The cross-section of a lean-to shelter is in the shape of a triangle. The base of the triangle is 66​ feet more than twice its height. If the area of the triangle is 108108​ square feet, determine the length of the base and the height of the triangle in feet

the three equivalent ratios to the ratio 1 : 3 will be 2 : 6 , 3 : 9 and 4 : 12.

We are given a fraction 1 / 3

This can also be written as a ratio as 1 : 3

Now, the equivalent ratios to it will be:

First one:

1 × 2 : 3 × 3

= 2 : 6

Second one:

1 × 3 : 3 × 3

= 3 : 9

Third one:

1 × 4 : 3 × 4

= 4 : 12

Therefore, the three equivalent ratios to the ratio 1 : 3 will be 2 : 6 , 3 : 9 and 4 : 12.

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The function is exponential growth function and the y- intercept is (0,$2000).

Given that the we put $ 2000 into a college savings account for four years and the account pays 6% interest annually.

Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.

If a is positive and b is greater than 1 then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 then it exponential decay.

When we put $2000 in our college savings account  and we receive  6% annual interest then this situation can be modeled by using equation f(x)=a(1+r)ˣ in which we put a=$2000, r=6%, x=4

Thus we will receive the amount after 4 years:

f(4)=2000(1+(6/100))⁴

Since equation is an exponential growth function so it is also an exponential growth function.

Now, to find the y-intercept we will put x=0.

So, y-intercept is (0,$2000).

Hence, By putting $2000 into a college savings account for four years and the account pays 6% interest annually the function is exponential growth function and the y-intercept is (0,2000).

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The solutions of the expressions are as below:

13. (a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis

(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis

(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis

(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis

10. -9x - 2; x = -4

-9x - 2 for x = -4

= -9 * -4 - 2

= 36 - 2

= 34

11. 24 - 8x; x = -2.25

= 24 - 8 * - 2.25

= 24 + 18

= 42

12. 15x + 9; x = -1/10

= 15 * -1/10 + 9

= -1.5 + 9

= 7.5

13.

a are points in the x axis and b are points in the y axis

(a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis

(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis

(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis

(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis

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Answer:

hola

Si por qué le tenías que restar ala fracción equivalente

Answer:

3(4 + 5)

Step-by-step explanation:

Answer: TRUE

Step-by-step explanation:

i got it right.

Answer:

5miles : 1hour

Step-by-step explanation:

source: trust me

no really dont

Answer:

This is for #12

-2 > x

set notation: {x│x < -2}

interval notation: x∈(-∞, -2)  

Step-by-step explanation:

-3(x+2) > 10+5x

-3x-6 > 10+5x

+3x           +3x

-6 > 10+8x

-10   -10

-16 > 8x

÷8    ÷8

-2 > x

set notation: {x│x < -2}

interval notation: x∈(-∞, -2)

The value of  ln x-ln 3=4 is 163.7

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to create a specific number x, is represented by the logarithm of that number.

given, our equation is -

ln x-ln 3=4

It can be expressed in the form of

⇒ loge (x/3) = 4

⇒ e⁴ = x/3

⇒ x = 3e⁴

⇒ 163.7

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Answer:

x = 12

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{XY}{RS}[/tex] = [tex]\frac{XZ}{RT}[/tex] ( substitute values )

[tex]\frac{5x-3}{3x+2}[/tex] = [tex]\frac{60}{40}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2(5x - 3) = 3(3x + 2) ← distribute parenthesis on both sides )

10x - 6 = 9x + 6 ( subtract 9x from both sides )

x - 6 = 6 ( add 6 to both sides )

x = 12

Answer:

320

Step-by-step explanation:

Use PEMDAS - order of operations

5(2)^2 + 3(10)^2

5 x 4 + 3 x 100

20 + 300

320

In this case, the population consists of an insurance company's policyholders. The sample consists of his 200 policyholders under study. The sample size is 200.

H0: µ ≥ $5,000

Ha: µ < $5,000 (claimed)

As we can see that the sample size is 200, which is way greater than 30, so a z-test is appropriate here.

z(test) = (4800 - 5000) / (1300 / √200) = -2.1757

p (z = -2.1757) = 0.0148

The critical z-value for the left-sided test at α = 0.05 is -1.645

The tested value of z is less than the critical value, so we reject the null hypothesis. The hypothesis drawn here ( null hypothesis) will be rejected as an alternate decision because the p-value is less than the significance level (0.05).

