Which theorem(s) can be used to prove that the given triangles are congruent to each other with only the information shown? Select all that apply.



A. ASA similarity
B. AA similarity
C. SAS similarity
D. SSS similarity

Answer:

Black

Step-by-step explanation:

Black-White-Yellow-Brown

Also can you please rate this as the most brainliest because I need it to level up?

Final answer:

After spending $37 on pizza and $89 on concert tickets, John overdrawn his account by $26. This calculation subtracts the total expenses from his initial amount, resulting in a negative balance.

Explanation:

John initially has $100, and we need to calculate how much money he will have on Monday after his expenses over the weekend. He bought pizza for $37 and concert tickets for $89, totaling $126 in expenses. To find out how much money John has left, we subtract his total expenses from his initial amount:

Initial Amount: $100
Total Expenses (Pizza + Concert Tickets): $37 + $89 = $126

Now, subtract the total expenses from the initial amount:

$100 - $126 = -$26

This means John will have a deficit of $26. Since he spent more than what he initially had, it implies he has overdrawn his account by $26.

Answer:

1553 cm^2.

Step-by-step explanation:

Surface area of the top part = area of the lateral part of the cylinder + area of the top circle

= 2π*6*10 + π*6^2 = 490.09 cm^2

Surface area of the bottom part

= surface area of the cube - surface area of the bottom of the cylinder

= 6 * 14^2 - π*6^2 = 1062.90

Total surface area = 490.09 + 1062.90 = 1553 cm^2.

Answer:

[tex]\large\boxed{y^\frac{1}{5}=\sqrt[5]{y}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\to a^\frac{1}{n}=\sqrt[n]{a}\\\\y^\frac{1}{5}=\sqrt[5]{y}[/tex]

The equivalent expression for y^1/5 using radicals is √(y) where y is the base and 5 is the index of the radical.

The expression

y^1/5

is the fifth root of y. In mathematics, when we talk about roots, we're essentially talking about the inverse operation of exponentiation. If we represent the expression y^1/5 using radicals, it would be written as

√(y)

. Here, the number inside the radical sign (y) is the base, and the index of the radical (in this case 5) is the root. Thus, √(y) and y^1/5 are equivalent expressions.

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The length AB of the triangle is 31.2 inches.

The side AB of the triangle can be found using sine rule for triangles as follows:

Using sine law,

a / sin A = b / sin B = c / sin C

Hence,

22 / sin 43 = AB / sin 75

cross multiply

AB sin 43 = 22 sin 75

divide both sides by sin 43

AB = 22 sin 75 / sin 43

AB = 21.2503681784 / 0.68199836006

AB = 31.1629271154

AB = 31.2 inches

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Answer:

$25.20

Step-by-step explanation:

Find 21% of $960

.21*960=201.6

Since there are 8 years, the cost per year will be the total cost divided by 8.

201.6/8=25.2

The cost per year is $25.20 on the extended warranty.

Answer:

50

Step-by-step explanation:

Answer:

[tex]\boxed{\text{274.5 cm; }71.3^{\circ}}[/tex]

Step-by-step explanation:

If we open the surface of the pole and lay it flat, we will get a rectangle with the red stripe as a diagonal.

l = 260 cm.

The width of the rectangle is enough for two revolutions (i.e., twice the circumference).

w = 2C = 2 × 2πr = 4π × 14/2 = 28π cm = 87.96 cm

Length of stripe

The stripe is the diagonal of the rectangle.

d² = 260² + (28π)² = 67 600 + 87.96² = 67 600 + 7738 = 75 338

d = √(75 338) = 274.5 cm

Angle with horizontal

tanθ = 260/(28π) = 260/87.96 =2.956

θ = arctan2.956

θ = 71.3°

The stripe is [tex]\boxed{ \text{274.5 cm}}[/tex] long and the angle with the horizontal is [tex]\boxed{71.3^{\circ}}[/tex].

Final answer:

The red stripe on the barber pole is approximately 520.8 cm long and makes an angle of about 71.1 degrees with the horizon.

Explanation:

The problem describes a cylinder (barber pole) with a helical stripe wrapping around it. To find the length of the stripe, we need to construct a right-angled triangle by unwrapping the helix. One side of the triangle is the height of the pole (260 cm), and the other side is the circumference of the pole multiplied by the number of revolutions (2).

First, calculate the circumference using the diameter given:

The length of the stripe is then the hypotenuse of the right triangle, which can be found using the Pythagorean theorem:

For the angle with the horizon, θ, we use the tangent function:

The angle with the horizon is approximately 71.1 degrees. So, the length of the stripe is about 520.8 cm, and it makes an angle of roughly 71.1° with the horizon.

Find the missing side of the right triangle using Pythagorean Theorem:

10^2 =8.7^2 +x^2;

x^2=100-75.69=24.31

x= sqrt 24.31~ 4.93

Area of trapezoid is area of triangle+area of a rectangle.

A=(8.7x4.93/2)+(12x4.93)

A=80.6055 ~81 ft^2

Ok so you do height times width

Answer: THE ANSWER IS R(x)=9x+69

Step-by-step explanation:

Answer:

[tex]R(x)= 20x^2+300x+1080[/tex]

Step-by-step explanation:

The number of teams who entered in  basketball tournament

[tex]T(x)=4x+24[/tex]

The entire fee paid by each team to enter the tournament

[tex]F(x)=5x+45[/tex]

Total entry fees = Number of teams * fee paid by each term

[tex]R(x)= T(x) * F(x)[/tex]

[tex]R(x)= (4x+24) *(5x+45)[/tex]

USe FOIL method to multiply it

[tex]R(x)= 20x^2+180x+120x+1080[/tex]

combine like terms

[tex]R(x)= 20x^2+300x+1080[/tex]

Answer:

  8.89 feet

Step-by-step explanation:

The square of the side length is 79 ft², so the side length is the square root of that:

  √(79 ft²) ≈ 8.88819 ft ≈ 8.89 ft

Answer:

Step-by-step explanation:

[tex]P(A|B)=\dfrac{P(A\ \cap\ B)}{P(B)}\\\\\text{A and B are independent events. Therefore}\ P(A\ \cap\ B)=P(A)\cdot P(B).\\\\\text{Substitute:}\\\\P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}\qquad\text{cancel}\ P(B)\\\\P(A|B)=P(A)\to P(A|B)=0.3[/tex]

Final answer:

Since A and B are independent events, P(A/B) is equal to P(A), which is 0.30.

Explanation:

The student is asking for the calculation of P(A/B), which is the probability of event A given that event B has occurred. However, since A and B are independent events, the occurrence of B does not affect the probability of A happening. Hence, P(A/B) is simply P(A), which is 0.30.

For independent events, the probability of A occurring given B has occurred is the same as the probability of A occurring on its own, because the two events do not influence each other:

P(A/B) = P(A) = 0.30

Answer:

1 5/9

hope it helped

Step-by-step

divide 5 1/4 by 3 3/8 to get 1 5/9

Answer:

The solution to this system is (-2, 1, -3).

Step-by-step explanation:

Let's eliminate variable x first.  Combine the first two equations, obtaining:

3x - 0y + 2z  = -12.

Now subtract the third equation from this result:

 3x - 0y + 2z  = -12

-(3x −   y −   z =  −4)

----------------------------

           y + 3z  = -8

Similarly, combine the second and third original equations to eliminate x again.  To do this, subtract  2(x + y + z = -4) from the first equation:

2x−y+z=−8

-2x - 2y - 2z = 8

-----------------------

    -3y - z = 0

Now we have eliminated x completely, and find from -3y - z = 0 that z = -3y.  Substitute this -3y for z in the equation y + 3z  = -8 found above:

y + 3(-3y)  = -8.  Then y - 9y = -8, and so y must = 1.  From -3y - z = 0, substituting 1 for y, we find that z = -3(1), or z = -3.

Finally, subst. 1 for y and -3 for z in the second equation:

x + 1 - 3 = -4

So, x - 2 = -4, and thus x must be -2.

The solution to this system is (-2, 1, -3).

Answer:

  it depends

Step-by-step explanation:

The endpoints of the hypotenuse are insufficient to specify a right triangle. The perimeter can range from twice the distance between these points, about 18.868 units, to 1+√2 times the distance between these points, about 22.776 units.

___

In the attached figure, the colored numbers are the total length of the two legs of that color. The hypotenuse and its length are in black.

_____

The distance between two points is given by the formula ...

  d = √((x2-x1)^2 +(y2 -y1)^2)

The perimeter will be the sum of the distances between pairs of points that define the vertices of the triangle. We need to know the third vertex to answer the question precisely.

Answer:

5/8 pounds of butter

Step-by-step explanation:

You have to subtract 3 1/4 and 2 5/8. Once you get them in common denominators, you get 3 2/8 - 2 5/8. Next you turn 3 2/8 into 2 10/8. Then when you subtract it, you get 5/8 pounds of butter.

1. [tex]P(X<5)[/tex] is the area under the curve to the left of [tex]x=5[/tex], which is a trapezoid with "bases" of length 2 and 5 and "height" 0.2, so

[tex]P(X<5)=\dfrac{5+2}2\cdot0.2=0.7[/tex]

2. Find the area under the curve for each of the specified intervals:

[tex]P(X\le2)=\dfrac{2\cdot0.2}2=0.2[/tex] (triangle with base 2 and height 0.2)

[tex]P(X\ge4)=\dfrac{1\cdot0.4}2=0.2[/tex] (triangle with base 1 and height 0.4)

[tex]P(2\le X\le4)=\dfrac{0.2+0.4}2\cdot2=0.6[/tex] (trapezoid with "bases" 0.2 and 0.4 and "height" 2)

[tex]P(1\le X\le3)=\dfrac{0.1+0.3}2\cdot2=0.4[/tex] (trapezoid with "bases" 0.1 and 0.3 and "height" 2)

The required probabilities are found using the  given graphs of the

probability distributions.

Response:

1) P(X< 5) is D) 0.7

2) The probability equal to 0.2 are;

The probabilities are given by the area under the curve of the graph of

the probability distribution, which are found as follows;

1) The given figure is a trapezium, which gives;

[tex]Area \ of \ a \ trapezium = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]

Where;

a, and b are the parallel sides of the trapezium

h = The height

Therefore;

[tex]P(X < 5) = \dfrac{5 + 2}{2} \times 0.2 = \mathbf{0.7}[/tex]

2) The probabilities equal to 0.2 are found as follows;

1) At P(X ≤ 2), the area is a triangle, which gives;

[tex]Area \ of \ a \ triangle = \mathbf{\dfrac{1}{2} \times Base \ length \times Height\sqrt{x}}[/tex]

[tex]P(X \leq 2) = \dfrac{1}{2} \times 2 \times 0.2 = \mathbf{0.2}[/tex]

2) At P(X ≥ 4), has a triangular area, which gives;

[tex]P(X \geq 4) = \mathbf{\dfrac{1}{2} \times 1 \times 0.4}= 0.2[/tex]

3) P(2 ≤ X ≤4) has a trapezoidal area, which gives;

[tex]P( 2 \leq X \leq 5) = \mathbf{\dfrac{0.2 + 0.4}{2}} \times 0.2 = 0.6[/tex]

P(2 ≤ X ≤4) = 0.6 ≠ 0.2

4) P(1 ≤ X ≤ 3) has a trapezoidal area, which gives;

[tex]P( 1 \leq X \leq 3) = \dfrac{0.1 + 0.3}{2} \times 2 = 0.4[/tex]

P(1 ≤ X ≤ 3)  = 0.4 ≠ 0.2

Therefore;

The probabilities that are equal to 0.2 are;

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Step-by-step answer:

The maximum and minimum values are the positive sum and difference of the two magnitudes.  The magnitude of u+v can range between these two limits, namely 5+4=9, and 5-4=1.

Therefore among the given choices, the possible values of u+v are 1 unit and 9 units.  11 and 13 are greater than the maximum so do not apply.

Answer:

1 unit

9 units

Step-by-step explanation:

PLATO

Answer:

option D

[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]

Step-by-step explanation:

Given in the question an expression,

[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}[/tex]

Step 1

Divide and multiple by [tex]\sqrt{x}+\sqrt{x-3}[/tex] to remove radical sign from denominator.

[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}*\frac{\sqrt{x} +\sqrt{x-3}}{\sqrt{x} +\sqrt{x-3}}[/tex]

Step 2

Apply a² - b² = (a+b)(a-b)

[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{\sqrt{x^{2}}-\sqrt{(x-3)^{2}}}}[/tex]

Step 3

[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{x-x+3}[/tex]

Step 4

[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{3}[/tex]

Step 5

[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]

No specific question was provided. Therefore, a clear question related to a specific subject and grade needs to be put forward for a detailed, example-filled explanation.

Since there is no specific question provided, it is not possible to provide an accurate and factual answer. Therefore, in order to give a comprehensive answer, a clear and specific question related to a given subject like Mathematics, History, English, Biology, Chemistry, Physics, etc., and grade (Middle School, High School, College) needs to be provided. Once the question is presented, I would be delighted to provide a detailed explanation, using relevant examples and details to help you understand the concept.

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ANSWER

See below

EXPLANATION

Given

[tex]f(x) = \frac{ {x}- 9 }{x + 5} [/tex]

and

[tex]g(x) = \frac{ - 5x - 9}{x - 1} [/tex]

[tex](f \circ \: g)(x)= \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5} [/tex]

[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} } [/tex]

Expand:

[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9x + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} } [/tex]

[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9x + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} } [/tex]

[tex](f \circ \: g)(x)= \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} } [/tex]

Since the denominators are the same, they will cancel out,

[tex](f \circ \: g)(x)= \frac{ - 14x}{ - 14} = x[/tex]

Answer:

141.12 cm^2

Step-by-step explanation:

   Since the area of a trapezoid is the average of the bases multiplied by the height, we can just plug these numbers into the equation! Since the average of 10.2 and 12.2 is 11.2, and the height is 12.6, we multiply them to get the area to be 141.12 cm^2.

Answer:

141.12cm^2

Step-by-step explanation:

I do not know if this is the correct way to do it, but I split the trapezoid in half, then putting it on top of each other to create a rectangle, which is (10.2cm+12.2cm)(12.6cm/2)

Answer:

L = 10, w = 17

Step-by-step explanation:

Area of a rectangle is A = Lw.  We are told that the width is 3 less than twice the length, so we will change the width into some expression in terms of the length.

w = 2L - 3 and

length = L.

Filling in the area formula now, knowing that the area is given as 170:

170 = (2L - 3)(L) so

[tex]170=2L^2-3L[/tex]

Get everything on one side of the equals sign and throw it into the quadratic formula to factor it and solve for the values of L.  When we do this we get that L = 10 and L = -8.5

Since the 2 things in math that will NEVER EVER be negative are time and distance/length measures, it is safe to disregard the -8.5.  Therefore,

if L = 10, then

w = 2(10) - 3 and

w = 17

Answer: OPTION C

Step-by-step explanation:

You need to use this formula for calculate the surface area of the right cylinder:

[tex]SA=2\pi r^2+2\pi rh[/tex]

Where "r" is the radius and "h" is the height.

You can identify in the figure that:

[tex]r=6units\\h=14units[/tex]

Knowing this, you can substitute these values into the formula [tex]SA=2\pi r^2+2\pi rh[/tex], therefore you get that the surface area of this right cylinder is:

[tex]SA=2\pi (6units)^2+2\pi (6units)(14units)[/tex]

[tex]SA=240\pi\ units^2[/tex]

Answer is C

A=2πrh+2πr^2

A=2π*6*14+2π*(6)^2

A=π*(2*6*14+2*6^2)= 240 π

Answer:

C

Step-by-step explanation:

The area of the sector and the whole circle are proportional to the central angles.

a / A = x / 360°

a = (x / 360°) A

So the answer is C.

Answer:

Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.

Step-by-step explanation:

The volume is given in terms of x as  [tex]V(x)=x^3-6x^2+8x[/tex].

We factor the GCF to get;

[tex]V(x)=x(x^2-6x+8)[/tex].

We split the middle term of the trinomial in the parenthesis.

[tex]V(x)=x(x^2-4x-2x+8)[/tex].

We now factor the expression within the parenthesis by grouping;

[tex]V(x)=x[x(x-4)-2(x-4)][/tex].

[tex]V(x)=x(x-2)(x-4)[/tex].

Since the width of the box is [tex]x-2[/tex] units, the linear expression for the height and length is [tex]x(x-4)[/tex]

Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.

Answer:

D) 168 ft3

Step-by-step explanation:

The formula to find the volume of a cone is V=π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex].

We need to plug in the radius, 4, and the height, 10, into this equation.

V=π[tex](4)^{2}[/tex][tex]\frac{10}{3}[/tex]

V=π16[tex]\frac{10}{3}[/tex]

V=π53.33

V=167.55

If we round up to the nearest whole number, we get 168 [tex]ft^{3}[/tex]. Therefore, the correct answer is D) 168 ft3.

I hope I helped!

The volume of a cone is calculated using the formula V = (1/3)πr²h. For a cone with a radius of 4 ft and a height of 10 ft, the volume rounds to approximately 168 ft³. Hence, the correct answer is D) 168 ft³.

The question asks for the volume of a cone with a radius of 4 ft and a height of 10 ft. The formula for the volume of a cone is V = (1/3)πr²h, where π (π approximately equals 3.14) is Pi, r is the radius of the base, and h is the height of the cone. Plugging the given values into this formula, we calculate the volume as follows:

V = (1/3)π(4 ft)²(10 ft) = (1/3) ∗ 3.14 ∗ 16 ft² ∗ 10 ft ≈ 167.55 ft³, which rounds to roughly 168 ft³.

Therefore, the correct answer is D) 168 ft³, rounding to the nearest cubic foot as requested.

Answer:

False

Step-by-step explanation:

The surface area of the cone is

[tex]V=\pi r^2 +\pi rl[/tex]

[tex]SA=\pi r^2 +\pi\times r\times 2r[/tex]

[tex]SA=\pi r^2 +2\pi\times r^2[/tex]

[tex]SA=3\pi r^2[/tex]

The surface area of the cylinder is:

[tex]SA=2\pi r^2 +2\pi rh[/tex]

[tex]SA=2\pi r^2 +2\pi\times r\times r[/tex]

[tex]SA=4\pi r^2 [/tex]

Answer:

we know that

surface area=2*area of the base+perimeter of base*height 

area of the base=b*h/2

b=8 ft

h=15 ft

so

area of triangle=8*15/2-------> 60 ft²

perimeter of base=a+b+c

a=15 ft

b=8 ft

c=?

applying the Pythagoras theorem

c²=a²+b²------> c²=15²+8²------> c²=225+64------> 289

c=√289------> c=17 ft

perimeter=15+8+17=40 ft

height of the prism=20 ft

surface area=2*60+40*20------> 920 ft²

the answer is the option

B. 920 ft 2

Answer: 30r

Step-by-step explanation:

2(8r2+r)-4r

2(17r)-4r

34r-4r

30r

Answer:

16r^2-2r

Step-by-step explanation:

2(8r^2+r)-4r

(16r^2 +2r)-4r               Distribute the 2

16r^2+(2r-4r)                Regroup like terms

16r^2-2r

Hope this helps!

Answer:

x = 58.0

Step-by-step explanation:

We can use the inverse of cos to solve for x once you set up the equation

[tex]cosx = \frac{9}{17}[/tex]

This is as 9 is the adjacent side and 17 is the hypotenuse of the triangle.

We can then solve for x using the inverse of cos

[tex]x= cos^{-1} (\frac{9}{17} )[/tex]

When plugged into a calculator you get

x= 58.03 degrees

this rounds to 58.0 degrees

Answer:

A. 176

Step-by-step explanation: First, to find the surface area to each triangle, you multiply the base times the height by 1/2. It is 28 for each triangle. Multiply that by 4, and you get 112. Then, the surface area of the square on bottom is 64. When added together, you get 176. No rounding needed. Hope it helped and is correct!

Answer:

Step-by-step explanation:

First, to find the surface area to each triangle, you multiply the base times the height by 1/2. It is 28 for each triangle. Multiply that by 4, and you get 112. Then, the surface area of the square on bottom is 64. When added together, you get 176. No rounding needed. Hope it helped and is correct!