a^2 = 225/64 ​
what does a equal

The variable have positive integer exponent. so f(x) = -5x² + 3x +3 is a polynomial function.

A polynomial function is one that uses only non-negative integer powers or positive integer exponents of something like a variable in an equation such as the quadratic equation, cubic equation, and so on. For illustration, 2x+5 is a polynomial with an exponent of one.

A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, as well as division (No division operation by a variable).

f(x) = -5x² + 3x +3

Make the leading coefficient positive:

= 5x² - 3x -3

identify the coefficient:

a = 5, b = -3, c = -3

substituting into the:

[tex]$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$[/tex]

[tex]$x=\frac{-(-3)+\sqrt{(-3)^2-4 \times 5 \times(-3)}}{2 \times 5}$[/tex] or [tex]$x=\frac{-(-3)-\sqrt{(-3)^2-4 \times 5 \times(-3)}}{2 \times 5}$[/tex]

[tex]$x=\frac{3+\sqrt{3^2+4 \times 5 \times 3}}{2 \times 5}$[/tex] or

[tex]$x=\frac{3+\sqrt{9+4 \times 5 \times 3}}{2 \times 5}$[/tex]

[tex]$x=\frac{3+\sqrt{69}}{10}$[/tex]

x = ± [tex]\frac{3+\sqrt{69}}{10}$[/tex]

As we can see that the general form of a power function is f(x) = axⁿ , where a is a non zero co-efficient and 'n' is a real number.

so the given function is not a power function.

So,

the variable have positive integer exponent. so f(x) = -5x² + 3x +3 is a polynomial function.

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Answer:

Step-by-step explanation:  You could try to times 15 by each side or add them or turn it into an expression like E*15=0

Answer:

A. You can write the number as a Ratio of two entegers

D. You know what the next number is

Step-by-step explanation:

3xy² - x²

x = 2, y = 3

well, we simply replace every variable in the expression by the actual value and calculate.

3×2×3² - 2² = 6×9 - 4 = 54 - 4 = 50

Answer:

(9p^4+10)(9p^4−10)

The domain and the range of the graph in interval notation are (-∝, ∝) and [-3, ∝) respectively

The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.

The graph represents the given parameter

Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph

On the graph, we can see that:

The x values extend indefinitely on the graph;

This means that the domain is (-∝, ∝)

While y values start from -3 and increases up

This means that the range is [-3, ∝)

Hence, the domain and the range of the function in interval notation are (-∝, ∝) and [-3, ∝) respectively

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The simplification of the expression 20(6) - 7 using the laws of equation gives 113

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

20(6) - 7

Firstly, solve the equation inside the bracket to get:

120 - 7

Taking the difference of the two terms gives:

113

The simplification of the expression 20(6) - 7 using the laws of equation gives 113

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Answer:8977/1000

Step-by-step explanation:

The value of 8.977 as a ratio of two integers would be equal to 8977/1000  

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to Write 8.977 as a ratio of two integers.

We know that negative divided by a negative is positive, then;

8.977 can be written as;

8977/1000

Therefore, The value of 8.977 as a ratio of two integers can be written as

8977/1000

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The perimeter of the walkway in terms of y will be y = 50 + 8x. The slope will be 8.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that the length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden.

The perimeter will be calculated as:-

Perimeter = 2 ( W + L )

Perimeter = 2 [ ( 15 + 2x ) + ( 10 + 2x ) ]

Perimeter = 2 ( 10 + 2x + 15 + 2x )

Perimeter  = 2 ( 25 + 4x )

y = 50 + 8x

Compare the equation with the general form of the equation:-

y = 50 + 8x

y = mx + c

Slope = 8

Therefore, the perimeter of the walkway in terms of y will be y = 50 + 8x. The slope will be 8.

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Answer:

6.505

Step-by-step explanation:

[tex]\frac{7}8}[/tex]  Put in your calculator 7 ÷ 8 and you will get .875  

So, 10 [tex]\frac{7}{8}[/tex] is 10.875  now subtract this from 4.37.  You can line up the decimals and then subtract or just have the calculator do this for you, if you are allowed.

10.875 - 4.37 = 6.505

Answer: 1. -4<n<4

2. n<-3 or n>19

3. n<=-36 or n>=44

Step-by-step explanation:

n=number

units from a number is measured using absolute value sign

1. 4 units from 0: |n-0|<4 ==> |n|<4

n<4, n>-4 ==> -4<n<4

2. 11 units from 8: |n-8|>11

n-8>11

n-8+8>11+8

n>19

n-8<-11

n-8+8<-11+8

n<-3

n<-3 or n>19

3. half a number is at 2 units from 20:  |n/2-2|>=20

n/2-2>=20

n/2>=22

n>=44

n/2-2<=-20

n/2<=-18

n<=-36

n<=-36 or n>=44

The appropriate way to calculate the monthly rent over time is 1190 × 1.017^n.

From the information, it was stated that the monthly rent for the first house is $1,190, and the Bainters can expect it to increase 1.7% every year and that the Bainters want to calculate their monthly rent over time.

Therefore, the appropriate expression will be:

= 1190 × (1 + 1.7%)^n

where n = number of years

= 1190 × 1.017^n

Therefore, the appropriate way to calculate the monthly rent over time is 1190 × 1.017^n.

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The probability that Nacho will get all 4 questions wrong will be 0.3164.

From the information, Nacho takes a multiple choice test, the test has 4 questions and each question has 4 choices.

The probability of getting the correct option is 1 out of 4 which is 0.25 and the incorrect option is 0.75.

Therefore, the probability that Nacho will get all 4 questions wrong will be:

= (0.75)⁴

= 0.3164

Therefore, the probability that Nacho will get all 4 questions wrong will be 0.3164.

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The transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations).

Given:

Population mean,

μ=27.7 years

Population standard deviation,

σ=3.2 years

Winner's age =31 years

According to given question we have

If "x" represents the age of the winner then the z-score for "x":

z=x−μ/σ

a) Transforming the winner's age to a z-score

 z=31−27.7/3.2

   =1.03

(b) Interpretation of the z-score:

The winner's age of 31 years is 1.03 standard deviation below the mean age of the winners.

Therefore, the transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.

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To find the

a) Transforming the winner's age to a z-score

(b) Interpretation of the z-score

is missing

Using the z-distribution, the limits of the 95% confidence interval are given as follows:

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the parameters are given as follows:

[tex]n = 200, \pi = \frac{152}{200} = 0.76[/tex]

Then the bounds are given as follows:

Which are the lower and upper limits, respectively.

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Answer:

Step-by-step explanation:

x + 139 + 37 + 53 = 360

              x + 229 = 360

                       x = 360-229

                       x = 131 degrees

Answer:

s = √77

it is not rational since 77 not a perfect square

Step-by-step explanation:

area = s^2 = s * s = 77

==> s = √77

Answer:

For 12a - 37 > 0 answer is   a > 37/12

For 6a ≤ 42 answer is a ≤ 7

Step-by-step explanation:

We use Integers in everyday life when we solve real-world problems.

Let’s understand a real-life problem using integers.

Christian borrowed $1000 to buy a computer. After some time, she has paid back $250. How much does Christian still owe?

First, we will write a simple equation to represent the problem.

Let the amount that Christian still owes = 'x'

1000 = 250 + x

Now, we will rearrange the equation to isolate .

Then, solve for x.

The answer is 750.

Christian still owes = $750.

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It will take 12 weeks for Praisys corn to be ready for picking.

We have been given that,

 Maya plants corns In = 4 rows

 Praisy plants corns in  = 6 rows

Maya corns ready to be picked in = 8 weeks

We have to find the number of weeks will it take Praisys corn to be ready for picking.

To find we will use the unitary method that is,

            4 rows = 8weeks

            6 rows = 8/4*6 weeks

                         = 12 weeks

Thus 12 weeks will it take Praisys corn to be ready for picking.

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The area is 108yd2(square yards).

In the given triangle a base

24yd and the corresponding height of 6 yds are given, so to calculate the area we can use:

A=12×b×h

If we substitute the given numbers we get:

A=[tex]\frac{1}{2}[/tex]×24×18

=12×9

=108

The units of base and height are the same (yards), so the calculated area is in yd2

The area is the quantity that expresses the extent of a region on the plane or on a curved surface. the world of a plane region or plane area refers to the area of a shape or planar lamina, while area refers to the area of an open surface or the boundary of a three-dimensional object. The area is often understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the quantity of paint necessary to cover the surface with a single coat. it's the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

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The variance and standard deviation for the given frequency of pupils per teacher in some states of US is

Variance= 4.62 = 4.6

Standard Deviation = 2.14 = 2.1

The frequency distribution shows the average number of pupils per teacher in some states of the United States.

Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data. On the other hand, if data consists of individual data points, it is called ungrouped data. The sample and population variance can be determined for both kinds of data.

The standard deviation(σ) of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.

That means Standard Deviation = √variance.

For the given data the sum of frequencies(ni) = 1+16+11+7+1+2= 38.

Midpoint(mi) is 12,15,18,21,24,27.

ni * mi = 12,240,198,147,24,54.

Sum of ni * mi = 675.

Mean (u) =  17.76

mi - u    is -5.76,-2.76,0.24,3.24,6.24,9.24.

(mi - u)^2 is 33.17,7.61,0.057,10.49,38.93,85.37.

Sum of (mi - u)^2 = 175.62.

Variance = Sum of (mi - u)^2 / sum of frequencies

=> 175.62/38

=> 4.62 = 4.6.

Standard deviation = √variance.

=> √4.62

=> 2.14 = 2.1.

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Answer:

If it takes one minute to use 5.7 calories, it’ll take 190/5.7 minutes to use 190 calories. This simplifies to 100/3 minutes. So this person must walk for 33 minutes and 20 seconds to use 190 calories (assuming the rate of calorie usage remains constant throughout).

The value of f(x) when x equals -5 is 15. Option D

A function can be defined as an expression, law or rule that explains the relationship between two variables;

Given the function;

f(x) = 5x + 40

To determine the value of the function when x = - 5, we have to substitute the value of x as -5 in the function.

With this, we have;

f(-5) = 5(-5) + 40

Now, expand the bracket

f(-5) = -25 + 40

Add the values, we have;

f(-5) = 15

We can see that the value of the function with the input of the variable x as -5 is 15

Thus, the value of f(x) when x equals -5 is 15. Option D

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Answer: D

Step-by-step explanation: It said the grandparents were less than 89 years old, if it said that the grandparents that were 89 and younger had remembered that's when you would use a solid circle because the 89 would be included. But since 89 isn't included then it's an open circle.

Answer:

[tex]\frac{\pi r^2}{2}[/tex]

Step-by-step explanation:

The area of a semicircle is half the area of a circle

The area of a circle is [tex]\pi r^2[/tex], where r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant, approximately 3.14. The area of the semicircle is half the area of the circle, or [tex]\frac{\pi r^2}{2}[/tex].

Answer:

Step-by-step explanation:

It's just a countdown sequence

2 1 0 -1 -2 ....

Because the remainder is 0, then the binomial x + 3 is a factor of the polynomial (-3)^2 + 5(-3) + 6

A division problem is an expression or an equation that involves the quotients of numbers or polynomials

To create the division problem, we make use of the following expression

(x^2 + 5x + 6)/(x + 3)

Using the remainder theorem, we have

Dividend = x^2 + 5x + 6

Divisor = x + 3

Set the divisor to 0,

So, we have

x + 3 = 0

This gives

x = -3

Substitute x = -3 in the dividend to get the remainder

So, we have

Remainder = (-3)^2 + 5(-3) + 6

Evaluate

Remainder = 0

Because the remainder is 0, then the binomial x + 3 is a factor of the polynomial (-3)^2 + 5(-3) + 6

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