Consider the graph of function f below. A diagonal curve declines through (negative 6, 7), (negative 5, 5), (negative 4, 3), (negative 3, 1), (3, negative 1, negative 3), (0, negative 5) and (1, negative 7) on the x y coordinate plane. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g? A. g(x) = f(x) - 1 B. g(x) = f(x + 4) C. g(x) = f(x - 1) D. g(x) = f(x) + 4

The limit [tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex] without using L'Hopital's Rules has a value of 1

From the question, we have the following parameters that can be used in our computation:

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex]

By substitution, we have

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = \frac{1}{3^{}\infty}+3^{\frac{1}{\infty}}[/tex]

So, we have

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+3^0[/tex]

Evaluate the exponents

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+1[/tex]

Evaluate the sum

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 1[/tex]

Hence, the solution is 1

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The given operation of the matrix is expressed as: -9y + 2z = 12

Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.

The simultaneous equations formed by the matrix are:

x + 2y + z = -5

    4y - 2 = 3

4x - y + 6 = -8

We are told to Multiply row 1 by -4 and this gives us:

-4x - 8y - 4z = 20

Adding it to row 3 gives us:

-9y + 2z = 12

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Answer:

it would be 9x

Step-by-step explanation:

because subtract 3 from 12 and leave the x

Answer:

f(1) = 1

Step-by-step explanation:

Open holes on a graph means that the function is not defined at that point, so we ignore the open hole.

At f(1), there is both an open hole at y=-2 and a closed hole at y=1

We ignore the open hole as it is not defined so the answer would be the closed hole, y = 1

So f(1) is 1

Answer:

A B

Step-by-step explanation:

Is between A or B

Answer:  A yes

Step-by-step explanation:

The answer is A because they divided both sides by 5

Not by variable and they didn't add/sub  

This equations are  equivalent

Answer: w = –27i + 35j

Step-by-step explanation:

Answer:

f'(x) = 2x, so f'(x) = f'(3) = 2(3) = 6.

The number of sun flowers with a height  of 27¹/₂ inches or more are 4 more than those with a height of less than 27¹/₂ inches

A dot plot, which is also known as a strip plot or dot chart, is a simple form of data visualization that comprises of data points plotted as dots on a graph with an x- and y-axis. These types of charts are used to graphically depict certain data trends or groupings.

The number of heights below 27¹/₂ inches that exists in the given dot plot is seen to be 8 in number.

Similarly, the number of dot plots that exists above or equel to 27¹/₂ inches from the given dot plot are 12 in number.

Therefore, we can say that:

Difference in total number for both parameters = 12 - 8= 4

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Answer: 15y2 - 19y + 6 = 0

Step-by-step explanation:

The first term is,  15y2  its coefficient is  15 .The middle term is,  -19y  its coefficient is  -19 .The last term, "the constant", is  +6 Step-1 : Multiply the coefficient of the first term by the constant   15 • 6 = 90 Step-2 : Find two factors of  90  whose sum equals the coefficient of the middle term, which is   -19 .

The evaluations are:

i. 11!  = 39916800

ii. 24! = 2.045 x 10^37

Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;

5! = 5 x 4 x 3 x 2 x 1!

   = 120

To evaluate the given expressions;

a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!

       = 39916800

Also,

b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!

          = 204484017332398 x 10 ^23

          = 2.045 x 10^37

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840 different numbers can be created selecting 4 of the digits from the number

From the question, we have the following parameters that can be used in our computation:

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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Time taken by final lesson is 48 minutes and time consumption will not be affected if first lesson takes less time to finish.

Given that;

The time to finish five lessons = 4 hours

Then one lesson takes = 4/5 hours to finish

(a) Since  each lesson takes equal amount of time

Therefore,

The time taken by final lesson in minutes = (4/5)x60

                                                                      = 48 minutes

(b) Since each lesson has own capacity of time so the time consumption for other lesson is not affected if first lesson takes less time.

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The other value of x where g(x) = 15 is 16 in the absolute value function

Since the vertex of the absolute value function is at (10,0), the equation for the function can be written as:

g(x) = a|x - 10|

To find the value of a, we can use the fact that the function passes through the point (4,15):

15 = a|4 - 10|

15 = 6a

a = 2.5

So the equation for the absolute value function is:

g(x) = 2.5|x - 10|

To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:

2.5|x - 10| = 15

|x - 10| = 6

x - 10 = 6 or x - 10 = -6

x = 16 or x = 4

Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.

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The equation for line n that is perpendicular to the x-axis and passes through the point (–3,–7) is x = -3, and its slope is undefined.

Since line n is perpendicular to the x-axis, it is parallel to the y-axis. Therefore, its slope is undefined since the y-axis is a vertical line with no defined slope.

To write the equation for line n, we know that the y-coordinate of every point on the line will be constant since the line is parallel to the y-axis. We also know that the line passes through the point (-3,-7), so we can write the equation as:

x = -3

This means that for any value of y, the x-coordinate will always be -3. Graphically, this represents a vertical line passing through the point (-3,-7) and parallel to the y-axis.

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Answer:

[tex]\large\boxed{\tt Area = Length \times Width}[/tex]

[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]

[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the area of a 2D Rectangle.}[/tex]

[tex]\large\underline{\textsf{What is Area?}}[/tex]

[tex]\textsf{Area for 2D shapes is how much space is inside between edges. Consider edges}[/tex]

[tex]\textsf{as the sides of a shape.}[/tex]

[tex]\underline{\textsf{How are we able to find Area?}}[/tex]

[tex]\textsf{Many shapes require different formulas to find the area. Some have the same}[/tex]

[tex]\textsf{formulas however it depends on how many sides the shape has, and the number of}[/tex]

[tex]\textsf{dimensions shown in the shape. For a Rectangle it's simple. Because a Rectangle}[/tex]

[tex]\textsf{has 2 Dimensions (Length and Width), to find the area we should multiply}[/tex]

[tex]\textsf{the dimensions together, hence resulting in the amount of space inside the shape.}[/tex]

[tex]\large\underline{\textsf{Formula;}}[/tex]

[tex]\large\boxed{\tt Area = Length \times Width}[/tex]

[tex]\large\underline{\textsf{Plug in Values;}}[/tex]

[tex]\textsf{The Length and Width aren't mentioned in the question, but it doesn't matter}[/tex]

[tex]\textsf{since we're still going to get the same answer no matter which place they're in.}[/tex]

[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]

[tex]\large\underline{\textsf{Solving for the Area;}}[/tex]

[tex]\textsf{We have our formula, now multiply the dimensions together.}[/tex]

[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]

The missing parameters of the regular polygons are listed below:

Case 1: θ = 45°, a = 10.864 cm

Case 2: θ = 72°, s = 5.812 cm

In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:

Central angle

θ = 360 / n

Relationship between apothema and side length

a = s / [2 · tan (180 / n)]

Where:

Now we proceed to find missing parameters:

Case 1: s = 9 cm, n = 8

θ = 360 / 8

θ = 45°

a = (9 cm) / [2 · tan (180 / 8)]

a = 10.864 cm

Case 2: a = 8 cm, n = 5

θ = 360 / 5

θ = 72°

s = 2 · a · tan (180 / n)

s = 2 · (8 cm) · tan (180 / 5)

s = 5.812 cm

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Answer: 3t(9t + 5)

Step-by-step explanation:

Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.

To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.

So we start by factoring out the 3t:

27t² + 15t = 3t(9t + 5)

Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:

3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t

Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).

The value of A, B, C,D are 33, 36,25 and 16 respectively

A word problem is a math problem written out as a short story or scenario. We use this word problem to solve the unknowns.

The total number of students is 60 and 24 students prefer volley ball. therefore the number of students that prefer basketball = 60-24 = 36 students

Since 11 student are girls that prefer basketball, therefore the number of boys that prefers basketball = 36-11 = 25

C = 25

and B = 36

55% of the students are boys, therefore the number of boys = 55/100 × 60 = 33

A = 33

therefore the number of boys that prefer volley ball= 33-25 = 8

Number of girls = 60-33 = 27

therefore number of girls that prefer volley ball = 27-11 = 16

D= 16

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The perimeter of the composite figure is 46 metres.

The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.

Therefore, the perimeter of the figure can be found as follows:

perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12

perimeter of the shape = 11 + 9 + 11 + 15

perimeter of the shape =20 + 11 + 15

perimeter of the shape = 31 + 15

perimeter of the shape = 46 metres

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We have 20 marbles in the bag. The probability of a marble that is not green is 20/20.

So the probability of the randomly that the marble is not green is 20/20 or just 20.

