what is the equation of the line shown below? Give your answer in slope-intercept form. (5,4) (-4,-5)

ANSWER

[tex]15 {x}^{2} + 22x - 5[/tex]

EXPLANATION

It was given that, the length of the rectangular building is

[tex](3x + 5) \: meters[/tex]

and the width of the is

[tex](5x - 1) \: meters[/tex]

The area of a rectangular building is calculated using the formula for finding the area of a rectangle.

[tex]A = l \times w[/tex]

Since the dimensions are given in terms of x, the area is also a function of x,

[tex]A(x) = (3x +5 )(5x - 1)[/tex]

We expand to get,

[tex]A(x) = 3x(5x - 1) + 5(5x - 1)[/tex]

[tex]A(x) = 15 {x}^{2} - 3x + 25x - 5[/tex]

[tex]A(x) = 15 {x}^{2} + 22x - 5[/tex]

meters square

Answer:

D. 15x^2 + 22x -5

Step-by-step explanation:

I just took the test

Answer: rotation

Step-by-step explanation:

Rotation is required to map DEF onto D'EF'

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Rotation exists as the operation or act of turning or circling something.

Rotation exists in the circular movement of an object around an axis of rotation. A three-dimensional object may include an infinite numeral of rotation axes.

To know more about rotation refer to :

https://brainly.com/question/2283733

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Answer:

(a + b, c )

Step-by-step explanation:

Using the midpoint formula

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[ [tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex] ]

let (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(2a+2b, 2c), then

midpoint = [ [tex]\frac{0+2a+2b}{2}[/tex], [tex]\frac{2c}{2}[/tex] ]

               = [tex]\frac{2(a+b)}{2}[/tex], c ] = (a + b, c )

Answer:

C

Step-by-step explanation:

As with most problems of this type, you need to draw an actual line that has approximately the same number of data points on each side of it.  If you'll do that you'll see that this line crosses the y-axis at approx. y = 4.  Only Answer C has that y-intercept.

Answer: It's easy and simple!

Step-by-step explanation: Split it into rectangles and multiply the height and length. Than add it together and Then you have your answer.

Answer:

It depends on the figure.

Step-by-step explanation:

The compound figures we're generally concerned with are combinations of rectangles, triangles, circles or parts of circles, with or without cutouts of those shapes. The area is the sum of the areas of the component shapes, less the areas of any cutouts.

__

Consider the attached examples:

7) This is half a circle together with two triangles. Or, the two triangles can be considered to be a rectangle with a triangular cutout.

The area is the sum of the areas of the semicircle and the rectangle, less the area of the triangular cutout.

__

8) This can be considered as a square with a square cutout. The area is the difference between the area of the larger square and the area of the smaller one. Alternatively, one can find the area by finding the length of the centerline of the shaded area and multiplying that by the width of the shaded area.

__

9) The area of this figure can be considered to be the total of the area of the bottom rectangle and the top triangle. Alternatively, one can cut the figure into two trapezoids (with a vertical line) and sum their areas.

Answer:

see explanation

Step-by-step explanation:

Corresponding angles are associated with parallel lines

L and M would have to be parallel but not so cannot name a corresponding angle.

If they were parallel then ∠7 would correspond to ∠3

Answer:

7, 5

Step-by-step explanation:

_________________________________________________

Answer:

7 and 5

Step-by-step explanation:

So we can start with 1 and 4. We can see they added 3 to 1. Ok, that's the first part.

Then, they took 4 and subtracted 2. We can see they subtracted 2. Ok, that's the second part.

We can see they keep doing this:

Add 3, subtract 2. Add 3, subtract 2. and so on, until we get to 4. They just subtracted 2, so we can add 3. So, our first unknown number would be 7. We can then subtract 2, making the second unknown number 5.

Hope I helped, soz if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Answer:

c

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math.  The LCD is sin(x) cos(x).  Multiplying that in to each term looks like this:

[tex][sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?[/tex]

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

[tex]\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?[/tex]

Put everything over the common denominator now:

[tex]\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?[/tex]

Since [tex]sin^2(x)+cos^2(x)=1[/tex], we will make that substitution:

[tex]\frac{1}{sin(x)cos(x)}[/tex]

We could separate that fraction into 2:

[tex]\frac{1}{sin(x)}[/tex]×[tex]\frac{1}{cos(x)}[/tex]

[tex]\frac{1}{sin(x)}=csc(x)[/tex]  and  [tex]\frac{1}{cos(x)}=sec(x)[/tex]

Therefore, the simplification is

sec(x)csc(x)

Answer:

False

Step-by-step explanation:

Let's list all the odd numbers less than 15.

