Type the correct answer in each box. Use numerals instead of words.
Harry buys a boat in 2010. He plans on selling it in 2020. In 2010, the boat costs $20,000. The value of the boat depreciates over time
as is shown in the graph below, where the y-axis represents the value of the boat, in dollars, and the x-axis represents the number of
years since 2010.

Answer:Case I

When we know two sides of the right triangle, in which case, we will use the Pythagorean theorem

Case II

When we know 1 side and 1 angle of the right triangle, in which case, we will use good old sohcahtoa

Step-by-step explanation:

Answer:

x^2+13x+40

Step-by-step explanation:

To solve this, use the FOIL method. Multiply the first terms, then the outside, then the inside and finally the last terms.

We have the binomials:

(x+5) and (x+8)

The first terms are x and x. The outside terms are x and 8. The inside terms are 5 and x. The last terms are 5 and 8.

Multiply these values.

F (first): x and x

x*x= x^2

O (outside): x and 8

x*8=8x

I (Inside): x and 5

x*5=5x

L ( Last): 5 and 8

5*8=40

Now, add all the products together.

x^2+8x+5x+40

Combine like terms. In this case, the like terms are 8x and 5x.

x^2+13x+40

The final trinomial (three terms) is: x^2+13x+40

Answer:

the bottom one

Step-by-step explanation:

Answer:

B) 16%

Step-by-step explanation:

First, we need to standardize 58 and 66 inches using the following equation:

[tex]z=\frac{x-m}{s}[/tex]

Where m is the mean and s is the standard deviation, so 58 and 66 are equivalent to:

[tex]z=\frac{58-70}{4}=-3\\z=\frac{66-70}{4}=-1\\[/tex]

Then, the percent of men whose heights falls between 58 inches and 66 inches is calculated as:

P(58<z<66) = P(-3<z<-1)

So, using the normal table, we get:

P(-3<z<-1) = P(z<-1) - P(z<-3)

P(-3<z<-1) = 0.1587 - 0.0013

P(-3<z<-1) = 0.1574

Finally, 0.1574 rounded to the nearest whole percent is equal to 16%

Answer:

[tex]x=\sqrt{26}-4,\:x=-\sqrt{26}-4[/tex]

Step-by-step explanation:

[tex]x^2+8x=10[/tex]

Write this equation in the form of: [tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]

Solve for a:

[tex]2ax=8x[/tex]

[tex]\frac{2ax}{2x}=\frac{8x}{2x}[/tex]

[tex]a=4[/tex]

Add [tex]a^2=4^2[/tex] to both sides:

[tex]x^2+8x+4^2=10+4^2[/tex]

[tex]\left(x+4\right)^2=26[/tex]

[tex]x+4=\sqrt{26}[/tex]

[tex]x+4-4=\sqrt{26}-4[/tex]

[tex]x=\sqrt{26}-4[/tex]

[tex]x+4=-\sqrt{26}[/tex]

[tex]x+4-4=-\sqrt{26}-4[/tex]

[tex]x=-\sqrt{26}-4[/tex]

Answer:

[tex]2x-16/5[/tex]

Step-by-step explanation:

[tex]2x+14-18+0.8[/tex]

[tex]2x-3.2[/tex]

Answer:

2x + 16/5

Step-by-step explanation:

= 2x + 14 - `18 + 4/5

= 2x + 4 + 4/5

= 2x + 16/5

Hope this helps!

Answer:

Sum of the first 3 terms is 9245

See explanation below

Step-by-step explanation:

The question is not clear. From the question we can tell we are to determine the sum of the first 3 terms of a geometric series. I would show you how to calculate sum of n terms given first term and common ratio.

Let's consider the question below.

Given that the first term is 15 and the common ratio is 6, find the first 3 terms

Solution:

Sum of geometric series has two formulas: one is for common ratio(r) > 1 and the other is for common ratio (r) < 1

Since the r in the question is > 1. We would apply the formular that applies to it.

