Peter is a college professor. His gross salary is
$112,000. If he has to pay 25% income tax what is
Peter's net income?

Answer:

1) The factorized form of the polynomial is [tex](x-5)\cdot (x+2) = 0[/tex].

2) The factorized form of the polynomial is [tex](x+6)\cdot (x-4) = 0[/tex].

3)  [tex]r_{1} = -3[/tex], [tex]r_{2} = -2[/tex]. (Option D)

4) [tex]r_{1} = -7[/tex], [tex]r_{2} = 5[/tex]. (Option A)

Step-by-step explanation:

All exercise are case of factorization of second grade polynomials of the form [tex]x^{2} +(-r_{1} - r_{2})\cdot x + r_{1}\cdot r_{2}[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the two roots of the polynomial. Now we proceed to solve each polynomial:

1) [tex]x^{2}-3\cdot x-10 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = -3[/tex]

[tex]r_{1}\cdot r_{2} = -10[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = 5[/tex], [tex]r_{2} = -2[/tex].

Then, the factorized form of the polynomial is:

[tex](x-5)\cdot (x+2) = 0[/tex]

2) [tex]x^{2}+2\cdot x -24 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = 2[/tex]

[tex]r_{1}\cdot r_{2} = -24[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = -6[/tex], [tex]r_{2} = 4[/tex].

Then, the factorized form of the polynomial is:

[tex](x+6)\cdot (x-4) = 0[/tex]

3) [tex]x^{2} + 5\cdot x +6 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = 5[/tex]

[tex]r_{1}\cdot r_{2} = 6[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = -3[/tex], [tex]r_{2} = -2[/tex].

Hence, the correct answer is D.

4) [tex]x^{2}+2\cdot x -35 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = 2[/tex]

[tex]r_{1}\cdot r_{2} = -35[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = -7[/tex], [tex]r_{2} = 5[/tex].

Hence, the correct answer is A.

Answer:

x³-3x²-40x+84

Step-by-step explanation:

y = (x-7)(x-2)(x+6)

 = (x²-9x+14)(x+6)

 = (x³-9x²+14x)+(6x²-54x+84)

 = x³-3x²-40x+84

Answer:

The answer is b.

Answer:

Cheapest cost to pay = £906

Step-by-step explanation:

Given that:

Rice to supply = 50 tonnes

Option A:

Big van has capacity of 15 tonnes.

Number of big vans = [tex]\frac{50}{15}=3.33[/tex]

It means that 4 big vans will be needed for transporting 50 tonnes of rice.

Cost of 4 vans = 4*250 = £1000

Option B:

Small van has capacity of 9 tonnes.

Number of small vans = [tex]\frac{50}{9} = 5.55[/tex]

It means that 6 small vans will be nedded for transporting 50 tonnes of rice.

Cost of 6 vans = 6*151 = £906

Therefore,

The company can transport the rice through small vans.

Hence,

Cheapest cost to pay = £906

Answer:

It is because not all sides of a rectangle are equal in length; unlike a square.

Step-by-step explanation:

Let's start by drawing the first diagonal.

You know already how a rectangle looks. It has 4 sides and 2 sets of parallel sides. Each pair of parallel sides has the same length.

A diagonal is a line crossing from one edge of a four-sided shape to the opposite edge; such that it divides the shape into two equal halves.

Now place your rectangle horizontally. Let the two longer sides be on the horizon while the two shorter sides go vertical.

We draw the first diagonal from the edge on the top right to the opposite edge (down left). This will divide the shape into two equal halves and each half will be a triangle; a congruent one at that.

When you fold this rectangle along its diagonal, the two triangles will not overlap! The resulting shape will be like two triangular mountains lying side by side. You can use a paper (cut in the shape of a rectangle) for this experiment.

Why does this happen, instead of the two triangles covering each other (overlapping)?

This happens because a rectangle doesn't have 4 equal sides. Check out a square and you'll see that both triangles will overlap after a diagonal is drawn across the square.

Draw the second diagonal of the rectangle (from up-left to down-right) and the same thing is observed.

Answer:

The expression for the perimeter of the rectangle is: [tex]P = 4x - 18[/tex]

Step-by-step explanation:

Perimeter of a rectangle:

A rectangle has length l and width w. It's perimeter is given by:

[tex]P = 2(l + w)[/tex]

In this question:

[tex]l = x - 9, w = x[/tex]

So

[tex]P = 2(x - 9 + x) = 2(2x - 9) = 4x - 18[/tex]

The expression for the perimeter of the rectangle is: [tex]P = 4x - 18[/tex]

Given that the dealer sells a dozen tires for $240, every 3-tire set costs $60. There are six 2-tire sets in a dozen. Thus, his total revenue should be $360. The total profit is the difference between the total revenue and the total cost. The answer is therefore, the first choice, $120.

Answer:

min: 51.25

max: 68.75

Step-by-step explanation:

240-35=205

205/4=51.25

240+35=275

275/4=68.78

Answer:

2 loops

Step-by-step explanation:

If Tessa wants to run a total of 3.1 miles, then she has to complete 2 loops.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Tessa is training for her town's annual fun run.

Today, she plans to run along a 1.55-mile loop trail in a nearby park.

If Tessa wants to run a total of 3.1 miles.

Then the number of the loop will be

[tex]\rightarrow \dfrac{3.1}{1.55}\\\\\rightarrow 2[/tex]

Then the total number of the loops is 2.

