Mathematics High School

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Answers

Answer 1

Answer:

15.0 in

Step-by-step explanation:

You want the height of a cone with radius 8 in and slant height 17 in.

Pythagorean theorem

The right triangle shown in the figure has height h, base x = 8 in, and slant height y = 17 in. The Pythagorean theorem tells you the relationship between these side lengths:

x² +h² = y²

8² +h² = 17²

h² = 17² -8² = 289 -64 = 225

h = √225 = 15.0

The height of the cone is 15.0 inches.

Additional comment

A triple of 3 integers that form the sides of a right triangle is called a "Pythagorean triple." The triple in this problem is one of those: {8, 15, 17}. Other Pythagorean triples you will often see in algebra, trig, and geometry problems are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}. You will also see multiples of these, for example 3×{3, 4, 5} = {9, 12, 15}.

It can be worthwhile to remember some of these. For this problem, recognizing 8 and 17 as part of the triple {8, 15, 17} means you can write down the answer with no further work.

Related Questions

HELPPP ASAPPPPP What is the surface area of the square pyramid represented by the net?

Enter your answer in the box.

m²

Answers

Answer:

144 m²

Step-by-step explanation:

You want to know the surface area of a square base pyramid with a side length of 6 m and a slant height of 9 m.

Surface area

The area of the given net is the sum of the areas of 4 congruent triangles and one square. The areas of these can be found using the relevant formulas.

SA = square area + 4 × triangle area

SA = 6² + 4 × 1/2(6)(9) = 36 +108

SA = 144 . . . . square meters

Additional comment

The area of a square of side s is A = s².

The area of a triangle with base b and height h is A = 1/2bh.

Surface are. Help!!!!!!!!

Answers

The surface areas of the prisms are listed below:

Case 1: 94 in²

Case 2: 72 cm²

Case 3: 40.5 m²

Case 4: 39.1 mm²

Case 5: 130 ft²

Case 6: 136 m²

How to find the surface area of a prism

In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:

Rectangle

A = b · h

Triangle

A = 0.5 · b ·h

Where:

A - Areab - Widthh - Height

Now we proceed to determine the surface areas:

Case 1

A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)

A = 40 in² + 24 in² + 30 in²

A = 94 in²

Case 2

A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²

A = 12 cm² + 20 cm² + 15 cm² + 25 cm²

A = 72 cm²

Case 3

A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)

A = 10.5 m² + 21 m² + 9 m²

A = 40.5 m²

Case 4

A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)

A = 16 mm² + 6 mm² + 17.1 mm²

A = 39.1 mm²

Case 5

A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)

A = 100 ft² + 10 ft² + 20 ft²

A = 130 ft²

Case 6

A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)

A = 24 m² + 70 m² + 42 m²

A = 136 m²

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Question 3 (1 point)
A sixth-grade class collected data on the number of siblings in the class. Here is the dot plot of the data they collected.

How many students had zero brothers or sisters?

Answers

The number of students who had zero brothers or sisters is 1.

What is the probability of students with zero brothers or sister?

The probability of students with zero brothers or sisters is calculated from the ratio of the total number of students to the number of students with zero brothers or sisters.

Total number of students = 65

Number of zero siblings = 1

The probability = 1 / 65

So based on this information, we can conclude that in the sixth-grade class and based on the collected data, the number of students who had zero brothers or sisters is 1.

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What is the rate of change?

Answers

Answer:

The rate of change is 0.5/2

Explanation:

For every time the x axis increases by two, the y axis increases by 2/4

2/4 = 0.5

So the rate of change is 0.5/2

Define:
Permutation
Factorial
Series
Circular permutation

Answers

Answer: Permutation: A permutation is an course of action of a set of objects in a particular arrange. The number of conceivable changes of a set of n objects is n factorial (n!), which is the item of all positive integrability up to n.

Factorial: The factorial of a non-negative numbers n is signified by n! and is characterized as the item of all positive integrability less than or rise to to n. For case, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Series: A arrangement may be a entirety of terms organized in a particular arrange. The entirety of the terms in a arrangement is called its add up to.

Circular permutation: A circular stage may be a stage of a set of objects in a circular course of action, where the arrange of objects things, but the beginning point is subjective. For case, orchestrating the letters A, B, and C in a circle would result in 3 circular stages: ABC, BCA, and CAB. The number of conceivable circular stages of a set of n objects is (n-1)!.

Step-by-step explanation:

Permutation-
the action of changing the arrangement, especially the linear order, of a set of items.

Factorial-
relating to a factor or factorial.

Series-
a set of quantities constituting a progression or having the several values determined by a common relation.

Circular permutation-
permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing all other elements of X. If S has k elements, the cycle is called a k-cycle.

a. ( 24 – 59 ) – ( 48:2 -60)

Answers

Answer:

Step-by-step explanation:

Stein Corp. reported the following information for 2013 and 2014.Accounts payable, December 31, 2013 $ 51,000Accounts payable, December 31, 2014 46,000Purchases--2014 467,000How much cash was paid for merchandise purchases during 2014?A. $421,000B. $462,000C. $467,000D. $472,000

Answers

The total amount of cash paid by Stein Corp. for merchandise during the interval of 2014 is $462,000, under the condition that accounts payable, for December 31, 2013 is $ 51,000 and accounts payable, for December 31, 2014 is $46,000
Purchases-2014 is $467,000.

In order to evaluate the cash paid for merchandise purchases during 2014, it is crucial to calculate the change in accounts payable from December 31, 2013 to December 31, 2014 and summation of purchases made during 2014.

Accounts payable change

= Accounts payable at December 31, 2014 - Accounts payable at December 31, 2013
= $46,000 - $51,000
= -$5,000

This explains that accounts payable decreased by $5,000 from December 31, 2013 to December 31, 2014.

Cash paid for merchandise purchases in 2014

= Purchases during 2014 + Change in accounts payable
= $467,000 - $5,000
= $462,000

The total amount of cash paid by Stein Corp. for merchandise during the interval of 2014 is $462,000, under the condition that accounts payable, for December 31, 2013 is $ 51,000 and accounts payable, for December 31, 2014 is $46,000
Purchases-2014 is $467,000.

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15PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY

Answers

Option a. The car is 115.47 feet from the building is correct for the given right triangle.

What is law of sines?

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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Randy is designing a circular garden that is 18 feet in diameter. He is buying plastic edging that costs $1. 50 per foot. He can only buy edging in whole-foot amounts. How much does it cost Randy to buy edging for his garden? Use 3. 14 for pie.

Answers

If the diameter of circular-garden is 18 feet, then it will cost Randy an amount of $85.50 to buy edges for his garden.

The "Circumference" of circle is defined as the "total-length" of the boundary or the outer edge of the circle.

The circumference formula is : Circumference = π × Diameter,

The "diameter" of garden is = 18-feet,

So, Circumference = 3.14 × 18 = 56.52 feet,

Since, Randy needs to buy plastic-edging to cover the entire circumference of garden, he needs to buy 56.52 feet of edging.

We know that, Randy can only buy edging in whole-foot amounts,

So, rounding up to the nearest whole foot, we get 57 feet,

The cost of edging is = $1.50 per foot,

So, "total-cost" for Randy to buy edging for his garden is,

⇒ Total Cost = (Cost per foot) × (Number of feet),

⇒ $1.50 × 57,

⇒ $85.50

Therefore, it will cost Randy $85.50 to buy edging for his circular garden.

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Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.

Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54

If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding

Question 12

A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?

There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.

Answers

The activity with a central angle of 54° is Kayaking and there were about 557 principals in attendance based on the prediction

The activity with a central angle of 54°

The formula to calculate the central angle for an activity is:

central angle = (number of campers for the activity / total number of campers) x 360°

Using this formula, we can calculate the central angle for each activity:

Kayaking: (15/100) x 360° = 54°

Wakeboarding: (11/100) x 360° = 39.6°

Windsurfing: (7/100) x 360° = 25.2°

Waterskiing: (13/100) x 360° = 46.8°

Paddleboarding: (54/100) x 360° = 194.4°

Therefore, the activity with a central angle of 54° is Kayaking.

Predicting the number of principals in attendance at the conference?

To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.

In the exhibit room, out of 70 people, 52 were principals.

So, the proportion of principals in the exhibit room was 52/70

We can predict the number of principals in attendance at the conference as follows:

Number of principals = proportion of principals x total number of attendees

If we plug in the values, we get:

number of principals = 52/70 x 750 = 557

So, based on this prediction, we can say that there were 557 principals in attendance at the conference.

Answers

The satellite should be insured for 98 months (rounded up to the nearest month) to be 96% confident that the microchip will last beyond the insurance date.

To answer this question, we need to find the number of months for which we can be 96% confident that the microchip will not malfunction. This means we want to find the value of x such that P(X > x) = 0.04, where X is the random variable representing the life expectancy of the microchip.

We know that X follows a normal distribution with mean μ = 92 months and standard deviation σ = 3.6 months. Therefore, we can standardize X to the standard normal distribution Z ~ N(0, 1) using the formula

Z = (X - μ) / σ

We can then rewrite the probability P(X > x) as

P(X > x) = P(Z > (x - μ) / σ)

1.75 = (x - 92) / 3.6

Solving for x, we get

x = 98 months

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The given question is incomplete, the complete question is:

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt.for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date?

Help, please, is for today.

Answers

Answer:

Measure of angle 2= 62 degrees

Step by Step:

The ratio of the angles is 1:2

So you add 1+2=3

Then divide 102/3, which equals 34

Finally multiply 34*2 to get 68

MULTIPLE CHOICE QUESTION
True or False: Involuntary deductions
from a person's gross pay go to their
employer.

Answers

False. Taxes and Social Security contributions are not deducted from a expressions person's total compensation and do not go to their employer.

what is expression ?

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

False. Taxes and Social Security contributions are not deducted from a person's total compensation and do not go to their employer. They are instead often paid to government agencies or other approved beneficiaries.

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Erik is growing vegetables in a square garden in his backyard. Each side of the vegetable garden is 6 feet long. He is also growing herbs in a rectangular garden that is 4 feet long and 3 feet wide. How many square feet larger is the vegetable garden than the herb garden?

Answers

the vegetable garden is 24 square feet larger than the herb garden. The area of the square vegetable garden is equal to the length of one side squared.

what is larger than ?

"larger than" is a comparative term used to describe a situation where one thing has a greater size, quantity, value, or magnitude than another thing. It is used to indicate a comparison between two or more objects or quantities.

In the given question,

The area of the square vegetable garden is equal to the length of one side squared. Each side of the square garden is 6 feet long, so the area of the vegetable garden is:

6 feet × 6 feet = 36 square feet

The area of the rectangular herb garden is equal to its length multiplied by its width. The length of the herb garden is 4 feet and the width is 3 feet, so the area of the herb garden is:

4 feet × 3 feet = 12 square feet

To find the difference in area between the two gardens, we subtract the area of the herb garden from the area of the vegetable garden:

36 square feet - 12 square feet = 24 square feet

Therefore, the vegetable garden is 24 square feet larger than the herb garden.

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What is the volume and total surface area of each shape combined?

Answers

The volume and total surface area of each shape combined is calculated below.

How to find the volume and total surface area of each shape combined?

For cone-hemisphere shape

Volume = volume of cone + volume of hemisphere

Volume = 1/3πr²h + 2/3πr³

where r = 9/2 = 4.5 m

h = √(13² - 4.5²) (Pythagoras)

h = 12.20 m

Volume = 1/3πr²h + 2/3πr³

Volume = (1/3 * 3.14 * 4.5² * 12.2) + (2/3 * 3.14 * 4.5³)

Volume = 449.33 m³

Surface area = curved surface area of cone + curved surface area of hemisphere

Surface area = πrl + 2πr², where l = 13 m

Surface area = (3.14 * 4.5 * 13) + (2 * 3.14 * 4.5²)

Surface area = 310.86 cm²

For hemisphere-cylinder shape

Volume = volume of hemisphere + volume of cylinder

Volume = 2/3πr³ + πr²h

where r = 22/2 = 11 ft

height of cylinder (h) = 45 - 11 = 34 ft

Volume = (2/3 * 3.14 * 11³) + (3.14 * 11² * 34)

Volume = 15704.19 ft³

Surface area = curved surface area of hemisphere + curved surface area of cylinder + curved surface area circular base of cylinder

Surface area = 2πr² + πr² + 2πrh

Surface area = 3πr² + 2πrh

Surface area = (3 * 3.14 * 11²) + (2 * 3.14 * 11 * 34)

Surface area = 3488.54 ft²

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find the slope of (6,1) and (6,-3)

Answers

Answer:

Step-by-step explanation:

Find the equation of the line that is perpendicular to the line AB and passes through the point. (0,2)

Answers

The equation of a line perpendicular to line AB and passing through point (0,2) is y = -4x + 2.

The given line has a slope of 1/4, so the slope of any line perpendicular to it will be -4 (the negative reciprocal).

Using the point-slope form of a line, we can write the equation of the line passing through the point (0,2) with slope -4 as

y - 2 = -4(x - 0)

Simplifying, we get

y - 2 = -4x

Adding 2 to both sides, we get

y = -4x + 2

Therefore, the equation of the line passing through the point (0,2) which is perpendicular to the line y=1/4x+5 is y = -4x + 2.

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Which number sentence shows the area of this figure

Answers

Answer:

Step-by-step explanation:

It would be a bit helpful if you uploaded a picture, since I don't see one.

Help PLEASEEEE!!!!!!!!!

Answers

After simplifying the equation, the answer is C, -k^4m^9!

For Exercises 16-18, use the following information. Brian invests $200 in an
account that pays 5% annual interest compounded continuously.
16. Write a function that models the amount y in the account after x years.
17. Write the domain and range using inequalities. Explain their meaning in this context.
18. How much will Brian have in the account after 8 years?

Answers

1. The function that models the amount in the account after x years is [tex]y(x) = 200e^{0.05t}[/tex]

2. The domain is [tex]x > = 0[/tex]. The range is [tex]y > = 200[/tex]

3. After 8 years, Brian will have $298.37 in the account.

How much money will Brian have after x years?

Function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The formula for continuous compounding is [tex]A = Pe^{rt}[/tex] where the A is the amount, P is the principal, e is Euler's number, r is the annual interest rate and t is the time in years.

Data:

A = ?

P = 200

t = ?

r = 5% = 0.05

Plugging in the values, we get: [tex]A = 200e^{0.05t}[/tex]which is the function.

2. The domain of the function is x >= 0 which means the number of years must be non-negative.

The range of the function is y >= 200 since the amount in the account cannot be negative and it starts with an initial investment of $200.

3. To get amount in the account after 8 years, we will plug in x = 8 into the formula:

[tex]y = 200 * e^{0.05*8}\\y = 200 * 1.49182469764\\y = 298.364939528\\ y = $298.37.[/tex]

Answers

b. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. In this case, the radius of the cone is 3 inches and the height is also 5 inches, so the volume of the cone is:

V = (1/3)π(3^2)(5) = 15π cubic inches

c. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 3 inches and the height is 5 inches, so the volume of the cylinder is:

V = π(3^2)(5) = 45π cubic inches

The fraction of the cylinder's volume that is the cone's volume can be found by dividing the volume of the cone by the volume of the cylinder:

(15π) / (45π) = 1/3

Therefore, the cone's volume is 1/3 of the cylinder's volume.

If you make $15 per hour and work 20 hours per week, how much will you
make in 16 weeks?

Answers

Answer:

4800

Step-by-step explanation:

15 x 20 = 300 x 16 = 4800

$15 times 20 equals 300 and 300 times 16 equals 4,800

5. A path bounds a circular lawn at a park. If the inner edge of the path is 132 ft. Around, approximate the amount of

area of the lawn inside the circular path. Use T < 22

6. The area of a circle is 367 cm?. Find its circumference.

7. Find the ratio of the area of two circles with radii 3 cm and 4 cm.

8. If one circle has a diameter of 10 cm and a second circle has a diameter of 20 cm, what is the ratio of the area of

the larger circle to the area of the smaller circle?

9. Describe a rectangle whose perimeter is 132 ft. And whose area is less than 1 ft?. Is it possible to find a circle whose

circumference is 132 ft. And whose area is less than 1 ft?? If not, provide an example or write a sentence explaining

why no such circle exists.

10. If the diameter of a circle is double the diameter of a second circle, what is the ratio of area of the first circle to the

area of the second?

Answers

The circumference of a circle: C = 67.98 cm

Radius of the circular lawn, which is difference between outer radius of path and inner radius of path.

outer radius: [tex]r1 = (132 + 2T)/2 = (132 + 2(22))/2 = 88 ft[/tex]

inner radius: [tex]r2 = 132/2 = 66 ft[/tex]

radius of circular lawn is r = r1 - r2 = 22 ft

Now using formula for the area of a circle:

A = πr^2 = π(22^2) ≈ 1520.53 ft^2

To find the circumference of a circle with area 367 cm^2, we can use the formula for the area of a circle to find the radius:

[tex]A = \pi r^2 \\r^2 = A/\pi = 367/\pi[/tex]

r ≈ 10.80 cm

Then we can find the circumference using the formula for the circumference of a circle:

C = 2πr ≈ 2π(10.80) ≈ 67.98 cm

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Error Analysis Taniya incorrectly says that the solution of the system of equations is (-3,-2). What is the correct solution?
What error might Taniya have made?
6g-3h=-3
5=h-4g

Answers

The correct solution for the given equation 6g-3h = -3 is (-4, -7) respectively.

What are equations?

A mathematical assertion that proves the equality of two mathematical expressions is what an equation in algebra means.

For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the 'equal' sign separating them.

So, we have the equation:

6g-3h = -3

Solution: (-3, -2)

Solve as follows:

6(-3)-3(-2) = -3

-18 + 6 = -3

-12 ≠ -3

Wrong solution.

Then, the correct solution could be:

6g-3h = -3

Solution: (-4, -7)

Solve as follows:

6g-3h = -3

6(-4)-3(-7) = -3

-24 + 21 = -3

-3 = -3

Correct solution.

Therefore, the correct solution for the given equation 6g-3h = -3 is (-4, -7) respectively.

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Answer Immeditely Please

Answers

The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units

What are similar triangles?

Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.

The similar triangles are; ΔABD, ΔBCD, ΔACB

∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)

[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]

4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16

4 × 16 = 64 = [tex]\overline{BD}[/tex]²

[tex]\overline{BD}[/tex] = √(64) = 8

The length of the segment [tex]\overline{BD}[/tex] = 8 units

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(a) Three squares have the areas of 7 cm², 17 cm² and 10 cm², (i) Will the squares exactly surround a right angled triangle? (ii) Explain your answer.

Answers

Answer:

(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

Step-by-step explanation:

To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled 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.

Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:

a² = 7 cm²

b² = 17 cm²

c² = 10 cm²

We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.

We can rearrange the equations above to solve for a, b, and c:

a = √7 cm ≈ 2.65 cm

b = √17 cm ≈ 4.12 cm

c = √10 cm ≈ 3.16 cm

Now, we can check whether the Pythagorean theorem holds:

c² = a² + b²

(√10 cm)² = (√7 cm)² + (√17 cm)²

10 cm = 7 cm + 17 cm

This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

what is the difference between 1/2 and 1/2%

Answers

Answer:

1/2 is half a number while 1/2% means 50%

A piece of metal with a mass of 611 g is placed into a graduated cylinder that contains25.1 mL of water, raising the water level to 56.7 mL. What is the density of the metal?A) 2.70 g/cm3 B) 7.13 g/cm3 C) 8.96 g/cm3 D) 10.5 g/cm3 E) 19.3g/cm3

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The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.

The given mass of the metal is 611 g and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal volume can be evaluated by subtracting the initial volume from the final volume of water released by the metal.

Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL

Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.

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PLEASE HELP
Consider this system of equations.
system
(PICTURE 1)
The system can be represented by the following matrix equation where A is a 3×3 matrix and b is a 3D vector
(PICTURE 2)

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The matrix of dependent coefficients and the vector column of independent variables of the system of linear equations are:

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

How to represent a system of linear equation by matrices

In this question we find a representation of a system of three linear equations with three variables {x, y, z}. This system can be described by following expression according to linear algebra:

[tex]\vec A \,\bullet \,\vec x = \vec B[/tex]

Where:

[tex]\vec {A}[/tex] - Matrix of dependent coefficients. [tex]\vec x[/tex] - Vector column of variables. [tex]\vec B[/tex] - Vector column of independent variables.

Please notice that operator "•" represents a dot product.

Then, the matrix of dependent coefficients and the vector column of independent variables are, respectively:

Matrix of dependent coefficients

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

Vector column of independent variables

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

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Find the value of x and y in each triangle

Answers

Answer:

x=4 y=3

Step-by-step explanation:

because y=3 and x=4

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