13, 11, 9, 7, 5, 3, 1

Prime numbers are numbers that can only be multiplied by 1 and themselves. But, we can see, that 9 can be multiplied by 3 and 3, making it a not-prime number (sorry I don't remember the exact name for that, I'm blanking out).

The number 9 makes that statement false.

Hope I helped! ouo.

~Potato.

Copyright Potato 2019.

Answer:

False

Step-by-step explanation:

Consider the odd numbers less than 15

1, 3, 5, 7, 9, 11, 13

A prime number has only 2 factors, namely 1 and itself

9 has factors : 1, 3, 9 ← not Prime

The statement is therefore False

Answer:

d. :)

Step-by-step explanation:

Answer:

D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.

Step-by-step explanation:

The difference between C and D interval is the lowest.

This means that line is increasing more quickly at interval D as compared to others.

Therefore, option D is the right answer.

Answer:

10.4 cm

Step-by-step explanation:

The volume (V) of a pyramid is calculated using

V = [tex]\frac{1}{3}[/tex] area of base × height (h)

area of square base = 6² = 36, thus

[tex]\frac{1}{3}[/tex] × 36h = 120

12h = 120 ( divide both sides by 12 )

h = 10 cm

To find the slant height (s) consider the right triangle from the vertex to the midpoint of the base and from the midpoint of base to the side.

That is a right triangle with hypotenuse s and legs 10(h) and 3 (midpoint of the base )

Using Pythagoras' identity then

s² = 10² + 3² = 100 + 9 = 109

Take the square root of both sides

s = [tex]\sqrt{109}[/tex] ≈ 10.4 cm

1. Same length.

2.vertically opposite angle.

3.BAC =BDE

4.AC = DE

Hope this helps you ___!!❤

Answer:

[tex]\texttt{The summation form} = \sum\limits_{n=1}^{15} 3^{(n-1)}=7,174,453[/tex]

Step-by-step explanation:

We can find the total number of shaded triangles in the first 15 figures by first finding the pattern between the first, second, and the third triangles.

We can see that the number of shaded triangles of T₂ is 3 times more compared to T₁. Also, the number of shaded triangles of T₃ is 3 times more compared to T₂. Then we can conclude that the numbers of shaded triangles form a geometric sequence with:

For the summation form, we can find each term using the geometric sequence formula:

[tex]\boxed{U_n=U_1\cdot r^{(n-1)}}[/tex]

[tex]U_n=1\cdot 3^{(n-1)}[/tex]

[tex]U_n=3^{(n-1)}[/tex]

Then, the summation form for the 1st 15 term =

[tex]\displaystyle\sum\limits_{n=1}^{15} 3^{(n-1)}[/tex]

We can also find the summation by using the geometric series formula:

[tex]\boxed{S_n=\frac{U_1(r^n-1)}{r-1} ,\ \texttt{for r > 1}}[/tex]

Then, for S₁₅:

[tex]\begin{aligned}S_{15}&=\frac{U_1(r^{15}-1)}{r-1}\\\\&=\frac{1(3^{15}-1)}{3-1} \\\\&=\bf 7,174,453\end{aligned}[/tex]

Answer:

D. 28 feet

Step-by-step explanation:

a²+b²=c²

45²+b²=53²

2025+b²=2809

b²=784

[tex]\sqrt{784}[/tex]=[tex]\sqrt{b}[/tex]

b=28

Answer:

D. 28 feet

Step-by-step explanation:

ANSWER

$16,384

EXPLANATION

From the question we have that,

Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.

This forms a geometric sequence,

[tex]1,2,4,...[/tex]

The first term of this sequence is

[tex]a = 1[/tex]

The common ratio is

[tex]r = \frac{2}{1} = \frac{4}{2} = 2[/tex]

The general term of a geometric sequence is given by the formula:

[tex]f(n) = a {r}^{n - 1} [/tex]

To find the 15th term, we plug in a=1, r=2 and n=15.

