You can spend up to $35 on a shopping trip.

a. You want to buy a shirt that costs $14. Identify an inequality that represents the amount of money, x (in dollars), you will have left if you buy the shirt.


x+14≥35

x+14≤35

x−35≥14

x−35≤14
Question 2
Solve the inequality.
The solution is .

Question 3
b. You notice that the shirt is on sale for 30% off. Identify the new inequality.


x+9.8≥35

x+35≤9.8

x+9.8≤35

x+9.8≤24.5

Question 4
c. Do you have enough money to buy the shirt that is on sale and a pair of pants that costs $23? Which best explains your answer?


no; The cost of the shirt and the pants is $37, which is more than $35.

yes; The cost of the shirt and the pants is $32.80, which is less than $35.

no; The cost of the shirt and the pants is $32.80, which is more than $21.

yes; The cost of the shirt and the pants is $21, which is less than $23.

y=-1x-6 is your answer

Answer:

a) [tex]0.4[/tex] grams

b) [tex]0.053[/tex] grams

c) [tex]5.4[/tex] decigrams

d) [tex]2300[/tex] milligrams

Step-by-step explanation:

a)

To convert centigrams to grams you have to divide by 100.

[tex]40[/tex] centigrams = [tex]\frac{40}{100}[/tex] grams

                                        =[tex]0.4[/tex] grams

b)

To convert milligrams to grams you have to divide by 1000.

[tex]53[/tex] milligrams = [tex]\frac{53}{1000}[/tex] grams

                                        =[tex]0.053[/tex] grams

c)

To convert grams to decigrams you have to multiply by 10.

[tex]0.54[/tex] grams = [tex]0.54*10[/tex] decigrams

                                        =[tex]5.4[/tex] decigrams

d)

To convert grams to milligrams you have to multiply by 1000.

[tex]2.3[/tex] grams = [tex]2.3*1000[/tex] milligrams

                                        =[tex]2300[/tex] milligrams

b represents rate of change

Answer:

rate of change

Step-by-step explanation:

Answer:

[tex]a_{n}=12n-8[/tex]

Step-by-step explanation:

We have been given a recurrence relation [tex]a_{n+1}=a_{n}+12[/tex] and the first term of the sequence [tex]a_{1}=4[/tex].

We can rewrite the given recurrence relation as: [tex]a_{n+1}-a_{n}=12[/tex]

We know that if difference between two consecutive terms is always constant, the sequence is called an arithmetic sequence. So we are dealing with an arithmetic sequence with first term as 4 and common difference as 12.

We can therefore, write an explicit formula for nth terms of the sequence as.

[tex]a_{n}=a_{1}+(n-1)d\\a_{n}=4+(n-1)(12)\\a_{n}=4+12n-12\\a_{n}=12n-8\\[/tex]

This is the required explicit function rule for the given sequence.

Here we are given the information that an insurance agent receives 16% commission on every premium paid.

Now we are given that a premium of $497.69 is paid.

Let us say $x is the commission paid on the policy with a premium of $497.69.

Let us try to find the amount x here.

So we have to find 16% of 497.69 to get the commission amount x.

So finding 16% of 497.69.

x= 16% of 497.69 = 0.16*497.69 = 79.63

Answer: Commission of $79.63 is paid on a policy with a premium of $497.69.

Answer:

$ 79.6304 of commission was paid on policy with a premium of $497.69.

Step-by-step explanation:

Percentage on amount received on every premium = 16% of the premium

So, when the premium of the $ 497.69 was paid , the commission received by an agent will be: 16% of the $497.69 .

[tex]\$497.69\times \frac{16}{100}=\$79.6304[/tex]

$ 79.6304 of commission was paid on policy with a premium of $497.69.

Comparing the probability values for each Container, Hence, both containers give equal chances of winning .

Complete question:

Container __ Red ___ Blue

A ________ 6 ______ 4

B ________ 60 _____ 40

Using the probability formula:

For Container A :

For Container B :

Since the probability values are the same, then both Container gives equal Chances of winning.

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Answer:

The answer is 8.

