A triangular right prism is cut perpendicular to the base. What is the shape of the cross section?


hexagon


rectangle


trapezoid


triangle

Answer:

14.2 squared units

Step-by-step explanation:

Always draw a diagram for the question. Capital letters are usually angles, and their opposite side is the same letter as a lowercase. (See diagram) The opposite side of angle B is side b.

The formula for area of a triangle is A = bh/2

"A" is for area.

"b" is for base (usually bottom side)

"h" is for height (perpendicular to base).

We know the measurement for the base c = 7.1. We need to find the height.

Notice when you draw in the height, it form two right triangles. We can use trigonometric ratios for right triangles.

Remember the trigonometric ratios using SohCahToa:

sinθ = opposite/hypotenuse;

cosθ = adjacent/hypotenuse and;

tanθ = opposite/adjacent, where θ means the angle of reference.

Focus on the triangle on the left side. We know one angle (∠B = 80°) and one side (a = 4.1). We can find "h", the missing side.

Since ∠B is our angle of reference, "h" is opposite. Since "a" is a longest side, it's the hypotenuse. Use the sine ratio because it uses the opposite and hypotenuse sides.

sinθ = opp/hyp             General sine ratio formula

sinB = h/a                  Variables you use in this problem

sin80° = h/4.1               Isolate "h". Multiply both sides by 4.1

h = 4.1(sin80°)                 Multiply with calculator

h = 4.1(0.98480775...)         Unrounded sin80

h = 4.03771178...                 Round this number

Note the number of decimal places given in the question.

h ≈ 4.0                Round to one decimal place

Now we can use the formula for the area of a triangle.

A = bh/2           Don't confuse side "b" with the base in this question

A = (7.1)(4.0)/2           Simplify the division

A = (7.1)(2.0)                   Multiply

A = 14.2                     Final answer for area

Since we don't know what the units are, you can say the answer is:

A = 14.2u²  or  14.2 squared units

Answer:

Therefore (28,45,53) is a Pythagorean triple.

Step-by-step explanation:

A Pythagorean triple consists of three positive integers a,b and c such that

a²+b²=c²

1.

3²+6²=45  and 12²=144

∴3²+6²≠144

Therefore (3,6,12) is not a Pythagorean triple.

2.

8²+16²= 330   and 32²= 1024

∴8²+16²≠32²

Therefore (8,16,32) is not a Pythagorean triple.

3.

12²+34²=1024 and   34²=5611

∴12²+34²≠34²

Therefore (12,34,30) is not a Pythagorean triple.

4.

28²+45²=2809   and   53²=2809

∴28²+45²=53²

Therefore (28,45,53) is a Pythagorean triple.

Answer:

A

Step-by-step explanation:

Consider Δ JKL and Δ GDF

If the ratios of corresponding sides are equal then the triangles are similar.

[tex]\frac{JK}{GD}[/tex] = [tex]\frac{24}{20}[/tex] = [tex]\frac{6}{5}[/tex]

[tex]\frac{xJL}{GF}[/tex] = [tex]\frac{18}{15}[/tex] = [tex]\frac{6}{5}[/tex]

[tex]\frac{KL}{DF}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex]

Since the ratios are equal then Δ JKL and Δ GDF are similar by SSS postulate.

The expression '6a + 3' consists of two terms: '6a' and '3'. In mathematical expressions, terms are separated by addition or subtraction operations.

The expression given, 6a + 3, is a mathematical expression that involves operations of addition and multiplication. In this expression, there are two terms separated by a plus sign. To clarify, a term refers to the separated parts of an expression when it is written as a sum or difference. This expression contains one numerical value (3) and one algebraic term (6a).

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Answer:

$6

Step-by-step explanation:

9 tubes of paint costs

$70 - $16 = $54

1 tube of paint cost

$54 : 9 = $6

Answer:

Step-by-step explanation:

Answer:

15.7

Step-by-step explanation:

8 1/5= 8.2

4 2/5= 4.4

3 3/10= 3.1

4.4 + 3.1 = 7.5

7.5 + 8.2 = 15.7

Answer:

Step-by-step explanation:

Combine fractions with similar denominators

81/5 + 42/5 + 33/10

Add 81 and 42

123/5 + 33/10

To write 123/5 as a fraction with a common denominator, multiply by 2/2

123/5 >2/2 + 33/10

Write each expression witha common denominator of 10

123 . 2/10 + 33/10

Common numerator over denominator

123 . 2 + 33/10

Simplify

279/10

Thus answer = 279/10 0r 27.9

Answer:

18 minutes

Step-by-step explanation:

the beaver is 18 minutes so multiply that by 3 which equals 54 then add those two together then you get 72 then add 23 qhich then you end up with 95 minutes total.

To solve the problem, we create an equation representing the total time all three animals can hold their breath. Solving it reveals that a beaver can hold its breath for 18 minutes.

Let's denote the time a beaver can hold its breath as 'x' minutes. According to the problem, a Greenland whale can hold its breath three times as long as a beaver, so that's '3x' minutes. A hippopotamus can hold its breath for five minutes more than a beaver, making it 'x+5' minutes.

The combined time for all three animals is given as 95 minutes, so we can set up the following equation:

x (beaver) + 3x (Greenland whale) + x + 5 (hippopotamus) = 95

Simplified, it becomes:

5x + 5 = 95

Next, you subtract 5 from both sides:

5x = 90

Finally, divide by 5:

x = 18

So, a beaver can hold its breath for 18 minutes.

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Answer:

Yes, you can

Step-by-step explanation:

The standard form of the equation of a parabola is [tex]y=ax^2+bx+c[/tex]

When given three points, you substitute each point into the equation to obtain 3 simultaneous linear equations.

You then solve the three equations simultaneously to find the values of the constants a,b, and c.

You then substitute these constants into [tex]y=ax^2+bx+c[/tex]

(6) The value of [tex]\sqrt{64}[/tex] is 8.

(7) The value of [tex]-\sqrt{31}[/tex] is -5.6

(8) The value of [tex]-\sqrt{16}[/tex] is -4

Explanation:

(6) The expression is [tex]\sqrt{64}[/tex]

Since, 64 is a perfect square, this can be written as [tex]8 \times 8[/tex].

Thus, the expression can be written as

[tex]\sqrt{64}=\sqrt{8 \times 8}=\sqrt{8^{2} }[/tex]

The square root gets cancelled. Thus, we have,

[tex]\sqrt{64}=8[/tex]

Thus, the value of [tex]\sqrt{64}[/tex] is 8.

(7) The expression is [tex]-\sqrt{31}[/tex]

Since, 31 is not a perfect square and solving the expression using a calculator, we get,

[tex]-\sqrt{31}=-5.56776[/tex]

Rounding off to the nearest tenth, we get,

[tex]-\sqrt{31}=-5.6[/tex]

Thus, the value of [tex]-\sqrt{31}[/tex] is -5.6

(8) The expression is [tex]-\sqrt{16}[/tex]

Since, 16 is a perfect square, this can be written as [tex]4\times 4[/tex]

Thus, the expression can be written as

[tex]-\sqrt{16}=-\sqrt{4\times 4}=-\sqrt{4^{2} }[/tex]

The square root gets cancelled. Thus, we have,

[tex]-\sqrt{16}=-4[/tex]

Thus, the value of [tex]-\sqrt{16}[/tex] is -4.

Answer:

Part a) 3 inches

Part b) Yes, her scale model drawing will fit on the piece of paper 8.5 by 7 inches

Step-by-step explanation:

we know that

The scale drawing is

[tex]1\ inch:2\ feet[/tex]

That means

1 inch in the model represent 2 feet in the actual

Part a) What is the length of the garden in her model?

we know that

The length of the garden is 6 feet in the actual

so

Find out the length of the garden in her model, using proportion

[tex]\frac{1}{2}\ \frac{in}{ft}=\frac{x}{6}\ \frac{in}{ft}\\\\x=6/2\\\\x=3\ in[/tex]

Part b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?

we know that

The model width is described as 5 inches. Both the 3-inch length and the 5-inch width are less than the 8.5 inch and 7 inch dimensions of the paper Kelly is using.

therefore

She can easily draw her model on that size paper.

Answer:

  15 inches

Step-by-step explanation:

The space diagonal of a rectangular prism is the root of the sum of the squares of the edge lengths. The longest straight part that will fit in the box will be at most ...

  l = √(4² +4² +14²) = √228 ≈ 15.10 . . . . inches

The greatest length the part could have been is 15 inches.

456cm^2

Step-by-step explanation:

AFB is 152 and times 3 it is 456cm^2

Answer: 10

Step-by-step explanation:

2 * 4 = 8

8/2 = 4

2 * 2 = 4

4/2 = 2

4 + 2 = 6

2 * 2 = 4

4 + 6 = 10

The first number is 8

Solution:

Let the first number be "x"

The second number is 6 times the first

Second number = 6x

The third number is 15 less than the second

Third number = second number - 15

Third number = 6x - 15

The sum of three numbers is 89

Therefore,

First number + second number + third number = 89

[tex]x + 6x + 6x - 15 = 89\\\\13x - 15 = 89\\\\13x = 89+15\\\\13x = 104\\\\Divide\ both\ sides\ by\ 13\\\\x = 8[/tex]

Thus the first number is 8

Answer:

1/8, 1/4, 3/8, 9/16, 3/4, 1

Step-by-step explanation:

The fractions have been arranged in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.

Fractions with different denominators can be compared by making the denominators the same. For example, take 1/4 and 1/2. The LCM of these fractions is 4. Now we can alter the fractions so that they have the same denominators as follows:

1/4 and 2/4

We can see that 2/4 is greater than 1/4.

The given fractions are: 3/4, 1/8, 9/16, 1, 1/4, 3/8

The lowest common multiple of these fractions is 16.

