List two advantages of buying and two advantages of renting

When cosθ >0 then , b² + c² > a².

" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."

Formula used

As per Cosine Rule

For a given ΔABC,

cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]

According to the question,

cosθ >0

⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0

⇒ b² + c² >a²

Hence, we conclude that Option D is correct.

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To find the maximum safe angle of elevation for a 110-foot ladder used at a height of 100 feet, we use the tangent inverse function with the ladder's maximum safe height as the opposite side and the ladder's hypothetical base length as the adjacent side. The angle of elevation is calculated using θ = tan⁻¹(100/adjacent). The specific calculation of the adjacent side isn't needed as the angle of elevation will be the same regardless of the actual length of the ladder along the ground.

The question is asking to find the maximum safe angle of elevation at which a 110-foot fire department ladder can be used, given that it can be safely used for rescues up to 100 feet off the ground. This is a trigonometry problem that involves the use of right-angled triangles.

To solve this problem, we will use the trigonometric function tangent (tan), which relates the angle of elevation θ to the opposite side of the triangle (the height of the building) and the adjacent side (the length of the ladder along the ground). The formula is θ=tan⁻¹(opposite/adjacent).

In this case, the opposite side is the maximum safe height of 100 feet, and the adjacent side would be the length of the ladder laid on the ground when the ladder reaches 100 feet high. We can find the length of the adjacent side using the Pythagorean theorem. However, we do not need to calculate it, as the angle of elevation does not depend on the horizontal distance but only on the ratio of the opposite side to the adjacent side.

The calculation would be: θ = tan⁻¹(100/adjacent).

Since the ladder length is greater than the height it needs to reach, the ladder base (adjacent) will be inside the triangle formed by the ladder and the building. The maximum safe angle of elevation θ can be calculated using the inverse tangent function of the height over the hypothetical base length, which is less than 110 feet.

Graphing an inequality is a great way to visualize a range of possible solutions and steps for graphing the inequality are shown below.

We have to give that,

Graph of inequality.

Here's a step-by-step guide to help graph an inequality:

Step 1:

Understand the inequality. Start by reading and understanding the given inequality. Is it greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality? This will determine the type of graph you will create.

Step 2:

Convert the inequality into slope-intercept form if possible. Rewrite the inequality in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Step 3:

Plot the y-intercept. Identify the y-intercept from the equation obtained in Step 2, and mark it on the graph. This is the point where the line crosses the y-axis.

Step 4:

Determine the slope. If the inequality is in slope-intercept form, the coefficient of x will be your slope. If not, rearrange the inequality to isolate y and find the coefficient of x to determine the slope.

Step 5:

Plot additional points. Use the slope to find one or two more points on the line. To do this, start from the y-intercept and move up or down based on the slope (rise over run). Connect these points to form a line.

Step 6: Determine the shading. Determine whether the inequality represents a region above or below the line. If the inequality is greater than or greater than or equal to, shade the region above the line. If the inequality is less than or less than or equal to, shade the region below the line. You can use dots or arrows to indicate whether the line is included or not.

Step 7: Finalize the graph. Extend the line beyond the plotted points, making sure it remains parallel. Then, label the graph and include any necessary units or context.

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Answer:

D.Rotate 180 about the origin (0,0)

Step-by-step explanation:

Answer:

D) 4 7/10

Step-by-step explanation:

Any fraction may be written as a mixed number. This type of number is formed by one or more whole parts plus a fractional part.

4.7 = 4 + 0.7

4 + 7/10

4 7/10

Following this same reasoning we can turn a mixed number into improper fraction and improper fraction into mixed number.

Final answer:

The orange juice provides approximately 7.14% of the RDA of niacin.

Explanation:

To find the percentage of the Recommended Daily Allowance (RDA) of niacin provided by the orange juice, we need to compare the amount of niacin in the orange juice to the RDA. Given that 8 ounces of orange juice contain 1 mg of niacin and the RDA for niacin is 14 mg, we can calculate the percentage using the formula:

Percentage = (Niacin in orange juice / RDA) x 100

Substituting the values, we get:

Percentage = (1 mg / 14 mg) x 100 = 7.14%

Therefore, the orange juice provides approximately 7.14% of the RDA of niacin.

Answer:

4.012 to 3 decimal places

Step-by-step explanation:

The division of decimal numbers can be done easily by multiplying the numerator and denominator with a number whose power of 10 completely removes the decimal.

For 7.984 ÷ 1.99

= (7.984 × 10^3) ÷ (1.99 × 10^3)

= 7984/1990

= 4.012060302

≈ 4.012 to 3 decimal places

Answer:

I think it is D

Step-by-step explanation:

Option D is correct, "Use the straightedge to draw a line through points X and Y."

A perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.

To draw perpendicular bisector of line segment AB. There are following steps:

1) Draw arcs from points X and Y on the both sides of XY.

2) Name the intersection points as A and B.

3) Use the straightedge to draw a line through points A and B.

4) Name the point as O

Hence we have construct perpendicular bisector AB of XY by using straightedge to draw a line through points X and Y.

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Answer: [tex]y+7=25(x+4)[/tex]

Step-by-step explanation:

We know that the point slope form of a line that passing through (a,b) and has slope m is given by :-

[tex](y-b)=m(x-a)[/tex]

Given : Slope: m = 25   ; Point : (a,b) =(−4, −7)

Then, the point slope form of the line with slope 25 that passes through the point (−4, −7) will be :-

[tex](y-(-7))=25(x-(-4))\\\\\Rightarrow\ y+7=25(x+4)[/tex]

PR = QR

5n = 32 +n

 subtract 1 n from each side

4n = 32

divide both sides by 4

n = 32/4 = 8

n=8

PR = 5n = 5*8 = 40

PR = 40

The measure of PR from the diagram given is 40

The given diagram is an isosceles triangle, For an isosceles triangle, two of sides and angles are equal. hence;

PR = QR

5n = 32 + n

Collect the like terms;

5n - n = 32

4n = 32

n = 32/4

n = 8

Get the measure of PR;

PR = 5n

PR = 5(8)

PR = 40

Hence the measure of PR from the diagram given is 40

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The angle measures 40 degrees, and its complement, which is 25% larger than the angle, measures 50 degrees. This is solved using elementary algebra by setting up an equation with the angle as 'x' and its complement as '90-x', and then simplifying the equation to solve for 'x'.

The question involves finding the measure of an angle and its complement when given that the complement exceeds the measurement of the angle by 25%. To solve this, let's use algebra. Let the measure of the angle be x degrees.

Since the complement of an angle adds up to 90 degrees with the angle itself, the complement can be represented as 90 - x degrees. According to the problem, the complement is 25% more than the angle, so we can write the equation:

90 - x = x + 0.25x

Simplifying, we get:

90 - x = 1.25x

90 = 2.25x

Dividing both sides by 2.25 gives us the measure of the angle x:

x = 40 degrees

Since the complement is 90 - x, we find:

Complement = 90 - 40 = 50 degrees

Therefore, the angle measures 40 degrees, and its complement measures 50 degrees.

To evaluate (4/9)^1/2, you find the square root of 4, which is 2, and the square root of 9, which is 3, hence the result is 2/3.

The student has asked to evaluate the expression (4/9)^1/2. To do this, you take the square root of both the numerator and the denominator separately. The square root of 4 is 2 and the square root of 9 is 3, therefore, the evaluation of the expression (4/9)^1/2 is equivalent to 2/3.

Nearsighted. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.

(a) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?

(b) What proportion of children in this sample are nearsighted?

(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z-statistic).

(d) What is the p-value for this hypothesis test?

(e) What is the conclusion of the hypothesis test?

Given:

The temperature is given in Fahrenheit (13 degree F).

To Find:

The correct temperature in Celsius.

Answer:

The temperature in Celsius is approximately -11 degree C.

Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.

Step-by-step explanation:

Any temperature can be changed from F to C by using the formula

[tex]C=(\frac{5}{9})(F-32)\\\\C=\frac{5(F-32)}{9}[/tex]

So, we will convert the given temperature in F to C by performing three simple steps.

Step 1 - We will subtract 32 from the Fahrenheit temperature.

Step 2 - Multiply this number by 5.

Step 3 - Divide the resulting number by 9.

So,

Step 1: 13-32 = -19

Step 2: -19*5 = -95

Step 3: -95/9 = -10.55 approx

Thus, the temperature in Celsius is approximately -11 degree C.

Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.

Kyle has got an incorrect answer because instead of subtracting 32 form the temperature, he has added it.

Given:

Kyle is converting 13°F to °C.

The formula used to convert F to C is

C= 5/9 (F- 32)

Now, Substitute F= 13 into the formulas as

C=  5/9 (13 - 32)

C = 5/9 (-19)

C= -95/ 9

C= -10.55

Thus, the temperature in Celsius is -11 degree C.

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The area of a rectangular backdrop is 18.75 square feet and container has enough paint.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, the rectangular backdrop is 60 inches by 45 inches.

We know that, 1 feet =12 inches

So, 60 inches = 60/12 = 5 inches

45 inches = 45/12 = 3.75 inches

Here, Area = 5×3.75

= 18.75 square feet

If his container of paint can cover 25 square feet.

So, Jose has enough paint.

Therefore, the area of a rectangular backdrop is 18.75 square feet and container has enough paint.

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Answer:

C. is correct

Step-by-step explanation:

The equation equivalent to y - 6 = -12(x + 4) is c. y = -12x - 42.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

y - 6 = -12(x + 4)

Expanding the bracket we get,

y - 6 = -12x - 48

Adding 6 both the side we get,

y - 6 +  6 = -12x - 48 +  6

Solving we get,

y = -12x - 42

which is equivalent to the given equation.

Thus, the equation equivalent to y - 6 = -12(x + 4) is c. y = -12x - 42.

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