The sides of a triangle are 56, 80, and 42. Use the Pythagorean Theorem to determine
if the triangle is right, acute, or obtuse. And the largest size

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. The theorem can be proven using various methods, one of which is the geometric proof.

Geometric Proof of the Pythagorean Theorem:

Consider a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse. By drawing squares on each side, we create four congruent right-angled triangles within the larger square formed by the hypotenuse. The area of the larger square is equal to the sum of the areas of the four smaller squares.

The area of the larger square is c^2, and the area of each smaller square is a^2, b^2, a^2, and b^2, respectively. Therefore, we have c^2 = a^2 + b^2, which is the Pythagorean theorem.

Converse of the Pythagorean Theorem:

The converse of the Pythagorean theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle.

To prove the converse, we assume that a triangle with sides of lengths a, b, and c satisfies the condition c^2 = a^2 + b^2. By comparing this equation to the Pythagorean theorem, we can conclude that the triangle must have a right angle opposite the side of length c.

This is one way to prove the Pythagorean theorem and its converse, demonstrating the relationship between the lengths of the sides in a right-angled triangle.

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The parallelogram can be odd one out depending on there sides, diagonals and how diagonals are intersecting to each other

A parallelogram is a special kind of quadrilateral in which both pairs of opposite sides are parallel.

   There are four basic properties of parallelogram:

          1.Opposite sides of a parallelogram are equal.

          2.Opposite angles of parallelogram are equal.

          3.Diagonals divide the parallelogram into two congruent triangles.

          4.Diagonals of the parallelogram bisect each other.

Special parallelograms are:

  1.Rectangle

                             Measure of each interior angle is 90°

                             Opposite sides are equal

                             Diagonals are congruent

                             Each diagonal is angle bisector of opposite angle

 2.Rhombus

                             All sides are congruent.

                             Diagonals bisect each other at right angles.

                             Opposite angles are equal and each diagonal is          angle bisector of opposite angle.

3. Square

                          Measure of each interior angle is 90°

                          All sides are equal

                          Diagonals are congruent

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Answer:

eliminated, the bedtime increases by one minute. ... Description: This activity requires students to tell time to the half-hour (e.g. 4:00, 5:30, 11:30).

Step-by-step explanation:

Answer:

I think it's A) <1 and <2

Step-by-step explanation:

I am not 100% on this, but Adjacent angles are two angles that have a common vertex and a common side but do not overlap. In the figure, ∠1 and ∠2 are adjacent angles. They share the same vertex and the same common side.

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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#a

\(\\ \rm\Rrightarrow f(-4)\)

\(\\ \rm\Rrightarrow 3(-4)+2\)

\(\\ \rm\Rrightarrow -12+2\)

\(\\ \rm\Rrightarrow -10\)

#b

#1

\(\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}\)

Find y

\(\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}\)

Inverse is

\(\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}\)

#2

\(\\ \rm\Rrightarrow gof(x)\)

\(\\ \rm\Rrightarrow g(f(x))\)

\(\\ \rm\Rrightarrow g(3x+2)\)

\(\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+3}{3}\)

If we factor out

\(\\ \rm\Rrightarrow \dfrac{2x+1}{1}\)

\(\\ \rm\Rrightarrow 2x+1\)

#c

\(\\ \rm\Rrightarrow f(x)=g(x)\)

\(\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow 3(3x+2)=2x-1\)

\(\\ \rm\Rrightarrow 9x+6=2x-1\)

\(\\ \rm\Rrightarrow 7x=-7\)

\(\\ \rm\Rrightarrow x=-1\)

Answer:

Given functions:

\(f(x)=3x+2\)

\(g(x)=\left(\dfrac{2x-1}{3}\right)\)

Part (a)

\(\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}\)

Part (b)(i)

\(\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}\)

Part (b)(ii)

\(\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}\)

Part (c)

\(\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}\)

Answer:

(m-15)(m+2)

Step-by-step explanation:

m^2-13m-30

(m-15)(m+2)

Answer:

the answer 56 cubic units

Step-by-step explanation:

Question:

The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.

What is the value of h?

Answer:

A. 5

Step-by-step explanation:

Given

Solid Shape: Cone

Volume = 250/7

Diameter = Height

Required

Find the height of the cone

Provided that the diameter (D) and the height (h) are equal; This implies that

D = h ------ (1)

Also, Diameter (D) = 2 * Radius (r)

D = 2r

Substitute 2r for D in (1)

2r = h

Multiply both sides by ½

½ * 2r = ½ * h

r = ½h

Volume of a cone is calculated by;

Volume = ⅓πr²h

⅓πr²h = 250/7

Substitute ½h for r

\(\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}\)

Take π as 22/7, the expression becomes

\(\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}\)

Open the bracket

\(\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}\)

Multiply both sides by 7

\(7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7\)

\(\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250\)

Multiply both sides by 3

\(3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3\)

\(22 * \frac{1}{4}h^2 * h = 750\)

Multiply both sides by 4

\(4 * 22 * \frac{1}{4}h^2 * h = 750 * 4\)

\(22 * h^2 * h = 3000\)

\(22 * h^3 = 3000\)

Divide both sides by 22

\(h^3 = \frac{3000}{22}\)

\(h^3 = 136.36\)

Take cube root of both sides

\(h = \sqrt[3]{136.36}\)

\(h = 5.15\)

\(h = 5\) (Approximated)

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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There is about a 33.7% probability that a case of 48 cans will contain at least two cans with a defective ball.

To solve this problem, we can use the binomial distribution. Let's define "success" as getting a can with no defective ball and "failure" as getting a can with at least one defective ball.

The probability of success in one can is:

P(success) = 1 - P(failure) = 1 - 0.025 = 0.975

The probability of failure in one can is:

P(failure) = 0.025

Now, let's define X as the number of cans in a case of 48 that have at least one defective ball. We want to find the probability that X is greater than or equal to 2.

We can use the binomial distribution formula to calculate this probability:

P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

P(X = 0) = (0.975)^48 ≈ 0.223

P(X = 1) = 48C1 (0.975)^47 (0.025)^1 ≈ 0.44

where 48C1 is the number of ways to choose one can out of 48.

Therefore, the probability that a case of 48 cans will contain at least two cans with a defective ball is:

P(X ≥ 2) ≈ 1 - 0.223 - 0.44 ≈ 0.337

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Answer:

slope=5/6

Step-by-step explanation:

m=y2-y1/x2-x1

3-(-2)=5

2-(-4)=6

5/6

hope this helps :3

if it did pls mark brainliest

Answer:

5/6

Step-by-step explanation:

The graph goes up 5 units and goes right 6 units.

Slope is rise/run. y2-y1

                            x2-x1

So 3 - (-2)        that equals 5/6

     2 - (-4)

*note that whichever y coordinate you start with is the same x coordinate you start with

Please mark brainliest!!! Thanks.

Answer:

y>6

Step-by-step explanation:

y>48/8

y>24/4

y>12/2

y>6

Answer:

6

Step-by-step explanation:

divide both side by 8 for y to stand alone then 8 will cancel 8 and 48 divided by 8 = 6

8y\8 > 48/8

y= 6

The point estimate of the population proportion is 0.565.

The point estimate of the population proportion is the proportion of the sample that supports strengthening state laws regarding child safety restraints in vehicles.

Point estimate = (number of individuals in sample who support the strengthening of laws) / (total number of individuals in the sample)

Point estimate = 1247 / 2208

Point estimate ≈ 0.564 or 56.4% (rounded to one decimal place)

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Mark should use the volume formula to determine the number of cubic feet of soil needed to fill the planter half-full. To fill the planter half-full, he would require 18 cubic feet of soil.

In order to determine the amount of soil needed to fill the planter half-full, Mark should use the volume formula. The volume of a rectangular box is calculated by multiplying its length, width, and height. In this case, the length of the planter is 12 feet, the width is 6 feet, and the height is 3 feet. By multiplying these dimensions together (12 x 6 x 3), Mark can find the total volume of the planter, which is 216 cubic feet.

However, the question specifies that Mark needs to fill the planter only half-full. Therefore, he would require half of the calculated volume, which is 216 cubic feet divided by 2, resulting in 108 cubic feet. Therefore, Mark needs 108 cubic feet of soil to fill the planter half-full.

It's worth noting that the trick detail mentioned in the question is the requirement for the planter to be half-full. This means Mark needs to consider only half of the total volume when calculating the amount of soil required.

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Answer:

distance: 7.81 miles

Explanation:

simply use distance formula:  \(\sf \sqrt{(y_2 -y_1)^2 + (x_2-x_1)^2}\)

using the equation:

\(\hookrightarrow \sf \sqrt{(8-3)^2+(10-4)^2}\)

\(\hookrightarrow \sf \sqrt{(5)^2+(6)^2}\)

\(\hookrightarrow \sf \sqrt{25+36}\)

\(\hookrightarrow \sf \sqrt{61}\)

\(\hookrightarrow \sf 7.81 \ miles\)

Answer:

D.

Step-by-step explanation:

Not for sure sorry but i think its D or A so so sorry

Answer:

b = 7

Step-by-step explanation:

We know that the three interior angles of a triangle add up to 180 degrees.

The missing angle is 45 degrees (since 180 = 45 + 45 + 90).  Since we have two angles equal opposite the sides of length 7 and b, we know that b = 7.

When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.

Here,

The length of side=10 inch

The length of diagonal= 12 inch

Let the length of diagonal be x.

6²+(x/2)²=10²

(x/2)²=64

x/2=8

x=16 inch

The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.

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The given measure of ∠ DEC = 80 degrees

We have the following details

m ∠BAC = 46 degrees

m ∠ CBA = 54 degrees

We are to find the measure of angle DEC

This is a question that shows us two similar triangles

We have ∠BAC = DCE

∠ CBA = ∠ EDC

then ∠ DEC  = ∠ BCA

The measure of the angles that are in a triangle is given as 180 degrees

we have ∠BAC + ∠ CBA + ∠ BCA = 180

46 + 54 + ∠ BCA = 180 degrees

∠ BCA = 180 - 100

∠ BCA = 80 degrees

We know that corresponding angles are equal when we have parallel lines

since ∠ DEC  = ∠ BCA

∠ DEC = 80 degrees

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The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

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By Question it's given that the sum of two numbers is 15 . And we need to find out the numbers. So ,

Let us take :-

According to the Question :-

\(\sf\implies x + x +1=15\\\\\sf\implies 2x = 15-1\\\\\sf\implies 2x =14 \\\\\sf\implies x =14/2 \\\\\sf\implies\red{ x = 7 }\)

Therefore :-

Hence the two numbers are 7 and 8.

The correct statement regarding the mode of the sample is given as follows:

a. can be larger, smaller or equal to the mode of the population.

The mode of a data-set is the observation that appears the most often in the data-set.

The mode of the sample is simply the most frequently occurring value in the sample. It is not necessarily expected to be the same as the mode of the population, which is the most frequently occurring value in the entire population.

As a sample is a group taken from an entire population, the observation that appears the most in the sample can be different from the more common observation in the population,

Hence, option (a) is correct.

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Answer: 1,200 pounds

5 feet = 1,000 pounds

5 x 200 = 1,000

6 feet = 1,250 pounds

6 x 200 = 1,200

Answer = 1,200 pounds

1000 pounds / 5 feet = 200 pounds per foot.

200 pounds per foot x 6 feet = 1200 pounds.

The answer is 1,200 pounds.

The linear model for the snow (S) in terms of hours (h) during the snowstorm is S = 2h + 8, where S represents the snow in inches and h represents the number of hours since the start of the snowstorm.

To write a linear model for the snow (S) in terms of hours (h) during the snowstorm at the ski resort, we can use the information given:

The initial amount of snow on the ground when the snowstorm began is 8 inches.

The snow is falling at a rate of 2 inches per hour.

Based on this information, we can establish the following linear relationship:

S = 2h + 8

In this linear model, 'S' represents the amount of snow in inches, and 'h' represents the number of hours since the start of the snowstorm. The coefficient of 'h' is 2, representing the rate of snowfall per hour. The constant term 8 represents the initial amount of snow on the ground before the snowstorm started.

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Answer:

1,920

Step-by-step explanation:

288/3 = 96

96 x 20 = 1920

Answer:

1920 eggs

Step-by-step explanation:

make a ratio and cross multiply

20/3=x/288

3x=5760

x=1920

Answer:

B.

Step-by-step explanation:

Possible amount of hours to install 100 windows = 16 hrs.

The correct option is (B).

In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.

Given,

Number of windows Jason can install in 1 hour = 6 ≤ x ≥ 8

Time taken in installing 1 window = 1/6 ≤ 1/x ≥ 1/8

Time taken in installing 100 windows = 1/6 × 100 ≤ 1/x × 100 ≥ 1/8 × 100

Time taken in installing 100 windows = 12.5 ≤ t ≥ 16.67

Then the possible amount of time taken will be in range of 12.5 to 16.67 hrs.  

Hence, Jason will take around 16 hrs. to install 100 windows.

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