Evaluate the expression when
x = 6.
x² +8x-3

Answer:

[tex]g(x)=\log_3(x+4)[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

  [tex]f(x)=\log_3x[/tex]

From inspection of the graph:

If there was a vertical translation, the end behaviors of both g(x) and f(x) would be the same in that the both functions would be increasing from -∞ in quadrant IV.

As the x-intercepts of both functions is different, and g(x) increases from -∞ in quadrant III, this indicates that there has been a horizontal translation of 4 units to the left.

Therefore:

[tex]g(x)=f(x+4)=\log_3(x+4)[/tex]

Further Proof

Logs of zero or negative numbers are undefined.

From inspection of the graph, [tex]x=-3[/tex] is part of the domain of g(x).

Therefore, input this value of x into the answer options:

 [tex]g(-3)=\log_3(-3)-4\implies[/tex] undefined

 [tex]g(-3)=\log_3(-3)+4\implies[/tex] undefined

 [tex]g(-3)=\log_3(-3-4)=\log_3(-7)=\implies[/tex] undefined

 [tex]g(-3)=\log_3(-3+4)=\log_3(1)=0[/tex]

Hence proving that [tex]g(x)=\log_3(x+4)[/tex]

The equation that represents g(x) is:  [tex]g(x) = log_3(x + 4)[/tex]

The correct answer is: the fourth option:

[tex]g(x) = log_3(x + 4)[/tex].

Here, we have to find the equation that represents g(x) using f(x), we need to consider how the graph of g(x) is related to the graph of f(x).

The graph of f(x) = log base 3 of x starts from negative infinity in quadrant four, passes through (0, 1), and increases to positive infinity.

The graph of g(x) is increasing from negative infinity in quadrant two, passes through (0, -3), and increases to positive infinity.

So, we can see that the graph of g(x) is the graph of f(x) shifted 4 units to the left along the x-axis.

Therefore, the equation that represents g(x) is:

[tex]g(x) = log_3(x + 4)[/tex]

The correct answer is: the fourth option:

[tex]g(x) = log_3(x + 4)[/tex].

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Step-by-step explanation:

a) Jill ended her scooter at her house

b) 2/3 or 0.67

c) The domain is [0,19] , The domain tell about the Elapsed Time of the Jill's scooter ride

d) The range is [2,6] , The range tell about the Distance travelled from Jill's House

I hope it helps you

Treat Please :)

The measure of BD and BC are 7 and 7√2 respectively

A triangle is a shape with 3 sides and angles.

According to the theorem

CD/BD = BD/DA

From the given figure

CD = DA  = 14/2

CD = DA = 7

Substitute

7/BD = BD/7

BD² = 7²

BD² = 49
BD = 7

Determine the measure of BC

sin 45 = BD/BC
sin45 = 7/BC
BC = 7/sin45

BC = 7√2

Hence the measure of BD and BC are 7 and 7√2 respectively

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The probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

Let A represent Female and B represents civil engineering.

The above representation means that the given parameters are:

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

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Answer:

4 years

Step-by-step explanation:

Each year the guitar is worth 80% of its previous worth

1875 ( .80)^n   = 768     where n = years

n=4

Answer:

the orange one

Step-by-step explanation:

(10 + 10) : (5-3) =

20 : 2 =

10

Answer:

its it a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A right triangle must have one of its 3 angles equal to 90°

the only triangle with an angle of 90° is Triangle C

Answer:

B:Triangle

Step-by-step explanation:

Answer: D

Step-by-step explanation:

An example of exponential function is  p(x) = 500(1.02)x Option D

An exponential function is a mathematical function of the form f(x) = [tex]a * b^x[/tex], where 'a' and 'b' are constants, and 'x' is the variable. The function p(x) = [tex]500(1.02)^x[/tex] is in this form

Where 'a' is 500, 'b' is 1.02, and 'x' is the variable.

The variable 'x' is an exponent, which makes it an exponential function. Option D

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Answer:

he will buy 4 tickets

Step-by-step explanation:

firts u have to mutilpy 7.50 by a number and start at 1 and go up till u get 30

hope this helps:)!!

Answer:

Step-by-step explanation:

a) the number of graduates planning to continue studying :

= (37 1/2% + 12 1/2% + 16 2/3%) × 200

[tex]=\frac{\left( 37\frac{1}{2} +12\frac{1}{2} +16\frac{2}{3} \right) }{100} \times200[/tex]

= (37.5 + 12.5 + 16.666666666667)×2

= 133.333333333334

…………………………………

b) the measurement of the angle representing those who plan to work :

= (360× 33 1/2)÷100

= (360× 33.333333333333)÷100

=119.999999999999

The equation which has the correct sign on the product is 27(-5) = -135

- × - = +

- × + = -

+ × - = -

+ × + = +

Given equations:

27(-5) = -135

(-4)(-4) = -16

(-61) (3) = 183

22 × 4 = -88

Correct equation:

27(-5) = -135

(-4)(-4) = 16

(-61) (3) = -183

22 × 4 = 88

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Answer:

dividing a company's yearly accounts receivable balance by its yearly total net sales

assuming simple interest

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 1\%\to \frac{1}{100}\dotfill &0.01\\ t=years\dotfill &3 \end{cases} \\\\\\ A=900[1+(0.01)(3)]\implies A=900(1.03)\implies A=927[/tex]

Answer:

No solution.

Step-by-step explanation:

[tex]|2x+1| = -13\\\\\text{No solution for}~ x\in \mathbb{R}~ \text{because absolute value cannot be negative.}[/tex]

Answer: C) 2.4

Given one opposite angle, two known sides and one missing side.

Hence use cosine rule:

[tex]\sf c = \sqrt{a^2 + b^2- 2ab \ cos\theta}[/tex]

insert values

[tex]\sf c = \sqrt{1.2^2 + 1.4^2- 2(1.2)(1.4) \ cos(134)}[/tex]

simplify

[tex]\sf c = 2.3945 \quad \approx \quad 2.4[/tex]

Answer:

No (2, 11) is not a solution.

Step-by-step explanation:

y = 3x - 2

Plug in the points:

11 = 3(2) - 2

Solve:

11 = 6 - 2

11 = 4

11 does not equal 4.

Hope this helps.

Answer:

(2,11) is not a solution

Step-by-step explanation:

Substitute the value of x and y in the equation.

  y = 3x - 2

Substitute(2,11)

   11= 3*2 -2

        = 6 - 2

    11 ≠ 4

(2,11) is not an solution of the equation

Reason:

There are 4 outcomes we don't want (rolling 1,2,3 or 4) and 2 outcomes we do want (rolling 5 or 6)

This gives the odds against ratio of 4:2 or 2:1

This can be written out as "2 to 1" or "two to one".

Having 2 to 1 odds means that we're twice as likely to get something we don't want vs something we do want.

Side note: the odds in favor will have us flip the ratio.

Benjamin has 340 cents or $3.40.

Proportion in Mathematics is an equation where two or more ratios are made to be equal.

If a : b = c : d, then we can write a/b = c/d

We know that,

1 nickel = 5 cents

8 nickel = x cents

Using ratio and proportion,

1 : 5 = 8 : x

x = 8 × 5 = 40 cents

Similarly,

1 quarter = 25 cents

12 quarters = 12 × 25 = 300 cents

Total cents Benjamin has = 300 + 40 = 340 cents = $3.40

Hence, Benjamin has a total of $3.40.

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The equation of the function g(x) will be g(x) = (1/2) x². Then the correct option is B.

The complete question is attached below.

Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given below.

f(x) = x²

Then the function g(x) will be

g(x) = a · x²

Then the value of will be

From the graph, at x = 2, g(x) will be 2.

Then we have

2 = a · 2²

a = 1/2

Then the equation of the function g(x) will be g(x) = (1/2) x².

Then the correct option is B.

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A) Composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks is f[s(w)] = 50w + 25.

B) The unit of measurement for the composite function is flowers.

C) Number of the flowers for 30 weeks will be 1525.

A function is said to be a composite function when a function is written in another function. The composite function that represents the number of flowers is f[s(w)] = 50w + 25. and the number of flowers for 30 weeks is 1525.

Part A: Write a composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks.

From the given data we will find the function for the number of flowers with time.

f(s) = 2s + 25

We have  s(w) = 25w

f[(s(w)]=2s(w) + 25

f[(s(w)] = 2 x ( 25w ) +25

f[s(w)] = 50w + 25.

