multiply the quantity by 5/18.

as 1 KM=1000 m

1 hour=3600 seconds

x* 1000/3600

x*5/18

According to the formula "To convert km/hr to m/s, multiply the quantity by 5/18," 65 km/hr will equal 18.05 m/s.

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• We are given 2y +4x = 5

This can be rewritten as :

2y = -4x +5

y = -4/2x +5/2

y = -2x +5/2

• A line parallel to this line will also have the exact, same slope

Therefore m = -2

in order to find the equation , we will use the following formula

y = mx +c , where m = -2 :

y = -2x + c , at point (5;2)

2 = -2(5) +c

2 +10 = c

Therefore c = 12

finally;

y = -2x +12 is our equation .

If (x,y) is a point in the graph of a line then its coordinates x and y form a solution to the equation of that line. In slope-intercept form this equation looks like this:

What we are going to do here is choose two points from the line in the picture and use them and the expression above to construct two equations for m and b.

As you can see (0,1) and (3,0) are part of the line so we have the following two equations:

From the first equation we get b=1. If we use this value of b in the second equation we obtain the following:

We can substract 1 from both sides:

Then we divide both sides by 3:

Then we have this equation for the line in the picture (we take y=f(x)):

Then the answer is option A.

If the model plane is built at a scale of 1 inch to 32 feet

let x be the actual length of the airplane

1/32 = 8/x

cross-multiply

x = 32 times 8

x = 256 inches

The unit rate is 4 passengers per car

We need to find the unit rate.

576 passengers in 144 cars

rate = 576/144

rate = 4 passengers per car

Therefore, the unit rate is 4 passengers per car

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Explanation

The Inscribed Quadrilateral Theorem states that a quadrilateral can be inscribed in a circle if and only if the opposite angles of the quadrilateral are supplementary

Answer 1: True

Also, Given a triangle, the circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet.

Answer 2: True

Let's use the variable L to represent the length and W to represent the width.

If the perimeter is 600 ft, we have:

The width is half the length, so we have:

Now, if each fence segment is 5 ft, we number of segments needed is:

Problem

Solution

For this case we we can find the area on this way:

And solving we got:

The area for this case is 88 unit^2

Using the law of sines:

Using the heron formula:

The values on the table are:

a) the steepest slope is m=-2 (from the third option). We can see this because in the first option, the rate of change is 1 and in the second option is 1/5. Then for each increase of x, the value of y will be modified but not as much as in the equation y=-2x.

b)the equation y=-2x represents a decreasing line, since the slope is negative.

Since the arc BAE is a semicircle, it measures 180°, and the angle that inscribes it, that is, angle ∠BCE, has half the measure, so ∠BCE = 90°.

The angle ∠ACE inscribes the arc AE, so the arc AE has double the measure of the angle ∠ACE, so AE = 56°.

Calculating the measure of the arc AB, we have:

So the first option is correct.

For the second option, these two angles inscribes the same arc (arc AE), so they have the same measure of half the measure of the arc. Therefore, they are congruent, so the second option is correct.

For the third option, there is nothing that proves that these angles are congruent, so the third option is false.

For the fourth option, there is nothing that proves that AC is a diameter, so the fourth option is false.

For the fifth option, the angle ∠BDE inscribes an arc of 180° (semicircle), so it has half the measure of the arc, therefore ∠BDE = 90°. So the fifth option is correct.

Given

mean = 3 days

standard deviation = 1.7 days

Find

a. What is the distribution of X?

b. What is the median recovery time?

c. What is the Z-score for a patient that took 4.1 days to recover?

d. What is the probability of spending more than 2.4 days in recovery?

e. What is the probability of spending between 2.7 and 3.4 days in recovery?

f. The 80th percentile for recovery times

Explanation

a) Distribution of X is given by X ~ N( 3 , 1.7)

b) for the normal distibution ,the median is the same as the mean .

so , the median recovery time is 3 days

c) z - score for the patient that took 4.1 days to recover is

d) probability of spending more than 2.4 days in recovery

e) probability of spending between 2.7 and 3.4 days in recovery

Hence , the above are the required answers.

The given graph represents a function, also notice that it is a one to one function because using the vertical line theorem we have that for all vertical lines it only intercepts the graph in just one point.

If we want to calculate the inverse, we have to solve for x the following equation

Therefore the inverse function is