Write the equation of the perpendicular bisector of RS. Point R is located at (–1, 3), and point S is located at (3, 1).

Answer:

a - 21 inches

Step-by-step explanation:

Following the formula [tex]Area = l*w[/tex], we can find the length of the rectangle by plugging in values into the formula, then solving for [tex]l[/tex].

[tex]357=l*17[/tex]

[tex]\frac{357}{17} =\frac{l*17}{17} \\\\21=l\\l=21[/tex]

Answer:

Line MN is the answer

Step-by-step explanation:

Answer:

270

Step-by-step explanation:

Just multiply.

5*6*9=270

Answer: There would be 270 leaves of a tree diagram.

Step-by-step explanation:

Since we have given that

Number of salads = 5

Number of entrees = 6

Number of desserts = 9

If we draw a tree diagram, we need to find the number of leaves there would be :

So, the number of leaves there would be is given by

[tex]5\times 6\times 9\\\\=270[/tex]

Hence, there would be 270 leaves of a tree diagram.

After simplifying the original expression, the equivalent expressions to  [tex]21^x/7x[/tex] are C.  [tex]3^x[/tex] and F. [tex](21/7)^x.[/tex]

The original expression in the question is  [tex]21^x/7x[/tex]. To find equivalent expressions, we first simplify the original expression. The expression  [tex]21^x[/tex]is the same as [tex](7*3)^x,[/tex] which, by property of exponents, can be written as  [tex]7^x * 3^x.[/tex]Then, given the expression is divided by 7x, the x in the denominator cancels out with the x from [tex]7^x.[/tex] Hence, the simplified form will be  [tex]3^x.[/tex] Now, we compare it with the given options.

Option C is directly equal to the simplified form. While options A,D, E, and B are not equivalent to the original expression. Considering option F, 21/7 simplifies to 3 and so, [tex](21/7)^x[/tex] can be rewritten as  [tex]3^x[/tex] which is equal to the simplified form. Therefore, the equivalent expressions are C. [tex]3^x[/tex]and F.  [tex](21/7)^x.[/tex]

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The equivalent expressions to [tex]21^x/7x[/tex] are 3^x and [tex]7^x * 3^x/ 7^x[/tex], and[tex](21/7)^x,[/tex]which can all be simplified to result in 3^x.

The expressions equivalent to 21^x/7x are checked by determining if they simplify down to the same value as the original expression. Taking the original expression 21^x/7x, it's clear that 21 can be rewritten as 7*p, so 21^x/7x simplifies to [tex](7*3)^x/7x = 7^x*3^x/7x = 3^x[/tex] (because [tex]7^x/7^x = 1).[/tex]

From the given options, Option C: 3^x, and Option E: [tex]7^x * 3^x/ 7^x[/tex]satisfy this criterion, as they also simplify to 3^x. Option F: (21/7)^x also simplifies as explained earlier to 3^x. So, options C, E, and F are equivalent to the original expression.

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Answer:
10) 35
14) x = 1/2
18) 10 cm

Explanation:
For question 10, we can set up a proportional equation, cross-multiply and solve for the missing number:

[tex]\frac{x}{14} = \frac{5}{2}[/tex]

2x = 14(5)
2x = 70
2x / 2 = 70 / 2
x = 35

The missing number is 35

For question 14, we isolate variables on one side of the equation and constants on the other by performing whatever operations are necessary and then solve for the variable:
14x + 2 = 9
14x + 2 - 2 = 9 - 2
14x + 0 = 7
14x = 7
14x / 14 = 7 / 14
x = 7 / 14
x = 1/2

x = [tex]\frac{1}{2}[/tex]

For question 18, there are 10 millimeters (mm) in 1 centimeter (cm) so we can use this relationship so set up a conversion factor and cross-multiply to find the missing value like we did in question 10:
[tex]\frac{10}{1} = \frac{100}{x}[/tex]

10x = 100(1)
10x = 100
10x / 10 = 100 / 10
x = 10

There are 10 cm in 100 mm.

Answer:

[tex]a=7[/tex]

Step-by-step explanation:

we have

[tex]7(a-10)=13-2(2a+3)[/tex]

Solve for a

[tex]7a-70=13-4a-6[/tex]

Group terms that contain the same variable and move the constants to the other side

[tex]7a+4a=13-6+70[/tex]

Combine like terms

[tex]11a=77[/tex]

Divide by [tex]11[/tex] both sides

[tex]a=7[/tex]

Periodic data is useful for analyzing trends over time, helping to forecast future events, and measure frequencies of occurrences. It is applicable in various fields including business, environmental science, and health for planning strategies and understanding patterns.

Periodic data is useful when we are interested in analyzing and understanding trends over regular intervals of time. It helps us to observe patterns and forecast future occurrences based on historical information. For example, in business, we may look at quarterly sales figures to identify seasonal effects on sales and plan inventory accordingly. In environmental science, climate data recorded over decades can be critical for studying changes in weather patterns and predicting future climate events. In health, collecting epidemiological data periodically can enable public health officials to track the spread of diseases and the effectiveness of interventions.

