Factor -4.3 out of 12.9b - 21.5

The equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y - 0 = 1/3(x - 5). The correct option is b. y - 0 = 1/3(x - 5)

From the question, we ae to write the equation of a line that has the given slope and x-intercept.

From the equation for the point-slope form of a line,

y - y₁ = m(x - x₁)

Where m is the slope

and (x₁, y₁) is a point on the line

From the given information,

m = 1/3

and

The x-intercept is 5, that is, (5, 0)

Thus,

The equation of the line is

y - 0 = 1/3(x - 5)

Hence, the equation is y - 0 = 1/3(x - 5)

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Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer:

  45 minutes

Step-by-step explanation:

At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...

  t = d/s

  t = (7.5 mi)/(10 mi/h) = 0.75 h

to catch Peter.

Mitchell will catch Peter in 45 minutes.

__

Alternate Solution

Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:

  3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter

_____

You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.

Answer:

  125 -v³ = (5 -v)(v² +5v +25)

Step-by-step explanation:

You want to factor the expression 125 -v³.

From your knowledge of the cubes of small integers, you recognize that 125 = 5³. That lets you see this expression is the difference of cubes, which has a factor pattern:

  a³ -b³ = (a -b)(a² +ab +b²)

Your difference factors as ...

  5³ -v³ = (5 -v)(5² +5v +v²)

  125 -v³ = (5 -v)(v² +5v +25)

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

32

Step-by-step explanation:

To solve, simply put 4 in place of x. 8 times 4 is 32

Answer:

Step-by-step explanation:

In mathematics, it should be noted that an area model is a rectangular diagram which is used to multiply and divide two numbers or expressions, in which the factors or the quotient and divisor define the length and width of the rectangle.

When solving problems involving multiplication and division in mathematics, an area model is a model or rectangular diagram where the length and width of the rectangle are determined by the factors or quotient and division.

You can calculate the area of a rectangle whose length is 48 units and width is 21 units by multiplying 48 by 21. In this case, this can be Illustrated in an area model.

Note that your information is incomplete and a overview was given.

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The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Using the concept of simple interest and compound interest, the first equation is \(S = 200(1.1)^t\), while the second is S = 250 + 20t

c. It will take over 7 years for the accounts to be equal.

The similarities between simple interest and compound interest is that both deals with saving of money over certain period of time with a fixed rate. While the difference between both is that in compound interest, the interest are compounded while in simple interest it is not. This implies that compound interest is an exponential function while simple interest is a linear function.

Simple interest = P(1 + rt)

Compound interest = P(1 + r/n)ⁿˣ

To solve this, we can write equations;

For the first scenario;

\(S = 200(1.1)^t\)

For the second scenario;

S = 250 + 20t

NB: The first case is a compound interest while the second is a simple interest.

c. To determine when the two accounts will be equal;

\(250 + 20t = 200(1.1)^t\)

Solving for t;

t = 7.01 ≈ 7 years

Therefore, it will take over 7 years for the accounts to be equal

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For the initial fee, Bob charges less than Ginny.

A unit rate means a rate for one of something.

Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.

Ginny initial charge = $80

Bob initial charge =$60

Hence, For the initial fee, Bob charges less than Ginny.

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Answer:

Step-by-step explanation:

L=3W

P=2L+2W

40= 2 (3W)+2W

40=6W+2W

8W=40

W=40/8

W=5 in

L=15 in (3W= 3*5=15)

Answer:

B. $48

Step-by-step explanation:

First we find the tip amount by multiplying the percent by the bill

20% * 40 = 8

We then add the tip amount to the bill

40 + 8

They payed a total of $48

Answer:

S

Step-by-step explanation:

SD

Answer:

I need this answer as well l. let me know

Answer:

65.7

Step-by-step explanation:

8^2 + 5/3

64 + 5/3

= 65.7

the absolute value function written as a piecewise function is:

f(x) = x + 8      if     x ≥ -8

f(x) = -(x + 8)     if    x + < -8

The absolute value function:

y = |x|

works as follows:

That is a piecewise function.

Now, in our case:

f(x) = |x + 8| can be rewritten to:

f(x) = x + 8      if     (x + 8) ≥ 0

f(x) = -(x + 8)     if    (x + 8) < 0.

