Given the function f(x) = −2x2 + 4x − 7, find f(−4). −55 −7 9 25

Answer:

[tex]344=12x+80[/tex]

[tex]a=344[/tex]

[tex]b=12[/tex]

[tex]c=80[/tex]

Step-by-step explanation:

Let x be number of balls shot through the hoop by Central City High School's robot.

We have been given an equation [tex]a=bx+c[/tex] and we are asked to find the values of a, b and c.

We are told that Central City High School's team earned an additional 12 points for each ball the robot shot through a hoop. So the points earned by shooting x balls through the hoop will be 12x.

The team also earned 80 points for their robot climbing over an obstacle. So total number of points earned by team will be equal to [tex]12x+80[/tex].

We are also told that the team won the round with 344 total points. We can represent this information in an equation as: [tex]344=12x+80[/tex]

Upon comparing this equation with our given equation we will get,

[tex]a=344[/tex]

[tex]b=12[/tex]

[tex]c=80[/tex]

Therefore, the equation [tex]344=12x+80[/tex] can be used to find the number of balls, x, team's robot shot through the hoop.

Answer: 5:7

Step-by-step explanation:

The person above is right

I just did the test

Answer:

Which equation represents the scenario?

✔ 6.25x + 12 = 30.75

How many people went to the movies?

✔ 3

Step-by-step explanation:

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The price of a ticket = $6.25

As a group, they spend $12 on refreshments.

Total spent money = $30.75

Now,

Let number of people go to the movie = x

Then, Total price spent on ticket = $6.25x

And, As a group, they spend $12 on refreshments.

So, Total spent money is equal to $30.75, as;

$6.25x + $12 = $30.75

This equation represents the scenario.

Now, Solve the equation for number of people as;

$6.25x + $12 = $30.75

Subtract 12 both side,

6.25x + 12 - 12 = 30.75 - 12

6.25x = 18.75

Divide by 6.25,

x = 3

Thus, There are 3 peoples go to the movie.

Therefore,

1. There are 3 peoples go to the movie.

2. The equation to represent the scenario is,

⇒ 6.25x + 12 = 30.75

Where, x is number of people.

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Answer:

The answer is 12

Step-by-step explanation:

Final answer:

The total cost for fixing a drain that takes 7 hours is $226. If the plumber charges a total of $310, he spent 11 hours fixing the drain.

Explanation:

The cost function given by the plumber is C(h) = 79 + 21h, where C represents the total cost and h represents the number of hours spent fixing the drain.

Answer:

The tax will be $42,750.

Step-by-step explanation:

Mel Company has a net income, before taxes, of $95,000.

The treasurer of the company estimates 45% of net income will have to be paid for federal and state taxes.

So, the tax for both federal and state is:

[tex]0.45\times95000=42750[/tex] dollars

Therefore, the tax will be $42,750.

At 4:00 PM, the distance between the ships is changing at a rate of 6160 km/h.

To find the rate at which the distance between the ships is changing, we can use the concept of relative velocity. At 4:00 PM, ship A has been sailing east for 4 hours, covering a distance of 40 km/h * 4 h = 160 km. Ship B has been sailing north for 4 hours, covering a distance of 20 km/h * 4 h = 80 km.

To find the distance between the ships at 4:00 PM, we can use the Pythagorean theorem. The distance between the ships is the hypotenuse of a right triangle with legs of 170 km and 80 km. Using the theorem, we find that the distance between the ships is √(170^2 + 80^2) ≈ 186.45 km.

To find the rate at which the distance is changing, we can use the derivative of the distance formula. Let D be the distance between the ships. Then, D^2 = (170 + 40t)^2 + (80 + 20t)^2, where t is the time in hours. Taking the derivative of D^2 with respect to t and solving for dD/dt, we get: dD/dt = (170 + 40t)(40) + (80 + 20t)(20).

Substituting t = 4 into the expression, we find that dD/dt = (170 + 40(4))(40) + (80 + 20(4))(20) = 6160 km/h. Therefore, the distance between the ships is changing at a rate of 6160 km/h at 4:00 PM.

John needs to use the inequality 72 + 78 + 70 + x ≥ 289 to determine the minimum number of additional test points required to pass his math class.

The student, John, needs to determine how many more test points he requires to pass his math class. Given his current test scores, the inequality to represent this scenario should account for the minimum points he needs to achieve the threshold.

Therefore, the inequality should include an 'at least' condition, meaning the total points must be greater than or equal to the pass mark of 289. Adding his current scores of 72, 78, and 70 gives a total of 220, so the inequality will include an unknown variable, x, which represents the additional points needed. The correct inequality is D. 72 + 78 + 70 + x ≥ 289.

Final answer:

John needs to use the inequality 72 + 78 + 70 + x ≥ 289, which simplifies to x ≥ 69, to determine he requires at least 69 more points to pass. Option D

Explanation:

John needs to determine how many more points he requires to pass his math class, with a target score of at least 289 points. He already has test scores of 72, 78, and 70. To find out the least number of additional points he needs, he should use an inequality that allows for the sum of his scores and an unknown quantity x (representing the points he needs) to be at least as great as 289. This is represented by the inequality 72 + 78 + 70 + x ≥ 289. This can be simplified to x ≥ 69, which means John needs at least 69 more points to pass the class.

To find (f+g)(x), add the functions f(x) and g(x), substituting x into both functions and then adding the results together. The result is (f+g)(x) = 4x + 16.

To find (f+g)(x), we need to add the two functions f(x) and g(x). f(x) = 3x + 7 and g(x) = x + 9. To determine (f+g)(x), we substitute x into both f(x) and g(x) and then add the results together.

So, (f+g)(x) = f(x) + g(x) = (3x + 7) + (x + 9) = 4x + 16.

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Answer:

On Zira's birthday Lizzy, Amy Wilson Amara, and Ria want only 3/4 inches of the cake how much cake do you need for all of them?

Solutions 5 x3/4 = 3.75 inches of cake

Step-by-step explanation:

Answer:

The answer is the next table:

x    y

0   1

3   0

6   -1

9   -2

Step-by-step explanation:

In order to determine the table with ordered pairs, we have to know about replacing values.

In a linear function, there are two variables, the dependent variable (y) and the independent variable (x). If we replace any value in the "x" variable, we get the "y" value. The process is called "replacing value".

To get the table, we choose some value to replace in the "x" variable:

[tex]x=0\\y=-\frac{1}{3}(0)+1=1\\[/tex]

[tex]x=3\\y=-\frac{1}{3}(3)+1=-1+1=0[/tex]

[tex]x=6\\y=-\frac{1}{3}(6)+1=-2+1=-1[/tex]

[tex]x=9\\y=-\frac{1}{3}(9)+1=-3+1=-2[/tex]

The table with some ordered pairs is:

x    y

0   1

3   0

6   -1

9   -2

I have attached an image that shows a graph with the ordered pairs.

1/13 = 0.0769 = 7.7%

9/26 = 0.346 = 34.6%

5/26 = 0.192 = 19.2%

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Answer:

First let us calculate for his salary this year. We know that 3000 is only 8% of his salary, hence:

0.08 * salary = 3000

salary = 3000 / 0.08

salary = 37,500

Therefore his previous salary is:

previous salary = 37,500 + 2,000

previous salary = $39,500

Step-by-step explanation:

The like radicals to 3x√5 from the given options is: D. y√5.

Like radicals can be defined as radicals having the same root number (i.e. square) and also have the same radicand.

Given, 3x√5, the root here is a square, while the radicand is 5. Thus, like radicals to 3x√5 will have same root and radicand.

Therefore, the like radicals to 3x√5 from the given options is: D. y√5.

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The like radical to 3x sqrt 5 is y sqrt 5.

Given the expression 3x sqrt 5, we can see that the square root is applied only to 5 and not to 3x. To find a like radical, we need to find an expression in which the square root is also applied only to the same number.

Looking at the options, the only expression that matches this criterion is y sqrt 5. The square root is applied only to 5, just like in the original expression. Therefore, y sqrt 5 is the like radical to 3x sqrt 5.

For 2 1/2 times the doubled recipe, starting with an initial amount of 3 1/3 cups of heavy cream, the total amount needed would be 16 2/3 cups of heavy cream.

To calculate how much heavy cream is needed, we must first understand the initial amount required and then apply the necessary adjustments to upscale the recipe.

If the original recipe calls for 3 1/3 cups of heavy cream and we want to double the recipe, we would need 2 x 3 1/3 cups which is 2 x (10/3) cups = 20/3 cups or 6 2/3 cups.

Now, if we want to make 2 1/2 times the amount of the doubled recipe, we multiply 6 2/3 cups by 2 1/2 (5/2), resulting in (20/3) x (5/2) cups. Simplifying this, we get:

(20/3) x (5/2) = (100/6) cups = 16 2/3 cups.

Therefore, for 2 1/2 times the doubled recipe, you would need 16 2/3 cups of heavy cream.

Answer:

Triangle GHI is rotating 180° counterclockwise .

Step-by-step explanation:

Given : Triangles.

To find : Which is the image of Triangle ABC for a 180° counterclockwise rotation about P.

Solution : We have triangle ABC .

If we Rotate GHI triangle in counterclockwise 180 degree we get triangle ABC.

We can prove it by rotating triangle ABC in clockwise direction 180° We get triangle GHI.

Therefore, Triangle GHI is rotating 180° counterclockwise .

Answer

0.5

Explanation

0.05 is 1/10 the value of?

In other words the question is asking, what must be multiplied by 1/10 to give 0.05.

let that value be X.

1/10 × X = 0.05

X/10 = 0.05

X = 0.05 × 10

    = 0.5

The value that must be multiplied by 1/10 which gives 0.05 would be 0.5.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We need to find the value that must be multiplied by 1/10 which gives 0.05.

Let that value be X.

1/10 × X = 0.05

X/10 = 0.05

X = 0.05 × 10

   = 0.5

Thus, the value that must be multiplied by 1/10 which gives 0.05 would be 0.5.

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Answer:

Wee is the independent variable, and deposit is the dependent variable

Step-by-step explanation:

Given that Olivia started her banking account with $100 and is increasing the account $20 per month.

Here the variable which changes independently is the independent variable

Hence no of weeks elapsed would be the independent variable

The dependent variable would be the variable which changes whenever number of weeks changes.

Here dependent variable is the total balance in the account in a particular week

D=100+20n wbere n= no of weeks that eapsed

and D= depositisin in the bank

The probability of rolling a 2 on a die and then rolling an odd number on a second roll is 1/12.

The probability of rolling a 2 on a die is 1/6 because there are six sides on a die, each with an equal chance of landing face up. When rolling the dice a second time, there are three odd numbers (1, 3, and 5), so the probability of rolling an odd number is 3/6, or 1/2. To find the combined probability of both events occurring in sequence (rolling a 2 first and then an odd number), we multiply the individual probabilities: (1/6) × (1/2) = 1/12.

Answer:

90 degrees

Step-by-step explanation: