Solve the right triangle. Round decimal answers to the nearest tenth. find the sides and angles

The statement correctly describes the relationship between △DEF and △D'E'F' is option (D) △DEF is congruent to △D′E′F′ because you can map △DEF to △D′E′F′ using a reflection across the x-axis, which is a rigid motion.

In the given figure

Consider the ΔDEF

The coordinates of the each point is

D = (0,-1)

E = (-3,-4)

F = (6, -4)

The coordinates of the △D′E′F′

D' = (0,1)

E' = (-3,4)

F' = (6,4)

Here we can see that there is a reflection across the x axis which is a rigid motion

Hence, the statement correctly describes the relationship between △DEF and △D'E'F' is option (D) △DEF is congruent to △D′E′F′ because you can map △DEF to △D′E′F′ using a reflection across the x-axis, which is a rigid motion.

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Answer:

Step-by-step explanation:

3x<-9

x<-3

-4x+5<1

-4x<-4

x>1

Step-by-step explanation:

Here is the solution...hope it helps:)

Answer:

-7i - 9

-11i + 12

Step-by-step explanation:

i stands for imaginary number, in which i² = -1

6i² = 6 * -1 = -6

-6 - 7i - 3

Combine like terms:

-6 - 3 = -9

-7i - 9

2i^2 = 2 * -1 = -2

Combine like terms:

-11i + 14 - 2

-11i + 12

~

Answer: 64 d^4 - 24 d^2

Factor 8 d^2 out of 64 d^4 - 24 d^2:

Answer:  8 d^2 (8 d^2 - 3)

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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The given equation is 6 sec^2(x) - 6 = 0. To find all solutions in the interval [0, 2π), we first need to solve for sec^2(x).

1. Isolate sec^2(x) by adding 6 to both sides of the equation:

6 sec^2(x) - 6 + 6 = 0 + 6
6 sec^2(x) = 6

2. Divide both sides of the equation by 6:

sec^2(x) = 1

3. Since sec(x) is the reciprocal of cos(x), we can rewrite the equation as:

1/cos^2(x) = 1

4. Take the reciprocal of both sides:

cos^2(x) = 1

5. Now, find the square root of both sides:

cos(x) = ±1

6. Find the values of x within the interval [0, 2π) for which cos(x) equals 1 or -1:

cos(x) = 1, x = 0, 2π
cos(x) = -1, x = π

Therefore, the solutions to the equation 6 sec^2(x) - 6 = 0 in the interval [0, 2π) are x = 0, π, and 2π. The final answer is: x = 0, π, 2π.

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Answer:

Volume of rectangular prism = 175 / 6 inch³

Step-by-step explanation:

Given:

Base area of rectangular prism = 23 ¹/₃ inch² =  70 / 3 inch²

Height of rectangular prism = 1 ¹/₄ inch = 5 / 4 inch

Find:

Volume of rectangular prism

Computation:

Volume of rectangular prism = Base area of rectangular prism x Height of rectangular prism

Volume of rectangular prism = [70 / 3] x [5 / 4]

Volume of rectangular prism = [350 / 12]

Volume of rectangular prism = 175 / 6 inch³

The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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Therefore, the answer to the provided equation is 27.385 cm longer than what we would anticipate Mike's arm span to be compared to George's.

An equation is referred to as linear when all of the highest powers of the variables are equal to one. They are connected via links. A one-degree equation is another term for this kind of issue. You will learn how to solve a linear equation expression in one or two variables by following the steps in the paragraphs that follow.

Here,

we must use the equation to determine how many millimeters more Mike should have than George.

y= 4.5x + 0.977 x

where y=arm length

where x = height

Given:

Mike is 175 cm tall, so x=x.

Mike's arm span is therefore y=4.5 x + 0.977 x.

= 4.5* (175) + 0.977* (175) (175)

= 787.5 + 170.975

= 958.475 cm

George is 170 cm tall, so x=x.

George's arm span is therefore y=4.5 x + 0.977 x.

= 4.5* (170) + 0.977* (170) (170)

= 765 + 166.09

= 931.09 cm

Mike's arm span is greater than George's arm span because Mike has a larger arm span.

= 958.475 - 931.09

= 27.385 cm.

Therefore, the answer to the provided equation is 27.385 cm longer than what we would anticipate Mike's arm span to be compared to George's.

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Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

The required equation is y=90x-80 and slope is 90 and y intercept is -80.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the table we can observe that y represents the number of people abs x represents the number of minutes.

Let us find the equation by taking two points

(1,10) and (2, 100)

m=100-10/2-1=90

Now let us find the y intercept

10=90(1)+b

10=90+b

-80=b

The equation is y=90x-80

The slope is 90 and y intercept is -80.

Hence, equation is y=90x-80 and slope is 90 and y intercept is -80.

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Answer:

$200 : $40

(i divided 240 by 6 because there are six parts in the ratio, and got 40. 40*5=200 and the other 40 makes it 240 in the ratio of 5:1)

Step-by-step explanation:

Answer:

Alex : Burton

    5 : 1

5+1=6

240/6=40

5 times 40=200

1 times 40 =40

= 200:40                                                                                                                                                                                     this means alex gets $200 and burton gets $40

Answer:

the solution to the equation 2x^+4=8^x is x = 1.

Step-by-step explanation:

To solve the equation 2x^+4=8^x, we can start by simplifying both sides of the equation.

First, we can rewrite 8^x as (2^3)^x, using the property that 8 is equal to 2 raised to the power of 3.

So, the equation becomes:

2x^+4 = (2^3)^x

2x^+4 = 2^(3x)

Next, we can rewrite 2x^+4 as 2^2 * 2^x, using the property that a^b * a^c = a^(b+c).

So, the equation becomes:

2^2 * 2^x = 2^(3x)

2^(x+2) = 2^(3x)

Now, we can equate the exponents on both sides of the equation:

x + 2 = 3x

2x = 2

x = 1

Therefore, the solution to the equation 2x^+4=8^x is x = 1.

Answer:

Below

Step-by-step explanation:

2  x^4  =  8^x        <====not sure syntax is correct(?)

Solving GRAPHICALLY shows x = - .61181

During the current year, merchandise was sold for $662,100. Of this amount, $114,000 was cash sales and $548,100 was on account. The cost of goods sold was $423,700. Therefore, the gross profit was $238,400.

The gross profit is calculated by subtracting the cost of goods sold from the total sales. The cost of goods sold is the direct cost of producing the goods that were sold. It includes the cost of materials, labor, and overhead.

The gross profit is an important measure of a company's profitability. It shows how much money the company makes from its core business activities, before deducting other expenses.

In this case, the company's gross profit margin is 35.8%. This means that for every $100 of sales, the company makes $35.80 in gross profit. A high gross profit margin is generally considered to be a sign of a healthy business.

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The margin for the runners is 50% and the Margin percentage is 33.33% (to the nearest percent).

When the shop sells runners at a mark-up of 50%, we need to find out the margin for these runners.

What is markup?

The mark-up is a percentage that you add to the cost price of a product to get the selling price. The mark-up percentage is calculated based on the cost price of the product.

Let the cost price of the runner be CP and the markup percentage be M%

Since the shop is selling the runners at a 50% markup, the selling price of the runners would be 150% of their cost price.

Selling price = (100 + M)% × Cost priceSelling price = (100 + 50)% × CP = 150% × CP = 1.5 × CP

Therefore, the margin for the runners can be calculated as follows:

Margin = Selling price - Cost price

Margin = 1.5 × CP - CP = 0.5 × CP

Clearly, the margin on runners is 50% of their cost price.

The percentage of margin can be calculated as follows:

Margin percentage = (Margin / Selling price) × 100Margin percentage = (0.5 × CP / 1.5 × CP) × 100Margin percentage = (1/3) × 100Margin percentage = 33.33%

Therefore, the margin for the runners is 50% and the margin percentage is 33.33% (to the nearest percent).

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Answer: y = -1/3x + 17/3

Step-by-step explanation:

Hey there! I will be showing and giving the formula/steps to solve this problem. If there are any questions then feel free to ask in the comments.

Formula: y = mx + b

Step 1 - Find M

m = (6 - 4) / (-1 - 5) = -2/6 = -1/3

The m is the slope.

Step 2 - Use (5, 4) to find point B

y = -1/3x + b

4 = 1/3 * 5 + b

b = 17/3

Answer: y = -1/3x + 17/3

You will plugin 4 for y and b is the intercept.

~I hope I helped you :)~

The length of the other leg is (c) √43

From the question, we have the following parameters that can be used in our computation:

Hypotenuse = 7

One leg = √6

The length of the other leg can be calculated using

The length of the other leg = √(Hypotenuse^2 - One leg^2)

So, we have

The length of the other leg = √(7^2 - √6^2)

Evaluate

The length of the other leg = √43

Hence, the length is (c) √43

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Complete question

A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.

THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

TO FIND c I WILL SUBSTITUTE THE GIVEN KNOWN POINTS.

\( - 5= \frac{1}{2} (2) + c \\ - 5= 1 + c \\ c = - 5 - 1 \\ c = - 6\)

THEREFORE WE NOW HAVE

\( y= \frac{1}{2} x - 6\)

ATTACHED IS THE SOLUTION

we have the next information

48 ft in 24 hours

x ft in 15 hours

x is the height of the drill after 15 hours

x can be calculated if we multiply 15 by 48 and then we divide the result between 24

the height that was drill after 15 hours was 30 ft

Answer:

u+2b=22

Unicycles have one wheel and bicycles have two, so the coefficient of 2 should go before the variable representing each bike.

