Can someone help me with these problems please

The equation of the line is y = 3/2x - 3

The points are given as:

(0, -3), (2, 0), and (4, 3).

Start by calculating the slope (m) using:

m = (y2-y1)/(x2 -x1)

This gives

m = (3 + 3)(4 - 0)

Evaluate

m = 3/2

The equation is the calculated as:

y = m(x - x1) + y1

This gives

y = 3/2(x - 0) - 3

y = 3/2x - 3

Hence, the equation of the line is y = 3/2x - 3

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Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

[tex]S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23[/tex]

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.

Given that slant height is 10 units and base lengths of 6 units.

We are required to calculate total surface area of regular square pyramid.

We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.

Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]

=36+6[tex]\sqrt{36+400}[/tex]

=36+6[tex]\sqrt{436}[/tex]

=36+6*20.88

=36+125.28

=161.28

Nearest option is 168 square inches.

Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.

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Profit function : p(x) = 53 x - 12

Cost is the total cost of producing the output.

The cost function consists of two different types of costs:

- Variable costs

- Fixed costs.

Variable costs vary with output (number of units produced). Total variable costs can be

expressed as the product of variable costs per unit and the number of units produced. If there are multiple items

manufactured costs are higher.

Fixed costs usually do not vary with performance.

Revenue is the total payment received from the sale of goods or the provision of a service.

The revenue function R() reflects the revenue from selling “” quantity of output items at price

"p" after item.

() =

Profit functions

The profit function P() is the difference between the revenue function R(x) and the total cost function C()

So P() = R() – C()

=−

Now, Profit = Revenue - Cost

= 60 x - ( 12 + 7 x)

= 60 x -12 -7 x

Profit = 53 x - 12

Hence, Profit function : p(x) = 53 x - 12

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The solutions of the equations x - 5y = 0 and 15x + 10y = 17 at x and y is 1 and 1/5 respectively.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Given that:

The linear equations are:

x - 5y = 0

15x + 10y = 17

Solve the equations using elimination method:

Multiply equation 1 by 2

2(x - 5y) = 0

15x + 10y = 17

This can be solved as:

2x-10y = 0.....(1)

15x + 10y = 17....(2)

On subtracting equation 1 from 2

17x = 17

x = 1

The value of x is 1.

Substitute the value of x in equation (1)

2(1)-10y = 0

2=10y

y = 1/5

Thus, the value of x and y is 1 and 1/5 respectively.

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The factorise form of the two expression are as follows:

b. (x - 3)(2 / 3 x - 6) = 0

Therefore, let's open the brackets

2 / 3 x² - 6x -2x + 18 = 0

2 / 3 x²  - 8x + 18 = 0

multiply through by 3

2x² - 24x + 54 = 0

Hence,

 2 (x - 3)  (x - 9)

c.

(-3x - 15)(x + 7)  = 0

Therefore,

-3x² - 21x - 15x - 105 = 0

-3x² - 36x - 105 = 0

-3(x + 5)(x + 7)

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The dimensions of the rectangle are: length= 18 in and width =1 in.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².

For this question, the length exceeds its width by 17 inches - l=w+17. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=l*w

18=(w+17)*w

18=w²+17w

w²+17w-18=0

Next step will be solve the previous equation ( W²+17W-18=0)

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

Therefore,

[tex]w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18[/tex]

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², you have.

18=l*w

18=l*1

l=18 in

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Answer:

x > - 3

Step-by-step explanation:

6(x + 2) > x - 3 ← distribute parenthesis on left side

6x + 12 > x - 3 ( subtract x from both sides )

5x + 12 > - 3 ( subtract 12 from both sides )

5x > - 15 ( divide both sides by 5 )

x > - 3

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏

✏[tex]\bigstar\textsf{Solution \quad Steps:-}[/tex] ✏

use the distributive property

[tex]\sf{\longmapsto 6x+12 < x-3}[/tex]

subtract both sides by x and 12

[tex]\sf{\longmapsto{5x < -15}[/tex]

divide both sides by 5

[tex]\sf{\longmapsto x < -3}}[/tex]

`hope it's helpful to u ~

The system has:

A system of two linear equations is given by:

y = a*x + b

y = c*x + d

1) The system has no solutions when both lines are parallel lines, this happens when both lines have the same slope and different y-intercept.

y = a*x + b

y = a*x + d

2) The system has one solution when the lines have different slopes:

y = a*x + b

y = c*x + d

3) The system has infinite solutions when both equations describe the same line:

y = a*x + b

y = a*x + b

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The value of w(u(4)) is 73.

u( x ) = - 2*x + 2

w( x ) = 2*x^2 + 1

w( u( x ) ) = w( - 2*x + 2  )

⇒ w( u( x ) ) = 2*( - 2*x + 2  )^2 + 1

⇒ w( u( x ) ) = 2*[ 2^2 + ( 2*x )^2 - 2*2*( 2*x ) ] + 1

⇒ w( u( x ) ) = 2*[ 4 + 4*x^2 - 8*x ] + 1

⇒ w( u( x ) ) = 8 + 8*x^2 - 16*x + 1

⇒ w( u( x ) ) = 8*x^2 - 16*x + 9

⇒ w( u( 4 ) ) = 8*4^2 - 16*4 + 9

⇒ w( u( 4 ) ) = 8*16 - 16*4 + 9

⇒ w( u( 4 ) ) = 128 - 64 + 9

⇒ w( u( 4 ) ) = 73

In mathematics, a feature from a set X to a fixed Y assigns to each detail of X exactly one detail of Y. The set X is called the domain of the function and the set Y is referred to as the codomain of the function. features were firstly the idealization of how various quantity relies upon any other quantity.

These elementary functions include

A function is defined as a relation between a set of inputs having one output each. In simple phrases, a function is a courting among inputs wherein every entry is associated with exactly one output. every function has a site and codomain or range. A characteristic is normally denoted through f(x) in which x is the input.

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The correct option is the third one:

-1 ≤ y - 3 and y - 3 ≤ 1

Which compound inequality represents the absolute value inequality?

Here we have:

|y - 3| - 4 ≤ -3

We can rewrite it to:

|y - 3| ≤ -3 + 4

|y - 3| ≤ 1

This can be decomposed in two inequalities, which are:

(y - 3) ≤ 1

(y - 3) ≥ -1

Then we can see that the correct option is the third one, as both inequalities must be meet.

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Answer:

x=m/9

Steps:

m=9x

m/9=x

x=m/9

Answer:

12  and 3

Step-by-step explanation:

Let  x= length

If you draw a rectangle.  two sides would be the length x.  The other two sides would be (x-9).

(length)(width) = Area

(x)(x-9) = 36

x^2 - 9x = 36 Substitute in x and x-9 for the length and width

x^2 - 9x - 36 =0  Subtract 36 from both sides

(x-12)(x+3) = 0   We are looking for 2 number that add to -9 and mult. to -36

x-12=0 and x+3=0  Set both factors to 0 and solve

x = 12 and x =-3.  It does not make sense that a length could be -3 so we reject that answer.  If the length is 12, then the width is 3

If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.

5 - 5 = 0

6 - 6 = 0

Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.

Hope this helps!

I think its (B)

V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

Given equation:

[tex]x-\left(2x-\dfrac{3x-4}{7}\right)=\dfrac{4x-27}{3}-3[/tex]

Expand the left side:

[tex]\implies x-2x+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Let all terms on the left side have the same denominator of 7:

[tex]\implies \dfrac{7x}{7}-\dfrac{14x}{7}+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Join the terms on the left side:

[tex]\implies \dfrac{7x-14x+3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Let all the terms on the right side have the same denominator of 3:

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-\dfrac{9}{3}[/tex]

Join the terms on the right side:

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27-9}{3}[/tex]

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-36}{3}[/tex]

Cross multiply:

[tex]\implies 3(-4x-4)=7(4x-36)[/tex]

Expand:

[tex]\implies -12x-12=28x-252[/tex]

Add 12x to both sides:

[tex]\implies -12=40x-252[/tex]

Add 252 to both sides:

[tex]\implies 240=40x[/tex]

Divide both sides by 40:

[tex]\implies 6=x[/tex]

[tex]\implies x=6[/tex]

The average speed is 50 meters per second

The given parameters are:

Laps = 4

Time = 2 minutes

1 lap = 25 meters

Start by calculating the total distance

Distance = Laps * Meters

Distance = 4 * 25 meters

Distance = 100 meters

The average speed is then calculated as:

Speed = Distance/Time

This gives

Speed = 100 meters/2 minutes

Evaluate

Speed = 50 meters per second

Hence, the average speed is 50 meters per second

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Answer:

  II only

Step-by-step explanation:

The positive leading coefficient and even degree of f(x) tell you its graph is U-shaped and opens upward.

