Solve a triangle proof

The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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Answer: 20 weeks

Step-by-step explanation:

If he has $412 in his bank account, and he withdraws 20 each week, at 10 weeks he would have $212 left, at 20 weeks he will be left with $12.

Hence, the right answer is 20 weeks.

Answer: Tiffany

Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.

The picture has the dimension of a rectangle and will have the area of 66.166 in square feet.

We have to convert the length and width to be in same unit, before calculating for the area by multiplying the length by the width, and then convert the result to be in square feet.

1 cm = 0.394 inches

126 cm = 126 × 0.394 inches

126 cm = 49.644 inches

So the picture has length 16 inches and width 49.644 inches

area of picture = 16 inches × 49.644 inches

area of picture = 794.304 square inches

1 inch = 0.0833 feet

794.304 square inches = 794.304 × 0.0833 square feet

794.304 square inches = 66.166 square feet.

In conclusion, the picture has an area of 66.166 square feet.

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Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

In the graph showing fuel consumption for a car during a test run the correct statement is

The information given in the problem will help to find the equation of the graph in the form

y = mx + c

definition of variable to suit the problem

y = output variable = number of gallons

m = slope

x = input variable = number of miles

c = y intercept

The slope

= (3.5 - 0) / (73.5 - 0)

= 0.05

the y intercept is 0

the equation of the line is y = 0.05x

Only option the last option fits the equation as shown

number of gallons = 0.05 * number of miles

= 0.05 * 84 miles

= 4.2 gallons

= 4 gallons

hence the last option is the correct choice

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The surface area of the triangular prism is 136 square units

From the question, we have the following parameters that can be used in our computation (see attachment):

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25

From the question, we have the following parameters that can be used in our computation:

x  0   1   2   3  4   5

y 3   6  12   24 48 96

The interval is given as

0 ≤ x ≤ 4

On the table, we have

x = 0 and y = 3

x = 4 and y = 48

This means that

f(0) = 3 and f(4) = 48

The average rate of change is then calculated as

Average rate of change = [f(4) - f(0)]/[4 - 0]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [48 - 3]/[4 - 0]

Evaluate

Average rate of change = 11.25

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Answer:

Step-by-step explanation:

it is c

The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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The length of Adrian's shadow measured by his friend and the distance directly from Adrian's head to the tip of his shadow can be used to find Adrian's height using Pythagorean Theorem. Using an example of the measurement values, Adrian's height is about 5.5 feet

Pythagorean Theorem states that the sum of the square of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse side.

The diagram in the question appears left out. Please find attached a drawing made using the measurement lengths in the following example, created with MS Word.

The measurements Adrian had his friend to do are;

The length of Adrian's shadow on the sidewalk and the length from Adrian's head to the tip of the shadow.

Let x represent the length of Adrian's shadow, let r represent the distance from Adrian's head to the tip of the shadow, and let y represent Adrian's height

According to Pythagorean Theorem, we get;

r² = x² + y²

Therefore, the Adrian's height, h = √(r² - x²)

When r ≈ 8.14, and x = 6, we get;

h = √(8.14² - 6²) ≈ 5.5

Adrian's height is about 5.5 feet in the example situation

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Answer:

it's c trust me I had the same problem

The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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The interest earned in 5 years is $1096.

Interest is the fee a business pays a lender (creditor) to borrow money.

Given that, Brendan deposited $3,967 in an account earning 5% interest compounded annually.

A = P(1+r/100)ⁿ

n = 5, r = 5% = 0.05, P = 3967 and a = amount earned

A = 3967(1+0.05)⁵

A = 3967(1.05)⁵

A = 5063

Interest earned = amount - principal

Interest = 5063-3967

Interest = $1096

Hence, Brendan earned $1096 as interest.

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Answer:

$1096.01

Step-by-step explanation:

The complete equation in the slope-intercept form is y = 4x-1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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The significant figure by multiplying 101 with 52 is 5000.

Here given,

101 x 52

Round 101 to 100 and 52 to 50, then multiply together to get 5000.

Significant Figures: 1

Decimals: 0

The significant notation: 5e+3

Therefore the significant notation is 5000.

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The initial mass of the sample after two days = 8483.45 kg

Given that,

It is known as exponential decay when a population or group of something is deteriorating and the quantity of decline is proportional to the size of the population. In an exponential decay, the overall value falls but the percentage that departs stays the same throughout time.

The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula.

The standard  formula for this type of behavior which is written below:

A = [tex]Pe^{-rt}[/tex]  

Where

A refers the amount left after time t

P refers the initial amount at t = 0

r refers the rate

Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day.

A sample of this radioactive substance was taken after two days.

And we need to find if the sample has a mass of today, then the initial mass of the sample.

Now, we have to substituting the values,

Let us assume,

P = 9575 kg

r = 0.12

t = 1

Then we get the equation as,

A = (9575 kg) [tex]e^{-0.12*1}[/tex]

When we simplify this one, then we get,

A = (9575 kg) [tex]e^{-0.12}[/tex]

A = (9575 kg) 0.886

A = 8483.45 kg

Therefore,

The initial mass of the sample after two days = 8483.45 kg

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The conclusion is that the angle which measures 120° is not Acute angle.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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A Type I error in this scenario would mean that Miley would conclude that the noise impacts the students when in fact it doesn't.

The definitions of Type I errors and Type II errors are presented as follows:

The hypotheses tested in this problem are given as follows:

A Type I error would mean that she rejected a true null hypothesis, meaning that Miley would conclude that the noise impacts the students when in fact it doesn't.

(rejected null hypothesis means that there is enough evidence to conclude that there are differences).

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Answer:

garden=400/2

=200

4× side = perimeter=200

So,  =200/4

=50 m.

Step-by-step explanation:

Answer:

Length of garden is 50 m.

Step-by-step explanation:

Fence required for 1 time,

→ 400 ÷ 2

→ 200 m

Perimeter of square formula is,

→ P = 4 × L

Now length of the garden will be,

→ P = 4 × L

→ 200 = 4L

→ 4L = 200

→ L = 200/4

→ [ L = 50 m ]

Hence, length of garden is 50 m.

Answer: D. Zero is not a rational number

Step-by-step explanation:

[tex]0=\frac{0}{1}[/tex]. Thus, by definition, zero is rational.

We can conclude that the number of possible schedules for next semester could she make is 7920.

In more mathematical terms, the factorial of a number (n!) is equal to

n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

Given that,

The student needs 11 more classes to graduate.

And, possible schedules for next semester could she make if she plans to take 4 classes

Based on the given expression, the calculation is as follows:

The combination formula is given to be:

[tex]n_{C} _{r} =\frac{n!}{r!(n-r)!}[/tex]

= [tex]11_{C} _{4}[/tex] ! * 4 !

= [tex]\frac{11 !}{4!(11-4)!}[/tex]  * 4 !

= [tex]\frac{11!}{4!7!}[/tex] * 4 !

= [tex]\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}[/tex] * 4 !

We can cancel the coefficients,

= [tex]\frac{11*10*9*8}{4*3*2*1}[/tex] * 4 !

= [tex]\frac{7920}{24}[/tex] * 4 !

= 330* 4 !

= 330 * 4*3*2*1

= 7920

Therefore,

We can conclude that the number of possible schedules for next semester could she make is 7920.

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Using the provided points, Applying the substitution of the points in these system of linear equations. The equations which satisfies the points are the required answer. The answer is A) 3x+13y =14 and 6x+11y=-2

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.

point = (-4,2)

for option A) 3*-4 +13*2 =14

14=14

and 6*-4 + 11*2 = -2

-2 = -2

For other options these equality doesn't holds.

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The operations between functions are:

a) h(f(3)) = 5

b) (f×g)(4) = -8

c) f(  g(h(0))) -1

The first thing we want to find is a composition, we want to find:

h(f(3))

That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4

Replacing that we get:

h(f(3)) = h(-4)

And on the graph, we can see that h(-4) = 5

then h(f(3)) = 5

b) Now we have the product:

(f×g)(4) = f(4)*g(4)

Again, looking at the graph:

f(4) = -4

g(4) = 2

Then:

(f×g)(4) = f(4)*f(4)

(f×g)(4) = -4*2

(f×g)(4) = -8

c) Finally we have other composition:

f(  g(h(0)))

So we have 2 compositions, first we find:

h(0) = 5

f(  g(h(0))) = f(g(5))

Then:

g(5) = 0

f(  g(5)) = f(0)

Finally, look at the graph and you can see that f(0) = -1

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Answer:

  parallel

Step-by-step explanation:

You want to know the parallel/perpendicular status of the lines described by the equations ...

Parallel lines have the same slope. The slope is the coefficient of x when the equation is written in the form ...

  y = mx +b

as is the second equation.

The first equation can be put in that form by solving for y.

  2x -5y = 25 . . . . . . given equation

  2x -25 = 5y . . . . . . add 5y -25

  2/5x -5 = y . . . . . . divide by 5

The coefficient of x (slope) is 2/5, same as the second equation.

The lines are parallel.

__

Additional comment

Your graphing calculator can help you figure this out, too. The graphed lines are parallel.

0.563 $ is he paying per load of laundry

What is business mathematics?

Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.

Simple arithmetic, elementary algebra, statistics, and probability are all frequently utilized in business. More complex arithmetic, such as calculus, matrix algebra, and linear programming, may be used to solve some management challenges.

According to question:

Total scoop contained in detergent box = 195 scoops.

Scoops used by each load of laundry = 11/2  scoops = 5.5 scoops

Number of laundry he can do with this box = 195/5.5

                                               = 35.45 laundries.

Price of detergent box = 19.99 $

Price he paying for each load = Total price/ Number of loads

                                                  = 19.99/35.45

                                                  = 0.5638928067700

                                                  = 0.563 $ (Approx)

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44 is the proportion of the botched dressing will be olive oil.

Given, Miguel is mixing up a salad dressing. regardless of the number of servings,

the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if he accidentally doubles the vinegar and forgets the sugar altogether,

we have to find the proportion of the botched dressing that will be olive oil.

first we will find the amount of the even mixture of salt, pepper and sugar.

as, olive oil + vinegar + even mixture of salt, pepper and sugar = 100

58 + 14 + mixture of salt, pepper and sugar = 100

mixture of salt, pepper and sugar = 100 - 72

mixture of salt, pepper and sugar = 28

if he mixed doubles of the vinegar i.e. 28 then olive oil be,

x + 28 + 28 = 100

x = 100 - 56

x = 44

Hence, 44 is the proportion of the botched dressing will be olive oil.

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The inequality which can represent the above scenario is 3 ≤ p  

What is Inequality  ?

In mathematical expressions, inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. The symbols we will use in this instead of equals to are Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.

≤ - less than or equal to

≥ - greater than or equal to

≠ - Not equal  

Main Body:

Given:  

On the day of the test, the teacher instructed the students to take out at least 3 pencils from their backpacks.

To find:

Determine which inequality represents this scenario.

Let us know about Inequality

In the given scenario,

The teacher asked the to take out at least 3 pencils from their backpacks. which the students can take out 3 pencils or 2 or 1 pencil (which is less than 3) but not greater than 3.  

Therefore,The inequality which can represent the above scenario is 3 ≤ p

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