If f(x) is a linear function and given f(3)=−3 and f(8)=1, determine the linear function. a.) What is the slope? (Be sure to leave your answer in reduced fraction form.) b.) What is the y-intercept? (Be sure to leave your answer in reduced fraction form.) c.) What is f(x)? f(x)=

Answer:

\(\frac{10\sqrt{6} }{3}\) and \(\frac{11\sqrt{3} }{3}\)

Step-by-step explanation:

(a)

A = \(\frac{1}{2}\) × 4\(\sqrt{2}\) × \(\frac{5}{\sqrt{3} }\)

   = 2\(\sqrt{2}\) × \(\frac{5}{\sqrt{3} }\)

   = \(\frac{10\sqrt{2} }{\sqrt{3} }\) × \(\frac{\sqrt{3} }{\sqrt{3} }\) ← rationalise the denominator

= \(\frac{10\sqrt{6} }{3}\) units²

(b)

Using Pythagoras' identity in the right triangle

let hypotenuse be h , then

h² = (4\(\sqrt{2}\) )² + (\(\frac{5}{\sqrt{3} }\) )²

    = 32 + \(\frac{25}{3}\)

    = \(\frac{96}{3}\) + \(\frac{25}{3}\)

    = \(\frac{121}{3}\) ( take the square root of both sides )

h = \(\sqrt{\frac{121}{3} }\) = \(\frac{11}{\sqrt{3} }\) × \(\frac{\sqrt{3} }{\sqrt{3} }\) ← rationalise the denominator

h = \(\frac{11\sqrt{3} }{3}\)

Answer:where’s the expression?

Step-by-step explanation:

Answer:

90-30=60

60+2=62

answer:62

The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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The percentage increase per year in the winner's check over the given period. If the winner's prize increases at the same rate, it will be $1,454,735,139.69 in 2040.

To calculate the percentage increase per year in the winner's check over the period from 1895 to 2007, we can use the following formula:

Percentage Increase = (Final Value - Initial Value) / Initial Value * 100

a. Calculating the percentage increase:

Initial Value = $140

Final Value = $1,171,000

Percentage Increase = (1,171,000 - 140) / 140 * 100 ≈ 835,714.29%

b. To estimate the winner's prize in 2040, we can assume the same annual percentage increase will continue. We need to calculate the number of years from 2007 to 2040 and apply the percentage increase to the 2007 prize.

Number of years = 2040 - 2007 = 33 years

Estimated prize in 2040 = 1,171,000 * (1 + (Percentage Increase / 100))^33

Estimated prize in 2040 = 1,171,000 * (1 + (835,714.29 / 100))^33 ≈ $1,454,735,139.69

Therefore, if the winner's prize increases at the same rate, it is estimated to be approximately $1,454,735,139.69 in 2040.

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The infix expression given is (A-B)+C*(D/E)

Steps to draw the expression tree

The order of operations should be considered while drawing the expression tree.

The following steps are followed:

First, draw a node for the operator with the highest precedence,

which is multiplication (symbol *).Second,

draw nodes for the other operators, in the order of their precedence, which is division (symbol /), and addition (symbol +).

Third, draw the leaf nodes for the operands in the order that they appear in the infix expression.

A B CD E- /* + Steps to re-write in prefix form

The prefix form of the infix expression is obtained by traversing the expression tree in the pre-order fashion.

That is, the operator is written before its operands.

The prefix form of the infix expression (A-B)+C*(D/E) is obtained as follows:+ - A B * C / D E

Steps to re-write in postfix form

The postfix form of the infix expression is obtained by traversing the expression tree in the post-order fashion.

That is, the operator is written after its operands.

The postfix form of the infix expression (A-B)+C*(D/E) is obtained as follows: A B - C D E / * +

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Step-by-step explanation:

volume of the sphere=4/3×π×r³

=4/3×3.14×11³

=5572.4533ft³

The initial fee that Jabari collects is $50.

It should be noted that Jabari is power washing houses for a summer job and for every job, he charges an initial fee plus a $30.

In this case, the amount collected was $170 for a four hours job. Let the initial fee be represented as x.

Therefore, this will be illustrated as:

x + (30 × 4) = 170

where x = initial fee

x + 120 = 170

Collect like terms

x = 170 - 120

x = 50

The initial fee is $50.

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Jabari is power washing houses for a summer job. For every job, he charges an initial fee plus a $30 sign, 30 for each hour of work. His total fee for a 4-hour job, for instance, is $170 sign, 170.

Jabari's total fee, f for a single job is a function of the number, t, of hours it takes him to complete the job. What is the initial fee?

Answer:

1:3

Step-by-step explanation:

We see that for every x increase, the y increase by 3, so the ratio is 1:3.

Answer:

125 inches cubed

Step-by-step explanation:

volume= height*width*length

5*5*5=125

The equation of the line in slope-intercept form is y = 6x + 55.

Equations can involve variables, which are placeholders for unknown values that we wish to find. For example, the equation x + 3 = 7 asserts that the value of x plus 3 is equal to 7. We can solve for x by subtracting 3 from both sides of the equation, obtaining x = 4.

Equations can be linear or nonlinear, and they can involve one or more variables. They can be represented in various forms, such as standard form, slope-intercept form, or quadratic form.

To find the equation of the line in point-slope form, we need to first find the slope of the line. We can use any two points from the table to find the slope using the formula:

slope = (change in y)/(change in x)

Let's use the first and last points in the table:

slope = (295 - 175)/(40 - 20) = 120/20 = 6

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line. Let's use the first point (20, 175):

y - 175 = 6(x - 20)

To write this equation in slope-intercept form, we need to isolate y:

y - 175 = 6x - 120

y = 6x + 55

So the equation of the line in slope-intercept form is y = 6x + 55.

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Answer:

n= plus or minus (+-) square root 69/ 3 -2

Step-by-step explanation:

Answer:

n = -2[+/-] (2 \(\sqrt{69}\))/3

Step-by-step explanation:

in other words, the answer is

n=0.768875

and

n = -4.76887

Answer:

x = 148

Step-by-step explanation:

( Note that ∠DPB = 32° and ∠CPB is x )

∠DPB and ∠CPB are supplementary angles.

Supplementary angles add up to 180°

This means that ∠DPB + ∠CPB must equal 180

If ∠DPB = 32° and ∠CPB = x , then 32 + x = 180

( Note that we've just created an equation that we can use to solve for x )

We now solve for x using the equation we just created

x + 32 = 180

* subtract 32 from both sides *

we're left with x = 148

Answer:

2

Step-by-step explanation:

Answer:

x = - 1, x = 2

Step-by-step explanation:

Given

x + (x + 1) + (x + 2) = (x + 1)² ← expand using FOIL , then

x + x + 1 + x + 2 = x² + 2x + 1 , that is

3x + 3 = x² + 2x + 1 ( subtract 3x + 3 from both sides )

0 = x² - x - 2 ← in standard form

0 = (x - 2)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 2 = 0 ⇒ x = 2

Answer:

4x+8y=16

8y=4x+16

4/8. 16/8

y=1/2x+2

The factorization  of the polynomial is:

(x - 4)*(x + i)*(x - i)

If (x - x₁) is a factor of a polynomial, then x₁ is a zero of the polynomial.

Now we can evaluate the polynomial in the values of the options and see which ones are zeros.

if x = 4

p(4) = 4³ - 4*4² + 4 - 4 = 0

So (x-  4) is a factor.

if x  = i

p(i)= i³ - 4*i² + i - 4

     = -i + 4 + i - 4  = 0

(x - i) is not a factor.

if x = -i

p(-i) = (-i)³ - 4*(-i)² - i - 4

        = i + 4 - i - 4 = 0

Then the factorization is:

(x - 4)*(x + i)*(x - i)

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Answer:

a/b =3/7

Step-by-step explanation:

I hope it helps

the steps are actually long so I had to snap it

Answer:

10x^2+8x+3

Step-by-step explanation:

Answer:

10x^2 + 8x + 3

Step-by-step explanation:

Hope this helps.

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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Answer:

Your answer is D

Step-by-step explanation:

45 divided by 5 equals 9

Answer:

easy 45 dived by 9 is 5

Step-by-step explanation:

hope it helps

Answer: base is 12

Step-by-step explanation:

Answer:

The answer is r={-8,1/4}

The union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].

What is an interval?

⇒ An interval is an expression that involves a subset of numbers on the actual line. These intervals contain all the actual numbers between the two numbers in the interval.

There are three types of intervals, these are:

⇒ The intervals can be joined if in the math problem the result is between one end of the real line and the other end of the real line. There are two intervals with the sign of union in the middle of them.

The representation of the union of these intervals is given as follows:(2,3]∪[3,4]  , the union is denoted by ∪

Now as in every interval the three is part, we can express this union of this set as one in the following way:

⇒ (2,4]

Hence, the union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].

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Answer:

m∠C = 102°

Step-by-step explanation:

This is is a cyclic quadrilateral

• The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

If you look at the above diagram properly, you will notice there are are angles outside the circle. We refer to this an exterior or external angles in a cyclic quadrilateral

• Note that m∠B is Opposite the exterior angle m∠CDA

Hence,

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

• m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

• Another external angle we need to find is m∠DAB

m∠DAB = m∠DA + m∠AB

We know that m∠DA = 84°, therefore,

m∠DAB = 84° + 120°

m∠DAB = 204°

• The final step is to solve for m∠C

m∠DAB is Opposite m∠C

Hence

m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

For no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.

We have the system of equations:

x + y + z = 2   …(1)

a x + b y + c z = 10   …(2)

x - 2 y + z = 4     …(3)

a. The system has no solution.

Put a = b = c = -1 in (2)

We get:

- x - y - z = 10

Now add (1) and (2)

0 = 12

which is not possible.

So, no solution.

b. The system has exactly one solution.

a = 1 and b = c = 0

We have the equations as:

x + y + z = 2   …(1)

x = 10   …(2)

x - 2 y + z = 4     …(3)

c. The system has infinitely many solutions.

a = b = c = 5

We will have the equations:

x + y + z = 2   …(1)

5 x + 5 y + 5 z = 10   …(2)

x - 2 y + z = 4     …(3)

Therefore, we get that, for no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.

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The expression for the height is given as 3V/pir³

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the ape-x or vertex.

The formula for calculating the volume of a cone is expressed according to the equation;

V = 1/3pir³h

We are to make h the subject of the formula;

V = 1/3pir³h

Cross multiply

3V = pir³h

Divide both sides by pir³

3V/pir³ = pir³h/pir³

3V/pir³ = h

Swap

h = 3V/pir³

Hence the expression for the height is given as 3V/pir³

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Answer:

Step-by-step explanation:

Total students = 120

Number of students studying Mathematics P(A) = 90

Number of students studying Science P(B) = 72

Number of students who doesn't study both subjects P(AUB)'= 10

1) Number of students studying atleast on subject = 120 -10 = 110

2) Number of students studying both math and science = (90 +72) -110

                     = 162 -110 = 52

3) Number of students studying only mathematics = 90 -52 = 38

4) Number of students studying only science = 72 -52 = 20

The size of the crowd that fit 5 feet deep and 1 mile long on one side of the street is 8448.

Given:

in 5ft by 5ft = 25ft^2, there can be 1 person

A normal street is 30ft wide

Then, if we want the width such that is 5 ft deep (from both sides)

Then we should subtract two times 5 ft:

30ft - 5ft - 5ft = 20ft.

Now the length is 1 mile.

and 1 mile = 5280 ft

Then the area is:

There are 5280 feet in a mile. So, that's exactly 1056 lengths of 5 feet each.  To estimate, 5250 is 5×1050 lengths

In each 5 ft by 5 ft square, 8 people fit comfortably.  So, estimating, 8×1050 is 8400

To check (or verify),   8(5280/5) = 8448 exactly.    Our estimate is close enough

Hence we get the required answer.

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Answer: (2, 0)

Step-by-step explanation:

The coordinate of the point is  (2/5, 8/5), that divides a line segment in ratio 2:3, that has end points R(-2, - 2) and S(4, 1).

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given points are R(-2, - 2) and S(4, 1).

To find the coordinates of point the is 2/3 of the way from point R to S

Use formula, coordinates of point,

{[(mx₂+nx₁)/(m+n)], [(my₂+ny₁)/(m+n)]}

The coordinate of the point that divide the line made by points  R(-2, - 2) and S(4, 1) in ratio 2:3,

= {[(2 × 4 + 3 × (- 2)) / (2 + 3)],[(2 × 1 + 3 × 2) / (2 + 3)]}

= [(8-6)/5, (2+6)/5]

= (2/5, 8/5)

The coordinate of the point that divides the line segment in ratio 2:3, that has end points R(-2, - 2) and S(4, 1) is  (2/5 , 8/5),

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Answer:

We need to remove 3 points from 3 duplicated pairs so this graph  so that it will be a function.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

From the graph, we can determine the table such as:

x            y

-3           2

-3           3

1             4

1            -4

2           -2

2            -4

It is clear that the values of x = -3, x = 1, and x = 2 are repeated twice.

In other words, there are 3 duplicated pairs.

We know that we can not have duplicated inputs as there should be only 1 output for each input.

Thus, we need to remove 3 points from 3 duplicated pairs so this graph  so that it will be a function.