Step-by-step explanation:

If is

[tex]\sqrt{r^{64}}=\sqrt{r^{32\cdot2}}=\sqrt{(r^{32})^2}=r^{32}[/tex]

Used:

[tex](a^n)^m=a^{nm}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]

If is

[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]

Hello, Jssoyg! I've solved the problem for you below. I hope it helps.

Slope equation is[tex]\frac{y2 - y1}{x2 - x1}[/tex]. The two points are (0,1) and (4,2), so the equation becomes [tex]\frac{2 - 1}{4 - 0} = \frac{1}{4}[/tex]. We now know that the slope is 1/4, so now let's write it in the [tex]y = mx + b[/tex] format. Plug in the m, x, and y values:[tex]2 = 4*\frac{1}{4} + b[/tex].

This becomes [tex]2 = 1 + b[/tex] which means b = 1.

Your answer is y = 1/4x + 1. Hope this was helpful. :D

Lets x and y are the value of two numbers.

x + y = 16

x - y = 2.4

If x + y = 16 then x = 16 - y

Substitute x = 16 - y into x - y = 2.4

16 - y - y = 2.4

16 - 2y = 2.4

2y = 13.6

 y = 6.8

x = 16 - y

x = 16 - 6.8

x = 9.2

Answer:

The value of two numbers are 9.2 and 6.8

Do you need all the coordinates or just A' and B'

-33/5 belongs to the set of

Rational numbers

Real numbers

Complex numbers

(all at the same time)

60 divided by 10 =6

3x6=18

Raul would ride 18 miles.

Hope this helped :)

Raul would ride 18 miles for 60 minutes at the same speed.

To find out how many miles Raul would ride for 60 minutes at the same speed, we can set up a proportion. If Raul rides 3 miles for 10 minutes, then we can say that 3 miles is to 10 minutes as x miles is to 60 minutes. Setting up this proportion, we get: 3/10 = x/60. To solve for x, we can cross multiply and then divide both sides by 10. This gives us: x = (3/10) * 60 = 18 miles.

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Step 1 = Distributive Property ( multiplying the 2 by each term in parenthesis)

Step 2 = Addition Property ( adding like terms)

Step 3 = Addition Property (adding 34x to each side)

Step 4 = Division Property. ( dividing both sides by 17)

a.) [tex]769-362 = 407[/tex]

Checking: Since, [tex]407+362 = 769[/tex]

Therefore, our answer is correct.

b.) [tex]502+17 = 519[/tex]

Checking: Since, [tex]519-17 = 502[/tex]

Therefore, our answer is correct.

c.) [tex]7802-3461 = 4341[/tex]

Checking: Since, [tex]4341+3461 = 7802[/tex]

Therefore, our answer is correct.

d.) [tex]1432+2568 = 4000[/tex]

Checking: Since, [tex]4000-2568 = 1432[/tex]

Therefore, our answer is correct.

Answer:

Consider the numbers:

a) 769 - 362 = ?

Subtract the numbers.

769 - 362 = 702

Therefore, the value is 702.

Now, check using the inverse operation.

407 + 362

Add the numbers.

407 + 362 = 769

Thus, the answer is correct.

Consider the numbers:

b) 502 + 17 = ?

Add the numbers.

502 + 17 = 519

Therefore, the value is 519.

Now, check using the inverse operation.

519 - 17

Subtract the numbers.

519 - 17 = 502

Thus, the answer is correct.

Consider the numbers:

c) 7802 - 3461 = ?

Subtract the numbers.

7802 - 3461 = 4341

Therefore, the value is 4341.

Now, check using the inverse operation.

4341 + 3461

Add the numbers.

4341 + 3461 = 7802

Thus, the answer is correct.

d) 1432 + 2568 = ?

Add the numbers.

1432 + 2568 = 4000

Therefore, the value is 4000.

Now, check using the inverse operation.

4000 - 2568

Subtract the numbers.

4000 - 2568 = 1438

Thus, the answer is correct.

Answer: The correct reason for [tex]\angle4\cong \angle7[/tex] is property of corresponding angles and the reason for [tex]\angle4+\angle6=180[/tex] is substitute [tex]\angle7=\angle4[/tex] and the third error is the forget the property that the sum of consecutive interior angles is 180.

Explanation:

It is given that m is parallel to n.

When  two parallel lines intersected by a transversal eight angles are produced as shown in the given figure, where m and n are parallel and l is the transversal line.

In this case corresponding angles are congruent. Example [tex]\angle1\cong \angle5[/tex],[tex]\angle2\cong \angle6[/tex] etc.

So, [tex]\angle4\cong \angle7[/tex] by the property of corresponding angles.

[tex]\angle7+\angle6=180[/tex] because these are supplementary angles.

Substitute [tex]\angle7=\angle4[/tex]

[tex]\angle4+\angle6=180[/tex]

So, the correct reason is substitution.

Hence proved [tex]\angle4+\angle6=180[/tex]

The third error is the forget the property that the sum of one side interior angles is 180. Since the alternate interior angles are congruent therefore the consecutive interior angles are supplementary angles around the sum of consecutive interior angles is 180 degree.

x=16/3 or 5.33333333

Answer:

Step-by-step explanation:

multiply by 3 the whole equation

6×3 = (x)×3  + (2/3) ×(3)

18 =3x + 2

subtracting 2 both sides

18-2 = 3x +2-2

16= 3x

dividing by 3 both sides

16/3 = 3x / 3

16/3 = x

[tex]|\Omega|=20\cdot19=380\\|A|=4\cdot12=48\\\\P(A)=\dfrac{48}{380}\approx0.13[/tex]

we are given

[tex]f(x)=e^x sin(x)[/tex]

(a)

Firstly, we will find critical numbers

so, we will find derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

now, we can set it to 0

and then we can solve for x

we get

[tex]x=\frac{3\pi }{4} ,x=\frac{7\pi }{4}[/tex]

now, we can draw a number line and then locate these values

and then we can find sign of derivative on each intervals

increasing intervals:

[tex][0,\frac{3\pi}{4} )U(\frac{7\pi}{4} , 2\pi][/tex]

Decreasing interval:

[tex](\frac{3\pi}{4} ,\frac{7\pi}{4} )[/tex]

(b)

Local maxima:

It is the value of x where function changes from increasing to decreasing

so, local maxima is at

[tex]x=\frac{3\pi}{4}[/tex]

Local minima:

It is the value of x where function changes from decreasing to increasing

so, local minima is at

[tex]x=\frac{7\pi}{4}[/tex]

now, we will plug critical numbers and end values into original function

and we get

At x=0:

[tex]f(0)=e^0 sin(0)[/tex]

[tex]f(0)=0[/tex]

At [tex]x=\frac{3\pi}{4}[/tex]:

[tex]f(\frac{3\pi}{4})=e^{\frac{3\pi}{4}} sin(\frac{3\pi}{4})[/tex]

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

At [tex]x=\frac{7\pi}{4}[/tex]:

[tex]f(\frac{7\pi}{4})=e^{\frac{7\pi}{4}} sin(\frac{7\pi}{4})[/tex]

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

At [tex]x=2\pi [/tex]:

[tex]f(2\pi)=e^{2\pi} sin(2\pi )[/tex]

[tex]f(2\pi )=0[/tex]

Global maxima:

It is the largest value among them

so, we get

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

Global minima:

It is the largest value among them

so, we get

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

(c)

now, we can find second derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

[tex]f''(x)=\frac{d}{dx}\left(e^x\sin \left(x\right)+e^x\cos \left(x\right)\right)[/tex]

[tex]=\frac{d}{dx}\left(e^x\sin \left(x\right)\right)+\frac{d}{dx}\left(e^x\cos \left(x\right)\right)[/tex]

[tex]=e^x\sin \left(x\right)+\cos \left(x\right)e^x+e^x\cos \left(x\right)-e^x\sin \left(x\right)[/tex]

[tex]f''(x)=2e^x\cos \left(x\right)[/tex]

now, we can set it to 0

and then we can solve for x

[tex]f''(x)=2e^x\cos \left(x\right)=0[/tex]

so, we get

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

now, we  can draw number line and locate these values

and then we can find sign of second derivative on each intervals

concave up intervals:

[tex][0,\frac{\pi}{2})U(\frac{3\pi}{2}, 2\pi][/tex]

Concave down intervals:

[tex](\frac{\pi}{2} ,\frac{3\pi}{2})[/tex]

Turning points:

