evaluate the expression for the given value of the variuble with step by step explanation
-4b-8 + -1-b^2 +2b^3 b=-2

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 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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Answer:

Step-by-step explanation:

We convert into decimals and then multiply

Otherwise we can convert everything into one unit and then multiply.

10 hg = 1 kg and 100x1000 cg = 1kg

Using this

a. 9 kg 3 hg 1 cg × 9 = 9.300001x9=83.700009 kg

b.  11 dg 4 cg × 12 = 11.400004x12 =16.8000048kg

c. 10 g 5 dg × 6 = 10.5x6 =63.0 kg

d. 5 g 3 dg 4 cg × 8 =5.300004x8 = 42.400032

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)

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

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.

12x - 3y

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

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

Answer: D. Yes because it passes the vertical line test.

Step-by-step explanation

A function cannot have duplicate x-coordinates.

When given a table or a set of coordinates, if there is an x-coordinate that is paired with two different y-coordinates then it is not a function.

When given a graph, the simplest way to determine if it is a function is to use the vertical line test.  If you can draw a vertical line anywhere through the graph and it passes through two points, then it is not a function.

In the given graph, it passes the vertical line test so it IS a function.

Answer: The correct option is (D) (5, -2).

Step-by-step explanation:  We are given to use the method of substitution to solve the following system of equations :

[tex]3x+7y=1~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (ii) in equation (i), we get

[tex]3x+7y=1\\\\\Rightarrow 3x+7(x-7)=1\\\\\Rightarrow 3x+7x-49=1\\\\\Rightarrow 10x=50\\\\\Rightarrow x=\dfrac{50}{10}\\\\\Rightarrow x=5,[/tex]

and from equation (ii) again, we get

[tex]y=x-7=5-7=-2.[/tex]

Thus, the required solution is (x, y) = (5, -2).

Option (D) is CORRECT.

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.

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

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

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:

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!

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]

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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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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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

The answer would be B. x^2+8x+15

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.

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

The complete solution is in image attached.