Evaluate 5a^2 + 2b^3 when a=4 and b =-4

Answers

Answer 1

Hello there! How are you today?

5a^2 + 2b^3, solve when a = 4 and b = -4

To solve for this, we must replace "a" with 4, and "b" with -4.

I will set it up;

5(4^2) + 2(-4^3)

Simplify the parenthesis (PEMDAS).

5(16) + 2(-64)

Remove the parenthesis by multiplying them by the numbers to the outside of them.

5 x 16 = 80
2 x -64 = -128

We are now left with:
80 - 128

Simplify.

-48 is your final answer.

I hope this helps!

Related Questions

Choose the best definition for the following term:substitution

Answers

the action of replacing someone or something with another person or thing

A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.

The slopes of perpendicular line segments are 1/2 and d/3 What is the value of d?

d=-6
d=-3/2
d=3/4
d=6

Answers

perpendicular slopes have a product of -1, thus [tex]\bf \cfrac{1}{2}\cdot \cfrac{d}{3}=-1[/tex]

solve for "d"

perpendicular lines have slopes that multiply to get -1
so

1/2 times d/3=-1
d/6=-1
times both sides by 6
d=-6

What is the formula for finding the area of a regular polygon with perimeter P and apothem length a?

Answers

Answer:

[tex]A=\frac{1}{2}Pa[/tex]

Step-by-step explanation:

Let

P------> the perimeter of a regular polygon

a-----> the apothen

A-----> the area of a regular polygon

we know that

The formula to calculate the area of a regular polygon is equal to

[tex]A=\frac{1}{2}Pa[/tex]

The formula for finding the area of a regular polygon with

perimeter P and apothem length a is 1/2Pa.

What is a Polygon?

This is referred to as a plane figure which has a finite number of

straight line segments connected to form a closed polygonal

chain.

The formula for calculating the area of a regular polygon is

1/2Pa where P is the perimeter of a regular polygon and a is the

apothem.

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what is the maximum value of the function y = −3x2 − 15x + 9?

Answers

y = -3x² - 15x + 9
The graph of this equation is an n-shape. It will go up to a maximum point and then arc back downwards.
In order to find this point, there are two ways I can think of, I will show the one I prefer:
First, take out the coefficient of the x² terms:
y = -3(x² + 5x - 3)
Now, CTS (complete the square):
y = -3((x + 5/2)² - 25/4 - 3)
y = -3(x + 5/2)² + 111/4
Maximum Point: (-5/2, 111/4) or (-2.5, 27.75)

A line contains points (−2,−2) and (1,4). Find the distance between the line and the point (6,−1).

Answers

In analytical geometry, derived equations are already available for finding the distance between a point and a line. The equation is

[tex]d = \frac{|Ax + By+ C|}{ \sqrt{ A^{2}+ B^{2} } } [/tex]

This is basing on the standard equation of a line in the form of:
Ax + By + C = 0, where A, B and C are coefficients.
These constants are coming from the equation of the line, while the point (x,y) is substituted to the x and y terms of the equation.

However, we must first know the equation of the line. Let us use the slope-intercept form: y = mx + b, where m is the slope which is equal to (y2-y1)/(x2-x1) while b is the y-intercept. For points (−2,−2) and (1,4), the slope is

m = (4--2)/(1--2) = 2

Then, we substitute any of those points to determine b. The answer would be the same either way. Let's use (-2,-2).
-2 = 2(-2) + b
b = 2

Thus, the equation of the line is y = 2x + 2. Rearranging into the standard form, it becomes 2x - y + 2 = 0. Therefore, A=2, B=-1 and C=2. Substituting the values to the equation by replacing x and y with coordinates of point (6,−1),

[tex]d = \frac{|2(6) + (-1)(-1)+ 2|}{ \sqrt{ 2^{2}+ (-1)^{2} } }[/tex]

d = 3√5 or 6.71 units

Four is no less than the quotient of a number x and 2.1

Answers

Since quotient is dividing, 4 is greater than or equal to x/2.1 and 4≥x/2.1. Multiplying both sides by 2.1, we get 8.4 ≥x

A triangle has an area of 180 cm2 and the base that is 20 cm long. what is the height of the triangle answers

Answers

that is the answer i'm just writing thing because i needed to write something but there you go, i hope this helps

Base (b) = 20 cm

Height (h) = ?

