For what values of x is the expression below defined?A.x < 1B.x < 0C.x = 0D.x > 0

Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.

Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

AC = sqrt((2 - (-2))^2 + (4 - 1)^2)

AC = sqrt(4 + 9) = sqrt(13)

Now that we know the side length of the square, we can use this information to find the coordinates of the remaining vertices. We know that vertex B has the same y-coordinate as vertex A, but the x-coordinate is 2 units to the left of vertex C. Therefore, the coordinates of vertex B are (-2 + 2sqrt(13), 1).

Similarly, we know that vertex D has the same x-coordinate as vertex A, but the y-coordinate is 4 units down from vertex C. Therefore, the coordinates of vertex D are (-2, 1 + 4sqrt(13))

So, the coordinates of the remaining vertices are (2sqrt(13),1) and (-2, 4sqrt(13)) respectively.

Step-by-step explanation:

Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.

We know that, to find volume:

Volume = π * \(r^2\) * h

For the smaller stockpot:

Radius (r) = 2.5 inches

Height (h) = 10 inches

Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches

For the larger stockpot:

Radius (r) = 2.5 inches

Height (h) = 16 inches

Volume = π * (2.5)² * 16

             ≈ 628.32 cubic inches

Thus, the volume of larger one is 628.32 cubic inches.

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Answer:

35 cubic inches

Step-by-step explanation:

The volume of a pyramid is \(\frac{1}{3} bh\), where b = base and h = height. To find the area of the base, we multiply 3 by 5 and then divided by 2.

Next, we multiply 7.5 by 14.

Lastly, we divide by 3.

Therefore, the answer is 35 cubic inches.

Answer: x=8

Step-by-step explanation:

4x+6y=50

4x+6(3)=50

4x+18=50

4x=32

x=8

The value of x when y = 3 in the linear function 4x + 6y = 50 is x = 8.

Use the concept of linear fucntion defined as:

The formula for a linear function is f(x) = mx + b, where m and b are real values. The slope-intercept form of a line is represented by the equation,

y = mx + b.

The given linear fucntion is:

4x+6y= 50

To find the value of x when y = 3,

Substitute y with 3 in the equation and solve for x.

4x + 6(3) = 50

4x + 18 = 50

To isolate x,

Subtract 18 from both sides:

4x = 50 - 18

4x = 32

Now we divide both sides by 4:

x = 32/4

x = 8

Hence,

When y = 3, the value of x in the linear function 4x + 6y = 50 is 8.

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We can calculate the slope of a line "m" by means of the following equation:

Where (x1,y1) and (x2,y2) are two points of a line.

We could take any point where the line passes through, for example, we can take (0,20) and (10,70), then we get:

Then, the slope of the line equals 5

The quadratic function graphed is defined as follows:

y = x² - 10x + 9.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

From the graph, the roots are given as follows:

x = 1 and x = 9.

Hence the function as a product of it's linear factors is defined as follows:

y = a(x - 1)(x - 9)

y = a(x² - 10x + 9).

When x = 5, y = -16, hence the leading coefficient a is obtained as follows:

-16 = a(5² - 10(5) + 9)

-16a = -16

a = 1.

Thus the function is:

y = x² - 10x + 9.

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Answer:

625

Step-by-step explanation:

have a great day <3

Answer:

5x5x5x5=625

5x5x5x5= \(5^{4}\)

Step-by-step explanation:

9514 1404 393

Answer:

  5) 76°

  7) 34°

Step-by-step explanation:

5) An angle bisector creates two congruent angles, so ...

  ∠WUV = 2(∠1)

  9x +4 = 2(5x -2)

  9x +4 = 10x -4

  8 = x

Then ...

  ∠WUV = 9(8) +4 = 76

The measure of angle WUV is 76°.

__

7) An angle bisector creates two congruent angles, so ...

  ∠1 = ∠2

  2x -3 = x +7

  x = 10 . . . . . . . . add 3-x

Then ...

  ∠XVW = 2(∠2) = 2(10 +7) = 34

The measure of angle XVW is 34°.

Answer:

that is 9

Step-by-step explanation:

i hope this helps you

Answer:

Checking account, savings account, money market account, and CD.

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

took the test on edge

Answer:

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gzgixxhcxc

vxtuixzdfhvxxgjknn

jfhujhgcxvjkmvcghj

mvhuiknbb5542698755

8423675369

8823

The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)

In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:

y = b · aˣ

Where:

By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.

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Answer:

2^52

Step-by-step explanation:

(8^-5/2^-2)^-4 = (2^-15/2^-2)^-4= (2^-13)^-4= 2^((-13*(-4))= 2^52

The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Answer:

34n=306

Step-by-step explanation:

Use inverse operation to find it, 306÷34= 9, check again 34(9)=306, so it's correct!

The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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Answer:

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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Answer:

3/3/8

Step-by-step explanation:

Let's start by defining some variables:

Let's call Jamal's age "J".

Let's call Alex's age "A".

From the problem statement, we know that:

J = A - 5 (Jamal is 5 years younger than Alex)

J * A = 300 (the product of their ages is 300)

We can use the first equation to substitute J in the second equation:

(A - 5) * A = 300

Expanding the left-hand side:

A^2 - 5A = 300

Moving all terms to the left-hand side:

A^2 - 5A - 300 = 0

We can solve for A using the quadratic formula:

A = (-(-5) ± sqrt((-5)^2 - 41(-300))) / (2*1)

A = (5 ± sqrt(25 + 1200)) / 2

A = (5 ± sqrt(1225)) / 2

Since A is a positive integer, we take the positive solution:

A = (5 + 35) / 2 = 20

Now we can use the first equation to find J:

J = A - 5 = 20 - 5 = 15

Therefore, Jamal is 15 years old.

The questions are illustrations of probability and the usage of two-way tables

To do this, we make use of the following representations:

So, the given parameters are:

Total = 1000

x = 781

x and y = 133

x' and y' = 192

Using the above data values, we have:

y = Total - x

x and y' = x - x and y

x' and y = y - x' and y'

This gives

y = 1000 - 781 = 219

x and y' = 781 - 133 = 648

x' and y = 219 - 192 = 27

See attachment for the complete table.

Probability that cats prefer flying

This is calculated as:

P = Flying/Total

So, we have:

P = 20/100 = 1/5

Probability that a selected cat is an alley cat

This is calculated as:

P = Alley Cat/Total

So, we have:

P = 41/100

Probability that a selected alley cat prefers invisibility

This is calculated as:

P = Alley Cat and Invisible/Alley Cat

So, we have:

P = 21/41

Probability that a selected home cat prefers invisibility

This is calculated as:

P = Home Cat and Invisible/Home Cat

So, we have:

P = 22/59

Probability of Peanut Butter Crunch

The given parameters are:

Peanut Butter Crunch = 1

Flavors = 52

This probability is then calculated as:

P = Peanut Butter Crunch/Total

So, we have:

P = 1/52

Theoretical probability of Cotton Candy

In this case, we have:

Cotton Candy = 1

Flavors = 5

This probability is then calculated as:

P = Cotton Candy/Flavors

So, we have:

P = 1/5

Experimental probability of Mango

In this case, we use the table results i.e.

Mango = 1

Friends = 15

This probability is then calculated as:

P = Mango/Friends

So, we have:

P = 1/15

Hence, the experimental probability of Mango is 1/15

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\((\stackrel{x_1}{40}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{20}-\underset{x_1}{40}}} \implies \cfrac{ -2 }{ -20 } \implies \cfrac{ 1 }{ 10 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{ 1 }{ 10 }}(x-\stackrel{x_1}{40})\implies {\Large \begin{array}{llll} y=\cfrac{1}{10}x+4 \end{array}}\)

The value of x is 8  

If all of the corresponding sides and angles of two triangles are identical, then those triangles are said to be similar triangles. In similar triangles, the ratio of the corresponding sides will be equal.

If two triangles ΔABC and ΔXYZ are similar triangles the ratio of the corresponding sides will be equal

=> AB/XY = BC/YZ = AC/ZX

Here we have

ΔDEF and ΔABC  

From both triangles,

The ratio of corresponding sides = DE/AB and FD/AC

As we calculate,  \(\frac{19.2}{3.2} = \frac{39}{6.5} = 6\)    

Thus the ratio of corresponding sides is same and equal to 6

=> \(\frac{FE}{BC} = 6\)  

=> \(\frac{48}{x} = 6\)

=> \(6x = 48\)

=> x = 8  

Therefore,

The value of x is 8    

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Answer:

0.75

Step-by-step explanation:

there is 1000 grams in 1 kilogram so I divided 750 by 1000 to get 0.75.

Answer:

The number of acres that were planted by the farmer if the year is 2/3 will be 3.

Step-by-step explanation:

I’ve done this before

Answer:

y=-2/3x-5

Step-by-step explanation:

For slope, you have to do rise over run which means start from one of the points and rise(up or down) to the next point and then run(right or left) to the next point. The y-intercept is pretty easy all you have to do is look for the point that's on the y-axis or the one that's vertical.

Answer:

Mean= 8.3

Standard deviation=7.8

Step-by-step explanation: