Suppose that the function f is defined, for all real numbers, as follows.
f(x)= {5x-4 if x≤1
-x+4 if x>1
Graph the function f. Then determine whether or not the function is continuous.

First write the equation in the form y=mx+c

[tex] \frac{3y}{3} = \frac{6x}{3} + \frac{12}{3} \\ y = 2x + 4[/tex]

YOU CAN SEE THAT NOW THE SLOPE OF THE LINE IS 2 TO GET THW Y INTERCEPT WE KNOW THAT AT THE Y-AXIS x=0

PLUG IN 0 IN THE PLACE OF X TO GET Y IN THE EQUATION OF THE LINE.

[tex]y = 2(0) + 4 \\ y = 4[/tex]

THE Y-INTERCEPT IS (0,4)

THEREFORE THE LINE HAS A SLOPE 2 AND A Y INTERCEPT (0,4)

FIRST OPTION IS THE ANSWER.

The area of triangle DEF = 4 ( area of triangle QRP) which is determined that by comparing the expression for the lengths of PR and QR.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

According to the data provided,

Triangle ΔDEF is an isosceles triangle having DE, EF, and FD sides.

Since DE = EF and P,R, and Q are the midpoints of the sides DF, EF, and DE,

We know from isosceles triangle theorems that the area of a triangle formed by uniting the midpoints of two isosceles triangles is one-fourth the area of the isosceles triangle.

As evidence, consider the following:

Because point Q is the halfway of DE, its coordinates are (a, b). (Because the midpoint of a line segment always has coordinates that are half the total of the coordinates of the end points.)

Because point R is the midpoint of FE, its coordinates are (3a,b).

The length of the base, DF, in triangle DEF is 4a and the height is 2b. As a result, its area is 4ab. (Because the area of a triangle equals 1/2 its base × height.)

The length of the base, QR, of the triangle QRP is 2a, while the height is b.

As a result, its area is ab.

Therefore, the area of triangle DEF is four times that of triangle QRP.

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The simple interest formula is:

where P is the principal, r is the interest rate and t is the time.

In this case the principal is $1800, the interest rate is 0.035 (in decimal form) and t is 2. then the interest he pays is:

Therefore in total he will pay $1926

a. The area under the curve is 1.

b. The value of the median is 4.5338.

c. The value of the mode is 4.5338.

d. The value of the variance is 0.0108.

It should be noted that the weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g.

In this case, for a normal distribution, mean = median = mode. The median is 4.5338

The mode is also 4.5338.

The variance will be the square of the standard deviation. This will be:

= (0.1039)²

= 0.0108.

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The area of a square is 256cm2

What is the length of its side?

Remember that

the area of a square is equal to

A=b^2

wheer

b is the length side

in this problem we have

A=256 cm2

substitute

256=b^2

square root both sides

b=16 cm

answer is

The Solution:

Given:

Required:

To find the measure of angle A.

By sine rule:

Answer:

slope = -2/3

Step-by-step explanation:

Locations of points: (-3 , 2) and (3 , -2)

slope = rise / run

between two plotted points this means that:

slope = change in y / change in x

slope = (-2 - 2) / (3 - (-3))

slope = -4/6

reduce:

slope = -2/3

We have here two sets of numbers, and we have to find the value for one of the operations of sets, that is, the intersection operation.

The result of this operation is the values that are common to both sets.

If we saw set A and set B, we will have:

Both sets have five elements. However, they have no common elements (or nothing in common). Therefore, the result will be the empty set:

That means both sets have no common elements ---> empty set.

In summary, we have that:

The dimensions that we must use in this problem, are the dimensions of the screen of a TV of 75 inches:

• W = width = 65.4" ,

• H = heigh = 36.8".

• The form of the TV is a rectangle, we compute the area A of the rectangle by the following formula:

• The aspect ratio r is given by the quotient of the width (W) by the height (H):

• The length of the TV diagonal L can be computed using Pitagoras Theorem:

Answer

• width = 65.4",

• heigh = 36.8",

• area = 2406.72in²,

• aspect ratio = 1.777

• length of the diagonal = 75.04in.

Let:

The coordinates for the new figure will be given by:

Where:

O = Center of dilation at (a,b) = (3,2)

k = Scale factor = 0.1

So:

Since:

(2.8,2), (2.8,1.9), (2.9, 1.9) and (2.9,2) are much closer to the center of dilation we can conclude that the dilated figure is closer to the center of dilation.

Taking x as the measure of the first triangle, we know that the second one measures three times as x:

And the third one measures 55 degrees more than the first:

We know that the sum of the angles of a triangle is 180, use this information to find x:

It means that the first angle measures 25°. Use this value to find the second and third angles:

It means that the second angle measures 75° and the third one measures 80°.

Answer:

C is the correct statement. Since the sea lion started at 2 feet below sea level and went down another 8 feet, the sea lion is now at 10 feet below sea level.

Answer:

Explanation: The discriminant is the part of the quadratic formula underneath the square root symbol As we know that square root of any number is both plus and minus of a certain value:

Using this information about the discriminant we can determine the x-intercepts of the graph as follows:

Quadratic equation solution:

Graph

Note! The plot of f(x) above confirms that there are no x-intercepts of this function, so the reason for complex values of x. also discriminant is the square root of -56

Answer:

let the unknown be x

=x+6/2=0

=0=x+6

=-x=6

divide both sides by -1

=-x/-1=6/-1

=x=-6

ANSWER

36

EXPLANATION

We want to evaluate the expression for when c = 3 and d = 3.

The expression given is:

To do this, we will simply replace the values of c and d with the values given:

That is the answer.

Answer: 2(3x^2-5x-1) or 6x^2-10x-2

Step-by-step explanation: combine like terms, and then factor by grouping :)

Answer:

I am a little confused because it says the point-slope formula, but then tells you to solve for y and to distribute.  Attached , I put the answer in the point slope form, but if they want the equations solves for y, then the answer would be in the slope intercept form.  Below the answers are in point slope form, but I will put the answer in slope intercept form here.

1  y = 2x -1

2. y = 1/2x +3

3.  y = 2/3x + 4

4. y = -3/4x -7

5.y = -2x + 1

6. y = 1/3x -5

7. y = -5/3x + 7/3

8 y = 3x + 1

Step-by-step explanation:

Differentiation from First Principles is a formal method for determining a tangent's gradient.

Finding a function's derivative is the process of differentiation. It is also the process of determining how quickly a function changes in relation to its variables.

According to the Sum rule, a sum of functions' derivatives equals the sum of those functions' derivatives. The derivative of two different functions is the difference of their derivatives, according to the Difference rule.

Differentiation from First Principles is a formal method for determining a tangent's gradient. The straight line connecting any two locations on the curve that are fairly near to one another will have a gradient that is similar to that of the tangent at those places.

s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c

substituting the values t = 3, we get

s(-3) = (-cos(-3π))/π + c = 0

simplifying the above equation, we get

(-cos(3π))/π + c = 0

1/π + c = c

c = -1/π

Therefore, the correct answer is s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π.

The complete question is:

Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0

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Answer:

Explanation:

Given the below equation;

To solve for x, the 1st step is to subtract 2x from both sides of the equation;

The 2nd step is to add 7 to both sides of the equation;

The final step is to divide both sides of the equation by 3;

the equation for the saved money is

195 = 8w + 35

here w = no. of weeks.

so the answer is 8w + 35 = 195

Answer:

I forgot maybe someone else knows

Step-by-step explanation:

:) ;) <*)))))<

We have an inequality, this inequality is as follows

To solve the inequality we must clear "x" and see what it tells us

The inequality indicates that "x" belongs to the set of numbers equal to or greater than 28

Of the set of numbers we have, the only ones that meet this condition are numbers 28 and 33

In conclusion, Only options D and F are correct

For this exercise you need to use the following formula:

Where "FV" is the future value, "PV" is the present value, "r" is the interest rate (in decimal form), and "n" number of periods.

In this case, analyzing the information given in the exercise, you can identify that:

Remember that a percent can be written in Decimal form by dividing it by 100. Then:

Since she earns interest at 3% per annum and it is compounded monthly, you can determine that the interest rate per month is:

Knowing that 1 year has 12 months, you know that:

Then:

Therefore, you can substitute all those values into the formula and then evaluate, in order to find the future value of Joan’s investment after 1.5 years:

Hence, the answer is: $209.19 (approximately).

BISECTRIZ: Divide the interior or exterior angle of each vertex into two congruent angles. Then we have that the angle that ES starts and that shares the 2 right triangles is the same:

As we can see, both triangles share the angle and the hypotenuse, that is, their height is also the same, so the height of PC is equal to 8

The linear function passing through points (1,7) and (2.5, 1) is given by:

y = -4x + 11.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

y = mx + b

In which the coefficients are described as follows:

For this problem, the two points that form the function are given as follows:

(1,7) and (2.5, 1).

The slope is given by change in y divided by change in x, hence it is given by:

m = (1 - 7)/(2.5 - 1) = -4.

Then:

y = -4x + b.

When x = 1, y = 7, hence we can find the intercept b of the function as follows:

7 = -4(1) + b

b = 7 + 4

b = 11.

Hence the equation is:

y = -4x + 11.

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distribute the parentheses

substract 32.8 on both sides

Given the rectangle WXYZ, the angle m∠WXY=6a²-6

The given angle is a corner angle, and as you might remember all corner angles of a rectangle are right angles, so we can say that the given expression equals 90 degrees:

From this expression you can calculate the value of a.

First step is to add 6 to both sides of the equation so that the a-related term stays alone in the left side of the equation and all costants are in the other side:

Next divide both sides by 6:

And calculate the square to both sides of the variable to reach the possible value of a:

Now, just because the result is positiv, that does not mean that is the only possible value for a, if you square -4 you can also get 16 as a result, so a can be negative 4 or positive 4:

a=±4

The correct option is B.