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Answer:

1. B. 5.76 × 10¹⁴ miles.

2. D. $15,494.70

Step-by-step explanation:

Question 1: We have,

Distance light traveled in one year = 5.88 × 10¹² miles.

Since, the star is 9.8 × 10¹ light years away.

So, we get,

Total number of miles the star is away = 5.88 × 10¹² × 9.8 × 10¹ = 57.62 × 10¹³ miles.

Hence, the total number of miles are 5.76 × 10¹⁴ miles.

Question 2: We have,

Principle amount, P= $1,600

Rate of interest, r = 7% = 0.07

Time period, t = 33 years

Moreover, the interest is compounded twice per year i.e. n=2.

Since, Amount = [tex]P(1+\frac{r}{n})^{nt}[/tex]

i.e. Amount = [tex]1600(1+\frac{0.07}{2})^{2\times 33}[/tex]

i.e. Amount = [tex]1600(1+\frac{0.035)^{66}[/tex]

i.e. Amount = [tex]1600(1.035)^{66}[/tex]

i.e. Amount = [tex]1600\times 9.68418}[/tex]

i.e. Amount = $15,494.70

Hence, the balance in the account is $15,494.70.

Answer:

3 minutes polish 2 minutes hungarian

Step-by-step explanation:

I just did it on Kahn Academy, and this was correct.

Answer:

2m+2n+7

Step-by-step explanation:

Given: Two polynomial

[tex]P_1=m+n+3[/tex]

[tex]P_2=m+n+4[/tex]

We need to find the sum of polynomial.

[tex]Sum=P_1+P_2[/tex]

[tex]\Rightarrow (m+n+3)+(m+n+4)[/tex]

write like term together  

[tex]\Rightarrow m+m+n+n+3+4[/tex]

Combine the like term

[tex]\Rightarrow 2m+2n+7[/tex]

Hence, The sum of two polynomial is 2m+2n+7

Answer:

The answer is the second option

[tex]32\ cm[/tex]

Step-by-step explanation:

we Know that

Each trapezoid in the figure below is congruent to trapezoid ABDC

so

[tex]CE=AC=3\ cm[/tex]

[tex]EF=AB+CD=4+6=10\ cm[/tex]

[tex]FG=AC=3\ cm[/tex]

[tex]GH=AC=3\ cm[/tex]

[tex]AH=AB+BH=AB+CD=4+6=10\ cm[/tex]

the perimeter is equal to

[tex]P=AC+CE+EF+FG+GH+AH[/tex]

substitute the values

[tex]P=3+3+10+3+3+10=32\ cm[/tex]

The mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.

To find a mathematical model that gives the demand, y, in terms of the price, x, we can use the formula for inverse variation. Inverse variation is described by the equation y = k/x, where k is a constant. To find the value of k, we can use the given information: when x = 3.5, y = 450. Substituting these values into the equation, we get 450 = k/3.5. Solving for k, we find that k = 1575. Therefore, the mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.

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The solution to the function y = 12 - x is the ordered pair (6, 6) because when we substitute x = 6 into the function, the result, y, is also 6, which matches the given y-value in the pair.

To find the ordered pair that is a solution for the function y = 12 - x, we need to substitute the x-values of each given ordered pair into the equation and see which one gives a resulting y-value that matches the one in the pair.

Therefore, the solution to the function is the ordered pair (6, 6).

Answer:

To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).

Step-by-step explanation:

The range of the function is {-1, 3, 15}.

The set of a function's potential output values is known as its range.

Given that, the domain of the function is {0,2,-6}.

The range is the set of the output of the functions for the given domain values.

The value of y for x = 0 is:

y = -2(0) + 3

y = 3

Similarly, the values of y for x = 2 and x = -6 are:

y = -2(2) + 3

y = -1, and

y = -2(-6) + 3

y = 15

Hence, the range of the function is {-1, 3, 15}.

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This should get you a hundred on the 4.11 quiz. :)

The correct option is the x-coordinate of the vertex representing the length.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As it is given that the perimeter of the rectangular fencing is 1600 m.

Now, since the shape of the fence is rectangular, therefore, the x-coordinate of the vertex represents the length that results in the largest possible area, while the y-coordinate is the width of the rectangular fencing.

Hence, the correct option is the x-coordinate of the vertex representing the length.

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Final answer:

To find the dimensions of the barn's wall, we set up the equation w x (2w + 4) = 96 and solved for w to find the width is 8 feet. Then, we used the width to find the length, which is 20 feet.

Explanation:

To solve the problem of finding the dimensions of the rectangular wall of the barn, we need to set up and solve an algebraic equation. Let's call the width of the wall w feet. According to the problem, the length is 4 feet longer than twice the width, so we can express the length as 2w + 4 feet.

The area of the rectangle is given by multiplying the length by the width. We know the area is 96 square feet, so our equation to solve is w × (2w + 4) = 96.

Expanding this equation gives us 2w^2 + 4w - 96 = 0. This is a quadratic equation that we can solve by factoring, completing the square, or using the quadratic formula.

Factoring the quadratic equation, we look for factors of -96 that add up to 4. These factors are 12 and -8. So, we can write our equation as (2w + 12)(w - 8) = 0.

Setting each factor equal to zero gives us two possible solutions for w: w = -6 or w = 8. Since width cannot be negative, we discard w = -6 and keep w = 8 feet. The length is then 2(8) + 4 = 16 + 4 = 20 feet.

Therefore, the width of the barn's wall is 8 feet, and the length is 20 feet.

The answer would be ≈60mph, hence the answer is B.

Answer:

The scale factor of the dilation is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Let

z------> the scale factor

so

[tex]z=\frac{K'J'}{KJ}=\frac{K'H'}{KH}=\frac{J'H'}{JH}[/tex]

substitute the values

[tex]z=\frac{K'J'}{KJ}[/tex] ----->  [tex]z=\frac{1}{4}[/tex]

The scale factor is less than 1

therefore

The dilation is a reduction

Answer:

Q(2, −1), S(−6, 5)

Step-by-step explanation:

The original ordered pairs were  (2, 1) and (−6, −5). When you reflect across the x-axis the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).

so since the original ordered pairs were  (2, 1) and (−6, −5), the reflected ordered pairs would be  Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.

Hope this helped fellow FLVS student!!

The coordinates are Q(2, −1) and S(−6, 5)

A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.

Given that, On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis.

We know that, when you reflect across the x-axis, the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).

So, since the original ordered pairs were  (2, 1) and (−6, −5), the reflected ordered pairs would be  Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.

Hence, The coordinates are Q(2, −1) and S(−6, 5)

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Answer:

[tex]S_{30}=2940[/tex].

Step-by-step explanation:

Given  : [tex]a_{n} =6n+5[/tex].

To find : The sum of the first 30 terms .

Solution: We have given [tex]a_{n} =6n+5[/tex].

For n = 1

[tex]a_{1} =6(1)+5[/tex].

[tex]a_{1} =6+5[/tex].

[tex]a_{1} =11[/tex].

For n =2

[tex]a_{2} =6(2)+5[/tex].

[tex]a_{2} =17[/tex].

Common difference = 17 - 11 = 6.

Sum of nth term : [tex]S_{n} =\frac{n}{2}[2a+(n-1)d][/tex].

d = common difference = 6.

For  n = 30 .

[tex]S_{30} =\frac{30}{2}[2(11+(30-1)6][/tex].

[tex]S_{30} =15[22+29 *6][/tex].

[tex]S_{30} =15[22+29 *6][/tex].

[tex]S_{30} =15[22+174][/tex].

[tex]S_{30} =15[196][/tex].

[tex]S_{30}=2940[/tex].

Therefore, [tex]S_{30}=2940[/tex].

The range of the scores is B) 52.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Since the range would be the difference between the highest and the lowest score

WE are given that the math test scores of Mrs. Hunter's class are shown below.

48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100

Highest = 100

lowest = 48

here, we have,

range = 100 - 48 = 52

Hence, The solution is, range = 52.

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Answer:

g (x) = 3lx+2l-8

Step-by-step explanation:

Carlosego made a mistake on the horizontal shift.

y = f (x + c) shifts the graph c units to the left.

Therefore, g (x) = 3lx - 2 + 4l - 8 is

g (x) = 3lx+2l-8

The length of side AB (c) in triangle ABC is 31.38 m.

In triangle ABC, angle BCA is a right angle with a measure of 90 degrees, and angle CAB has a measure of 42 degrees.

The side BC has a length of 21 m and the side AB has a length of c.

To find the length of side c, we can use the trigonometric function sine.

By using the sine function and the given angle CAB, we can calculate the length of side c as follows:

c = AB = BC * sin(CAB) = 21 * sin(42) = 31.38 m

Therefore, The length of side AB (c) in triangle ABC is 31.38 m.

The probable question may be:

In triangle ABC, Angle BCA= 90 degree, angle CAB=42 degree, Side BC (a)=21 m, Side AB=c, find the measure of side c.