[tex]f(15) = 1 {(2)}^{15 - 1} [/tex]

[tex]f(15) = {2}^{14} [/tex]

[tex]f(15) = 16384[/tex]

The amount he will save on the 15th day is $16,384

Answer:

1. x=2, y=3

2. n=7, m=-6.8

3. x=6, y=3

4. q=-2, p=-1

5. c=2, d=0

Step-by-step explanation:

4x + 3y = 17

5x – 3y = 1

first make it so either x or y can cancel out in both equations, then combine the equations, giving you 9x=18. solve for x, x=2. substitute 2 for x in either equation, 4(2) + 3y = 17. solve for y, 8+3y=17, 3y=9, y=3

–5m + 6n = –8

–5m + 8n = 6

first make it so either m or n can cancel out in both equations, multiply –5m + 6n = –8 by -1, 5m - 6n = 8, then combine the equations, giving you 2n=14. solve for n, n=7. substitute 7 for n in either equation, 5m - 6(7) = 8. solve for m, 5m - 42 = 8, 5m = -34, m = -6.8

2x – 7y = –9

6x + 7y = 57

first make it so either x or y can cancel out in both equations, then combine the equations, giving you 8x=48. solve for x, x=6. substitute 6 for x in either equation, 2(6) – 7y = –9. solve for y, 12 – 7y = –9, –7y = –21, y = 3

5p – 4q = 3

–5p – 4q = 13

first make it so either p or q can cancel out in both equations, then combine the equations, giving you -8q=16. solve for q, q=-2. substitute -2 for q in either equation, 5p – 4(-2) = 3. solve for p, 5p + 8 = 3, 5p = -5, p = -1

6c + d = 12

c – d = 2

first make it so either c or d can cancel out in both equations, then combine the equations, giving you 7c=14. solve for c, c=2. substitute 2 for c in either equation, 6(2) + d = 12. solve for d, 12 + d = 12, d = 0

[EDIT] question 2 is impossible.

Answer:

Step-by-step explanation:

Let s represent the length of the shortest side. Then the other two sides are ...

The perimeter is the sum of the lengths of the three sides, so is ...

  56 ft = s + (s+6) + (2s-6) = 4s . . . . collect terms

  14 ft = s . . . . . . . divide by the coefficient of s

The shortest side is 14 ft; the second side is 20 ft; the third side is 22 ft.

Final answer:

Using the given information about the sides of the triangular deck and its perimeter, we set up an equation to solve for the shortest side and then used that to find the lengths of the other two sides. The three sides of the triangular deck are 14 feet, 20 feet, and 22 feet.

Explanation:

To solve the problem, we need to set up an equation based on the given information. Let's define the shortest side of the triangle as x feet. According to the problem, the second side is x + 6 feet, and the third side is 2x - 6 feet. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 56 feet.

We can set up the following equation:

x + (x + 6) + (2x - 6) = 56

Combining like terms, we get:

4x = 56

Divide both sides by 4:

x = 14

Now we can find the lengths of the sides:

The shortest side: 14 feet

The second side: 14 + 6 = 20 feet

The third side: 2(14) - 6 = 22 feet

Answer:

  27,409.308

Step-by-step explanation:

Compute the given sum. If you're really stuck, your calculator can help you.

Answer:  The correct option is

(A) at the most 10.

Step-by-step explanation:  Given that Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10 on food.

Also, she wishes to buy some books and each book costs $3.

We are to solve the inequality to find the number of number of books that she can buy.

Let the number of books that Mary can buy be n.

Then, according to the given information, we have

[tex]20+10+n\times3\leq 60\\\\\Rightarrow 30+3n\leq 60\\\\\Rightarrow 3n\leq 60-30\\\\\Rightarrow 3n\leq 30\\\\\Rightarrow n\leq \dfrac{30}{3}\\\\\Rightarrow n\leq 10.[/tex]

Thus, Mary can buy at most 10 books.

Option (A) is CORRECT.

To express the given information in a linear equation, the setup time and hourly rate per square foot should be considered in the equation y = 4 + (1/1000)x.

To express the information in a linear equation:

7,4 is the answer to the question

Answer:

[tex]x=7/4[/tex]

Step-by-step explanation:

the equation is:

[tex]xy=k[/tex]

To find the value of [tex]x[/tex], we need to substitute the values that we know for [tex]y[/tex] and [tex]k[/tex]:

[tex]y=4[/tex]

and

[tex]k=7[/tex]

so, we substitute this values into the equation

[tex]xy=k[/tex]

[tex]x(4)=7[/tex]

and we clear for [tex]x[/tex], for this we move the 4 to the right dividing:

[tex]x=7/4[/tex]

Sorry this is a little late, but I hope it'll still help someone in the near future.

