Are the triangles similar? if so, what postulate or theorem proves their similarity?
A. yes, by SSS Similarity Theorem
B. yes, by SAS Similarity Theorem
C. yes, by AA Similarity Theorem
D. no the triangles are not similar

Using the Pythagorean theorem a^2 + b^2 = c^2 where a and b are the side and bottom of the triangle and c is the hypotenuse ( length of rope).

Let the tent pole = a

Lhe distance from the pole be b = 10 ft.

The length of rope would vce c = 26 ft.

Now you have:

a^2 + 10^2 = 26^2

Simplify:

a^2 + 100 = 676

Now subtract 100 from each side:

a^2 = 576

To get a, take the square root of both sides:

a = √576

a = 24

The tent pole is B. 24 ft

Answer: -5

Step-by-step explanation:

You start with 50.

Then subtract the 3 transactions: 50-(3×5)=50-15=35

Then you subtract the 2 ills: 35-(2×20)=35-40=-5

And that's how get the answer!

[tex]\tt 4c-d-c-3d=3c-4d[/tex]

Answer:

3c -4d

Step-by-step explanation:

4c -d -c -3d

Combine like terms

4c -c     -d -3d

3c -4d

Answer:

see below

Step-by-step explanation:

g(x) = x^3 − x^2 − 4x + 4

We know the graph will have up to 3 zero's because it is a cubic

g(x) = x^3 − x^2 − 4^x + 4

I will factor by grouping, taking an x^2 from the first 2 terms and -4 from the last 2 terms

  g(x)=  x^2(x-1) -4(x-1)

Now factor out x-1

  g(x)= (x-1)(x^2 -4)

We can factor the (x^2-4) as a difference of squares

g(x) = (x-1) (x-2)(x+2)

Using the zero product property

0= (x-1) (x-2)(x+2)

x-1 =0   x-2 =0   x+2=0

We have zeros at x=1   x=2  and x=-2

Then we can plot points to determine where the function is between the points We will pick negative infinity 0 1.5 and infinity

at g(-inf) =  -inf  because x^3 dominates and that goes to -infinity

at g(0) = 0+000+4 =4

at g(1.5) =-.875

at  g(inf)=because x^3 dominates and that goes to infinity

Answer:

x = 500.

Step-by-step explanation:

log20x^3 - 2logx = 4

By the laws of logs:

log20x^3 - logx^2 = 4

log(20x^3 / x^2) = 4

20x^3 / x^2 = 10^4

20x = 10,000

x = 10,000 / 20

x = 500.

The solution of the given logarithmic equation is x = 500.

Any equation in the variable x that contains a logarithm is called a logarithmic equation.

Given logarithmic equation

[tex]log20x^{3} -2logx=4[/tex]

Using [tex]mloga=loga^{m}[/tex]

[tex]log20x^{3} -logx^{2}=4[/tex]

Using [tex]loga-logb=log(\frac{a}{b})[/tex]

[tex]\frac{log20x^{3} }{x^{2} }=4[/tex]

[tex]log20x=4[/tex]

[tex]20x=10^{4}[/tex]

[tex]x=\frac{10000}{20}[/tex]

[tex]x=500[/tex]

The solution of the given logarithmic equation is x = 500.

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Answer:

Part A) [tex]\$42,888.48[/tex]  

Part B) [tex]A=\$22,304[/tex]

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12[/tex]  

substitute in the formula above  

[tex]A=8,500(1+\frac{0.0812}{12})^{12*20}[/tex]  

[tex]A=8,500(1.0068)^{240}[/tex]  

[tex]A=\$42,888.48[/tex]  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=20\ years\\ P=\$8,500\\r=0.0812[/tex]

substitute in the formula above

[tex]A=8,500(1+0.0812*20)[/tex]

[tex]A=\$22,304[/tex]

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

[tex]A(t)=8,500(1.0068)^{12t}[/tex] ------> equation A

[tex]A(t)=8,500(1+0.0812t)[/tex]  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

The retirement account will be worth $27,627.24 after 20 years with compound interest and $23,180 with simple interest. Compound interest grows at a faster rate and becomes better than simple interest when the compounding periods are more frequent.

To calculate the value of the retirement account after 20 years with compound interest, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal deposit, r is the interest rate, n is the number of times compounded per year, and t is the number of years. In this case, P = $8,500, r = 8.12%, n = 12 (monthly compounding), and t = 20. Plugging in these values, we get A = $8,500(1 + 0.0812/12)^(12*20) = $27,627.24.