All values of x for which concavity changes

so, we get turning points at

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

fff

[tex]f(x) = e^x sin (x)[/tex]

To find increasing and decreasing intervals we take derivative

[tex]f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)[/tex]

Now we set the derivative =0  and solve for x

[tex]e^x(sinx+cosx)=0[/tex]

sinx + cosx =0

divide whole equation by cos x

[tex]\frac{sinx}{cosx} + \frac{cosx}{cosx} =0[/tex]

tanx +1 =0

tanx = 1

[tex]x=\frac{3\pi }{4}[/tex] and  [tex]x=\frac{7\pi}{4}[/tex]

Now we pick a number between 0 to  [tex]\frac{3\pi }{4}[/tex]

Lets pick  [tex]\frac{\pi }{2}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))[/tex]

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, [tex]x=\frac{3\pi }{4}[/tex])

Now we pick a number between   [tex]\frac{7\pi}{4}[/tex] to 2pi

Lets pick  [tex]\frac{11\pi}{6}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))[/tex]

= 116 is positive

So the graph of f(x) is increasing on the interval [tex](\frac{7\pi }{4}, 2\pi)[/tex]

Increasing interval is [tex](0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)[/tex]

Decreasing interval is [tex](\frac{3\pi}{4}, \frac{7\pi}{4})[/tex]

(b)

The graph of f(x) increases and reaches a local maximum at [tex]x=\frac{3\pi}{4}[/tex]

The graph of f(x) decreases and reaches a local minimum at [tex]x=\frac{7\pi}{4}[/tex]

(c)

f(0) = 0

[tex]f(2\pi)=0[/tex]

[tex]f(\frac{3\pi }{4})=7.46[/tex]

[tex]f(\frac{7\pi}{4})=-172.64[/tex]

Here global maximum at [tex]x=\frac{3\pi}{4}[/tex]

Here global minimum at [tex]x=\frac{7\pi}{4}[/tex]

Part A.

You spend $6 per lawn and charge $35 per lawn, so the profit per lawn is $35 - $6 = $29. Let the number of lawns you mow be n. You earn a profit of $29 pewr laun, so you earn a profit of 29n for mowing n lawns.

29n = 450

Divide both sides by 29.

n = 450/29 = 15.517...

You must mow 16 lawns to make profit.

Part B.

3 lawns per day for 5 days per week means 15 lawns per week. Since you make a profit of $29 per lawn, you will make a profit of 15 * $29 for 15 lawns in each week. 15 * $29 = $435.

You want to make $2500 profit, but you must spend $450 on the lawn mower, so you need to earn a total of $2500 + $450 = $2950.

Let n be the number of weeks. In one week, you make $435 in profit. In n weeks, you make 435n in profit.

435n = 2950

Divide both sides by 435.

n = 6.7816...

If you work for 7 weeks, you will make at least $2500 in profit.

Since the summer vacation is longer than 7 weeks, it is a reasonable goal, but you must take into account the time it takes to mow three lawns in one day.

with the distributive property of multiplication you can take ba+ca and rewrite it as a(b+c)=ab+ac=ba+ca

$1.25x + $10 + $15 (less than or equal to) $50

Answer:

So, with the reaming 25 dollars she can play at max 20 games.

Step-by-step explanation:

Given that

Amount Courtney has to spend = $ 50

Amount Spent on Admission = $ 10

Amount Spent on Snacks = $ 15

Price of a Game at Share = $ 1.25

Now, lets find the total amount spent by her already

Amount Spent = 50 - 10 - 15 = $ 25

Suppos x represent the number of games so, we can represent the remaining amount and in term of games that can be purchased by using it

[tex]1.25x\leq25[/tex]

the above inequality can be simplified as follows

[tex]x\leq\frac{25}{1.25}[/tex]

[tex]x\leq20[/tex]

So, with the reaming 25 dollars she can play at max 20 games.

Answer:

[tex]10x-6[/tex]

Step-by-step explanation:

[tex]f(x) = 5x+2x\\g(x)=3x-6[/tex]

[tex](f+g)(x)\\f(x)+g(x)[/tex]

[tex]5x+2x+3x-6\\10x-6[/tex]

The value of (f+g)(x) is 10x - 6

We are taking into consideration the following two functions f(x) and g(x). The sum of these functions can be written f(x) + g(x) or as (f + g)(x). . The sum of the two functions is the sum of the two polynomials. Or in other words, the sum of any two functions gives us the addition of the terms present inside the function.

