Write an equation in slope-intercept form of the line containing the points (3,-1) and (6, 7).
=x-9
y=x-7
y = -x +9
y = 3x - 11

The value of x such that f(x) = g(x) is x = 3

Given the following expressions as shown

f(x) = x^3-3x^2+2 and;

g(x) = x^2 -6x+11

Equate the expressions

x^3-3x^2+2 = x^2 -6x+11

Equate to zero

x^3-3x^2-x^2+2-11 = 0

x^3-3x^2-x^2 + 6x - 9 = 0

x^3-4x^2+6x-9 = 0

Factorize

On factorizing the value of x = 3

Hence the value of x such that f(x) = g(x) is x = 3

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The next step in constructing a line perpendicular to a point on the line is A. Place a compass at point D, and draw an arc that intersects the arc above line DF.

To make a perpendicular line:

Therefore, the next step would be to Place a compass at point D, and draw an arc that intersects the arc above line DF.

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Hello !

[tex]\frac{25}{100}=0.25[/tex]

Have a nice day ;)

Answer:

25

Step-by-step explanation:

25

Answer: 25% of 100 is 25.

Answer:

a. The graph is concave up in the interval 0 ≤ x ≤ +∞

b. The graph is concave down in the interval -∞ ≤ x ≤ 0

To answer the question, we need to know what intervals are

Intervals are range of values in which a function is valid. It can either be the range of values of input or output of the function.

From the graph, we see that the function is concave up in the interval 0 ≤ x ≤ +∞

So, the graph is concave up in the interval 0 ≤ x ≤ +∞

From the graph, we see that the function is concave down in the interval -∞ ≤ x ≤ 0

So, the graph is concave down in the interval -∞ ≤ x ≤ 0

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The change in volume is -88π

The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.

Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement

The radius is decreasing at 2 inches per minute

The height is given as decreasing at 4 inches per minute

So let [tex]\frac{dr}{dt}=-2[/tex] and

[tex]\frac{dh}{dt}=-4[/tex]

and we have radius r=6,

                     height h=5

The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]

Then

[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]

[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]

[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]

So the volume change is [tex]-88\pi[/tex]

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Answer: B: 11 and 12

Step-by-step explanation:

- An integer is simply a whole number

- So consecutive integers are simply whole numbers that follow each other (ex: 1, 2, 3)

- The square root of 125 (in decimals) is 11.1803398875, meaning it is higher than 11 but less than 12

- So 11.1803398875 falls between 11 and 12, making the answer B

hope this helps :)

Subtract the largest power of 2 from 798 such that the difference is not negative.

2⁹ = 512 and 2¹⁰ = 1024, so the largest power of 2 smaller than 798 is 2⁹, and

798 = 512 + 286 = 2⁹ + 286

Repeat this process with the remainder, 286.

2⁸ = 256, so

286 = 256 + 30 = 2⁸ + 30

⇒   798 = 2⁹ + 2⁸ + 30

2⁴ = 16 and 2⁵ = 32, so

30 = 16 + 14 = 2⁴ + 14

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 14

2³ = 8, so

14 = 8 + 6 = 2³ + 6

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 6

2² = 4, so

6 = 4 + 2 = 2² + 2¹

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 2² + 2¹

or more completely,

798 = 1×2⁹ + 1×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 0×2⁰

Then the base-2 representation of 798 is

11 0001 1110₂

The sample size which is required in order to estimate the mean per capita income at the 85% level of confidence with an error of at most $0.46 is 866.

Given mean income of $31.3 and standard  deviation of $9.4.

We have to calculate the  sample size of confidence interval of 85% and at an error of $0.46.

Margin of error is basically the difference between actual values and calculated values.

Mean =$31.3

Standard deviation=$9.4

Confidence level=85%

Margin of error=$0.46

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

0.46=1.44*9.4/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=1.44*9.4/0.46

[tex]\sqrt{n}[/tex]=29.42

squaring both sides

n=865.53

Round off and we get the following:

n=866.

Hence the sample size needed to estimate the mean per capita income at the 85% level of confidence is 866.

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Answer:

7 (option B)

Step-by-step explanation:

the area of a trapezoid can be found using the formula:

[tex]A = \frac{a+b}{2}h[/tex]

where

A: area

a: base

b: other base

h: height

here, we can plug in our known variables to solve for h (height)

A: 119

a: 10

b: 24

h: ??

[tex]A = \frac{a+b}{2}h[/tex]

[tex]119 = \frac{10+24}{2}h[/tex]

{now, simplify!}

[tex]119 = \frac{10+24}{2}h[/tex]         {add 10 + 24}

[tex]119 = \frac{34}{2}h[/tex]            {divide 34 by 2}

119 = 17 · h

119     =    17 · h

÷ 17       ÷17             {divide both sides by 17to isolate h}

7 = h

So, the height (h) of this trapezoid is 7

hope this helps! have a lovely day :)

A model without any simplifying assumptions b.is highly complex and likely unworkable.

As their call implies, simplifying assumptions are assumptions that are protected within the version to simplify the evaluation as tons as feasible. While a simplified version now does not predict the conduct of the actual issue within perfect bounds, too many simplifying assumptions have been made.

While a scientific version enables us to make predictions, it's more valued. As clinical models are representations of simplified explanations, they do not are looking for to explain each scenario or every detail. This means that medical models often aren't equal to the 'real international' from which they are derived.

Mathematical models can help college students apprehend and discover the that means of equations or valuable relationships.

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Her work is correct, but there is one solution rather than no solution.

Linear equations are equations that has a degree of 1. Given the equation below;

3(2x + 1 ) = 2(x + 1) + 1

Expand

3(2x) + 3(1) = 2(x) + 2(1) + 1

Simplify

6x + 3 =2x + 2 + 2

6x + 3 = 2x + 3

Collect the like term

6x - 2x = 3 - 3

4x = 0

x =0

Hence we can conclude that Her work is correct, but there is one solution rather than no solution.

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Step-by-step explanation:

A.Confidence Level: 99.7%; Confidence Interval: 42 to 48 

B.Confidence Level: 95%; Confidence Interval: 43 to 47

 C.Confidence Level: 68%; Confidence Interval: 44 to 46 

D.Confidence Level: 95%; Confidence Interval: 44 to 46

The value of b in the expression is -2.

a + a + b = 14

b + b + c = 8

a + b + c = 18

Therefore,

2a + b = 14

2b + c = 8

c = 8 - 2b

Hence,

a + b + 8 - 2b = 18

a - b = 18 - 8

a - b = 10

2a + b = 14

a - b = 10

3a = 24

a = 8

8 - b = 10

b = 8 - 10

b = -2

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Answer:

a = 8

b = -2

c = 12

Step-by-step explanation:

a + a + b = 14

2a + b = 14 ⇒ ( 1 )

b + b + c = 8

2b + c = 8 ⇒ ( 2 )

a + b + c = 18 ⇒ ( 3 )

First, let us make a as the subject in equation 1.

2a + b = 14

2a = 14 - b

[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex]   ⇒ ( 4 )

Let us make c as the subject in equation 2.

2b + c = 8

c = 8 - 2b ⇒ ( 5 )

Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.        

And now let us solve the equation 3 to find the value of b.

[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]

[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]

[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]

And now let us find  the value of a

For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.

[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]

Now, let us find the value of c.

For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.

[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]

The angle that corresponds to ∠N after transformation is: A. ∠N'.

Transformation is a process of manipulating a figure to create an identical figure either by dilation, rotation, or translation.

In the transformation performed in the image shown below, the new image formed is congruent to the original figure. This means polygon LMNOP ≅ L'M'N'O'P.

Therefore, the angle that corresponds to angle N is: A. Angle N'

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Answer: A). Angle N'

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

these measure do not form a right triangle

The index form of the expression is 5^-1m

Note that index form means in a power form

We have that;

= 4m/20m

Find the similar factor

= 1/5m

The inverse of a number, is that number to the power of -1

Then,

1/5m = 5^-1m

Thus, the index form of the expression is 5^-1m

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Work Shown:

f(x) = 5x - 7

f(3) = 5(3) - 7 .... every x replaced with 3

f(3) = 15 - 7

f(3) = 8

[tex] \: [/tex]

Given :

To Find :

Calculating the value of x :

[tex]\sf : \implies \: 5x - 7[/tex]

[tex]\sf : \implies \: 5(3) - 7[/tex]

[tex]\sf : \implies \: 15 - 7[/tex]

[tex]\bf : \implies \: 8[/tex]

Hence,

[tex] \implies \boxed{ \bf \: \therefore \: The \: value \: of \: x \: is \: 8 \: } \\ \\ [/tex]

Answer: False

Step-by-step explanation:

   This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.

   A function must have only one output [y-value] for every input [x-value].

The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ

An equation is an expression that shows the relationship between two or more variables and numbers.

Let f(x) and g(x) represent the value in the savings account of Jack and Susie respectively after x years. Hence:

f(x) = 1000(1.015)ˣ, g(x) = 800(1.015ˣ

Hence:

Total savings = 1000(1.015)ˣ + 800(1.015)ˣ = (1.015)ˣ[1000 + 800] = 1800(1.015)ˣ

The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ

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Answer:

P = 60 inches

Step-by-step explanation:

Perimeter is the distance around the outside of a shape. So, to find perimeter, add up all the sides.

The side lengths were given, add them:

15 + 20 + 25

= 60

The perimeter is 60 inches.

The given equality 2 divided by 9 = 5/2 divided by 5/4 is seen to be; False because LHS ≠ RHS

We are given the equality;

2 divided by 9 = 5/2 divided by 5/4

We want to check whether the left hand side of the equality is equal to the right hand side. Thus;

Left hand side can be expressed as;

2 divided by 9 = 2/9

Now, right hand side can be expressed as;

5/2 ÷ 5/4

⇒ (5/2) * (4/5)

⇒ 2

Therefore we can see that LHS is not equal to RHS and so the equality is false.

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Answer: no solution

Step-by-step explanation:

if we simplify this equation, we derive that 9=2.

this is a false statement, which means this equation has no real solutions.

Answer:

0.00003mm

Step-by-step explanation:

We know that 1mm=1000000nm

To convert small unit to big we divide

So 30÷1000000=0.00003nm

The true statement about the graph's slope is (c) Its slope is zero.

From the question, we have:

A horizontal line is at y = 2.5.

The horizontal line implies that the cost of lunch do not change

Horizontal lines have a slope of 0

Hence, the true statement about the graph's slope is (c) Its slope is zero.

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The correct statements regarding the linear function are given as follows:

A linear function is modeled by:

y = mx + b

In which:

In this problem, the line goes through points (-6,-7) and (8,0), hence the slope is given by:

[tex]m = \frac{0 - (-7)}{8 - (-6)} = \frac{7}{14} = \frac{1}{2} = 0.5[/tex]

Hence:

y = 0.5x + b

When x = 8, y = 0, hence the y-intercept is given as follows:

0 = 0.5(8) + b

b = -4.

When x = -2, we have that:

y = 0.5(-2) - 4 = -1 - 4 = -5.

The points (–2, –5) and (8, 0) are also on the line.

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Answer:

B,C,E

Step-by-step explanation:

took the test on edge and got 100

The value of this car when it is 9 years old is equal to $16,757.00.

In order to determine the value of this car when it is 9 years old, we would use an exponential function which also relates to compound interest as follows:

A = P(1 - r)^t

Substituting the given parameters into the formula, we have;

A = 32,200(1 - 0.07)^9

A = 32,200(0.93)^9

A = 32,200 × 0.5204

A = $16,757.00.

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Answer:

Step-by-step explanation:

There are several ways you can find the values of an exponential function for different values of the independent variable. You can read them from its graph, evaluate the formula, or recognize the relationship between the values.

The graph shows you the population is 10 in year 1, up by a factor of 2 from the population of 5 in year 0. The exponential nature of the function means the population will double in each of the next few years:

  2 years: 2 × 10 = 20

  3 years: 2 × 20 = 40

  4 years: 2 × 40 = 80

__

Additional comment

You can always use a calculator to evaluate the function for different values of t.

Answer:

The expression for the statement using absolute value notation is [tex]$|p-0.08| \leq 0.015$[/tex].

Step-by-step explanation:

It is given in the question that the true proportion p of people who give a favourable rating to Congress is 8% with a margin of error of 1.5%. It is required to express the statement using absolute value notation.

To express the statement using absolute value notation, deduce the statement in the form of an equation.

The error margin for the hypothesis is 1.5% which implies the absolute difference between p and 8% should be less than or equal to 1.5%.[tex]$$|p-0.08| \leq 0.015$$[/tex]

[tex]\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}[/tex]

Answer:

26

Step-by-step explanation:

√(24 - 0)2 + (10 - 0)2

= √(24)2 + (10)2

= √676 and that would equal

26

The term that describes point N is centroid. The correct option is C. Centroid

The centroid of a triangle is the point in which the three medians of the triangle intersect.

The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

In the given diagram, we can observe that the lines join the midpoints of each side to the corresponding opposite vertex.

Point N is the point where the lines intersect.

Hence, the term that describes point N is centroid. The correct option is C. Centroid

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Answer:

B. Circumcenter

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