Based on the graph, what is the initial value of the linear relationship?

(A) −2
(B) 0
(C) 2/3
(D) 3

The expression [tex]\(5x + 2x - 3\)[/tex] is a linear expression.

The expression [tex]\(5x + 2x - 3\)[/tex] represents a linear expression because it consists of terms involving only the variable \(x\) raised to the power of 1. In other words, each term is a linear term.

Linear expressions depict relationships that are straight lines when graphed on a Cartesian plane. In this case, \(5x\) and \(2x\) are both linear terms since they involve the variable \(x\) raised to the first power, while the constant term \(-3\) does not involve \(x\) at all.

The expression simplifies to [tex]\(7x - 3\),[/tex] maintaining its linear form. Linear expressions are fundamental in algebra and represent relationships with constant rates of change.

This is an arithmetic sequence

The value of the 3rd term is 72

There are 4 terms in this sequence

The sequence starts at 60 and adds 6 repeatedly

Answer:

b, c, f, g

Step-by-step explanation:

Answer:

[tex]\large\boxed{f(x)-g(x)=x^2+2x+6}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2+1\\\\g(x)=2x-5\\\\f(x)-g(x)=(x^2+1)-(2x-5)\\\\f(x)-g(x)=x^2+1-2x-(-5)\\\\f(x)-g(x)=x^2+1-2x+5\qquad\text{combine like terms}\\\\f(x)-g(x)=x^2+2x+(1+5)\\\\f(x)-g(x)=x^2+2x+6[/tex]

Final answer:

To identify where an error might have occurred, students should be aware of common mistakes, review personal feedback, and reflect on their thought processes. This helps in understanding and correcting errors, leading to improvement in critical and reflective thinking.

Explanation:

The first step in identifying an error in a student's work is to be cognizant of common mistakes that students make. By reviewing a common errors list and reflecting upon feedback from instructors, a student can pinpoint problem areas in his or her academic practice. Starting with the prediction and diagnosis of one's own learning process is essential. This may include recognizing patterns in mistakes, understanding why an error was made, or consulting with a teacher for further clarification. Once the source of the error is identified, the student can work on corrective measures to avoid similar issues in the future. Frequently, errors in thinking or application are not due to a lack of intelligence, but rather to the way our minds are wired, leading to characteristic mistakes that can be anticipated and mitigated with practice and reflection.

Answer:

x=+-4

Step-by-step explanation:

Answer:

630

Step-by-step explanation:

if you add the percentages of the trucks, sport cars and vans you get:

30% + 25% + 10% = 65%. So to find the percentage of vehicles that aren't in this categories you substract this percentage from 100%.

100% - 65% = 35%

This means that 35% of the vehicles aren't in those categories, so to find the amount you just multiply the total of vehicles with the percentage an then divide by 100

(1,800*35)/100 = 630 vehicles

Answer:

In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list statements and the reasons the statements are true.

A paragraph proof is a two-column proof in sentence form.

Step-by-step explanation:

A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column

The statements regarding proofs are,

(1)In a paragraph proof, statements and their justifications are written in sentences in a logical order.

2. A two-column proof consists of a list of statements and the reasons the statements are true and

(4) A paragraph proof is a two-column proof in sentence form.

We have given that the statement is,In a paragraph proof, statements and their justifications are written in sentences in a logical order.

A two-column proof consists of a list of statements and the reasons the statements are true.

A flowchart proof gives a visual representation of the sequence of steps without justifications.

A paragraph proof is a two-column proof in sentence form.

A flowchart proof gives a visual representation of the sequence of steps without justifications.

A paragraph proof is a two-column proof in sentence form.

A two-column proof lists only the given information and what is to be proven.

Logical order is when all of the messages and segments within a group are in their logical sequence.

So we have the correct statements are

A paragraph proof is only a two-column proof written in sentences. However, since it is easy to leave steps out when writing a paragraph proof.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true.

The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column

Therefore the statement 1. 2 and 4 are true.

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Answer:

$45

Step-by-step explanation:

Multiply 4.5 by 5 to give you the total amount lost over 5 days,which is 22.5. If you lost 22.5 and started with 67.5, subtract the two to get your answer

Answer:

Part 1) The number is 0.008

Part 2) The number is 0.05

Step-by-step explanation:

Part 1) we have

0.08 is ten times great as ...

That means----> 10 times a number is equal to 0.08

Let

x -----> the number

To find the number divide 0,08 by ten  

so

0.08=10x

x=0.08/10

x=0.008

Part 2) we have

0.5 is ten times great as...

That means----> 10 times a number is equal to 0.5

Let

x -----> the number

To find the number divide 0,5 by ten  

so

0.5=10x

x=0.5/10

x=0.05

Answer:

$528.92

Step-by-step explanation:

The subscription given is $499 plus 8% tax

Add tax

108/100 * $499 = $538.92

$538.92 for 30 days.

If its being promoted for 7 days there is a $10 off coupon, this will be;

$538.92-$10 = $528.92

Final cost = $528.92

Answer:Communitive Property

Step-by-step explanation: You can only do this property with addition and multiplication because you are able to switch the places and still get the same answer

Answer:

[tex]g(x) = x + 2[/tex]

Step-by-step explanation:

Parent function [tex]f(x) = x + 5[/tex], is shifted 3 units to the right.

If f(x) is shifted 'a' units to the right then f(x) becomes f(x-a)

If f(x) is shifted 'a' units to the left then f(x) becomes f(x+a)

[tex]f(x) = x + 5[/tex], is shifted 3 units to the right.

Then we subtract 3 from x

So , [tex]f(x) = x + 5[/tex] becomes [tex]f(x-3) = x-3 + 5=x+2[/tex]

[tex]g(x) = x + 2[/tex]

The equation of function will be;

g (x) = x + 2

Option d is true.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

Parent function, f(x) = x + 5 is shifted 3 units to the right.

Since, If a function f(x) is shifted 'a' units to the right then function f(x) becomes f(x-a).

So, The equation of function will be calculated as;

The parent function is shifted 3 units to the right.

Then, we subtract 3 as;

g (x) = x + 5 - 3

g (x) = x + 2

Thus, The equation of function will be;

g (x) = x + 2

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Answer: the correct answer is B

The correct option is C. 3 ÷ 1 > 3 ÷ 3.

To solve this problem, we need to evaluate each of the given number sentences to determine which one is true.

A. 3 ÷ 1 < 0 ÷ 3

First, we perform the divisions:

3 ÷ 1 = 3

0 ÷ 3 = 0

Now we compare the results:

3 < 0

This statement is false because 3 is not less than 0.

B. 0 ÷ 3 > 3 ÷ 3

Again, we perform the divisions:

0 ÷ 3 = 0

3 ÷ 3 = 1

Now we compare the results:

0 > 1

This statement is false because 0 is not greater than 1.

C. 3 ÷ 1 > 3 ÷ 3

We perform the divisions:

3 ÷ 1 = 3

3 ÷ 3 = 1

Now we compare the results:

3 > 1

This statement is true because 3 is greater than 1.

D. 3 ÷ 3 < 4 ÷ 4

We perform the divisions:

3 ÷ 3 = 1

4 ÷ 4 = 1

Now we compare the results:

1 < 1

This statement is false because 1 is not less than 1; they are equal.

Therefore, the only true statement is C. 3 ÷ 1 > 3 ÷ 3.

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

The required, 5.241 divided by 3 equals approximately 1.747.

To divide 5.241 by 3, we can perform the division as follows:

    1.747

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

3 | 5.241

To start, we divide the whole number part, 5, by 3. The result is 1, which becomes the whole number part of the quotient.

Next, we bring down the decimal point and consider the decimal part of the dividend, which is 0.241. We can continue the division process by adding a decimal point to the quotient and placing a 0 to the right of the decimal point.

   1.747

 3 | 5.241

     - 3

     -----

       24

Now, we divide 24 by 3, which gives us 8. We bring down the next decimal digit, which is 1, and continue the division:

   1.747

 3 | 5.241

     - 3

      -----

       24

     - 24

      -----

         1

Since there are no more decimal digits to bring down, we have finished the division. The final quotient is 1.747, rounded to three decimal places.

Therefore, 5.241 divided by 3 equals approximately 1.747.

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Answer:

6 AO

Step-by-step explanation:

If you compare the vector formed with AO it is 6 AO.

You can do it mathematically too converting each point in coordinates (x, y). But since it didnt say how to do it, the simplest is just drawing an hexagon and summing the vectors

Answer:

2.5

Step-by-step explanation:

Use the given functions to set up and simplify  

D

.

x

=

0.5

x

+

4

+

0.9

x

=

x

+

5

=

x

=

2.5

A

=

x

=

2.5

x

=

2.4

=

x

=

2.5

B

=

x

=

2.5

x

=

0.42

=

x

=

2.5

C

=

x

=

2.5

x

=

0.4

=

x

=

2.5

D

=

x

=

2.5

x

=

2.5

=

x

=

2.5

The solution for x in the equation 0.5x + 4 + 0.9x = x + 5 is 2.5.

Given that:

0.5x + 4 + 0.9x = x + 5

It is required to find the value of x.

In order to find the value of x, first operate the like terms together and then solve it to find the value of x.

Consider,

0.5x + 4 + 0.9x = x + 5

1.4x + 4 = x + 5

Subtract both sides by x.

0.4x + 4 = 5

Subtract both sides by 4.

0.4x = 5 - 4

0.4x = 1

Now, divide both sides by 0.4.

x = 1 / 0.4

x = 2.5

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Answer:

She should earn $540 in a 40 hour week

Step-by-step explanation:

we know that

Her pay for 22 hours is $297

so

using proportion

Find out how much should she earn in a 40 hours week

[tex]\frac{22}{297}=\frac{40}{x}\\\\x=297*40/22\\\\x= \$540[/tex]

Answer:

x = - 1.10 and x = 1.10

Step-by-step explanation:

Given

25x² - 30 = 0 ( add 30 to both sides )

25x² = 30 ( divide both sides by 25 )

x² = [tex]\frac{30}{25}[/tex] ( take the square root of both sides )

x = ± [tex]\sqrt{\frac{30}{25} }[/tex]

x = - 1.10 and x = 1.10 ( to the nearest hundredth )

The correct answer is a.  x = -1.10 and  x = 1.10 .

To solve the quadratic equation [tex]\( 25x^2 - 30 = 0 \)[/tex], we first add 30 to both sides of the equation to isolate the quadratic term:

[tex]\[ 25x^2 = 30 \][/tex]

Next, we divide both sides by 25 to solve for [tex]\( x^2 \)[/tex]:

[tex]\[ x^2 = \frac{30}{25} \] \[ x^2 = 1.2 \][/tex]

 Now, we take the square root of both sides to solve for x. Remember that when taking the square root of a number, we must consider both the positive and negative square roots:

[tex]\[ x = \pm\sqrt{1.2} \][/tex]

Using a calculator, we find the square root of 1.2 and round to the nearest hundredth:

[tex]\[ x = \pm1.095445115... \][/tex]

Rounded to the nearest hundredth, the solutions are:

[tex]\[ x = -1.10 \] \[ x = 1.10 \][/tex]

Therefore, the correct options are  x = -1.10 and  x = 1.10 . The other options provided [tex](\( x = -26.15 \)[/tex] and x = 1.15 ,  x = 0 ,  x = -0.83  and  x = 0.83 are incorrect and do not satisfy the original equation.

The complete question is- Solve [tex]25x^2-30=0[/tex]

Round the answer to the nearest hundredth

a. x=-1.10 and x=1.10

b. x=-26.15 and x=1.15

c. x=0

d. x=-0.83 and x=0.83​

Answer:

25% of the students were absent.

Step-by-step explanation:

100/392=0.26*98=25

To check 25%=1/4

so, 98*4=392

which makes sense.

Answer: 7/12

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

The problem is asking us to find what fraction of students watch between 0 and 2 hours of TV a day:

The information we have is:

0 - 1 hours = 1/6

1 1/2 - 2 hours = 5/12

We only need this information because it is asking us for 0 to 2 hours.

Now we have to add the fraction of students that watch TV 0-1 hours and the fraction of students watch TV 1 1/2 - 2 hours:

1/6 + 5/12

To be able to solve this we have to have the same denominator and to do it we have to multiply the first fraction by 2:

(1/6) *2 = 2/12

Now we can add:

2/12 + 5/12 = 7/12

We add the numerators and the denominator stays the same.

Answer:

it's the third one

Step-by-step explanation:

Answer:

x = 45

Step-by-step explanation:

The average is calculated as

average = [tex]\frac{score}{count}[/tex]

here the average = 50 , thus

[tex]\frac{36+44+75+x}{4}[/tex] = 50

Multiply both sides by 4

36 + 44 + 75 + x = 200

155 + x = 200 ( subtract 155 from both sides )

x = 45

The answer is [tex]-28w^2[/tex]

Answer:solution

Step-by-step explanation:

I got it right

Answer:

55%

Step-by-step explanation:

all you have to do is divide 114.4 by 208 to get 0.55, then turn that into a percentage by moving the decimal 2 times to the right.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\begin{array}{ccc}208&-&100\%\\\\114.4&-&p\%\end{array}\qquad\text{cross multiply}\\\\208p=(100)(114.4)\\\\208p=11440\qquad\text{divide both sides by 208}\\\\p=\dfrac{11440}{208}\\\\p=55[/tex]

[tex]\bold{METHOD\ 2}\\\\\text{Calculate the quotient of given numbers and convert it to the percent:}\\\\\dfrac{114.4}{208}=0.55\\\\0.55\cdot100\%=55\%[/tex]

In order to get the answer to this question you will have to multiply the whole number as many times as it's exponent so in this case you will have to multiply 10, 15 times.

[tex]10^{15}[/tex]

[tex]10^{15} = 10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10[/tex]

[tex]10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10 = 1000000000000000[/tex]

[tex]= 1000000000000000[/tex]

Therefore your answer is "1,000,000,000,000,000."

Hope this helps.

For this case we have the following solutions:

[tex]x_ {1} = 1 + \sqrt {5}\\x_ {2} = 1- \sqrt {5}[/tex]

Then, the factorized equation is of the form:

[tex](x- (1+ \sqrt {5})) (x- (1- \sqrt {5})) = 0\\(x-a) (x-b) = 0[/tex]

We apply distributive property:

[tex]x ^ 2-bx-ax + ab = 0\\x ^ 2- (1- \sqrt {5}) x- (1+ \sqrt {5}) x + (1+ \sqrt {5}) (1- \sqrt {5}) = 0\\x ^ 2-x + \sqrt {5} x-x- \sqrt {5} x + (1 ^ 2- \sqrt {5} + \sqrt {5} - (\sqrt {5}) ^ 2) = 0\\x ^ 2-2x + (1-5) = 0\\x ^ 2-2x-4 = 0[/tex]

ANswer:

The equation is [tex]x ^ 2-2x-4[/tex]