Given functions,  f(x) = 5x + 2x

and g(x) = 3x - 6

Sum of the two functions -

∴ (f+g)(x) = f(x) + g(x) = 5x + 2x + 3x - 6 = 10x - 6

Therefore (f+g)(x) = 10x - 6

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nickel

cardboard

bubble wrap

steam

not 100% sure though

Solve:

(3x    −   4)(2x^2     +      2x    −   1)

Simplify:

(3x     −      4)(2x^2      +       2x     −    1)

=      (3x     +    −4)(2x^2     +        2x        +        −1)

=   (3x)(2x^2)    +   (3x)(2x)   +   (3x)(−1)    +    (−4)(2x2)   +    (−4)(2x)     +     (−4)(−1)

=      6x^3    +   6x^2    −   3x    −  8x^2   −   8x   +   4

Answer   =      6x^3    −   2x^2     −   11x   +   4

Hope that helps!!!!                                         : )

Final answer:

The product of (3x - 4) and (2x² + 2x - 1) is calculated by multiplying each term in the first polynomial by each term in the second and combining like terms, resulting in the final expression 6x³ - 2x² - 11x + 4.

Explanation:

The product of the polynomials (3x − 4) and (2x2 + 2x − 1) is obtained by applying the distributive property, otherwise known as FOIL (First, Outer, Inner, Last) method in this context. Each term in the first polynomial is multiplied by each term in the second polynomial and then the results are summed together. The step-by-step calculation is as follows:

Multiply the First terms: (3x) × (2x2) = 6x3.

Multiply the Outer terms: (3x) × (2x) = 6x2.

Multiply the Inner terms: (− 4) × (2x2) = − 8x2.

Multiply the Last terms: (− 4) × (− 1) = 4.

Once these calculations are done, we combine like terms:

6x3 (no like terms to combine here)

6x2 − 8x2 = -2x2

(3x) × (2x) = 6x2 (already accounted for in the previous step)

(3x) × (−1) = -3x

(− 4) × (2x) = − 8x

4 (no like terms to combine here)

So, adding all these up, we get:

6x3 − 2x2 − 3x − 8x + 4

Combining the x terms, we have:

− 3x − 8x = − 11x, so the final answer is:

6x3 − 2x2 − 11x + 4

You can solve this using long division. The answer should end up being 2.3.

Answer:

2.3

Step-by-step:

[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]

To find (f+g)(x), add f(x) and g(x) together. (f + g)(x) is calculated as (5x - 2) + (2x + 1), which simplifies to 7x - 1. Therefore, the correct answer is C. 7x - 1.

The question asks to find the sum of two functions, f(x) and g(x).

To find (f+g)(x), we add the two functions together.

Here's how we calculate it:
First, we take the function f(x) = 5x - 2 and the function g(x) = 2x + 1.
Then, we add them together: (f + g)(x) = f(x) + g(x).
So, (f + g)(x) = (5x - 2) + (2x + 1).
Combining like terms, we get (f + g)(x) = 5x + 2x - 2 + 1.
This simplifies to (f + g)(x) = 7x - 1.

Therefore, the correct answer is C. 7x - 1.

Final answer:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. The function f(x) is given as f(x) = 5x-2 and the function g(x) is given as g(x) = 2x+1. To add the functions, we simply add the coefficients of the variable and the constant terms. So, (f+g)(x) = (5x-2) + (2x+1) = 7x-1. Therefore, the correct answer is C. 7x-1.

Explanation:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. The function f(x) is given as f(x) = 5x-2 and the function g(x) is given as g(x) = 2x+1.

To add the functions, we simply add the coefficients of the variable and the constant terms. So, (f+g)(x) = (5x-2) + (2x+1) = 7x-1. Therefore, the correct answer is C. 7x-1.

Answer:

9y - 3xy + 2x - 6

= 3y(3 - x) + 2(x - 3)

= -3y(x - 3) + 2(x - 3)

= (2 - 3y)(x - 3)