Evaluate the Function at each specified value ​

The value of x in the equation (x – 0.8) / 1.2 = 6 is 8.

Given,

The equation = (x – 0.8) / 1.2 = 6

We have to expand this equation and find x.

That is,

(x – 0.8) / 1.2 = 6

Multiply 1.2 both sides.

(x – 0.8) x (1.2) / 1.2 = 6 x 1.2

(x – 0.8) = 6 x 1.2

(x – 0.8) = 7.2

Shift 0.8 to right hand side

Then we get,

x = 7.2 + 0.8

x = 8

Therefore, the value of x in the equation (x – 0.8) / 1.2 = 6 is 8.

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Based on the cost of the car and the simple interest loan amount, the amount of Darren's monthly payment is $363.33

First, find the simple interest on the loan:

= 12,000 x 3% x 3 years

= $1,080

The total amount to be repaid:

= 1,080 + 12,000

= $13,080

The monthly payment is:

= 13,080 / (12 x 3 years)

= $363.33

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Answer: its 363.33

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

3/4 = 6/8. so 6/8-1/8= 5/8. 5/8 is the answer.

The value of logarithmic expression x log₄m+1/y log₄n - log₄p is log₄(m^x  * n^1/4)/p.

By considering the given logarithmic expression

x log₄m+1/y log₄n - log₄p

log₄m^x+  log₄n^1/4- log₄p

log₄(m^x  * n^1/4)- log₄p

log₄(m^x  * n^1/4)/p

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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The given number written in scientific notation is 1.4398 × 10⁴

From the question, we are to write the given number in scientific notation.

The given number is 14,398.

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Thus,

To write the numbers in scientific notation, we will express the number as the multiplication of a number between 1 and 10 and a power of 10.

A number between 1 and 10 that can easily be formed from the number is 1.4398

Then, we can write that

14,398 = 1.4398 × 10⁴

Hence, the given number written in scientific notation is 1.4398 × 10⁴

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In percentage, the 10% of her collection is a 18 coins.

According to the statement

We have to find that the 10% of her collection.

So, For this purpose, we know that the

A percentage is a number or ratio expressed as a fraction of 100.

From the given information:

Aisha has a collection of 180 coins. how many coins represent 10% of her collection

Then

The percentage of the collections of the 180 coins = 10% of 180 coins

Then

Collection of the coins = 10% of 180

Collection of the coins = 10/100*180

Collection of the coins = 0.1*180

Collection of the coins = 18.

So, In percentage, the 10% of her collection is a 18.

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Answer:

if x=2

P(2) = (2)² + 5(2) -3

= 4 + 10 - 3

= 14 - 3

= 11

Answer:D

Step-by-step explanation:  3 over 9 = .333 repeating which is greater then .22 and lower then 33

The fifth term of the arithmetic sequence is 84

The formula for determining the nth term of an arithmetic sequence is expressed as;

Tn = a + (n -1)d

Where;

To determine the fifth term, we have to substitute the value of nas 5, we have;

T5 = 4 + (5-1) 20

T5 = 4 + 4(20)

expand the bracket

T5 = 4 + 80

T5 = 84

Thus, the fifth term of the arithmetic sequence is 84

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The complete question;

An arithmetic sequence has first term 4 and constant difference 20. Find the fifth term of the sequence

The logarithmic form of the given equation (5⁴=625)is  = log₅(625) = 4.

Logarithmic functions are the inverses of exponential functions. So a log is an exponent! y=logbx if and only if by=x for every x>0 and 0b1.

Logarithms depict changes in terms or multiplication: in the instances above, each step is 10x larger. Each step on the natural log is "e" (2.71828...) times longer. When dealing with a sequence of multiplications, logarithms let us "count" them in the same way that addition counts on our behalf when effects are added.

using the property of log:

5⁴=625

Apply logarithmic definition: aⁿ = b gives logₐᵇ = n

so,

a = 5

b = 625

n = 4

equation would be as follows:

log₅(625) = 4

The  logarithmic form of the given equation (5⁴=625)is  = log₅(625) = 4

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Answer: [tex]log_{5} 625 = 4[/tex]

Step-by-step explanation:

The ratio that relates the number of students who take a music class to the number of students who take an art class is 3 : 1 .

Let the number of students taking arts class be "x"

and number of students taking music class be "y".

It is given that 11 students take an art class which can be given by

                x = 11           ...(1)

There are 3 times as many students who take a music class as students who take an art class which can be given by

             y = 3x = 3(11) = 33       ....(2)

On dividing equation (1) by (3) , we get

          x/y = 11/33 = 1/3

This can be written as x : y = 1 : 3 but here we are asked about the ratio of music class to the art class then ratio is given by y : x = 3 : 1

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The stated logarithm equation log₇8 in changed by the Base Formula is logₓ8 - logₓ 7.

A logarithmic notation is one where variable x contains a logarithm.

The variable in an exponential equation is depicted by an exponent. To solve exponential equations, first see if both sides of the formula could be written as powers of the same number. If you can't, consider taking the common logarithm of both equation sides and solve the problem using property.

Now, as per the stated conditions;

The given equation is; log₇8

Apply the Base Rule and re-write the equation;

= logₓ8 / logₓ 7

This obtained equation can also be written on the form by applying product rule.

=  logₓ8 - logₓ 7

Therefore, the logarithm equation log₇8 in expressed by the Base Formula is logₓ8 - logₓ 7.

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The statements that describes the effect and value of k in the functions f(x) = −x + 3 and g(x) as shown in the graph where function g(x) is a transformation of f(x), such that g(x) = kf(x) and k is a rational number, is

a. The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.

A vertical stretch refers to a movement in the upward direction. A transformation that leads to a vertical stretch is as a result of multiplying by a positive number that is above or greater than 1.

The given graphs f(x) was factored and this lead to a vertical stretch to produce g(x), and the factor that leads to vertical stretch is a positive number greater that 1. Hence we say that The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.

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The value of the given fraction 3/8 - 8/11 after the evaluation is -31/88.

So, evaluation of 3/8 - 8/11:

Now,

Therefore, the value of fraction 3/8 - 8/11 after the solution is -31/88.

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Answer:

0.25

Step-by-step explanation:

group like terms: 0.42b+9.14b-8.3=-5.91

add similar elements: 9.56b-8.3=-5.91

multiply both sides by 100: 956b-830=-591

add 830 to both sides: 956b-830+830=-591+830

simplify: 956b=239

divide each side by 956: you know what that looks like

simplify: b=1/4

convert to decimal: 0.25

Answer:

b = 0.25

Step-by-step explanation:

Given:

[tex]\sf 0.42b - 8.3 + 9.14b = -5.91[/tex]

Collect like terms:

[tex]\implies\sf 0.42b+ 9.14b - 8.3 = -5.91[/tex]

Combine like terms:

[tex]\implies \sf 9.56b - 8.3 = -5.91[/tex]

Add 8.3 to both sides:

[tex]\implies \sf 9.56b - 8.3+8.3 = -5.91+8.3[/tex]

[tex]\implies \sf 9.56b=2.39[/tex]

Multiply both sides by 100:

[tex]\implies \sf 9.56b \times 100=2.39 \times 100[/tex]

[tex]\implies \sf 956b=239[/tex]

Divide both sides by 956:

[tex]\implies \sf \dfrac{956b}{956}=\dfrac{239}{956}[/tex]

[tex]\implies \sf b=\dfrac{239}{956}[/tex]

Write 956 as 4 × 239:

[tex]\implies \sf b=\dfrac{1 \times 239}{4 \times 239}[/tex]

Cancel the common factor 239:

[tex]\implies \sf b=\dfrac{1}{4}[/tex]

[tex]\implies \sf b=0.25[/tex]

The measure of the segment MP is 29 units.

In this question we have been given a parallelogram LMNO

The diagonals of parallelogram LMNO intersect at point P.

The diagonals of parallelogram LMNO are LN and MO.

The point P divides each diagonal into exactly two equal parts.

So, MP = OP

If MP = 2x + 5 and OP = 3x − 7, we need to find MP.

As, MP = OP

2x + 5 = 3x − 7

2x - 3x = -7 - 5

-x = -12

x = 12

So, the value of the MP would be,

MP = 2x + 5

      = 2(12) + 5

      = 24 + 5

      = 29

Therefore, the measure of the segment MP is 29 units.

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Answer:

y = 3/4x - 8

Step-by-step explanation:

The scale factor of △DEC to △RST is 13 : 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

A multiplicative inverse or reciprocal for a number y, denoted by 1/y or y⁻¹, is a number that when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction b/a is a/b.

The scale factor of △RST to △DEC is 3 : 13.

Now, △DEC to △RST is the inverse of  △RST to △DEC

Therefore,

[tex]\frac{\Delta RST}{\Delta DEC} = \frac{3}{13}[/tex]

[tex]\frac{\Delta DEC}{\Delta RST} =\frac{13}{3}[/tex]

Hence, the scale factor of △DEC to △RST is 13 : 3.

