Which expressions are equivalent?

3x - 7y and -7y + 3x
3x - 7y and 7y - 3x
3x - 7y and 3y - 7x
3x - 7y and -3y + 7x

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:

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:

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!

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:

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:

Its C just got it right.

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

Given that at the end of each semester in college, a survey is given to students to get feedback on the course. One of the questions on the survey is shown below.

The course met my expectations.

1. Strongly Agree

2. Slightly Agree

3. Agree

4. Slightly Disagree

5. Strongly Disagree

The problem in this survey is the difference in people's mind set about saying the answer. One person may say strongly agree for agree also while other person may do the reverse.

Hence option C is right

C. The answer choices could be interpreted differently by different students.

Answer:

4.62%

Step-by-step explanation:

To find the percentage of patient with AB blood type, we would need:

If you see the Row labeled "AB" and go to the last column labeled "Total", we can see that 33 patients have blood type AB.

If you look at the right most block, we see the grand total of all patients of all blood types, which is 714 patients.

To find our answer, we divide 33 by 714 and multiply by 100 to get percentage.

Percentage of patients with blood type AB = [tex]\frac{33}{714}*100=4.62[/tex]

Answer:

4.6%

Step-by-step explanation:

To find the percentage of patient with AB blood type, we would need:

total number of patients with blood type AB

total number of all patients of all blood types

(33/714)* 100 = 4.6%

Answer:

1,560

Step-by-step explanation:

156=2

2x10=20

156x10=1560

Answer:156 times 10 thats your answer

Step-by-step explanation:

Answer: Third Option

-2

Step-by-step explanation:

I want to find the minimum value of a function with the form

[tex]y = asin (x-c)[/tex]

But we do not know the value of the coefficient "a", which is the amplitude, nor of the constant c.

However, in the attached graph we have the function.

The minimum value of a function is the lowest value of the variable y that the function can reach.

Observe in the graph that the function is periodic and reaches its maximum value at [tex]y = 2[/tex] and its minimum value at [tex]y = -2[/tex]

Therefore the minimum value would be [tex]y = -2[/tex]

Answer:

y = 8

Step-by-step explanation:

Since the 2 triangles are similar then the ratio of corresponding sides are equal, that is the sides 15 and 10 and y + 4 and y, thus

[tex]\frac{15}{10}[/tex] = [tex]\frac{y+4}{y}[/tex] ( cross- multiply )

10(y + 4) = 15y ← distribute left side

10y + 40 = 15y ( subtract 10y from both sides )

40 = 5y ( divide both sides by 5 )

8 = y

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:

N=N(sub o)e^-kt  

N/N(sub o)=e^-kt  

70/100=e^-kt  

ln .7=-.0001t  

t=ln .7/-.0001

ur welcome that is your Answer.

Step-by-step explanation:

Answer:

Final answer in simplified form is [tex]9x^2-4x+5 [/tex]

Step-by-step explanation:

Given expression is [tex](x+2)-(-9x^2+5x-3) [/tex]

Now we need to find an equivalent expression for[tex](x+2)-(-9x^2+5x-3) [/tex]

First we can distribute the negative sign and remove the parenthesis the combine like terms

[tex](x+2)-(-9x^2+5x-3) [/tex]

[tex]=x+2+9x^2-5x+3 [/tex]

[tex]=9x^2+x-5x+2+3 [/tex]

[tex]=9x^2-4x+5 [/tex]

Hence final answer in simplified form is [tex]9x^2-4x+5 [/tex]

Secant sec(x) = 1/cos

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:

C

Step-by-step explanation:

Given

cosB = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{A B}[/tex] = [tex]\frac{255}{257}[/tex]

Then the hypotenuse AB = 257 and BC = 255

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{255}{257}[/tex]

A = [tex]sin^{-1}[/tex] ([tex]\frac{255}{257}[/tex]) = 82.8° → C

Answer:

P(A ∩ B) = 11/15 ⇒ answer A

Step-by-step explanation:

* Lets revise the meaning of ∪ and ∩

# A ∪ B means all the elements in A or B without reputation

- Ex: If A = {2 , 3 , 5} and B = {3 , 4 , 7}

∴ A ∪ B = {2 , 3 , 4 , 5 , 7} ⇒ we don't repeat the element 3

# A ∩ B means all the elements in A and B

- Ex: If A = {2 , 3 , 5} and B = {3 , 4 , 7}

∴ A ∩ B = {3}

- From the examples above

∵ n(A) = 3 and n(B) = 3

∵ n(A ∪ B) = 5

∵ n(A ∩ B) = 1

∴ n(A) + n(B) = n(A ∪ B) + n(A ∩ B)

* Now lets solve the problem

∵ P(A ∪ B) = 11/15

∵ P(x) = n(x)/total

- That means the total elements in the problem is 15 and n(A ∪ B) is 11

∴ n(A ∪ B) = 11

∵ P(A) = 2/3 ⇒ simplest form

- To find P(A) without simplification and you now the total is 15

  then multiply up and down by 5

∴ P(A) = (2×5)/(3×5) = 10/15

∴ n(A) = 10

∵ P(B) = 4/5 ⇒ simplest form

- To find P(B) without simplification and you now the total is 15

  then multiply up and down by 3

∴ P(B) = (4×3)/(5×3) = 12/15

∴ n(B) = 12

- To find n(A ∩ B) use the rule above

∵ n(A) + n(B) = n(A ∪ B) + n(A ∩ B)

∵ 10 + 12 = 11 + n(A ∩ B) ⇒ subtract 11 from both sides

∴ 11 = n(A ∩ B)

- The number of elements in A ∩ B is 11

∵ P(A ∩ B) = n(A ∩ B)/total

∴ P(A ∩ B) = 11/15

Answer: [tex]JK=8[/tex]

Step-by-step explanation:

You can observe in the figure that JK is a tangent and KH is a secant and both intersect at the point K. Then, according to the Intersecting secant-tangent Theorem:

[tex]JK^2=KE*KH[/tex]

You know that:

[tex]KH=KE+HE[/tex]

Then KE is:

[tex]KE=KH-HE[/tex]

[tex]KE=16-12[/tex]

[tex]KE=4[/tex]

Now you can substitute the value of KE and the value of KH into  [tex]JK^2=KE*KH[/tex] and solve for JK. Then the result is:

[tex]JK^2=4*16\\JK^2=64\\JK=\sqrt{64}\\JK=8[/tex]

Both intersecting point K, JK is a tangent and KH is a secant. You can use the intersecting secant-tangent Theorem:

JK^2=KH*EK

First you can do

KH=EK+EH

KE=4

Then you can substitute.

JK^2=64

JK=8

Answer:

It would take Jenny 20 minutes to walk 1 mile

Step-by-step explanation:

To find how many minutes it would takes her to walk 1 mile, you have to find out the rate of her walking 2.5 miles.

So divide 2.5/50

She walked 0.05 miles per minute

there are 20 0.05 in one mile so

It would take Jenny 20 minutes to walk 1 mile

Hope this helps! If you don't mind, please mark as brainliest! Thx! :)

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.

Answer:

  $328.95

Step-by-step explanation:

By the Pythagorean theorem, the diagonal of the garden has a length that is the root of the sum of the squares of the side lengths:

  d = √(77² +36²) = √7225 = 85

Then the cost of the fence is the product of this number of feet and the cost per foot:

  (85 ft)·($3.87/ft) = $328.95

The total cost of the length of the fence is $328.95

The garden is in the form of a rectangle. A line that divides the rectangle from one corner to the other corner is known as an hypotenuse. The hypotenuse divides the rectangle into two right-angles triangles. The length of the hypotenuse has to be first determined using Pythagoras theorem.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

77² + 36²

5929 + 1296 =7225

√7225 = 85 feet

Cost of the total length of the fence = length of fence x cost per foot

$3.87 x 85 = $328.95

To learn more about Pythagoras theorem, please check: brainly.com/question/20936855?referrer=searchResults

The answer is x=8.6 units

After simplifying the fraction, we find that x = 7/17.

In
ΔABC, J is on AB, K is on BC, and JK is parallel to AC. We're given that JB = 5, AJ = 17, BK = x+4, and KC = 5x. By the properties of parallel lines and similar triangles, we can state that ΔAJK ~ ΔACB. Considering the sides of these triangles, the ratios of corresponding sides must be equal, which gives us the proportion:

AJ/JB = AC/BC

Substituting in given values and variables, we get:

17/5 = (17 + 5)/(5x + x + 4)

Solving for x, we multiply each side by the denominators to eliminate the fraction:

17(5x + x + 4) = 5(22)

85x + 17x + 68 = 110

102x + 68 = 110

102x = 42

x = 42/102

x = 7/17

After simplifying the fraction, we find that x = 7/17.

Answer:

Step-by-step explanation:

It's a quadratic function. The graph is a parabola.

The coefficient of x² is equal 1 > 0. Therefore the parabola is open up.

Conclusion: The minimum is in a vertex.

[tex]f(x)=ax^2+bx+c\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a},\ k=f(h)[/tex]

We have

[tex]g(x)=x^2-6x-12\to a=1,\ b=-6,\ c=-12\\\\h=\dfrac{-(-6)}{2(1)}=\dfrac{6}{2}=3\\\\k=g(3)=3^2-6(3)-12=9-18-12=-21\\\\(3,\ -21)-vertex[/tex]

Answer:

  5

Step-by-step explanation:

Vertices are where edges meet. Count the circles on the diagram below.

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:

x=54

Step-by-step explanation:

Because one side of the triangle is tangent (touching) to the circle while the other is the radius itself, we can conclude that the angle that is not named is 90°.

Knowing this, we can then add 36° and 90° to get 126°.

All of the angles in a triangle add up to 180°; therefore, we can subtract 126° from 180° to get 54°.

I really hope this helps and explains it well!

Answer:

x = 54°

Step-by-step explanation:

Since the lower segment is a tangent to the circle then

the angle between the tangent and the diameter is right.

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 known angles from 180 for x, that is

x = 180° - (90 + 36)° = 180° - 126° = 54°

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:

The correct answer option is D) 2.

Step-by-step explanation:

We are given the value of x and f(x) in a table and we are to find the average rate of change for the given function from x = 1 to x = 4.

To find that, we will calculate the ration of change in y to change in x.

Average rate of change = [tex] \frac { 1 0 - 0 } { 4 - ( - 1 ) } = \frac { 1 0 } { 5 } [/tex] = 2

The average rate of change of the function from x = 1 to x = 4 is calculated by subtracting the function values at these points and dividing by the difference in x-values, which results in 2.

To calculate the average rate of change, you subtract the values of the function at the two points, and then divide by the difference in the x-values. For the function given with range x = 1 to x = 4, the average rate of change is calculated as follows:

[f(4) - f(1)] / (4 - 1) = (10 - 4) / (4 - 1) = 6 / 3 = 2.

Therefore, the average rate of change for the specified range is 2

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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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