Mr. Smith has saved $1,800 each year for 20 years. A year after the saving period ended, Mr. Smith withdrew $7,500 each year for a period of 5 years. In the sixth and seventh years, he only withdrew $5,000 per year. In the eighth year, he decided to withdraw the remaining money in his account. If the interest rate was 6% per year throughout the whole period, what was the amount he withdrew at the end of the eighth year?

Answer:

(Exponential) Growth

Step-by-step explanation:

Given that the growth rate is greater than 1, this is exponential growth where the growth rate is 2%.

The height of the rock ledge will be 20.35 meters.

The height of the tree will be 58.75 meters

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The angle of elevation to the top of a tree is 22°.

And, The angle of depression to the base of the tree is 12°.

Now,

Let the height of the rock ledge = x

So, By figure, we get;

⇒ tan 12° = x / 96

⇒ x = 96 × tan 12°

⇒ x = 20.35 meters

And, Let total height of the tree = x + y

                                                = 20.35 + y

Hence, By figure, we get;

⇒ tan 22° = y / 96

⇒ y = 96 × tan 22°

⇒ y = 96 × 0.40

⇒ y = 38.4 meter

Thus, The height of tree = 38.4 meters + 20.35 meters

                                      = 58.75 meters

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To find:-

Answer:-

Part A :-

Here we can see that the distance between the rock ledge and the base of the tree is 96m . Also the angle of elevation to the top of the tree from the rock is 22° .

Firstly, we can see that,

[tex]\implies \angle CAD =\angle EDA = 12^o\\[/tex]

This is so because they are alternate interior angles .

Now , in ∆ADE ,

[tex]\implies \tan\theta =\dfrac{p}{b}=\dfrac{AE}{ED}\\[/tex]

[tex]\implies \tan 12^o =\dfrac{AE}{96m} \\[/tex]

[tex]\implies AE = 96\tan12^o m \\[/tex]

[tex]\implies AE = 96 (0.21)m \\[/tex]

[tex]\implies AE = 20.16 \ m \\[/tex]

Hence the height of the rock ledge is 20.16 m.

_______________________________________

Part B :-

Now in ∆ACB , we have;

[tex]\implies \tan\theta =\dfrac{BC}{AC} \\[/tex]

[tex]\implies \tan 22^o =\dfrac{BC}{96m} \\[/tex]

[tex]\implies BC = 96\tan 22^o \ m \\[/tex]

[tex]\implies BC = 96(0.4) m \\[/tex]

[tex]\implies BC = 38.4 \ m \\[/tex]

Now the total height of the tree will be = BC + AE

[tex]\implies h_{tree}= BC + AE \\[/tex]

[tex]\implies h_{tree}=38.4\ m + 20.16 \ m =\boxed{58.56\ m} \\[/tex]

Hence the height of the tree is 58.56m.

and we are done!

to get the equation of any straight line, we simply need two points off of it, let's use those ones in the picture below.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{53}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{53}-\stackrel{y1}{32}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{8}}} \implies \cfrac{ 21 }{ 7 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{32}=\stackrel{m}{ 3}(x-\stackrel{x_1}{8}) \\\\\\ y-32=3x-24\implies {\Large \begin{array}{llll} y=3x+8 \end{array}}[/tex]

From the classification angles, it was possible to find the arcs:

UL=40, UY= 90, TY=50, YLE =270, LE=140 and UET=220.

If UE= 180 and TE=40, you have:

UET=UE+TE

UET=180+40

UET=220

They are a lot of classifications for angles like complementary angles, supplementary angles, right angles, and others. See below:

The question gives mTE=40, and it asks:

UL is opposite the arc TE, therefore its value is also 40.

The figure shows a right angle, then UY is equal to 90.

If UY is equal 90, YE is equal to 90 too, because they are supplementary. If YE=90 and TE=40, you have:

TE+TY=90

40+TY=90

TY=90-40

TY=50

YLE = YE+UE. The figure shows YE=90 and UE represents a semicircle (180). Thus,

YLE= 90+180=270

If UE= 180 and UL=40, you have:

UE=UL+LE

180=40+LE

LE=180-40

LE=140

If UE= 180 and TE=40, you have:

UET=UE+TE

UET=180+40

UET=220

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y2 = 14

y1 = 2

Solution

m = (14 - 2) / (8 - 2)

m = 4 / 4 = 1

Remark

Why is the slope one? I should be 2 shouldn't it? No because there is a common factor to be taken out -- the common factor is 2Answer:

Step-by-step explanation:

y = 2x - 2

x        y

2       2

4       6

6      10

8       14

I will use Desmos to get the line.

The slope  should be 2

Formula

Slope (m) = ( (y2 - y1) / (x2 - x1) )

Givens

x2 = 8

x1 = 4

y2 = 14

y1 = 6

Solution

m = ( (14 - 6) / ( 8 - 4)

m = 8 / 4

m = 2

Answer:

50.3

Step-by-step explanation:

--o-=o=-o-o-o=--o-=o=-o-o-o-o=-

Answer:

7 times a number increased by 4 times the number

Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:

7 times a number: 7x

4 times the number: 4x

The phrase increased by means we add 4x to 7x:

7x + 4x

Simplifying, we get: (7 + 4)x

11x

Step-by-step explanation:

Answer:

c would be it

Step-by-step explanation:

Answer:

B. or D., not sure the inequality for B. & D.

Step-by-step explanation:

substitute 7 to the inequalities to find if it's true:

A. - 4 + 3x < 17 => -4 + 3(7) < 17 => 17 < 17 (false)

C. -7 - 2x > 1 => -7 - 2(7) > 1 => -21 > 1 (false)

Expression: x² - 6x + 9

Factored form: (x - 3)²

Using the concept of factorization.

The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.

Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.

Given that,

x² - 6x

Now, to find the value of c = (b/2)²

divide the coefficient of x by 2.

So, divide 6 by 2 we get: ( -1.3)²

Next, multiply -1 by 3: (-3)²

Now, raise -3 to the power of 2, we get: 9

So, the expression becomes: x² - 6x + 9

Factorized form: (x - 3) (x -3)

or we can write (x - 3)²

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Answer:

56 possible outcomes

Step-by-step explanation:

Order does not matter in this case, so we will find all the possible combinations:

8 nCr 3 = 8! / ((8 – 3)! 3!) = 40320 / 720 = 56

Therefore, there are 56 possible outcomes.

The value of x and y in equations 17x - y = 40 and 2x + 4y = 50 are x = 3 and y = 11.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

17x - y = 40  ⇒ (1)

2x + 4y = 50 ⇒ (2)

(1)* 4

68x - 4y = 160

Adding equation (1) and (2)

68x - 4y = 160

2x + 4y = 50

⇒ 70 x = 210

        x = 3

Substituting the value of x in equation (1)

17*3 - y = 40

51 - y = 40

-y = 40 - 51

-y = -11

y = 11

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Answer:

It depends on what q is.

Step-by-step explanation:

Is d is less than q then q will be greater.

Answer:

q would be anything that’s over 3

Step-by-step explanation:

If d=3, then q>3, so q is any number larger then 3

Answer:

Obtuse - over 90°

Acute - less than 90°

Right - 90°

Straight - 180°

1. Obtuse

2. Acute

3. Right

Answer:

i think A

Step-by-step explanation:

correct me if I wrong k

Answer:

Step-by-step explanation:

14 MAY BE

Answer:

C

Step-by-step explanation:

If you read the question carefully, you find that the function goes through (- 2,0) and (2,0)

Where the y value = 0 you have points that are x intercepts. The answer is anything where the y value = 0

The x intercepts are (-2, 0 ) and (2,0)

The answer is C

Answer:

c

Step-by-step explanation

(2, 0) and (-2, 0)

9/200

Step-by-step explanation:

I hope this helps :), have a nice day!

Answer:

let the number be 'x'

now,

so, the number is 6.

hope it helps

stay safe, healthy and happy.

Answer:

-3w2-11w-3

Step-by-step explanation:

take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets

2y-8x-8-5y-3x+5

note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs

then you collect like terms:

2y-5y-8x-3x-8+5= -3y-11x-3

now put substitute back w2=y and w=X

-3w2-11w-3

if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same

Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.

If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.

Step-by-step explanation:

The value of y is 130°

The angles occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Given here:

Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.

Thus the angle adjacent to the 50-degree angle will be 130

but this angle corresponds to the angle y thus y=130 as corresponding angles are equal when a transversal intersects two parallel lines

Hence, The value of y is 130°

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Please provide your question with a math problem in the form of an image or text.

Answer:

60.5 or 60 1/2

Step-by-step explanation:

7 (2)

8.5 (1)

9 (1)

9.5 (2)

10 (1)

14 + 8.5 + 9 + 19 + 10

60.5

Answer:

I wanna say 348?? maybe.... I think

Answer: 3/4 is right

Step-by-step explanation:

Answer:

12√2 units

Step-by-step explanation:

Step-by-step explanation:

perimeter of a square=4side

perimeter= 4s= 48 units

S= 48/4

S = 12 units

digonal BD = S√2

= 12√2 Units

BD = 12√2 Uits

Given:

The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).

To find:

The equation of the quadratic function.

Solution:

A quadratic function is defined as:

[tex]y=ax^2+bx+c[/tex]            ...(i)

It is passes through the point (0,11). So, substitute [tex]x=0,y=11[/tex] in (i).

[tex]11=a(0)^2+b(0)+c[/tex]

[tex]11=c[/tex]

Putting [tex]c=11[/tex] in (i), we get

[tex]y=ax^2+bx+11[/tex]               ...(ii)

The quadratic function passes through the point (5,31). So, substitute [tex]x=5,y=31[/tex] in (ii).

[tex]31=a(5)^2+b(5)+11[/tex]

[tex]31-11=a(25)+5b[/tex]

[tex]20=25a+5b[/tex]

Divide both sides by 5.

[tex]4=5a+b[/tex]                  ...(iii)

The quadratic function passes through the point (3,11). So, substitute [tex]x=3,y=11[/tex] in (ii).

[tex]11=a(3)^2+b(3)+11[/tex]

[tex]11-11=a(9)+3b[/tex]

[tex]0=9a+3b[/tex]

Divide both sides by 3.

[tex]0=3a+b[/tex]                 ...(iv)

Subtracting (iv) from (iii), we get

[tex]4-0=5a+b-3a-b[/tex]

[tex]4=2a[/tex]

[tex]\dfrac{4}{2}=a[/tex]

[tex]2=a[/tex]

Putting [tex]a=2[/tex] in (iv), we get

[tex]0=3(2)+b[/tex]

[tex]0=6+b[/tex]

[tex]-6=b[/tex]

Putting [tex]a=2,b=-6[/tex] in (ii), we get

[tex]y=(2)x^2+(-6)x+11[/tex]

[tex]y=2x^2-6x+11[/tex]

Therefore, the required quadratic equation is [tex]y=2x^2-6x+11[/tex].

Answer:

1. Gorgeous

2. Tremendous

3. Coarse

4. Crackling

5. Appetizing

Step-by-step explanation:

Those are the only words that make sense in each square.

Answer:

1.) gorgeous

2.) tremendous

3.) crackling

4.) coarse

5.) appetizing

6.) buttery

7.) magnificent

Hope this helps!

Answer:

Complementary

x = 15

Step-by-step explanation: