(-3x^3+5x^2-6x-7) / (x+4)

Answer -

[tex] \frac{61}{4} [/tex]

Step-by-step explanation:

Greetings !

Given expression( function )

[tex]h(x) = \frac{12}{2x} + 16[/tex]

Thus, plug in -8 in the variable x and solve as follows:-

[tex]h( - 8) = \frac{12}{2( - 8)} + 16[/tex]

Multiply the numbers 2.(-8) = -16

[tex] = \frac{12}{ - 16} [/tex]

Apply the fraction rule

[tex] \frac{a}{ - b} = - \frac{a}{b} [/tex]

[tex] = - \frac{12}{16} [/tex]

[tex] = - \frac{ 12}{16} + 16[/tex]

cancle

[tex] \frac{12}{16} = \frac{3}{4} [/tex]

Factor the number: 12 = 4.3

[tex] = \frac{4.3}{16} [/tex]

Factor the number 16 = 4.4

[tex] = \frac{4.3}{4.4} [/tex]

cancel the common factor =4

[tex] = \frac{3}{4} [/tex]

Thus,

[tex] = \frac{ - 3}{4} + 16[/tex]

Convert 16 to fraction :

Apply the fraction rule

[tex]a = \frac{ab}{b} [/tex]

[tex] = \frac{16.4}{4} [/tex]

Multiply the numbers 16.4=64

[tex] = \frac{64}{4} [/tex]

[tex] = - \frac{3}{4} + \frac{64}{4} [/tex]

Apply the fraction rule

[tex] \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c} [/tex]

[tex] = \frac{ - 3 + 64}{4} [/tex]

Add the numbers -3+64 ==61

[tex] = \frac{61}{4} [/tex]

Hope it helps !!

The time taken before the two automobiles meet is determined as 1.33 hours.

Apply the principle of relative velocity as shown below;

Vat + Vbt = D

(Va + Vb)t = D

where;

(20 + 25)t = 60

45t = 60

t = 60/45

t = 1.33 hours

Thus, the time taken before the two automobiles meet is determined as 1.33 hours.

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Answer:

I believe I did it right. I solved it with distance formula.

Answer : D =

[tex] \sqrt{104} [/tex]

= 10.2

Answer: 11

Step-by-step explanation: 132/12 = 11

You divide the actual car length by the model and you get the scale factor.

The scale factor of the model to the actual car is 1/11 inches.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

A small model car is 12 inches long and the actual car is 132 inches long.

To find the scale factor:

When both the original dimensions and the new dimensions are known, the scale factor may be determined.

The following is a basic formula to determine a figure's scale factor:

Scale factor = Dimension of the new model ÷ Dimension of the actual car

Scale factor = 12 / 132

Scale factor = 1/11

Therefore, the scale factor is 1/11 inches.

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The fixing of east and west Germany's currencies at a 1:1 ratio to each other during the German unification in 1990 is an example of a fixed exchange rate policy

We know

The fixed exchange rate policy is the rule to ties the country's official currency exchange rate to another country's currency which set by the central bank or government.

Here,

The fixing of east and west Germany's currencies at a 1:1 ratio to each other during the German unification in 1990. The fixed exchange policy is used here

Hence, The fixing of east and west Germany's currencies at a 1:1 ratio to each other during the German unification in 1990 is an example of a fixed exchange rate policy

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Answer: 99 x 76= 7524

Step-by-step explanation:

Answer:

7524

Step-by-step explanation:

The answer is 23

Step-by-step explanation:

7 + 2^4 ÷ 4 + 2(3² × 2 ÷ 6 + √9)

7 + 16 ÷ 4 + 2(9 × 2 ÷ 6 + √9)

7 + 4 + 2(3 + 3)

11 + 2(6)

11 + 12

= 23

The results of the computation using the laws of exponents are 2^12 and 2401/256

When we have two numbers, one serving as the base and the other being the index, we could be able apply the laws of indices when we are solving the problem. There are several laws of indices such as; multiplying, dividing, power of 0, brackets, negative and fractional powers.

In order to solve these problems, we need to apply the statements of the laws of indices.

In the first case we have;

2^16 ÷ 2^4

2^16/2^4

Using the subtraction law;

2^16 - 4 = 2^12

Again;

(7/4)^4

By the power law

7^4/4^4 = 2401/256

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Answer:

[tex]A = \frac{a+b}{2} + h[/tex]

Step-by-step explanation:

A is the area. a and b are the lengths of the two bases. h is the height of the trapezoid.

Answer:

Step-by-step explanation:

A=[tex]\frac{base1+base2}{2}height[/tex]

The typical household income in both cities is $80,000.

