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olchik [2.2K]
2 years ago
5

Enter the correct answer in the box.

Mathematics
1 answer:
fomenos2 years ago
7 0

Answer: F(x)=e^x-2+9

Step-by-step explanation: for plato users

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Please help! Will mark brainliest!
vlada-n [284]
I think it’s 96. That’s what I got.
8 0
2 years ago
PLEASE HELP ASAP WILL MARK THE BRAINLEST
statuscvo [17]

Answer:

similar triangles

Step-by-step explanation:

First of all, what are similar shapes? Well, two shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling. That means you can make one shape bigger or smaller. In this case, we know that triangles ABC and DEF are mathematically similar. The area of triangles ABC is , so we need to know the area of triangle DEF.

From math, let's call  the scaling factor, so we know that for any similar figures, the ratio of the areas of any are in proportion to . In other words, if  is the area of triangle ABC, and  is the area of triangle DEF, then we can write the following relationship:

4 0
3 years ago
I have an assignment and I am having trouble with it. Can someone please help ASAP???
bezimeni [28]

Answer:

A) Find the sketch in attachment.

In the sketch, we have plotted:

- The length of the arena on the x-axis (90 feet)

- The width of the arena on the y-axis (95 feet)

- The position of the robot at t = 2 sec (10,30) and its position at t = 8 sec (40,75)

The origin (0,0) is the southweast corner of the arena. The system of inequalities to descibe the region of the arena is:

0\leq  x \leq 90\\0\leq y \leq 95

B)

Since the speed of the robot is constant, it covers equal distances (both in the x- and y- axis) in the same time.

Let's look at the x-axis: the robot has covered 10 ft in 2 s and 40 ft in 8 s. There is a direct proportionality between the two variables, x and t:

\frac{10}{2}=\frac{40}{8}

So, this means that at t = 0, the value of x is zero as well.

Also, we notice that the value of y increases by \frac{75-30}{8-2}=7.5 ft/s (7.5 feet every second), so the initial value of y at t = 0 is:

y(t=0)=30-7.5\cdot 2 =15 ft

So, the initial position of the robot was (0,15) (15 feet above the southwest corner)

C)

The speed of the robot is given by

v=\frac{d}{t}

where d is the distance covered in the time interval t.

The distance covered is the one between the two points (10,30) and (40,75), so it is

d=\sqrt{(40-10)^2+(75-30)^2}=54 ft

While the time elapsed is

t=8 sec-2 sec = 6 s

Therefore the speed is

v=\frac{54}{6}=9 ft/s

D)

The equation for the line of the robot is:

y=mx+q

where m is the slope and q is the y-intercept.

The slope of the line is given by:

m=\frac{75-30}{40-10}=1.5

Which means that we can write an equation for the line as

y=mx+q\\y=1.5x+q

where q is the y-intercept. Substituting the point (10,30), we find the value of q:

q=y-1.5x=30-1.5\cdot 10=15

So, the equation of the line is

y=1.5x+15

E)

By prolonging the line above (40,75), we see that the line will hit the north wall. The point at which this happens is the intersection between the lines

y=1.5x+15

and the north wall, which has equation

y=95

By equating the two lines, we find:

1.5x+15=95\\1.5x=80\\x=\frac{80}{15}=53.3 ft

So the coordinates of impact are (53.3, 95).

F)

The distance covered between the time of impact and the initial moment is the distance between the two points, so:

d=\sqrt{(53.5-0)^2+(95-15)^2}=95.7 ft

From part B), we said that the y-coordinate of the robot increases by 15 feet/second.

We also know that the y-position at t = 0 is 15 feet.

This means that the y-position at time t is given by equation:

y(t)=15+7.5t

The time of impact is the time t for which

y = 95 ft

Substituting into the equation and solving for t, we find:

95=15+7.5t\\7.5t=80\\t=10.7 s

G)

The path followed by the robot is sketched in the second graph.

As the robot hits the north wall (at the point (53.3,95), as calculated previously), then it continues perpendicular to the wall, this means along a direction parallel to the y-axis until it hits the south wall.

As we can see from the sketch, the x-coordinate has not changed (53,3), while the y-coordinate is now zero: so, the robot hits the south wall at the point

(53.3, 0)

H)

The perimeter of the triangle is given by the sum of the length of the three sides.

- The length of 1st side was calculated in part F: d_1 = 95.7 ft

- The length of the 2nd side is equal to the width of the arena: d_2=95 ft

- The length of the 3rd side is the distance between the points (0,15) and (53.3,0):

d_3=\sqrt{(0-53.3)^2+(15-0)^2}=55.4 ft

So the perimeter is

d=d_1+d_2+d_3=95.7+95+55.4=246.1 ft

I)

The area of the triangle is given by:

A=\frac{1}{2}bh

where:

b=53.5 ft is the base (the distance between the origin (0,0) and the point (53.3,0)

h=95 ft is the height (the length of the 2nd side)

Therefore, the area is:

A=\frac{1}{2}(53.5)(95)=2541.3 ft^2

J)

The percentage of balls lying within the area of the triangle traced by the robot is proportional to the fraction of the area of the triangle with respect to the total area of the arena, so it is given by:

p=\frac{A}{A'}\cdot 100

where:

A=2541.3 ft^2 is the area of the triangle

A'=90\cdot 95 =8550 ft^2 is the total area of the arena

Therefore substituting, we find:

p=\frac{2541.3}{8550}\cdot 100 =29.7\%

4 0
3 years ago
Nando is on a rehabilitation program following a car accident. For the first month, he needs to exercise at most five hours per
emmasim [6.3K]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of hours per week Nando is brisk walking  and y be the number of hours per week Nando is  biking at a moderate pace.

For the first month, he needs to exercise at most five hours per week, then

x+y\le 5

Brisk walking burns about 350 calories per hour, then it burns 350x calories per x hours.

Biking at a moderate pace burns about 700 calories per hour, then it burns 700y calories per y hours.

Nando must burn at least 2,000 calories per week, so

350x+700y\ge 2,000

You get the system of two inequalities:

\left\{\begin{array}{l}x+y\le 5\\ 350x+700y\ge 2,000\end{array}\right.

The attached graph shows the solution set to this system of inequalities. In this diagram, red region represents the solution set to the first inequality, blue region represents the solution set to the second inequality and their intersection is the solution set to the system of two inequalities.

4 0
3 years ago
Brainliest, what is the total measure of angles 8 and 5 of angle 7 equals 61
guapka [62]
Lines equal 180°. The line with angles 5 and 7 equals 180°. If angle 7 equals 61°, then angle 5 equals 119° (180° - 61°= 119°).

Angles 5 and 8 are opposite vertical angles, which are always congruent (equal), so angles 5 and 8 both equal 119°.

119° (angle 5) + 119° (angle 8)= 238°


ANSWER: The two angles total 238° (bottom choice).

Hope this helps! :)
7 0
3 years ago
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