Part B: What are the units of measurement for the composite function in Part A

The expression f[s(w)] = 50w + 25 will give the number of the flowers blooming over a number of the weeks so the unit of measurement will be flowers.

Part C: Evaluate the composite function in Part A for 30 weeks.

The expression f[s(w)] = 50w + 25 will be used to find the number of flowers blooming in 30 weeks put the value w = 30 to get the number of the flowers.

f[s(w)] = 50w + 25.

f[s(w)] = (50 x 30) + 25.

f[s(w)] = 1525 flowers.

Therefore the composite function is f[s(w)] = 50w + 25. unit will be flowers and the number of flowers in 30 weeks will be 1525.

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Answer:

0+1

Step-by-step explanat

Any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.

The result we get after adding some quantity is called the sum of the data.

Given we need to find two numbers whose sum is 1,

So, we can consider in this case two consecutive numbers of opposite sign the greater number should have a positive sign and the smaller number should have negative sign,

For example =

-4+5 = 1

-3+4 = 1

-2+3 = 1

-9+10 = 1

So, any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.

Hence, there can be many numbers which can give sum of 1.

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40

Step-by-step explanation:

[tex]{ \red{ \tt{given \: }}} \: :- \: { \green{ \tt{x = - 3}}}[/tex]

Then, Substitute the value of "x" in this below equation..

[tex]{ \orange{ \tt{ {x}^{2} - 7x + 10}}}[/tex]

[tex]{ \orange{ \tt{ {( - 3)}^{2} - 7( - 3) + 10}}}[/tex]

[tex]{ \orange{ \tt{9}}} \: + \: { \orange{ \tt{21}}} \: + \: { \orange{ \tt{10}}}[/tex]

[tex] = { \orange{ \tt{40}}}[/tex]

Answer: (2,-2)

Step-by-step explanation:

Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)

Answer:

-7/2 or 2 are inputs that give 19 as output.

Step-by-step explanation:

The problem gives us a quadratic function [tex]\displaystyle \large{f(x)=2x^2+3x+5}[/tex]. When its output is 19, we want to know the input value(s).

Since an output which is f(x) = 19. Therefore:

[tex]\displaystyle \large{19=2x^2+3x+5}[/tex]

Rearrange the expression in quadratic equation.

[tex]\displaystyle \large{0=2x^2+3x+5-19}\\\\\displaystyle \large{0=2x^2+3x-14}\\\\\displaystyle \large{2x^2+3x-14=0}[/tex]

Factor the expression.

[tex]\displaystyle \large{(2x+7)(x-2)=0}[/tex]

Solve like linear equation which we get:

[tex]\displaystyle \large{x=-\dfrac{7}{2}, 2}[/tex]

If you input these x-values in the function, you will get 19 as the output which satisfies the condition.

Hence, inputs are -7/2, 2

Answer:

[tex]x=2, \quad x=-\dfrac{7}{2}[/tex]

Step-by-step explanation:

Set the function to 19:

[tex]\implies 2x^2+3x+5=19[/tex]

Subtract 19 from both sides:

[tex]\implies 2x^2+3x-14=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:  7 and -4

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 2x^2-4x+7x-14=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 2x(x-2)+7(x-2)=0[/tex]

Factor out the common term (x - 2):

[tex]\implies (2x+7)(x-2)=0[/tex]

Therefore the function's input values that when evaluated give a value of 19 are:

[tex](2x+7)=0 \implies x=-\dfrac{7}{2}[/tex]

[tex](x-2)=0 \implies x=2[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The name of the expression under the radical symbol in a radical function is called a radicand.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The radical is the symbol that is used to represent the root in the expression n√x. The name of the expression under the radical symbol in a radical function is called a radicand.

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Reason:

See the screenshot below. I used GeoGebra to plot the points.

The sub group of points D, E, F form a bowl shaped region. Imagine a small parabola passing through these points. Point E is either the local min or very close to it. This is because point E is at the bottom of the bowl shape.

Answer:

6

Step-by-step explanation:

Answer:

[tex]\frac{2}{3}x^{12}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{6x^{18}}{9x^6}=\frac{6}{9}*\frac{x^{18}}{x^6}=\frac{2}{3}*x^{18-6}=\frac{2}{3}x^{12}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x^{18}}{9x^6}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{18-6}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2}{3}x^{12}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2x^{12}}{3}[/tex]