100 points! Algebra question, photo attached. Please show as much work as possible. Thank you!

Answer:

Step-by-step explanation:

Pythagorean theorem

           (x + 40)² = 60² + x²

x² + 80x + 1600 = 3600 + x²

                   80x = 2000

                      x = 25

Answer:

Current worth of stock is $141.538

Current worth of stock rounded to nearest cent is $142

Step-by-step explanation:

price of stocks= $141

percentage increase in price of stocks = 1.8% of initial price of stock

dollar value increase in price of stocks = 1.8% of initial price of stock

increase in price of stocks = 1.8% of  $141

increase in price of stocks = 1.8/100 * $141 =$ 253.8/100 = $2.538

Current worth of stock = initial price of stock+increase in price of stocks

substituting the value of initial price of stock and increase in price of stocks we have

Current worth of stock =$141 + $2.538 = $141.538

Since we need to find stock worth now, to nearest cent, as after decimal there .5 and any value greater than or equal to .5 is rounded to one then after rounding,  $141.538 becomes  $142

Step 1. The first line has the following two points:

(0, 6) and (4, 9)

The second line has the following points:

(3, 6) and (2, 3)

Step 2. To find the system of equations, we will need to find the line equation for each of the two lines.

To find the equations, we will first find the slope of the lines using the slope equation:

Where (x1, y1) and (x2, y2) are two points on the line.

Step 3. For the first line:

Therefore, the slope is:

Step 4. For the second line:

Therefore, the slope is:

Step 5. Now, to find the equations, we will use the point-slope equation:

Step 6. Substituting the values of (x1,y1) and m for the first line:

Simplifying:

re-writing the equation to have the variables on the left-hand side:

That is the equation of the first line.

Step 7. Substituting the values of (x1,y1) and m for the second line:

Simplifying:

and rewriting the equation to have all of the terms on the left side:

That is the equation of the second line.

Answer:

The area of the rectangle is  (14 + 1/3)  square yards.

We know that for a rectangle of length L and width W, the area is:

A = L*W

Here we know that:

L = (4 + 2/3) yards.

W = (3 + 1/4) yards.

We just need to take the product between these two numbers, we will get:

area =  (4 + 2/3)* (3 + 1/4) yd²

Expanding the product:

(4 + 2/3)* (3 + 1/4) yd² = [ 4*3 + 4*(1/4) + (2/3)*3 + (2/3)*(1/4)] yd²

                                    = [ 12 + 1 + 2 + 2/6] yd²

                                     = (14 + 1/3)  yd²

That is the area of the rectangle.

Learn more about rectangles at:

https://brainly.com/question/17297081

#SPJ1

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

Learn more about radius of circle here: https://brainly.com/question/12269818

#SPJ1

1. Variable: A symbol or letter that represents an unknown value or quantity in algebraic expressions and equations.

2. Equation: A mathematical statement that shows the equality between two expressions, typically represented by an equal sign (=).

3. Coefficient: The numerical factor that is multiplied by a variable in a term.

4. Expression: A mathematical phrase that may contain variables, constants, and operations, but does not have an equal sign.

5. Linear Equation: An equation in which the highest power of the variable is 1, written in the form ax + b = 0, where a and b are constants and x is the variable.

Variable: In algebra, a variable is a symbol (usually a letter) that represents an unknown value or quantity. It allows us to express mathematical relationships and solve equations.

Equation: An equation is a mathematical statement that shows the equality between two expressions.

It consists of an equal sign (=) and can include variables, constants, and operations.

Solving equations involves finding the values of the variables that make the equation true.

Coefficient: A coefficient is the numerical factor that is multiplied by a variable in a term.

It represents the scale or magnitude of the variable.

For example, in the term 3x, the coefficient is 3.

Expression:

An expression is a mathematical phrase that can contain variables, constants, and operations, but does not have an equal sign.

Expressions can be evaluated or simplified, but they cannot be solved since they lack the equality found in equations.

Linear Equation:

A linear equation is an equation where the highest power of the variable is 1.

It can be written in the form ax + b = 0,

where a and b are constants and x is the variable.

Solving linear equations involves finding the value(s) of x that satisfy the equation.

These are just a few key definitions that form the foundation of understanding introductory algebra.

Mastering these concepts will provide a solid basis for further exploration and learning in algebraic principles and problem-solving.

For  similar question on algebraic expressions.  

https://brainly.com/question/4344214  

#SPJ8

Answer:

33°

Step-by-step explanation:

you add the two numbers together and subtract from 180° to get your answer

\(\\ \sf\longmapsto x+4-5x-2\)

\(\\ \sf\longmapsto x-5x+4-2\)

\(\\ \sf\longmapsto -4x+2\)

\(\\ \sf\longmapsto -2(2x+1)\)

Answer:

-4x + 2

Step-by-step explanation:

Combine like terms.

\(x+4-5x-2\\-4x+2\)

Answer:

7/30

Explanation:

To write the ratio in its simplest form, we first convert hours to minutes

1 hr = 60 min

4 hrs = 240 min

Therefore,

Dividing both the numerator and the denominator by 8 gives

Hence, the simplest ratio is 7 / 30.

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

Learn more about confidence intervals;

https://brainly.com/question/24131141

#SPJ1

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

For more such questions on interest rates, click on:

https://brainly.com/question/25720319

#SPJ8

Answer:

Scott is C) 20

Step-by-step explanation:

Twice Evan's age would be 24

4 years less than that would be 20

Answer: D

Step-by-step explanation:

Evan=x

Scott=2x-4

Evan=12

So 2x-4=12

So 2x=16

And x=8

Answer:

See below

Step-by-step explanation:

\(\overline{X} \cdot\overline{Z} +\overline{X} \cdot Y + \overline{X} \cdot Z +XY\)

\(=\overline{X} (\overline{Z}+Y+Z) +XY\)

Recall that

\(\overline{Z} + Z = 1\)

and the identity \(\boxed{A \cdot 1 = A}\), therefore

\(\overline{X} (\overline{Z}+Y+Z) = \overline{X}\) because \(\overline{Z}+Y+Z\) will always be \(1\).

Thus,

\(\overline{X} \cdot\overline{Z} +\overline{X} \cdot Y + \overline{X} \cdot Z +XY\)

\(=\overline{X} (\overline{Z}+Y+Z) +XY\)

\(= \overline{X} + XY\)

Now considering the Absorption Law,

\(( \overline{A} \cdot \overline{B}) + B = (\overline{A}+ B) \cdot (\overline{B} +B)\)

Once \(\overline{B}+B=1\), therefore

\(\overline{A} +B\)

we know

\(= \overline{X} + XY = \boxed{\overline{X} +Y}\)

Answer: the answer is 4

Step-by-step explanation:

Answer:

I think its 229

if you take how many yellow marbles he got out of 7 it would be 3/7 and then I divided 400 by 7 and got 57. something so I multiplied 3 times 57 and got 171. So if you take 400-171 you get 229

The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:

2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person

So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

Learn more about fractions here:
https://brainly.com/question/30193711

#SPJ9

Answer:

3/5

Step-by-step explanation:

Answer: I would say 3 divided by 2 or it would be 3/2.

Step-by-step explanation: Hit me up if i got it right:)

A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point X (0, 4)  →  Coordinates of point Y = (0, -4)

Coordinates of point X (1, 3)  →  Coordinates of point Y = (-1, -3)

In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.

Read more on rotation here: brainly.com/question/28515054

#SPJ1

When the base and the height of a triangle are the same. the hypotenuse is that number times sqrt2.

B and C are 7, so a would also be 7

Answer:

n = -24/7

Step-by-step explanation:

3 -7n = 27

-7n = 24         Subtract 3 from both sides

n = -24/7        Divided by -7 both sides

So, the answer is n = -24/7

Answer:

Below

Step-by-step explanation:

Subtract 3 from both sides of the equation THEN divide both sides of the equation by  - 7

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

for more such question on matrix visit

https://brainly.com/question/2456804

#SPJ8

Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

Answer:

Option B. is correct

Step-by-step explanation:

Let \(x\) denotes time taken by Mia alone to clean the room and \(y\) denotes time taken by Holly alone to clean the room.

As Mia and Holly can clean their room in 20 min, working together,

\(\frac{1}{x}+\frac{1}{y} =\frac{1}{20}\,\,\,...(i)\)      

Also,

Mia, working alone, can do the job in 30 min.

So,

\(\frac{1}{x}=\frac{1}{30}\,\,\,\,\,...(ii)\)

Put (ii) in (i)

\(\frac{1}{30}+\frac{1}{y}=\frac{1}{20}\\\frac{1}{y}=\frac{1}{20}-\frac{1}{30}\\\frac{1}{y}=\frac{3-2}{60} \\\frac{1}{y}=\frac{1}{60}\)

Therefore,

Holly can clean the room alone in 60 minutes.

Option B. is correct

Answer:

its a right angle and a its an acute angle as well so it be 5

c)there are not interval in which the function is constant

Explanation

Step 1

The interval is increasing if the value of the function f(x) increases with an increase in the value of x and it is decreasing if f(x) decreases with a decrease in x

so,let's check the graph

so, we can see the function is increasing starting at zero,so

and

b) decreasing

when a function is constant , the graph is a horizontal line, we can't see any horizontal line in eh graph, so we can conclude

there are not intervals in which the function is constant

I hope this helps you