Expand and simplify (2x^2+3)(4x+5)-8x(x^2-2)

The vertex form of the function is  [tex]y = (x+4)^{2} - 19[/tex]

Vertex form of function:

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The vertex form of the equation is written as,

[tex]y = (x+h)^{2} + k[/tex]

Given function is,

y = x² + 8x + 16 - 3 -16

It is observed that,  

x² +8x + 16 = (x+4)²

So that, we can write as above function,

y = x² + 8x + 16 - 3 -16 = (x+4)² - 3 -16

or

y =  (x+4)² - 19

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Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

[tex]f(x)=3^x+9[/tex]

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

Answer:

slope = 1

Step-by-step explanation:

[tex]m=\frac{0-3}{7-10} =\frac{-3}{-3} =1[/tex]

Hope this helps.

Answer:

$82.21

Step-by-step explanation:

cost of meal: $78.30

15% discount: 15% of $78.30 = 0.15 × $78.30 = $11.75

tip: 20% of $78.30 = 0.20 × $78.30 = $15.66

total cost = $78.30 - $11.75 + 15.66 = $82.21

Answer: $82.21

Answer: 4.5

Step-by-step explanation:

The solution to the system of equations is (2.68, 1.01)

From the question, we have the following parameters that can be used in our computation:

2.5x+3.75y=10.5

1.25x−8.5y=−5.25

Express properly

2.5x + 3.75y = 10.5

1.25x − 8.5y = −5.25

Next, we make a plot of the system to determine the solution

The point of intersection in the plot represent the solution to the equations

In this case, the intersection has a coordinate of (2.68, 1.01)

Hence, the solution is (2.68, 1.01)

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Step-by-step explanation:

x current age of the father

y current age of the son

first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y

second equation (y+5) : (x+5)= 2:7

so (y+5)*7=(x+5)*2

let's replace x we found at the first equation with the one at second equation

(y+5)*7=(35-y+5)*2

7y+35=(40-y)*2

7y+35=80-2y

7y+2y=80-35

9y=45

y=5

x=35-y=35-5=30

The function in Excel that we should use to find a measurement M given a right-tail probability (or area) A is = NORM.INV(1-A, mu, sigma)

In order to find a measurement M given a right-tail probability A in Excel, we can use the NORM.INV function. The NORM.INV function in Excel returns the inverse of the normal cumulative distribution for a given probability.

The formula for NORM.INV function is:

= NORM.INV(1-A, mu, sigma)

where:

A is the right-tail probability (or area)

mu is the mean of the distribution

sigma is the standard deviation

The function returns the measurement M such that the right-tail area from M to infinity under the normal curve is equal to A.

Note - In some versions of Excel, the function may be called NORM.INV.RT instead of NORM.INV.

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Answer:

taking your points

Step-by-step explanation:

The value of correlation cofficient between the number of people who complete successfully complete each jump, y and height of jump, x is equals to the - 0.091.

We have a table which consists height ( in feet ), x and completions, y present above figure. We have to calculate the correlation coefficient for variables x and y. Correlation coefficients are used to measure how strong the relationship is between two variables. The commonly used cofficient in linear regression is Pearson's correlation (also called Pearson's R) coefficient . Formulas return a value between -1 and 1, where,

Formula used to determine the cofficient is r = (n∑ xy - (∑x)(∑y))/√[ n∑x² - (∑x)²][n∑y² - (∑y)²]

Here, n = 6, ∑xy = 375.8 , ∑ x =22.4, ∑y

= 102, ∑ x² = 96.5, ∑y² = 1978

so, r = 6×(375.8) - 102(22.4))/√[(6×96 - (22.4)²)(6×1978 - 102²)]

= -30/329.68

= - 0.091

Hence, required value of r is - 0.091.

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Complete question:

The above table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places.

answer:

Huh?

Step-by-step explanation:

students at the college what...?

Speed of Ana =  7.5miles/hour

Step-by-step explanation:

Given,

Ana runs 3/4 mile in 6 minutes.

To find,

The speed of Ana in miles per hour

Recall the formula,

Speed = distance travelled/time taken

60 minutes = 1 hour

Solution:

Distance traveled = 3/4 mile

Time taken = 6 minutes

Since 60 minutes = 1 hour, we have

1 minute =1/60 hour

6 minutes = 6/60 hour

=1/10  hour

Hence speed  = distance travelled/time taken

=  3/4 / 1/10 miles/hour

= 15/2 miles/hour

= 7.5miles/hour

∴ Speed of Ana =  7.5miles/hour

3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.

4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.

