What is the range of the equation?
5x + 3y = 30

Answer:

the answer is A

The first term [tex]a_{1}[/tex] = 2 and the sum of first 30 terms [tex]s_{30}[/tex] = 930

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Arithmetic sequence is gotten by adding a known term by a constant value.

if [tex]a_{33}[/tex] = 66 and d = 2 and [tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n -1)d and n = 33

Then

[tex]a_{33}[/tex] =  [tex]a_{1}[/tex] + 32d,

making  [tex]a_{1}[/tex] subject of the equation we have

[tex]a_{1}[/tex] =66 - 32 x 2

[tex]a_{1}[/tex] = 66 - 64

[tex]a_{1}[/tex] = 2

if n = 30,  [tex]a_{1}[/tex] =-2, d = 2

Then

[tex]a_{30}[/tex] = 2 + ( 30 - 1) x 2

[tex]a_{30}[/tex] = 2 + 29 x 2

[tex]a_{30}[/tex] = 60

if [tex]s_{n}[/tex] = n/2([tex]a_{1}[/tex] + [tex]a_{n}[/tex])

Then,

[tex]s_{30}[/tex] = n/2 ( [tex]a_{1}[/tex] + [tex]a_{30}[/tex]) where n = 30

[tex]s_{30}[/tex] = 30/2( 2 + 60)

[tex]s_{30}[/tex] = 930

In conclusion, the sum of he first 30 terms is 930 and the first term is 2

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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 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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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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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:

R = 4.47

Step-by-step explanation:

Simply just R = sqrt(20)

Answer:

(32, 8)

Step-by-step explanation:

Substitute 4y for x in x + y = 40 and solve for y. Then find x.

[tex]4y + y = 40[/tex]

[tex]5y = 40[/tex]

[tex]y = 8[/tex]

[tex]x = 4(8) = 32[/tex]

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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Answer:

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

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!

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 ).

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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 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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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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Money is anything generally accepted as final payment for goods, services, and debt.

First, let us understand the money supply:

The money supply is the total amount of currency and liquid assets in a country's economy on the day measured. Cash and deposits that can be utilized virtually as quickly as cash are roughly included in the money supply.

Money supply refers to the total amount of money held by the public for a particular point.

Governments print paper money and coins through a combination of central banks and treasuries. Bank regulators impact the money supply available to the public by requiring banks to retain reserves, determining how to grant credit, and other monetary matters.

We can say that we are using the money for goods purchasing, service requirements, and for the debt taken.

Thus, money is anything generally accepted as final payment for goods, services, and debt.

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Answer:

f(-7) = 18

f(-3) = 14

f(4) = 7

Step-by-step explanation:

f(-7)

l-7-8l + 3

l-15l + 3

15 + 3

18

F(-3)

l-3-8l + 3

l-11l + 3

11 + 3

14

F(4)

l4-8l + 3

l-4l + 3

4 + 3

7

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 EF is the diameter. Then the area of the circle is  113.04  square meters.

circle :

A circle is a circular shape without corners or line segments. In terms of geometry, it has the shape of a closed curve.

EF = diameter

EF = 12 meter

then, radius  = d/2 = 12/2 = 6 meter

Area of the circle is calculated  as:

area = πr²

area = 3.14 x 6 x 6

area = 113.04 square meter

The given que is incomplete . The correct question is given as :

The EF is the diameter. If EF measures 12 meters, the approximate area of circle B is square meters.

The EF is the diameter. Then the area of the circle is  113.04  square meters.

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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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The graph of the function is increasing when x>0.

What is graph?

Graph a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

What is cube root parent?

The basic parent cube root function is of the form f (x) = ∛x. It increases on the interval (-∞, ∞). It increases on the interval [0, ∞). It is positive on (0, ∞) and negative on (-∞, 0). It is a non-negative function always (on [0, ∞)). Its absolute min is 0 but no absolute max. Its domain and range is the set of all real numbers.

Given,

The function f(x) = ∛x

Let x = 1, we get f(x) = 1,

x =2, f(x) = 8

if x =3, f(x) = 27.

As we know, with increase in the value of x, the value of f(x) is also increasing.

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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:36

Step-by-step explanation:

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

Step-by-step explanation:

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 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: [tex]\frac{11}{5}[/tex]

Step-by-step explanation

(y2-y1)/(x2-x1)

which means (5-(-6))/-4-(-9)=[tex]\frac{11}{5}[/tex]

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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Step-by-step explanation:

Using Triangle Intersection Theorem,

2(LM)=2+x

[tex]2(2x - 11) = 2 + x[/tex]

[tex]4x - 2 2 = 2 + x[/tex]

[tex]3x = 24[/tex]

[tex]x = 8[/tex]