If there is an interval where the function is negative, it must lie between the two x-intercepts. The graph will be above the x-axis (f(x) > 0) for x-values outside that interval.

The only reasonable answer choice is ...

  II  (-1, 4) . . . . only

The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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Answer:

D

Step-by-step explanation:

We will use the order of operations to evaluate the expression.

From left to right , Multiplication/Division followed by Addition/Subtraction.

21 / 3 + 8 - 4

= 7 + 8 - 4

= 15 - 4

= 11

Therefore, the answer is D

Answer:

D) 11

Step-by-step explanation:

Division and multiplication always comes first in an equation. Since there is no multiplication in the expression, we can divde first.

21 / 3 = 7

Our new expression will be: 7 + 8 - 4

Now we can just add (7) , (8), and (-4) not caring about the order, since they are all addition or subtraction.

I'll do the addition first, but order does not matter.

7 + 8 = 15

15 - 4 = 11

So 11 is our final answer.

Looking at the answer choices, D has 11, so D is our answer for this question.

This question is asking to create 5 of your own questions, so here are mine with the process on how I got each:

Question 1: Given c(x) = 8x + 32, find the range of c for the domain {1, 3, 5}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 8, and adding by 32.

c(1) = 8(1) + 32 = 8 + 32 = 40

c(3) = 8(3) + 32 = 24 + 32 = 56

c(5) = 8(5) + 32 = 40 + 32 = 72

Range: {40, 56, 72}

Question 2: Given d(x) = x - 7, find the range of d for the domain {-2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, and subtracting 7.

d(-2) = -2 - 7 = -9

d(3) = 3 - 7 = -4

Range: {-9. -4}

Question 3: Given f(x) = 7x + 738, find the range of f for the domain {1.5, 11}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by 7, and adding 738.

f(1.5) = 7(1.5) + 738 = 10.5 + 738 = 748.5

f(11) = 7(11) + 738 = 77 + 738 = 815

Range: {748.5, 815}

Question 4: Given g(x) = -2804x + 7268, find the range of g for the domain {50, 75, 256}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -2804, and adding 7268.

g(50) = -2804(50) + 7268 = -140200 + 7268 = -132932

g(75) = -2804(75) + 7268 = -210300 + 7268 = -203032

g(256) = -2804(256) + 7268 = -717824 + 7268 = -710556

Range: {-132932, -203032, -710556}

Question 5: Given h(x) = -3x - 4, find the range of h for the domain {1, 2, 3}.

Answer w/ Process:

For each equation, I am plugging in each domain value for x in the function, multiplying by -3, and subtracting by 4.

h(1) = -3(1) - 4 = -3 - 4 = -7

h(2) = -3(2) - 4 = -6 - 4 = -10

h(3) - -3(3) - 4 = -9 - 4 = -13

Range: {-13, -10, -7}

b(-3)

b(5)

b(9)

Range

Rest questions

#1

k(x)=2x²-5

Find the range of k for domain {1,2,6}

#2

h(x)=9x³

Find the range of h for domain {9,0,8}

#3

o(x)=6x-7

find the range of o for domain {0,1,9}

#4

p(x)=23x²-5x

Find the range of p for domain {3,4,8}

The quotient of the polynomials [tex]2x^{3} +3x^{2} -5x-6[/tex] divided by (x+1) is [tex]2x^{2} -x-6[/tex].

Given two polynomials [tex]2x^{3}+3x^{2} -5x-6[/tex] and (x+1).

We have to determine whether [tex]2x^{3}+3x^{2} -5x-6[/tex] is divisible by (x+1).

Factors are the numbers which are multiplied to get the number whose factors are given. The factor theorem is a theorem which links factors and zeroes of a polynomial.

Polynomial is an expression of more than two algebraic terms may be in addition or subtraction.

We have to first find the factors of polynomial [tex]2x^{3}+3x^{2} -5x-6[/tex].

[tex]2x^{3}+3x^{2} -5x-6[/tex]=[tex]2x^{3}+3x^{2} -4x-x-6[/tex]

=[tex]x^{2}[/tex](2x+3)-2(2x+3)-x

=[tex](x^{2} -x-2)[/tex](2x+3)

=([tex]x^{2}[/tex]-x-2)(2x+3)

=[[tex]x^{2}[/tex]-2x+x-2](2x+3)

=[x(x-2)+1(x-2)](2x+3)

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

Because (x+1) is a factor of [tex]2x^{3}+3x^{2} -4x-x-6[/tex],so it is divisible by (x+1).

Hence using factor theorem we can say that [tex]2x^{3}+3x^{2} -4x-x-6[/tex]is divisible by (x+1).

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The missing data item for the given set of data if the median is 14 is 18.

The Median is the "middle" of a sorted list of numbers.

Therefore, the missing data item for the given set of data if the median is 14 can be calculated as follows:

10 10, 11, 11, 12, 12, 14, 15, 16, 18, 19, 19,

Therefore, if you add 18 the middle number of the sorted numbers will be 14.

10 10, 11, 11, 12, 12, 14, 15, 16, 18, 18, 19, 19,

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Answer:

69%

Step-by-step explanation:

Overall grade = 0.35*minor grade + 0.65*major grade

major grade: 0.65*61 = 39.65

minor grade: 0.35*84 = 29.4

total: 39.65+29.4 = 69.05

Rounded = 69%

Based on the number of years till maturity and the required rate of return, the price of the zero-coupon bond is $852.22.

When a bond's par value is not given, assume it is $1,000.

the price of a zero coupon bond is:

= par value / (1 + rate) ^ number of years till maturity

solving gives:

= 1,000 / (1 + 3.25%)⁵

= 1,000 / 1.17341139582939453125

= $852.22

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Answer:

1000xm

Step-by-step explanation:

1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️

It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.

Given:

Distance traveled by light = 10,000 km

Time taken by light = 3.0 x 10² seconds

To convert km to meters, we know that 1 km = 1 x 10³ m, so:

10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m

Now, we can find the time taken to travel one meter by dividing the total time by the total distance:

Time taken to travel one meter = Total time / Total distance

Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)

To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:

Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)

Now, we get the final answer:

Time taken to travel one meter = 3.0 x 10⁻⁵ seconds

So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.

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Answer:   y = -x + 2

Step-by-step explanation:

Point slope form is y - y = m(x - x)

m = the slope of the line

Slope-intercept form is y = mx + b

m = the slope of the line

b = y-intercept

So because the - is in the m spot in the point-slope form, that means that is the slope of the line meaning it will also be in the m spot in slope-intercept form. The y-intercept of the line is found when x is 0.  When we look at the two coordinates provided you can see that one of them shows when x is 0.  We see that when x is 0, y is 2  which means that the y-intercept is 2.

So when you put the 2 in place of b,  you get   y = -x + 2

The equation of a trend line that passes through the points (7, 450) and (14, 401) is y = -7x+99.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Points are: (7, 450) and (14, 401)

Slope(m)=(401-450)/(14-7)

              = -49/7

              = -7

Equation of trend line:

(y-450)= -7(x-7)

y-450= -7x+49

y= -7x+49+450

y= -7x+499

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The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.

Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.

We have to calculate the percentage of great  lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.

Because we have not given the sample size taken so we will use any test.We are using z test.

We know that,

z=X-μ/σ

where μ is population mean and σ is population standard deviation.

We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.

P value between $234.5 and $318:

z=234.5-318/83.5

=-83.5/83.5

=-1

p value of -1 is 0.1587

P value between $318 and $401.5:

z=401.5-318.5/83.5

=83.5/83.5

=1

p value of z=1 is 0.3413

Total p value=0.1587+0.3413

=0.5

Total percentage=0.5*100

=50%

Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.

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