If the deposit were compounded monthly with simple interest, we can use the formula A = P + (P*r*t), where A is the final amount, P is the principal deposit, r is the interest rate, and t is the number of years. In this case, P = $8,500, r = 8.12%, and t = 20. Plugging in these values, we get A = $8,500 + ($8,500 * 0.0812 * 20) = $23,180.

To compare the two situations on a graph, we can plot the value of the retirement account over time for both compound and simple interest. We would see that the compound interest account grows at a faster rate and reaches a higher value compared to the simple interest account. Compound interest becomes better than simple interest when the compounding periods are more frequent, as it allows the interest to be reinvested more often and generate additional earnings.

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Answer:

x=3 or x= 1/3

Step-by-step explanation:

Let the number = x

The reciprocal of the number = 1/x

According to the given statement:

x+1/x=10/3

x²+1/x=10/3

3(x²+1)=10x

3x²+3=10x

Move 10x to the L.H.S

3x²-10x+3=0

Break the middle term:

3x²-9x-x+3=0

3x(x-3)-1(x-3)=0

(x-3)(3x-1)=0

x-3=0 , 3x-1=0

x=0+3 ,  3x=0+1

x=3    , 3x=1

x=3    ,x = 1/3

So x=3 or x= 1/3 ....

Answer:

5.75

Step-by-step explanation:

[tex]3 + 11 + 4 + 3 + 10 + 6 + 4 + 5 = 46 \\ 46 \div 8 = 5.75[/tex]

The total amount of numbers are : 8

To find the mean, we calculate the sum of all values and divide that sum by the amount of numbers there are.

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[tex]\huge{\boxed{\frac{1}{20}}}[/tex]

To convert from a decimal to a percentage, multiply the decimal by [tex]100[/tex].  [tex]0.05*100=5[/tex], so the percentage equivalent is [tex]5\%[/tex].

Percentages are fractions when you use a denominator of [tex]100[/tex], so [tex]5\%[/tex] is the same as [tex]\frac{5}{100}[/tex].  Divide the numerator and denominator each by [tex]5[/tex] to get the fraction in simplest form, which is [tex]\frac{1}{20}[/tex].

Answer: 5.

Step-by-step explanation:

6+9 = 15

10 + x = 15

-10 -10

x = 5

Answer:

x=5

Step-by-step explanation:

6+9=10+x

15=10+x

x=15-10

x=5

Answer:

f(x) = 4.5x + 3/8

Answer: Third Option

[tex]f(x) = \frac{3}{8}x + 54[/tex]

Step-by-step explanation:

We want to propose an equation that models the distance traveled by the caterpillar as a function of time, we have a constant initial quantity of 4.5 feet and then we know that every minute the caterpillar advances 3/8 of an inch

Then the distance that the caterpillar to advanced after x minutes is:

[tex]f(x) = \frac{3}{8}x[/tex]

Then we know that initially the caterpillar was at a distance of 4.5 feet or 54 inch

Then the equation for the distance in inch is:

[tex]f(x) = \frac{3}{8}x + 54[/tex]

9m = 4.5

divide by 9 for 9m and 4.5

9m/9= 4.5/9

m= 0.5

3v= -105

divide by 3 for 3v and -105

3v/3=- 105/3

v= -35

17m = 85

divide by 17 for 17m and 85

17m/17= 85/17

m= 5

Answers: 0.5,-35 and 5

Answer:

[tex]\boxed{\text{3; is not}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}p(x) & = & (x - 7)(x^{2} - 2x + 4) + 3\\\\\dfrac{p(x)}{x - 7} & = &x^{2} - 2x + 4 + \dfrac{3 }{x-7 }\\\\\end{array}\\\\\text{The number }\boxed{\mathbf{3}}\text{ is the remainder when $p(x)$ is divided by $(x - 7)$,}\\\\\text{so $(x - 7)$ }\boxed{\textbf{is not}} \text{ a factor of $p(x)$.}[/tex]

Answer:

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

We have f(x) = 3ˣ + 10 and g(x) = 2x - 4. Substitute:

(f - g)(x) = (3ˣ + 10) - (2x - 4) = 3ˣ + 10 - 2x - (-4) = 3ˣ + 10 - 2x + 4

(f - g)(x) = 3ˣ - 2x + 14

The line segment drawn from point A to point A′, after reflecting the triangle over the y-axis, is perpendicular to the y-axis. This is because the reflection mirrors the image across the y-axis resulting a right-angle formation between the line segment and the axis.

The line segment drawn from point A to point A′, after a reflection of Triangle HAM over the y-axis, would be perpendicular to the y-axis. This is because in a reflection over the y-axis, the x-coordinates of the points change sign and the y-coordinates stay the same. This procedure mirrors the image over the y-axis and creates a segment from A to A′ that is perpendicular to the y-axis and bisects the distance between A and A′.

