The table below represents a linear equation

Which function has a greater slope and greater y-intercept than the linear function represented in the table?
A. y = 2x + 8.5
B. y = 3x +7.5
C. y = 5x + 6.5
D. y = 10x + 5.5

Answer:



Step-by-step explanation:

The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13

A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.

The possible polynomial in the question is; x³ + 5·x² - 11·x + 104

The factor of the polynomial is; (x + 8)

The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.

The other steps of synthetic division can then be presented, summarily as follows;

Therefore;

-8 | 1[tex]{}[/tex]   5     -11   104

   |   [tex]{}[/tex]   -8    24  104          

     1   -3    [tex]{}[/tex] 13      0

The factors of the polynomial

The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13

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The smallest fraction is 8/12, which is equivalent to 2/3.

To compare fractions, it's best to convert them all to a common denominator.

3/4 is equivalent to 9/12

2/3 is equivalent to 8/12

10/12 is equivalent to 5/6

2/1 is equivalent to 24/12

So, the smallest fraction is 8/12, which is equivalent to 2/3.

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The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis

The ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.

If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).

If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).

The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.

Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.

Solving the given problem:

f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]

At x= 0 on the y- axis

f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]

Thus, only option C satisfies this condition.

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Answer: 97.5

Step-by-step explanation:

Just do base times height divided by 2, which I'm assuming is 13x15 , that'd be 195. 195 divided by 2 is 97.5

To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.

How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.

For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:

V = l × w ×h

The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.

Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.

V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.

We arrive at a total volume of 792 cubic meters by adding these volumes together.

To the nearest hundredth=904.600 cubic meters.

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Answer:

17/x = x/8

x^2 = 136, so x = 2√34

By looking at the y-values of the points, we can see that the first four terms are.

2, -2, -6, -10

We know that the x-value of each of the points is the index of the term, so:

x = 1 is the first term

x = 2 is the second term.

And so on.

The y-value will be the actual value of the term.

Here we can see 4 points graphed, these are:

(1, 2), (2, -2), (3, -6), (4, -10)

Then the values of the first four terms of the sequence are:

2, -2, -6, -10

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The graph seems to be a left symmetrical distribution and most people watched action movies

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

The graph (see attachment)

From the graph, we have the following readings and observations

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

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Answer:

C

Step-by-step explanation:

The area of a rectangle is 2 dimensions so it would be measured in square meters.

a = lwh

26241 = lw(17)  Divide both sides by 17

1542 = lw

The lw is he area of the base.

Helping in the name of Jesus.

Answer:

1,3,5,7,9

Step-by-step explanation:

0 can't be, let's take 10 or 20 or 30 for example, not a prime number.

1 can be because let's take 11, 31 as example, they're prime numbers.

2, 4, 6, 8 can't be the answer because they have factors

The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59

Answer:

$2,440 + $1,220 = $3,660

Step-by-step explanation:

If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:

$61,000 x 0.04 = $2,440

Since her employer has a 50% match on the first 4% of her salary, they would contribute:

$2,440 x 0.5 = $1,220

Answer:

2 (n - 3) (n - 6)

Step-by-step explanation:

[tex]-7n+5n^2+6-3n^2-11n+30[/tex]

Group like terms and combine...

[tex]2n^2-18n+36[/tex]

Observe that all terms contain a factor of 2.  Factor out a 2...

[tex]2(n^2-9n+18)[/tex]

The leading coefficient is 1.  The shortcut applies.  Find the factors of "c" (18)

Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").

Finish factoring the trinomial into two binomials:

[tex]2(n-3)(n-6)[/tex]

To verify that this is a valid factoring, distribute, and recombine terms:

[tex]2(n-3)(n-6)[/tex]

[tex]2(n^2-3n-6n+18)[/tex]

[tex]2(n^2-9n+18)[/tex]

The solutions to the equation over the interval [0°, 360°) are: x = 45°, 135°, 225°, 315°.

We can rewrite this equation as:

1 - sin² x = sin²x

Solving for sin x, we get:

sin x = ±✓(1/2)

Since sin x is positive in the first and second quadrants and negative in the third and fourth quadrants, we have:

sin x = ✓(1/2) = 1/✓(2) in the first and second quadrants, corresponding to x = 45° and 135°.

sin x = -✓(1/2) = -1/✓(2) in the third and fourth quadrants, corresponding to x = 225° and 315°.

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The value of x in the equation x² = -20 is x  = 2i√5

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

x² = -20

To start with, we take the square root of both sides of the equation

So, we have

√x² = √-20

When the square roots are evaluated, we have

x  = √-20

Express -20 as 4 * -5

So, we have

x  = √4 * -5

This gives

x  = 2√-5

The expression √-5 is a complex number

So, we have

x  = 2i√5

Hence, the value of x in x² = -20 is x  = 2i√5

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Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].

In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.

Here,

The linear approximation of sin⁻¹(x) at a = 0 is given by:

sin⁻¹(x) ≈ x

To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:

d/dx(sin⁻¹(x)) = 1/√(1-x²)

d/dx(sin⁻¹(x))|x=0 = 1

Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.

To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.

Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:

-0.099 ≤ x ≤ 0.099

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The number of kg of maize was left with Ali is 73350 Kg.

Given that, Ali had 3469 bags of maize each weighing 90 kg.

Ali sold 2654 of them.

Number of bags left = 3469-2654

= 815

Number of Kg's of maize left = 815×90

= 73350 Kg

Therefore, the number of kg of maize was left with Ali is 73350 Kg.