The distribution is more evenly distributed in Statstown . At least 25% of the total values in Medianville are between $60,000 and $80,000, as can be shown. As a result, more than 25% of people have annual incomes between $50,000 and $80,000. 25% of people in Statstown make between $40,000 and $80,000 per year. Therefore, less than 25% of people have annual salaries between $50,000 and $80,000.

What proportion of Americans earn more than $100,000 annually?

In 2020, 24% of Americans had a yearly salary of over $100,000. 34% of American households have a yearly income of $100,000 or more. American households making over $100,000 annually climbed by 4.1% in the five years leading up to 2022.

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An advantage of a cumulative frequency polygon over a histogram or frequency polygon is that: it can directly compare two or more frequency distributions.

Now,

Hence, an advantage of a cumulative frequency polygon over a histogram or frequency polygon is that: it can directly compare two or more frequency distributions.

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The mean rate the Grand Canyon has been eroded into the Colorado plateau within the past 6 million years is [tex] \frac{4 }{15} \: mm/year [/tex]

The possible part of the question as obtained from a similar question includes;

The time at which the western Grand Canyon began to be evacuated by river erosion = 6 million years ago

The depth of the Grand Canyon = 1.6 km

(a) The average value or the mean is given by the formula;

[tex]Average = \frac{Depth \: of \: erosion }{Time \: taken } [/tex]

The depth of erosion = 1.6 km

Time of erosion = 6 million years

The average rate at which the Grand Canyon has been eroded into the Colorado plateau is therefore;

[tex]Average = \frac{1.6 \: km }{6 \times {10}^{6} \: years} [/tex]

1.6 km = 1,600,000 mm

Therefore;

[tex]Average = \frac{1600000 \: mm }{6 \times {10}^{6} \: years} = \frac{4 }{15} \: mm/year [/tex]

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The difference between partitioning a directed line segment MN in a 2:7 ratio versus a 7:2ratio because of following

To understand this let us take the line segment MN which is of a length is divided into 9 equal parts. Here, we are dividing it into nine parts because the proportions 2 and 7 make a sum of 9.

When we divide the line segment MN in the ratio 2:7, the first two parts out of the nine from the left side are separated from the rest 7. This means that the first proportion from the left hand side of the line is smaller than the other.

Now, when we divide the line segment MN in the ratio7:2, the first seven parts out of the nine from the left side are separated from the rest two. This means that the first proportion from the left hand side of the line is larger than the other.

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The equation of a circle in the xy-plane is found as (x + 2)² + (y - 1)² = 5.

A circle is a two-dimensional closed figure in which the set of all points with in plane is equidistant from the a given point known as the "centre."

Circle Formula: (x - h)² + (y - k)² = r² ;

Where, (h, k) is the centre & r is the radius of the circle.

Use the distance formula for(-2, 1) and (0,2)

[tex]\begin{aligned}&r=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} \\&r=\sqrt{(0+2)^2+\left(2-1\right)^2} \\&r=\sqrt{(2)^2+\left(1\right)^2}\end{aligned}[/tex]

Further simplifying;

r = √(4 + 1)

r = √5

Centre (h, k) = (-2, 1)   Radius (r) = √5.

(x - h)² + (y - k)² = r²

(x + 2)² + (y - 1)² = √5²

(x + 2)² + (y - 1)² = 5 is the equation of the circle.

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Answer: 4 times a number equals 2 plus 3 times a number

Step-by-step explanation: (NMA)

Step-by-step explanation:

A has no solution.

15x - 45 = 15x + 75

-45 = 75

is false for every value of x.

in other words, when you add to the same thing different amounts, the result cannot be identical ever.

B has a solution

-45x - 45 = -75x + 75

-120x = 120

-x = 1

x = -1

C has a solution

45x - 45 = -15x + 75

60x = 120

x = 2

D has a solution

15x - 45 = 75x + 75

-120 = 60x

-2 = x

The phrase "Degrees of Freedom" in the computation of sample standard deviation is, n - 1.

Degrees of freedom:

Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.

Degrees of freedom is calculated by subtracting one from the number of items within the data sample.

Given,

Here we need to find the meaning for the phrase​ degrees of​ freedom as it pertains to the computation of the sample standard​ deviation

It means, There are n-1 degrees of freedom in the computation of s because an unknown parameter is estimated by the sample mean.

For each parameter estimated, 1 degree of freedom is lost.

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Answer:

20000 rabbits

Step-by-step explanation:

It should be noted that 16 divided by 2 2/3 is 6.

It should be noted that the information is to compute 16 divided by 2 2/3.

Therefore, this will be:

16 ÷ 2 2/3

= 16 ÷ 8/3

= 16 × 3/8

= 2 × 3

= 6

Therefore, the value is 6.

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Answer: The answer is 27

Step-by-step explanation: 6 x 6 x 6 = 216. 216 is the numerator. 2 x 2 x 2 = 8. 8 is the denominator.

216 / 8 = 216 '/. 8 = 27

Answer:

8300

Step-by-step explanation:

First, do parenthesis

Then, do the rest of the PEMDAS

Last, you're done!

The equation using the polynomial function is a x⁴ - 6x³ + 7x² + 6x - 8.

According to the statement

We have to find that the equation using the polynomial function.

So, For this purpose, we know that the

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation

From the given information:

The standard form with zeros 1,-1, 2, and 4:

Polynomial with Zeros 1, - 1, 2 and 4 can be expressed thus :

x = 1 : x - 1

x = - 1 :x + 1

x = 2 :x - 2

x = 4 :x - 4

Hence, we have :

(x - 1)(x + 1)(x - 2)(x - 4) = 0

We can then expand ;

(x - 1)(x + 1) = x² + x - x - 1 = x² - 1

(x² - 1)(x - 2) = x³ - 2x²-x + 2

(x³ - 2x² - x + 2)(x - 4)

x⁴ - 4x³ - 2x³ + 8x² - x² + 4x + 2x - 8

x⁴ - 6x³ + 7x² + 6x - 8.

So, The equation using the polynomial function is a x⁴ - 6x³ + 7x² + 6x - 8.

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Answer:

I answered you in another answer

Step-by-step explanation:

Answer:

10 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (3, - 6 ) and (x₂, y₂ ) = (3, 4 )

d = [tex]\sqrt{(3-3)^2+(4-(-6))^2}[/tex]

  = [tex]\sqrt{0^2+(4+6)^2}[/tex]

  = [tex]\sqrt{0+10^2}[/tex]

  = [tex]\sqrt{0+100}[/tex]

  = [tex]\sqrt{100}[/tex]

  = 10

The bending strength of beams by bending 10 beams untll they break will be estimated as-

Flexural strength is a material property that refers to the highest stress in a material well before yielding in a bending test. It is also recognized as bending strength or transverse rupture strength.

Some key features regarding the bending strength are-

Flexural strength is defined as the maximum tensile stress value under bending before the beam and rod fails.

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If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

Given,

The percentage of people own dogs= 51%

We know,

Probability = Number of favorable outcomes / Total outcomes.

If you choose random guy and probability that guy own a dog = 0.51

Here the probability of having a dog is independent events

Then,

Probability that they both own a dog = Probability of first person own a dog × Probability of second person own a dog

= 0.51×0.51

=0.2601

Hence, If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

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Answer:

51 and 12

Step-by-step explanation:

    ➲ Let a be the bigger number

    ➲ Let b be the smaller number

         [tex]a = 3b + 15\\a = 3 \cdot b + 15\\a + b = 63\\\bold{Solve:b}\\3b + 15 + b = 63\\3b + b = 4b\\4b + 15 = 63\\4b = 63 - 15\\4b = 48\\b = 12\\\\\bold{Solve:a}\\a = 3b + 15 \rightarrow a = 3 \cdot 12 + 15 = 51[/tex]

Thus,

b = 12, a = 51

_______________________________

Wrapping up:

➲ Hope this helps.

➲ Address concerns if needed.

➲ Have a great day!

The given expression is negative as after the solving fraction the value is:  -17/15

Examine the fractions' denominators. Find the LCM of the denominators and rationalize them to make the denominators of both fractions the same. Add the fraction numerators while keeping the denominator constant. To find the final sum, simplify the fraction.

Given fraction are : -1/3 , -4/5

Applying the fraction addition formula:

by calculating and reasoning the LCM of denominators Add the fraction numerators while keeping the denominator constant. To find the final sum, simplify the fraction.

= (-1/3)+( -4/5)

Applying the fraction addition rule:

= [tex]\frac{-1}{3}[/tex] -  [tex]\frac{-4}{5}[/tex]

Finding the LCM of the denominators:

= [tex]\frac{-5}{15} - \frac{12}{15}[/tex]

= -17/15

The given expression is negative as after the solving fraction the value is:  -17/15

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The lower quartile of the data is said to fall between  1.5 and 2.5 respectively in the box plot that we have here.

The lower quartile is the lower 1/4th of the data distribution. It is the 25th percentile of the distribution that we have in the question.

This point is what is marked at the starting point of the box that we have in this question.

The lower quartile is given by 2 and we can see that that it is bounded by the two numbers of 1.5 and 2.5.

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