∆ABC and ∆FDE are congruent by the criterion. (Use the three-letter abbreviation without spaces.)
The value of x is , and the value of y is .

Answer:

The polynomial that represent the volume of the box is [tex]V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

we have

[tex]L=(x+3)\ in[/tex]

[tex]W=x\ in[/tex]

[tex]H=(x+1)\ in[/tex]

substitute in the formula

[tex]V=(x+3)(x)(x+1)\\V=(x^{2} +3x)(x+1)\\V=x^{3}+x^{2} +3x^{2} +3x\\ V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]

Answer:

A  Open circle at 6, line going to the right

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

We know the area is greater than 24

24 < l*w

One dimension is 4

24 < 4*w

Divide each side by 4

24/4 < 4w/4

6 < w

The other dimension must be greater than 6

Open circle at 6, line going to the right

The graph of f(x) = sin(x) - 2 is a sinusoidal wave shifted down 2 units with period 2π and amplitude 1.

To graph the function, we can start by plotting the points where the graph intersects the x-axis. These points occur when sin(x) = 0, which is when x = 0, ±π, ±2π, and so on. Since the graph is shifted downwards by 2 units, these points will all be 2 units below the x-axis.

Next, we can plot the points where the graph reaches its maximum and minimum values. These points occur when sin(x) = ±1, which is when x = ±π/2 + 2πn, where n is any integer.

Since the graph is shifted downwards by 2 units, the maximum points will be 1 unit above the x-axis, and the minimum points will be 3 units below the x-axis.

Once we have plotted a few points, we can sketch the rest of the graph by connecting the points with a smooth curve. The graph should oscillate between -2 and 0, with a period of 2π.

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Answer:

ROI = 66.67%

Step-by-step explanation:

Given:

josh investment= $12,000

Received sum= $20,000

ROI=?

ROI is the return on investment that gives the loss or gain in any investment and is calculated by the following formula:

ROI= (interest/investment) x 100

Finding interest:

interests= received sum- investment

              = 20,000-12,000

              =8000

Putting values in ROI formula we get:

ROI= (8000/12000) x 100

      = 66.67%

Hence the return on investment is 66.67%!

Let the number = X

Then to get four less you need to subtract 4 from x so you have X-4.

Then that equals 17, so the equation would be:

x - 4 = 17

The equation of the sentence 'four less than a number is 17' is  x – 4 = 17

Let the number be x

Four less than the number means x - 4

Therefore,

Four less than a number is 17 means x – 4 = 17

Therefore, option x – 4 = 17 is the correct answer

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Answer:

x<2

Step-by-step explanation:

-x+8>6

-x>6-8

-x>-2 (flip the sign)

x<2

Answer:

x < 2

Step-by-step explanation:

-x+8>6

Subtract 8 from each side

-x+8-8>6-8

-x > -2

Divide each side by -1.  Remember to flip the inequality

-x/-1 < -2/-1

x < 2

The answer is (3,11) because both lines pass through this point.

If you plug these coordinates into the equations in place of x and y :

3+8= 11

3(3)+2= 11

So we know that the coordinates (3,11) are correct, however the answer is C. because solutions to systems of equations are represented by a point of intersection.

The answer is:

The correct option is the second option:

(3, 11) because both lines pass through this point

To find which statement shows the solution to the system of equations, we need to find which of the given points are solutions to the system of equations. We must remember that if a point is a solution to a system of equations, it will satisfy both equations.

So, we are given the lines:

Line C

[tex]y=x+8[/tex]

Line D

[tex]y=3x+2[/tex]

Now, evaluating the first point to see if satisfies the line equations:

Evaluating (3,11)

Line C

[tex]11=3+8[/tex]

[tex]11=11[/tex]

We have that the point (3,11) satisfy the equation of the Line C, so, the linea pass through this point.

Line D

[tex]y=3x+2[/tex]

[tex]11=3*3+2[/tex]

[tex]11=11[/tex]

We have that the point (3,11) satisfies the equation of the Line C, so, the linea pass through this point.

Hence, we have that the points satisfies both lines, so it's a solution to the system of equation.

So, the correct option is the second option:

(3, 11) because both lines pass through this point

Have a nice day!

Answer:

[tex]w=11[/tex]

Step-by-step explanation:

we have

[tex]5=w/2.2[/tex]

Solve for w

That means----> isolate the variable w

Multiply by 2.2 both sides

[tex](2.2)*5=(2.2)*w/2.2[/tex]

Simplify

[tex]11=w[/tex]

Rewrite

[tex]w=11[/tex]

The solution to the equation 5 = w/2.2 is 11

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

5 = w/2.2

Rewrite the equation as follows

w/2.2 = 5

So, we have

w = 5 * 2.2

Evaluate the product of 5 and 2.5

So, we have

w = 11

Hence, the solution to the equation is 11

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Answer:

Point I

Step-by-step explanation:

Point I is the farthest away from the line of best fit

Answer:

Whoa that's easyyyy

Step-by-step explanation:

Point I because it's not close to the others and it's not anywhere near becing connected to another letter

Answer:

Choice B is correct

Step-by-step explanation:

The graph of the parabola opens towards the left. This implies that the general form of the equation of the parabola will be;

[tex]y^{2}=f(x)[/tex]

Nevertheless, the points (-2, -4) and (-2, 4) lie on the graph of the parabola. We substitute x = -2 in the equations having the form above.

In the second equation, we have;

[tex]y^{2}=-8(-2)\\\\y^{2}=16\\\\y=\sqrt{16}=+4, -4[/tex]

This is thus the equation of the parabola graphed.

Answer: D x^2=6y

Step-by-step explanation:

Answer:

$2.04

Step-by-step explanation:

Note that: 1 yard = 3 feet.

First, change the amount of yard (6) to feet:

6 x 3 = 18

6 yard = 18 feet.

Note: 18 feet = $36.72

Find the cost per foot (1 feet). Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides.

(18 ft)/18 = ($36.72)/18

1 ft = 36.72/18

1 ft = 2.04/1

1 ft = $2.04

~

Answer:

$2.04

Step-by-step explanation:

36.72/6

So that would make the answer $2.04

Here,

[tex]1.578 \times {10}^{ - 5} miles = 1 \: inches \\ 1 \: miles = \frac{1}{1.578 \times {10}^{ - 5} } \: inches\\ 1425 \: miles = \frac{1}{1.578 \times {10}^{ - 5} } \times 1425 inches\\ = 9.03 \times {10}^{7} inches[/tex]

I hope it helps you

The correct representation of the given set using the listing method is {2, 3, 4, 5}. The second option is correct.

The set {x | x I, 2 ≤ x ≤ 5} can be represented using the listing method.

Here, the set consists of all values of x that satisfy the condition 2 ≤ x ≤ 5. The values of x within this range are 2, 3, 4, and 5.

Therefore, the set can be represented as:

{2, 3, 4, 5}

This set includes all the values of x that are greater than or equal to 2 and less than or equal to 5, as indicated by the condition 2 ≤ x ≤ 5.

The elements listed in the set are 2, 3, 4, and 5, and no other values are included.

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Answer:

[tex]\large\boxed{the\ radius\ R=\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a volume of a sphere:

[tex]V=\dfrac{4}{3}\pi R^3[/tex]

We have

[tex]V=\dfrac{1}{6}\pi[/tex]

Substitute:

[tex]\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi[/tex]        divide both sides by π

[tex]\dfrac{4}{3}R^3=\dfrac{1}{6}[/tex]          multiply both sides by 3

[tex]3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}[/tex]

[tex]4R^3=\dfrac{1}{2}[/tex]          divide both sides by 4

[tex]R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}[/tex]

Answer:

Step-by-step explanation:

A recipe for sabayon calls for 2 egg yolks, 3 tablespoons of sugar, and ¼ cup of white wine. After cracking the eggs, you start measuring the sugar, but accidentally put in 4 tablespoons of sugar. How can you compensate?

Note that we put  in 4/3 more sugar than we wanted, because 3(4/3) = 4

So we need to increase eveything else by 4/3

So 2(4/3)  = 8/3  = 2 +2/3 egg yolk    and      (1/4)(4/3) =4/12 = 1/3 cup of wine

To counterbalance the additional tablespoon of sugar in the recipe, you could increase the other ingredients by a third as well. Hence, you'd require roughly 3 egg yolks and 1/3 cup of white wine.

In this recipe situation, since you accidentally put in 4 tablespoons of sugar instead of the required 3 tablespoons, you've essentially increased the sugar quantity by a third. To compensate for this, your best option would be to increase the quantities of the other ingredients by a third as well. Therefore, you would need:

Using these measurements, you should retain the balance of ingredients in your recipe. Nevertheless, remember that cooking often involves personal taste. You might want to adjust the recipe according to your taste preferences afterwards.

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Answer:

5.625π m³

Step-by-step explanation:

The formula for the volume of a cylinder of radius R and length L is:

V = π·R²·L.

Here, V = π·(1.5 m)²(2.5 m) = 5.625π m³

Answer:

Step-by-step explanation:

Givens

r = 1.5 meters.

h = 2.5 meters.

Formula

V = pi * r^2 * h

Solution

V = pi * 1.5^2 * 2.5

V = pi * 2.25 * 2.5

V = 5.625 pi

5x+2+x+2=40

5x+x=40-2-2

6x=36

x=36/6

x=6

Son=6

David=5*6=30

The question involves solving two linear equations. By solving these equations, we find that the son is currently 6 years old and David is 30 years old.

This question is based on linear equations in mathematics. Let's use the given conditions to form two equations and solve them accordingly.

Let's assume that the son's age is 'x'. According to the information provided, David is five times older than his son, so David's age is '5x'.

In two years, David will be 5x + 2 years old and his son will be x + 2 years old. The sum of their ages in two years is given as 40, which leads us to the equation 5x + 2 + x + 2 = 40. After simplifying, we get '6x + 4 = 40', or '6x = 36', and then 'x = 6'.

Hence, currently the son is 6 years old and David is 30 years old.

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0.55

Hope this helps :)

Answer: 0.55

This is the answer... hope this will help y'all. If I'm wrong, please tell me. Thanks ☺️

I'm going to assume that you meant y = mx + b not y = my + b

To do this move 7x to the right side by subtracting it to both sides

(7x - 7x) - y = 8 - 7x

0 - y = 8 -7x

-y = 8 - 7x

Y still isn't full isolated! There is still the negative sign that you have to get rid of. To do this divide -1 to both sides

-y/-1 = (8 - 7x)/ -1

y = -8 + 7x

y = 7x - 8

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

4 feet

Step-by-step explanation:

It is given that:

• At 2:30 p.m., the water depth was 2.6 feet.  

• It is now 5:00 p.m., and the depth of the water is 3.6 feet.

So in 2.5 hours ( 5pm - 2:30pm) the water rose 1 feet (3.6 - 2.6).

Now we can find how much water rises in 1 hour by setting up a ratio (let x be the depth increase of water in 1 hr):

[tex]\frac{2.5}{1}=\frac{1}{x}\\2.5x=1*1\\2.5x=1\\x=\frac{1}{2.5}\\x=0.4[/tex]

So, in 1 hour, the water level will rise 0.4 feet

So, at 6pm (1 hour from 5 pm) it will rise to 3.6 + 0.4 = 4 feet

The depth of the water is increasing at a rate of 0.4 feet per hour, so by 6:00 p.m., the depth will be 4 feet.

We are given the information that water is being pumped into a cylindrical tank and the height of the water increases linearly over time. At 2:30 p.m. the depth was 2.6 feet, and at 5:00 p.m. it was 3.6 feet. To find the rate of change in height, we need to first calculate the time difference and the change in height of the water:

Dividing the change in height by the time gives us the rate of change, which is 0.4 feet per hour (1 foot / 2.5 hours). Now we use this rate to predict the height at 6:00 p.m., which is one hour after 5:00 p.m.:

Depth at 5:00 p.m. = 3.6 feet + (0.4 feet per hour * 1 hour) = 4 feet.

Therefore, the expected depth of the water at 6:00 p.m. is 4 feet.

Answer:

The best measure of location or center is the median.

The best measure of spread or dispersion is the interquartile range (I.Q.R).

Step-by-step explanation:

The data set is skewed to the left since most of the data values fall in the upper end of the distribution. In other words the data set is negatively skewed since it is tailed to the left.

For any skewed data set;

The best measure of location or center is always the median. This is because the median is robust to outliers unlike the mean.

On the other hand, the best measure of spread or dispersion is the interquartile range (I.Q.R).

Answer:

B and D

Step-by-step explanation:

Answer:

It is 1/6

Step-by-step explanation:

This is because there are 6 sides to a dice and the number 3 is only on one of those sides. So, it is 1 in 6 or 1/6

Answer:

1/6

Step-by-step explanation:

The question is asking for the probability of rolling a 3 on a fair-sided die.

Dice have 6 faces.

The number "3" is only on 1  those faces

So, the probability of rolling a 3 on a dice is 1/6

I hope this helps! :)

Answer:

I believe it is surface area

Answer:

Step-by-step explanation:

c

Answer:

5.50 + 75g <= 15

5.50 - 5.50 + 75g <= 15 - 5.50

75g <= 9.5

75g / 75 <= 75 / 15

g = 5

Step-by-step explanation:

ANSWER

about 44.64

EXPLANATION

The standard deviation is the square root of the variance.

So we can write the equation or formula;

[tex]standard \: \: deviation = \sqrt{variance} [/tex]

From the question, it was given that, the variance is 1992.8

To find the standard deviation, we plug in the given value of the variance.

[tex]standard \: \: deviation = \sqrt{1992.8} [/tex]

Take your scientific calculator and the given square root.

You should obtain:

[tex]standard \: \: deviation = 44.64078852[/tex]

We round to the nearest hundredth to obtain; 44.64

Answer:

3.28 feet

Step-by-step explanation:

One meter equals to 3.28 feet.

The question isn't exactly clear what Gema wants to use her wire for, because "wrap one meter" isn't correct.

You wrap something around something else...  and you can't wrap something around a meter.  You can wrap around a square meter by doing the perimeter... but then you'd need more than meter to do the perimeter of a square meter (the perimeter can be around 4 meters).

So, assuming she has a length of 1 meter to cover, she would need 3.28 feet.

For this case we have by definition, that the volume of a sphere is given by:

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

Where:

r: It is the radius of the sphere

If the radius is divided by 3 we have:

[tex]\frac {r} {3}:[/tex]

[tex]V = \frac {4} {3} \pi * (\frac {r} {3}) ^ 3\\V = \frac {4} {3} \pi * \frac {r ^ 3} {27}\\V = \frac {4} {81} \pi * r ^ 3[/tex]

ANswer:

the volume decreases considerably because the denominator increases

For this case we must find the quotient of[tex]6x ^ 2 + 23x + 20[/tex] between [tex]5 + 2x.[/tex]

As you can see in the figure, we must build a quotient in such a way that when multiplied by the divisor, we eliminate the terms of the dividend until we reach the remainder.

Answer:

[tex]3x + 4[/tex]

See attached image

[tex]\sin x>0[/tex] when [tex]x[/tex] is in quadrant II, so

[tex]\cos^2x+\sin^2x=1\implies\sin x=\sqrt{1-\cos^2x}=\sqrt{1-(-0.2)^2}\approx1.02[/tex]

Answer:

Step-by-step explanation:

note : cos²x + sin²x = 1

         (- 0.2)² + sin²x =1

          0.04 + sin²x = 1

sin²x = 1 - 0.04

sin²x = 0.96

sinx = √0.96  or sinx = - √0.96

in quadrant II : sinx > 0    ...so : sinx = √0.96

Answer:

[tex]\large\boxed{x=\dfrac{11}{2},\ y=\dfrac{86}{35}}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}12x-14y=-8\\-8x-14y=-52&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}12x-14y=-8\\8x+14y=52\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad20x=44\qquad\text{divide both sides by 20}\\.\qquad x=\dfrac{44:4}{20:4}\\\\.\qquad x=\dfrac{11}{5}\\\\.\qquad\boxed{x=2.2}\\\\\text{Put the value of x to the second equation}\ 8x+14y=52:[/tex]

[tex]8(2.2)+14y=52\\17.6+14y=52\qquad\text{subtract 17.6 from both sides}\\14y=34.4\qquad\text{divide both sides by 14}\\y=\dfrac{34.4:2}{14:2}\\\\y=\dfrac{17.2\cdot10}{7\cdot10}\\\\y=\dfrac{172:2}{70:2}\\\boxed{y=\dfrac{86}{35}}[/tex]

The solution to the system of equations is: [tex]\[x = 2.2, \quad y = 2.457\][/tex]

To solve the system of linear equations:

[tex]\[12x - 14y = -8\]\[-8x - 14y = -52\][/tex]

We can use the method of elimination to find the values of x and y.

First, let's eliminate y by subtracting the second equation from the first equation. Before that, we should multiply the equations to have the same coefficients for y with opposite signs:

Multiply the first equation by 1:

12x - 14y = -8

Multiply the second equation by -1:

8x + 14y = 52

Now, add the two equations:

[tex]\[(12x - 14y) + (8x + 14y) = -8 + 52\][/tex]

Simplifying this, we get:

[tex]\[20x = 44\]Solve for \(x\):\[x = \frac{44}{20}\]\[x = \frac{22}{10}\]\[x = 2.2\][/tex]

Now that we have x, we can substitute this value back into one of the original equations to find y. Using the first equation:

12x - 14y = -8

Substitute x = 2.2:

[tex]\[12(2.2) - 14y = -8\]\[26.4 - 14y = -8\][/tex]

Subtract 26.4 from both sides:

[tex]\[-14y = -8 - 26.4\]\[-14y = -34.4\][/tex]

Divide both sides by -14:

[tex]\[y = \frac{-34.4}{-14}\]\[y = 2.4571 \approx 2.457\][/tex]

Thus, the solution to the system of equations is:

[tex]\[x = 2.2, \quad y = 2.457\][/tex]

To ensure accuracy, let's substitute x and y back into the original equations and verify that they hold true.

Check the first equation:

[tex]\[12(2.2) - 14(2.457) = -8\]\[26.4 - 34.398 = -8\]\[-7.998 \approx -8 \quad \text{(approximately correct)}\][/tex]

Check the second equation:

[tex]\[-8(2.2) - 14(2.457) = -52\]\[-17.6 - 34.398 = -52\]\[-51.998 \approx -52 \quad \text{(approximately correct)}\][/tex]