Use vertical multiplication to find the product of: x2 + 3x + 2 x x - x2-1 O - A. ** - 3x4 – x2-3x+ - *- 2 O B. x + 2x4 – x2-3x2 – 3x-2 - C. + 3x4 - X2-3x2-3x O D. +2x4- *° - 3x2 - 3x-2 x

We are asked to find the surface area of a triangular prism. To do that we must add the areas of each of the faces of the prism, that is, three rectangles and two triangles. The area of each rectangle is:

Solving the operations we get:

Now we find the area of the triangles, knowing that the area of a triangle is the product of its base by its height over two, like this:

The base is 5 cm and the height is 6cm, replacing we get:

Now we add both areas having into account that there are two triangles, like this:

Replacing we get:

therefore, the surface area is 210 square centimeters

Hello!

First of all, let's write the initial temperature:

• 6am: 58ºF

In next 5 hours, the temperature rose 1ºF per hour, so:

• 7am: 59ºF

• 8am: 60ºF

• 9am: 61ºF

• 10am: 62ºF

• 11am: 63ºF

In the next 3 hours, it rose 3ºF per hour:

• 12pm: 66ºF

• 1pm: 69ºF

• 2pm: 72ºF

The temperature stayed steady until 6pm:

• In this part, we'll have a constant line until 6pm (it will be 72ºF in all).

In the next 4 hours, the temperature dropped 2ºF per hour:

• 7pm: 70ºF

• 8pm: 68ºF

• 9pm: 66ºF

• 10pm: 64ºF

Dropped steadily until 63ºF at midnight

• 12am: 63ºF

Now, let's make the graph!

Given:

the sequence shown below that starts with n = 1

The rule of the sequence will be as follows"

The first term = 1, when n = 1

The second term = 4 = 2², when n = 2

The third term = 9 = 3², when n = 3

..

..

So, the rule will be:

We know that the sum of interior angles of a triangle equals 180, then, in this case we have the following:

solving for x, we get:

therefore, x = 9

Given the function:

The graph of the function is as shown in the figure:

The range of the function will be as follows:

The minimum value of y = 0

And the maximum value of y = 8 (open circle)

So, the range of the function = [0, 8)

We have this equation

The following is the slope intercept form

add 3x on both sides of the equation

simplify

rearrange

So, the above is the equation in slope-intercept form

Now, let's graph the equation

since this is a linear equation, we need to find 2 points and plot them in the chart

let's find point 1. Let's say x = 0 and replace: y = 3x+4 = 3*0 + 4 = 0 + 4 = 4

so, when x=0, then y = 4 , so our 1st point is (0,4)

now, let's suppose, y=0 , in that case, y = 3x + 4 = 0 , then 3x = -4 , so the value of x is -4/3 = -1.3333

in that case, our seconds point is (-4/3 , 0)

just to make sure, we can also plot a 3rd point, let's say we make x = 2, then y = 3*2 + 4 = 6 + 4 = 10

so, our 3rd point is (2, 10)

using the points above, we can plot something like this...

Conn Math increase by 3 , each week

Conn Sci increase doubling number, every week

Then now fill table

. Week. 1. Conn Math. Conn Sci

. Week 1. 25. 25

. Week 2. 28. 50

. Week 3. 31. 75

. Week 4. 34. 100

Now part. B

A linear model is when data fits in a straight line

hence Then

Then

First model of Conn Math is

Visitors. = 25 + 3 W

Second model for Conn Sci

Visitors = 25 x

Simplify the given expression as shown below

On the other hand,

Solving for y using the special triangle shown below

Thus,

Then,

The two sets of solutions are

We have a feasibility region and we have to find at which point of the region the function P can be maximized:

As this is a linear function, the maximum value will be in one of the vertices of the region. We can identify the vertices as:

We can calculate the value of P for each of the vertices and see which one has a maximum value. We can already guess that P(8,0) will be greater than P(0,8) as the coefficient for x is greater than the coefficient for y.

We can calculate the three values as:

Answer: the maximum value of P is 28.

Answer:

[tex][d(A, B)]^2=\boxed{85}[/tex]

[tex][d(A,C)]^2+[d(B,C)]^2=\boxed{85}[/tex]

[tex]\sf Area=\boxed{17}\; units^2[/tex]

Step-by-step explanation:

From inspection of the given diagram, the vertices of the triangle are:

If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side.  This is the definition of Pythagoras Theorem.

Use the distance formula to find the side lengths of the triangle.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-5))^2+(-2-5)^2}\\&=\sqrt{(6)^2+(-7)^2}\\&=\sqrt{36+49}\\&=\sqrt{85}\end{aligned}[/tex]

[tex]\begin{aligned}d[(A, C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-1-(-5))^2+(6-5)^2}\\&=\sqrt{(-4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\end{aligned}[/tex]

[tex]\begin{aligned}d[(B, C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-1-1)^2+(6-(-2))^2}\\&=\sqrt{(-2)^2+(8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\end{aligned}[/tex]

Therefore:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

The triangle is a right triangle if:

[tex][d(A,C)]^2+[d(B,C)]^2=[d(A,B)]^2[/tex]

Substitute the found side lengths into the formula:

[tex]\implies [\sqrt{17}]^2+[\sqrt{68}]^2=[\sqrt{85}]^2[/tex]

[tex]\implies 17+68=85[/tex]

[tex]\implies 85=85[/tex]

Therefore, this proves that ΔABC is a right triangle.

To find the area of a right triangle, half the product of the two shorter sides:

[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,C)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{17} \cdot \sqrt{68}\\&=\dfrac{1}{2} \cdot \sqrt{17 \cdot 68}\\&=\dfrac{1}{2} \cdot \sqrt{1156}\\&=\dfrac{1}{2} \cdot \sqrt{34^2}\\&=\dfrac{1}{2} \cdot 34\\&=17 \sf \; units^2\end{aligned}[/tex]

Therefore, the area of the given triangle is 17 units².

Answer:

p - 5

Step-by-step explanation:

5 - p = p - 5

The supplement is when two angles add up to 180° and complement is when two angles add up to 90°

let:

x = the angle.

180 - x = its supplement.

90 - x = its complement

then x = 2(90-x) + 20 means the measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20

The function we have is:

First, we need to find the rate of change of this function and then we can compare it with the rate of change of each option.

To find the rate of change, we compare the given equation with the general slope-intercept equation:

Where m is the slope, also called the rate of change and b is the y-intercept.

By comparing the two equations, we find that the rate of change is:

So now we will analyze the given options to see in which of them we find a rate of change of -1.

Option A:

In this option (and in option B) we have a table of values for x and y.

We calculate the rate of change by taking two (x,y) points from the table,

Here, we will take the first two (x,y) values and label them as follows:

And we calculate the rate of change "m" using the slope formula:

Substituting the values we get:

Solving the operations:

The rate of change if NOT -1, this option is not correct.

Option B. We do the same as in the first option.

Label the first two (x,y) values as follows:

And use the slope formula:

Substituting the values:

Again, the slope or rate of change is NOT -1, this is also not the option we are looking for,

Option C. In options, C and D we have a graph. To find the rate of change from the graph of a line, we take two points where the line passes, and find the rate of change as follows:

For the graph in C, we will take the following red points

Drawing a triangle between the points we can find the change in y and the change in x:

Thus, the rate of change is:

C is the correct option.

Observe the given graph carefully.

It is evident that 'b' is the independent variable (representing the number of books read) for the function f(b) (representing the number of points earned).

The domain of a function is the set of all values of the independent variable that lie within the function.

The graph is plotted from x=0 to x=24.

And the number of books cannot be fractional.

So it can be concluded that the domain of the function is the set of whole numbers from 0 to 24. Also, the function is also defined at the end-points. So the set will be inclusive of the end-points 0 and 24.

Therefore, the 2nd option is correct for the first blank.

The domain is a subset of all possible values of variable 'b'. So it will represent the number of books that Jacob reads.

Thus, the 1st option is the correct choice for the second blank.

Multiply each side by 10, then simplify

Here, we want to know how to proceed with solving the equation

As we can see, we have the division sign between the terms on the left hand side of the equation

To solve the equation, we have to find the value for x by isolating it

What this mean here is that we will have to multiply both sides by 10; so that we can isolate x

Thus, the correct answer here is to multiply each side by 10, then simplify

The solid is formed by 6 rectangles.

Calculate the area of each one and then add them to obtain the surface area (SA),

Area of a rectangle: Length x width

A1 = 8 x 5 = 40 mm2

A2= 25x5 = 125 mm2

A3 = 8 x 5= 40 mm2

A4 = 25 x 8 = 200 mm2

A5 = 25x5 = 125 mm2

A6 = 25 x 8 = 200mm2

SA = A1+A2+A3+A4+A5+A6 = 40 + 125 +40 +200 +125+ 200 = 730 mm2

Given a rectangular prism with the following dimensions:

H = Height = 26

L = Length = 20

W = Width = 12

To be able to determine its volume, we will be using the following formula:

We get,

Therefore, the volume of the rectangular prism is 6,240.

To find the total surface area of this cone, we have that the total lateral area is given by the formula:

Where

s is the slant height of the cone, s = 12 inches.

r is the radius of the base of the cone, r = 7 inches.

To that area, we need to add the area of the base of the cone:

That is, this is the area of a circle with this radius. Then, the total surface area is:

Substituting the values in this formula, we have:

Then

Hence, the total area is equal to 417.62 square inches.

Solve;

The solution is x = 48

Given:

Square SQRE has coordinates S(2, 2) Q (5,2), and R (5. – 1).

To find:

The coordinates of E.

Explanation:

Let (x, y) be the coordinates of E.

Using the midpoint formula,

As we know,

The diagonals of the square are intersected by its midpoint.

So, the Midpoint of SR and QE is the same in a given square SQRE.

Equating the coordinates we get,

Therefore, the coordinate of E is (2, -1).

Final answer:

The coordinate of E is (2, -1).

Since he has 15 vessels and needs to choose 5, we can use a combination of 15 choose 5 to calculate the number of possible ways, since the order of the vessels inside the group of 5 is not important.

The formula to calculate a combination of n choose p is:

Then, for n = 15 and p = 5, we have:

So there are 3003 ways to choose the 5 vessels.

The perimeter can be calculated by adding the legnths off all 4 sides.

Since it is 5 inches wide and 3 inches tall, it has 2 sides of 5 inches and 2 sides of 3 inches. So, the perimeter is:

16 inches.

Given:

One time payment, p = $300

Payment per month, q = $65

Number of months paid, n = 5

The objectiv is to find the amount she paid in 5 months.

Let x be the amount she paid in 5 months. Then the the formula is,

Let's substitute the values.

Hence, total amount paid in 5 months is $625.

Answer

The solution to the equation is x = 4.

Explanation

We are told to find the solution to the equation

2x + 2(x - 5) = 6

The first step is to open the bracket by multiplying through by the number outside the bracket, that is, 2.

2x + 2x - 10 = 6

4x - 10 = 6

Add 10 to both sides to leave only 4x on the Left Hand Side.

4x - 10 + 10 = 6 + 10

4x = 16

Divide both sides by 4 to obtain the value of x.

(4x/4) = (16/4)

x = 4

Hope this Helps!!!

We are asked which of the given combinations will produce a number that is less or equal to 25.

For A we have:

Let's remember that for a mixed fraction we have:

Therefore, we can change the mixed fraction and we get:

Solving the operations:

Since we get a number greater than 25 this is not a trail he can ride.

For B we have:

Changing the mixed fraction:

To solve the operation we will apply the distributive property:

Now, we simplify the fraction:

Now, we use the fact that 1/2 = 0.5:

Since we get a number that is less than 25 this is a train he can ride.

For C we have:

Changing the mixed fraction:

Now, we apply the distributive property:

Solving the operations. We use the fact that 1/4 = 0.25:

Since we get a number greater than 25 this is not a trail he can ride.

For D.

Now, we change the mixed fractions:

Now, we use the distributive property:

Simplifying the fraction:

Now, we add the fractions, we have into account that when fractions have the same denominator we can add the numerators and use the common denominator, like this:

Simplifying the fraction we get:

Solving the operations:

Since we get 25 this is a trail that he can ride.

Answer:

No solution.

Step-by-step explanation:

Why I say this problem has no solution is due to the fact that the amount of pages is unclassified. This leads you to guessing how many pages there might be for each chapter of the students' individual books, and guessing would not be an effective method as it could lead you to thinking of any random number between 1 - 60 at the most. Therefore, this problem has no solution. If you have further concerns about this problem, I recommend addressing them to your teacher. Otherwise, have a great day. :)

ANSWER

$3,450

EXPLANATION

She started the savings account with $3,000.

The simple interest rate is 3% and the number of years is 5 years.

To find the amount of money in the account after 5 years, we have to first find the interest and then add it to the initial amount saved.

Simple Interest on an amount of money (Principal) at a rate R for a number of years T is given as:

Therefore, the interest is:

Therefore, the amount in the account after 5 years is:

Amount = Principal + Interest

Amount = 3000 + 450

Amoun = $3,450

That is the amount in the account.

We will have that the best way to write it in standard form is B, we clear the parentheses and solve for x.

*That is because the function is already factored, and we will combine like terms and equal to 0 in the remaining steps.

Answer

Explanation

To draw the image of this figure, we need to first obtain the coordinates of the edge of the image of this figure.

And to do that, we need to first write the coordinates of the edges of the original figure.

When a given coordinate A (x, y) is reflected across the x-axis, the coordinates become A' (x, -y).

The coordinates of the original image include (-2, -4), (1, -3) and (3, -4)

After the reflection, we will now have

(2