Brainliest to correct!

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer: 28.4

Step-by-step explanation:

Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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Answer:

Step-by-step explanation:

when 13 bought we find these inequalities

x + 12y < 7  no

2x + 11y < 7.5 no

3x + 10y < 8 no

4x + 9y < 8.5 no

5x + 8y >  9  yes

When 14 bought we find these inequalities

x + 13y < 7.5 no

2x + 12y < 8 no

3x + 11y < 8.5 no

4x + 10y > 9 yes  

We want to find and solve a system of inequalities to determine some possible solutions to Arianna's situation.

The possible solution is:

x = 2

y = 12

And the graph can be seen at the end.

Now let's see how to solve this.

First, we need to write the system of inequalities, the information given is:

Now we can define the variables:

Then we must have:

x + y ≥ 13   (this means that she buys at least 13 fruits)

x*$1 + y*$0.50 ≤ $9  (this means that she can't spend more than $9)

Now we just need to graph these two lines, we can rewrite them as:

y ≥ 13 - x

y ≤ $9.00/$0.50 - x*$1/$0.50 = 18 - x*2

Then we just need to graph the two lines, and shade the region above the first one, and the region below the second one, the graph can be seen below:

Any point inside the double shaded region in the first quadrant is a possible solution. (we restrict only to the first quadrant because we can not use negative values for x nor for y).

Then a possible solution that we could choose is:

x = 2

y = 12

This means that she buys 2 peaches and 12 mangos.

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Answer:

diameter = 2(radius)

Step-by-step explanation:

not sure what your question is but the diameter of a circle is equal to 2 times the length of its radius

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

She should win approximately 30 times.

Step-by-step explanation:

Since the probability of winning is 3/8, we multiply 3/8 with 80 to get 30.

Answer:

17/20

Step-by-step explanation:

Answer:

He can lift 160 pounds

Step-by-step explanation:

125 (from last year) + 35 (more pounds) = 160 (total pounds)

125 + 35 = 160

Answer:

2) 476.637

7) 2.2 and 2.20

8) 8.10 and 8.100

9) 9.5 and 9.500

10) 4.2 and 4.20

Step-by-step explanation:

2) First, solve 1/10 1/100, and 1/1000. That would be 0.1, 0.01, and 0.001.

Then, add all the numbers up.  Do multiplication first. 4 x 100 = 400.  Your answer would be 400 + 70 + 6 + 0.6 + 0.03 + 0.007. Add the big numbers. 476 + 0.637.

7) 2.2 and 2.20. It doesn't change the value no matter how many 0's you put.

8) 8.10 and 8.100

It doesn't change the value no matter how many 0's you put.

9) 9.5 and 9.500

It doesn't change the value no matter how many 0's you put.

10) 4.2 and 4.20

It doesn't change the value no matter how many 0's you put.

-kiniwih426

9514 1404 393

Answer:

  y = -1

Step-by-step explanation:

Sides marked with the same marking are congruent, so we have two equations:

Adding the equations gives ...

  5x = 25

  x = 5 . . . . . . divide by 5

Then the second equation tells us ...

  y = 9 -2x = 9 -2(5) = -1

The value of y is -1.

Step-by-step explanation:

Area of equalaterial triangle is 1/2bh

Here the base is 7.

The height is 4.2

\( \frac{1}{2} (7)(4.2) = 14.7\)

The true similarity statement are using Right Triangle Altitude Theorem :

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

By the Right Triangle Altitude Theorem,

If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.

Using this,

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.

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The complete question is given below.

Answer:

THE SLOPE IS 1

Step-by-step explanation:

the slope of a line is always the x and x = 1. For example, y = 2x -9, 2 is the slope.

Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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Step-by-step explanation:

Greetings !

Firstly, find the class-midpoints (X) to solve for the mean.

Thus, mid points of each classes are

\(5.15.25.35.45\)

Solve, for p using mean grouped data formula

\( \frac{5(3) + 15(4) + 25(p) + 35(3) + 45(2)}{3 + 4 + p + 3 + 2} = 24\)

multiply each values add them and solve for p.