We can convert the fractions as shown below:

12/16< 2/16< 9/16< 16/16< 4/16< 6/16

Now we can arrange them in ascending order easily as shown below:

2/16, 4/16, 6/16, 9/16, 12/16, 16/16

or 1/8< 1/4< 3/8< 9/16< 3/4< 1

Therefore, we have arranged the fractions in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.

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Answer:

7D

Step-by-step explanation:

2D + 5D

Add the figures

Answer:

A

Step-by-step explanation:

3,-12,15,-21

The product 3 x [1 -4 5 -7] of [ -3  12  -15  21 ]

In mathematics, when we multiply a scalar (a single number) by a vector, the result is a new vector where each element of the original vector is multiplied by that scalar.

In this case, we have the scalar 3 and the vector [1  -4  5  -7].

1. Multiply each element of the vector by the scalar 3:

  3 x 1 = 3  

  3 x (-4) = -12  

  3 x 5 = 15  

  3 x (-7) = -21

2. Arrange the results in order:

  -3  12  -15  21

So, the product of 3 and the vector [1  -4  5  -7] is the new vector [-3  12  -15  21].

In this process, we essentially scaled each component of the original vector by a factor of 3, either increasing or decreasing the magnitude based on the sign of the original component.

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Answer:

[tex]m=\frac{1}{ab}[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have the points

(a,1/b) and (b,1/a)

substitute

[tex]m=\frac{1/a-1/b}{b-a}[/tex]

[tex]m=\frac{\frac{b-a}{ab}}{b-a}[/tex]

[tex]m=\frac{1}{ab}[/tex]

The slope of the line joining the points (a,1/b) and (b,1/a) is calculated using the slope formula and is found to be 1 divided by the product of a and b, assuming a and b are not equal and neither is zero.

To find the slope of the line joining the points with coordinates (a,1/b) and (b,1/a), we use the slope formula, which is the change in y divided by the change in x. We can write the formula as:

slope (m) = (y2 - y1) / (x2 - x1)

Substituting the given points into the formula gives us:

slope (m) = (1/a - 1/b) / (b - a)

If we assume that a does not equal b and neither a nor b is zero, the slope can be calculated by simplifying the numerator and the denominator:

slope (m) = ((b - a) / (ab)) / (b - a)

The (b - a) terms cancel out, leaving us with:

slope (m) = 1 / (ab)

Therefore, the slope of the line is the reciprocal of the product of a and b.

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Eva has $20.00, Justin has $27.50 and Emma has $15.50

Step-by-step explanation:

The given is:

We need to find how much money each person has

Assume that Eva has $x

∵ Eva has $x

∵ Justin has $7.50 more than Eva

- Add 7.50 to x

∴ Justin has = x + 7.50

∵ Emma has $12 less than Justin

- Subtract 12 from (x + 7.50)

∴ Emma has = x + 7.50 - 12 = x - 4.50

∵ Together, they have a total of $63.00

- Add x , (x + 7.50) and (x -4.50), then equate the sum by 63.00

∴ x + (x + 7.50) + (x - 4.5) = 63.00

- Add like terms

∴ (x + x + x) + (7.5 - 4.5) = 63.00

∴ 3x + 3 = 63.00

- Subtract 3 from both sides

∴ 3x = 60.00

- Divide both sides by 3

∴ x = 20.00

Substitute x by 20.00 in each expression above

∴ Eva has = $20.00

∴ Justin has = 20.00 + 7.50 = $27.50

∴ Emma has = 20.00 - 4.50 = $15.50

Eva has $20.00, Justin has $27.50 and Emma has $15.50

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Answer:

z ÷ 3 + z

Step-by-step explanation:

Yo sup??

Area of the figure=A

A=l*b

=2x(x+2)

=2x^2+4x

Therefore the correct answer is option B

Hope this helps

f(x) = 3x - 1 is the linear function for the line represented by the point-slope equation

Solution:

Given point slope equation is:

[tex]y - 5 = 3(x-2)[/tex]

We have to find the linear function for the line

The formula y = mx + b is said to be a linear function

Rearrange the given equation

[tex]y - 5 = 3(x-2)\\\\y - 5 = 3x - 6\\\\Move\ the\ varibale\ y\ to\ one\ side\ and\ constants\ and\ x\ to\ other\ side\\\\y = 3x - 6 + 5\\\\y = 3x - 1[/tex]

Let y = f(x)

Then we get,

f(x) = 3x - 1

Thus the linear function is found

Answer:

the answer will be B. f(x)=3x-1

Answer:1 8/45

Step-by-step explanation:73-20/45

53/45

1 8/45

Answer:

4 29/45

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello :

-6(w+1) < 2(w+5)

-6w-6< 2w+10

-6w-2w< 6+10

-8w < 16

8w > -16

w > -2

The area of a rectangle is length*width

Since we have the width, we can do 5346/66 to get the length

So the length is 81 cm

Hope this helped

Answer:

81 cm

Step-by-step explanation:

Area = Length × Width

5346cm² = length × 66cm

Length = 5346 ÷ 66

Length = 81cm

Answer:

8x-6

Step-by-step explanation: