The grid above shows the graph of the parent function f(x)= |x| and a translated functions graph.


Use f(x)=|x| f(x) is shifted left 5 and shifted up 2 to create g (x). write the equation g(x).

After solving the given inequality the answer is x∈(-∞, 1].

To solve the inequality:

Given: 2(4)x⁺³≤8

Then,

[tex]\begin{aligned}&2 \cdot 4 x^3 \leq 8\\&8 x^3 \leq 8\\&8 x^3+(-8) \leq 8+(-8)\\&8 x^3-8 \leq 8-8\\&8 x^3-8 \leq 0\\&2^3 \cdot x^3-2^3 \leq 0\\&2^3\left(\frac{2^3 \cdot x^3}{2^3}-\frac{2^3}{2^3}\right) \leq 0\\&8\left(x^3-1\right) \leq 0\\&x^3-1 \leq 0\\&x^3-1^3 \leq 0\end{aligned}[/tex]

Then,

[tex]\begin{aligned}&(x-1)\left(x^2+x+1\right) \leq 0\\&\left\{\begin{array}{l}x-1=0 \\x^2+x+1=0\end{array}\right.\\&\left\{\begin{array}{l}(x-1)+1=1 \\x_1=\frac{-1+\sqrt{1-4}}{2} \\x_2=\frac{-1-\sqrt{1-4}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x-1+1=1 \\x_1=\frac{-1+\sqrt{-3}}{2} \\x_2=\frac{-1-\sqrt{-3}}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot \sqrt{-1}}{2} \\x_2=\frac{-1-\sqrt{3} \cdot \sqrt{-1}}{2}\end{array}\right.\end{aligned}[/tex]

So,

[tex]\begin{aligned}&\left\{\begin{array}{l}x=1 \\x_1=\frac{-1+\sqrt{3} \cdot i}{2} \\x_2=\frac{-1-\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1+\sqrt{3} \cdot i}{2}\end{array}\right.\\&\left\{\begin{array}{l}x=1 \\x_1=-\frac{1}{2}+\frac{\sqrt{3}}{2} i \\x_2=-\frac{1}{2}-\frac{\sqrt{3}}{2} i\end{array}\right.\\&\left\{\begin{array}{l}x \leq 1 \\x \geq 1\end{array}\right.\end{aligned}[/tex]

So, finally, it gives:

[tex]2 \cdot 4 x^3 \leq 8\\2 \cdot 4 \cdot 0^3 \leq 8\\\begin{aligned}&x \leq 1 \\&x \in(-\infty, 1]\end{aligned}[/tex]

Therefore, after solving the given inequality the answer is x∈(-∞, 1].

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The probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.

Probability may be defined as the possibility of occurrence of an event. Probability of an event can be 0 or 1 but it can never be negative. If probability is 0 then the event will not occur and if probability is 1 then the event will definitely occur. Probability is given by the formula.

Probability = Favorable outcomes/Total number of outcomes.

Here, total number of outcomes = 20.

Now in the first case we need to find probability of picking a girl so favorable outcome is 2.

Probability of picking a girl = 2/20

Probability of picking a girl = 1/10

In the second case we need to find probability of picking a left-handed girl, so the favorable outcomes are 2 + 9 = 11 as total number of girls are 2 and total number of left-handed people are 9.

Probability of picking left-handed girl = 9 + 2/20

Probability of picking left-handed girl = 11/20

Thus, probability that a girl is chosen is 1/10 and the probability that a left-handed girl is chosen is 11/20.

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Answer:

61

Step-by-step explanation:

The volume of the triangular prism that is 16 ft long is calculated as: 288 ft³

A triangular prism has two triangular bases. The volume of the triangular prism can be found by using the formula below:

Volume of triangular prism = 0.5 * b * h * L, where:

Given the parameters below:

Length of the the base of the triangular face (b) = 4 ft

Height of the triangular face (h) = 9 ft

the length is triangular prism (L) = 16 ft

Volume of the triangular prism = 0.5 * 4 * 9 * 16

Volume of the triangular prism = 288 ft³

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The given quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) is x² y⁴.

This question can be easily solved by using the concept of roots. The two root terms mentioned in the question are ∛8 ( cubic root of 8 ) and  √4 (square root of 4 ). This question can be solved in 4 easy steps

Determining the power of the root and find the LCM of those numbers..

In this case, the powers of root for ∛8 and √4 are 3 and 2, respectively. Take LCM of 3 and 2.

LCM = 3 x 2 = 6

=> We get the LCM of 3 and 2 as 6.

Writing the given numbers as fractional powers.

∛8 = 8¹ˡ³  => The power of 8 = 1/3

√4 = 4¹ˡ²  => The power of 4 = 1/2

Step 3 : Multiply and divide the powers of the base number ( in this case 8 and 4 ) with a number such that you get the denominator as the LCM's ( in this case 6 )

1/3  can be multiplied and divided by 2 to get the denominator as 6

=> 1 * 2 / 3 * 2 = 2/6

1/2  can be multiplied and divided by 3 to get the denominator as 6

=> 1 * 3 / 2 * 3 = 3/6

Step 4 : Divide the two terms

6√8² x 6√4³ = 6√( 4 x 2 x 4 x 2 / 4 x 4 ) = 6√1 = 1

Also,  x⁶ y¹² / x⁴ y⁸ = x² y⁴

Therefore, using the concept of roots and fractions, we get The quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) as x² y⁴.

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The simplified expression is [tex]-\sqrt{2} x^{2} \sqrt{x}[/tex].

English expressions, also commonly known as expressions, are words, or groups of words that when used in a certain way convey a certain meaning. Expressions come in many forms, for instance, some of them are collocations, others are common phrases, while others are idioms or even phrasal verbs.

The written expression refers to a highly complex, cognitive, self-directed process. Higher-order components include planning, translating (drafting), reviewing, and revising.

Emotional expression is simply the acknowledgment of these emotions we are built to feel. Healthy expression allows us to understand emotions, truly feel them, and move on.

[tex]\sqrt{8x^{5} } =2\sqrt{2} x^{2} \sqrt{x}\\\sqrt{18x^{5} }=\sqrt{2} 3x^{2} \sqrt{x}\\=2\sqrt{2} x^{2} \sqrt{x}-\sqrt{2} 3x^{2} \sqrt{x}\\=-\sqrt{2} x^{2} \sqrt{x}[/tex]

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Answer:

X = 4

Step-by-step explanation:

Answer:

81 times.

Step-by-step explanation:

A dice has 6 sides.

The dice is fair, so each side has a 1/6 chance of being rolled.

The are 3 numbers greater than 3 - 4, 5 and 6.

Each of those numbers have a 1/6 chance of being rolled.

Together, their chance of being rolled is:

1/6 + 1/6 + 1/6 = 3/6 = 1/2

The dice is rolled 162 times.

162 x 1/2 = 81

Gordon should roll a number greater than 3 81 times.

The function y=0.0015(10)ˣ showcases exponential growth.

So,

Given function: y=0.0015(10)ˣ

If we put x = 1 as follows:

Then, if we put x = 2 as follows:

Hence, we see that 0.15 > 0.15.

Therefore, the function y=0.0015(10)ˣ showcases exponential growth.

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Answer:

x = -7

Step-by-step explanation:

to solve this first subtract 5 to both sides

5 - x - 5 = 12 - 5

- x = 7

now multiply -1 to both sides

-x(-1) = 7(-1)

x = -7

that is your answeer

Answer:

75

Step-by-step explanation:

there is a pattern in which you can get your answer 75 to 79 you are counting in three 75,76,77,78,79 if you look closely you will see the pattern and you continue to his sixth test and that is how you will get your answer

Answer:  55 degrees

Step-by-step explanation: If the Whole is 180 and you subtract 125 degrees you are left with 55.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 4- 0~~)^2 + (~~ -1- 3~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4 )^2 + ( -4)^2}\implies \boxed{BC=\sqrt{32}}[/tex]

[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) ~\hfill CE=\sqrt{(~~ 2- 4~~)^2 + (~~ -3- (-1) ~~)^2} \\\\\\ ~\hfill CE=\sqrt{( -2)^2 + ( -2)^2}\implies \boxed{CE=\sqrt{8}} \\\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad F(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ -2- 2~~)^2 + (~~ 1- (-3)~~)^2} \\\\\\ ~\hfill EF=\sqrt{( -4)^2 + ( 4)^2}\implies \boxed{EF=\sqrt{32}}[/tex]

[tex]F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill FB=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill FB=\sqrt{( 2)^2 + ( 2)^2}\implies \boxed{FB=\sqrt{8}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter} }{\sqrt{32}+\sqrt{8}+\sqrt{32}+\sqrt{8} ~~ \approx ~~ \text{\LARGE 16.97}}[/tex]

Real and complex zeros of a polynomial function can be find as:

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has exponent equal to 1.

Given:

We have to find all real and complex zeros of a polynomial function.

first convert the polynomial to factored form. Once all factors are found, set each individual factor equal to zero to solve for the real zeros

So, according to fundamental theorem of Algebra

It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

A complex zero is a complex number that is a zero of a polynomial. For example, i (the square root of negative one) is a complex zero of the polynomial x² + 1, since i² + 1 = 0.

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Inverse of the given function F(x) = 3 x³- 4 is F⁻¹(x) = ∛[ ( y + 4 ) / 3 ]

Given is a function of x, F(x) = 3 x³- 4

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = 3 x³- 4 becomes y =  3 x³- 4

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = 3 x³- 4, we get

x =  3 y³- 4

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x =  3 y³- 4

=> x + 4 = 3 y³

=> 3 y³ = x + 4

=> y³ = ( x + 4 ) / 3

=> y = ∛( x + 4 ) / 3

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = ∛( x + 4 ) / 3 becomes F⁻¹(x) = ∛( x + 4 ) / 3

Therefore, we get the inverse of the given function F(x) = 3 x³- 4 as F⁻¹(x) = ∛( x + 4 ) / 3

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The answer to the question is 1350.68

so we are given $500 is deposited at the start of the first year and the interest rate is 2 percent

so the interest =2/100×500 =$10

total amount =$510

we are given that $200 is deposited at the start of the next year, now total amount =$710

interest rate is 2 percent

so the interest =2/100×710 =$14.2

total amount =$724.2

we are given that  $600 is deposited at the start of the following year now total amount =1324.2

interest rate is 2 percent

so the interest =2/100×1324.2 =$14.2

total amount =$1350.68

Hence the answer is $1350.68

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Answer:

39.13%

Step-by-step explanation:

14/23=60.87%

Since the question asks how much has miss Taylor cohort fallen by we do this:

100%-60.87%=39.13%

Answer = 39.13%

Hope this helps :)

Answer:

Step-by-step explanation:

33

The difference in price between the two brands when buying 800 g of hot chocolate is 0.

What is arithmetic operation?

A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.

For brand A

For 160g of hot chocolate is $2.85

For 1g of hot chocolate is 2.85/160

For 800g of hot chocolate is [tex]\frac{2.85}{160} \times 800[/tex]

                                             = 2.85 [tex]\times[/tex] 5

                                             = $14

For brand B

For 200g of hot chocolate is $3.40

For 1g of hot chocolate is 3.40/200

For 800g of hot chocolate is [tex]\frac{3.40}{200} \times 800[/tex]

                                             = 3.40 [tex]\times[/tex] 4

                                             = $14

Difference of brand A and brand B of hot chocolate of 800g is $14 - $14 = 0.

Therefore, the difference in price between the two brands when buying 800 g of hot chocolate is 0.

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The statements that completes the two column proof table, obtained through the use of complementary, and angle addition postulates, arranged using the numbering on the given table are as follows;

The reasons that completes the two column proof table are as follows;

1. ‹PQR is a right angle; Given ‹PQR is a right angle

2. m‹PQR = 90°; Definition of Right Angles

3. m‹PQS + m‹SQR = m<PQR; Angle addition postulate

4. m‹PQS + m‹SQR = 90°; Substitution

5. ‹PQS and ‹SQR are complementary angles; Definition of Complementary Angles

6. ‹TQP and <SQR are complementary angles; Given ‹TQP and <SQR are complementary angles

7 [tex] \angle PQS \cong \angle TQP[/tex]

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It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected

Let the number of fish collected in sample be represented as N.

Let the number of fish affected in it be represented by X.

Therefore, the proportion will be;

= X/N

Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.

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Answer:The probability would be 5 out of 12.

Answer:

Yes they are equivalent.

In fact any value of x will make both equations equivalent.

Step-by-step explanation:

The extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.

We are given an equation:

√3 x + 3 - 1 = x

√3 x + 2 = x

Subtract 2 from both the sides, we get that:

√3 x = x - 2

Raise both sides to the power 2, we get that:

3 x² = x² + 4 - 4 x

2 x² = 4 - 4 x

x² = 2 - 2 x

x² + 2 x - 2 = 0

x = - 1 ± √ 3

Therefore, we get that, the extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.

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An asymptote of the tangent occurs at θ=π/2 , and repeats every π units.

Asymptote of the tangent

Due to the fact that tan(x)=sin(x)cos(x), the tangent function is undefined for cos(x)=0. In light of this, whenever cos(x)=0 the tangent function exhibits a vertical asymptote. Similar to the sine function, the tangent function has zeros for integer multiples of because tan(x)=0 when sin(x)=0.

Typically, dashed lines are used to separate asymptotes from the function itself. The vertical lines that frequently appear on the tangent function's graph are spaced 180 degrees apart from one another.

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The value of x is 14 and the measure of angle J s 103

The given angles are external angles of parallel lines and a transversal

So, we have:

6x - 7 + 7x + 5 = 180

Evaluate the like terms

13x = 182

Divide both sides by 13

x = 14

Substitute x = 14 in J = 7x + 5

J = 7 x 14 + 5

Evaluate

J = 103

Hence, the value of x is 14 and the measure of angle J s 103

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The values of x and angle J are 14 and 103 degrees respectively.

It is important to note that angles on a transversal line are supplementary, that is, they sum up to 180 degrees

Given the angles as;

Equate the angles

6x - 7 + 7x + 5 = 180

collect like terms

6x + 7x = 180 +2

13x = 182

Make 'x' the subject

13x/ 13 = 182/ 13

x = 14

But angle J = 7x + 5 = 7(14) + 5 = 98 + 5 = 103

Thus, the values of x and angle J are 14 and 103 degrees respectively.

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The length is greater then width with degree one so f(x) = x + 7 and g(x) = x + 3 represents length and width respectively so option (A) will be correct.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Perimeter of rectangle = 2( length + width).

A rectangle has two dimensions of size one is greater called length and another is small known as width.

The length and width both are on units of length only such that meter, cm.

In the given option

x + 7 > x + 3 so f(x) will be length and g(x) will be width.

In the option (B) x - 7 < x - 3 so it will not.

Option (C) x² + 7 can not be a unit of length.

Option (D) x - 7 < x - 3 so it will not.

Hence "The length is greater then width with degree one so f(x) = x + 7 and g(x) = x + 3 represents length and width respectively".

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Answer: is A

Step-by-step explanation:

I did that

Rick paddles in still water at a rate of 6.5 mph. The rate of the current is 1.5 mph.

The rate at which an object moves from one point to another is also called speed. It can be measured by dividing the distance over time.

rate = distance/time

Let x = rate at which Rick paddles

c = rate of the current

If Rick paddles a kayak 20 miles upstream in 4 hours, and going upstream means the current is against your direction, then the equation for the travel is:

x - c = 20 miles/4 hours

x - c = 5     (equation 1)

If the return trip downstream takes him 2.5 hours, and downstream means that the current is going the same direction as you are, then the equation for the downstream travel is:

x + c = 20 miles/2.5 hours

x + c = 8     (equation 2)

Using elimination method, solve the two equations.

x + c = 8

x - c = 5

2x     = 13

x = 6.5

rate at which Rick paddles = 6.5 mph

Substitute x in equation 1 and solve for c.

x - c = 5     (equation 1)

6.5 - c = 5

c = 6.5 - 5

c = 1.5

rate of the current = 1.5 mph

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Answer:

2/5+9+7+4+11 or 2/11

Step-by-step explanation:

2 is the smallest then we just add everything on the bottom together

Or just 2/11 since 2 is the smallest and 11 is the biggest

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