Find the volume of this prism.



pls ;( ​

1. Answer (D). By the law of sines, we have [tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex] in any [tex]\triangle ABC.[/tex]

2. Answer (C). The law of cosines, [tex]c^2=a^2+b^2-2ab\cos C,[/tex]accepts up to three sides and an angle as an input.

3. Answer (D). Although this triangle is right, we are not given enough information to uniquely determine its sides and angles - here, we need either one more side or one more angle.

4. Answer (D). Don't get tripped up by answer choice (C) - this is just a rearrangement of the statement of the law of cosines. In choice (D), the signs of [tex]a^2[/tex] and [tex]2ab\cos C[/tex] are reversed.

5. Answer (B). By the law of sines, we have [tex]\frac{5}{\sin 40^\circ}=\frac{3}{\sin\theta}.[/tex] Solving gives [tex]\theta\approx \boxed{23^\circ},157^\circ.[/tex] Note that this is the ambiguous (SSA) case of the law of sines, where the given measures could specify one triangle, two triangles, or none at all!

6. Answer (A). Since we know all three sides and none of the angles, starting with the law of sines will not help, so we begin with the law of cosines to find one angle; from there, we can use the law of sines to find the remaining angles.

Answer:

AD and BE is perpendicular => angle BED = 90 deg.

Otherwise angle CED = arc CD = 30 deg

=> angle BEC = angle BED - angle CED = 90 - 30 = 60 deg

Suppose a, b and c are 3 sides of a triangle in which a < b < c.

As property of length of sides a, b, and c of a triangle:

c - b < a < c + b

b - a < c < b + a

c - a < b < c + a

=> 6.7 inches, 1.1 inches, and 7.9 inches are not sides of a triangle

Check:

7.9 - 1.1 < 6.7 <=> 6.8 < 6.7  <=> invalid!

Hope this helps!

:)

Answer:

2(9+6)

Step-by-step explanation:

Answer:6/12

Step-by-step explanation:

Answer:

5.3 cm

Step-by-step explanation:

[tex]area \: of \: \triangle = \frac{1}{2} \times base \times height \\ \\ 10.6 = \frac{1}{2} \times base \times 4 \\ \\ 10.6 = base \times 2 \\ \\ base = \frac{10.6}{2} \\ \\ base = 5.3 \: cm[/tex]

Answer:

Step-by-step explanation:

The number of dollars Left always needs to be even if you want to buy albums last because we can never have half an album. So if you download 4 songs that leaves you left with $8.

0.25x4

=1

Now with the rest of the money you can download 4 albums.

4 individual songs, 4 albums.

0.25x4+4x2

=1+8

= $9

12 individual songs, 3 albums

0.25x12+2x3

= 3+6

=$9

20 individual song, 2 albums

0.25x20+ 2x2

= 5+4

= $9

Answer:

2sqrt5, 5, sqrt13, 14.5

Step-by-step explanation:

Just use vectors to calculate the change in the x and y axis during each movement and then apply the Pythagoras Theorem.

Answer:

BXBXBXBXBXB

Step-by-step explanation:

The term without exponent is b*b*b*b*b*b,

B:  (b³)² = b⁶.

The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given the term (b³)²

we know a² = a*a

so (b³)² = b³*b³

and a³ = a*a*a

(b³)² = b³*b³ = b*b*b*b*b*b

so (b³)² without exponent is b*b*b*b*b*b

and we know (aⁿ)ˣ = aⁿˣ

(b³)² = b⁶

Hence term without exponent is  b*b*b*b*b*b and compared power is b⁶.

Learn more about Exponential Function;

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Answer:

[tex](3,29)[/tex]

Step-by-step explanation:

There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is [tex]x=\frac{-b}{2a}[/tex]

We have the function [tex]g(x)=-3x^2+18x+2[/tex]

From this function, we can find that

[tex]a=-3\\b=18\\c=2[/tex]

We can plug in our know values into the formula to get

[tex]x=\frac{-18}{2(-3)\\} \\x=\frac{-18}{-6} \\\\x=3[/tex]

Then we can plug in our x-value to find the y-value of the vertex

[tex]g(3)=-3(3)^2+18(3)+2\\\\g(3)=-3(9)+54+2\\\\g(3)=-27+54+2\\\\g(3)=29[/tex]

This means that the vertex would be [tex](3,29)[/tex]

Answer:

C. (3,29)

Step-by-step explanation:

Edge 2020

Answer:

S(t) = a.sin (b.t) + d

a = -1.5, b = (2π/365), d = 3.47

S(t) = -1.5 sin (2πt/365) + 3.47

Step-by-step explanation:

Complete Question is presented in the attached image to this solution.

- Dingane has been observing a certain stock for the last few years and he sees that it can be modeled as a function S(t) of time t (in days) using a sinusoidal expression of the form

S(t) = a.sin(b.t) + d.

On day t = 0, the stock is at its average value of $3.47 per share, but 91.25 days later, its value is down to its minimum of $1.97.

Find S(t). t should be in radians.

S(t) =

Solution

S(t) = a.sin(b.t) + d.

At t = 0, S(t) = $3.47

S(0) = a.sin(b×0) + d = a.sin 0 + d = 3.47

Sin 0 = 0,

S(t=0) = d = 3.47.

At t = 91.25 days, S(t) = $1.97

But, it is given that T has to be in radians, for t to be in radians, the constant b has to convert t in days to radians.

Hence, b = (2π/365)

S(91.25) = 1.97 = a.sin(b×91.25) + d

d = 3.47 from the first expression

S(t = 91.25) = a.sin (91.25b) + 3.47 = 1.97

1.97 = a.sin (2π×91.25/365) + 3.47

1.97 = a sin (0.5π) + 3.47

Sin 0.5π = 1

1.97 = a + 3.47

a = -1.5

Hence,

S(t) = a.sin (b.t) + d

a = -1.5, b = (2π/365), d = 3.47

S(t) = -1.5 sin (2πt/365) + 3.47

Hope this Helps!!!

Answer:

Step-by-step explanation:

You can see by the markings that ST is congruent to AY, and that TA is congruent to YS. Those are 2 sides, so so far we have SS. One important thing that comes up WAY TOO OFTEN IN GEOMETRY TO IGNORE is the fact that both of those triangles share the side SA. This is called the reflexive property. The theorem for congruency between these 2 triangles is SSS.

Answer:

9,670

Step-by-step explanation:

8,219.5 ÷ 85% (0.85) = 9,670

The height of the volcano is reduced after the eruption, then the original height of the volcano is 9670 feet.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the given information in the question,

Height of the volcano after eruption = 8,219.5 feet

Let the original height of the volcano is x.

85% of x = 8219.5

x = (8219.5 × 100)/85

x = 9670 feet.

To know more about percentages:

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Answer:

2 9

Step-by-step explanation: yikes

Answer:

24,53cm²

Step-by-step explanation:

rectangle area=length×width=7×3

=21cm²

circle area=1/2Π r²

=1/2×3.14×1.5×1.5

=3.5325cm²

add the two areas

21+3.53=24,53cm²

Answer:

16.5 ft

Step-by-step explanation:

Circumference is 2πr, so radius being 5.25/2 would calculate to 16.5

Answer:

I believe you have to add 15.9 on both sides

Answer:

60%

Step-by-step explanation:

184 - 115 = 69

[tex]\frac{69}{115} =.6\\\\[/tex]

.6 × 100 = 60%

115 + 60% = 69

Answer: 3) cos 46 degrees

Step-by-step explanation:

Answer:

there will be 16 bags

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that

We are given the following:

1. Boys who do play video games = 1593

2. Boys who do not play video games = 858

3. Total boys = 2451

4. Girls who do play video games = 1361

5. Boys who do not play video games = 1635

6. Total Girls = 2996

7. Total number of candidates = Total boys + Total girls

=(2451 + 2996) = 5447

8. Total number of students, who play video games = 2954

9. Total number of students, who do not play video games = 2493

Percentage of boys who play video games:

[tex]\dfrac{1593}{2451} \times 100 = 64.99\%[/tex]

So, option A is not correct.

Percentage of girls who play video games:

[tex]\dfrac{1361}{2996} \times 100 = 45.43\%[/tex]

so option B is correct. The percentage is near about 45%,

Percentage of Total number of students, who do not play video games:

[tex]\dfrac{2493}{5447} \times 100 = 45.77\%[/tex]

So, option C is not correct.

Answer:

A =452.16 m^2

Step-by-step explanation:

The diameter is 24, so the radius is 1/2 of the diameter

r = 24/2 = 12

The area of a circle

A = pi r^2

A = 3.14 * (12)^2

A =452.16 m^2

The right answer is 452.16 square meters.( option C)

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

15%

Step-by-step explanation:

first find the difference in profit:

3162.50-2750 = 412.50

Now find the percentage increase:

412.50/2750 x 100 = 15%

Hope this helps.

Good Luck

Answer:

Answer: The profit percentage increase = 15%

Step-by-step explanation:

Subtract 3162.50 - 2750 = 412.5

412.5/2750 x 100 = 15  percent

Answer:

Each graph has one y-intercept, which is a solution.

Step-by-step explanation:

I used the process of elimination, so none of the others were true, or explained why there were two solutions.

I hope this helps you!

Answer:

80%

Step-by-step explanation:

We need to find the percent of change from 3,545 pt to 709 pt.

Original value is 3,545

Changed value is 709

Percent change is given by :

[tex]\%=\dfrac{\text{difference in values}}{\text{original value}}\times 100\\\\\%=\dfrac{3545-709}{3545}\times 100\\\\\%=80\%[/tex]

So, there is 80% of change from 3,545 pt to 709 pt.

Answer:

Fraction of the garden used =  [tex]\frac{5}{8}[/tex]

Step-by-step explanation:

The fifth graders to plant a butterfly garden.

We are given that

Clover grows in ½ of the garden

Daisies grow in ¼ of the garden

Coneflowers grow in ⅛ of the garden

milkweed grows in ⅛ of the garden

The fifth graders notice that the butterflies land on the clover and milkweed.

We are asked to find out the fraction of the garden that the butterflies used.

Fraction of the garden used = clover + milkweed

Fraction of the garden used =  [tex]\frac{1}{2} + \frac{1}{8}[/tex]

The LCM of 2 and 8 is 8

Fraction of the garden used =  [tex]\frac{4 +1}{8}[/tex]

Fraction of the garden used =  [tex]\frac{5}{8}[/tex]

Therefore, the butterflies used [tex]\frac{5}{8}[/tex] fraction of the garden.

Answer:

14 square inches

Step-by-step explanation:

Given shape is obtained by joining two rectangles of dimensions 4 by 2 inches and 3 by 2 inches.

Hence,

[tex]Area \: of \: the \: figure \\ = 4 \times 2 + 3 \times 2 \\ = 8 + 6 \\ = 14 \: {inches}^{2} [/tex]

Answer:

option C

Step-by-step explanation:

[tex]\frac{\frac{2x-1}{x+2}}{\frac{7}{x^{2}-12}}=\frac{2x-1}{x+2}*\frac{x^{2}-12}{7}\\\\\\=\frac{(2x-1)(x^{2}-12)}{7(x+2)}[/tex]

Answer:

5.78

Step-by-step explanation:

S=[tex]\frac{1}{2}[/tex](a+b)*h

a = 1.8

b = 5

h = 1.7

S = [tex]\frac{1}{2}[/tex](1.8+5)*1.7

S = (6.8*1.7)/2

S = 11.56/2

S = 5.78