Given f(2) = 2x – 3, find f(1).

Answer:

1)

Nicole: [tex]95x+240[/tex]

Milan: [tex]125x[/tex]

2)

[tex]95x+240=125x[/tex]

Step-by-step explanation:

Question 1)

We know that Nicole opened her account with a starting amount of $240. She also puts in $95 per month.

So, we can write the following expression:

[tex]95x+240[/tex]

Where 240 represents the initial deposit of $240 and the 95x represents the $95 for x months.

Milan opened his account with no starting amount, and he's putting in $125 per month.

So, we can write the following expression:

[tex]125x[/tex]

Since he didn't put anything at the start, out initial deposit is simply 0. The 125x represents the $125 for x months.

Question 2)

We want to write an equation that shows when the two accounts will have an equivalent balance.

So, we can simply set the two expressions above equal to each other:

[tex]95x+240=125x[/tex]

And we're done!

Notes:

Let's solve for x to determine when the two accounts will have the same amount of money. Subtract 95x from both sides:

[tex]240=30x[/tex]

Divide both sides by 30:

[tex]x=8[/tex]

So, after 8 months, the amount in Nicole's and Milan's account will be equivalent.

Answer:

Use the formula for direct variation, and this will help answer the last part of the question.

Step-by-step explanation:

An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.

An arithmetic sequence is a linear function. Instead of y=mx+b, we write an=dn+c where d is the common difference and c is a constant (not the first term of the sequence, however).

A recursive definition, since each term is found by adding the common difference to the previous term is ak+1=ak+d.

For any term in the sequence, we've added the difference one less time than the number of the term. For example, for the first term, we haven't added the difference at all (0 times). For the second term, we've added the difference once. For the third term, we've added the difference two times.

The formula for the general term of an arithmetic sequence is: an = a1 + (n-1) d.

To learn more about  arithmetic sequences refer to:

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The explicit rule for the sequence in the graph is f(n) = 9.5 + 2(n - 1)

From the question, we have the following parameters that can be used in our computation:

The graph

In the graph, we can see that 2 is added to the previous term to get the new term

This means that

First term, a = 9.5

Common difference, d = 2

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 9.5 + 2(n - 1)

Hence, the explicit rule is f(n) = 9.5 + 2(n - 1)

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Answer:  D

Step-by-step explanation:

Answer: 32

Step-by-step explanation:

Multiply 8 by 4.

If one cup is 8 ounces, I assume they have the same value.

Answer:

The original price is 180$

Answer:

Step-by-step explanation:

If there is a 10 percent discount, that means that this is 90 percent of the total.

So, let us find 10 percent is made up of how many dollars.

$162/9=$18 (do note that the slash sign means divide! When you write down the equation on a paper, please write the actual divide sign. Sorry for the inconvenience)

Since the original price is 100 percent, and we have 10 percent, that means we can just multiply the 10 percent by 10, to get 100 percent, as 10 times 10 is hundred.

$18x10=$180

Hope this helped! If you need another method, along with a different explanation, or separate, do comment below, so I can know. Any part you do not understand, please don't be afraid to tell me. If you think I can improve my answer, or change any parts to perhaps make it clearer, i'm open to suggestions!

Answer:

0.075758 miles per minute

Step-by-step explanation:

3600 divided by 9 = 400

400 ft = 0.075758 miles

Answer:

a) [tex](x-4)^2=25[/tex]

Step-by-step explanation:

[tex](x^2-8x+16)=9+16\\ (x)^2-2*x*4+(4)^2=25\\ (x-4)^2=25\\x-4=5\\x=5+4\\x=9[/tex]

Answer:

247.60 round down because it is lower than five hope this helps<3

Step-by-step explanation:

Answer:

the answer is 23,100

Step-by-step explanation:

1.

2.

3.

Answer:

24 comic books

Step-by-step explanation:

18 - 6 = 12

12*2 = 24

24/2 = 12

12 + 6 = 18

Answer:

888

Step-by-step explanation:

Answer:

[tex]x = 0.25[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 8x - 2\\ g(x) = -8x + 2[/tex]

Required

Determine their point of intersection

To do this, we simply do:

[tex]f(x) = g(x)[/tex]

This gives:

[tex]8x - 2 = -8x + 2[/tex]

Collect Like Terms

[tex]8x + 8x = 2 + 2[/tex]

[tex]16x = 4[/tex]

Solve for x

[tex]x = 4/16[/tex]

[tex]x = 0.25[/tex]

Hence:

Their point of intersection is at [tex]x = 0.25[/tex]

Answer: w = 110°     x = 83°     y = 87°      z = 97°

Step-by-step explanation:

∠(x - 13) and ∠w form a linear pair so their sum is equal to 180°

x - 13 + w = 180        →     w = -x + 193

∠(x + 10) and ∠y form a linear pair so their sum is equal to 180°

x + 10 + y = 180        →    y = -x + 170

∠x  and ∠z form a linear pair so their sum is equal to 180°

x + z = 180             →    z = 180 - x

∠x and ∠y and ∠w are the angles of a triangle so their sum equals 180°

x + y + w = 180

x + (-x + 170) + (-x + 193) = 180                   Substitution

                       -x + 263 = 180                    Add Like Terms

                       -x            = -83                    Subtracted 263 from both sides

                                  x = 83                      Divided both sides by -1

w = -x + 193                     y = -x + 170                     z = 180 - x

w = -83 + 193                  y = -83 + 170                   z = 180 - 83

w = 110                           y = 87                             z = 97

Answer:

z= 120, ∠x= 60°, ∠y= 50°, ∠w= 70°

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

x = 9

Step-by-step explanation:

QR + RS = QS

6x - 20 + 5x - 24 = 55

11x - 44 = 55

11x = 99

x = 9                <--- This is the answer

Hope this helps!

Answer:

n=15

Step-by-step explanation:

[tex]\frac{5}{2}=\frac{n}{6}\\\\n=6(\frac{5}{2})\\\\n=15[/tex]

Answer:

n=15

Step-by-step explanation:

6÷2=3

3×5=15

Answer:

Step-by-step explanation:

Payment is

Divide both by 4/5 to find payment per hour

9.00 unit of money per 1 hour

Answer:

$9 per hour.

Step-by-step explanation:

7.2 ÷ 4/5

7.2/1 * 5/4

36/4

9

Best of Luck!

Answer:

921.05

Step-by-step explanation:

Answer:

921.05

Step-by-step explanation:

If 19% of a number is 175, then what is 100% of that number? Setup the equation.

Solve for Y

Using cross multiplication of two fractions, we get

19Y = 175 x 100

19Y = 17500

Y = 17500

100 = 921.05

Answer:4.00000

Step-by-step explanation:

 Slope = 2

 x-intercept = -4/2 = -2

 y-intercept = 4/1 = 4.00000

Answer:

la recta

Step-by-step explanation:

Answer:

 8.300 > 8.3 = False

Step-by-step explanation:

Answer:

Here we can take advantage of exactly the property suggested by Xisca... that is, sqrt(44)=2sqrt(11), which reduces the calculation to more accuracy with a lesser knowledge of the squares of numbers.

As a first approximation, we know that 33*33=1089, or 3.3*3.3=10.89, which is already very close to 11.  

Thus a first approximation to sqrt(44)=2sqrt(11)=2*3.3=6.6 (approximately).

To refine the calculation of sqrt(11), we use Newton's approximation, namely

a better approximation is given by 3.3 + (11 - 3.3^2) / (2*3.3) = 3.3+0.11/6.6 = 3.3+1/60

which gives

sqrt(44) = 2(3.3+1/60) = 6.6+1/30 = 6.6333,

actually accurate almost to the nearest 1/10000.

All of the above can be done mentally

For those who need help with rounding to the nearest hundredth (0.01), we drop digits AFTER the 2nd decimal, namely *.**33.  If the first digit dropped is 5 or more, add one to the last digit retained, otherwise, retain only the two digits after the decimal.  In this case, the first digit dropped is 3, so it will simply be dropped.  The final answer is then 6.63, to the nearest hundredth.

Answer:

x = 0.256286, 89.7437

Step-by-step explanation:

Step 1: Write equation

102x + 11 = (x + 6)² - 2

Step 2: Solve for x

Answer:

A. –9.6

D.–2.4

Step-by-step explanation:

Answer:

0.83 more ounces

Step-by-step explanation:

What we know:

// Yip is 3.62 ounces

// Yap is 2.79 ounces

What we need to find out:

How much heavier Yip is than Yap.

Solve:

3.62 - 2.79 = 0.83

- You can also use a calculator or do it out on paper.

Hope this helps!

Answer:

0.83 ounces

Step-by-step explanation:

3.62-2.79=0.83

Answer:

about 15-16 years

Step-by-step explanation:

Answer: 9 years 7 months and 6 days.

Step-by-step explanation: May I have brainliest, please.

Answer:

(f x g)(x) = -11

Step-by-step explanation:

(f x g)(x)

f(g(x))

g(x) = -2²-3

g(x) = -4-3

g(x) = -7

f(-7) = (-7)-4

f(-7) = -11

The radius of the Cylindrical cup is approximately 4.44 cm.

The radius of the cylindrical cup, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Where:

- Volume is the capacity of the cup (780 cubic centimeters),

- π is a mathematical constant approximately equal to 3.14159,

- r is the radius of the base of the cylinder (which we need to find),

- h is the height of the cylinder (12 cm).

We can rearrange the formula to solve for the radius (r):

r^2 = Volume / (π * h)

Substituting the given values:

r^2 = 780 / (3.14159 * 12)

Calculating the value:

r^2 ≈ 19.7384

To find the radius (r), we take the square root of both sides:

r ≈ √19.7384

r ≈ 4.44 cm (rounded to two decimal places)

Therefore, the radius of the cylindrical cup is approximately 4.44 cm.

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Answer:

[tex]\huge\boxed{(1, -3)}[/tex]

Step-by-step explanation:

In order to find the solution to this system of equations, our goal is to get one variable on one side of the equation.

With the equations d [tex]10x-2y=16[/tex], and [tex]10x-2y=16[/tex], we know that we can multiply [tex]10x-2y=16[/tex] by -1 and the x terms will cancel out (as 10 - 10 = 0).

[tex]-1(10x-2y=16) = -10x + 6y = -16[/tex]

Now we add this equation to the first.

[tex]10x+9y=-17[/tex]

[tex]-10x+2y=-16[/tex]

_______________

[tex]11y=-33[/tex]

Divide both sides by 11 and we get [tex]y=-3[/tex].

Now that we know the value of y, we can substitute it inside an equation and find the value of x. Let's substitute it inside  [tex]10x-2y=16[/tex].

[tex]10x-2(-3)=16\\10x+6=16\\10x=10\\\\x=1[/tex]

So x = 1.

Hope this helped!

Hope this helped!

Answer:

C.

Step-by-step explanation:

To get a perpendicular line, the slope will be the opposite of what you currently have. You have a slope of 2, so the opposite reciprocal slope will be -1/2. Then, you use the equation y = mx+b and substitute (2,5) for the y and the x (2 for the x and 5 for the y). This is to solve for b. Then, you have your equation! Hope this helped.