The Bainter family is moving to a new town and needs a place to live. The Bainters are considering renting or purchasing a home and have found a suitable option for each option. …
what is the total first-year cost when purchasing the home?
a) 37,041.84
b) 39,711.84
c) 9,711.84
d) 7,041.84

Answer:

answer is 100 pages per hour

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Answer:

Domain: x \(\geq\) -5

Range: y \(\geq\) -3

Step-by-step explanation:

The domain is all the possible inputs or x value.  x will be greater than -5.

The range is all of the possible outputs or y value.   y will be greater than -3

Answer:

Domain:  [-5, ∞)

Range:  [-3, ∞)

Step-by-step explanation:

The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

The domain of a function is the set of all possible input values (x-values).

As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the  graphed function is:

The range of a function is the set of all possible output values (y-values).

From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:

Answer:

c=109.96

Step-by-step explanation:

Answer:

109.96

Step-by-step explanation:

Answer and Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

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

where:

A = the future value of the investment

P = the initial principal ($8,000.00 in this case)

r = the annual interest rate (10% in this case)

n = the number of times the interest is compounded per year (since interest is compounded quarterly, n = 4)

t = the number of years (17 - 3 = 14 years in this case)

We want to find the future value of the investment on Courtney's 17th birthday, so t = 14 years. Substituting the values into the formula:

A = $8,000.00(1 + 0.10/4)^(4*14)

A = $8,000.00(1.025)^56

Using a calculator:

A ≈ $44,322.42

Therefore, the certificate will be worth approximately $44,322.42 on Courtney's 17th birthday, assuming a 10% annual interest rate compounded quarterly.

The certificate will be worth $23,683.96 on Courtney's 17th birthday.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + r/n)^{nt}\)

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

To find the value of the certificate on Courtney's 17th birthday, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{nt}\)

where:

A = the amount at the end of the investment period

P = the principal investment amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case,

The principal (P) is $8,000.

The annual interest rate (r) is 10%, or 0.1 as a decimal.

The interest is compounded quarterly, so n = 4.

The investment period is 14 years, so t = 14.

Plugging these values into the formula, we get:

A = 8000(1 + 0.1/4)^(4 x 14)

A = 8000(1 + 0.025)^56

A = 8000(1.025)^56

A = 8000(2.960496)

A = $23,683.96

Therefore,

The certificate will be worth $23,683.96 on Courtney's 17th birthday.

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Answer:

B

Step-by-step explanation:

the side length is equal to sqrt(33)

sqrt(33)  = 5.74, closest to 5 3/4

Answer:

\((9x^3y^2)^2\)

Step-by-step explanation:

The expression, as a square of a monomial, will be given by:

\((\sqrt{81x^6y^4})^2\)

Now, we calculate the root, applying it's properties. So

\(\sqrt{81x^6y^4} = \sqrt{81} \times \sqrt{x^6} \times \sqrt{y^4} = 9 \times x^{\frac{6}{2}} \times y^{\frac{4}{2}} = 9x^3y^2\)

The expression as a square of a monomial is given by

\((9x^3y^2)^2\)

The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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Answer:

5. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

i am so sorry if its wrong

Each of the triangles making up the sides and base have a base of 8 cm and a height of 6.9 cm. Then the area of the pyramid is that of 4 such triangles.

 A = 4×(1/2)×b×h

 A = 2×(8 cm)×(6.9 cm)

 A = 110.4 cm²Step-by-step explanation:

well, the tax amount is simple, it was $71 and it went up to $86.45, that's a 15.45 difference, so that IS the tax amount.

now, if we take 71(origin amount) to be the 100%, what's 15.45 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 71 & 100\\ 15.45& x \end{array} \implies \cfrac{71}{15.45}~~=~~\cfrac{100}{x} \\\\\\ 71x=1545\implies x=\cfrac{1545}{71}\implies x\approx 21.76\)

Answer:

-3

Step-by-step explanation:

7-1=6

6-8=-2

A line connects the points (8, 1) and (6, 7). The angle is -3.

Therefore,

Slope (m) = ΔY/ΔX

= 3/-1

= -3

The slope =  -3

θ = arctan(ΔY/ΔX) + 180°

=1 08.43494882292°

ΔX = 6 – 8 = -2

ΔY = 7 – 1 = 6

Distance (d) = √ΔX2 + ΔY2 = √40 = 6.3245553203368

Equation of the line:

y = -3x + 25

When x = 0, y = 25

When y = 0, x = 8.3333333333333

Hence,  A line connects the points (8, 1) and (6, 7). The angle is -3.

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Answer:

f(2) = -3

g(-3) = -5

Step-by-step explanation:

----------------------

Answer:

Now first we have to found the decrease length.

which is:4mm-3mm=1mm

Now

we have to use formula to calculate the percentage which is

= decrease length/total length ×100%

=. 1/4×100%

=. 25 %

Therefore,the decrease rate is 25%.

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

The statement about the function is: "The function is decreasing for all real values of x where x < -4." D.

The given information tells us that the graph represents a downward-opening parabola.

The vertex of the parabola is located at (-4, 4) indicates that this point is the highest point on the graph.

As we move to the left of the vertex, the function values decrease, indicating a decreasing trend.

Moreover, the graph passes through the point (-6, 0), which lies to the left of the vertex.

This confirms that the function is decreasing for all real values of x less than -4, including x < -6.

On the other hand, the graph also passes through the point (-2, 0), which lies to the right of the vertex.

This does not impact the conclusion that the function is decreasing for x < -4, as the graph's behavior to the right of the vertex is not relevant to this particular statement.

Based on the given information and the properties of the downward-opening parabola, we can conclude that the function is decreasing for all real values of x where x < -4.

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Answer:

A. To convert pounds to kilograms, we need to multiply by 0.453592. Therefore, the fish from region A weighs about 130 kg (286 x 0.453592), rounded to the nearest whole number.

B. Similarly, the fish from region B weighs about 279 kg (614 x 0.453592), rounded to the nearest whole number.

We need to find the equation of the line passing through the points ( -1 , 7) and ( 2 , -8 )

The general equation of the line is :

Where m is the slope and b is a constant represents y - intercept

The slope m will be calculated as following:

Slope = Rise/Run

Rise = -8 - 7 = -15

Run = 2 - (-1) = 2 + 1 = 3

So, the slope is:

The equation of the line will be :

b will be calculated using the point ( 2 , -8 ) as following:

when x = 2 , y = -8

So,

So, the equation of the line will be:

So, the answer is option C. y = -5x + 2

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

B

Step-by-step explanation:

Equation of line II:

y-intercept = b = -1

y = mx + b

y = mx - 1

Plugin the point(2,0) in the above equation,

0 = 2m- 1

2m = 1

m = 1/2

Equation of line :

\(y = \dfrac{1}{2}x - 1\)

Both have same y-intercept and the same rate of change.

Answer:

∠ DCF = 45°

Step-by-step explanation:

given AB is parallel to CD , then

∠ BAF and ∠ AEC are alternate angles and are congruent , that is

∠ AEC = ∠ BAF = 75°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ AEC is an exterior angle of Δ CEF , then

∠ DCF + ∠ CFA = ∠ AEC

∠ DCF + 30° = 75° ( subtract 30° from both sides )

∠ DCF = 45°

Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

Answer:

Angles of Intersecting Chords Theorem

Step-by-step explanation:

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Answer: If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and it's vertical angle.

Step-by-step explanation: Example: In the circle, the two chords -PR and -QS intersect inside the circle. since vertical angles are congruent, m<1=m<3 and m<2=m<4

Answer:

  3.3 ft

Step-by-step explanation:

Side NO is opposite the angle M, so the applicable trig relation is ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse×Sin

  NO = MN×sin(39°) = (5.3 ft)sin(39°)

  NO ≈ 3.3 ft

Given :

On a map with a scale 1: 25000 .

The area of a lake is 33.6 square centimeters.

To Find :

The actual area of the lake.

Solution :

Let, actual area of lake is A.

So,

\(\dfrac{33.6}{A}=\dfrac{1}{25000}\\\\A = 840000\ cm^2\)

We know , \(1 \ cm^2 = 10^{-10}\ km^2\)

Area in km² is :

\(A = 840000\times 10^{-10}\ km^2\\\\A = 8.4 \times 10^{-5}\ km^2\)

Hence, this is the required solution.