Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?

Answer:

9 pounds/135 cubic inches

= 1 pound/15 cubic inches

= .07 pounds/cubic inch

Check the picture below.

bearing in mind that a vertical line always has that slope.

The dimension of the rectangle is 50 meters by 10 meters

The perimeter of a figure is the sum of all the external sides of the figure

The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]

If the length is 40 meters longer than the width, then:

[tex]\text{l} = 40 + \text{w}[/tex]

Substitute

[tex]120 = 2(40+2\text{w})[/tex]

[tex]60 = 40 + 2\text{w}[/tex]

[tex]30 = 20+ \text{w}[/tex]

[tex]\bold{w = 10 \ meters}[/tex]

Since [tex]\text{l} =40 + \text{w}[/tex]

[tex]\text{l} =40 +10[/tex]

[tex]\bold{l=50 \ meters}[/tex]

Hence the dimension of the rectangle is 50 meters by 10 meters

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Answer:

92.5

Step-by-step explanation:

First, we need to put the data in order from smallest to largest:

$71, 81, 89, 92, 93, 94, 94, 99$

There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.

The middle two numbers are 92 and 93, so the median is:

$(92+93)/2 = 92.5$

Therefore, the median of the data is 92.5.

The coordinates of point P are (-1, 1 8/11).

We have,

G(4, 4) and H(-7, 1)

m :n = 5:6

Using Section formula

x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)

Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1

So, x = (5(-7) + 6(4))/ 11  and y = (5(-1) + 6(4))/ 11

x = -35+24/11 and y = -5 + 24/11

x = -11/11 and y = -19/11

x = -1 and y = 1 8/11

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The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.

We have,

From the given data, we can see that the number of mice is being multiplied by 2 every month.

That means the growth is exponential.

We can use the formula for exponential growth:

[tex]m(t) = a \timesr^t[/tex]

where m(t) is the total number of mice after t months, a is the initial number of mice (when t = 0), and r is the common ratio

From the given data, we can see that when t = 0, there are 3 mice.

So, a = 3.

Also, we can see that the common ratio is 2 (i.e., the number of mice is being multiplied by 2 every month).

Now,

The equation that models how many mice there will be in the lab after 10 months is:

m(10) = 3 × 2^10

Simplifying this equation gives:

m(10) = 3 × 1024

m(10) = 3072

Therefore,

The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.

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Answer:

The angle of the intersection is 90 degrees

Step-by-step explanation:

How I know this is because EF is the diameter, which means that arc EF is equal to 180 degrees. Because we know this that means when it is spilt into two parts, the arc and angle measure has to be 90 degrees.

Another way to do this is to remember that a circle is 360 degrees and the circle is split into 4 parts. So all you have to do is divide 360/4 to get 90. Your answer.

The ordered pair that is a solution to the equation 3y = -2x - 4 is given as follows:

(1, -2).

The equation for this problem is defined as follows:

3y = -2x - 4

To verify whether an ordered pair is a solution to the equation, it must make the equation true.

When x = 1 and y = -2, we have that:

Hence the ordered pair (1,-2) is a solution to the equation for this problem.

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Answer:

Dividing both sides by 4, we get:

4m/4 = 28/4

Simplifying, we get:

m = 7

Therefore, the answer is D. 7.

Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:

A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]

B. (f × g)(x) = [tex]8^{7x}[/tex]

C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]

(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]

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The mistake is when you try to divide by X - 1, because you can't divide by zero.

Here we start by defining:

X = 1

The second step makes sense, we are adding the same value in both sides:

X + X = X + 1

2X = X + 1

Now subtract 2 in both sides:

2X - 2 = X + 1 - 2

2X - 2 = X - 1

Here is the mistake, you divide both sides by X - 1

But we already defined that X = 1

Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.

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Answer:

its not a function

Step-by-step explanation:

Answer:

perimeter = 84 feet

Step-by-step explanation:

using Pythagoras' identity in the right triangle to find a

a² + 35² = 37²

a² + 1225 = 1369 ( subtract 1225 from both sides )

a² = 144 ( take square root of both sides )

a = [tex]\sqrt{144}[/tex] = 12

then

perimeter = 35 + 37 + 12 = 84 feet

The amount she invested at each rate of interest for the simple interest are $39,100 and $78,200.

Given that,

Jolene invests her savings in two bank accounts.

Rate of interest for one account = 6% per year

Rate of interest for the other account = 10% per year

Let x be the principal amount invested in the account yielding 10% interest.

Interest amount = 0.1x

Principal amount in the account of 6% interest = 2x

Interest amount = 0.06 × 2x = 0.12x

Annual interest = $8602

0.1x + 0.12x = 8602

0.22x = 8602

x = $39,100

Amount invested for 10% interest account = $39,100

Amount invested for 6% interest account = 2 × $39,100 = $78,200

Hence the amount invested are $39,100 and $78,200.

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The exact value of tan2θ in simplest radical form is  -21/√7.

The value of tan2θ is calculated as follows;

From Pythagorean identity, we know that;

sin² θ + cos² θ = 1

cos² θ is calculated as follows;

(3/4)² + cos² θ = 1

9/16 + cos² θ = 1

cos² θ = 1 - 9/16

cos² θ = 7/16

cos θ = √(7/16)

tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7

Now, we will find tan 2θ;

tan 2θ = 2tan θ / (1 - tan² θ)

tan 2θ = 2(3/√7) / (1 - (3/√7)²)

tan 2θ = (6/√7) / (-2/7)

tan 2θ = -21/√7

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Answer:

Step-by-step explanation:

the square base = 5 * 5 = 25

each of the triangular sides = 4*2.5=10

so… 25+(10*4)=25+40=65

The three numbers are -2, 42 and 16 these we obtained by solving the equations

Let the three numbers x, y, and z. We know that:

x + y + z = 56 (Equation 1)

z - x = 44 (Equation 2)

x + y = 16 (Equation 3)

From Equation 3, we can solve for one of the variables in terms of the other:

y = 16 - x

Substituting this into Equation 1, we get:

x + (16 - x) + z = 56

Simplifying this equation, we get:

z = 40 - x (Equation 4)

Substituting Equation 4 into Equation 2, we get:

(40 - x) - x = 44

Simplifying this equation, we get:

40 - 2x = 44

Subtracting 40 from both sides, we get:

-2x = 4

Dividing both sides by -2, we get:

x = -2

z = 40 - (-2) = 42

Finally, using Equation 1, we can solve for y:

-2 + y + 42 = 56

y=16

Hence, the three numbers are -2, 42 and 16

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Answer:

1728 square ft²

Step-by-step explanation:

48x36=1728

Answer:

[tex]\large \boxed{\mathrm{Area}}[/tex] = [tex]\large \boxed{\mathrm{12 \ ft^2}}[/tex]

Steps:

12 inches = 1 foot

48 / 12 = 4 [tex]\meduim \boxed{\mathrm{feet}}[/tex]

36 / 12 = 3 [tex]\large \boxed{\mathrm{feet}}[/tex]

Answer:

3 x 4 = 12 ft²

Answer:

53

Step-by-step explanation:

20+8=28

90-28=62

62-9=53

90 angle!

The number of days required to complete the job in exponent form is 10¹ = 10.

The exponent form of the number of days is calculated as follows;

number of pages that can be printed by all machines = n x P

where;

N = 100 x 104

N = 10400 pages/day

However, the Ted's company needs 10 days to print 106 pages, our equation is formed as follows;

x = log(y)

where;

10ˣ = y

10ˣ = 10

x = 1

so the exponential form = 10¹ = 10

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Answer:

To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)

P = monthly deposit

r = annual interest rate (which is 9%)

n = number of times interest is compounded per year (which is 12 for monthly compounding)

t = number of years until retirement (which is 65 - 28 = 37)

Substituting the given values, we get:

1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)

Simplifying and solving for P, we get:

P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)

P ≈ $524.79

Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.

Step-by-step explanation:

The distance between Garret and Dino to the nearest yard is: 21 yds

The Law of Cosines is defined as a numerical formula that expresses the relationship between  the side lengths and points of any triangle. It usually expresses that the square of any particular side of a triangle is equal to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be expressed as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus, the distance here is expressed as:

d² =  15² + 17² - 2(15 * 17)cos(81)

d = √434.218

d = 20.838 yds

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c

Step-by-step explanation:

To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.

According to the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C)

Plugging in the given side lengths:

14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)

196 = 144 + 441 - 504 * cos(C)

504 * cos(C) = 389

cos(C) = 389 / 504

C = arccos(389 / 504)

Using a calculator to find the approximate value of C, we get C ≈ 43.5°.