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The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as  51 square units.

A graph is described as a mathematical representation of a network and it describes the relationship between lines and points.

The first step is to divide the figure is into two rectangles and a triangle.

we notice that the points B, C, E, and F will form a rectangle with base BC and height of 7 units.

We also notice that the  points A, D, and G form a rectangle with base AG and height 5 units.

we notice that  points C, D, and E form a triangle with base CE and height 4 units.

we notice that the  length of BC is 4 - 4 = 0, therefore  the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is  (9.7, 14.7).

Here, we have,

1. Identify the given information:

 - Confidence level (c) = 0.95

 - Sample mean (x) = 12.2

 - Sample standard deviation (s) = 3.0

 - Sample size (n) = 8

2. Determine the degrees of freedom (df) for the t-distribution:

 - df = n - 1 = 8 - 1 = 7

3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:

 - You can use a t-table or an online calculator for this.

 - The t-value for a 0.95 confidence level and 7 df is approximately 2.365.

4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):

 - ME = t-value * (s / sqrt(n))

 - ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5

5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):

 - Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7

 - Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7

So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).

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Answer:

64.14

Step-by-step explanation:

Reading the passage I see that you have to multiply then divide

The surface area of the larger solid is,  171.7 mm²

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The volumes of two similar solids are 857.5 mm³ and 540 mm³.

And, The surface area of the smaller solid is 108 mm².l

Now, Let us assume that;

The surface area of the larger solid is, x

Hence, We get;

857.5 / x = 540 / 108

Solve for x as;

857.5 x 108 = 540 x

92,718 = 540x

x = 171.7 mm²

Thus, The surface area of the larger solid is,  171.7 mm²

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Answer:

B. 1

Step-by-step explanation:

Let's use the formula for finding the mean of a set of data:

mean = (sum of all data values) / (number of data values)

We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:

2.2 = (sum of all 10 data values, including x) / 10

Multiplying both sides by 10, we get:

22 = sum of all 10 data values, including x

We can then subtract the sum of the known data values from both sides to find the missing value:

22 - (01 + 12 + 23 + 31 + 42 + 51) = x

22 - (0 + 2 + 6 + 3 + 8 + 5) = x

x = 22 - 24 = -2

However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:

If the missing score is 0:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10

2.2 = 18 / 10

2.2 = 1.8

This is not true, so the missing score cannot be 0.

If the missing score is 1:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10

2.2 = (18 + ?) / 10

22 = 18 + ?

? = 4

So the missing score is 1, and the answer is B.

Answer:

Answer is B

Total scores/total frequency =mean

54/24=2,25

If you added a score of 1

55/25=2,2

Step-by-step explanation:

hope that helps you

The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³

Given data ,

The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis

The formula for Area under definite integral is

∫ₐᵇ f ( x ) = f ( b ) - f ( a )

Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x

The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)

Using these expressions for r and h, we can write the volume of each cylindrical shell as:

V(x) = 2πx[f(x + Δx) - f(x)]Δx

V = ∫₀² 2πx[f(x + Δx) - f(x)]dx

As Δx approaches zero, this integral becomes:

V = ∫₀² 2πx√(1 + (f'(x))²) dx

where f'(x) is the derivative of f(x), which is:

f'(x) = x/√(x² + 9)

Substituting this expression for f'(x) into the integral, we get:

V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx

This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:

V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx

V = [4/5 π(x² + 9)^(5/2)]₉¹³

V = 44.46 units³

Hence , the volume of the solid is 44.46 units³

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The simplified expression of  2x multiplied by 7 with the exponent of 4 is 4,802x.

The expression is simplified by applying the rules of multiplication and exponent rules.

the expression = 2x(7⁴)

simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401

Multiply the resultant solution of 2,401 as follows;

= 2,401 x (2x)

= 4,802x

Thus, the simplified expression of  2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.

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To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.

Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.

First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.

Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.

Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.

The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.

The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.

The y-coordinate of this point is 1, so sin(183π/2) = sin(16,470 degrees) = 1.

It should be noted that go find cos(5π), we first need to convert 5π to degrees. We know that π radians is equal to 180 degrees, so 5π radians is equal to 5π × (180/π) = 900 degrees. The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.

Also, to find sin(-9π/2), we first need to convert -9π/2 to degrees. We know that π radians is equal to 180 degrees, so -9π/2 radians is equal to -9π/2 × (180/π) = -810 degrees. The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.

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Andy has $32 money left after spending $18 on school supplies and $47 on new clothes.

To find out how much money Andy has left, we need to start with the total amount of money he saved and then subtract the amount he spent on school supplies and new clothes.

The total amount Andy saved is:

$32 + $27 + $38 = $97

The amount Andy spent is:

$18 + $47 = $65

To find out how much money Andy has left, we can subtract the amount he spent from the amount he saved:

$97 - $65 = $32

So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.

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Answer:10-x

Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.

Carlos can expect the value of the computer to be $580 three years after purchase.

To model the value of the computer, we can use the formula:

y = abˣ

We know that the initial value of the computer is $1,350, so a = 1350.

We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:

810 = 1350b

b= 0.6

b = 0.6

So our exponential equation is:

y = 1350(0.6)ˣ

To find the value of the computer 3 years after purchase, we can substitute x = 3:

y = 1350(0.6)³

y = 583

Hence, Carlos can expect the value of the computer to be $580 three years after purchase.

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