At the 0.05 significance level, the prevention plan effectively reduced the average amount of harm. Insurers should continue these plans and try to improve them where possible.

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Answer:

8n-18

Step-by-step explanation:

You can use this formula: 1st term+(n-1)(difference)

First term of sequence: 10

Difference between each term: 8

-10+(n-1)(8)

= -10+8n-8

= 8n-18

An expression which represent his father's age three (3) years from now is: A. 3x + 15.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to write and solve this word problem, we would assign variables to the son's and father's age and then evaluate the resulting algebraic expression.

Translating the word problem into an equation, we have;

y = 4x

y + 2 + 3  = 3(x + 2 + 3)

y + 5 = 3(x + 5)

y + 5 = 3x + 15

Therefore, an expression which represent his father's age three years from now is 3x + 15.

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The Magnitude of earthquake that hit Texas is 5.8; The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex].

Given:

To find: Magnitude of earthquake that hit Texas.

Finding:

=>  [tex]\frac{I_2}{I_1}[/tex] =  [tex]30^M[/tex]

For  [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:

=> 74900 = [tex]30^M[/tex]

Taking logarithm on both sides, with base 10 gives:

=> log (74900) = log ([tex]30^M[/tex])

As [tex]log_b(a)^m = m(log_b(a))[/tex],

=> log (74900) = M ( log (30))

=> [tex]\frac{log(74900)}{log (30)}[/tex] = M

=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.

Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.

The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]

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Answer:

724,862.58

Step-by-step explanation:

7 (hundred thousands)

2 (ten thousands)

4 (one thousands)

,

0 (hundreds)

6 (tens)

2 (ones)

.

5 (tenths)

8 (hundreths)

Answer:

I think that your answer would be 724,862.58

Step-by-step explanation:

The length of the longest altitude of the triangle is 24 √5 cm.

The sides of the triangle that are given are:

35 cm, 54 cm and 61 cm

We need to find the longest altitude of the triangle.

We know that:

s = ( a + b + c ) / 2

s = ( 35 + 54 + 61 ) / 2

s = 150 / 2

s = 75

s - a = 75 - 35

s - a = 40

s - b = 75 - 54

s - b = 21

s - c = 75 - 61

s - c = 14

Area, A = √ s (s − a)(s − b)(s − c)

A = √ 75 (40) (21) (14)

A = 420 √ 5 cm²

Now, area is also equal to:

Area = 1 / 2 × b × h

420 √5 = 1 / 2 × 35 × h

h = 420 √ 5 × 2 ÷ 35

h = 24 √5 cm

Therefore, the length of the longest altitude of the triangle is 24 √5 cm.

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32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 32 = 2 x 2 x 2 x 2 x 2 = [tex]2^{5}[/tex]

Prime factorization of 256= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = [tex]2^{8}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e., [tex](x^{m})^{n} = x^{mn}[/tex]

Another law of indices says that if two terms having same base are multiplied together, then their indices are added.

i.e., [tex]a^{m} . a^{n } =a^{m+n}[/tex]

According to the given condition,

∴[tex]32 = 2^{5}[/tex]

[tex]256^{\frac{1}{2}} = (2^{8})^{\frac{1}{2} }[/tex]

∴ 32. [tex]256^{\frac{1}{2} }[/tex]  = [tex]2^{5}[/tex] × [tex](2^{8})^{\frac{1}{2} }[/tex]

Applying the laws of indices mentioned above,

32. [tex]256^{\frac{1}{2} }[/tex]  = [tex]2^{5}[/tex] × [tex](2^{8 X }^{\frac{1}{2} })[/tex]

= [tex]2^{5}[/tex] × [tex]2^{4}[/tex]

= [tex]2^{5 + 4}[/tex] = [tex]2^{9}[/tex]

= 512.

Thus, 32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.

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The simplification of 25p^6q^9 / 45p^8q^4 using a positive exponent;

Algebraic expressions are expressions made up of factors, variables, terms, coefficients and constants.

They are also comprised of arithmetic operations such as addition, subtraction, multiplication, division, etc

We also know that index forms are also know as standard forms.

They are mathematical expressions showing the power of exponent of a variable in terms of another variable.

Given the index algebraic forms;

25p^6q^9 / 45p^8q^4

Using the rule of indices, we take the negative exponent of the divisor and multiply through.

We have;

5p^6 q^9 × 9p^-8 q^-4

Add exponential values

5/9 p^6-8 q^9 -4

5/9 p^-2 q^5

Thus, the expression is simplified to 5/9 p^-2 q^5

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Answer:

0.2 billion visits per year

Step-by-step explanation:

-

Hope that helps.

Answer:

Find K between M(1, -3) and N(4, 6) such that the

ratio of MK to KN is 1:2.

Step-by-step explanation:

Find K between M(1, -3) and N(4, 6) such that the

ratio of MK to KN is 1:2.

The coordinates of point K are (2, 0).

Given that there are three points M, K and N, such that M = (1, -3) and N = (4, 6) and the ratio of MK to KN is 1:2.

We need to find the coordinates of point K.

To find point K between M(1, -3) and N(4, 6) such that the ratio of MK to KN is 1:2, we can use the concept of section formula.

Let's assume the coordinates of point K are (x, y).

The section formula states that if a point K divides a line segment MN in the ratio m:n, then the coordinates of K are given by:

x = (n·x₁ + m·x₂) / (m + n)

y = (n·y₁ + m·y₂) / (m + n)

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

In this case, the ratio of MK to KN is 1:2, so m = 1 and n = 2.

Substituting the coordinates of M(1, -3) and N(4, 6) into the formula:

x = (2·1 + 1·4) / (1 + 2)

= (2 + 4) / 3

= 6 / 3 = 2

y = (2·(-3) + 1·6) / (1 + 2)

= (-6 + 6) / 3

= 0 / 3

= 0

So, the coordinates of point K are (2, 0).

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The algebraic expression is 6(a+ b)² + 4(ab)².

The concept of representing numerical values with letters or alphabets without providing their precise values The fundamentals of algebra taught us how to represent an unknown value using letters like x, y, and z. Here, these letters are referred to as variables. A mathematical expression may have both variables and constants. A coefficient is any value that is introduced before and increased by a variable.

Given that,

So, six times the sum of (a+ b)

Then, four times the product of (ab)

Therefore, the algebraic expression is 6 (a+ b)² + 4(ab)².

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Answer: (262 - 70) ÷ 24

Step-by-step explanation:

The probability that at least one of the top three cards is a jack, queen, or king is 0.289%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A deck has a total of 52 cards.

A deck of cards has four jacks.

A deck of cards has four queens.

A deck of cards has four kings.

The total number of jacks, queens, and kings is 4 + 4 + 4 = 12.

Then the probability that at least one of the top three cards is a jack, queen, or king will be:

P = ( 12 / 52 ) × ( 8 / 51 ) × ( 4 / 50 )

P = ( 6 / 26 ) × ( 8 / 51 ) × ( 2 / 25)

P = 96 / 33150

P = 0.289%

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If the expression is log₇49 x y z, then the expansion of the expression is 2+log x/ log 7+log y/log 7 +log z/ log 7.

Given that  expression is log₇49 x y z.

We are required to find the expanded value of the expression.

The change of base formula is basically used to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₇49 x y z.

log₇49xyz= (log 49+log x+log y+log z)/log 7

We know that log mn=log m+ log n.

=log [tex]7^{2}[/tex]/ log 7+log x/log 7+log y/ log 7+ log z/log 7

=2 log 7/log 7+log x/log 7+log y/ log 7+ log z/log 7

=2+log x/log 7+log y/ log 7+ log z/log 7

Hence if the expression is log₇49xyz, then the expanded form is

2+log x/log 7+log y/ log 7+ log z/log 7.

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Using the law of sines, the length of side x, to 1 decimal place, is: 10.8 cm.

The law of sines states that:

Sin A/a = sin B/b = sin C/c.

Let:

Measure of angle A = 81°

a = x = ?

Measure of angle B = 40°

b = 7 cm

Plug in the values into Sin A/a = sin B/b to find the value of x

Sin 81/x = sin 40/7

Cross multiply

(x)(sin 40) = (sin 81)(7)

Divide both sides by sin 40

(x)(sin 40)/sin 40 = (sin 81 × 7)/sin 40

x = (sin 81 × 7)/sin 40

x = 10.8 cm (to 1 decimal place)

Therefore, using the law of sines, the length of side x, to 1 decimal place, is: 10.8 cm.

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Answer: inverse of 2,48 there is none and the inverse of 56,2130 there is none

Step-by-step explanation: hope this helps

Answer:

If you have 2 dollars and 65 cents per day, and you get 25 dollar commission.

Step-by-step explanation: