suppose you are given the following information and the coordinate plane below

Answer:

[tex]\displaystyle{1.) \ \ f(x) = \dfrac{2}{3}x-8}\\\\\displaystyle{2.) \ \ f(x) = -4x+11}[/tex]

Step-by-step explanation:

- Range is a set of all y-values in a set of coordinate points.

A linear equation or function always have range equal to set of real number because you can substitute f(x) as any numbers and you'll still be able to solve for x-variable.

An quadratic equation or function may have range equal to set of positive real number or negative real number depending whether if the coefficient of x² is in positive or negative but consider this:

Suppose we have f(x) = x², f(x) cannot be negative number because that'd make the equation not real. Therefore, a quadratic function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range.

For an exponential function, it's same as quadratic equation. It depends whether if a base is in negative or positive. You can consider like this:

Suppose we have [tex]\displaystyle{f(x)=2^x}[/tex], f(x) cannot be negative number because there are no x-values that make the equation true. Therefore, an exponential function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range as well.

Step-by-step explanation:

answer=18^2/3

according to the congruent triangles are present there.

so divide corresponding sides

Answer:

36

Step-by-step explanation:

75/100

75/100=0.75

0.75*48 =36

Answer:

c

Step-by-step explanation:

By the Pythagorean theorem,

[tex]28^2 + 15^2 = s^2 \\ \\ s^2 = 1009 \\ \\ s = \sqrt{1009}[/tex]

Answer:

  (b)  (x -10)(x +10)

Step-by-step explanation:

The factorization of the difference of squares is a special form:

  a² -b² = (a -b)(a +b)

Your expression is recognizable as the difference of squares:

  x² -100 = x -10²

Using the above form, the factorization is ...

  = (x -10)(x +10) . . . . . . . . matches the second choice

The solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9

x + 2y = -4

2x + 5y = 1

Using Substitution method

From equation (1)

x = -4 - 2y

Substitute x = -4 - 2y into equation (2)

2x + 5y = 1

2(-4 - 2y) + 5y = 1

-8 - 4y + 5y = 1

- 4y + 5y = 1 + 8

y = 9

Substitute y = 9 into

x + 2y = -4

x + 2(9) = -4

x + 18 = -4

x = -4 - 18

x = - 22

Therefore, the solution to the given simultaneous equation; x + 2y = -4, 2x + 5y = 1 using substitution method is x = -22 and y = 9

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Answer:

23370 students live with in 500 miles of the university.

Step-by-step explanation:

large university students =24000

selected students = 750

surveyed students =120 lives far away from university.

students live with in 500mile=?

750-120=630

24000-630=23370

Answer:

.00476

Step-by-step explanation:

Step-by-step explanation:

x = number of heavy equipment operators

y = number of general laborers

x + y = 37 (37 people were hired)

out if this we get e.g.

x = 37 - y

124x + 82y = 3916 (daily rate for each role, in total 3916)

now we use the first equation in the second :

124(37 - y) + 82y = 3916

4588 - 124y + 82y = 3916

672 - 42y = 0

672 = 42y

y = 16

x = 37 - y = 37 - 16 = 21

21 heavy equipment operators were hired.

16 general laborers were hired.

Answer:

D is the correct answer -3+8=5 ,1+4=5

The percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.

Percentage remaining = 100% - 50%

= 50%

Sponge cake = 1/5

Percentage of sponge cake = 1/5 × 50%

= 1/5 × 0.5

= 10%

Percent that likes cheesecake = Total - (fruits cake + sponge cake)

= 100% - (50% + 10%)

= 100% - (60%)

= 40%

Therefore, the percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.

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Answer:

1 and 4

Step-by-step explanation:

x-1 = 0

x = 1

x^2 - 5x + 4

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

x can't be 1 or 4

Answer:  1 and 4

Step-by-step explanation:

1. To find excluded values, we need to make the denominator equal to zero.

x² - 5x + 4 = 0

2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:

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

x - 4 = 0          x - 1 = 0

    x = 4               x = 1

These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.

Answer: No

Step-by-step explanation:  proportional means corresponding in size or amount to something. However, the number of her sit-ups isn't consistent, so it isn't proportional to the time she spends doing them.

The dependent variable in this situation is; the speed at which the car travels.

Speed = Distance / Time

The dependent variable in this situation is; the speed at which the car travels.

The independent variable; The distance the car has traveled.

This is the variable whose value depends on one or more variables in the equation.

Independent variable

This is the variable whose value is not dependent on any other in the equation.

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Step-by-step explanation:

that question is fundamentally wrong.

"appropriate" completely depends on the situation and circumstances.

if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.

if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".

because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.

if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.

Answer:

you better give me brainliest

Step-by-step explanation:

The answer is the first two

Answer:

9900

Step-by-step explanation:

You start with 300, and add 300 32 times (once for every 3 months in 8 years).

[tex]300+9600=9900[/tex]

(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.

The formula for finding the confidence interval for population variance is:

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.

Here it is given that,

α/2 = 0.02/2 = 0.01

1 - α/2 = 1 - 0.01 = 0.99

For (n - 1) degrees of freedom,

[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and  [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)

Using the formula we get,

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]

[tex]730.72 < \sigma^{2} < 4569.53[/tex]

The confidence interval for the population variance is (730.72, 4569.53)

Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.

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12x² + 102x² + 114x - 84

Answer:

Solution Given:

1st term: 6x²+39x-21

Taking common

3(2x²+13x-7)

doing middle term factorization

3(2x²+14x-x-7)

3(2x(x+7)-1(x+7))

3(x+7)(2x-1)

2nd term: 6x²+54x+84

taking common

6(x²+9x+14)

doing middle term factorization

6(x²+7x+2x+14)

6(x(x+7)+2(x+7))

2*3(x+7)(x+2)

Now

Least common multiple = 2*3(x+7)(2x-1)(x+2)

2(x+2)(6x²+39x-21)

(2x+4)(6x²+39x-21)

2x(6x²+39x-21)+4(6x² + 39x-21)

12x³+78x² - 42x+4(6x² + 39x-21)

12x³+78x² - 42x + 24x² + 156x-84

12x³ + 102x²-42x + 156x - 84

12x² + 102x² + 114x - 84

Answer:

[tex]12x^3+102x^2+114x-84[/tex]

Step-by-step explanation:

Given polynomials:

[tex]\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}[/tex]

Factor the polynomials:

Polynomial 1

[tex]\implies 6x^2+39x-21[/tex]

[tex]\implies 3(2x^2+13x-7)[/tex]

[tex]\implies 3(2x^2+14x-x-7)[/tex]

[tex]\implies 3[2x(x+7)-1(x+7)][/tex]

[tex]\implies 3(2x-1)(x+7)[/tex]

Polynomial 2

[tex]\implies 6x^2+54x+84[/tex]

[tex]\implies 6(x^2+9x+14)[/tex]

[tex]\implies 6(x^2+7x+2x+14)[/tex]

[tex]\implies 6[x(x+7)+2(x+7)][/tex]

[tex]\implies 6(x+2)(x+7)[/tex]

[tex]\implies 2 \cdot 3(x+2)(x+7)[/tex]

The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.

Therefore, the LCM of the two polynomials is:

[tex]\implies 2 \cdot 3(x+7)(x+2)(2x-1)[/tex]

[tex]\implies (6x^2+54x+84)(2x-1)[/tex]

[tex]\implies 12x^3+108x^2+168x-6x^2-54x-84[/tex]

[tex]\implies 12x^3+102x^2+114x-84[/tex]

Answer: C: 12-7x

Step-by-step explanation:

This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.

Any difference of two squares [tex]a^2-b^2[/tex] can be factored into the sum of their square roots times the difference of their square roots [tex](a+b)(a-b)[/tex].

Let's factor our expression.

[tex]144-49x^2=(12+7x)(12-7x)[/tex]

Out of all the options given, only [tex]12-7x[/tex] is a factor. Hence, option C is correct.

The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

The function is given as:

f(x)=−2x3+x2−4x+1 is divided by x+3.

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Calculate f(-3)

f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1

Evaluate the expression

f(-3)= 76

Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

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Answer:

42 - 24 = 18

18/24 = 3/4

the answer would be 1 and 3/4 days

Answer:

1 and 3 over 4 days

Step-by-step explanation:

Since 24 hours is 1 day  all we have to do is divide 42 into 24 and see what the resulting fraction is

42/24 = 7/4  (reducing to lowest fraction)

7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)

Answer:
1 and 3 over 4 days

Answer:

i think 10 because in triangle there is 180 and 180-170 = 10

Answer:

Step-by-step explanation:

hjhj

Using translation concepts, the transformations are described as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

[tex]f(x) = 2^x[/tex]

The transformed function is:

[tex]g(x) = -2^x + 4[/tex]

We have that the transformations in this problem can be described as follows:

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Answer:

False

Step-by-step explanation:

Consider an isoscles trapezoid with angles 75° and 105°.

Answer:

45%

Step-by-step explanation:

Simply, 25/55 which gives you 0.454545.

Convert that to a percentage and you get 45%