More about the division link is given below.

https://brainly.com/question/369266

#SPJ2

Answer:

The slope of parallel line m = -7 is an integer

Step-by-step explanation:

Explanation:-

Given that the parallel line

                     -7x-y = 2

we know that the slope of the two parallel lines are equal

m₁ = m₂

The given parallel line equation

                           - 7 x - y = 2

The slope-intercept form

                             y = - 7x -2

comparing

                             y = mx +C

slope of parallel line m = -7 is an integer

y- Intercept  c = -2

Answer: the answer is C

Edg. 2021

Answer:

C

Step-by-step explanation:

edg 2021

Answer: Set A is greater than set B

Step-by-step explanation:

You can see that the scale of set A is larger than the scale of set B. Therefore making set A greater than set B

Answer:

-3.3 (Choice 3)

Answer:

-3.3

Step-by-step explanation:

1/2=0.5 so 3+0.5=3.5

4.5-3.5=1 Brackets comes first because BIDMAS

-2.3-1= -3.3

Answer:

1. SUN

2. EVAPORATION

3. CONDENSATION

4. EVAPORATION

5. PRECIPITATION

6. CRYSTALLIZATION

Answer:

I have made it in above pic hope it helps

Step-by-step explanation:

there is no need to rationalize simply add √3-√5=1-√2

Answer:

384 sq ft.

Step-by-step explanation:

Given:

L = 12 ft

W = 9 ft

H = 4 ft

Required:

Surface area of the rectangular prism

SOLUTION:

Surface Area of rectangular prism = 2(LW + LH + WH)

SA = 2(12*9 + 12*4 + 9*4)

SA = 2(108 + 48 + 36)

SA = 2(192)

SA = 384 ft²

Answer:

Assuming 1 container per train car..

180 * 80

can be done mentally as

18 * 8 = 144

add the two zeroes onto the answer

180 * 80 = 14,400

14,400 train cars would be needed

Answer:

We conclude that:

Step-by-step explanation:

Given

h(a) = a² - 5

g(a) = -4x

To determine

(hog)(2)

Using the formula

(hog)(2) = h(g(2))

First determining the g(2)

substitute x = 2 in g(a) = -4x

g(a) = -4x

g(2) = -4(2) = -8

so

(hog)(2) = h(g(2)) = h(-8)

now determining the h(-8)

substitute x = -8 in h(a) = a² - 5

h(a) = a² - 5

h(-8) = (-8)² - 5

h(-8) = 64 - 5

h(-8) = 59

so

(hog)(2) = h(g(2)) = h(-8) = 59

Therefore, we conclude that:

Answer:

 8 pages per minute

Step-step explanation:

24 / 3

Answer: see below

Step-by-step explanation:

If this is a 6 sided die then the only possible roll that isnt an odd, a 2, or a 4 is 6.

The probability of something happening is also the probability of something not happening. So in order to not roll an odd, a 2 or a 4 in two rolls, you have to roll a 6 twice.

P = 1 - (1/6)(1/6) = 1 - (1/36) = (35/36)

The line has a positive slope. Let's look at all the slopes:

1) -3

2) -3

3) 3

4)3

Which ones are positive? That's right, 3 and 4. We don't know which equation would be the equation of the line. That's where the other information comes in.

The line intersects the y-axis at at a point that has a negative y-coordinate. Lets write the last two equations in slope-intercept form.

1) y = -3/2x - 5/2

2) y = -3/2x + 5/2

We have to graph both of the lines now. The graphs are at the very bottom. Take a look at them. In the first one, the y-intercept is a negative and in the second one, the y-intercept is positive.

The third one AKA 3x + 2y = -5 is the equation of the line. I hope this helps! Let me know if I got it wrong or if you need any more help.

Answer:

its c i just did it

Step-by-step explanation:

Answer:

86 thousand 5 hundred and 3

Step-by-step explanation:

Answer:

Length of first piece = 5 inches

Length of second piece = 10 inches

Length of third piece = 26 inches

Step-by-step explanation:

Given that:

Length of piece of steel = 41 inch

Let,

x be the length of first piece

y be the length of second piece

z be the length of third piece

According to given statement;

x+y+z = 41          Eqn 1

y = 2x                Eqn 2

z = 5x+1            Eqn 3

Putting value of y and z from Eqn 2 and 3 in Eqn 1

[tex]x+2x+5x+1=41\\8x = 41-1 \\8x = 40[/tex]

Dividing both sides by 8

[tex]\frac{8x}{8}=\frac{40}{8}\\x=5[/tex]

Putting x=5 in Eqn 2 and 3

y = 2(5) = 10

z = 5(5) + 1 = 25+1 = 26

Hence,

Length of first piece = 5 inches

Length of second piece = 10 inches

Length of third piece = 26 inches

Answer:

27

Step-by-step explanation:

3x3x3=9x3=27

Answer:

Step-by-step explanation  Yes u did It right

Part (a)

She replaced x with -x to go from f(x) = 3(2)^x to g(x) = 3(2)^(-x). This will not reflect the graph of f(x) over the x axis. Instead, it will reflect over the y axis. This is because each input is negated from positive to negative, or vice versa. For instance the old input x = 2 becomes the new input -2. Applying this idea to every x input will mirror the curve over the vertical y axis.

==============================================

Part (b)

The correct equation should be g(x) = -3(2)^x

The negative out front is the same as -1.

We can think of it as g(x) = -1*f(x). The f(x) is the output value, or y value. If we multiply each y output by -1, this will flip every point over the horizontal x axis. A point like (0,3) moves to (0,-3) after doing this operation.

distribute the 4:

4x-36=-48x

subtract 4x

-36=-52x

divide by -52

x=1/2

Answer:

740,000

Step-by-step explanation:

500,000/100 = 5,000 ×3= 15,000

15,000×16= 240,000 increase in population

500,000+240,000= 740000

Answer:260,000

Step-by-step explanation:

500,000÷3 equal 15,000 that means it’s going every year by 15,000 times that by 16 equals 260,000