\( \frac{15 + 60 + 25p + 105 + 90}{12 + p} = 24\)

make a cross multiplication

\(270 + 25p = 24(12 + p) \\ 270 + 25p = 288 + 24p\)

subtract 270 from both sides

\(270 + 25p - 270 = 288 + 24p - 270 \\ 25p = 24p + 18\)

subtract 24p from both sides

\(25p - 24p = 24p + 18 - 24p \\ p = 18\)

Also refer the attached image for further details

Hope it helps!

Answer:

432 inches

Step-by-step explanation:

We need to convert feet to inches

1 ft = 12 inches

36 ft * 12 inches/ 1 ft = 432 inches

Answer: -2

Step-by-step explanation:

The slope of the line perpendicular to another slope is the opposite sign and flipped(reciprocal)

The slope of the line = 1/2

So the perpendicular slope = -2

Answer:

Step-by-step explanation:3/10

Answer:

10\(\sqrt{2\\} \\\) or 14.14 appromiximately

Step-by-step explanation:

Area of square = 100

So length on side = 10 because all sides of square equal.

Length of Diagonal = Side x \(\sqrt{2}\)

So the length of diagonal is 14.14 approximately

Answer:

B. 29

Step-by-step explanation:

We Know

4x = 6x - 58

Find x.

4x = 6x - 58

-2x = -58

x = 29

So, the answer is B. 29

Answer:

\(\boxed{\sf Yes}\;;\textsf{because $\angle 9$ and $\angle7$ are \boxed{\sf vertical} angles, $m \angle 9=$ \boxed{\sf 90\; degrees}}\;.\)

\(\textsf{Because $\angle6$ and $\angle8$ are \boxed{\sf complementary} angles, $m\angle6+m\angle8=$\;\boxed{\sf 90\;degrees}}\;.\)

\(\textsf{Thus}, \; \boxed{\sf m\angle9 = m\angle6 + m\angle8}\;.\)

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, ∠9  and ∠7 are vertical angles and:

⇒ m∠9 = m∠7 = 90°

Angles on a straight line sum to 180°

⇒ m∠6 + m∠8 + m∠7 = 180°

⇒ m∠6 + m∠8 + 90° = 180°

⇒ m∠6 + m∠8 = 90°

Complementary Angles

Two angles whose measures sum to 90°.

Therefore, ∠6 and ∠8 are complementary angles and:

⇒ m∠6 + m∠8 = 90°

As  m∠9 = 90°  and  m∠6 + m∠8 = 90°  then:

⇒ m∠6 + m∠8 = m∠9

Answer:

a) A sample size of at least 251 students is needed.

b) A sample of at least 97 students is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

(a) you are unwilling to predict the proportion value at your school

We need a sample size of at least n.

n is found when M = 0.08.

We wont predict a proportion value for the school, so we use \(\pi = 0.5\)

So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.08 = 1.96\sqrt{\frac{0.5*0.5}{n}}\)

\(0.08\sqrt{n} = 1.96\sqrt{0.5*0.5}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.08}\)

\((\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.08})^{2}\)

\(n = 150.1\)

Rounding up

A sample size of at least 251 is needed.

(b) you use the results from the surveyed school as a guideline.

Now we have that \(\pi = 0.2\)

So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.08 = 1.96\sqrt{\frac{0.2*0.8}{n}}\)

\(0.08\sqrt{n} = 1.96\sqrt{0.2*0.8}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.2*0.8}}{0.08}\)

\((\sqrt{n})^{2} = (\frac{1.96\sqrt{0.2*0.8}}{0.08})^{2}\)

\(n = 96.04\)

Rounding up

A sample of at least 97 students is needed.

Step-by-step explanation:

AD 3CM B 10 CM C TO SHADE IN THE REGION MORE THAN 2 CM FROM A ,OA Circle centre with radius 2cm OA Circle center D with radius 2 CM i