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The value of the given expression √9x⁴/ 36 in simplified form is  x² / 2.

√ 9x⁴ / 36

= √ 9 x⁴ / 9*4

= √ x⁴ / 4

4 = 2*2 = ( 2 )²  and x⁴ = x² * x² = ( x² )²

hence, √ x⁴ / 4 = ( x² / 2 )²

√ x⁴ / 4  = x² / 2

Therefore,  the value of the given expression √9x⁴/ 36 in simplified form is  x² / 2

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Answer:

a) -3

b)12

Step-by-step explanation:

For f(X)= 3x+2

Where x=-2(Substitute for x in the expression)

F(-2)=3(-2)+2

      = -6+2

       = -3

G(4)=

[tex]x^{2} -x\\4^{2} -4\\=16-4\\=12[/tex]

Answer:

The answer is in the attached screenshot (I wanted to show properly formatted fractions)

Explanation:

The explanation is in the attached screenshot (I wanted to show a properly formatted fraction)

Answer:

3.7

Step-by-step explanation:

Triangles BDE and BCE are congruent, so BC=BD=3.7.

Answer:

speed

Step-by-step explanation:

speed is the right answer hope its right

The actual dimensions of the bookcase is 234 cm tall, 162 cm wide and 30 cm deep

An equation is an expression that shows the relationship between two or more numbers and variables.

The scale of 1:30 is used to produce a diagram of a bookcase in an instruction booklet.

If the diagram is 7.8 cm tall 5.4 wide and 1 cm deep, hence:

Height of bookcase = 7.8 cm * 30 = 234 cm

Width of bookcase = 5.4 cm * 30 = 162 cm

Depth of bookcase = 1 cm * 30 = 30 cm

The actual dimensions of the bookcase is 234 cm tall, 162 cm wide and 30 cm deep

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the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

Given:

To find: Year when population is 8 billion, i.e., y = 8.

Finding:

8 = 6.72  ( [tex]1.014^x[/tex])

=> [tex]\frac{8}{6.72}= ( 1.014^x)[/tex]

Taking log on both sides

=> [tex]log(\frac{8}{6.72})= log( 1.014^x)[/tex]

=> log(1.19) = x (log 1.014) (as [tex]log_b(a)^m = m (log_b(a))[/tex] )

=> [tex]\frac{log(1.19)}{log (1.014)}[/tex] = x

=> x = [tex]\frac{0.0755}{0.006}[/tex]

=> x = 12.58

Hence, the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

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The value of (fof)(3) is 21.

When two or more functions are combined to form a new function, the new function is known as a composite function. For example- if there is a function f(x), then fof(x) is a composite function formed by repeating f(x) twice.

Here, we are given a function- f(x) = x + 9

if we put the value of x = 3, we get-f(3) = 3 + 9f(3) = 12

now, we need to find the value of (fof)(3)

This can also be written as- {f(f(3)}

we know that f(3) = 12

⇒ {f(f(3)} = f(12)

f(12) = 12 + 9f

(12) = 21

Thus, the value of (fof)(3) is 21.

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Your question was incomplete. Check for full content below-

f(x) = x + 9

What is (fof)(3)?

(F) 1 (G) 5 (H) 21 (I) 77

Calvin is incorrect. He should add 2 to each side not multiply each side by 2.

The correct answer is an option (C)

For given question,

Let l be the length of the rectangle and w be the width of the rectangle.

Assume that l = 10 units and w = 4 units

The perimeter of the rectangle is,

P = 2(length + width)

So, for above values the perimeter of the rectangle would be,

⇒ P1 = 2×(10 + 4)

⇒ P1 = 28 units

The length of each side is increased by 2 units.

so, l = 12 and w = 6 units

Then the perimeter of the rectangle would be,

P2 = 2(12 + 6)

P2 = 36 units

According to Calvin, if the length of each side of rectangle is increased by 2 units, the perimeter of the rectangle would double.

But from P1 and P2 we can clearly observe that, Calvin is incorrect.

Calvin possibly double the each side of the rectangle instead of increasing by 2 units.

If he double each side then l = 20 and w = 8

The perimeter of the rectangle would be,

P3 = 2(20 + 8)

P3 = 56

From P1 and P3, the perimeter of the rectangle is doubled.

Therefore,  Calvin is incorrect. He should add 2 to each side not multiply each side by 2.

The correct answer is an option (C)

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