Now we should simplify the inequalities, so we get:

f(x) = x + 8      if     x ≥ -8

f(x) = -(x + 8)     if    x + < -8

Here we have the absolute value function written as a piecewise function.

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\(\\ \bull\tt\longmapsto \left(-1\dfrac{2}{3}\right)^2\)

\(\\ \bull\tt\longmapsto \left(\dfrac{-1}{3}\right)^2\)

\(\\ \bull\tt\longmapsto \dfrac{(-1)^2}{3^2}\)

\(\\ \bull\tt\longmapsto \dfrac{1}{9}\)

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

x = 25

Step-by-step explanation:

The interior angle adjacent to the 123° angle is supplementary to it.

Its measure is 180° - 123° = 57°

The sum of the measures of the interior angles of a polygon is

(n - 2)180° = (4 - 2)180° = 2(180°) = 360°

3x + 7 + 96 + 5x + 57 = 360

8x + 160 = 360

8x = 200

x = 25

Answer:

The answer to the question is four.

Answer:

I think the answer might be 4.

Answer:

(2.5,5)

Step-by-step explanation:

y=3x/2 +5/4

4y=6x+5

-6x+4y=5

6x+12y=75

16y=80

y=5

x=5/2

23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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Answer: A

Step-by-step explanation:

\(P(x)= x^3 - 4x^2 - 9x + 36 \\D(x)=x + 3\\\\\begin{array}{|c|c|c|c|c|}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-4&-9&36\\x=-3&&-3&21&-36\\---&---&---&---&---\\&1&-7&12&0\\\end{array}\\\\\\P(x)= x^3 - 4x^2 - 9x + 36 \\=(x+3)(x^2-7x+12)\\=(x+3)(x^2-3x-4x+12)\\=(x+3)(x(x-3)-4(x-3))\\=(x+3)(x-3)(x-4)\\\\Answer \ A\)

Start with,

\((x^3-4x^2-9x+36)\div(x+3)\)

Look at first terms, \(x^3\) and \(x\) in divisor, with what do you have to multiply \(x\) so that you end up with \(x^3\)? The answer is \(x^2\).

So you write,

\((x^3-4x^2-9x+36)\div(x+3)=x^2\)

\(-(x^3+3x^2)\) (because you are subtracting \(x^2(x+3)\).

Which becomes when u subtract columns,

\((-7x^2-9x+36)\div(x+3)=x^2\)

Now repeat the procedure,

\((-7x^2-9x+36)\div(x+3)=x^2-7x\)

\(-(-7x^2-21x)\)

which becomes

\((12x+36)\div(x+3)=x^2-7x\)

And again,

\((12x+36)\div(x+3)=x^2-7x+12\)

\(-(12x+36)\)

becomes,

\(0=x^2-7x+12\)

Since the RHS is 0 that means \((x+3)\) is a factor.

Now you can factor \(x^2-7x+12=(x-4)(x-3)\) because \(-4\cdot-3=12\) and \(-4+(-3)=-7\).

Combine the factors and get \((x+3)(x-4)(x-3)\).

Hope this helps :)

Answer:

The Answer is -5(y - 3)(y - 7 )

The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.

A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).

Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.

Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.

a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:

f(x) = 0.005(6x²) = 0.03x²

b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:

g(x) = 0.004(6x²) = 0.024x²

Therefore, the quadratic functions are:

f(x) = 0.03x² for Design A

g(x) = 0.024x² for Design B

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The complete question is:

Answer:

Each party favor will have 23 pencils and 4 stickers.

Step-by-step explanation:

Betty can make the greatest number of party favors by finding the greatest common divisor (GCD) of 46 and 8. The GCD of 46 and 8 is 2. So Betty can make a maximum of 2 party favors with the same combination of pencils and stickers, with none left over. Each party favor will have 23 pencils and 4 stickers.

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

Y=4 is a function

Step-by-step explanation:

And to me function is relation

Hope i got this right and have a great day :)

Answer: Yes

Step-by-step explanation:

Yes, y = 4, which is often written as f(x) = 4, is a function that means “take any input, and no matter what it is, produce an output of 4”.

Answer:

1725

Step-by-step explanation: