Factor the expression completely.8y - 36

A 4(2y - 9)
B 8(y – 4)
C -4(2y + 9)
D 2(4y - 18)​

Answer:

5 years

Step-by-step explanation:

We are given;

We are required to determine the time taken for the value of the car to depreciate to half the original value.

Therefore;

$6,250 = $12,500(1 - r/100)^n

0.5 = (1 - 13/100)^n

0.5 = 0.87^n

Introducing log on both sides;

log 0.5 = n log 0.87

Therefore;

n = log 0.5 ÷ log 0.87

  = 4.977

  = 5 years

Therefore, it takes 5 years for the value of the car to depreciate to half the initial value.

Answer:

51.06

Step-by-step explanation:

So

P=$925

R=2.3%

T=2.4

So to get the answer we would need to multiply all of these together so first we would do 925 times 2.3% which would be 21.275. Then we would do 21.275 times 2.4 then we would get the answer of 51.06.

Answer:

D. 4.1 inches

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

We know the straight line is equal to 180°, and the three angles that make it are (x+12),100°, and x. We can use the equation 180=(x+12)+100+x to find x.

180=(x+12)+100+x

We can remove the parentheses and combine x plus x to 2x.

180=100+2x+12

100+12=112

so

180=112+2x

-112 -112

68=2x

÷2 ÷2

34=x

Answer:

[tex]t=46.4\ years[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=?\ years\\P=\$200\\A=\$500\\ r=1.98\%=1.98/100=0.0198\\n=4[/tex]  

substitute in the formula above

[tex]500=200(1+\frac{0.0198}{4})^{4t}[/tex]  

[tex]2.5=(1.00495)^{4t}[/tex]  

Apply property of exponents

[tex]2.5=[(1.00495)^{4}]^t[/tex]  

Apply log both sides

[tex]log(2.5)=log[(1.00495)^{4}]^t[/tex]  

[tex]t=log(2.5)/log[(1.00495)^{4}][/tex]  

[tex]t=46.4\ years[/tex]

Final answer:

To find when the investment of $200 at a 1.98% annual interest rate compounded quarterly will reach $500, we use the compound interest formula and solve for t, representing time in years.

Explanation:

The subject is Mathematics, specifically focusing on the concept of compound interest. To find out when the investment will reach $500, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested for in years.

In the case of the student's question:

P = $200

n = 4 (since the interest is compounded quarterly)

A = $500

We rearrange the formula to solve for t:

t = (log(A/P)) / (n×log(1+r/n))

Substitute the given values:

t = (log(500/200)) / (4×log(1+0.0198/4))

Use a calculator to compute t, which will give us the number of years it takes for the investment to reach $500.

Answer:

x = -5

Step-by-step explanation:

8x+32=1/5(25x−15)−4x

8x + 32 = 5x - 3 - 4x

8x + 32 = x - 3

7x = -35

x = -5

Answer:

x = -5

Step-by-step explanation:

Let's expand the parentheses on the right side first:

(1/5) * (25x - 15) = (1/5) * 25x - (1/5) * 15 = 5x - 3

Now put this back in:

8x + 32 = 5x - 3 - 4x

Move all the x terms to one side and all the constants to one side:

8x - 5x + 4x = -3 - 32

Combine like terms:

7x = -35

Divide both sides by 7:

x = -35/7 = -5

Thus, the answer is -5.

Hope this helps!

Answer:

square root of 13

Step-by-step explanation:

sqrt(13)=3.606...

pi=3.14...

2pi=6.28...

sqrt(13) is between

Answer:

Using ounces, the inequality should be:

15c + 70b < 112,000

Using pounds, the inequality should be:

0.9375c + 4.375b < 7,000

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Weight of a can of soft drink (c) = 15 ounces

Weight of a bottle of soft drink (b) = 70 ounces

The truck mist be carrying less than 7,000 pounds

2. Find the inequality describing this.

Let's recall that 1 pound = 16 ounces and 1 ounce = 0.0625 pounds

c = Number of cans in the truck

b = Number of bottles in the truck

Upon saying that, we can write the inequality either using ounces or pounds, this way:

Using ounces, the inequality should be:

15c + 70b < 7,000 * 16

15c + 70b < 112,000

Using pounds, the inequality should be:

15 * 0.0625c + 70 * 0.0625b < 7,000

0.9375c + 4.375b < 7,000

Answer:

57

Step-by-step explanation:

The midsegment is one half the length of the third side of the triangle, that is

6x + 3 = [tex]\frac{1}{2}[/tex](3x + 87)

Multiply both sides by 2 to clear the fraction

12x + 6 = 3x + 87 ( subtract 3x from both sides )

9x + 6 = 87 ( subtract 6 from both sides )

9x = 81 ( divide both sides by 9 )

x = 9

Thus

midsegment = 6x + 3 = 6(9) + 3 = 54 + 3 = 57

Answer:

Subtract 5x from both sides of the equation

-3y = 12 - 5x

Then, divide each term by -3 and simplify.

y = -4 + 5x

           ------

              3

After that, you'll do this

y= 5x

   ----- - 4

     3

Lastly, you put that into slope-intercept form.

y = 5

    ---- x - 4

     3

Answer:

4 hours.

Step-by-step explanation:

If Robbie earns 12 dollars per hour, it will take him 4 hours to earn 48 dollars. This is because 48/12 = 4.

48/12=hours

12+12+12+12=hours

4 hours

Answer:

5.75

Step-by-step explanation:

3 + 11/4

Use BIDMAS to help you

11/4 = 2.75

3+ 2.75 = 5.75

Plz mark brainliest i just need 3 more plz plz plz

Answer:

[tex]a^n=x[/tex]

Step-by-step explanation:

The complete question is in the attachment.

We want to find an expression that is equivalent to: [tex]\sqrt[n]{x} =a[/tex]

Note that: [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]

This implies that:

[tex]x^{\frac{1}{n}}=a[/tex]

Or

[tex]x^{\frac{1}{n}}=a^1[/tex]

[tex]x^{\frac{1}{n}*n}=a^{1*n}[/tex]

This simplifies to:

[tex]x=a^n[/tex]

Answer: The answer is X^n = a

Step-by-step explanation:

Got it right!

Answer:

D Price of a pencil

Step-by-step explanation:

In A the number of students has to be an integer because you can't have part of a student

In B most likely your teacher will give you your score in a whole number form like 95% and not 94.87% because they would round it if it isn't a whole number already

C is similar to A you can't have a part of a computer key

Lastly in D stores very frequently have there prices at something like $1.99 which isn't a integer

The situation that would most likely be represented by a rational number that is not an integer is the price of a pencil.

The situation that would most likely be represented by a rational number that is not an integer is D) price of a pencil. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. The price of a pencil can be a rational number in the form of a decimal, such as 0.99 or 2.50, which are not whole numbers.

https://brainly.com/question/36880638

#SPJ2

Answer:

18.18 miles.

Step-by-step explanation:

A truck uses 1 tablespoon of gasoline to drive 125 yards.

Now, 1 gallon of gasoline contains 256 tablespoons of gasoline.

So, the truck uses 1 gallon i.e. 256 tablespoons of gasoline to drive (256 × 125) = 32000 yards.

Now, 1-mile distance contains 1760 yards.

Therefore, the truck uses 1 gallon of gasoline to drive [tex]\frac{32000}{1760} = 18.18[/tex] miles. (Answer)  

Answer:

1. 22 * 3 = t

2. 4 + 7 = f

Step-by-step explanation:

Addison brought 66 treats to school and Brady caught 11 fish last weekend.

To determine how many treats Addison brought to school, we can write the following equation: t/22 = 3, where t represents the number of treats. To solve for t, we can multiply both sides of the equation by 22 to get t = 3 * 22 = 66. Therefore, Addison brought 66 treats to school.

To determine how many fish Brady caught last weekend, we can write the equation: f - 4 = 7, where f represents the number of fish. To solve for f, we can add 4 to both sides of the equation to get f = 7 + 4 = 11. Therefore, Brady caught 11 fish last weekend.

https://brainly.com/question/9585437

#SPJ12

Answer:

3 rows of roses and 9 daffodils each row. (3x9=27)

4 rows of roses, 9 in each row.

(4x9=36)

Hope that helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

9 roses in the 3 rows. 9 goes into 27, 3 equal times.

The lengths of the three sides of the triangle are 7m, 7m, and 12m.

Let the length of the two equal sides be 'x'.

The third side measures 2m less than twice the common length, so it is (2x - 2)m in length.

Given that the perimeter of the triangle is 26m, we can set up the equation:

x + x + (2x - 2) = 26

Simplifying the equation:

4x - 2 = 26

4x = 28

x = 7

So, the lengths of the three sides are 7m, 7m, and (2x - 2)m = (2 * 7 - 2)m = 12m.

https://brainly.com/question/32440372

#SPJ11

Final answer:

The triangle with two sides of equal length and a perimeter of 26 m has sides measuring 7 m, 7 m, and 12 m.

Explanation:

To solve for the lengths of the sides of the triangle described in the question, we can set up an equation based on the information given. Since two sides of the triangle have the same length, we can call that common length 'x'. The third side is described as being '2 m less than twice the common length', which can be written as '2x - 2'. The perimeter of the triangle, which is the sum of the lengths of all sides, is given as 26 m.

Therefore, the perimeter equation would be:

x + x + (2x - 2) = 26

This simplifies to:

4x - 2 = 26

Adding 2 to both sides, we get:

4x = 28

Dividing both sides by 4, we find x:

x = 7

Now we know that the two sides of equal length are both 7 m, and the third side is:

2x - 2 = 2(7) - 2 = 12

So the lengths of the three sides of the triangle are 7 m, 7 m, and 12 m.

Answer:2.0994

Step-by-step explanation:

You would want to set up the equation like this

120°×π/180 which will then be 2.094rad

120 degrees is equal to 2π/3 radians. You can convert degrees to radians by using the conversion factor π/180. This method simplifies to 2π/3 for 120 degrees.

Converting Degrees to Radians

To convert an angle from degrees to radians, you can use the conversion factor that 360° is equal to 2π radians. Therefore, 1 degree is equal to π/180 radians. To convert 120 degrees to radians, you can follow these steps:

Therefore, 120 degrees is equal to 2π/3 radians. This method ensures accurate conversion and is useful in various mathematical calculations.

Answer:

cos θ = -(√3)/2

tan θ = -1/√3

Step-by-step explanation:

[tex]\frac{\pi }{2} <\theta <\pi \ \ \ sin \ \theta = \frac{1}{2} \\[/tex]

Part A: find cos θ:

Using Pythagorean identity

sin²θ + cos²θ = 1

cos²θ = 1 - sin²θ = 1 - (1/2)² = 1 - 1/4 = 3/4

cos θ = ±√(3/4) = ±(√3)/2

∵(π/2) < θ < π  ⇒ ∴ cos θ = -(√3)/2

Part B: find tan θ:

sec θ = 1/(cos θ) = -2/√3

Using Pythagorean identity

tan²θ + 1 = sec²θ

tan²θ = sec²θ - 1 = 4/3 - 1 = 1/3

tan θ = ±√(1/3) = ± 1/√3

∵(π/2) < θ < π  ⇒ ∴ tan θ = -1/√3

Step-by-step explanation:est $ 6800

Samantha wants to invest $ 6800 in a saving account that pays 6% simple interest .

Let it will be take x year    

Principle =$6800

Interest = $ 6800

Rate of interest = 6%

Time = x(let)

According To Problem

6800=[tex]\frac{6800\times x\times 6}{100}[/tex]

⇔x = [tex]\frac{100}{6}[/tex] = 16.67 year

Therefore ,it will take 16.67 year .

Answer:

16.67 years.

Step-by-step explanation:

Samantha wants to invest $6800 in a savings account that pays 6% simple interest.

Let after y years the amount will be double in value.

So, using the formula of simple interest we can write

[tex]2 \times 6800 = 6800(1 + \frac{6\times y}{100})[/tex]

⇒ [tex]2 = 1 + \frac{6y}{100}[/tex]

⇒ 6y = 100

⇒ y = 16.67 years.

Therefore, after 16.67 years the amount will become double in value. (Answer)

Answer:

116

Step-by-step explanation:

2+2+5+3+6+4+6+2+5+78+2+1

4+5+3+6+4+6+2+5+78+2+1

9+3+6+4+6+2+5+78+2+1

12+6+4+6+2+5+78+2+1

18+4+6+2+5+78+2+1

22+6+2+5+78+2+1

28+2+5+78+2+1

35+78+2+1

113+2+1

116

Answer:

116

Step-by-step explanation:

Answer:DE and BC

Step-by-step explanation:

Sarah bought 4 first class tickets and 4 coach tickets for a total of 8 tickets, using her entire budget of $5080.

Sarah purchased tickets for a total of 8 people with a mix of coach and first class tickets. The cost for coach tickets was $290 each, and the cost for first class tickets was $980 each. With a total airfare budget of $5080, we need to determine how many of each type of ticket she bought.

Let's denote the number of first class tickets as x and the number of coach tickets as y. The two equations representing the situation are:

From the first equation, we can express y in terms of x: y = 8 - x. Substituting this into the second equation gives us:

980x + 290(8 - x) = 5080

Solving for x will give us the number of first class tickets, and using the value of x, we can find y, the number of coach tickets. After simplifying and solving, we find that:

980x + 2320 - 290x = 5080

690x = 2760

x = 4

Thus, Sarah bought 4 first class tickets. To find the number of coach tickets (y), we substitute x into the first equation:

y = 8 - 4

y = 4

Therefore, Sarah also bought 4 coach tickets.

Answer:

F(X)=7 is the even function

Step-by-step explanation:

f(x)=(x-1)2 is neither odd or even

f(x)=8x is a odd function

f(x)=x2-x is neither odd or even

and f(x)=7 is EVEN

The equation for line perpendicular to y = -3x - 2 and passing through the point (9,7)  in slope intercept form is:

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

Solution:

Given that we have to write the equation for line perpendicular to y = -3x - 2 and passing through the point (9,7)

Let us first find the slope of line

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given equation of line is:

y = -3x - 2

On comparing the above equation with eqn 1

m = -3

We know that product of slope of a line and line perpendicular to it is equal to -1

Therefore,

[tex]-3 \times \text{ slope of line perpendicular to given line } = -1\\\\\text{ slope of line perpendicular to given line } = \frac{1}{3}[/tex]

Now find the equation of line passing through the point (9, 7)

[tex]\text{Substitute } (x, y) = (9, 7) \text{ and } m = \frac{1}{3} \text{ in eqn 1 }[/tex]

[tex]7 = \frac{1}{3} \times 9+c\\\\7=3+c\\\\c = 4[/tex]

[tex]\text{Substitute } m = \frac{1}{3} \text{ and } c = 4 \text{ in eqn 1 }[/tex]

[tex]y = \frac{1}{3}x+4\\\\y = \frac{x}{3}+4[/tex]

Thus the equation of line in slope intercept form is found

Joyce: y = 2x + 7

Haley: y = 3x

From looking at these two equations, we can assume that Haley will eventually catch up and pass Joyce because she sells items for $3 whereas Joyce had a head start of $7, but only sells items for $2.

Using substitution, we plug in y = 3x into y in the first equation: 3x = 2x + 7

This leaves us at x = 7.

y = 3(7) or 21.

The point at which Haley's and Joyce's money will be exactly the same is (7, 21). After this point, Haley will have more money.

Answer:

what is the equation of f(x)

Step-by-step explanation:

Answer:

9 is the answer

Step-by-step explanation:

Answer:

Please read the answer below.

Step-by-step explanation:

Let's add the two expressions as they are written in the question:

- - 4.25r + 3 and 2.5r - 6 = 4.25r + 3 + 2.5r - 6

= 6.75r - 3

In case it wasn't written accurately and the expressions are (first on the left with just one negative sign):

- 4.25r +3 and 2.5r- 6 = - 4.25r + 3 + 2.5r - 6

= -1.75r - 3