Joe told Mickey he got an hourly raise at work and his new rate will be $10.25 per hour. Mickey wants to know what Joe’s hourly rate was before his raise. If r represents the amount of the raise, which expression represents Joe’s hourly rate before his raise?
r minus 10.25
10.25 minus r
10.25 + r
r + 10.25

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

for more such questions on quadrilateral

https://brainly.com/question/27991573

#SPJ8

The length of the hypotenuse is 10.61 yd.

We have,

The sum of the angles in a triangle = 180

Now,

Two angles are 45.

This means,

The side opposite to angle 45 are equal.

So,

a = c

And,

a = 7.5 yd

Now,

Applying the Pythagorean theorem.

b² = a² + c²

b² = 7.5² + 7.5²

b² = 112.5

b = √112.5

b = 10.61

Thus,

The length of the hypotenuse is 10.61 yd.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

answer

A) 11.7²+X.6²

B) 7²+10² 0²

The solutions for the given system of equations are (-9, 33) and(-2, 12).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are y=x²+8x+12 -----(i) and 3x+y=-6 -----(ii).

Here, y=-6-3x in the equation (i), we get

-6-3x=x²+8x+12

x²+8x+12+6+3x=0

x²+11x+18=0

Splitting middle term method, we get

x²+9x+2x+18=0

x(x+9)+2(x+9)=0

(x+9)(x+2)=0

x=-9 or x=-2

Substitute x=-9 in the equation (ii), we get

y=-6-3(-9)

y=33

Substitute x=-2 in the equation (ii), we get

y=-6-3(-2)

y=12

So, solutions are (-9, 33) and(-2, 12)

Therefore, the solutions for the given system of equations are (-9, 33) and(-2, 12).

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ1

Answer:

Sabrina is wrong because 3 is also a factor of 25

Step-by-step explanation:

25, 1, 3, and 5 are factors of 25

Answer:

Yes, Sabrina is correct.

Step-by-step explanation:

25 is the square of a prime number. Prime numbers only have 2 factors: the prime number and 1. 5*5=25. 5^2=25.

In this case, 5 is the prime number as the factors of 5 are 5 and 1.

25 has 3 factors since its factors are the same as of 5 and the additional factor is 25.

Hence, the factors of 25 are 25, 5, and 1, a total of 3 factors.

Answer:

-2 and suki was right aDriene was wrong as he added

Step-by-step explanation:

-8-(-6)

-8+6        (it becomes positive 6 as a negative and negative give u a positive )

= -2

The Suki answer is correct and the correct answer is -2.

It is required to find the error.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

Adrienne and Suki simplified the expression -8 -(-6)

We have to find the error was made by Adrienne or Suki .

The expression is

-8 -(-6)

Open bracket we have and both minus sign is multiply to get a plus sign as a result, we get

=-8+6

=-2

The correct answer is -2.

Therefore, the Suki answer is correct and the correct answer is -2.

Learn more details about expression here:

https://brainly.com/question/14083225

#SPJ2

Answer:

\(D=\sqrt{145 }\\\)

Step-by-step explanation:

We are actually using Pythagorean theorem here but to be simple

we can use the equation:

D(distance)=\(\sqrt{(x_{1}- x_{2} )^{2} +( y_{1}-y_{2})^{2}}\)

=

\(D=\sqrt{(15-3)^{2}+(6-7)^{2} } =\\D=\sqrt{(12)^{2}+(-1)^{2} } =\\\\D=\sqrt{144+1 } =\\D=\sqrt{145 }\\\)

(If you meant 16 instead of 6 the answer would be 15)

Hope this helps!

Answer:

distance = Sqrt((x2-x1)^2 +(y2-y1)^2)

Step-by-step explanation:

Answer:

20% of 45= 9 so you would subtract 9 from 45 getting you 39

Step-by-step explanation:

45-9=39 he would have to pay $39

Answer:

Read the explanation

Step-by-step explanation:

You cannot simplify 3/7 to 1/7. 3/7 is 3/7 and cannot be changed unless added, subtracted, divided, or multiplied. 1/7 x 2/9 is 2/63

3/7 x 2/9 is 6/63

Answer:

Answer:

\(x = 10.5\)

Solving steps:

3 1/2 = 5, x = 15

divide 3.5 by 5

=> 0.7

0.7 by 15

=> 10.5

9514 1404 393

Answer:

Step-by-step explanation:

The idea of a "production possibilities curve" is that there is a fixed relationship between possible production of one product and possible production of another. This relationship is presumed to exist because resources used to produce one product are then unavailable to produce the other product.

The graph of the curve generally has increased production in the direction away from the origin. So, points between the curve and the origin represent production choices that do not utilize all available resources of the kind that give rise to the curve. That is, points "inside" the curve represent under-utilization of resources.

1. Point C represents under-utilization.

__

2. Points "outside" the curve are unattainable, because the curve represents production using all available resources.

  Point E is unattainable.

__

3. The assumptions behind the curve are that there must be a tradeoff between production of one item and production of another that uses the same resources. That is, increasing production of one item will necessarily decrease production of the other, representing a cost of the increased production of the first item. We call this cost an "opportunity cost", because it represents production opportunity lost with respect to the second item.

  Choice B describes this situation.

_____

Additional comment

The very idea of a "production possibilities curve" represents the sort of simplification that is often used in the study of economics. The real world is much messier, and these curves are always dynamic. They are affected by the regulatory environment, resource quality, technology, product quality, and availability of alternate or competing products, among other things. The very existence of such a curve precludes the possibility of "win-win" situations, which we know are generally available if they are sought after.

The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

for such more question on system of equations

https://brainly.com/question/4262258

#SPJ8

71

that's all there is to it

Answer: 71

Step-by-step explanation: 6.39 /0.09

71

Answer:

Salary with $3300 raise per year:

t (years)     Salary

1            $69300

5            $82600

10            $95900

15            $1092000

20            $1225000

Salary with 4% raise per year:

t (years)      Salary

1             $68640

5             $83833

10             $102219

15             $124869

20             $152947

Note: The calculations for the 4% raise are done as follows:

Year 1: 66000 * 1.04 = $68640

Year 5: 66000 * 1.04^5 = $83833

Year 10: 66000 * 1.04^10 = $102219

Year 15: 66000 * 1.04^15 = $124869

Year 20: 66000 * 1.04^20 = $152947

Step-by-step explanation:

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

Learn more about the total Surface Area of the Cone :

https://brainly.com/question/15153049

Answer:

$1000

Step-by-step explanation:

It would be $1000 in total of all the people attending the party. This is because, you need to multiply, 50 and 20! The answer will be 1000.

Answer:

x = −4

Step-by-step explanation:

Add x to both sides of the equation. x + 4 + x = − 4 Add x and x . 2 x + 4 = −4

Subtract 4 from both sides of the equation. 2 x = −4 − 4 Subtract 4 from - 4. 2x = −8

Divide each term in 2x = −8 by 2. 2x/2 = −8/2

Cancel the common factor. 2x/ 2 = −8/2 Divide x by  1.  x = −8/2

Divide  −8 by 2. x = −4

Answer:

Step-by-step explanation:

50% mi amigo

The given statement " when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests. " is false. Because in distribution of sample means, population variance is unknown.

When the population variance is not known and must be estimated from the data, we use a t-statistic instead of a z-statistic for our hypothesis tests.

This is because the distribution of the sample means follows a t-distribution when the population variance is unknown, whereas it follows a standard normal distribution (z-distribution) when the population variance is known.

The t-distribution has fatter tails than the z-distribution to account for the extra uncertainty introduced by estimating the population variance from the sample.

To know more about hypothesis tests:

https://brainly.com/question/30588452

#SPJ4

The value of square root of x + y squared + z squared is 30

x = 2, y = 3 and z = -5

\(( \sqrt{x + y} )^{2} + z ^{2} \)

substitute the value of x, y and z

\( = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} \)

simplify the square root and square

\( = (2 + 3) + 25\)

\( = 5 + 25\)

\( = 30\)

Ultimately, x + y squared + z squared is 30

Read more on algebra:

https://brainly.com/question/4344214

#SPJ1

Answer:

C. 124°

Step-by-step explanation:

The angles that have measurements given must add up to 180 because together they create a straight line, which is 180°.

To solve, set up an equation like this:  \(\frac{2}{3}\)x + x + 40 = 180. Combine the  \(\frac{2}{3}\)x and x to get 1 \(\frac{2}{3}\)x. Then, subtract 40 from both sides and you'll end up with the equation 1 \(\frac{2}{3}\)x = 140.

Divide by sides by 1 \(\frac{2}{3}\) and the answer is x = 84.

Now you know the measure of x. Since angle ACD and angle BCE and vertical angles, they must have the same measure.

To solve, just find the measure of ACD by inputting 84 into the equation x+40. The answer is 124, meaning that the measure of angle BCE is also 124°.

I hope this makes sense and helps! Feel free to ask for clarification! ☺

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

For such more questions on simplified form

https://brainly.com/question/28323654

#SPJ8

Amplitude is the maximum displacement of a function on a graph.

Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.

It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.

But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.

Learn more about amplitude on:

https://brainly.com/question/25699025

#SPJ1

\( \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}\)

Step-by-step explanation:

\( \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54\)

Answer:

Correct ones A and F

------------------------------------------

Correct ones H and K

The square of  x² + 16x + 63 = 0 is given by (x + 8)² = 127.

Given that,
x² + 16x + 63 = 0
To complete the square of above given equation.

Power is the degree of values that are mentioned at the superscript of the value.

Here,
x² + 16x + 63 = 0
Dividing the coefficient of x by 2, and adding and subtracting the square of the quotient.
x² + 16x + 64 - 64 - 63 = 0
(x + 8)² = 127

Thus, the square of  x² + 16x + 63 = 0 is given by (x + 8)² = 127.

Learn more about powers here:
https://brainly.com/question/27809901

#SPJ1