Can the Pythagorean Theorem be used to find a distance in the coordinate plane?

ANSWER:

(1) The graphs of both f(x) and g(x) become wider

STEP-BY-STEP EXPLANATION:

We have the following functions:

When a function is multiplied by a value between 0 and 1, it produces a horizontal stretch.

Which means that the graph of the function is wider.

Therefore, the correct answer would be:

(1) The graphs of both f(x) and g(x) become wider

You need to deposit $1459.667 every month;

Let the amount needed to be deposited each month be 'x' ;

Monthly interest rate, i = 5%/12 = 0.4167% = 0.004167

Total amount  = $600,000

Total time (in months) = 20 × 12 = 240 years;

Therefore, according to question;

600,000 = x . [(1 + i)ⁿ -1]/i

600,000 = x. [(1 + 0.004167)²⁴⁰ - 1]/0.004167

x = 1459.667

The additional amount you must repay over and above the principal borrowed is called interest. This is how lending institutions turn a profit.

Typically, interest is expressed as an annual percentage of the principal.

Monthly interest is the interest that is paid every month or after every 30 days.

We compute the monthly interest rate by dividing the annual interest rate by 12 to calculate the monthly interest on a loan or investment.

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Answer:

A. 57m   B. 130m

Step-by-step explanation:

For problem A:

87m up a cliff - 30m up a cliff = 57m up a cliff

These are all positive values

For problem B:

100m above is talking about a positive value, making this a positive number

30m below is talking about a negative value, making this number -30

0 meters represents the surface

As you can see, this is forming a number line as of which

below the surface------------------------0m-------------------------above the surface

by substitution,

-30-----------------------------------------------0-------------------------------100

therefore, 100 - -30 = 130 meters

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

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The volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

To calculate the volume of the tree stump, we can use the formula for the volume of a cylinder, which is given by:

Volume = π * r^2 * h

Given:

Radius (r) = 20 inches

Height (h) = 0.7 feet

First, let's convert the height from feet to inches since the radius is already in inches. There are 12 inches in 1 foot, so:

Height (h) = 0.7 feet * 12 inches/foot = 8.4 inches

Now, we can substitute the values into the volume formula:

Volume = π * (20 inches)^2 * 8.4 inches

Calculating the volume:

Volume = 3.14159 * (20 inches)^2 * 8.4 inches

≈ 3.14159 * 400 inches^2 * 8.4 inches

≈ 1005.3096 cubic inches

Rounding the volume to the nearest tenth:

Volume ≈ 1005.3 cubic inches

Therefore, the volume of the tree stump is approximately 1005.3 cubic inches when rounded to the nearest tenth.

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Answer:

On a plane

Step-by-step explanation:

Answer:

A plane

Step-by-step explanation:

Answer: symmetric on the x-axis only.

Step-by-step explanation:

The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Answer:

C

Step-by-step explanation:

Can I have crown

 409/99

 4  13/99

Hi there !

4.131313.. = 4.(13) = 4  13/99 = (4*99+13)/99 = 409/99

Good luck !

Answer:

120 min

Step-by-step explanation:

step 1. divide 100% by 2.5 (=40)

step 2. 40 time 3 minutes = 120!

so by the time it gets to 120 minutes it 100% and guaranteed

Answer:

120 mn

Step-by-step explanation:

100 PTS/// If you have a 2.5% chance of getting something every 3 minutes how long will it take until that's guaranteed?

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Answer:

x²-6x+6=0

Step-by-step explanation:

(x-3)² = 3

(x-3)(x-3)=3

x²-6x+9=3

x²-6x+6=0

U is located in the plane or vector that A's columns span.

A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.

Part 1

To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.

Part 2

Why the answer in Part 1 is correct?

Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.

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a. Expenses: Books and supplies, Housing and food, Tuition and fees, Transportation and Personal expenses. Funding: Savings,

Scholarships, Grants and Student loans.

b. Total estimated expenses are $29,400

(a) Below is an estimate of all her expenses and sources of funding for her 2-year college education.

Expense:

Books and supplies: $1700

Housing and food: $14,020

Tuition and fees: $11,660

Transportation: $2040

Personal expenses: $2980

Funding:

Savings: $7800

Scholarships: $10,240

Grants: $11,600

Student loans: $6200

(b) What is the total of her estimated expenses?

To find the total estimated expenses, we need to add up all the expenses mentioned:

$1700 + $14,020 + $11,660 + $2040 + $2980 = $29,400

Therefore, the total estimated expenses for Nicole's 2-year college education is $29,400.

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By definition of tangent,

tan(A - π/4) = sin(A - π/4) / cos(A - π/4)

Expand the numerator and denominator using the angle sum identities for sin and cos:

tan(A - π/4) = (sin(A) cos(π/4) - cos(A) sin(π/4)) / (cos(A) cos(π/4) + sin(A) sin(π/4))

Divide through everything on the right by cos(A) cos(π/4):

tan(A - π/4) = (sin(A) / cos(A) - sin(π/4) / cos(π/4)) / (1 + (sin(A) sin(π/4)) / (cos(A) cos(π/4)))

Simplify the sin/cos terms to tan:

tan(A - π/4) = (tan(A) - tan(π/4)) / (1 + tan(A) tan(π/4))

tan(π/4) = 1, so we're left with

tan(A - π/4) = (tan(A) - 1) / (1 + tan(A))

Replace tan(A) with -√15:

tan(A - π/4) = (-√15 - 1) / (1 - √15)

Then the last option is the correct one.

Answer:

Step-by-step explanation:

The biconditional for the given statement is:

C. M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ .

In a biconditional statement, both the conditional statement and its converse are true. The statement "M is the midpoint of AB¯¯¯¯¯¯¯¯" is the condition, and "AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯" is the conclusion. The biconditional connects the condition and the conclusion, stating that they are true if and only if each other is true. Therefore, option C correctly represents the biconditional for the given statement.

The biconditional for the given statement is 'M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯'.

The biconditional for the given statement is M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯. This means that if M is the midpoint of line segment AB, then AM is congruent to MB, and vice versa. Both conditions must be met in order for the statement to be true. Option C correctly represents this biconditional in the answer choices.

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Answer:

I think it's 39 I'm wrong but that's what I think sorry

Answer:

14 + 3x

Step-by-step explanation:

6x2= 12

12 + 3x + 2

=14 + 3x

Answer:

y =-6(x-1/4)^2+19/8

Step-by-step explanation:

I hope this helps I don't have an explanation I just got it right on EDG 2021

God Bless You!!!!!

Answer:

D

Step-by-step explanation:

You can rewrite the equation into slope intercept form and you get Y=10-5x/2 (The whole problem is being divided by 2).

You can leave -5/2 as it is because it's a lot easier to plot the point using Rise over Run or Rise/Run.

Hope this helps! :)

Answer:

w = -100

Step-by-step explanation:

Step 1: Write out equation

166 = -w + 66

Step 2: Subtract 66 on both sides

100 = -w

Step 3: Divide both sides by -1

w = -100

Answer:

w=-100

Step-by-step explanation:

We are given the equation:

166= -w +66

To solve for x, we must get x by itself on one side of the equation.

66 is being added to -w. The inverse of addition is subtraction. Subtract 66 from both sides of the equation.

166-66= -w+66-66

166-66= -w

100= -w

-1 and w are being multiplied. The invers of multiplication is division. Divide both sides of the equation by -1.

100/-1= -w/-1

100/-1=w

-100=w

Let's check our solution. Plug -100 in for w.

166= -w+66

166= -(-100)+66

166=100+66

166=166

The statement above is true, so we know our solution is correct.

The solution to 166= -w+66 is w= -100

Answer: suppose that the region is bounded by y = x and y = 2x in the first quadrant, and the region is bounded by x = 0 and y = 2. let V_x be the volume of the solid obtained by rotating about the x-axis and let V_y be the volume of the solid obtained by rotating about the y-axis.

Step-by-step explanation:

Using the z-distribution, it is found that the margin of error for the true proportion of times this die would land on five dots is of 0.1338.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The estimate and the sample size are given as follows:

\(\pi = \frac{25}{30} = 0.8333, n = 30\).

Hence the margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 1.96\sqrt{\frac{0.8333(0.1667)}{30}}\)

M = 0.1338.

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A man who weighs 185 lb on Earth weighs 30.8 lb on the Moon

Two variables are said to be directly proportional if as one variable increases/decreases, the other variables does the same by the same amount.

Let y represent the weight of object on earth and x represent the weight of object on the moon.

y ∝ x

y = kx

When y = 66, x = 10.92, hence:

66 = 10.92k

k = 6

When y = 185 lb:

185 = 6x

x = 30.8 lb

A man who weighs 185 lb on Earth weighs 30.8 lb on the Moon

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Answer:

30.8lb

Step-by-step explanation:

Answer:

Arithmetic Finance.

Compound interest

Step-by-step explanation:

when you're given the year sequence, principal and rate.

Answer:

Step-by-step explanation:

A = P ( 1 + r)^ n

This formula is used to find the Amount in Compound interest.

P --- Principal - the value we are depositing or taking loan

r - rate of interest

n --- number of years

A- amount that we get after n years or the loan to paid after n years

Answer:

4/610=0.00655737704918

Step-by-step explanation:

Answer

0.00655737704

4/610 ≈ 0.007 or 0.01

Step-by-step explanation:

1) 4/610 = 0.00655737704

2) Since the number is too long, you can also round it to the nearest thousandth which is 0.007 or you can round to the nearest hundredth which is 0.01

However, the answer 0.00655737704 is the most accurate.

Hope this helps!

The length of the radius of the given circle will be 16.97 feet.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

A circle has an area of approximately 907.46 ft². Then the length of the radius of the circle is given as,

A = πr²

904.46 = 3.14 x r²

r² = 288

r = 16.97 feet

The length of the radius of the given circle will be 16.97 feet.

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Answer:

Becky is 7 years old.

Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.

Answer:

Becky's 7 seven years old

Step-by-step explanation:

If 21 = 3x

x = 21/3

x = 7

Hope this helps :)

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Answer: surface area is 215.27; volume is 297.1

Step-by-step explanation:

you have to find the radius first, c = 2(pi (3.14))r, the formula for surface area is 4(pi(3.14)r^2, the formula for volume is 4/3(3.14(pi))r^3