Find the y-intercept of the linear functions with a slope -4 and the point ( 2, 20 )
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The interval notation of the inequality 6<x<7 is:

(6,7)

Given the inequality is:

6<x<7

the interval notation is:

(6,7)

The leftmost number of the set, a comma, and the rightmost number of the set are written using interval notation. Depending on whether those two integers are part of the set, we either place parentheses around the pair or square brackets around it (sometimes we use one parenthesis and one bracket!).

Hence we get the required interval notation.

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Answer: [tex]\frac{\ln(241/200)}{4}[/tex]

Step-by-step explanation:

If [tex]P(t)[/tex] represents the number of bacteria after [tex]t[/tex] hours, then [tex]P(t)=2400e^{kt}[/tex], where [tex]k[/tex] is the hourly growth rate parameter.

Using the fact that [tex]P(4)=2892[/tex],

[tex]2892=2400e^{4k}\\\\e^{4k}=\frac{241}{200}\\\\4k=\ln(241/200)\\\\k=\frac{\ln(241/200)}{4}[/tex]

The triangle WXY an isosceles obtuse triangle and ∠WXY is an obtuse angle

What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

The three types of Isosceles Triangles are :

Given data ,

Triangle WXY with vertices

W ( -10 , 4) , X ( -3 , -1 ) and Y ( -5 , 11 )

From the coordinates , we can see that

Now ,

When two points are given P( x₁ , y₁ ) and Q( x₂ , y₂ ) , the distance between the two points is given by distance formula

D = √( x₂ - x₁)² + ( y₂ - y₁)²

So , length of WX = √( -3 - (-10) )² + ( -1 - 4 )²

WX = √( 49 + 25 )

WX = √74

WX ≈ 8.60

So , Length of WX = 8.6 units

And , Length of XY is given by

XY = √ ( -5 - (-3) )² + ( 11 - (-1) )²

XY = √ ( 4 + 144 )

XY = √ 148

XY ≈ 12.16

So , length of XY = 12.2 units

And , Length of YW is given by

YW = √( -5 - (-10) )² + ( 11 - 4 )²

YW = √( 25 + 49 )

YW = √74

YW ≈ 8.60

So , length of YW is 8.6 units

So , WX = YW

Since , the length of WX and YW are the same , we have 2 sides with equal length and therefore the triangle WXY is an isosceles triangle

And the ∠WXY can be obtuse because of the two equal sides and the base is of larger length and hence the triangle WXY is an Isosceles obtuse triangle

An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90° and 180°), and the other two acute angles are equal in measurement.

Hence , The triangle WXY an isosceles obtuse triangle and ∠WXY is an obtuse angle

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Answer:

D(30,60)

Step-by-step explanation:

It was way outside the other points that are around the line.

The point (30,60) is a high leverage point on the regression plot.

High leverage points are those that are extreme but follow the regression equation's trend.

High leverage points are distinct from outliers, which deviate from the graph's or plot's pattern or trend.

Looking closely at the regression plot, the coordinate (30,60) follows the trend of the plot, however, it is farther from the majority of the points on the graph.

Hence, the point (30,60) is a high leverage point on the regression plot.

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Answer:

the answer is A

Check the picture below.

[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ b = \sqrt{7^2+11^2~-~2(7)(11)\cos(92^o)} \\\\\\ b = \sqrt{ 170 - 154 \cos(92^o) }\implies b\approx 13.24~km[/tex]

now, to find the bearing from C to A hmmm, let's use the Law of Cosines again, to find the angle at A, once we get that, we'll simply add 37 to it :)

[tex]\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{7^2+13.24^2-11^2}{2(7)(13)}\right)\approx\measuredangle A \implies \cos^{-1}\left(\cfrac{ 103.3 }{ 185.36}\right)\approx\measuredangle A \\\\\\ 56.13^o\approx \measuredangle A\hspace{15em} \underset{\textit{Bearing of C from A}}{\stackrel{56.13~~ + ~~37}{\boxed{\approx 93.13^o}}}[/tex]

Answer:

The length of the straw in the simplest radical form is [tex]2\sqrt{30}[/tex] inches

Step-by-step explanation:

The length of the straw can be calculated as follow

The first step is to calculate the diagonal of the base of the rectangular box  by using Pythagorean theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

Where [tex]c[/tex] is the base diagonal or the hypotenuse, [tex]a[/tex] is the short leg, [tex]b[/tex] is the long leg

Substitute [tex]2[/tex] for [tex]a[/tex], [tex]4[/tex] for [tex]b[/tex] in the Pythagorean theorem

[tex]c^{2}=2^{2}+4^{2}[/tex]