Frequency, relative frequency, and cumulative relative frequency are measures that can describe how often certain events occur within periodic data. These measures help answer questions like 'How many students study five hours or more for an exam?' or 'What percent of families own two pets?' They are crucial for understanding the distribution of data and for making informed decisions based on that data.

Answer:You would earn .05 x $500 or $25 over that time period.

Step-by-step explanation:

Answer:

a is correct

Step-by-step explanation:

The first step is to calculate the length of the diagonal of the square opening.

The length of a diagonal of square = [tex] \sqrt{2} [/tex] * side

Given side = 3 feet

Length of the square hole = [tex] \sqrt{2} [/tex] *3 = 4.24 feet

since the diagonal is 4.24 feet and the shorter side of the plywood piece is only 4 feet, we can slide it through the square hole diagonally

Answer is YES since the diagonal 4.24 feet is greater than the shorter side of the plywood piece *4 feet

All options involve descriptive statistics, but option B is a classic example as it involves computation of a median, an important tool in descriptive statistics.

Descriptive statistics is used to describe, show or summarize data in a meaningful way. All the options given indicate the use of descriptive statistics because they all describe a given population or set of data using numerical measures. However, the most classical use of descriptive statistics is found in option B: 'A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.' This situation involves the computation of a median, a common measure in descriptive statistics, to summarize property price data.

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Final answer:

After computing the distances between the points L, M, and N using the distance formula and comparing them, it is clear that the sum of the lengths of any two sides is greater than the length of the third side, satisfying the conditions of a triangle.

Explanation:

To determine whether the given coordinates are the vertices of a triangle, we can check if the sum of the lengths of any two sides is greater than the length of the third side, which is a principle derived from the triangular inequality theorem. First, we calculate the distances between the points L(–24, –19), M(–22, 20), and N(–5, –7) using the distance formula: √((x2-x1)² + (y2-y1)²).

For LM: √((-22 + 24)² + (20 + 19)²) = √(4 + 1521) = √(1525)

For MN: √((-5 + 22)² + (-7 - 20)²) = √(289 + 729) = √(1018)

For LN: √((-5 + 24)² + (-7 + 19)²) = √(361 + 144) = √(505)

Now we compare the lengths:

LM + MN > LN

LM + LN > MN

LN + MN > LM

Since all three conditions are satisfied, the points L, M, and N form a triangle.

About 3 nails is correct on grad point

Answer:

6 truck containers can hold 144 cases

Step-by-step explanation:

A truck container holds 24 cases and we have to find number of cases would 6 truck container will hold.

We will solve this question by unitary method.

∵ One truck container holds cases = 24

∴ 6 truck containers will hold cases = 24×6 = 144

Therefore 144 cases is the answer.

Answer:

She worked [tex]6\frac{7}{8}[/tex]  hours in evening.

Step-by-step explanation:

Suppose, x be the hours waitress worked in evening,

Given,

She works 1.75 hours less in the afternoon than in the evening.

Thus, the number of hours she worked in afternoon = x - 1.75,

According to the question,

[tex]x-1.75 = 5\frac{1}{8}[/tex]

[tex]x-\frac{175}{100}=\frac{41}{8}[/tex]

[tex]x-\frac{7}{4}=\frac{41}{8}[/tex]

[tex]x=\frac{41}{8}+\frac{7}{4}[/tex]

[tex]x=\frac{41+14}{8}[/tex]

[tex]x=\frac{55}{8}=6\frac{7}{8}[/tex]

Therefore, she worked [tex]6\frac{7}{8}[/tex] hours in evening.

Answer:

Option A  is correct.

Step-by-step explanation:

Given:

AG = 6 ft ⇒ Radius of the circle , r = 6 ft

⇒ GB = AG = 6 ft

To find: Area of shaded Segment.

Area of Shaded Segment  = Area of Sector AGBA - Area of Δ AGB

Sector AGBA forming 90° angle at center. [tex]\implies\,\theta=90^{\circ}[/tex]

Area of Sector = [tex]\frac{\theta}{360}\times\pi r^2[/tex]

Area of Sector AGBA = [tex]\frac{90}{360}\times3.14\times6^2[/tex]

                                   = [tex]\frac{1}{4}\times3.14\times36[/tex]

                                   = [tex]28.26\:ft^2[/tex]

ΔAGB is a right angled triangle.

So, Area of ΔAGB = [tex]\frac{1}{2}\times AG\times GB[/tex]

                              = [tex]\frac{1}{2}\times6\times6[/tex]

                              = [tex]6\times3[/tex]

                              = [tex]18\:ft^2[/tex]

Area of Shaded Segment  = 28.26 - 18 = 10.26 ≈ 10.3 ft²

Therefore, Option A  is correct.