The statement, A midpoint is a location that is equidistant from both ends, is a

A) Definition

B) Hypothesis.

C) Postulate.

D) Theorem.

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.

Triangle Proportionality Theorem:

To prove this theorem, we begin by drawing a ΔABC with a line DE parallel to side AB. We then draw lines BD and CE, which intersect the parallel line DE at points F and G, respectively. By the properties of parallel lines, we know that ∠ADE and ∠ABD are congruent, and ∠AED and ∠ADB are congruent. Similarly, ∠CDE and ∠BDC are congruent, and ∠CED and ∠DCB are congruent.

We can then use the properties of similar triangles to show that ΔADE and ΔABC are similar, as are  ΔCDE and ΔACB. This means that the ratios of corresponding side lengths are equal:

BA/DE = CA/CE and CB/DE = AB/BD

We can then substitute CA - BA for CB in the first equation, and BD for AB in the second equation:

BA/DE = (CA - BA)/CE and CB/DE = BD/(CA - BA)

Cross-multiplying both equations, we obtain:

BA * CE = DE * (CA - BA) and CB * DE = BD * (CA - BA)

Adding the two equations, we get:

BA * CE + CB * DE = (DE + CE) * CA

Dividing both sides by CB * DE, we obtain:

BA/CB = (DE + CE)/CE * CA/DE = DE/CD

Thus, we have proven the Triangle Proportionality Theorem.

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The exercise above is referred to as Hypothesis Testing which is also called Significance Testing.

Significance testing is a method that is used to evaluate a research question. This is important because, after you have set a research question or hypothesis, the next step is to check whether it is Null or not.

Using ∝ = 0.05₂ tail, the conclusion is given as follows:

Z\(_{obt}\) = (84-90)/10/\(\sqrt{10}\)

      = - 6/10/‭3.1622777

      = -6/‭3.1622777

      = -1.8973666

Z\(_{crit}\) = for a two-tailed test with ∝ = 0.05 = = ± 1.960

Because we are looking at the left (negative, fewer) tail, Z\(_{crit}\) = -1.960

Since | Z\(_{obt}\) = -1.897 | \(\geq\) |  Z\(_{crit}\) = -1.960 |

It does fall within the critical region for rejection (left tail), therefore we reject the null hypothesis (H₀) and conclude that the average time spent in the institution for the sample of patients is significantly lower than the institution's average stay.

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Answer:

Step-by-step explanation:

67

Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.

Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.

This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.

He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.

Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.

Thus, looking at the provided options, option B ($850.00) would be the correct answer.

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Answer:

Solution given:

AB parallel BH parallel CH

1.

In triangle ∆AFD ,∆BGD ,∆CHD

<AFD=<BGD=<CHD

[being corresponding angle]

<DAF=<DBG=<DCH

[being corresponding angle]

<D is common for all.

So

∆AFD ~∆BGD ~∆CHD

[By A .A .A. axiom]

Step-by-step explanation:

2x²+11=131

2x²=131-11

2x²=102

x²=102

2

x²=51

x=√51

Answer:

Well, this could turn out to be a simple permutation problem: you have ten number choices (0-9) for each digit of a phone number and repetitions are allowed. Technically, there could be as many as \begin{align*}10^{10} = 10,000,000,000\end{align*}, or 10 billion possible phone numbers.

Step-by-step explanation:

:D

Questions:

1. 6 is not more than z.

2. The value of w is at least 12

3. Josiah plans to complete his 50 minutes of Mappers practice in 5 days and split the practice up evenly. Which inequality can he use to decide how many minutes he must complete each day?

4. Amy has $35.75 for her visit to the zoo. She must pay $7.25 for admission and wants to feed as many animals as she can. Food for the animals costs $1.25 each. What inequality represents the largest number of animal food that Amy can buy?

5. Jacob spent $40 on supplies to make 100 shirts for a baseball team fundraiser. Solve the inequality to help him decode how much to charge for each shirt to make a profit of more than $350.

100t-40 is greater than 350

Answers:

1. 6 is less than or equal to z (2nd option)

2. w is greater than or equal to 12 (1st option)

3. 5x is greater than or equal to 50 (1st option)

4. 1.25x + 7.25 is less than or equal to 35.75 (4th option)

5. t is great than 39 (3rd option)

Answer:

The scale of the drawing is 1 cm to 90 m. This means that every 1 cm on the drawing represents 90 m in real life. The length of the field is 450 m, so the length of the drawing will be 450 m / 90 m = 5 cm.

Therefore, the length of the dam drawing is 5 cm.

Step-by-step explanation:

For an exponential growth, the spike in share price must be proportional to what was already on ground.

We conclude that it is not an example of exponential growth.

the Answer: A

Step-by-step explanation:

We are given the following box

since the box is cubic, the height is the same as the length of the side length of its base.

The base would be a square of the following shape

where a is the length we are looking for. We are told that the area of the base is 49. Since the base has a side length of a, then we have the following equation

By taking the square root on both sides, we get

since a is a length, it should be positive. So, we have that

then, the height of the box is 7 inches.

Answer:

50

Step-by-step explanation:

:)

Answer:

80 games

Step-by-step explanation:

10wins/16 games=50 wins/? games

10 times 5=50 so 16 times 5 =80

10.g=16.50

10/g=800/10

g=80 games

The number of games they need to play to win 50 games is 80 games if the Arizona Cardinals won ten games out of sixteen of their games during the 2009 regular season.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The Arizona Cardinals won ten games out of sixteen of their games during the 2009 regular season.

Let x be the number of games they need to play to win 50 games

The rate:

10/16 = 50/x

1/16 = 5/x

x = 16x5

x = 80 games

Thus, the number of games they need to play to win 50 games is 80 games if the Arizona Cardinals won ten games out of sixteen of their games during the 2009 regular season.

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Answer:

4x+10

Step-by-step explanation:

Judith= x

Harry = 2x

Janessa= x+10

expression in total= x+2x+x+10 = 4x+10

We can Add 7 black beads to make ratio 3 : 1.

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)b : 3

Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3    

Both sides divisible by 3; reduce ratio

= 3 : 1        

Which is Correct ratio

Hence, There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore , we need to add 7 black beads.

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

edg 2021 unit test review

Answer:

64

Step-by-step explanation:

A square has 4 equal sides so all you have to do is divide 4 by 256. 256/4 is equal to 64. Therefore, the answer is 64 paving stones.

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Answer:

900 miles

Step-by-step explanation:

In 7 days she travels 525 miles.

So, in 1 day she travels: 525 ÷ 7 = 75miles

In 12 days she will have driven : 75 × 12 = 900 miles

Step-by-step explanation:

of at 7days Jill drove 525 miles

then she would drive x Miles in 12 days

7d = 525 miles

12 d = (12 ×525)/7

900 miles

The vοlume οf the prism is 14 cubic feet.

A three-dimensiοnal structure having six rectangular faces is called a prism. It is alsο knοwn as a rectangular cubοid οr a rectangular parallelepiped.

The prism is cοmpletely filled with 1750 cubes that have an edge length οf 1/5 ft. This means that the vοlume οf each cube is \((1/5)^3 = 1/125\) cubic feet.

Tο find the vοlume οf the prism, we can divide the tοtal vοlume οf the cubes by the number οf cubes:

Vοlume οf prism = (Vοlume οf οne cube) x (Number οf cubes)

Vοlume οf prism = (1/125) x 1750

Vοlume οf prism = 14 cubic feet

Therefοre, the vοlume οf the prism is 14 cubic feet.

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The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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Step-by-step explanation:

everything can be found in the picture

Answer:

h = \(\frac{K^2}{17}\)

Step-by-step explanation:

Given

K = \(\sqrt{17h}\) ( square both sides )

K² = 17h ( divide both sides by 17 )

\(\frac{K^2}{17}\) = h

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

LCM = 9450

Step-by-step explanation:

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer: both of them made ok estimates but i think issacs was better. hope this helps! ^-^

Step-by-step explanation:

The final frequency distribution is:

Age. Frequency

20-29 0

30-39 4

40-49 5

50-59 7

60-69 8

70-79 1

To complete a frequency distribution, we need to count how many times each age range appears in the data. The age ranges are determined by the given categories (20-29, 30-39, etc.).

Starting with the first category, 20-29:

No one in the data has an age in this range, so the frequency is 0.

Next, 30-39:

4 people have an age in this range (30, 33, 34, 37). The frequency is 4.

Continuing with the other categories:

40-49: 5 (38, 40, 41, 42, 47)

50-59: 7 (51, 53, 54, 55, 56, 56, 58)

60-69: 8 (60, 60, 64, 68, 68, 69, 70, 71)

70-79: 1 (81)

So the final frequency distribution is:

Age. Frequency

20-29 0

30-39 4

40-49 5

50-59 7

60-69 8

70-79 1

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Function graph that has y- intercept of 3 is g(x) = 3\((\frac{1}{4}) ^{x}\).

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5\((2)^{x}\)

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5\((0.5)^{x}\) + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3\((\frac{1}{4}) ^{x}\)

when x = 0

g(x) = 3

Here we get y intercept as 3.

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