Simplify the right side of the equation

[tex]c^{2}=4+16[/tex]

[tex]c^{2}=20[/tex]

Take the square root of the right side to get the value of [tex]c[/tex]

[tex]c=\sqrt{20}[/tex]

Factor [tex]20[/tex] by [tex]4[/tex]

[tex]c=\sqrt{4\times 5}[/tex]

Substitute [tex]2^{2}[/tex] for 4

[tex]c=\sqrt{2^{2}\times 5}[/tex]

Rewrite the value of [tex]c[/tex] in the simplest radical form

[tex]c=2\sqrt{5}[/tex]

Since the value of [tex]c[/tex] is [tex]2\sqrt{5}[/tex], then the length of the diagonal of the base is

[tex]2\sqrt{5}[/tex] inches

The second step is to calculate the length of the straw by using Pythagorean theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

Where [tex]c[/tex] is the diagonal from the bottom left corner to the top right back corner or the hypotenuse, [tex]a[/tex] is the short leg, [tex]b[/tex] is the long leg

Substitute [tex]2\sqrt{5}[/tex] for [tex]a[/tex], [tex]10[/tex] for [tex]b[/tex] in the Pythagorean theorem

[tex]c^{2}=(2\sqrt{5})^{2}+10^{2}[/tex]

Simplify the right side of the equation

[tex]c^{2}=20+100[/tex]

[tex]c^{2}=120[/tex]

Take the square root of the right side to get the value of [tex]c[/tex]

[tex]c=\sqrt{120}[/tex]

Factor [tex]120[/tex] by [tex]4[/tex]

[tex]c=\sqrt{4\times 30}[/tex]

Substitute [tex]2^{2}[/tex] for 4

[tex]c=\sqrt{2^{2}\times 30}[/tex]

Rewrite the value of [tex]c[/tex] in the simplest radical form

[tex]c=2\sqrt{30}[/tex]

Since the value of [tex]c[/tex] is [tex]2\sqrt{30}[/tex], then the length of the diagonal from the bottom left corner to the top right back corner or the hypotenuse is

[tex]2\sqrt{30}[/tex] inches

Since the length of the diagonal from the bottom left corner to the top right back corner is [tex]2\sqrt{30}[/tex] inches, then the length of the straw is [tex]2\sqrt{30}[/tex] inches

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Value of n is 3 when a line that includes the points (n, -9) and (5, 7) has a slope of 8.

A line's steepness is indicated by its slope. Any line's slope is constant along its length. The direction of the line on the coordinate plane can also be determined by the slope. A line's graph can be used to determine slope, or the coordinates of any two points on a line can be used.

Given,

Slope = 8

Points = (n,-9) and (5,7)

Formula:

Slope = y₂ - y₁/ x₂ - x₁

8 = 7 -(-9)/ 5-n

Cross multiplying,

8(5 - n) = 7 +9

(5-n) = 16/8

5 -n = 2

n = 3

Value of n is 3 when a line that includes the points (n, -9) and (5, 7) has a slope of 8.

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Answer:

X-intercept: (6, 0)

Y-intercept: (0, -9)

Step-by-step explanation:

Required: Find the X and Y intercept of the standard from equation:

-3x + 2y = -18.

We shall write equation in the form [tex]\frac{x}{a} +\frac{y}{b} =1[/tex] and find the intercepts on X and Y axis:

-3x + 2y = -18

∴ -3x + 2y = -18

∴ -3x/-18 + 2y/-18 = 1

∴ x/6 + y/-9 = 1

Comparing this equation with [tex]\frac{x}{a} +\frac{y}{b} =1[/tex], we get:

intercept of X-axis = a = 6

intercept of Y-axis = b = -9

Thanks.

Answer:

The y-intercept for the line is ( 0, -9 ).

Hope this helps!

Step-by-step explanation:

The y-intercept is where the graph intercepts the y-axis and is the y-value of the point, ( x, y ).

The arc length of the given curve is L= 1/2([tex]e^{4} - \frac{1}{e^{4} }[/tex]).

What is arc length?

The distance between two places along a segment of a curve is known as the arc length.

Main Body:

So, we have [tex]y=\frac{1}{2} (e^{x} +e^{-x} )[/tex]

This is in the form y=f(x), so we know arc length L on [0,4] is given by,

L=[tex]\int\limits^4_0{\sqrt{1+(\frac{dy}{dx} })^{2} \, dx[/tex]

The derivative y=

dy/dx= [tex]\frac{1}{2} (e^{x} +e^{-x} )[/tex]= sinhx

([tex]\frac{dy}{dx}^{2}[/tex])= sinh²x

L=[tex]\int\limits^4_0{\sqrt{1+sinh^{2}x \, dx[/tex]

L= [tex]\int\limits^4_0{\sqrt{cosh^{2}x \, dx[/tex]

L=[tex]\int\limits^4_0{coshx \, dx[/tex]

Now putting the limits as given=

L= [tex]sinhx\left \{ {{y=4} \atop {x=0}} \right.[/tex]

L= [tex]\frac{1}{2} (e^{x} -e^{-x} )[/tex]|⁴₀

L=1/2([tex]e^{4} - \frac{1}{e^{4} }[/tex])

Hence the answer is  1/2( [tex]e^{4} - \frac{1}{e^{4} }[/tex]).

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Answer:

Federalism

Step-by-step explanation:

refers to the division and sharing of power between the national and state governments.

Answer:

The maximum height of the rocket with respect to the ground can be obtained by evaluating the function h(t) for a time of 1.25 seconds. The rocket reaches a maximum height of 32 ft.

The average, the median, and the range of the given data are 75, 75.7, and 25.3, respectively.

We are given the weights of five people that go to the gymnasium to exercise. The weights are 58 kg, 75 kg, 83.3 kg, 83 kg, and 75.7 kg. The average is found by dividing the sum of all the weights by the number of persons.

A = (58 + 75 + 83.3 + 83 + 75.7)/5 = 375/5 = 75

Hence, the average weight is 75 kg. The median weight is the center value when all the weights are arranged in ascending or descending order. The weights arranged in the ascending order are 58 < 75 < 75.7 < 83 < 83.3. The third weight lies in the center. Hence, the median weight is 75.7 kg. The range of the data is the difference between the maximum and the minimum weight. The maximum and minimum weights are 83.3 kg and 58 kg, respectively.

R = 83.3 - 58 = 25.3

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The logarithm function can be used to convert large problem of multiplication and division into simple addition or subtraction. The value of x for the given equation is 2.

Logarithm function is defined as the inverse of the exponential function.

If a^(b) = c, then b = log(c) at the base of a.

The given equation is as below,

2^x=x^2

Take logarithm both sides,

x log(2) = 2 log(x)

=> x / log(x) = 2 / log(2)

Compare the denominator and numerator at both sides of the equation to get,

x = 2.

Hence the solution of the given equation is x = 2.

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Answer: C

Because X is less than or equal to 11 the number line can include 11 and because its less than the arrow should be decreasing or going towards negative infinity

Factor of the following polynomial function is (x-1)(x+7)(x-4+4i)(x-4-4i).

If 4-4i is a zero, then is its conjugate, 4+4i, as well.

Next 4-4i and 4+4i are zeros, this means that

x^4-2x^3-23x^2+248x-224=(x-4+4i)(x-4-4i)g(x), (A)

where g(x) is a degree 2 polynomial.

Since (x-4+4i)(x-4-4i)=x^2-8x+32,(A) is equivalent to

x^4-2x^3-23x^2+248x-224=(x^2-8x+32)g(x) (B)

Now dividing the LHS of (B) by x^2-8x+32 you find that g(x)=x^2+6x-7.

So,

x^4-2x^3-23x^2+248x-224=(x^2-8x+32)(x^2+6x-7) (C)

It is easy to see that x^2+6x-7=(x-1)(x+7).

Finally, you get

x^4-2x^3-23x^2+248x-224=(x-1)(x+7)(x-4+4i)(x-4-4i)

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The rate of change  radius of the balloon increasing  when the radius is 2 meters is 0.15  meters per minute.

A spherical balloon is being inflated with hot air at a rate

= 8 cubic meters per minute.

volume of a spherical balloon is :

[tex]volume = \frac{4}{3}\pi r^3[/tex]

rate of change of volume is given as :

dv/dt = (4/3) π 3 r² (dr/dt)

8 =  4πr²(dr/dt)

(dr/dt) = 8 / 4πr²

(dr/dt) = 8 / ( 4 x 3.14 x 2 x 2)

(dr/dt) = 0.15 Meter/mint

The rate of change  radius of the balloon increasing  when the radius is 2 meters is 0.15  meters per minute.

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Answer: Line perpendicular to  y = 2x - 5 is  y = (-1/2)x.

Step-by-step explanation:

Answer:

class A .................

The other three length are 9km,12km,14km as mode is 12km

What is mode?

The value that appears most frequently in a set of values is referred to as the mode. It is the value that shows up the most frequently. The value that consistently appears in a given set is known as the mode in statistics. The mode or modal value is the value or number that appears most frequently in a data set and has a high frequency. Along with mean and median, there are three other ways to measure central tendency.

The mean, median, and mode all have the same values for this distribution. This indicates that this value—the one that appears the most frequently in the data—is the average, the centre, and the mode.

Four lengths have a mode of 12 km and a range of 5 km.

The range is the largest number minus the smallest number.

As mode is 12 so one more number is 12 as well.

Now another number given 14km, so the last number is (14-5 = 9)

Hence the other three lengths are 9km,12km,14km.

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[tex]f(x) = \sqrt{x}[/tex] could be transformed to [tex]g(x) = \sqrt{x + 7}[/tex] responses horizontal shift of 7 units left.

What if graph transformation?

Graph transformation, often known as graph rewriting, is the process of algorithmically constructing a new graph from an original graph. It has several uses, including software engineering, layout algorithms, and image production.

Consider, the given equation of graph

[tex]f(x) = \sqrt{x}[/tex]

The graph becomes,  [tex]g(x) = \sqrt{x + 7}[/tex].

The constant value remains unchanged. As a result, the graph will not move vertically. The graph shifts in the horizontal direction as a unit's variable changes.

Therefore, the transformation of graph is, horizontal shift of 7 units left.

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Answer:

y+2>y

Step-by-step explanation:

Well, first of all. Adding any sum to y makes it greater then the same variable.

Greater than sign is >. Keeping that in mind now add them. y+2>y is gonna be you’re final answer!

17.16 is the estimated 22% of 78.

What is estimation?

To make calculations simpler and more realistic, estimation of a number refers to a plausible assumption of the actual value.

Estimation is the process of approximating a quantity with the necessary accuracy.

The result is quickly and roughly determined by rounding off the numbers used in the calculation.

Assumedly, 22% of 78.

78 comes out to 80.

Therefore, cut 22% to 1/5.

78 through 80 is increased.

80/5 = 16( close to 17.16) ( approximate to 17.16)

Or

22% = 22/100

22% of 78 = 22 × 78 /100 = 1716/100

= 17.16.

As a result, 17.16 is the estimated 22% of 78.

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We can cut 4 4/15 pieces from 5 1/3 inches candy bar if the length of each candy is 1 1/4 inch.

Length of candy bar is 5 1/3 which can be written as 16/3 in

Length of piece that is to be cut from long candy bar is 1 1/4 or 5/4 in

Number of pieces

= length of piece/ total length of candy bar

=  (16/3) / (5/4)

= 16/3 × 4/5

= 64/15

= 4 4/15 pieces

4 4/15 number of pieces can be cut from 5 1/3 inches long candy bar

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Answer:

R = 4.47

Step-by-step explanation:

Simply just R = sqrt(20)

Answer:

9.75

Step-by-step explanation:

[tex](-2)^{4}[/tex] - [tex]2.5^{2}[/tex]  Means

(-2)(-2)(-2)(-2) - (2.5)(2.5)

16 - 6.25

9.75

Answer:36

Step-by-step explanation:

The function [tex]24x^{3}[/tex] + [tex]Ax^{2}[/tex] -3x + B results to the equation A + 4B = 114 hen f(x) is divided by (2x - 1) and with a remainder 30.

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

For example, 10 is not exactly divided by 3. Since the closest value, we can get 3 x 3 = 9.

Hence, 10 ÷ 3 → 3 R 1, where 3 is the quotient and 1 is the remainder.

if ( 2x - 1) divides  [tex]24x^{3}[/tex] + [tex]Ax^{2}[/tex] -3x + B with a remainder 30, it means if x = 1/2 when substituted should give 30.

The substitute x = 1/2 into the given function and equate it to 30

24[tex](\frac{1}{2}) ^{3}[/tex] + A[tex](\frac{1}{2}) ^{2}[/tex] - 3(1/2) + B = 30

24[tex](\frac{1}{8})[/tex] + A[tex](\frac{1}{4})[/tex] - 3/2 + B = 30

3 + A/4 -3/2 + B = 30

multiply through by 4

12 + A -6 + 4B = 120

keeping A + 4B at the left we have

A + 4B = 120 -12 + 6

A + 4B = 114

Proved

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Using implicit differentiation, the value of y in terms of x and y is; y = 0.5/(dy/dx)

In implicit differentiation, what we do is that we differentiate each side of an equation using the two variables (usually x and y) by treating one of the variables to be as a function of the other.

We are given the equation;

4x = 4y² + 1

Thus, first differentiation gives;

4 = 8y(dy/dx)

y(dy/dx) = 0.5

y = 0.5/(dy/dx)

This is the result when using implicit differentiation on the given function where y is the subject of the formula.

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