FIND THE EQUATION FOR THE LINE SHOWN

The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given:

genera form of an exponential function is  y=aeᵇˣ

Now, equation for f(x) is

f(x) = [tex]e^{(log \;2)x} -2[/tex]

Similarly, graph for g(x) is

g(x) = [tex]-3e^{(log \;2)x} +6[/tex]

Comparing the two function a relation can  be establish

g(x) = -3[f(x)]

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Answer:

shifted to the left two units
g(x)=-f(x+2)

Step-by-step explanation:

The probability that the items drawn are two pencils and one highlighter is 0.25

To do this, we make use of the following representations:

Since there are three boxes, the number of possible outcomes is:

Outcomes = 2³

Outcomes = 8

See attachment for the tree diagram.

From the tree diagram, we have:

So, the probability is:

P = 2/8

Evaluate

P = 0.25

Hence, the probability that the items drawn are two pencils and one highlighter is 0.25

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Answer:

A dashed line down V on the (0,0) with the shading inside the V.

Step-by-step explanation:

- graph of y = -|x| is an upside down V

- less than sign means that there is dashed lines only

- plug in an x-value to determine whether the graph is shaded within the V or outside

Answer:

y=-x+4

Step-by-step explanation:

First use slope formula using 2 points.

(0,3) and (1,2)

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{2-3}{1-0}=\frac{-1}{1} =-1[/tex]

Slope is -1.

Now, use point-slope formula.

y-y1=m(x-x1)

Plug in the information that we have.

y-3=-1(x-0)

Use distributive property.

y-3=-x+1

Add 3 to both sides.

y=-x+4

It is now in slope-intercept form.

Hope this helps!

If not, I am sorry.

Answer:

4

Step-by-step explanation:

Is that a log with the base of   3√(2)  ?

If so....my calculator says the answer is   4

Let's see if we can do it w/ou the calculator:

3 sqrt(2)^x = 324 =  3^4 * 2^2     Now 'LOG' both sides:

x log (3 sqrt 2)  =   log (3^4 *2^2)  =  4 log ( 3 * 2^(2/4)) = 4 log (3 sqrt2)

                       now divide both sides by log (3 sqrt2 )

  x = 4        (If I did the math correctly ! )  

Solution: X=6

Detailed explanation:

In this problem we're asked to find "x" or the unknown.

The first step is to subtract 11x from both sides.

[tex]---\mapsto\boldsymbol{-11x+79=13}[/tex]

Next, subtract 79 from both sides.

[tex]---\mapsto\boldsymbol{-11x=-66}[/tex]

To finish this off, divide both sides by -11.

[tex]---\mapsto\boldsymbol{x=6}[/tex]

Voila! There's our answer!

___________________

Hope I helped.  Best wishes.

Reach far. Aim high. Dream big.

___________________

[tex]\large\green\longrightarrow \tt \large \:79 \: = \: 11x \: + \: 13[/tex]

[tex]\large\green\longrightarrow \tt \large \:79 \: - \: 13 \: = \: 11x[/tex]

[tex]\large\green\longrightarrow \tt \large \:66 \: = \: 11x[/tex]

[tex]\large\green\longrightarrow \tt \large \: \frac{ \cancel{66} \: \: ^{ \pink6} }{ \cancel{11}} \: = \: x \\ [/tex]

[tex]\large\green\longrightarrow \tt \large \:6 \: = \: x[/tex]

Hence , the value of x is 6

We have proven that line TU is parallel to line VW as shown below. That is, TU || VW

From the question, we are to prove that TU || VW

In the given image,

   Statements           Reasons

1. ST || UV                  Given

2. ∠T ≅ ∠U                Alternate angles

3. ∠T ≅ ∠V                Given

4. ∠U≅ ∠V                 Substitution property

5. TU || VW                 Alternate interior angles theorem

NOTE: If the alternate interior angles formed by a transversal of two lines are equal, then the lines are parallel

Hence, we have proven that line TU is parallel to line VW. That is, TU || VW

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Answer:

a c c

Step-by-step explanation:

The peasant had 28 hens and 42 rabbits

Represent hens with h, eggs with e and rabbits with r.

So, we have:

2r = 3h

e = 1/3h

Make h the subject in e = 1/3h

h = 3e

He got 72 pennies.