The statement that could be true for the domain of g is g(-4) = -11.

option A.

The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.

The given statements that could be true for g is calculated as follows;

Option A: g(-4) = -11

Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.

Therefore, this could be true.

Option B: g(-13) = 20

Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.

Option C: g(0) = 2

We are given that g(0) = -2, so option C is not true.

Option D: g(7) = -1

Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.

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The dimensions of the region which enclose the maximal area will be  40.5 feet in length by width 27 feet.

Given that the farmer has 162 feet of fencing, we will have:

2L + 3W = 162 feet

2L = 162 - 3W

L = 162 - 3W\2

L = 81 -3/2W  Eqn 1

Given that the area of a rectangle is A = L × W we will call this equation 2

Now we substitute the first equation in the second one to give

A = (81 -3/2W) × W

A = 81W -3/2W²

When we take the derivative W will equal

81/3 = 27

Now we substitute in the second equation, we will have:

= 81 - 3/2(27)

= 81 - 40.5

= 40.5.

So the length will be 40.5 feet while the width will be 27 feet.

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Answer:

f(-1)=0

Step-by-step explanation:

To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :

[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]

[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0

Hi again

I did it wrong

I'm here to redeem

When you have to factor these types of equations, you have to use a method called slide divide and bottoms up.

First you have to slide the a value to the end and mutiply with the c value so it is easily factorable

x^2+12x+35

Then you solve it like always

(x+7)(x+5)

Now, don't forget our buddy 7

7 is coming back

we divide 7 by 7 and 5 by 7

so

(x+1)(x+5/7)

7 has to move

So we move the 7 to the front

Therefore the answer is

(x+1)(7x+5)

If  you have questions please ask me

Answer:

(7x + 5) (x + 1)

Step-by-step explanation:

7x² + 12x + 5

general form ax² + bx + c

a = 7

b = 12

c = 5

we have to find number that, if

... × ... = a . c = 7 . 5 = 35

... + ... = b = 12

and it would be

7 × 5 = a . c = 7 . 5 = 35

7 + 5 = b = 12

7x² + 7x + 5x + 5

= 7x (x + 1) + 5 (x + 1)

= (7x + 5) (x + 1)

Answer: The man will make deposits for 66 - 45 = 21 years, or 21 x 4 = 84 quarters.

The quarterly interest rate is 4% / 4 = 1%.

Let's use the formula for the future value of an annuity:

FV = PMT x ((1 + r)^n - 1) / r

where FV is the future value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $2500, r = 1%, and n = 84. Substituting these values into the formula, we get:

FV = $2500 x ((1 + 0.01)^84 - 1) / 0.01

FV = $2500 x (5.409 - 1) / 0.01

FV = $2500 x 540.9

FV = $1,352,250

Therefore, there will be $1,352,250 in the account when the man retires at age 71.

Question: What are the two possible angles of a triangle with sides of 100 and 75 with a 40° as marked in the triangles above? Solution: Use the law of sines formula where the 75 length is opposite of 40°, and 100 is opposite of θ. Answer: The two possible angles for this triangle is 58.97° and 121.03°.

There are 25% chance of 5 more people in the party.

Hence option (a) is correct.

Relative frequency = (number of times of occurrence of an event )/ (number of trials)

For the given table

relative frequency for 1 people = 0.05 = 5%

relative frequency for 2 people = 0.46 = 46%

relative frequency for 3 people = 0.18 = 18%

relative frequency for 4 people = 0.22 = 22%

relative frequency for 5 people = 0.06 = 6%

relative frequency for 6 people = 0.03 = 3%

Since relative frequency for 1 people is 5%

Therefore,

Relative frequency for 5 people is = 5x5%

                                                         = 25 %

Hence,

Relative frequency of 5 more people 25%.

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There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

To test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.

Let p be the true proportion of mathematics research published by U.S. authors.

The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).

sample proportion, x/n = 62/130 = 0.477

The test statistic for a two-tailed test is given by:

z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)

= 2.41

Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.

Since  0.016 < 0.05

, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

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We have proven that m∠C = m∠A.

We have,

We are given that m∠A + m∠B = m∠B + m∠C.

We want to prove that m∠C = m∠A.

Using algebra,

We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.

This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.

We can also use the transitive property of equality to show that

m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that

m∠A = m∠C.

Therefore,

We have proven that m∠C = m∠A.

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