f(x)=(5x+3)(x−2)(3x+7)(x+5) has zeros at x = -5, x = -7/3, x = 2
What is the sign of f on the interval -7/3 < x < -3/5?

Answer:

7 hours

Step-by-step explanation:

He already worked 4 hrs at $3.75 an hour.

Meaning he has already accumulated 15 dollars. (4 * 3.75)

$40 - $15 = $25

So if he needs $25 and he makes $4 dollars an hour:

25/4 = 6.25

He needs to work at least 7 full hours to receive 25 dollars to add with the already earned 15 dollars to total 40 dollars.

Answer: 6.25 hours

Step-by-step explanation:

Step 1: find how much he earned from the odd job

3.75 per hour for 4 hours= 3.75x4= $15

Step 2: Write an inequality

4x+15≥40

Breaking it down:

'4x' means $4 per hour for an unknown number of hours, or just "a number of hours". The reason why you put the x next to the number is because to find the total amount of money he made from that job, you'll have to multiply 4 by however many hours he worked.

15 stands for the amount of money he has right now. He finished the job that paid 3.75 an hour, so don't put an x next to the 15.

40 is the amount of money he needs.

the ≥ sign means "greater than or equal to". In other words, to be able to buy the gift, he needs 40 or more dollars. The line underneath means "greater/less than or equal to". Also, the reason why I didn't put the normal greater sign that looks like >, is beacause that would be saying he needs MORE than 40 dollars to buy the gift, which is not a true statment.

Step 2: Solve the inequality

Solving an inequality is no different from solving an algebra equation. You just ignore the ≥ sign.

4x+15≥40

#1: Always do the inverse operation on the left side number first, never the x term. In other words, always start with addition or subtraction:

See how there is a +15. do the operate equation by subtracting 15 from both sides.

4x+15-15 ≥ 40-15

4x≥25

Now divide both sides by 4. This is because 4x stands for "4 multiplied by x" and the opposite of multiplication is division.

4x/4 ≥ 25/4

x≥6.25

Step 4: Checks

Substitute x for 6.25, but write it as en equation.

4x+15=40

4x6.25 +15 = 40

25+15= 40

40=40

Correct ✅

Answer= He needs to work 6.25, or 6 1/4, or 6 hours and 25 minutes, in order to have enough money for the gift.

Answer:

Ben and Alisha will meet at 11:40 a.m.

Step-by-step explanation:

Given: The time at which Ben leaves his house is 7a.m. and the constant speed at which he biked due east is 15mi/hr.

The time at which Alisha leaves her house is 8a.m. and the constant speed at which she biked due west is 10mi/hr.

The distance at which Alisha lives due east of Ben is [tex]$100 \mathrm{mi}$[/tex].

To find: The time at which they meet.

a. Analyze the given data.

b. Define a variable.

c. Form an equation.

d. Solve for the unknown variable.

e. Use addition, subtraction, multiplication, or division properties.

f. Find the required time.

Step 1 of 5

Let t represent the time (in hours) from 12a.m.

We can also assume the houses as being on the number line, where Ben's house is at 0 and Alisha's house is at 100 .

Ben starts biking at 7 a.m. and he moves right (along our imaginary number line) at 15 miles per hour.

So his position at a time t is 15(t-7).

Alisha starts biking at 8a.m. and she moves left at 10 miles per hour.

So her position at a time t is 100-10(t-8).

Step 2 of 5

Ben and Alisha will meet when their positions are equal. Thus equating both the equations, we get

15(t-7)=100-10(t-8)

Using the distributive property,

15t-105=100-10t+80

Step 3 of 5

By the addition and subtraction properties,

We get,

[tex]$$\begin{gathered}15 t+10 t=80+105 \\\Rightarrow 25 t=285\end{gathered}$$[/tex]

Step 4 of 5

By the multiplication and division properties,

[tex]$$\begin{aligned}t &=\frac{285}{25} \\\Rightarrow t &=11.4 \mathrm{~h}\end{aligned}$$[/tex]

Step 5 of 5

Converting the decimal into minutes,

[tex]$0.4 \times 60=24.0 \mathrm{~min}$[/tex]

Thus the required time is 11:24a.m.

Answer:

1. r = C/2π

2. A = π(C/2π)^2

Step-by-step explanation:

1. C = 2πr^2

C/2π = 2πr/2π

C/2π = r

r = C/2π

2. A = π(C/2π)^2

3. Look at screenshot

Answer:

C^2 = 4πA

Step-by-step explanation:

The first part asks us to isolate r in the equation C = 2πr. We can do that by dividing both sides by C: [tex]r=\frac{C}{2\pi }[/tex]. Note that C stands for the circumference of a circle.

The second step is to plug this value of r into the formula for the area of a circle. We know that the area of a circle is πr^2. We are given π and the exponent, so we just need to plug in [tex]\frac{C}{2\pi }[/tex] and we end up getting [tex]A=\pi (\frac{C}{2\pi })^{2}[/tex]

The third step is to square the term in the parentheses. Whenever we have to square a fraction, all we have to do is square the numerator and the denominator:

[tex](\frac{C}{2\pi })^2=\frac{C^2}{(2\pi )^2}=\frac{C^2}{2^2\pi ^2}[/tex]

In other words,

[tex]A=\pi *\frac{C^2}{2^2\pi ^2}[/tex]

For the fourth step, 2^2 can be evaluated to get 4. We end up getting the following if we do this:

[tex]A=\frac{\pi}{4 } *\frac{C^2}{\pi^2}[/tex]

For the fifth step, we can simplify because the π in the numerator of the first fraction and the π^2 in the denominator of the second fraction cancel (π^2 / π leaves π in the denominator and a 1 in the numerator). If we perform this cancellation, we get the following fraction:

[tex]A=\frac{C^2}{4*\pi}[/tex]

For the final step, we can isolate C^2 by multiply both sides by 4π. Then, we get that C^2 = 4πA

In other words, the circumference of the circle squared is equal to 4π times the area of the circle

Answer:

Step-by-step explanation:

4.009kg × 1000 = 4009g

Answer:

36. m^7

37. x^3 y

38. 6v^5

Step-by-step explanation:

Divide the exponents by the number in the radical sign,

so, If no number is given then divide exponents by 2 eg. question 38

36. 7√m^49 means m^(49/7) = m^7

37. 3√x^9y^3 means x^(9/3) y^(3/3) = x^3 y

38. √36v^10 means (√36) v^(10/2) = 6v^5 (√36 = 6)

Answer: 52

Step-by-step explanation:

We know that 25 percent is one-fourth, so whatever number divided by 4 equals 13. To do this, we can just multiply 13 by 4 to get our answer, 52.

Answer:

55 parking spaces

Step-by-step explanation:

Using unitary method:

For every 12 commuters , 5 spaces are needed.

∴ For 1 commuter:

5 ÷ 12 ⇒  [tex]\frac{5}{12}[/tex]  spaces are needed.

∴ For 132 commuters ⇒ [tex]\frac{5}{12}[/tex]  × 132 = 55 spaces.

Answer:

149 liters of test solution (C)

Step-by-step explanation:

We are given that 25 mL of dye are mixed with 1.5 L of water to create 1 bottle of solution. If we convert 25mL to L, we get that there is 0.025 L of dye in each solution, and the total amount of liquid in a bottle of test solution is 1.525 L (0.025 + 1.5). Since we have 98 bottles like, the total amount of test solution is 98*1.525, which is 149.45 L. Since we have to round to the nearest whole number, the answer is C, or 149 L.

Answer:

Step-by-step explanation:

The question asks you to dilate the rectangle by a scale factor of 1/3.

KEY TERM:

Dilate by a scale factor: You make a shape bigger or smaller by multiplying by a number.

Here, we are dilating by a scale factor of 1/3. Therefore, to solve the problem, you have to multiply each coordinate by 1/3. Also, we are making the shape smaller because we are multiplying by a fraction.

___

STEP 1: LINE UP ALL THE COORDINATE PAIRS

Point U: (-6,6)

Point R: (-6,-3)

Point T: (9,6)

Point S: (9,-3)

Now the easy part is done.

STEP 2: MULTIPLY BY 1/3

It is very important you know how to do this part because it determines the answer. So when i say "multiply by 1/3" i mean multiply each individual number by 1/3.

I'll explain for point u then do the rest:

Point U was originally: -6,6.

-6 x 1/3= -6/3= -2.

6x1/3= 6/3= 2

The "dilated" point U is: (-2,2). I multiplied each individual coordinate by 1/3, one by one.

Point R was originally: (-6,-3)

-6x1/3= -2

-3x1/3= -3/3= -1

The "dilated" point R is (-2,-1)

Point T was originally: (9,6)

9x1/3= 3

6x1/3= 2

The "dilated" point T is (3,2).

Point S was originally (9,-3).

9x1/3= 3

-3x1/3= -1

The "dilated' point S is (3,-1)

Finally, if you ever get confused about the order of the coordinates, it just stays the same. Like 9,-3 becomes the dilated 9 , dilated -3.

STEP 3: GRAPH THE NEW POINTS

see the screenshot, for reference :)

Answer:

Step-by-step explanation:

you dilate each coordinate by a scale factor of 1/3 , making the shape smaller.

Answer:

A & D

Step-by-step explanation:

If you can fit 3 fish in a 9 gallon tank, that means as a point on a line, that would be at (3, 9).

If you write this as a fraction it's 3/9. Simplifying that, you get 1/3. That means 1 fish needs 3 gallons.  If you make hat a point on the line, it's (1,3).

Another equivalent fraction would be 6/18. If you multiply the numerator and denominator by 2, 3/9 becomes 6/18.

B & C are not equivalent fractions.

Answer:

[tex]18 ft^2[/tex]

Step-by-step explanation:

You could calculate the area of the trapezoid and then subtract the area of the triangle.

Area of a trapezoid:

 [tex]A = \frac{a+b}{2}h[/tex]

Plug values in:

[tex]A = \frac{6+12}{2}(6)[/tex]

Add 6 and 12:

[tex]A = \frac{18}{2}(6)[/tex]

Simplify:

[tex]A = 54[/tex]

Area of a triangle:

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

Plug values in:

[tex]A = \frac{1}{2}(6)(12)[/tex]

Simplify:

A = 36

Subtract the area of the triangle from the area of the trapezoid

54 - 36 = 18

You could also calculate the area of the shaded region by assuming that they're congruent meaning the base would be half of 6 which is 3 and the height would be 6 so the area of one would be 1/2 (6)(3) but since they're is 2 you wouldn't need the 1/2 since multiplying by 2 would cancel it out so the area would be (6)(3) = 18

Answer:

Step-by-step explanation:I would make them make all of them into a decimal or fraction that's how I do it like this       5/2   .45     27.5%

make them into a decimal this time because it looks easy so 5/2 into a decimal will be 2.5. and then 0.45   27.5% into a decimal will be will be 0.275

boom order it         2.5,  0.45,  0.275

Answer:

Given:

To find:

The formula used to calculate percentage is:(value/total value)*100%.

Step-by-step explanation:

Step 1 of 2

After the 20%  sale, the coat costs

100*0.8 = 80 dollars.

Then 5 dollars are taken off for a cost of

80-5 = 75

Step 2 of 2

Now adding on the sales tax,

the final amount is 75(0.8) = 81 dollars

Answer:

x = 10

Step-by-step explanation:

First, subtract 10 from both sides

Next, Simplify

Then, subtract 5/3x from both sides

After, simplify

Lastly, multiply both sides by 3

Then finally simplify for your final answer of x = 10

Hope this helps! :)

Answer:

x = 10

Step-by-step explanation:

  x + 10 = 1/3(5x + 10)
  x + 10 = 5/3x + 10/3
3x + 30 = 5x + 10
       20 = 2x
        10 = x

Answer: 3rd, 4th, and 5th are correct.

Step-by-step explanation:

We know that the equation 6(t+2) can be simplified to 6*t+6*2, also 6t+12. This causes any statements saying a variable with a certain value applies to one side also applies to the other.

Answer:

- The value of both expressions when t = 3 is 30

- The value of both expressions when t = 7 is 54

- The expressions are equivalent

Step-by-step explanation:

Plug in each value of t into the expressions:

6t + 12, when t = 3 equals 30

6t + 12, when t = 7 equals 54

6(t + 2), when t = 3 equals 30

6(t + 2), when t = 7 equals 54

We have the same answers for both expressions, meaning they are equivalent.

Answer:

After July, Ana's monthly salary was $1920

Step-by-step explanation:

In May, Ana's monthly salary was $2000. During the next month, the salary increased by 20%, or (0.2)(2000)

[tex]2000+(0.2)(2000)=2000+400=2400[/tex]

So, in June, Ana's monthly salary was $2400. During the next month, the salary decreased by 20%, or (0.2)(2000)

[tex]2400-(0.2)(2400)=2400-480=1920[/tex]

Therefore, after the two changes, Ana's monthly salary was $1920

Answer:

Now Ana's monthly salary is 1920$.

Step-by-step explanation:

Given: Ana's salary in may =2000$

in June she received 20% raise

in July she received 20% pay cut.

To find Ana's monthly salary after the two changes in June and July.

we have to first find Ana's salary at the end of June month with 20% raise. and then her salary after the end of July month with the pay cut of 20%.

Step 1 of 2

Ana's salary after June month when she got 20% raise in his salary after May is equal to

[tex]=2000+(20 \% \cdot 2000)$\\ $=2000+\left(\frac{20}{100} \cdot 2000\right)$\\ $=2400 \$$[/tex]

her new salary after May will be 2400$.

Step 2 of 2

now she got a pay cut of 20% on his new salary from July month

so, her salary after that would be equal to

[tex]=2400-(20 \% \cdot 2400)$\\ $=2400-\left(\frac{20}{100} \cdot 2400\right)$\\ $=2400-480$\\ $=1920 \$$[/tex]

Answer:

Step-by-step explanation:

Good luck ✅.

Answer:

40%

Step-by-step explanation:

using our lovely knowledge of percents (or per 100s) we can see that 100-60 is 40, which means only 40% of the votes go to the losing candidate

Answer: Tuesday, Thursday, and Saturday

Step-by-step explanation:

Pretty self-explanatory.

Answer:

https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/sampling-distribution-proportion/a/sampling-distribution-sample-proportion-example

Step-by-step explanation:

Click there and it will tell you

Answer:

609

Step-by-step explanation:

All you must do is multiply 1450 by 0.42. That would give you the total.

Answer:

Hello! The answer to your question is 609 seats.

Step-by-step explanation:

To obtain your answer, you have to multiply the percentage of balcony seats by the total number of seats. 42% is converted to 0.42 because 42/100 = 0.42:

0.42 × 1450 = 609 seats

Answer:

The answer is B

Step-by-step explanation:

I learned this from my math teacher

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above1.8[/tex]

                   To turn kilometers, km, into meters, m, multiply the number

                    of km by 1,000.  This comes out as.

                   [tex]\boldsymbol{\sf{6.4\times1,000=6,400\:Metres}}[/tex]

                   To convert meters, m, into kilometers, km, divide the number

                   of m by 1,000. This comes out as

                   [tex]\boldsymbol{\sf{6,400\div1,000=6.4\:Kilometres}}[/tex]

#learnwithbrainly

[tex]\orange\hspace{300pt}\above2[/tex]

Ans: 1.1 miles more

Speed = distance/time

Time is 1/5 of an hour

1/5 of 1hr = 1/5 or 0.2 hrs

Speed = 16 mph

So, we're after distance.

Distance = speed x time

= 16mph x 0.2

= 3.2 miles

Walks for 3/7 hour at 5 miles per hour :

Time & speed given, distance is what we're after.

(3/7 of 1hr is 3/7)

Distance = speed x time

= 5mph x 3/7

= 15/7 miles or 2.14285...miles

So, distance is about 2.1 miles to 1 d.p

Thus, 3.2 - 2.142... (the full ans) = 1.057... miles

Well, he biked 1.06 miles or 1.1 miles (depending on how you want to round it) more than walking.

Hope this helps!

[tex]\boldsymbol{\dfrac{3}{4}x+0.25(x-6)+28.4 }[/tex]

Use the distributive property to multiply 0.25 by x−6.

[tex]\boldsymbol{\dfrac{3}{4}x+0.25x-1.5+28.4 }[/tex]

combine [tex]\bf{\frac{3}{4}x }[/tex] and 0.25x to get x.

[tex]\boldsymbol{x-1.5+28.4}[/tex]

Add −1.5 and 28.4 to get 26.9.

[tex]\boxed{\boldsymbol{x+26.9}} \ \ \to \ \ \bf{Answer}[/tex]

Answer:

62.5%

Step-by-step explanation:

since percents are just fractions, we have 5/8 and we need to convert it into a percentage. since 100 is not divisible by 8, we can use a trick by multiplying the numerator by 100. we get 500/8 which is 62.5.