A football team averaged a loss of 8 yards in each of 4 plays. If they did not gain any yards, what was the net yardage the team had after those 4 plays?
What is the answer?

The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial f(x) = x³ + 8x² - 23x - 30.

If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).

∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.

f₁(x) = x² + 11x + 10.

Now, x² + 11x + 10 = 0.

x² + 10x + x + 10 = 0.

x(x +10) + 1(x + 10) = 0.

(x + 10)(x + 1) = 0.

x + 10 = 0 Or x = 1 = 0.

x = - 10 Or x = - 1.

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Answer: 0

Step-by-step explanation:

Since y is 2, and it’s being multiplied by 4, you have 8 - 8 which =0

Y=2

4(2) - 8

8-8

0

Answer:

0

Step-by-step explanation:

4y - 8

Given that,

y = 2

To find the value of given expression, replace y with 2 and solve the expression.

Let us solve it now.

4y - 8

4 × 2 - 8

8 - 8

0

The answer to the given question is <0.01.

What is confidence level?

The confidence level is the percentage of times we expect to get near to the same approximate if we run our experiment again or resample the population in the same way. The confidence level is the probability that the null hypothesis is true.

What is p-value?

P-value is the probability of getting the results you did, given that the null hypothesis is true.

When we are conducting a hypothesis testing and we determine the confidence level needed is 99%; then in order to reject the null hypothesis, the p-value needs to be below 0.01 (<0.01).

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Answer:

Step-by-step explanation:           The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The question is incomplete.

The complete question is attached in the picture, please refer picture.

We have an expression:

Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

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Answer:10.75

Step-by-step explanation:

3/4 as a decimal is 0.75. add that to the 10 gives you 10.75

The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %

The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.

The initial number of black rhinos in 1970 = 60,500

The number of black rhinos remaining in 2011 = 4,000

The annual rate of depreciation can be found using the formula;

Where;

FV = The future value = 4,000

PV = The present value = 60,500

r = The annual depreciation rate

n = The number of years

[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]

[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]

[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]

The annual rate of depreciation is approximately 6.41%

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Answer:

35 square inches

Step-by-step explanation:

21x15=315

315/9=35

Therefore, the answer is 35 square inches

Answer:

gradient:

y2-y1/x2-x1

1-1/9-3

0/-6

= 0

The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

The correct option is (A).

What is the average rate of change of a function?

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

Using function notation, we can define the Average Rate of Change of a function f from a to b as:

                                     [tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]

The given function is  [tex]g(x) = 5(2)^{x}[/tex],

Now calculating the average rate of change of function from x = 1 to x = 2.

                               [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]

Now, calculate the average rate of change of function from x = 3 to x = 4.

                                 [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]

The jump from m = 10 to m = 40 is "times 4".

So option (A) is correct.

Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

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The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.

Density is defined as the quotient between mass and volume.

Here we know that the mass is:

9.43*10²⁷g

And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:

V = 3.14*(3/4)*R³

Then in this case the volume is:

V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³

Then the density is:

D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3

For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)

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If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.

D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

A horizontal line now has zero slopes.

The new road has a zero slope as a result.

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Answer:

Step-by-step explanation:

y=2/3x+4

Answer:

no solution

Step-by-step explanation:

12=-4(-6x-3)

12=24x+12

0=24x

Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14)  are (6x+2)/3 = -3x - 12 and  6x + 2 = -9x - 36 , the correct option is  (a) and (d) .

In the question ,

it is given that

the equation is (6x+2)/3 = 2 - (3x+14)

solving the brackets on the right side of the equation ,

(6x+2)/3 = 2 - 3x - 14

(6x+2)/3 = -3x - 12                     ....option(a)

On Cross Multiplying , we get

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36                      ....option(d)

Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14)  are (6x+2)/3 = -3x - 12 and  6x + 2 = -9x - 36  .

The given question is incomplete , the complete question is

Using Simplification , Select all equations that are equivalent to

(6x+2)/3 = 2 - (3x+14)

(a) (6x+2)/3 = -3x-12

(b) (6x+2) = 2 - (3x+14)

(c) 2x + 2/3 = 2 - (3x+14)

(d) 6x+2 = -9x-36

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All the angles in a triangle add up to 180 degrees.

40 + x + (5x + 14) = 180

54 + 6x = 180

6x = 126

x = 21 degrees

Answer:

x=21

Step-by-step explanation:

a triangle adds up to 180 degree so to find x we will use the formula

(5x+14)+x+40=180

subtract 40 from each side so we have

(5x+14)+x=140

we have 2 terms with the same factor (x) so combine like terms

6x+14=140

subtract 14 from both sides

6x=126

divide both sides by 6

x=21

check your answer

5(21)+14

105+14=119

119+ 21+40=180

so x is equal to 21

The distance between points  (-3,-4) and (2,8) is 13.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.

The horizontal distance = 5

And the vertical distance = 12

The vertical and horizontal lines make a right angle when they meet,

To find distance between points, use Pythagoreans theorem,

(D)² = (5)²+(12)²

(D)² = 25 + 144

(D)² = 169

D = 13

The distance between points  (-3,-4) and (2,8) is 13.

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Answer:

488

Step-by-step explanation:

2(20x8) + 2(20x3)+2(8x3)

Assuming the "x" is not a variable.

The answer is 488

However, if "x" is a variable. The equation would be

40x^8 + 56x^3

Answer:

488

Step-by-step explanation:

using BODMAS

METHOD 1.

[tex]2(20 \times 8) + 2(20 \times 3 + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) = \\ = 320 + 120 + 48 \\ = 448[/tex]

METHOD 2.

[tex]2(20 \times 8) + 2(2 \times 3) + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) \\ = 2(160 + 60 + 24) \\ = 2 \times 244 \\ =488[/tex]

The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))

To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer

Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically

10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² )      (factorize difference of two squares)

                     = 10+(n-(n-2))(n+(n-2))      

                     = 10+(n-n+2)(n+n-2)         (simplify)

                     = 10+(2)(2n-2)                  (factorize)

                     =  2(5+(2n-2))

Therefore, due to the factor of 2, the given expression is always even for integer n

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Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.

As here we have scale factor=3>1.

Hence, the dilation  changes the original will expand the original figure.

Hence, each of the coordinate of a figure get multiplied by 3.

Hence, the co

ordinates of the image are given as:

i.e. A(0,0) → A'(0,0)

B(2,3) → B'(6,9)

C(1,-2) → C'(3,-6)

D(-3,-3) → D'(-9,-9)

Step-by-step explanation:

Answer:5.3

Step-by-step explanation:

using the Pythagorean theorem 8²-6²=28    √28=5.3

5

Step-by-step explanation:

Pythagoras theorem states that

a²+b²=c²

therefore a²=b²-c²

a²=8²-6²

a=√8²-6²

=√64-36

=√28

=5.3 or approximately 5

By probability , 7 is degrees of freedom are there .

Describe probability using an example?

825 Observations and 8 categories .

Degree of freedom = k - 1

     df = 8 - 1

     df = 7

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Answer:

178 000

Step-by-step explanation:

178 383      8 is in the thousands place...if the number next to it (3) is ≥ 5 round it up by 1   o/w leave it alone

Answer:

178,000

Step-by-step explanation:

It's 178,000 because the number in front of the 8 in 178,383 was under five so the number dropped.

Answer: 4x + 29

Step-by-step explanation: add the like terms together.

Answer:

39 inches

Step-by-step explanation:

the triangle has all equal angles

this means it is equilateral and this also means all the sides are equal

so take 2 sides and set them equal to each other to find x

21 - x = x + 5

now solve

add x to both sides

21 = 2x + 5

subtract 5 to both sides

16 = 2x

divide everything by 2

8 = x

now flip it

x = 8

plug this is to one of the equations and multiply that by 3

8 + 5 = 13

13 * 3 = 39

that is the perimeter

The algebraic expression of the mentioned statement will be 5x-3.

According to the question,

An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.

Let the unknown number be taken as x.

If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,

x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).

For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).

Hence, algebraically the final statement will be 5x -3.

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The quotient of the polynomial is 4x - 9 and the remainder is 20

The resultant of the division is called the quotient while the Remainder is the number that is left after division.

In long division, the terms on top of the division symbol are called the quotient while that at the bottom is called the remainder.

When a division has no remainder it means that the polynomial is divisible by the divisor.

The body of the calculation is found in the attached file below.

In conclusion, the Quotient and remainder are 4x - 9 and 20 respectively.

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The simplified form of the given fraction is, 2/3.

What is greatest common factor?

The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.

Consider, the given fraction [tex]\frac{48}{72}[/tex]

The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So, from above the greatest common factor of 48 and 72 is 24.

Therefore,

[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]

Therefore, the simplified form of the given fraction is, 2/3.

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