Sum of the first 3 terms is 9245

See attachment for detail

Answer:

XW = 80 feet

Step-by-step explanation:

To answer this question, we shall be needing a diagrammatic representation of the triangle.

Please check the attachment for this.

We are told to calculate the length XW and this refers to the hypotenuse of the triangle.

The other side that we have is the adjacent.

So yo calculate the length of XW, we need a trigonometric identity that links hypotenuse and adjacent together.

The trigonometric identity to use here is the cosine.

Mathematically;

Cos of an angle = length of the adjacent/length of the hypotenuse

Cos 60 = 40/XW

XW = 40/Cos 60

Cos 60 = 1/2 or 0.5

XW = 40/0.5 = 80 feet

Answer:

4 * pi

Step-by-step explanation:

Given r = 10

Formula for the circumference of this full circle is:

2 * r * pi

2 * 10 * pi = 20 * pi

Given one (biggest) part = 16 * pi of this circle.

The other (smaller) part must therefore be:

20 * pi - 16 * pi

4 * pi

Answer:

m∠R = 112°, m∠S = 112°, m∠T = 68°

Step-by-step explanation:

In a cyclic quadrilateral QRST,

m∠R + m∠T = 180° [Since opposite angles of a cyclic quadrilateral measure 180°]

(3x + 40)° + (5x - 52)° = 180°

8x - 12 = 180

8x = 180 + 12

8x = 192

x = 24

m∠R = (3x + 40) = 3×24 + 40

                          = 72 + 40

                          = 112°

m∠T = 180° - m∠R

        = 180° - 112°

        = 68°

Since m∠Q = 68°

m∠S = 180° - m∠Q

        = 180° - 68°

        = 112°

Therefore, m∠R = 112°, m∠S = 112°, m∠T = 68°

Answer:

112, 112, 68

Step-by-step explanation:

It took me over 15 min to figure out what the answer was. When answering it, you have to be very specific.

Answer:

y = x +2

Step-by-step explanation:

4y=4x+8​

Slope intercept form is

y = mx+b so we need to solve for y

Divide each side by 4

4y/4 = 4x/4 +8/4

y = x +2

The slope is 1 and the y intercept is 2

Answer:

[tex]\frac{5\sqrt{6} +35}{43}[/tex]

Step-by-step explanation:

Step 1: Multiply by conjugate

5/(7 - √6) x (7 + √6)/(7 + √6)

5(7 + √6)/43

Step 2: Distribute

(35 + 5√6)/43

Answer:

No other given point lie on the same graph

Step-by-step explanation:

Equation : [tex]y =(x +8)^2+k[/tex]

We are given that The point (-4,7) lies on the graph of [tex]y =(x +8)^2+k.[/tex]

So, Point(-4,7) satisfies the given equation

So,[tex]7=(-4+8)^2+k[/tex]

7=16+k

-9=k

So, The equation is [tex]y =(x +8)^2-9[/tex]

Now substitute the given points

(12,4)

[tex]4=(12+8)^2-9[/tex]

4=400-9

[tex]4\neq 391[/tex]

So,(12,4) not lies on the graph

(-5,72)

[tex]72=(-5+8)^2-9[/tex]

72=9-9

[tex]72\neq 0[/tex]

So,(12,4) not lies on the graph

(5,72)

[tex]72=(5+8)^2-9[/tex]

72=169-9

[tex]72\neq 160[/tex]

So,(12,4) not lies on the graph

(4,12)

[tex]12=(4+8)^2-9[/tex]

12=144-9

[tex]12\neq 135[/tex]

So,(12,4) not lies on the graph

So, No other given point lie on the same graph

Answer: Think it is -3/5

Step-by-step explanation:

6-5(x)=9

6-5(-3/5)=9

6+3=9

9=9

Answer:

Equation:

5x - 6 = 9

Answer:

x = 3

Step-by-step explanation:

Let's break this down:

When six is subtracted from five times a number, the result is 9

"five times a number" simply means a variable, such as x, is being multiplied by 5

five times a number: 5x

Next step:

When six is subtracted from five times a number, the result is 9

"six is subtracted from" means 6 is being taken away from whatever comes next, in this case, '5x'

six is subtracted from: - 6

Final section:

When six is subtracted from five times a number, the result is 9

"the result is 9" means the entire equation equals nine

the result is nine: = 9

Put it all together:

5x - 6 = 9

Solve:

5x - 6 = 9

     +6  +6

5x = 15

/5     /5

x = 3

Therefore, the value of x is three.

Answer:

36.4miles per gallon

Step-by-step explanation:

Divide 45 1/2 by 1 1/4. This gives 36 2/5

Hope this helps.

Answer:

10.7 feet

Step-by-step explanation:

The ladder, the ground and the wall form the shape of a right angled triangle as shown in the image below.

The hypotenuse of the triangle is 14 feet (length of ladder)

The base of the triangle is 9 feet long (the distance from the base of the ladder to the wall)

We need to find the height of the triangle. We can apply Pythagoras rule:

[tex]hyp^2 = a^2 + b^2[/tex]

where hyp = hypotenuse

a = base of the triangle

b = height of the triangle

Therefore:

[tex]14^2 = 9^2 + b^2\\\\196 = 81 + b^2\\\\b^2 = 196 - 81 = 115\\\\b = \sqrt{115} \\\\b = 10.7 feet[/tex]

The wall reaches 10.7 feet high.

Answer:

Step-by-step explanation:

The area for a rectangle is A = LW. We know the area and we also know the length. We are solving for the width.

[tex]112=7\sqrt{x}[/tex] and

[tex]16=\sqrt{x}[/tex]

Siince the width is given as the square root of x, and the square root of x is equal to 16, then the width is 16. Now to find the value of x from the last statement in our equation. If

[tex]16=\sqrt{x}[/tex] and we want to solve for x, we will square both sides, since squaring undoes a square root. Since this is an equation, we have to square both sides.

256 = x

The area of the rectangle is 112 units and the width is 16 units

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

A = 112 units

Let the length of the rectangle be L = 7 units

Let the width of the rectangle be W = √x units

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of the rectangle = 7 √x

7√x = 112

Divide by 7 on both sides of the equation , we get

√x = 16

Taking the square on both sides of the equation , we get

x = 16²

x = 256

Therefore , the value of x is 256

Hence , the width of the rectangle is √x = 16 units

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Answer:

Step-by-step explanation:

This is a binomial probability distribution and the probability of success and value is the same for each trial.

Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success is

89.4/100 = 0.894

If exactly 7 of the 10 have the right shape, should the company stop the production line, it means that the probability of getting right shaped tires in this case is 7/10 = 0.7

This is actually below the known probability of success. Therefore, the correct option is

Yes, as the probability of seven having the correct shape is unusual

Answer:

3ft

Step-by-step explanation:

The value of length of SA is,

⇒ SA = 3 feet

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

Triangle ABC is shown in figure.

Now, Observe the given figure,

Since, Line ST is parallel to the line AC.

Therefore, By Basic Proportionality Theorem which states

" If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion".

Hence, We get;

SB/SA = BT / TC

10 / SA = 9 / 2.7

SA = 2.7 × 10 / 9

SA = 3 feet

Thus, The value of length of SA is,

⇒ SA = 3 feet

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Answer:

The answer is 8.3

Step-by-step explanation:

(I'm not that good at explaining things so bear with me please. I checked on Khan Academy so it's right)

I split the box on the right diagonally and got the equation

[tex]4^{2}[/tex] + [tex]2^{2}[/tex] = [tex]x^{2}[/tex]

=16 + 4 =[tex]\sqrt{20}[/tex]

≈4.5

The new triangle will help solve what d is

[tex]4.5^{2}[/tex] + [tex]7^{2}[/tex] = [tex]d^{2}[/tex]

=20.25 +49 = [tex]\sqrt{69.25}[/tex]

≈8.3

The diagonal of the rectangular prism shown is 8.3.

A polygonal is a closed, two-dimensional structure that is flat or plane and seems to have excellent dimensional.

A diagonal is a line segment that joins 2 opposing polygonal vertices.

In another word, a diagonal is an inclined line that connects two orthogonal lines to become a complete triangle.

Diagonal is the use for the idea of the length of sides, for example, if you want to measure the height of a tower knowing diagonal will surely help to do this.

Given a rectangular prism

Let x is the diagonal of the sides 7 and 4 then

By Pythagoras theorem

4² + 7² = x²

x² = 65

x=8.06

Now in the right-angle triangle of sides d,x and 2

d² = 65 + 4

D = √(69)

d  = 8.30 hence, the correct answer is 8.30.

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Answer:

Tank B

Step-by-step explanation:

To be proportional it must go through the origin, (0,0), And have a constant slope. Tank B follows this

Answer: X-7

Step-by-step explanation:

I put it into Tiger Algebra Calculator and that is what I got. Great tool btw I would recommend.

Answer:

3x+2x-4x+5-9+3

5x-4x+8-9

x-1

hope it helps

Answer:

Step-by-step explanation:

nonlinear ig?

Answer:

the answer is have to be equal.

Step-by-step explanation:

you can always equal two similar triangles so that they become congruent.

In the ratio of the length of their sides is equal to one, they are congruent. So, all congruent triangles have to be similar but all similar triangles need not be congruent......the ratio of corresponding sides,AB/A'B'=BC/B'C'=CA/C'A'. If the two triangles are congruent AB/A'B'=BC/B'C'=CA/C'A'=1

I am glad to help you!!!!

Answer:

Length of shed is 7 yards

Step-by-step explanation:

Mathematically the volume of the shed is the area of the base * height

Area of the base = length * width

let the length be x

Thus, the area of the base = x * 7 = 7x

Now, 7x * 3 = 147

21x = 147

x = 147/21

x = 7 yards

Answer:

Step-by-step explanation:

the shaded area is a solution.

Answer:

A, B, and C

Step-by-step explanation:

EDGE unit test 2020

The rows that stands for when (p ∧ q) ∨ (p ∧ r) is true is row A, B, and C. Check more about Truth table below

The truth table is known to be a table that depicts the real value of any kind of compound statement.

Note that for every truth-value of a statements there is a similar table depicting the value of the output for all of the value of all of the  input and as such, rows that stands for when (p ∧ q) ∨ (p ∧ r) is true is row A, B, and C.

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Answer:

The formula is: [tex](x+2)^2+(y-3)^2=25[/tex]

Step-by-step explanation:

Recall the formula for the equation of a circle with center at the point  [tex](x_0,y_0)[/tex]of radius "R' as:

[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]

Therefore for your case, the formula becomes:

[tex](x-x_0)^2+(y-y_0)^2=R^2\\(x-(-2))^2+(y-3)^2=5^2\\(x+2)^2+(y-3)^2=25[/tex]

Answer:

x = 87

Step-by-step explanation:

the ratio SR / RV is equal the ratio ST / TU (both ratios are equal to 1), and the angle in the vertex S is the same for both triangles SUV and STR, so we can affirm that these triangles are similar (case S-A-S).

Then, we have that the ratio SR / SV is the same as RT / UV:

SR / SV = RT / UV = 1 / 2

RT * 2 = UV

2*(x - 37) = x + 13

2x - 74 = x + 13

x = 87

Answer:

w = -4

Step-by-step explanation:

→Distribute the 3 to (-w + 6):

14 + 3(-w + 6) = -11w

14 -3w + 18 = -11w

→Add like terms:

-3w + 32 = -11w

→Add 11w to both sides:

8w + 32 = 0

→Subtract 32 from both sides:

8w = -32

→Divide both sides by 8

w = -4

Answer:

w= -4

work:

14-3w+18=-11w

32-3w=-11

-3w+11w=-32

8w=-32 divide by 8 then you will get your answer

w=-4