Area = 180 cm²

[tex] \frac{1}{2}bh = 180 [/tex]

[tex] \frac{1}{2} * 20 *h = 180[/tex]

10h = 180

h = 18

Hence, the height is 18 cm.

Evaluate the determinant for the following matrix: [1 4 4 5 2 2 1 5 5]

(This is a 3x3 matrix)

Answers

I would assume the order of the 3×3 matrix to be in this manner:

1 4 4
5 2 2
1 5 5

To determine the determinant of the matrix, you must multiply the number diagonally. For a 3×3 matrix, you must also form 3 diagonals up and 3 diagonals down. To do this, you copy the the first two columns and place it next to the third column.

1 4 4 1 4
5 2 2 5 2
1 5 5 1 5

The sum of the products of the diagonals down is subtracted to the sum of the products of the diagonals up. In other words,
Determinant = ∑(products of diagonal down) - ∑(products of diagonal up)
Determinant = [(1*2*5)+(4*2*1)+(4*5*5)]-[(1*2*4)+(5*2*1)+(5*5*4)]
Determinant = 0

The determinant of the matrix is zero.

Final answer:

The determinant of the given 3x3 matrix [1 4 4 5 2 2 1 5 5] is calculated by expanding across the first row and is found to be -60.

Explanation:

To evaluate the determinant of a 3x3 matrix, you can use the method of expansion across any row or any column. Given the matrix [1 4 4 5 2 2 1 5 5], let's expand across the first row:

The determinant of the matrix is the sum of the products of each element in the chosen row or column and the determinant of the 2x2 matrix that remains after removing the row and column of that element.

Multiply the first element of the first row by the determinant of the remaining 2x2 matrix, then subtract the product of the second element and its associated 2x2 matrix, and add the product of the third element and its 2x2 matrix.

Calculating the values, we get: 1*(2*5 - 2*5) - 4*(5*5 - 2*1) + 4*(5*2 - 2*1) = 1*0 - 4*23 + 4*8 = 0 - 92 + 32.

Therefore, the determinant of the given matrix is -60.

I Need Help ASAP! This is Due in 30 Minutes!

I don't Understand it at all and I need Help

Create a factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.

Answers

This looks like an odd problem.

Just start with a simple expression with 7 as a factor, and then multiply it out.

For example:

7(x+1)(x+2)

Here 7 could be the GCF.

Now multiply it out:

7(x^2+3x+2) =

7x^2+21x+14

So our factorable polynomial is 7x^2+21x+14

And its two equivalent forms are:

7(x^2+3x+2)
and
7(x+1)(x+2)

Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle.

Answers

Since we are given three points on the circle, and we know that each point is a distance equal to the radius to some point (x,y), we can set up a system of equations to solve for the center...

Knowing that the distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2 and these distances are all equal we can say

d^2=(x-0)^2+(y-0)^2, (x+3)^2+(y-0)^2, (x-1)^2+(y-2)^2

d^2=x^2+y^2, x^2+6x+9+y^2, x^2-2x+1+y^2-4y+4 now getting differences

0=-6x-9, 8x+4+4y

Since both of the equations above are equal to zero we can see that:

-6x-9=0

-6x=9

x=-9/6

x=-1.5, making 8x+4+4y=0 become:

8(-1.5)+4+4y=0

-12+4+4y=0

-8+4y=0

4y=8

y=2

So the center of this circle is at the point (-1.5, 2)

What is the end point and mid point

Answers

The endpoints are the points which represent or marks the end of a line segment or an interval. So, the endpoints would be the same points given which are ( 5/3, 1 ) and ( 0, 2). The midpoint, on the other hand, is the point that is located halfway through the line segment or the interval. It divides the segment into two parts with equal lengths. We calculate it by the formula,
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

We substitute the points given above to the formula as follows:

midpoint = ((5/3 + 0) / 2, (1 + 2) / 2)
midpoint = 5/6 , 3/2

So, the midpoint is located at point 5/6, 3/2.

Answer:

end point is (-5/3 , 3)

mid-point: (5/6, 3/2)

Step-by-step explanation:

ten less than twice a number is the same as 7 times the number. find the number

Answers

The number is -2 // Math [n is equivalent to number]: 2n -10 = 7n
2n = 7n + 10
-5n = 10
-n = 2
n = -2
// Hope this helped, please give me brainliest, thanks!! //

On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?

Answers

Tangential speed increases with distance. Rotational speed is constant.

Write the product cos(2x)sin(5x) as a sum

Answers

The product to sum identity formula states

cos(a)sin(b) = (1/2)[sin(a+b) - sin(a-b)]

So simply plug it into that, to get-

(1/2)[sin(2x+5x) - sin(2x-5x)]

Answer:

[tex]\cos(2x)\sin(5x)=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]

Step-by-step explanation:

Given: [tex]\cos(2x)\sin(5x)[/tex]

Formula:

[tex]\sin A+\sin B=2\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})[/tex]

[tex]\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})=\dfrac{\sin A+\sin B}{2}[/tex]

Compare the given expression with formula

[tex]\cos(2x)\sin(5x)=\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})=\dfrac{\sin A+\sin B}{2}[/tex]

Therefore,

[tex]\dfrac{A+B}{2}=5x\Rightarrow A+B=10x[/tex]

[tex]\dfrac{A-B}{2}=2x\Rightarrow A-B=4x[/tex]

Using two system of equation of A and B to solve for A and B

Add both equation to eliminate B

[tex]2A=14x[/tex]

[tex]A=7x[/tex]

Substitute A into A+B=10x

[tex]7x+B=10x[/tex]

[tex]B=3x[/tex]

Substitute A and B into formula

[tex]\cos(2x)\sin(5x)=\sin(\dfrac{7x+3x}{2})\cos(\dfrac{7x-3x}{2})=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]

Hence, Product as sum form [tex]\cos(2x)\sin(5x)=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]

Can square root of 27 be simplified

Answers

Yes, square root of 27 can be simplified

[tex] \sqrt{27}= \sqrt{9*3}=3 \sqrt{3} [/tex]

The roots up to 27 are 1 4 9 16 and 25. 9 is a factor of 27 so the answer is yes.
To take 9 out, write the root on the left side (3) and write what is left on the right (3 since 9 times 3 is 27) The answer to root 27 simplified is 3 root 3

Find the distance between each pair of points

Answers

The distance between both points is 5 points.

We could use the distance formula but because the line is vertical, there is no need to use the distance formula.

First point is at (-1, -2) and the second is plotted at (-1, 3). We x-coordinates don't change. Just take the absolute value of the difference between the -2 and 3.

|3 - (-2)| =
|3 + 2| =
|5| = 5

So, 5 units is the answer.

Use basic identities to simplify the expression.
cos θ - cos θ sin2θ

Answers

cos Ф - cos Ф.sin² Ф

sin² Ф = 1 - cos² Ф
cos Ф - cos Ф( 1-cos² Ф) = cos Ф - cos Ф - cos³ Ф = cos³ Ф

cos Ф - cos Ф.sin² Ф = cos³ Ф

The solution for the expression will be cos Ф - cos Ф.sin² Ф = cos³ Ф.

What are trigonometric identities?

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

The given trigonometric expression will be solved as below,

cos Ф - cos Ф.sin² Ф

We know that, sin² Ф = 1 - cos² Ф

E = cos Ф - cos Ф( 1-cos² Ф)

E = cos Ф - cos Ф - cos³ Ф

E = cos³ Ф

Therefore, the expression is cos Ф - cos Ф.sin² Ф = cos³ Ф.

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F leonard bought 2 packs of batteries for x amount of dollars, how many packs of batteries could he purchase for $5.00 at the same rate

Answers

1.
The rate at which Leonard bought was 2 packs per x dollars,

that is his buying rate was (2 packs)/(x dollars)=2/x (p/$)

2.

with 1 $ Leonard buys 2/x packs
then
with 5 $ Leonard buys (2/x)*5 = 10/x packs.

Answer: 10/x packs

We use ________ to determine the actual rate of change over intervals.
the dependent variable
the independent variable
absolute value
none of the above

Answers

I think the correct answer is the last option. The term to fill in the blank is not one of the choices given. I think the term would be slope. We use slope to determine the actual rate of change over intervals. It is also called the gradient. It shows how the dependent variable changes as the independent variable changes.

Find the degree of the monomial. 6y2w8

Answers

Degree of a monomial or polynomial is the highest exponent you can see in the expression. The two variables, y and w, both have exponent of 1. So, the degree of this monomial should be 1.

The table below represents the distance of a car from its destination as a function of time: Time (hours) x Distance (miles) y 0 900 1 850 2 800 3 750 Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3, and tell what the average rate represents. (4 points) Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)

Answers

The y-interception is y=900 or(0,900) which means that a car must travel 900 miles for the final destination. And every hour driven is 50 miles.

The average rate of change isIt represents how many miles per one hour changes the distance from a destination.

Domain of this function if the car traveled the same rate until it reached its destination:

0=-50x+900

50x=900

x=900/50=18

Domain: x∈ [0, 18].

Labor rate = $7.50 per hour Labor time = 6.5 hours Retail price of parts = $0 Total job cost = $82.00 Overhead rate?

Answers

Total cost job=
Retail price of parts+labor cost+manufacturing overhead

Total cost job 82

Retail price of parts 0

Labor cost=7.5×6.5=48.75

Manufacturing overhead ?

82=0+48.75+?

?=82−48.75

?=33.25

Manufacturing overhead is 33.25

Now find manufacturing overhead rate from the cost of labor
33.25÷48.75=0.682×100=68.2%

The answer 68.2%

i need help with this question

Answers

[tex]g(x)= \sqrt{x-5} , h(x)= x^{2} -6[/tex]

case (i):
the output of the first machine ([tex]\sqrt{x-5}[/tex]) is the input of the second machine, so we plug ([tex]\sqrt{x-5}[/tex]) or g(x) in function h and calculate, as follows:

[tex]h(g(x))=h(\sqrt{x-5})[/tex], now h is the function which squares whatever the input is and subtracts 6:

[tex]h(\sqrt{x-5})=(\sqrt{x-5}) ^{2}-6=x-5-6=x-11[/tex]

case (ii): we plug h in g:

[tex]g(h(x))= \sqrt{h(x)-5}= \sqrt{ x^{2} -6-5}= \sqrt{ x^{2} -11} [/tex]

a.

case1

[tex]h(g(x))=x-11=5 [/tex]

x=16

so for x=16, h(g(x))=5

case2

[tex]g(h(x))= \sqrt{ x^{2} -11}=5[/tex]

[tex] x^{2} -11=25[/tex]

[tex] x^{2} =36[/tex]

x=-6 or x=6

for both these values, g(h(x))=5

so since her input was 6, the order was g(h(x)), that is h(x) was the input of g(x)

b.

case1

[tex]h(g(x))=x-11=-5[/tex]

x=11-5=6,

so for x=6, h(g(x))=-5

case2

[tex]g(h(x))= \sqrt{ x^{2} -11}=-5[/tex]

the square root cannot be a negative number

Answer:

A. order is g(h(x))

B. yes, for h(g(x)) only

If the price of an item is $34 and the sales tax on it is $1.36, what is the sales-tax rate?

Answers

1.36/34 = 0.04

0.04 = 4%

1.36 / 34 = 0.04 = 4% <==sales tax rate

In a fast-food restaurant, the ratio of people eating hamburgers to people eating chicken is 4 : 3. There are 84 people in the restaurant. How many people are eating hamburgers and how many are eating chicken? A. 36 people are eating hamburgers; 48 people are eating chicken. B. 12 people are eating hamburgers; 72 people are eating chicken. C. 48 people are eating hamburgers; 36 people are eating chicken. D. 21 people are eating hamburgers; 63 people are eating chicken.

Answers

A

48:36 = 4:3 once both are divided by 12

48 + 36 = 84, everyone accounted for

Final answer:

By using the ratio 4:3 and the total number of people (84), we calculate that each part of the ratio represents 12 people. Multiplying 4 parts by 12 gives us 48 people eating hamburgers, and multiplying 3 parts by 12 gives us 36 people eating chicken, making option C correct.

Explanation:

To solve the problem of determining how many people are eating hamburgers and how many are eating chicken given the ratio and the total number of people, we need to divide the total number of people by the sum of the parts of the ratio to find out the value of each part. The ratio given is 4:3, which means for every 4 people eating hamburgers, there are 3 people eating chicken. To find the value of each part of the ratio, we add the parts of the ratio (4 + 3 = 7) and divide the total number of people in the restaurant (84) by this sum.

84 ÷ 7 = 12. This means that each part of the ratio is equivalent to 12 people. Now, we need to multiply the number of each part by the number of people that each part represents. For hamburgers, it's 4 parts, so 4 × 12 = 48 people. For chicken, it's 3 parts, so 3 × 12 = 36 people.

Therefore, the correct answer is C: 48 people are eating hamburgers and 36 people are eating chicken.

Watermelon cost $0.39 per pound. Joesphs watermelon costs between $4.00 and $5.00. Which compound inequality correctly represents the possible weights of this watermelon? Round to the nearest tenth.

Answers

possible weights are 4 / 0.39 = 10.256 and 5/39 = 12.821

if x is the weight the inequality is

10.3 < x < 12.8 rounded to the nearest tenth

Answer:

10.26<w<12.82 represents the weight of the watermelon.

Step-by-step explanation:

Watermelon cost $0.39 per pound. Let the weight of Joseph's water melon be w pounds.

Joesph watermelon costs between $4.00 and $5.00.

[tex]\frac{4}{0.39}= 10.26[/tex]

[tex]\frac{5}{0.39}= 12.82[/tex]

Means the melons are between 10.26 and 12.82 pounds.

Hence, the compound inequality is 10.26<w<12.82 which represents the weight of watermelon.

HELP PLEASE!!!!

The amount of people in the city of Blonton is increasing due to children being born and because people are moving to the area.

~The population is increasing due to births by 13% each year and about 2300 people move to the area in any given year.
~The increase due to people moving to the area is represented by the function M(t) = 2300t.
~The population at any time when taking into account new births is found by P(t) = 375,000(1.013)t where 375000 was the initial population and t stands for the number of years after 1990.

If we added these functions together, what would the sum represent?

Answers

This is based off this year so 1990-2017
Since there are 27 years it would be 2300*27 which would equal 62,100 people
The new births would be 375,000(1.013)^27 which would equal 531,479 people
Adding 531,479 with 62,100 equals 593,579 people

An activity book has 21 pages of crossword puzzles, 18 pages of cryptograms, and 12 pages of mazes. bianca randomly selects a page, completes the activity, and then randomly selects another page to complete. what is the probability that bianca first completes a maze and then completes a crossword puzzle?

Answers

21 crosswords, 18 cryptograms, 12 mazes....total of 51 activities

P(maze) : 12/51...reduces to 4/17
P(crossword) 21/50

P(both) : 4/17 * 21/50 = 84/850 = 42/425 <=

Final answer:

The probability that Bianca first completes a maze and then completes a crossword puzzle is approximately 9.8%.

Explanation:

To find the probability that Bianca first completes a maze and then completes a crossword puzzle, we need to calculate the probability of each event occurring and then multiply them together.

The total number of pages in the activity book is 21 + 18 + 12 = 51 pages.

The probability of selecting a maze page first is 12/51, and after completing the maze page, there are now 50 pages remaining in the book, 21 of which are crossword puzzles.

So, the probability of selecting a crossword puzzle page after completing a maze page is 21/50.

To find the probability of both events happening, we multiply the probabilities: (12/51) * (21/50) = 0.098 or 9.8%.

Assume that a researcher randomly selects 14 newborn babies and counts the number of girlsâ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting 9 or more girls.

Answers

Probability is the mathematics of chance. In other words, it is the fraction or percentage of a certain event successfully happening. For this problem, you want to determine the probability of selecting 9, 10, 11, 12, 13 or 14 girls. The solution is as follows:

P = nCr p^r q^n-r
where
n is number of total events (n = 14)
r is the number of events that could happen (9, 10, 11, 12 ,13 and 14)
p is the probability of an event being a girl (p = 50% or 0.5)
q is the probability of either an event being a boy (q = 1-p = 0.5)
nCr is a combination formula which is n!/(r!(n-r)!)

P = [14C9* (.5)^9 * (0.5)^5]+ [14C10* (.5)^10 * (0.5)^4]+[14C11* (.5)^11 * (0.5)^3]+[14C12* (.5)^12 * (0.5)^2]+[14C13* (.5)^13 * (0.5)^1]+[14C14* (.5)^14 * (0.5)^0]

P = 0.211 or 21.1%

Final answer:

To find the probability of selecting 9 or more girls out of 14 newborn babies, sum the probabilities for selecting 9 to 14 girls from the given table.

Explanation:

To find the probability of selecting 9 or more girls out of 14 babies, we need to calculate the sum of the probabilities of selecting 9, 10, 11, 12, 13, and 14 girls. Refer to the given table that summarizes the probabilities for each value of x. Add the probabilities for these values to get the probability of selecting 9 or more girls.

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Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Answers

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

So what we have to do is to look for the values of the variables:

For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9

c = 7 (distance from center to vertices; given from the foci)
c^2 = 49

By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2

b^2 = 49 – 9

b^2 = 40

Therefore the equation of the hyperbola is:

(x^2 / 9) – (y^2 / 40) = 1

Answer:

Hope this helps :)

Step-by-step explanation:

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