He perimeter of this pentagon is 280 cm. find the lengths of the sides.

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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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

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)

For more references on reflection of a point, click;

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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.

Answer:

{ 2,-2}

Step-by-step explanation:

In order to solve this set we just have to first clear the "q":

[tex]7q^{2} -28=0\\7q^{2} -28+28=+28\\7q^{2} =28\\\frac{7q^{2}}{7}  =\frac{28}{7} \\q^{2}=4\\\sqrt{q^{2}} =\sqrt{4} \\q= 2, -2[/tex]

So as we know the solution for a square root is always a negative and positive number, so the solutions ser for 7q2-28=0 is 2 and -2

Jerry's monthly payment can be calculated using the formula for the monthly payment on a loan. Plugging in the given values will give the exact monthly payment amount.

To calculate Jerry's monthly payment, we can use the formula for the monthly payment on a loan:

Monthly Payment = P × r × (1 + r)^(n) / ((1 + r)^(n) - 1)

Where:

Plugging in the values:

Monthly Payment = $9,000 × 0.0079 × (1 + 0.0079)^(24) / ((1 + 0.0079)^(24) - 1)

Simplifying this equation will give us the monthly payment amount.

To find the area of a rectangle, multiply the length by the width. For a rectangle that is 1/3 yards long and 2/3 yards wide, the area is 2/9 square yards, which is the answer in simplest form.

The question asks us to calculate the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to compute the area of a rectangle is length  imes width.

First, multiply the length and the width:

Length: 1/3 yards

Width: 2/3 yards

Area = (1/3) times (2/3) yards sq

Area = 2/9 square yards

This is the simplest form of the fraction, so this is the final answer: The area of the rectangle is 2/9 square yards.

♦Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.

Dawson is 42, with a 20 year premium coverage, which will amount to $13.68 per $1000. Multiply $13.68 with 180 (because there are 180 $10,000)

13.68 x 180 = $2462.40

annual premium = $2462.40

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To solve the next one, Rachel bought a 20 year life insurance, which amounts to $17.56 per $1000

$63.14 is your answer

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hope this helps

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.

Learn more about the range of the function:

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Final answer:

There are no real number solutions for the given equation.

Explanation:

The given equation is 2x² + 8x + 8 = 0. To find the number of real number solutions for this equation, we can use the discriminant of the quadratic equation. The discriminant is given by the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 2, b = 8, and c = 8. Substituting these values into the formula, we get D = 8² - 4(2)(8) = 16 - 64 = -48.

Since the discriminant is negative (-48), there are no real number solutions for the equation. Therefore, the answer is 0.

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

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).

The graph of f(x) = x2 is shifted left 3 units.

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].

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.

To find the height of the parallelogram, set up the equation (3x + 24) x = 384 using the formula for the area of a parallelogram. Solve the resulting quadratic equation to find that x, representing the height, is 8 inche

The student is trying to find the height of a parallelogram when the base is 24 inches longer than three times the height and the area is 384 square inches. Let the height of the parallelogram be represented by x inches. According to the problem, the base (b) is 3x + 24 inches. Using the formula Base x Height = Area of parallelogram, we can set up the equation:

(3x + 24) x= 384

Now solve for x using the distributive property:

3x^2 + 24x = 384

Next, set the equation to zero:

3x^2 + 24x - 384 = 0

Divide the entire equation by 3 to simplify:

x^2 + 8x - 128 = 0

Factor the quadratic equation:

(x + 16)(x - 8) = 0

Set each factor equal to zero:

x + 16 = 0 or x - 8 = 0

Since the height cannot be negative, x = 8 is the solution. Therefore, the height of the parallelogram is 8 inches.