So, we have:

r + h = 72

Multiply through by 2

2r + 2h = 144

Substitute 2r = 3h in 2r + 2h = 144

3h + 2h = 144

Evaluate the sum

5h = 144

Divide by 5

h = 28.8

Remove decimal

h = 28

Recall that:

2r = 3h

So, we have:

2r= 3 * 28

Divide by 2

r = 3 * 14

Evaluate the product

r = 42

Hence, the peasant had 28 hens and 42 rabbits

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Answer:

see explanation

Step-by-step explanation:

the domain is the set of x- coordinates from the ordered pairs , that is

domain : { - 7, - 3, 0, 5 }

the range is the set of y- coordinates from the ordered pairs, that is

range : { - 2, 1, 2, 5 }

Answer:

Part A = 36z² - 9z + 8

Part B = 5z³ + 4z² + 16z - 23

Part c = Yes.

Step-by-step explanation:

Polynomials : Polynomials are algebraic expressions that consist of variables and coefficients.

Trapezium: A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

Given the length of sides :

Side 1: 11z² - 4z + 2

Side 2: -2z + 3 + 12z²

Side 3: 3 - 3z + 13z²

and The perimeter of the trapezoid is 5z³ + 40z² + 7z - 15.

PART A:

The total length of sides 1, 2, and 3 of the trapezoid is obtained by the sum of the trapezoid :

11z² - 4z + 2 + (-2z + 3 + 12z²) + 3 - 3z + 13z²

11z² - 4z + 2 - 2z + 3 + 12z² + 3 - 3z + 13z²

36z² - 9z + 8

PART B:

The length of the fourth side of the trapezoid is given by the difference between the perimeter of the trapezoid and the sum of  length of sides 1, 2, and 3.

5z³ + 40z² + 7z - 15 - 36z² + 9z - 8

5z³ + 4z² + 16z - 23

PART C:

From part A, we can see that the addition of polynomials results in a polynomial.

Likewise, the subtraction of polynomials results in a polynomial.

Therefore, we can say that the polynomials are closed under addition and subtraction.

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Answer:

[tex]\frac{4}{60}[/tex] = [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

The range of the function will be all values that are greater than 17 that is y > 17

The range of a function is the dependent variable of the function for which it exists,

Given the linear function

y = 8x + 1

If the value of x is 2, hence;

y = 8(2) + 1

y = 17

Hence the range of the function will be all values that are greater than 17 that is y > 17

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Option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.

We have two tables given in the question.

The conditional relative frequency tables show the results of a survey asking students whether they are taking a foreign language or not.

The condition is: "Assuming a student is taking a foreign language"

Table B can be used to answer the above statement.

Thus, option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.

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Answer:

Option b: Table A, because the given condition is that the student is taking a foreign language.

Step-by-step explanation:

on ed

Answer:

From the graph in the attachment, it is clear that Option A is correct.

Step-by-step explanation:

The given inequalities are x - 4y ≤ 4 and y < x + 1.

Let us take the first line x - 4y ≤ 4 and remove the inequality and add equality, x - 4y = 4.

Now, we will find the intercept points. Putting y = 0 we will get x = 4 and putting x = 0 we will get y = -1. So, the points are (4,0) and (0,-1).

When we will solve the inequality, we find that portion above the graph satisfies this inequality.

Let us take the second line y < x + 1 and remove the inequality and add equality, y = x + 1.

Now, we will find the intercept points. Putting y = 0 we will get x = -1 and putting x = 0 we will get y = 1. So, the points are (-1,0) and (0,1).

When we will solve the inequality, we find that portion below the graph satisfies this inequality.

All these conditions satisfy the Option A.

The diagram is in the attachment.

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C. For the first card, there are three ways to choose the number of card.

For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.

Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.

D. The cards may have the same number, color, shapess, orshading.

However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.

If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.

what is Probability?

Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.

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Answer:

x = - 4 , x = - 2

Step-by-step explanation:

x² + 6x + 8 = 0

consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 6)

the factors are + 4 and + 2 , since

4 × 2 = 8 and 4 + 2 = 6 , then

(x + 4)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 2 = 0 ⇒ x = - 2

Answer:

The first option

Step-by-step explanation:

The domain of a rational function should be all real numbers except for when the denominator is equal to 0. To find when the denominator is equal to 0 you simply need to find the zeroes of the denominator... but in this case you can do that through factoring and using the quadratic equation.

So first step is going to be to factor out the GCF, which in this case is x. This gives you the equation. [tex]x(2x^2-x-15)[/tex]. So one of the zeroes is when x=0. Now to find the other two zeroes you can use the quadratic equation which is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\[/tex]. So to find the other zeroes you simply plug the values in. a=2, b=-1, c=-15

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-15)}}{2(2)}\\\\x=\frac{1\pm\sqrt{1-4(2)(-15)}}{4}\\\\x=\frac{1\pm\sqrt{121)}}{4}\\\\x=\frac{1\pm11}{4}\\\\x=\frac{12}{4}\\x=3\\\\x=\frac{-10}{4}\\x=-\frac{5}{2}[/tex]

Answer:

90°

Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

in an equilateral triangle also all 3 angles are equal and therefore 180/3 = 60°.

angle EDF = 60°.

angle DEF = 60°

all angles in a square are 90°.

so, angle ADC = 90°.

and therefore, ADF = 90°.

the angle ADE is then 90-60 = 30°.

the triangle ADE is isoceles (both legs are equal, and both angles of the legs with the baseline are equal).

so, the angle AED = angle ADE = 30°

the angle AEF is then angles AED + DEF = 30 + 60 = 90°

Answer:

See below.

Step-by-Step Explanation:

5) 8x+9-6x-7

8x + 2 - 6x (Subtract the numbers)

2x + 2 (Combine like terms)

2 (x + 1)  (Common factor - Factor by grouping twice)

6) 2y-6+5y+9

2y + 3 + 5y (Add the numbers)

7y + 3 (Combine like terms)

7) 3x+8+4x-9

3x - 1 + 4x (Subtract the numbers)

7x - 1      (Combine like terms)

8) 9y+16-12y+24

9y + 40 - 12y (Add the numbers)

-3y + 40 (Combine like terms)

9) 7g-5-8g+12

7g + 7 - 8g (Add the numbers)

-g + 7 (Combine like terms)

10) 11c-8+5c-8

11c - 16 + 5c (Subtract the numbers)

16c - 16 (Combine like terms)

16 (c - 1)   (Common factor - Factor by grouping twice)

11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)

10x + 15 (Distribute)

12) 5(-2x+3)

-10x + 15 (Distribute)

Hope this helps!

Answer: those are the answers its a long time.

Question  5  Answer: 2(x+1)

8x+9−6x−7

Multiply and combine like terms.

2x+2

Factor out 2.

2(x+1)

Questio 6 Answer : 7y + 3

2y−6+5y+9

Combine 2y and 5y to get 7y.

7y−6+9

Add −6 and 9 to get 3.

7y+3

Question 7  Answer: 3x+8+4x−9

Combine 3x and 4x to get 7x.

7x+8−9

Subtract 9 from 8 to get −1.

7x−1

Question 8 Answer: - 3y + 40

9y+16−12y+24

Combine 9y and −12y to get −3y.

−3y+16+24

Add 16 and 24 to get 40.

−3y+40

Question 9 Answer: -g + 7

7g−5−8g+12

Combine 7g and −8g to get −g.

−g−5+12

Add −5 and 12 to get 7.

−g + 7

Question 10 Answer: 16 ( c - 1 )

11c−8+5c−8

Combine 11c and 5c to get 16c.

16c−8−8

Subtract 8 from −8 to get −16.

16c - 16

Question 11 Answer: 10x +15

5(2x+3)

Use the distributive property to multiply 5 by 2x+3.

10x+15

Question 12 Answer: 15 - 10x

5(−2x+3)

Use the distributive property to multiply 5 by −2x+3.

−10x+15

if a + b is equal to 2 find the value of a cube plus b cube + 6ab

Answer:

2.15%

Step-by-step explanation:

If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.

Z-score:

550-400/2=3

500-400/2=2

Probability:

3 (from the Z-table) is .9987

2 (from the Z-table) is .9772

.9987-.9772= .0215

.0215 as a percentage is 2.15%

Mean: 400

Standard deviation: 50

Check to see if 500 and 550 fall within the standard deviations:

400+2(50) =500

400+3(50) =550

These values lie between the 2nd and 3rd deviations, so

the value is 0.0235

Percentage: 2.35%

Hope it helps!

Answer:

[tex]\fbox {53}[/tex]

Step-by-step explanation:

⇒ 3x² + 5

Substitute x = 4 :

⇒ 3(4)² + 5

⇒ 3(16) + 5

⇒ 48 + 5

⇒ 53

Answer:

zero (0)

Step-by-step explanation:

-4^0=-1

-1+1=0

Answer:

1. 0

2. undefined

3. -3/2

Step-by-step explanation:

y=-3/2. This value is constant and the x does not change the value at all. so the coordinate are going to be (x, -3/2) so if we take any 2 values you're going to get (-3/2 - (-3/2)) / (x2 - x1) = (-3/2 + 3/2) / (x2 - x1) = (0) / (x2 - x1) which is always going to be 0.

x=-3/2. This value is also constant except the x-value does not vary at all so x2 and x1 are always going to be equal which will result in a 0 as the denominator thus making the slope undefined

y=-3/2x. it's just -3/2 given the slope-intercept form y=mx+b where m is the slope

Answer:

0 underfined 3

—

2

Step-by-step explanation:

SOLVING STEP.

the line y= 3 is parallel to the x-axis,

—

— 2

so the slope is 0

the line x= 3 is perpendicular to the x-axis,

—

— 2

so the slope is underfined

the slope of the line y= 3 x 3

—

— — 2.

2

thank me later

The simplification of the algebraic expression to its simplest form is -3x³ + 2x² + 13x - 10

The simplest form of an algebraic expression is a stage at which the expression can no longer be further simplified.

From the given expression:

= -(x − 2)(3x² + 4x − 5)

= (-x +2)(3x² + 4x − 5)

Open brackets

= -3x³ - 4x² + 5x +6x² + 8x - 10

= -3x³ + 2x² + 13x - 10

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The value of y from the equation is 12

A triangle is a shape that has three sides and angles

From the given diagram, the equation is true based on angle bisector theorem

8/4 = y/6

Cross multiply

4y =48

y = 12

Hence the value of y from the equation is 12

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Answer:

m=-3

Step-by-step explanation:

Since the lines are parallel to each other, their gradients are equal.

∴ gradient of green line = gradient of red line

∴ m = -3

Solution: slope=-3

Detailed explanation:

This little problem asks us to find the slope of the line. Let's do this!

[tex]\searrow[/tex]

This is what parallel lines look like:

<------------------------------------------------------------------------------------------------------->

<------------------------------------------------------------------------------------------------------->

The two lines above will never intercept each other.

And that's what parallel lines are - they are lines that never intercept.

They can be vertical, horizontal, or diagonal, it doesn't matter. As long as both of them have the same slope and never intercept each other.

So, since parallel lines have identical slopes, the slope of the red line = slope of the green line (the problem provides us that both lines are parallel)

Slope of the red line = -3

Voila! There's our answer!

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Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

"reflection"

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Theta has a reference angle of 30° and is in Quadrant I or II.

Sin(theta) = ½

Basic angle: 30

The acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle sandwiched between the terminal side and the x-axis.

Angles: 30,

180-30 = 150

Because sin is positive in quadrants 1 and 2.

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The height of the target is 29 feet.

The correct option is (D)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given table path of the thrown ball,

where x represents the horizontal distance and f(x) represents the height of the ball.

Now,

when x = 1.25 feet horizontally, the height will be maximum.

also, the height of the ball at  distance x = 1.25 feet is

f(1.25) = 29 feet.

Hence, height of the target is 29 feet.

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Answer:

D. 29 feet

Step-by-step explanation:

The required piecewise function that represents the graph is given as:

[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]

The graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.

For the line crossing the negative x-axis

Using the coordinate points (-4, 2) and (-2, -4)

Slope = -6/2

Slope = -3

2 = -3(-4) + b
2 - 12 = b

b = -10

The equation of the line will be y = -3x-10

For the line crossing the negative y-axis

Using the coordinate points (-2, -4) and  (2,-2)

Slope = 2/4

Slope = 1/2

-2 = 1/2(2) + b
-2 - 1 = b

b = -3

The equation of the line will be y = -1/2x-3

For the line crossing the positive x-axis

Using the coordinate points (2, -2) and (3, 0)

Slope = 2/1

Slope = 2

0 = 2(3) + b
0 - 6 = b

b = -6

The equation of the line will be y = 2x-6

The required piecewise function that represents the graph is given as:

[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]

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