Ruth makes 35 working 5 hours at her job. How much will she make during an 8 hour workday

box number one: given

box number two: angle addition postulate

box number three: 51 degrees + 39 degrees = m DEF

box number four: 90 degrees = m DEF

box number five: DEF is a right angle

box number six: definition of a right triangle

just took the test and these are the correct answers, hope i helped :)

Solution:

Given : ∠ D E G= 51°, ∠GEF=39°

To prove: Δ D E F is a right triangle.

Proof:

A right angle triangle D E F.

∠ D E F =90°.

Point G is on segment D F, and segment E G is drawn.

Now, taking ∠DEG and ∠GEF into consideration,

∠DEG=51° and ∠GEF=39°→→(Given)

∠DEG + ∠GEF =

∠DEF=51° + 39°

∠DEF=90°,showing Triangle D E F is a right triangle.

The perimeter of a rectangle is twice the sum of the dimensions:

[tex] 2p = 2(w+l) [/tex]

We know two of the three unkowns, so we can solve for w:

[tex] 78 = 2(w+34) \iff 78 = 2w+68 \iff 10=2w \iff w=5 [/tex]

"·" - product

"+" - sum

x² - square of x

Answer: x · (6 + 8 · x²) = x(6 + 8x²)

The expression "the product of x and the sum of 6 and 8 times the square of x" can be written as [tex]\( x \cdot (6 + 8x^2) \)[/tex].

The mathematical expression "the product of x and the sum of 6 and 8 times the square of x" is represented as [tex]\( x \cdot (6 + 8x^2) \)[/tex]. To simplify, distribute x into the parentheses, yielding 6x + 8x^3. This expression captures the specified operation, where x is multiplied by the sum of 6 and 8 times the square of x.

It is essential to follow the order of operations, ensuring that the square of x is calculated first, then multiplied by 8, and finally added to 6 before multiplying the result by x. This expression forms the algebraic representation of the described mathematical operation.

Step 1. Move all terms to one side

[tex]x^2-4x-9-29=0[/tex]

Step 2. Simplify [tex]x^2-4x-9-29[/tex] to [tex]x^2-4x-38[/tex]

[tex]x^2-4x-38=0[/tex]

Step 3. Use the Quadratic Formula

[tex]x=\frac{4+2\sqrt{42} }{2} ,\frac{4-2\sqrt{42} }{2 }[/tex]

Step 4. Simplify solutions

[tex]x = 2 \sqrt{42,} 2-\sqrt{42}[/tex]

Let's solve your equation step-by-step.

[tex]x^{2}[/tex]−4x−9=29

Step 1: Subtract 29 from both sides.

[tex]x^{2}[/tex]−4x−9−29=29−29

[tex]x^{2}[/tex]−4x−38=0

Step 2: Use quadratic formula with a=1, b=-4, c=-38.

[tex]x=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]x=\frac{-(-4)+-\sqrt({-4})^{2} -4(1)(-38)}{2(1)}[/tex]

[tex]x=\frac{4-+\sqrt{168}}{2}[/tex]

Answer:

[tex]x=2+\sqrt{42}[/tex] or x = -2 [tex]\sqrt{42}[/tex]

Divide 5 pages by 3 hours to fins how many pages he wrote in 1 hour:

5 pages /  3 hours = 1 2/3 pages per hour.

Multiply 1 2/3 pages per hour by total hours to find total pages.:

1 2/3 x 8 = 13 1/3 pages (13.33)

Factor a^2−2ab−6by+3ay

a^2−2ab+3ay−6by

=(a−2b)(a+3y)

Answer:

(a−2b)(a+3y)

the factored expression is:

a(a + y) - 2b(a + 3y)

We can factor the expression [tex]a^2-2ab-6by+ay[/tex] using a combination of grouping and factoring by difference of squares:

We can group the terms based on common factors:

[tex](a^2 + ay) - (2ab + 6by)[/tex]

In the first group, a is the common factor: a(a + y)

In the second group, 2b is the common factor: 2b(a + 3y)

Then we combine the terms

a(a + y) - 2b(a + 3y)

Therefore, the factored expression is:

a(a + y) - 2b(a + 3y)

6. These angles are vertical angles, so D. is the correct answer!

7. These angles are not vertical angles, although I don't know what D. is....

8. D) MSN is the correct answer

We can write this line in y-intercept form, and then solve to convert it to standard form.

Y = mx + b

m = slope

b = y-intercept

Y = -1/4x - 2 is the slope-intercept form of the equation.

Now, we can convert this to standard form.

Add 2 to both sides.

y + 2 = -1/4x

Subtract y from both sides.

-1/4x - y = 2

Multiply all terms by -4.

x + 4y = -8 (This is your answer.)

Total investment is =$58500

Annual income produced = $3795

Rate of one investment = 5%

Rate of second investment = 7%

Let the amount invested at 5% be = x

Then, amount invested at 7% rate will be = [tex]58500-x[/tex]

The equation becomes:

5%x + 7%(58500-x) = 3795

= 0.05x + 0.07(58500-x) = 3795

0.05x + 4095 - 0.07x = 3795

0.02x = 300

x = 15000

Hence,  the amount invested at 5% is = $15000

Amount invested at 7% = 58500-15000 = $43500

Answer: The probability lies between 0 and 1

Step-by-step explanation:

As from the given information probability of an event lies between 0% to 100% .

To convert percent into integer or fraction we have to divide it by 100

[tex] 0\%= \frac{0}{100} = 0 [/tex]

And

[tex] 100\% = \frac{100}{100} = 1 [/tex]

From the above the probability of an event lie between integers 0 to 1.

I believe it would be 673.98

I hope this helps :)

673.983 rounded to the nearest hundredth is 673.98, as the third decimal digit (3) is less than 5.

To round the number 673.983 to the nearest hundredth, we need to look at the third decimal place, which is in the thousandths place. If this digit is 5 or greater, we round up. If it is less than 5, we keep the second decimal place as it is. In the case of 673.983, the third decimal digit is a 3, which is less than 5. Therefore, the number rounded to the nearest hundredth is 673.98.

ANSWER

[tex]\frac{4x^4+34x^3+44x^2+11x-27}{x+7}=4x^3+6x^2+2x-3- \frac{6}{x+7}[/tex]

EXPLANATION

See graph in attachment.

Answer

4x³+6x²+2x-3   remainder -6

Explanation

Find the attached  file.

The number 12079 could be said two ways in terms of hundreds, tens, and ones. It can be 'twelve thousand, seventy-nine' or 'one hundred and twenty hundred, seven tens and nine ones'

The number 12079 can be said in two different ways using hundred, tens and ones. First, you could say it as 'twelve thousand, seventy-nine.' This is because 12 is the thousands component (consisting of hundreds and thousands), and 79 is the ones and tens components. Secondly, you could say it as 'one hundred and twenty hundred, seven tens and nine ones'

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1 + 4x = -5 + 7x

1st step: you need to move 4x to the right and -5 to the left so that all the x's are in one place. 4x will be negative and -5 will be positive when you move them. So it will be:

1+5=7x-4x

2nd step:

3x=6

3rd step: you need to divide both sides into 3, because it is the common divisor.

x=2

1 + 4x = -5+7x

7x - 4x = 1 + 5

3x = 6

You can try to memorize the summary. However, it is better to understand the solution as a whole.

If you are just dividing percent's, then each grade would have 12.5 percent.

ANSWER

The solution is

[tex](3,2)[/tex]

EXPLANATION

We were given the equations

[tex]y=4x-10--(1)[/tex]

and

[tex]y=2----equation (2)[/tex]

This is a simultaneous equation in [tex]x[/tex] and [tex]x[/tex].

But the coefficient of [tex]x[/tex] in the second equation is zero. that is why it seems to be absent.

We solve these two equations simultaneously

by putting [tex]y=2[/tex] in to equation (1).

Tis gives;

[tex]2=4x-10[/tex]

We add 10 to both sides to get;

[tex]12=4x[/tex]

we divide through by 4 to get

[tex]3=x[/tex]

Hence the solution for the system is [tex](3,2)[/tex]

Answer:

(3, 2)  

Step-by-step explanation:

12x - 3y

Put the values of x = -14 and y = 3 to the expression:

12(-14) - 3(3) = -168 - 9 = -177

Answer:

2.81 and 0.3 are two decimals that give a product of 8.43 which is close to 8.4

Step-by-step explanation:

let consider a decimal number 0.3

now consider another decimal number 2.81

now if we multiply these two numbers then we get 8.43 which is also a decimal number and it is close to 8.4.

Answer:

Hence the approximate values are 2.91 and 2.89

Step-by-step explanation:

The area of a quadrilateral is expressed as

A=L*B

Where L=length

B=breadth or width

I. e assuming it has two of its sides equal

Say given area is

A=L*B=8.4 square feet

Let's take the square root of the area A=2.898

=2.89

Approximately

L= 2.9 feet

Let's us divide the area by L to get B

8.4/2.9= 2.91

ratio = 12 : 48 = 1 : 4 = [tex]\frac{1}{4}[/tex] as a fraction in simplest form

Aurora used 4 gigabytes of data in September.

To determine how many gigabytes of data Aurora used in September, we need to subtract the fixed phone service charge from her total bill. The difference will represent the additional charges for the data usage. Let's say she used x gigabytes. The equation for her bill can be written as: 65 + 12x = 113. To solve for x, we can subtract 65 from both sides and then divide both sides by 12 to isolate x. Solving this equation, we find that x = 4. So, Aurora used 4 gigabytes of data in September.

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C (third graph, the parabola); To find if it is a function or not draw a vertical line on the graph. If the vertical line could never intercept the figure more than once anywhere on the graph then it is a function.

From left to right of the pictures it's the 3rd photo. It's the 3rd photo because it passes the vertical line test witch means if a vertical line was drawn within the middle of the graph it would only pass through one line and not two. The other ones would pass through two lines instead of one. I hope this helped you!

To find the total change in the number of bushels the farmer has for sale after 5 days, multiply the average number of bushels sold per day by the number of days.

To find the total change in the number of bushels the farmer has for sale after 5 days, we need to multiply the average number of bushels sold per day by the number of days.

The average number of bushels sold per day is 16 and three fourths, which can be written as 16.75.

Multiplying 16.75 by 5 gives us the total change in bushels after 5 days, which is 83.75 bushels.

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Answer:

Domain is the set of all real numbers

Range is the set of all real numbers.

Step-by-step explanation:

Given a graph with curve which has y intercept -5, and x intercept 5.

The graph is  continuous at all points of x and y

We find that the graph is a straight line with positive slope of the form

x/5 +y/-5=1

Or x-y =5

The graph is defined for all values of x and y.

The domain is the set of values x can take  

In the graph horizontal axis is x axis.

Hence from the graph we see that x can take values from -infinity to + infinity

Hence domain is x = R

For range, we consider the values of y as per graph.

WE find that y is  taking values in the interval (-infinity, infinity)

Hence Range =R

The term 'domain' in mathematics refers to the complete set of possible values of the independent variable in a function. The 'range' on the other hand, represents the possible results of the function after an experiment or survey. These values are not always numerical but could be a set of words or phrases.

The domain of a function is the complete set of possible values of the independent variable. In the context of your question, it can be a list such as X = {English, Mathematics,...} representing all the majors offered at a university, or it can be a numerical set, for example Y = {0, 1, 2,...} representing the integers from zero up to the upper limit of classes. Even functions like Z where the domain includes any amount of money from zero upwards can exist.

Similarly, the range of a function is the set of all possible values that the function can take after the experiment is performed or the question is answered. For instance, if a function has a domain of hair color, its range would be the different hair colors like black, blond, gray, green, orange, etc. This shows that the domain and range of a function are not necessarily numerical.

The specific value x the function takes only becomes known after performing the experiment or survey. However, there might be certain values that are outside the domain of the function and as such, would not give a reliable prediction, just like 90 in the dataset from 65 to 75. Such an occurrence doesn't fall within the domain of the function and can't be accurately predicted.

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The number of students that practice the piano more than 3 hours a week is 6

From the dot plot (see attachment), we have the following highlights

Next, we add the total number of students

[tex]Total = 3 + 2 +1[/tex]

[tex]Total = 6[/tex]

Hence, the number of students that practice the piano more than 3 hours a week is 6

Read more about the dot plots at:

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Answer:

1. DF (option 3)

2. segment addition postulate

3. segment congruence postulate

4. DF (option 5)

Answer with explanation:

Given: E is the mid point of DF.

Prove: 2 DE=D F

Proof with explanation:

   It is given that [tex]\Bar{DE}[/tex] is mid point of [tex]\Bar{DF}[/tex].

1.→

 So, [tex]\Bar{DE}\cong\Bar{DF}[/tex]

                       -------------------------By Definition of mid point

2.→ DE=E F----------------Segment Congruence Postulate

3.→DE+E F=D F ----------------Segment Addition Postulate

4.→DE+DE=D F-------------By Substitution

5.→Simplifying gives

  2 DE=D F

integer 1: x

integer 2: x + 2

integer 3: x + 4

integer 4: x + 6

integer 1 + integer 2 + integer 3 + integer 4 = sum

     x       +     x + 2     +      x + 4   +     x + 6     = 300

4x + 12 = 300

      4x = 288

        x = 72

Answer: 72, 74, 76, 78