It should equal 22 because 15 represents the total number of seats and not wheels.

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

The unit volume explains it all.

Volumes are measured in units of length cubed. This also is the volume occupied by unit cubes.

By unit cubes, I meant, view the photo above

The volume of an object's says, how many of these cubes will fill that object.

It may not necessarily by a whole number.

So, the answer is Option A

Step-by-step explanation:

HELP making brainliest if it's correct and explain NO explaintion=no brainliest

The common approximation when X is near zero is sin(x) ~ x.  The maximum error in the approximation using n =2 is:

Sin(0.4) is approximately 0.4 with a maximum error of 0.0010667.

Sin(0.7) is approximately 0.7 with a maximum error of 0.11765.

1. For x = 0.4, sin(0.4) ~ 0.4.

The maximum error in the approximation using n = 2 is given by the Taylor remainder term with x = 0.4 and n = 2:

|R2(0.4)| <= (0.4)^3 / 3! * |cos(c)|, where c is between 0 and 0.4.

The maximum value of |cos(c)| is 1, so we have:

|R2(0.4)| <= (0.4)^3 / 3! = 0.0010667

Therefore, sin(0.4) is approximately 0.4 with a maximum error of 0.0010667.

2. For x = 0.7, sin(0.7) ~ 0.7:

The maximum error in the approximation using n = 2 is given by:

|R2(0.7)| <= (0.7)^3 / 3! * |cos(c)|, where c is between 0 and 0.7.

The maximum value of |cos(c)| is 1, so we have:

|R2(0.7)| <= (0.7)^3 / 3! = 0.11765

Therefore, sin(0.7) is approximately 0.7 with a maximum error of 0.11765.

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The statement that is not true about Juan's graph is (a) the domain of g(x) is x ≥ -3.

From the graph of the exponential function, we have the following highlight:

The smallest x value is greater than -3

This means that the domain of the graph is

x > -3

Hence, the false statement about Juan's graph is (a) the domain of g(x) is x ≥ -3.

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Answer:

A,C,D

Step-by-step explanation:

The only one you might use it the triangle

Step-by-step explanation:

Given

5x + 2y = 16 .....i)

x + 2y = 4 .....ii)

Subtracting equation I) and ii) we get

5x + 2y = 16

x + 2y = 4

- - -

4x = 12

x = 3

Putting x = 3 in equation ii)

3 + 2y = 4

2y = 4 - 3

y = 1/2

x =3 and y = 1/2

Hope it helps :)

Answer:

1) x=2 y=3 2) x=2 y=1

Step-by-step explanation:

The expected value is 2.3 if the payout probability distribution is payout  0 2 4 8 10  probability 0.45 0.3 0.1 0.1 0.05.

According to the given question.

We have the payout probability distribution.

payout(s): 0  2  4  8  10

Probability: 0.45  0.3  0.1  0.1  0.05

Multiply payout to probability such that:

0×0.45 = 0

2 × 0.3 = 0.6

4 × 0.1 = 0.4

8 × 0.1 = 0.8

10 × 0.05 = 0.5

Therefore, the expected value of the winnings from a game with the given payout probability distribution is

= 0 + 0.6 + 0.4 + 0.8 + 0.5

=2.3

Thus, the expected value is 2.3 if the payout probability distribution is payout  0 2 4 8 10  probability 0.45 0.3 0.1 0.1 0.05.

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Answer:

1/197136

Step-by-step explanation:

If there would be one pot and one plant the possibility would be 1 to take it.

It there were 2 plants and 1 pot it would be 1/2*1 = 1/2

If there were 2 plants and 2 pots it would be 1/2*2 = 1/4

With 444 plants and 444 pots it is 1/444*444 = 1/197136

There are 4×4 = 16 different combinations of plant and pot. Of those, 7 are either clay pot or cactus. Thus the probability you won't get a clay pot or a cactuis is 9/16.

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The radius of a sphere can be found by using the formula for the volume of a sphere and rearranging it to solve for the radius. In this case, the volume of the sphere is given as 2,929 1/3 times pi cm³, and we can solve for the radius using the formula for the volume of a sphere. Therefore, the radius of the sphere is approximately 12.84 cm.

The formula for the volume of a sphere is given as V = (4/3)πr³, where V represents the volume and r represents the radius.

In this case, we are given the volume as 2,929 1/3 times pi cm³. So, we can set up the equation as follows:

2,929 1/3π = (4/3)πr³

To solve for the radius, we can cancel out the common factor of π and simplify the equation:

2,929 1/3 = (4/3)r³

Next, we can isolate the radius by multiplying both sides of the equation by (3/4) and then taking the cube root:

r³ = (2,929 1/3) * (3/4)

r³ = 2,196

Taking the cube root of both sides, we find:

r = ∛2,196 ≈ 12.84 cm

Therefore, the radius of the sphere is approximately 12.84 cm.

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