Pleas help congruent, triangles, and classifying and solving for sides/angels

The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

In the question ,

it is given that ,

the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,

In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .

In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .

that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

let us find the roots of the function ,

f(x) [tex]=[/tex] 0

x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0

taking x³ common ,

x³(x² - 8x [tex]+[/tex] 16) = 0

x³(x² - 4x - 4x + 16) = 0    .... by using splitting the middle term method

x³(x(x - 4) - 4(x - 4)) = 0

x³(x - 4)(x - 4) = 0

which means x³ [tex]=[/tex] 0   and x-4 = 0  

that is x=0    and x = 4 .

So , the roots of the function f(x) are x=0 and x=4 .

This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.

Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

The given question is incomplete , the complete question is

What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?

(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞

(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞

(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞

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The change in temperature in United States since last night is -6 degree centigrade.

Given the temperature in United States last night is = -9 degree C

Now the temperature is = -3 degree C

So the change in temperature is given by,

= Final Temperature - Initial Temperature

= -9 - (-3)

= -9 + 3

= -6 degree C

Hence the change in temperature in United States since last night is -6 degree centigrade.

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Answer:

Below

Step-by-step explanation:

Any of the following  

-9    -8   -7   -6   -5   -4   -3  -2

The average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.

According to the question,

We have the following information:

A local video store has seen good linear growth in rentals since 2005. In 2009, the store had 23,500 rentals. In 2015, the store had 28,540 rentals.

a) Average rate of change of store's rentals =(Rentals in 2015-rentals in 2009)/Number of years

Now, the number of years passed between 2009 and 2015 is 6 years.

So, we have:

Average rate of change = (28540-23500)/6

Average rate of change = 5040/6

Average rate of change = 840 rentals per year

b) Now, the number of rentals in 2005:

(Number of rentals in 2009-number of rentals in 2005)/4 = 840

Let's take the number of rentals in 2005 to be x.

(23500-x)/4 = 840

23500-x = 3360

-x = 3360-23500

-x = -20140

x = 20,140

Hence, the average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.

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After finding the rate of change, this table representing a linear function can be completed as follows:

x                         y

1                        0

2                       10

5                       40

10                      90

Mathematically, the rate of change can be calculated by using this formula;

Rate of change, k = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, k = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x as follows:

Rate of change, k = (40 - 0)/(5 - 1)

Rate of change, k = 40/4

Rate of change, k = 10.

For the first blank, we have:

10 = (40 - y)/(5 - 2)

10 = (40 - y)/3

30 = 40 - y

y = 40 - 30

y = 10.

For the second blank, we have:

10 = (90 - 40)/(x - 5)

10 = (50)/(x - 5)

10x - 50 = 50

10x = 50 + 50

10x = 100

x = 10.

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Answer:

t - 10 = 61

Step-by-step explanation:

We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61

so t = 71.

Answer:

b)  f(x) = -16x² + 8x + 30

Step-by-step explanation:

When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.

The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.

Therefore,  f(x) = -16x² + 8x + 30  could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.

If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).

Kaitlin will have $4657 as the total amount in her account after 3 years which was found using the compound interest formula.

What exactly is Compound Interest?

Given: Kaitlin put $4000 into an account earning 5.2% annual compound interest.

We need to find how much will she have in the account after 3 years.

Let,

P = initial sum of money

r = interest rate, 

t = number of years in decimal form

A = total amount in her account

Using the compound interest formula we obtain,

A = P (1+r)^t

A = 4000(1 + 0.052)³

A = 4000(1.052)³

A = 4000(1.164)

A = $4657

Therefore, Kaitlin will have $4657 as the total amount in her account after 3 years.

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Answer:

3/2 month

Step-by-step explanation:

Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?

When x = months:

Sandy: 10x + 60

Randy: 20x + 45

You are looking for x when:

Sandy = Randy

10x + 60 = 20x + 45

subtract 45 from both sides:

10x + 60 - 45 = 20x + 45 - 45

10x + 15 = 20x

subtract 10x from both sides:

10x + 15 - 10x = 20x - 10x

15 = 10x

divide both sides by 10:

15/10 = 10x/10

x = 15/10

reduce:

x = 3/2

It will take 3/2 months of Sandy and Randy to have the same amount of money.

[3/2 month also equals 1.5 months, depending on the format of the answer you need]

A function that is negative over its entire domain can be having its values of x and y negative i.e. it can be (-3,-4). Yes, the graph has an X-intercept.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

X-intercept illustration:

Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).

Calculate the x-intercept:

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

An illustration of y-intercept:

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

If we can locate the x-intercept of a linear function, finding the zero should be simple. The x-coordinate of the x-intercept is zero.

The x-intercept can be positive or negative.

Summary:

The location on the graph where our line crosses the x-axis is known as the x-intercept.

Positive numbers are to the right of the origin and negative numbers are to the left of the origin on the x-axis.

The location on the graph where our line crosses the y-axis is known as the y-intercept.

The side of a graph is negative:

Consider the numbers as being on the x-axis to help us remember this. The positive values are located to the right of the origin, and the negative values are located to the left of the origin.

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The smallest number of roses the customer will have to buy from each vendor is 24.

It should be noted that the multiple simply means the product of a number.

In this case, Kristen's Blossoms sells roses in groups of 8 and across town, Hector's Blooms sells roses in groups of 12.

The multiples of 8 = 8, 16, 24, 32 ....

The multiples of 12 = 12, 24, 36...

Therefore, the least number of roses is 24.

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Answer: put it in a caculator

Step-by-step explanation:

Combine 18x^3 and 5x^3.

Combine x^2 and 6x^2.

Combine 9x and −14x.

Add −3 and 11.

The mean is  47.73.

The median is 46.

The dataset has no mode.

The midrange is 44.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Mean = (70 + 54 + 46 + 85 + 61 + 81 + 45 +  6 + 35+  39 + 3) / 11

= 525 /11 = 47.73

Median is a measure of central tendency that is used to determine the number that is at the center of a set of values when the numbers are arranged in either ascending or descending order.

3, 6, 35, 39, 45, 46, 54, 61, 70, 81, 85

The median is 46.

Mode is the most frequent number in a dataset. The jersey numbers only occur once. Thus, there is no mode.

Midrange is the average of the maximum and minimum values of the dataset.

Midrange = (maximum value + minimum value) / 2

Midrange = (3 + 85) / 2

Midrange = 88 / 2

Midrange = 44

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The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line which is 8 units.

According to the question,

We have the following information:

The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line.

We know that the distance can not be negative in any case even when the points given are negative.

So, when we find the distance from -8 to 0, then we have the distance as 8 units.

Now, when we find the distance from 8 to 0, then we have the distance as 8 units.

Hence, the distance from -8 to 0 is the same as the distance from 8 to 0 on the number line which is 8 units.

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The function that models the total amount, in dollars, that the sponsor will donate to the charity when the person walks m miles is F(d) = 7 + 0.25m.

Mathematically, a function is an expression involving two or more variables (independent and dependent) showing that a mathematical relationship exists between the expressions.

Functions use the equation symbol to show that the expressions are equal when the variables are substituted with integers.

Every function has a domain (input variable) and a range (output variable) or codomain.

Constant donation = $7

Variable donation per mile = $0.25

Function, F(d) = 7 + 0.25m

where d = the total amount donated

m = the total miles the person walks

Thus, the total donation made by the sponsor is represented by the function, F(d) = 7 + 0.25m.

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In hypothesis testing, the assumption for the Ztest for a mean when the σ is known then n > 30. Hence the answer is : None of the above

Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis. Given the data, the test provides evidence for the hypothesis's plausibility.

Statistical analysts put a hypothesis to the test by measuring and examining a random sample of the population under consideration. Because the distributions of small samples are not normal, a t-test is required. If the sample size is large (n> 30), statistical theory predicts that the sample mean is normally distributed and that a z test for a single mean can be used.

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The following statements are marked true or false accordingly

A: n²+2 is odd         true    

B: n(n + 1) is odd     false

C: (n+1)² is odd        false

D: n² + 1 is odd       false

E: n(n + 2) is odd    true

F: (n + 2)² is odd     true

Examples are used to support or counter the statements

A: n²+2 is odd

3^2 + 2

= 9 + 2

= 11 (true)

B: n(n + 1) is odd

= 5(5+1)

= 5 * 6

= 30 (false)

C: (n+1)² is odd

= (7 + 1)^2

= 64 (false)

D: n² + 1 is odd

= 9^2 + 1

= 81 + 1

= 82 (false)

E: n(n + 2) is odd

= 3 ( 3 + 2)

= 3 (5)

= 15 (true)

F: (n + 2)² is odd

= (13 + 2)²

= 225 (true)

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The total length of the road ditch is 1/2 mile and the measurement in square feet of the road ditch is 42,240 square feet.

According to the question,

We have the following information:

You built a driveway ½ mile long to your new house. You have an 8-foot-wide road ditch on both sides of the road.

a) Now, the length of the ditch will be equal to the length of the driveway.

Length of ditch = 1/2 mile

b) Measurement of the road ditch in square feet:

Area of rectangle = length*width

Converting length into feet:

1 mile = 5280 feet

1/2 mile= 2640 feet

Area of ditch =(2640)*8

Area of ditch =21,120 square feet

Now, ditch is on both sides:

So, total area of ditch = 2*21,120

Total area of ditch = 42,240 square feet

Hence, the total length of the road ditch is 1/2 mile and the measurement in square feet of the road ditch is 42,240 square feet.

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The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

1st triangle

tan 25° = b/8   (tan = opp/adj)

b = 8 tan 25° = 3.73m

2nd triangle

sin 21° = x/22    (sin = opp/hyp)

x = 22 sin 21° = 7.88 units

3rd triangle

cos 47° = 28/x    (cos = adj/hyp)

x =  28/cos 47° = 41.06 units

4th triangle

Use Pythagoras' theorem:

12² = 8² + y²

y² = 12² - 8²

y² = 144 - 64

y² = 80

y = √80 = 8.94 units

Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units

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if  price on the tag was $28, but Benjamin paid $15.40 before tax then the percent of discount is 45%.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Benjamin went shopping for a new phone because of a sale. The price on the tag was $28, but Benjamin paid $15.40 before tax

We need to find the percent discount that Benjamin received

Compare the difference between the original price and the discounted price to the original price, and then express that difference as a percentage of the original price.

We can use the following formula:

Percent Discount = (Original Price - Discounted Price) / Original Price × 100%

=28-15.4/28 × 100

=0.45×100

=45%

Hence, Benjamin received a discount of 45%

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The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr

Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray

The equation below relates the radiation intensity and distance:

I₁/I₂ = D₂²/D₁²

where:  I₁ = intensity  at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source

Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot

Using the formula:

100/I₂ = 1²/9²

100/I₂ = 1/81

I₂ = 100 × 81

I₂ = 8100 mR/hr

I₂ = 8100×10⁻³ R/hr                (1 mR/hr = 1×10⁻³ R/hr)

I₂ = 8.1 R/hr

Therefore, the radiation intensity in Roentgens is 8.1 R/hr

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Step-by-step explanation:

[tex] \sf - 18p = p^2+81 [/tex]

Moving all the expression to the Left side of the equation,

[tex] \sf -18p + p^2 - 81 = 0 [/tex]

To find the discriminant of the above equation we can simply use the Quadratic formula.

The discriminant formula of a quadratic equation[tex] \sf ax^2 + bx + c = 0 \: is \: (d = b^2 - 4ac )[/tex]

Where d represents the discriminant

a, b and c are the coefficient of the above equation,

p^2, here coefficient of p² is a = 1

-18p, here coefficient of p is b = -18

81, here the number is constant so coefficient is c = 81.

So simply by substituting the value of a, b and c in the above discriminant formula we get,

[tex] \sf d = b^2 - 4ac [/tex]

[tex] \sf d = (-18)^2 - (4 \times 1 \times 81) [/tex]

[tex] \sf d = 324 - 324[/tex]

[tex] \sf d = 0 [/tex]

Therefore, The discriminant of 18p = p² + 81 is 0.

Answer:

0 (zero)

Step-by-step explanation:

To find the discriminant of the quadratic equation -18p = p² + 81, we first need to rewrite the equation in standard form, which is of the form ax² + bx + c = 0.

[tex]\begin{aligned}-18p&=p^2+81\\p^2+81&=-18p\\p^2+81+18p&=-18p+18p\\p^2 + 18p + 81 &= 0\end{aligned}[/tex]

Compare the coefficients of the rewritten quadratic equation with the standard form:

The discriminant of a quadratic equation in the form ax² + bx + c = 0 is given by the formula:

[tex]\boxed{\textsf{Discriminant} = b^2 - 4ac}[/tex]

Substitute the values of a, b, and c into the formula:

[tex]\begin{aligned}\textsf{Discriminant} &= (18)^2 - 4(1)(81)\\&=324-4(81)\\&=324-324\\&=0\end{aligned}[/tex]

Therefore, the discriminant of the given quadratic equation is zero.

Answer:75/5 = x/7

Step-by-step explanation:

Complete this equation and you will end up with the answer 105

The strength of the solution is 2:5 g/ml expressed as a ratio and the strength expressed as percent is 20%

Total amount of drug = 20 gm

Total volume of solution = 50ml

Strength (as ratio)

= 20/50 g/mL

= 0.4 g /mL

Amount of drug = M = 20 g

Volume of solution = V = 50 mL

Concentration or strength (ratio) = M/V = 0.4 g/mL

Concentration or strength (percent)

= M/V × 100

=20/50 × 100%

= 40%

The concentration is 40% expressed as a percentage.

Solution concentration is the perfect measurement of how much of the  solute has been dissolved in a particular amount of solvent or solution.

A solution that contains a large amount of the dissolved solute is said to be highly concentrated. A solution that contains only a small quantity of dissolved solute is said to be diluted.

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The probability that the sum of the two die rolls is 9 is 4 / 11.

Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that the sum of the two die roll is 9 = number of sides that roll a sum of 9 / total number of sides that at least one of them is a 5

number of sides that roll a sum of 9 =(4,5) (6 , 3), (3 , 6), ( ,4) = 4

total number of sides that at least one of them is a 5 = (1, 5), (2, 5), (3, 5), (4, 5) , (5, 5), (6, 5), (5, 1), (5, 2) , (5, 3), (5, 4), (5, 6) = 11

Probability that the sum of the two die roll is 9 = 4/11

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The office manager will either put up a clearer calculation and model the equation to ascertain money remaining at each quaintly bought or a graph to present his calculations

A graph is a representation of data, it helps to analyze data clearly with lesser time

The calculation the office manager will do is to multiply the number of lamps with the unit price then subtract from the amount set aside to spend on new equipment

The calculation

let the money left be z

10000 = 300 * 72 + z

10000 = 21600 + z

subtraction

z = 10 000 - 21600

z = - 16000

The calculation shows that the money will not be enough

The equation is modeled as

y = 10000 - 300x

where x is the number of bulbs

y is amount left

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Answer: The required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).

Step-by-step explanation:  Given that the figure ABCD is reflected across the X-axis.

We are to find the co-ordinates of A, B, C and D after reflection.

From the figure, we note that the co-ordinates of the vertices of ABCD are

A(2, 3), B(5, 5), C(7, 3) and D(5, 2).

After reflection from X-axis, the y co-ordinate of each vertex will change its sign (y → -y).

Therefore,  the vertices of ABCD after reflection are

A(2, 3)  ⇒ A'(2, -3),

B(5, 5)  ⇒  B'(5, -5),

C(7, 3)  ⇒  C'(7, -3),

D(5, 2)  ⇒ D'(5, -2).

Thus, the required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).

Each set of prices should be matched with the correct percentage of increase or decrease as follows:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase = [original price - new price]/new price × 100

At original price: $63.00 and new price: $56.07, we have:

Percentage decrease = [63.00 - 56.07]/56.07 × 100

Percentage decrease = 6.93/56.07 × 100

Percentage decrease = 0.124 × 100

Percentage decrease = 12.4%.

At original price: $98.00 and new price: $108.78, we have:

Percentage increase = [108.78 - 98.00]/98.00 × 100

Percentage increase = 10.78/98.00 × 100

Percentage increase = 0.11 × 100

Percentage increase = 11%.

At original price: $37.50 and new price: $34.50, we have:

Percentage decrease = [37.50 - 34.50]/34.50 × 100

Percentage decrease = 3/34.50 × 100

Percentage decrease = 0.087 × 100

Percentage decrease = 8.7%.

At original price: $12.25 and new price: $13.23, we have:

Percentage increase = [13.23 - 12.25]/12.25 × 100

Percentage increase = 0.98/12.25 × 100

Percentage increase = 0.08 × 100

Percentage increase = 8%.

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