The next larger scale size is 2.827

Hope this helps :)

Answer:

Next larger scale size = 2.827

Step-by-step explanation:

For a certain font scale factor is 1.414 and one of the scale size is 1.999.

so we have to find the next larger scale size.

Since scale factor will be defined as the ratio of larger scale size of the font and smaller font size.

[tex]\text{Scale factor}=\frac{\text{Larger font size}}{\text{smaller font size}}[/tex]

1.414 = [tex]\frac{\text{Larger font size}}{1.999}[/tex]

Larger font size = 1.414 × 1.999 = 2.8266 ≈ 2.827

Next larger scale size = 2.827

Answer: OPTION B

Step-by-step explanation:

You need to remember that, to subtract radicals, the indices and the radicands must be the same.

Given the expression [tex]3\sqrt{2}-\sqrt{2}[/tex], you can identify that both have index 2 and the radicands are 2 (The numbers that are inside of radicals), therefore, you can conclude that the subtraction can be made.

Then, you must subtract the terms in front of the radicals. Therefore, you get:

[tex]3\sqrt{2}-\sqrt{2}=2\sqrt{2}[/tex]

You can observe that this matches with the option B.

Answer:

The correct answer is option B.  2√ 2

Step-by-step explanation:

It is given that, 3√ 2 – √ 2

To find the correct option

3√ 2 – √ 2  can be written as,

3√ 2 – √ 2  = √ 2 (3 - 1)   taking √ 2  as common

 = √ 2  * 2

 = 2√ 2

Therefore the correct answer is 2√ 2 .

The correct option is option b.  2√ 2

Answer:

A) x-3 and D) x+9

Step-by-step explanation:

x^2 + 6x - 27

You need to find two numbers that multiply to -27 and add up to 6

Those two numbers are -3 and 9, because 9 * -3 = -27 and 9+ -3 = 6

So you add those to x and those are your two factored binomials

(x-3) and (x+9)

D.(18.8) is the answer because the explanatory variable is the x-axis while the response variable is the y-axis.

Answer:  The correct option is (D) (18, 8).

Step-by-step explanation:  Given that the value of an explanatory variable is 18, while the corresponding value of the response variable is 8.

We are to find the co-ordinates of this data plot when plotted on a scatter plot.

Let y = f(x) be a function, where x is the independent variable and y is the dependent variable.

On a scatter plot, we plot any point satisfying this function as (x, y).

Explanatory variable = independent variable, x = 18

and

Response variable = dependent variable, y= 8

Therefore, the required coordinates of this data point when plotted on a scatter plot are (18, 8)

Option (D) is CORRECT.

Answer:

slope = -0.5

Step-by-step explanation:

Answer:

slope = change in y / change in x

slope = 0 -3.5 / 7 -0

slope = -3.5 / 7

slope = -.5

Step-by-step explanation:

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

The opposite side x is 7

Step-by-step explanation:

Step one

From the given expression in the picture

We can estimate x by applying the

SOH CAH TOA rule on the triangle

Since we have one side and one angle given

step two

From the given picture we have

We have θ and adjacent side given

Hence we need to apply

tan θ= opposite/adjacent =

Tan 35°=x/10

Step three

From 4 figure table or calculator

tan 35° is 0.7

0.7=x/10

x=0.7*10

x= 7

The area of the triangle will be 14 square units. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).

Then the area of the triangle is given as,

A = 1/2 | {[2 x (-3) + 1 x 1 + (-3) x 3] - [3 x 1 + (-3) x (-3) + 2 x 1]} |

A = 1/2 | {[-6 + 1 - 9] - [3 + 9 + 2]} |

A = 1/2 | {-14 - 14} |

A = 1/2 x 28

A = 14 square units  

The area of the triangle will be 14 square units. Then the correct option is C.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

Answer:

Option B is correct.

Step-by-step explanation:

300 cm^3 of snow melts into 33 cm^3 water. We need to find how much water is produced if 600 cm^3 of snow is melt.

Solving using unitary method:

300 cm^3 of snow melts into water = 33 cm^3

1 cm^3 of snow melts into water = 33/300

600 cm^3 of snow melts into water = 33/300 *600

                                                           = 66 cm^3

So, Option B is correct.

Answer:

True

Step-by-step explanation:

we know that

sin(90°)=1

sin(270°)=-1

sin(-90°)=-sin(90°)=-1

sin(-90°)=sin(270°)

therefore

For sin(x)=-1

the values of x are x=-90° and x=270° ------> is true