This idea correlates to the vector concept in physics where components of the vector may be viewed as sides of a right triangle. Much like in that context, the line segment from A to A′ and the y-axis form a right angle, hence they are perpendicular.

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Answer:

Width=4.7 ft

Length=16.1 ft

Step-by-step explanation:

Let the width of the table to be x ft

Then the length should be two more than three times the width= 2+3x ft

The area of the serving table should be 75 ft²

But you know the area of this table is calculated by multiplying the length by the width of the table

Hence, Area= length× width

Length=x ft  and width =2+3x ft

75ft²= (x ft) × (2+3x ft)

[tex]75=x*(2+3x)\\\\75=2x+3x^2\\\\3x^2+2x-75=0[/tex]

Apply the quadratic formula to solve this quadratic equation

The formula is ;

x= (-b ±√b²-4ac)÷2ac

where a=3, b=2 and c=-75

x= (-2 ± √2²-4×3×-75)÷(2×3)

x=(-2±√4+900)÷6

x=(-2±√904)÷6

x=(-2±30.1)÷6

x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)

or

x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4

Taking the positive value

x=width =4.7 ft

2+3x= length= 2+3(4.7)=16.1 ft

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

To express solutions to inequalities using interval notation.

I prefer to express solutions to inequalities using interval notation. Both formats are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

Hence, To express solutions to inequalities using interval notation.

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Answer:

[tex]\$620.07[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\A=\$700\\ r=0.0625\\n=1[/tex]  

substitute in the formula above  and solve for P

[tex]700=P*(1+\frac{0.0625}{1})^{2}[/tex]  

[tex]700=P*(1.0625)^{2}[/tex]  

[tex]P=700/(1.0625)^{2}[/tex]  

[tex]P=\$620.07[/tex]  

Answer:

9 ^ (-15)

Step-by-step explanation:

9^-3/9^12

We know that a^b/ a^c = a^(b-c)

9^-3/9^12 = 9 ^(-3-12)

                  =9^(-15)

The expression [tex]\frac{9^{-3}}{9^{12} }[/tex] written in the form  [tex]9^{n}[/tex] is [tex]9^{-15}[/tex]

From the question,

we are to rewrite the given expression (9^-3/9^12) in the form 9^n

First, write the expressions properly.

The given expression is

[tex]\frac{9^{-3}}{9^{12} }[/tex]

To rewrite the given expression in the form [tex]9^{n}[/tex], we will use the division law of indices

From the division law of indices, we have that

[tex]x^{y} \div x^{z}= x^{y-z}[/tex]

Then, the given expression becomes

[tex]\frac{9^{-3}}{9^{12} } = 9^{-3} \div 9^{12}[/tex]

[tex]= 9^{-3-12}[/tex]

[tex]=9^{-15}[/tex]

Hence, the expression [tex]\frac{9^{-3}}{9^{12} }[/tex] written in the form  [tex]9^{n}[/tex] is [tex]9^{-15}[/tex]

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Answer:

f⁻¹(x) = (4x)/5

Step-by-step explanation:

f(x) = 2x - 3x/4.

Assume y=f(x). Therefore:

y = 2x - 3x/4.

Make x the subject in the above equation.

y = (2x(4) - 3x)/4.

y = 5x/4.

4y = 5x.

(4y)/5 = x.

x = (4y)/5.

Therefore:

f(y) = (4y)/5.

Replace y with x.

f⁻¹(x) = (4x)/5.

Therefore, the inverse of f(x) = 2x - 3x/4 is f⁻¹(x) = (4x)/5!!!

Answer:

37

Step-by-step explanation:

Substitute x = 10 into g(x), then substitute the result into f(x)

g(10) = 10 - 4 = 6, then

f(6) = 6² + 1 = 36 + 1 = 37

Answer:

(f+g)(x)= 5x-11

(f-g)(x)= x-3

The value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

It is required to find the value of   (f+g)(x) and (f-g)(x).

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The functions are

f(x) = 3x - 7

g(x) = 2x - 4

We have to find the value of the function (f + g)(x) and  (f-g)(x) we get

According to given question we have,

The value of the function (f +g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 3x - 7 + 2x - 4

(f + g)(x) = 5x - 11

The value of the function (f - g)(x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 3x - 7 - (2x - 4)

(f - g)(x) = 3x - 7 - 2x + 4

(f - g)(x) = x - 3

Therefore,  the value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

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1. Commutative property of adfition

2. Multiplicative inverse

3. Associative property of addition

4. Distributive property

5. Additive identity

Answer:

1-------------- Commutative property of addition

You can commute the terms in a addition, so doesn't matter wat therm goes left or right,

2 ------------ is multiplicative inverse

Each number X has another number Y so X*Y=1

3-------------- Associative property of addition

When you have parentheses in this type of addition, the order in what you do te equation doesn't matter

4 ------------- distributive property

You can distribute the multiplication here, so x(a +b) = x*a + x*b

5 ------------ Additive identity

There exist one number a so for every number x, x+a = x, and the number a is te zero.

Answer:

A 3

Step-by-step explanation:

y-9 = 3(x-9)

This is in point slope form

y-y1 = m(x-x1)

where (x1,y1) is the point and m is the slope

A point on the line is (9,9) and the slope is 3

Answer:

-23 = x

Step-by-step explanation:

-(-9) = 9

The thing with double negatives is that they form a plus sign, so that is really a POSITIVE nine. Therefore you do the inverse to find x: -14 - 9 = -23.

I am joyous to assist you anytime.

Answer:

[tex]\Huge \boxed{X=-23}[/tex]

Step-by-step explanation:

[tex]\displaystyle x+9=-14[/tex]

[tex]\Large\textnormal{First, subtract by 9 from both sides of equation.}[/tex]

[tex]\displaystyle x+9-9=-14-9[/tex]

[tex]\Large\textnormal{Simplify, to find the answer.}[/tex]

[tex]\displaystyle -14-9=-23[/tex]

[tex]\Large\textnormal{x=-23, which is our answer.}[/tex]

Answer:

-10.2n - 1

Step-by-step explanation:

−2.4n − 3 + (−7.8n + 2) =

= -2.4n - 7.8n - 3 + 2

= -10.2n - 1

Answer:

-10.2n -1

Step-by-step explanation:

−2.4n−3 + −7.8n+2

Combine like terms

−2.4n −7.8n -3+2

-10.2n -1

Answer:

[tex]a_n=-\frac{1}{n}[/tex]

[tex]a_6=-\frac{1}{6}[/tex] is our sixth term.

[tex]a_7=-\frac{1}{7}[/tex]  is our seventh term.

[tex]a_8=-\frac{1}{8}[/tex] is our eighth term.

Step-by-step explanation:

So every number in this sequence is -.

If you write 1 as 1/1, then you should see the numerator is constant one while the denominator is going up by 1 each time.

So the patter is

[tex]a_n=-\frac{1}{n}[/tex]

Test if you like:

n=1 gives us [tex]a_1=-\frac{1}{1}=-1[/tex] which is our first term.

n=2 gives us [tex]a_2=-\frac{1}{2}[/tex] which is our second term.

n=3 gives us [tex]a_3=-\frac{1}{3}[/tex] which is our third term.

n=4 gives us [tex]a_4=-\frac{1}{4}[/tex] which is our fourth term.

n=5 gives us [tex]a_5=-\frac{1}{5}[/tex] which is our fifth term.

Now we are going to use [tex]a_n=-\frac{1}{n}[/tex]

to write our next three terms:

n=6 gives us [tex]a_6=-\frac{1}{6}[/tex] which is our sixth term.

n=7 gives us [tex]a_7=-\frac{1}{7}[/tex] which is our seventh term.

n=8 gives us [tex]a_8=-\frac{1}{8}[/tex] which is our eighth term.

Answer:

D. G(x) = (x+2)^2

Step-by-step explanation:

We can easily solve this problem by graphing each case with a graphing calculator or any plotting tool.

The equations are

A. G(x) = (x-2)^2

B. G(x) = (x)^2 + 2

C. G(x) = (x)^2 -2

D. G(x) = (x+2)^2

Se attached image.

The correct option is

D. G(x) = (x+2)^2

Answer:

C. G(x)=x²-2

Step-by-step explanation:

The midpoint of the graph has been displaced from x=0 to x=-2. this is a negative displacement.

Therefore the new equation G(x)=x²-2

This is because there is no tilt in the graph so it is a replica of the red graph.

Answer:

The correct answer is the second one

Step-by-step explanation:

Line BE and ED are congruent because they are the same length and E is the mid line.

Answer:

second option is correct

Step-by-step explanation:

By the given

ΔDEC≅ΔBEC

which means triangle DEC is congruent to triangle BEC

then by CPCTC (corresponding parts of congruent triangle are congruent)

there every side and angle of DEC will be equal to BEC

⇒BE= DE (by CPCTC)

hence second option is correct