5. Manu will pay R1,700, exchanging his old bike for a new bike.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.

The number of books bought = 12

The unit cost of each book = R250.75

The total cost of the 12 books = R3,009 (R250.75 x 12)

The amount advanced to the cashier = R4,000

The balance to be returned = R991 (R4,000 - R3,009)

The cost of a set of crayon = R25

The amount of money for the purchase = R2,750

The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).

The price of the new bicycle = R2,500

The value of the old bike for exchange = R800

The amount to be paid = R1,700 (R2,500 - R800)

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The price of the new bicycle is R2,500. The bike on exchange is worth R800.  How much does he pay for his new bike?

Answer: the correct answer is 51

Step-by-step explanation: i solved this on my quiz

i hope this helps!

Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.

What is the ratio?

A ratio is a relationship between two things when it is expressed in numbers or amounts. For example, if there are ten boys and thirty girls in a room, the ratio of boys to girls is 1:3, or one to three.

We can start by noticing that the ratio of cups of ice cream to cups of soda used to make the floats is always 1:3.

To find out how much soda Sidney will use for 17 cups of ice cream, we can set up a proportion:

3.5/10.5 = 8/24 = 12.5/37.5 = 17/x

Solving for x, we can cross-multiply:

3.5x = 10.5 * 17

x = 54

Therefore, Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.

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By determining the value of x when y = 0, (x, 0), and the value of y when x = 0, respectively, the x-intercept and y-intercept are determined (0, y).

A two-variable equation with a line-shaped graph is referred to as a linear equation. A collection of coordinate plane points that are all the solutions to the linear equation make up the graph. If all of the variables have true numerical values, the equation can be graphed by first drawing a sufficient number of points to identify a pattern, then connecting those points to include all of the points.

A linear equation is represented in standard form as

Ax+By=C,A,B≠0

The equation for y must first be solved before you may graph a linear equation in its usual form.

The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).

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Answer:

2. 3(x + 9) = 48

Step-by-step explanation:

We are given

If each playlist has 9 rock songs and x pop songs, then each playlist has 9 + x songs.

If there are three playlists, there are three playlists which each have x + 9 songs. In other words, 3(x+9). This represents the total number of songs, which is 48. Therefore the answer is 3(x+9)=48.

Hope this helps!

The coordinates  ( 6,-8 ) are plotted by moving 6 units right and 8 units down.

The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at which the x- and y-axes cross perpendicularly.

here, we have,

Given coordinates (6,-8)

for  the cartesian plane, we know that the origin has points (0, 0)

and divided into four Quadrants,

the left side of the origin is a negative x-axis and the right side is a positive x-axis.

and the upside of the origin is a positive y-axis and the downside is a negative y-axis.

here coordinates of x =6 and y = -8

6 is 6 units right from the origin

and -8 is 8 units down from the origin.

Hence for the coordinates , 6 units to the right and 8 units down , is correct.

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There are 10/4 ways ( [tex]\frac{10}{4}[/tex] ) to accomplish the given task by wearing the ties for a week according to the permutations and combinations.

Given if you wear tie for a week, where one need t wear 4 of his ties from the 10 of total. The number of ways to wear the ties will be equal to the value. So there are many ways to wear a tie of different types and also to remove the tie there are different ways. Now we will see the ways to wear a tie accordingly.

According to the permutations and combination rules the formula will be:

Number of ways: (Number of ties want to wear) / (Number of Total ties)

Therefore total number of ways to wear ties = 10/4

Number of ways this can be accomplished is 10/4

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Hi there, here's your answer:

Given 2 angles:

(6d + 8)° and (8d + 4)°

Observe the figure carefully. You will notice that the two angles form a linear pair.

We know that in a linear pair, sum of the two angles = 180°.

Hence,

(8d + 4 + 6d + 8)° = 180°

(14d + 12)° = 180°

(14d)° = (180 - 12)°

= 14d = 168°

Or

d = 12

Thus, we find the value of d to be d = 12.

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The probability of picking three black cards in a row, without replacement, from a standard deck of 52 playing cards is 2/17, or approximately 0.1176 (rounded to four decimal places).

The probability of picking a black card on the first draw = 26/52 = 1/2

        (since there are 26 black cards in the deck)

The probability of picking a black card on the second draw, given that a one was picked on the first draw and the card is not replaced = 25/51,    

        (since there are now only 25 black cards left out)

The probability of picking a black card on the third draw, given that the ones picked on the first two draws are not replaced = 24/50 = 12/25,

        (since there are now only 24 black cards left out)

To pick three black cards in a row, we need to multiply the probabilities of each individual draw = (1/2) * (25/51) * (12/25) = 6/51

Simplifying this fraction, we get = 6/51 = 2/17

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The surface area of the sphere is 113.2 ft².

The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.

The formula for a sphere's total surface area is given by

Here we have

The formula for the radius of a sphere r = 1/2 [√S/π]    

Diameter of the Moeraki boulder radius = 3 feet

=> 3 feet =  1/2 [√S/π]    

=> 6 = [√S/π]

Squaring on both sides

=> 36 = [√S/π]²  

=> S/π = 36

=> S = 36π  

=> S = 113.2  

Therefore,

The surface area of the sphere is 113.2 ft².

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The profit is £1,370. Then the percentage profit of the company will be 124.54%.

A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.

The profit is given as,

Profit = Selling price - Cost price

The number of pins left after the donation to charity is given as,

⇒ (1 - 0.35) x 1,000

⇒ 0.65 x 1,000

⇒ 650 pins

The selling price when 60% are sold for £3 and 40% are sold for £5 is given as,

Selling price = 0.60 x 650 x £3 + 0.40 x 650 x £5

Selling price = £1,170 + £1,300

Selling price = £2,470

The cost price is given as,

Cost price = £1.10 x 1,000

Cost price = £1,100

The profit is given as,

P = £2,470 - £1,100

P = £1,370

Then the percent of profit is given as,

P = [(£1,370) / £1,100] x 100

P = 124.54%

The profit is £1,370. Then the percentage profit of the company will be 124.54%.

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The sum of the geometric sequence for this problem is given as follows:

S = 665.

The sum of the first n terms of a geometric sequence of first term [tex]a_1[/tex] and common ratio q is given by the equation presented as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

The parameters for this problem are given as follows:

[tex]a_1 = 32, n = 6, r = 1.5[/tex]

Hence the sum is obtained as follows:

S = 32 x (1 - 1.5^6)/(1 - 1.5)

S = 665.

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The second option has the better value-for-money.

To find the price per gram, you need to take the quotient between the cost and the mass for each case.

The first brand costs $29.49 for 250 grams, then the cost is:

c = $29.49/250g = $0.12 per gram.

The other brand costs $69.99 for 750 grams, then the cost per gram is:

C = $69.99/750g = $0.09 per gram

We can see that the second option has the better vale-for-money.

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Answer: 0.1 decimal 1/9 fraction

Step-by-step explanation:

Answer:

0.1 or 1/9 i think so but I am sure

The percentage of winners driving a Chevrolet who won with an average speed of at least miles per hour is fifty percent (50%).

We can infer that for a Chevrolet car,

the percentage of average speed (in miles/hour) for the range of 150-159.9 is 25%,

the percentage of average speed (in miles/hour) for the range of 160-169.9 is 18.75%,

and the percentage of average speed (in miles/hour) for the range of 170-179.9 is 6.25%.

Thereby, the percentage of winners of the race who were driving a Chevrolet and had an average speed of at least 150 miles/hour is,

50%.

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The Average daily balance of the given scenario is $2083.

Suppose we're given that:

P_v = Present value of the loan amount

r = rate of interest (compound interest) per period of time

n = number of period of time in which loan is to be paid off

P = A fixed period payment needed to be done for paying off the loan in n number of periods.

Then, we get:

[tex]P = \dfrac{r\times P_v}{1 - (1 + r)^{-n}}[/tex]

Given;

APR= 25%

Cost of wheels and tires= $1500

Time=14days

Cost of brake calipers and leaking= $500

Time=30days

Now,

P= 25x2000/1-(1+25)^-30

P=50000/24

P=2083

Therefore, the monthly balance of loan will be $2083.

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The equations of the graphs are y = 1/2|x - 2| + 5 and y = -7|x + 2| - 11

From the question, we have the following parameters that can be used in our computation:

The graphs

The lines are absolute function graphs, and they can be represented as

y = a|x - h| + k

Where

Vertex = (h, k)

For the blue line, we have

(h, k) = (2, -5) and (x, y) = (0, -4)

So, we have

-4 = a|0 - 2| - 5

2a = 1

a = 1/2

So, the equation is y = 1/2|x - 2| + 5

For the red line, we have

(h, k) = (-2, 3) and (x, y) = (0, -11)

So, we have

-11 = a|0 + 2| + 3

2a = -14

a = -7

So, the equation is y = -7|x + 2| - 11

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Answer:

Solution to system of inequalities is y≥ 3x-2

Graph attached

Step-by-step explanation:

We have the following two inequalities:
y>-3x-5

y≥ 3x-2

To get the solution and graph

1. Graph each inequality separately

2. Choose a test point to determine which side of the line needs to be shaded

3. The solution will be the area where the shadings from each inequality overlap one another

The graph is attached. The heavily shaded region is the set of all points which satisfy all inequalities

We see that any point that satisfies y≥ 3x-2  also satisfies y>-3x-5

In other words, the solution set for y≥ 3x-2 is a subset of the solution set for   y>-3x-5