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2 years ago

On a piece of paper, graph f(x) =

Mathematics

1 answer:

nalin [4]2 years ago

6 0

Answer:

The correct option is D

Step-by-step explanation:

We have been given a piecewise function such that:

When x is less than 1, the value of the function f(x) is equal to x. Which means the when x =0, f(x) = 0, when x= -1, f(x) = -1 , when x=-5, f(x) = -5, and so one, as far as x is less than one. It means that the graph of this part is a linear increases/decreases which show the relationship bet f(x) and y.
When x is equals to or greater than 1, the value of f(x) becomes constants that is 1. Hence, at x=1 and after that, the graph neither increases or decreases, as it becomes a straight line at y=1.

Graph of the piecewise function is shown, it matches option D.

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In △EKL, m∠K = 90º, m∠E = 25º, EK = 3 cm, KH - altitude. Find EH.

laiz [17]

Answer:

EH = 3.31

Step-by-step explanation:

We have been given a right angle triangle EKL. As KH has been given as the altitude (perpendicular) of the right angled triangle, and K is the right angle, we can say that EK is tthe base of the triangle and EH is the only side lleft, which is the hypotenuse of the triangle.

Where,

EK = Base = 3

KH = perpendicular altitude

EH = Hypotenuse

m<K = 90

m<E = 25

We know that

cosθ = Base/ Hypotenuse

cos 25 = 3/ EH

EH = 3/cos25

EH = 3.31

Perpendicular alitutude can also be calculated by using the formula for tanθ.

3 0

2 years ago

Lawrence has two part-time jobs one at the movie theater and wanted a pet store he's paid by the hour at each job last week he w

alexandr402 [8]

Let x be the earnings/hour at the movie theater.
y be the earnings/hour at the pet store

Systems of equations:

$152.50 = 10x + 8y
$171 = 8x + 10y

Solving for x and y:
x = $4.36/ hour in the movie theater
y = $13.61/ hour in the pet store.<span />

8 0

2 years ago

Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answ

BaLLatris [955]

Answer:

$V = 11.2 cm^3$

Step-by-step explanation:

Given

Shape: Right Circular cone

Height, h = 12.5 cm

Base circumference, C = 5.8cm

Required:

Calculate Volume

The volume of a cone is calculated as thus;

Volume, $V = \frac{1}{3}\pi r^2h$

Where V, r and h represent the volume, the radius and the height of the cone respectively

But first we need to calculate the radius of the cone.

Using formula of circumference.

$C = 2\pi r$

We have C to be 5.8cm

By substituting this value;

$5.8 = 2\pi r$

Divide through by $2\pi$

$\frac{5.8}{2\pi} = \frac{2\pi r}{2\pi}$

$r = \frac{5.8}{2\pi}$

$r = \frac{2.9}{\pi}$

Now, we can calculate the volume of the cone

By substituting $r = \frac{2.9}{\pi}$ and h = 12.5 cm;

$V = \frac{1}{3}\pi r^2h$ becomes

$V = \frac{1}{3}\pi * (\frac{2.9}{\pi})^2 * 12.5$

$V = \frac{1}{3}\pi * \frac{8.41}{\pi^2} * 12.5$

$V = \frac{1}{3} * \frac{8.41}{\pi} * 12.5$

Take $\pi$ as 3.14

$V = \frac{1}{3} * \frac{8.41}{3.14} * 12.5$

$V = 11.15976$

$V = 11.2 cm^3$ ---- Approximated

Hence, the volume of the cone is; $V = 11.2 cm^3$

4 0

2 years ago

Which transformation of AB will produce a line segment A’B that is parallel to AB

tangare [24]

Answer:

Step-by-step explanation:

7 0

2 years ago

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The

qaws [65]

Answer:

A) Yes, because P (F∩S) = 0

Step-by-step explanation:

Hello!

50 customers of a store were asked to choose between two discounts:

Discount 1: 20% off all purchases for the day.

Discount 2: 10% off all purchases for the week.

28 choose discount 1

22 choose discount 2

F: the selected person choose discount 1.

S: the selected person choose discount 2.

Two events are mutually exclusive when the occurrence of one of them prevents the other from occurring in one repetition of the trial and the intersection between these two events is void with zero probability of happening.

In this case, since the customers were asked to choose one out of the two events, if the customer chooses the first one, then he couldn't have chosen the second one and vice-versa. Then the intersection between these two events has zero probability, symbolically:

P(F∩S)=0

I hope it helps!

8 0

2 years ago