1. Mark practices the piano for 2/3 of an hour, 6 times a week. How many hours does
he practice each week?

Answer:

-1/2 is correct

Step-by-step explanation:

Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]. To evaluate the expression (g - f)(2), you need to first find the values of g(2) and f(2), and then subtract f(2) from g(2).

Given:

[tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \) \\ \( g(x) = \log_4(x) \)[/tex]

Let's start by calculating the values of f(2) and g(2): 1. [tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \)[/tex]

Substitute (x = 2):   [tex]\( f(2) = \frac{2 + 3}{2^2 + 2 \cdot 2 - 3} = \frac{5}{7} \)[/tex]

2. [tex]\( g(x) = \log_4(x) \)[/tex]  Substitute ( x = 2):  [tex]\( g(2) = \log_4(2) \)[/tex]

Now, evaluate the expression [tex]\( (g - f)(2) \):[/tex]

[tex]\( (g - f)(2) = g(2) - f(2) = \log_4(2) - \frac{5}{7} \)[/tex]

To determine which option matches this value, calculate [tex]\( \log_4(2)[/tex]) and subtract [tex]\( \frac{5}{7} \)[/tex] from it.

Approximately,[tex]\( \log_4(2) \)[/tex] is around 0.5.

So, [tex]\( (g - f)(2) \approx 0.5 - \frac{5}{7} \)[/tex]. To compare this result with the options provided, convert the fractions to a common denominator:

[tex]\( \frac{5}{7} = \frac{35}{49} \)[/tex]. So, [tex]\( (g - f)(2) \approx 0.5 - \frac{35}{49} \)[/tex].

Now, simplify the subtraction: [tex]\( 0.5 - \frac{35}{49} = \frac{24}{49} \)[/tex]

Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]

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Answer:

The answer would be 201.06

Step-by-step explanation:1. You need to have the radius and not the diameter so you would divide 16 by 2 to get 8.
2. You would plug 8 into the formula A=π[tex]r^{2}[/tex], meaning it would be A=π[tex]8^{2}[/tex]
3. 8 Squared is equal to 64 so the formula would now be A=π64
4. 64 x π = 201.06 giving you your final answer.
I hope that helps!

Answer:

200.96 mi²

Step-by-step explanation:

Before, finding the area of the circle, first, let us find the radius.

Given that,

diameter ( d ) ⇒ 16 mi

Let us use the below formula to find the radius of the circle.

d = 2r

16 = 2r

Divide both sides by 2.

8 mi = r

And let us find the area of the circle using the below formula.

A = π r²

A = π × 8 × 8

A = 3.14 × 64

A = 200.96 mi²

Answer: 2^3 - 16 : 2 +  5^2 = 25/1 = 25

Step-by-step explanation:

Exponentiation: 2 ^ 3 = 8Divide: 16 / 2 = 8Subtract: the result of step No. 1 - the result of step No. 2 = 8 - 8 = 0Exponentiation: 5 ^ 2 = 25Add: the result of step No. 3 + the result of step No. 4 = 0 + 25 = 25

[tex] |2x - 1| = | - x - 2| [/tex]

Thus ;

[tex]2x - 1 = - x - 2[/tex]

Add both sides x

[tex]2x + x - 1 = - x + x - 2[/tex]

[tex]3x - 1 = - 2[/tex]

Add both sides 1

[tex]3x - 1 + 1 = - 2 + 1[/tex]

[tex]3x = - 1[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{ - 1}{3} \\ [/tex]

[tex]x = - \frac{1}{3} \\ [/tex]

[tex]2x - 1 = - ( - x - 2)[/tex]

[tex]2x - 1 = x + 2[/tex]

Subtract both sides x

[tex]2x - x - 1 = x - x + 2[/tex]

[tex]x - 1 = 2[/tex]

Add both sides 1

[tex]x - 1 + 1 = 2 + 1[/tex]

[tex]x = 3[/tex]

There u go ...

Answer:

4.5 or 4 1/2

Step-by-step explanation:

An easy way to do this problem is to divide 6 by 4, the denominator (1.5) then multiply it by the numerator, 3, which will now be 4.5.

Answer:

Purchase price = $412.94 (nearest cent)

Total price = $430.49 (nearest cent)

Step-by-step explanation:

Purchase price

If 4.25% = $17.55

⇒ 100% = (17.55 ÷ 4.25) × 100 = 412.9411765...

⇒ Purchase price = $412.94 (nearest cent)

Total price

total price = purchase price + sales tax

                 = $412.94 + $17.55

                 = $430.49

So let the original price be x

Total price:-

Answer:

[tex]2x^2\\\\[/tex]

Step by step explanation:

[tex]y=\displaystyle \int_{0}^x 2t^2 dt=\dfrac 23\left[t^3\right]^{x}_0=\dfrac 23 x^3\\\\\ y'= \dfrac 23 \cdot 3x^2 = 2x^2[/tex]

As Per Provided Information

Diameter of Circle is 27 units

Radius will be 27/2 units

Radius will be 13.5 units

Calculating Area of circle.

[tex] \boxed{ \qquad\huge\sf \:Area_{(Circle)} \: = \pi {r}^{2}}[/tex]

[tex] \qquad\longrightarrow\sf \:Area_{(Circle)} = 3.14 \times {13.5}^{2} \\ \\ \\ \qquad\longrightarrow\sf \:Area_{(Circle)} = 3.14 \times 182.25 \\ \\ \\ \qquad\longrightarrow\sf \:Area_{(Circle)} = 572.265 \\ \\ \\ \qquad\longrightarrow\sf \:Area_{(Circle)} \: = 572.3 \: square \: units[/tex]

Now finding the circumference of the circle.

[tex]\qquad\boxed{\huge\sf \: Circumference_{(Circle)} = 2 \pi \: r}\\\\\qquad\longrightarrow\sf \:Circumference_{(Circle)} = 2 \times 3.14 \times 13.5 \\ \\ \\ \qquad\longrightarrow\sf \:Circumference_{(Circle)} = 6.28 \times 13.5 \\ \\ \\ \qquad\longrightarrow\sf \:Circumference_{(Circle)} = 84.78 \\ \\ \\ \qquad\longrightarrow\sf \:Circumference_{(Circle)} = 85 \: units[/tex]

Step-by-step explanation:

Given :- Diameter of circle :- 27 units , radius :- 13.5 units

Area :- πr²

Area :- 3.14×13.5²

Area :- 572.265

rounding off to nearest hundredth = 572.3 sq. units

Circumference :- 2πr

= 2 ×3.14 × 13.5 units

= 84.78 units

rounding off to nearest hundredth = 85 units

Answer:

  380 = 40h +200 (equation)

  4 1/2 hours (solution)

Step-by-step explanation:

The total cost is the sum of labor cost and parts cost. The labor cost depends on the number of hours.

__

An equation describing Terry's charges might be ...

  total = labor cost + parts cost

  380 = 40h +200 . . . . . . labor was $40 per hour for each of h hours

  180 = 40h . . . . . . subtract 200

  4.5 = h . . . . . . divide by 40

Terry was charged for 4 1/2 hours of labor.

Answer:

Step-by-step explanation: Maybe you could try:

A movie is 9.75 seconds long and each 2.5 seconds there is an ad so how many ads are there during the movie?

Answer:

-3+-3=-6

Step-by-step explanation:

start from the right go to the left.

+- = a negative gain

Multiply liters per minute by number of minutes and add that to the starting amount.

W = 34t + 400

now replace t with 16 and solve:

W = 34(16) = 400

W = 544 + 400

W = 944

After 16 minutes there are 944 liters in the pond

Answer:

[tex]y = \frac{2}{3}x + 4[/tex]

Step-by-step explanation:

The rule for graphs is:

[tex]y = mx + c[/tex]

Where [tex]m[/tex] is the gradient and [tex]c[/tex] is the y-intercept (where the line crosses the y-axis)

We can work out c by looking at our graph.

Our line crosses the y-axis at (0, 4). So... [tex]c=4[/tex]

To work out our gradient of a straight line (which is what we have)

We use the formula:

[tex]m = \frac{\triangle y}{\triangle x}[/tex]

The triangle [tex]\triangle[/tex] just means the "change in" the coordinates between any two points.

To calculate the change in y, we can pick any two points on our line!

Let's go for (0, 4) and (-6, 0)

To work out the gradient:

[tex]m = \frac{\triangle y}{\triangle x} = \frac{0 - 4}{-6 - 0} = \frac{-4}{-6} = \frac{4}{6} = \frac{2}{3}[/tex]

Using our formula

[tex]y = mx + c[/tex]
[tex]y = \frac{2}{3}x + 4[/tex]

7.6 hours

Step-by-step explanation:

57 x 8 = 456 minutes

456÷60= 7.6

Answer:

r = 18 cm

Step-by-step explanation:

The formula for the circumference of a circle is 2πr.

Hence,

2πr = 36π

r = 18 cm

In order to solve this equation, we need to take the square root of both sides (in order to get rid of the square and isolate x, because we are asked to determine the value(s) of x)

x²=36

√x²=√36

x=6

Is this the only solution?

A negative times a negative is a positive...

-6 is another solution of this equation! :)

Hence, the answers are:-

[tex]\boxed{\boxed{\bold{x=6; ~x=-6}}}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Hello! My name's Cupcake, And I will be helping you today! :D

In order to solve this equation, we need to take the square root of both sides.

Why? Because we need to isolate x. Our goal is:- To find the value of x.

So in order to get rid of the square and find the value of x, we take the square root of both sides:-

x^2=36

x=6, x=-6 (solutions)

Hope it helps!

Any queries - comment !

Answer:

58

Step-by-step explanation:

hope this helps

Answer:

I believe 58

Step-by-step explanation:

Answer:

15÷86400=???×86400

Step-by-step explanation:

O 15 sendo dividido pelo 86400 dará o resultado e multiplicando o resultado com 86400

Answer:

α = 29°

Step-by-step explanation:

Given values

Missing value

Solving :

Considering the definition of axis of symmetry and vertex of a quadratic function, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).

Quadratic function

The general form of a quadratic function is f(x  = ax²+ bx+ c, whose graph is a parabola.

Axis of symmetry and vertex of a quadratic function

Quadratic functions have a maximum (if a<0) or a minimum (if a>0). This point is the vertex of the parabola.

That is, the vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is in the plane of symmetry of the parabola; anything that happens to the left of this point will be an exact reflection of what happens to the right.

In other words, the vertex divides the graph into two halves that are mirror images of each other, so that the axis of symmetry always passes through the vertex.

Vertex of f(x) = −x² − 10x + 16

In this case, you know that the axis of symmetry for the function is x = −5.

So the vertex on the x-axis has a value of -5. To calculate the value of the vertex on the y-axis, you must substitute the value of the vertex on the x-axis in the function:

f(-5) = −(-5)² − 10×(-5) + 16

Solving:

f(-5)= 41

In summary, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).

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Answer:

a

Step-by-step explanation:

a

Answer:

Infinitely many solutions

Step-by-step explanation:

To solve for x, start by expanding the left-hand side of the equation.

2(x +5)= 2x +10

2(x) +2(5)= 2x +10

2x +10= 2x +10

Subtracting 10 from both sides:

2x= 2x

Divide both sides by 2:

x= x

Thus, x has infinitely many solutions.

Answer:

I cannot change what is the truth

Step-by-step explanation:

attempt to change the truth would resulted in dinaur catastrophe

Answer:

[tex]\boxed{ \bold{x = -1 }}[/tex]

Explanation:

[tex]\rightarrow \sf 32x-16+48=0[/tex]

simplify

[tex]\rightarrow \sf 32x+32=0[/tex]

subtract both sides by 32

[tex]\rightarrow \sf 32x+32-32=0-32[/tex]

simplify

[tex]\rightarrow \sf 32x=-32[/tex]

divide both sides by 32

[tex]\rightarrow \sf \frac{32x}{32} =\frac{-32}{32}[/tex]

final answer

[tex]\rightarrow \sf x=-1[/tex]

[tex]32x - 16 + 48 = 0 \\ 32x - 16 = - 48 \\ 32x = 16 - 48 \\ 32x = - 32 \\ x = - \frac{32}{32} \\ x = - 1[/tex]

x = -1

Answer:

[tex]95\frac{5}6{[/tex] miles

Step-by-step explanation:

First, find base. 1 inch = [tex]\frac{25}{3}[/tex] miles.

multiply the map distance by base.

[tex]11.5\cdot\frac{25}{3} = 95.8\overline{3}=95\frac{5}{6}[/tex] miles

Answer:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2

\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2

Now substitute the point (-7, 5) into the equation to find r²:

\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2

\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2

\sf \implies 149=r^2⟹149=r2

Final equation:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

The balance in the account after 30 years will be $91,745.06, the total amount of money put into the account will be $54,000 and  the total interest earned will be $37,745.06.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for the future value of an annuity to answer these questions:

FV = PMT(((1 + r)ⁿ - 1) / r)

a. To find how much will be in the account in 30 years, we need to calculate the future value of the annuity after 30 years of monthly deposits.

There are 12 months in a year, the number of months is:

n = 30 years × 12 months/year = 360 months

The monthly interest rate is:

r = 3% / 12 = 0.0025

Substituting the given values into the formula, we get:

FV = $150 × (((1 + 0.0025)³⁶⁰ - 1) / 0.0025)

= $91,745.06

b. To find the total amount of money put into the account, we need to multiply the monthly payment by the number of months:

Total amount = $150/month × 360 months
= $54,000

c. To find the total interest earned, we need to subtract the total amount of money put into the account from the future value of the annuity:

Total interest = $91,745.06 - $54,000

= $37,745.06

Therefore, the balance in the account after 30 years will be  $91,745.06, the total amount of money put into the account will be $54,000 and  the total interest earned will be $37,745.06.

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Answer:

Alright, so, the ratio is 2:5

In total, there are 7

So, 56/7=8

8x2=16

8x5=40

So after moving 2 students,

14 on the van, 42 on the bus

(you can use the true/false now)

Answer:

1. False

2. True

3. True

4. False

Step-by-step explanation:

Going to the museum:

Total: 56 students

van:bus = 2:5

2x + 5x = 56

7x = 56

x = 8

2x = 16

5x = 40

16 students go by van

40 students go by bus

40 - 16 = 24

Going back to school:

14 students go by van

42 students go by bus

van:bus = 14/42 = 1:3

42 - 14 = 28

Questions:

1. False

2. True

3. True

4. False

Answer:

Length = 8+7 = 15

Width = 8

Step-by-step explanation

                      Length = x+7 , x+4

Width = x ,x+2

(x+7) x = (x+4)( x+2)

expand and simplify x =8