If f(x) = x/2 - 3 and g(x) = 4x^2 + x - 4, find (f + g)(x)

A

in mathematics the product of numbers means multiply the numbers

let x be the number, then the product of x and 3 = 3x

the result of this multiplication is 87

so 3x = 87 is the equation to solve the problem

the solution is x = 29

The equation used to solve this problem is 3x = 87. The solution, found by isolating x, is 29.

The equation that could be used to solve the problem 'The product of a number and 3 is 87. What is the number?' is 3x = 87. This equation represents 'the product of a number (x) and 3 equals 87'. You would solve this by dividing both sides by 3 to isolate x, resulting in the solution x = 29. Thus, the number that when multiplied by 3 equals 87 is 29.

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To complete the square, you can add (and subtract) the square of half the x coefficient.

... y = x² -10x + 30

... y = (x² -10x +25) + (30 -25)

... y = (x -5)² +5

Answer:

Step-by-step explanation:

let X be the random variable for number of times the clock fails .

X is Poisson with average = 6.8% = 0.0068

PDF of x = e^(-0.0068) 0.0068^x/x!

a) The probability that the​ student's alarm clock will not work on the morning of an important final​ exam = P(X=0) = 0.00675

b) If the student has two such alarm​ clocks,  the probability that they both fail on the morning of an important final​ exam:

Since both clocks are  independent prob for both failing is

P(x1 fails) *P(x2 fails) = 0.00675(0.00675) = 0.000455625

c) the probability of not being awakened if the student uses three independent alarm​ clocks = Prob for all 3 fails = 0.00675^3

= 0.00000307546

d) Yes. Because all three fail probability is almost zero.

D. ​Yes, because you can always be certain that at least one alarm clock will work.

Answer:

There are four (4) whole-number solutions to these inequalities:

... {(4, 1), (5, 0), (6, 0), (7, 0)}

Step-by-step explanation:

These are nicely solved by graphing. Whole numbers are non-negative integers, so x and y can be any values 0, 1, 2, .... The area of overlap on the graph clearly shows that y=0 and y=1 are the only viable choices for y, and that the values for x are limited in each of these cases.

I'd start with setting up the equations. Calling x the number of students in most popular country 1, and y in country 2.

x + y = 44740

x - y = 5672

now solve for x1 and x2. You can subtract second from first:

0 + 2y = 39068

y = 19534

so

x = 5672 + 19534 = 25206

Add a sentence to answer it in words.

total students= 44740 divided by 2 countries= 22370 for each country. if were trying to get a difference of 5672 students, then were gonna divide that 5672 by 2 which is gonna = 2836 students. country 1= 22370 students + 2836 of country 2's students. country 2 is 22370 students - 2836 students that we gave to country 1. so now, country 1 ends up with 25206 students, country 2 end up with 19534 students. a difference of 5672.

Answer:

Option A is the correct answer.

Explanation:

 Any vector can be resolved in to two components. Horizontal component and vertical component.

Consider a vector F which is at angle θ⁰ to the horizontal, we can resolve this vector in to two.

Horizontal component = F cos θ

Vertical component = F sin θ

Here we have Force , F = 50 pounds

Angle with horizontal = 80°

Horizontal component = F cos θ = 50* cos 80 = 8.68 pounds

                                      ≅ 9 lb.

Option A is the correct answer.

the last digits of the numbers being multiplied are 6 and 3

resulting in a product of 18

thus the last digit in her answer would have to be an 8 not a 3

C

a ratio of 5 : 5 simplifies to 1 : 1, which basically means we require the midpoint of the line segment

using the midpoint formula

M = [[tex]\frac{1}{2}[/tex] (0 + 20 ), [tex]\frac{1}{2}[/tex] (15 + 0)] = (10, 7.5 )

Answer:

Option C). (10, 7.5)

Step-by-step explanation:

We have to find the coordinates of point M that divides the segment AB into a ratio of 5:5.

Vertices A and B are (0, 15) and (20, 0)

Ratio 5:5 is simply the ratio 1:1 means point M is the midpoint of segment AB.

So x-coordinate of M will be [tex]\frac{(20+0)}{2}=10[/tex]

and y - coordinate will be = [tex]\frac{(15+0)}{2}=7.5[/tex]

Therefore Option C. (10, 7.5) are the coordinates of point M.

For this case we have the following equation:

[tex](2x + 3) ^ 2 + 8 (2x + 3) + 11 = 0[/tex]

Let [tex]u = 2x + 3[/tex]

We have:

[tex]u ^ 2 + 8u + 11 = 0[/tex]

By definition, given an equation of the form [tex]ax ^ 2 + bx + c = 0[/tex]

The quadratic formula, to find the solution can be written as:

[tex]x = \frac{-b+/-\sqrt{b ^ 2-4 (a) (c)} }{2(a)}[/tex]

In this case we have:

[tex]a = 1\\b = 8\\c = 11[/tex]

Substituting in the quadratic formula we have:

See attached image

Answer:

Option B

x = (- 7 ± √5) / 2

use the substitution u = 2x + 3

equation can now be written as

u² + 8u + 11 = 0

solve for u using the quadratic formula with a = 1, b = 8 and c = 11

u = ( - 8 ± √( 64 - 44 ) )/2

  = ( - 8 ± √20 )/2 = ( - 8 ± 2√5 ) / 2 = - 4 ± √5

change the variable back into terms of  x

2x + 3 = - 4 ± √5 ( subtract 3 from both sides )

2x = - 7 ± √5 ( divide both sides by 2 )

x = ( - 7 ± √5 ) / 2

To evaluate the expression (5/2)^2 + 3^3/4, we simplify each part separately, then add the results. The final value of the expression is 13.

To evaluate the expression (5/2)^2 + 3^3/4, we'll start by simplifying each part separately.

The first part, (5/2)^2, means we raise 5/2 to the power of 2. To do that, we multiply the numerator and denominator of 5/2 by itself:

(5/2)^2 = (5/2) x (5/2) = 25/4.

The second part, 3^3/4, means we raise 3 to the power of 3, and divide the result by 4:

3^3/4 = 27/4.

Now we can add the two simplified parts together:

(5/2)^2 + 3^3/4 = 25/4 + 27/4 = 52/4 = 13.

72 - 16 = 56

-Nicole :) <3

72 - 16 = 56

If a question says "find the difference" it usually means that you can use subtraction :)

Answer:

The rate of change would be 50

Step-by-step explanation:

The rate of change in any equation is simply the amount in changes for every value of x. Since it goes up by 50 for every increase of the week, it means that the rate of change is 50.

Expanded, the function is ...

... p(x) = x² -x +1

Compared to

... ax² +bx +1

_____

The negative discriminant means there are no real roots, hence no x-intercepts.

Answer: The value of a is 1. The value of b is -1. The value of c is 1. The value of the discriminant is -3. The quadratic function will not intersects the  x-axis.

Explanation:

The standard form of a quadratic equation is,

[tex]ax^{2} +bx +c[/tex]

It can be written as,

[tex]x^{2} -x+1[/tex]

Answer:

  about 35

Step-by-step explanation:

This question is asking for an estimate, which means you round the number(s) to something convenient to perform the calculation.

Here, 47% is conveniently rounded to 50% = 50/100 = 1/2. Then 1/2 of 70 is ...

  1/2·70 = 70/2 = 35

A reasonable estimate of 47% of 70 is 35.

___

As you get more sophisticated in your estimating, you can also estimate the error. This estimate is about 3% (of 70) high, so is high by 3/100·70 = 2.1. That means the real answer is 35 - 2.1 = 32.9.

You could also estimate the error as 3% of 100 = 3/100·100 = 3, so you could say the actual value is between 35-3 = 32 and 35. Since 100 is larger than 70, you know that 3% of 100 is larger than 3% of 70, so this is an over-estimate of the error.

The function is linear, so its rate of change is the same everywhere. That rate of change is the coefficient of the variable x, so is $2.90. Since the units of x are feet, and the units of P(x) are dollars, the rate of change $2.90 must be ...

... A. $2.90 per square foot

The average rate of change for the given cost function over the interval [2,000, 2,500] is calculated using the slope formula, resulting in an average rate of $2.90 per square foot, corresponding to option A.

The question asks to find the average rate of change of the cost function P(x) = $2.90x + $103.00, where x represents the square footage of the carpet, over the interval of [2,000, 2,500 square feet]. To calculate the average rate of change, we use the formula of the slope between two points on the function:

(P(x_2) - P(x_1)) / (x_2 - x_1).

So for the interval [2,000, 2,500], we have:

(P(2500) - P(2000)) / (2500 - 2000) = (($2.90 \times 2500 + $103.00) - ($2.90 \times 2000 + $103.00)) / (2500 - 2000).

This simplifies to:

($7250 + $103 - $5800 - $103) / 500 = $1450 / 500 = $2.90 per square foot.

Therefore, the average rate of change over the interval [2,000, 2,500] is $2.90 per square foot, which corresponds to option A.

The empirical rule tells you 68% of the population is within 1 standard deviation of the mean. Your limits are 1 standard deviation from the mean, so your percentage is ...

... 68%

_____

98.20 - 0.62 = 97.58 . . . 1 standard deviation below the mean

98.20 + 0.62 = 98.82 . . . 1 standard deviation above the mean

Approximately 68% of healthy adults have body temperatures between 97.58°F and 98.82°F, as per the empirical rule which states that about 68% of data falls within one standard deviation of the mean in a bell-shaped distribution.

Using the empirical rule (also known as the 68-95-99.7 rule), we can determine the approximate percentage of healthy adults with body temperatures between 97.58°F and 98.82°F. The empirical rule states that for a bell-shaped distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% falls within two standard deviations.

Approximately 99.7% falls within three standard deviations.

Given that the mean body temperature is 98.20°F and the standard deviation is 0.62°F:

One standard deviation from the mean includes temperatures from 98.20°F - 0.62°F to 98.20°F + 0.62°F, which is 97.58°F to 98.82°F.

Therefore, approximately 68% of healthy adults have body temperatures between 97.58°F and 98.82°F according to the empirical rule.

Answer:  [tex]7:8:9 = 10.5:12:13.5[/tex]

Step-by-step explanation:

Suppose,  [tex]7:8:9= x:12:y[/tex]

Now according to the ratio, the equations will be........

[tex]\frac{7}{8}=\frac{x}{12}\\ \\ 8x=7*12=84\\ \\ x=\frac{84}{8}=10.5[/tex]

and

[tex]\frac{8}{9}=\frac{12}{y}\\ \\ 8y=9*12=108\\ \\ y=\frac{108}{8}=13.5[/tex]

So, the ratio will be  [tex]7:8:9 = 10.5:12:13.5[/tex]

The ratio is [tex]\boxed{7:8:9 = 10.5:12:13.5}[/tex].

Further Explanation:

Given:

The ratio is [tex]7:8:9[/tex] and is equal to [tex]{\text{\_\_\_}}:{\text{12}}:{\text{\_\_\_}}[/tex].

Calculation:

Consider the number in the first blank as [tex]x[/tex].

Consider the number in the second blank as [tex]y[/tex].

Therefore, the ratio is [tex]7:8:9[/tex] and is equal to [tex]{{x}}:{\text{12}}:{{y}}[/tex]

From the given equation the ratio of [tex]7:8[/tex] is equal to the ratio of [tex]x:12[/tex].

Now equate [tex]\dfrac{7}{8}[/tex] and [tex]\dfrac{x}{12}[/tex] to obtain the value of [tex]x[/tex].

[tex]\begin{aligned}\frac{7}{8} &= \frac{x}{{12}} \\ \frac{7}{8} \times 12 &= x \\ \frac{{21}}{2} &= x \\ 10.5 &= x \\ \end{aligned}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]10.5[/tex].

From the given equation the ratio of [tex]8:9[/tex] is equal to the ratio of [tex]12:y[/tex].

Now equate [tex]\dfrac{8}{9}[/tex] and [tex]\dfrac{12}{{y}}[/tex] to obtain the value of [tex]y[/tex].

[tex]\begin{aligned}\frac{8}{9} &= \frac{{12}}{y} \\ \frac{9}{8} &= \frac{y}{{12}} \\ \frac{9}{8} \times 12 &= y \\ \frac{{27}}{2} &= y \\ 13.5&= y \\\end{aligned}[/tex]

Therefore, the value of [tex]y[/tex] is [tex]13.5[/tex].

Hence, the ratio is [tex]\boxed{7:8:9 = 10.5:12:13.5}[/tex].

Learn more:

1. Learn more about product of binomial and trinomial https://brainly.com/question/1394854

2. Learn more about line segments https://brainly.com/question/909890

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Ratio and Proportion

Keywords: number, reciprocal, fraction, ratio, equation, proportion, 7:8:9, fill blank.

y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )

the equation of a line in point-slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 3, 4)

m = [tex]\frac{4+1}{-3-4}[/tex] = [tex]\frac{5}{-7}[/tex] = - [tex]\frac{5}{7}[/tex]

use either of the 2 points as a point on the line

using (a, b) = (- 3, 4 ), then

y - 4 = - [tex]\frac{5}{7}[/tex](x + 3 )

A computer desk, originally priced at $83, is now on sale for $78.85

originally priced at $83. After discount the price becomes $78.85

Discount amount =  $83 - $78.85 = $4.15

Decrease rate = discount amount divide by original price

Decrease rate = [tex]\frac{4.15}{83}= 0.05[/tex]

Decrease rate = 0.05

To find percent of decrease we multiply by 100

0.05 * 100 = 5%

Decrease percentage = 5%

To find the number of 30-day periods until the value of the gift cards will be equal, we set up and solve an equation. The value of each card will be $10 when they have equal value.

To solve this problem, we can set up an equation to represent the value of each gift card over time and find when they will be equal.

Let x be the number of 30-day periods that have passed. After x periods, the value of the first gift card will be $50 - $2x, and the value of the second gift card will be $40 - $1.50x.

Setting the two expressions equal, we get:

$50 - $2x = $40 - $1.50x

Simplifying the equation, we have:

$10 = $0.5x

Dividing both sides by $0.5, we get:

x = 20

So, after 20 periods (or 20 months), the value of each gift card will be equal.

To find the value of each card at that point, we can substitute x = 20 into one of the expressions. Let's use the first gift card:

Value = $50 - $2(20) = $50 - $40 = $10

Therefore, when they have equal value, each gift card will be worth $10.

Either A or B on Spinner 1 can be paired with any of 1, 2, 3, 4 on Spinner 2. The appropriate choice is ...

... C.) {A1, A2, A3, A4, B1, B2, B3, B4}

8 1/3 you have to do keep, change, flip

[tex]\frac{25}{3}[/tex]

change division to multiplication and turn the fraction upside down

5 ÷ [tex]\frac{3}{5}[/tex]

= 5 × [tex]\frac{5}{3}[/tex] = [tex]\frac{25}{3}[/tex] in simplest form

Answer:

-20

Step-by-step explanation:

Final answer:

The inequality models a situation where you have at least 45 dollars and you are adding $10 for each additional unit.

Explanation:

The inequality 5 + 10w ≥ 45 can be modeled by a situation where you have at least 45 dollars and you are adding $10 for each additional unit. Let's solve it step by step:

1. Subtract 5 from both sides of the inequality: 10w ≥ 40.

2. Divide both sides by 10: w ≥ 4.

The solution to the inequality is w ≥ 4. This means that the situation being modeled is where you have at least 4 units of something.

Answer:

[tex]y = \frac{3}{5}x - 2[/tex]

Step-by-step explanation:

Using the point slope form of a line equation, substitute m = 3/5 and the point (0,-2).

[tex]y - y_1 = m(x-x_1)\\y --2 = \frac{3}{5}(x - 0)\\y + 2 = \frac{3}{5}x \\ y = \frac{3}{5}x - 2 [/tex]

We are given

[tex]f(n+1)=-10f(n)[/tex]

we are given

[tex]f(1)=1[/tex]

At n=1:

we can plug n=1 into formula

[tex]f(1+1)=-10f(1)[/tex]

[tex]f(2)=-10f(1)[/tex]

[tex]f(2)=-10*1[/tex]

[tex]f(2)=-10[/tex]

At n=2:

we can plug n=2 into formula

[tex]f(2+1)=-10f(2)[/tex]

[tex]f(3)=-10f(2)[/tex]

[tex]f(3)=-10*-10[/tex]

[tex]f(3)=100[/tex]................Answer

A function assigns the value of each element of one set to the other specific element of another set. The value of f(3) is 100.

A function assigns the value of each element of one set to the other specific element of another set.

As the recursive function is given to us, f(n + 1) = –10f(n), also the value of f(1)=1 , therefore, the value of f(2) can be written as,

[tex]f(n + 1) = -10f(n)\\\\f(1 + 1) = -10f(1)\\\\f(2)= -10 \times 1\\\\f(2)=-10[/tex]

Now, the value of f(3) can be written as,

[tex]f(n + 1) = -10f(n)\\\\f(2 + 1) = -10f(2)\\\\f(3)= -10 \times -10\\\\f(3)= 100[/tex]

Hence, the value of f(3) is 100.

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The length of the three sides of the triangle is 17cm, 25cm, and 12cm.

To solve this problem, let's assign variables to the three sides of the triangle. Let x represent the shortest side, (x + 8) represent the longest side, and (x - 5) represent the third side.

Using the perimeter given, we can set up an equation:

x + (x + 8) + (x - 5) = 56

Simplifying the equation, we have 3x + 3 = 56, then 3x = 53, and finally x = 17.

Therefore, the three sides of the triangle are:
Shortest side: 17cm
Longest side: 17 + 8 = 25cm
Third side: 17 - 5 = 12cm

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