Region R is bounded by the curves y = 4x^2 and y = 4. A solid has base R, and cross sections perpendicular to the y-axis are semicircles with the diameter lying in R. The volume of this solid is
A. pi/4
B. pi/2
C. pi
D. 2pi

Answer:

the answer= y=5−x/2

Answer: [tex]y=-\frac{1}{2} x+5[/tex]

Step-by-step explanation:

We need to isolate y by itself

Step 1) Subtract 3x from both sides

[tex]3x+6y=30\\3x-3x+6y=30-3x\\6y=30-3x[/tex]

Step 2) Divide both sides by 6 to isolate y

[tex]6y=30-3x\\\frac{6y}{6} =\frac{30}{6}-\frac{3x}{6} \\y=5-\frac{1}{2}x[/tex]

Step-by-step explanation:

Substitute y = 4 into the first equation:

[tex]4=2x^2+x-6[/tex]

Subtract 4 from both sides:

[tex]2x^2+x-10=0[/tex]

We can factor in order to find values of x.

Factor the equation:

[tex]2x^2+x-10=0[/tex]

Factors of 10 we'll use:

5 and 2.

[tex](2x+5)(x-2)=0[/tex]

Set the parentheses equal to 0 then find the values of x:

[tex](2x+5)=0[/tex]

[tex]x=-2\frac{1}{2}[/tex]

[tex](x-2)=0[/tex]

[tex]x=2[/tex]

[tex]x=2, \: or \: -2\frac{1}{2} .[/tex]

Check:

[tex]4=2(2)^2+2-6[/tex]

[tex]4=2(4)+2-6[/tex]

[tex]4=4 \: \checkmark[/tex]

[tex]4=2(-2\frac{1}{2} )^2-2\frac{1}{2} -6[/tex]

[tex]4=2(6\frac{1}{4})-2\frac{1}{2} -6[/tex]

[tex]4=12\frac{1}{2} -2\frac{1}{2} -6[/tex]

[tex]4=10-6[/tex]

[tex]4=4 \: \checkmark[/tex]

[tex] \Large{\boxed{\sf x = -15}} [/tex]

[tex] \\ [/tex]

Given equation:

[tex] \sf 9 - 3x = 54 [/tex]

[tex] \\ [/tex]

Subtract 9 from both sides:

[tex] \sf 9 - 3x - 9 = 54 - 9 \\ \\ \sf -3x = 45 [/tex]

[tex] \\ [/tex]

Divide each side by -3 :

[tex] \sf \dfrac{-3x}{-3} = \dfrac{45}{-3} \\ \\ \\ \boxed{\boxed{\sf x = -15}} [/tex]

[tex] \\ \\ [/tex]

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If x = 1/4 and Y = 3/7

Evaluate the following expression: 7x - 4y

[tex] \\ [/tex]

[tex] \rm{7 ( \frac{1}{4}) - 4( \frac{3}{7} ) } \\ [/tex]

[tex] \rm { \orange{7 \times \frac{1}{4} }} - 4 \times \frac{3}{7} \\ [/tex]

[tex] \rm{ \frac{7}{4} - \orange{ 4 \times \frac{3}{7 }} } \\ [/tex]

[tex] \rm \orange{ \frac{7}{4} - \frac{12}{7} } \\ [/tex]

[tex] = \small{\boxed{{\sf{ \frac{1}{28} }}}}[/tex]

Therefore, the answer is 1/28.

Answer:

Step-by-step explanation:

[tex]\text{Substitute the values of x and y in the expression}[/tex]

[tex]7x - 4y = 7*\dfrac{1}{4}-4*\dfrac{3}{7}[/tex]

            [tex]\sf =\dfrac{7}{4}-\dfrac{12}{7}\\\\ [LCM \ of 4 \ and \ 7 = 28]\\\\ =\dfrac{7*7}{4*7}-\dfrac{12*4}{7*4}\\\\=\dfrac{49}{28}-\dfrac{48}{28}\\\\=\dfrac{1}{28}[/tex]

Answer:

94 Wins

Step-by-step explanation:

Here we need to find the mean, to do this we add up all the values then divide the sum by how many values we started out with.

97 + 103 + 92 + 95 + 84 = 471

471 / 5 = 94.2

since we got a decimal we can round to find an exact number; since the decimal is under .5 we will round down, 94

So 94 wins would be the correct answer. Hope this helped!

Answer:

4(3x-y)

Step-by-step explanation:

Given:

[tex]\displaystyle \large{3(3x-y)-(y-3x)}[/tex]

To factor this kind of expression, first, find the common factor.

[tex]\displaystyle \large{3(3x-y)-(-3x+y)}\\\displaystyle \large{3(3x-y)+(3x-y)}[/tex]

Notice that in the expression, we have both same (3x-y). Therefore, (3x-y) is our factor.

Let u = 3x-y

[tex]\displaystyle \large{3u+u}\\\displaystyle \large{4u}[/tex]

Change u back to 3x-y:

[tex]\displaystyle \large{4(3x-y)}[/tex]

Therefore, the factored expression is 4(3x-y).

Answer:

n=3.3

Step-by-step explanation:

9n²-10=890    1. + 10 on both sides

9n² = 900

[tex]9n²[/tex]= 9n

[tex]900[/tex] = 30

9n=30  2. /9 on both sides

n=3.33

the 3's repeat

The probability that the next three guests in the movie theater will get a soda, when the probability of getting a soda at the movie theater is 70% is 0.343 or 34.3%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

The probability of getting a soda at the movie theater is 70%.

[tex]P=70\%\\P=\dfrac{70}{100}\\P=0.7[/tex]

By the chain rule, the probability of getting the soda to the next 3 guest is equal to the cube of the probability of getting a soda at the movie theater.

Thus, the probability that the next three guests in the movie theater will get a soda is,

[tex]P^3=0.7^3\\P^3=0.343[/tex]

Thus,the probability that the next three guests in the movie theater will get a soda, when the probability of getting a soda at the movie theater is 70% is 0.343 or 34.3%.

Learn more about the probability here;

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Answer: C: -4, -6 B:-14, -6 A:-14, -18

Step-by-step explanation: Multiply all of your points by 2

Answer:

Step-by-step explanation:

Tan 70 = 16/x

x = 16/tan70

x = 5.824 to the nearest thousandth

tan 41 = 16 / (x + y)

tan 41 = 16 /(5.8235 + y)

tan41(5.8235 + y) = 16

5.8235 + y = 16/ tan41

y = (16/ tan41) - 5.8235

y = 12.582 to the nearest thousandth

Answer:

area of the four walls

= a^2 x 4

Answer:

0

Step-by-step explanation:

→ First find inverse cosine 1/2

60°

→ Now multiply this answer by 3 because then if you substitute it in you get 0.5

∝ = 180°

→ Now find sine of 180°

0

Answer:

Step-by-step explanation:

Boys Girls

84 50

%decrease %decrease

-25% -16%

84=100% 50=100%

75% 84%

75/100×84 84/100×50

=63 =42

84+50=134

63+42=105

134-105=29

134=100%

29

29/134×100

21.6%

Answer:

y = -3/4x - 1/2

Step-by-step explanation:

Given:

Point 1: (1, -4)

Point 2: (3, -5)

Find:

The equation for the line that passes through Point 1 & Point 2

Solution:

y = mx + b

Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept

m = ( y2 - y1 ) / ( x2 - x1 ) = ( -5 - (-4) ) / ( 3 - 1 ) = -1 / 2

∴ m = - 1/2

Using either P1 or P2, plug in one of their respective x- and y-values into:

y = -1/2 x + b

I'll do (3, -5):

-5 = -1/2 ( 3 ) + b

-2 = -3/2 + b

-4 = -3 + 2b

-1 = 2b

∴ b = -1/2

∴ y = -3/4x - 1/2 is the equation of the line that passes thru both points (-5, 4) and (3, -2)

Answer:

Your answer(s) is $1,706.67, $1,462.86, or $1,280

Step-by-step explanation:

This really varies based on whether you take $80 as equal to 6 people, 7 people, or 8 people.

I'll list all three explanations and you can choose one.

6 people: 1,706.67 (rounded to nearest cent)

128 ÷ 6 = 21.33333333

21.33333333 × 80 = 1,706.67

7 people: 1,462.86 (rounded to nearest cent)

128 ÷ 7 = 18.28571428571429

18.28571428571429 × 80 = 1,462.86

8 people:

128 ÷ 8 = 16

16 × 80 = 1,280

Answer:

f<25, she can make less than 25 flowers to have enough time, (I think the inequalitie sign should have a line underneath it tho meaning, less than or equal to 25 flowers, which would only make sense)

Step-by-step explanation:

First you need I subtracted 15 from 90 which got me 75.

15 + 3f<90

-15       -15

_________

0           75

3f<75

__

3f  

75 divided by 3f= 25

Answer:

42 degrees

Step-by-step explanation:

The measure of the indicated angle is 42 degree.

An isosceles triangle has two equal sides regardless of the direction the apex (or peak) of the triangle points. Some useful information regarding isosceles triangles is as follows:

We have a Triangle.

Then, using Isosceles Triangle Theorem

Angles opposite an isosceles triangle's equal sides are also equal.

According to the isosceles triangle theorem, if two sides of a triangle are congruent, then the angles opposite the congruent sides are likewise congruent.

So, x= 42 degree.

Learn more about Isosceles Triangle Theorem here:

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Answer:

10 cm

Step-by-step explanation:

the can is shaped like a cylinder

first step is to find the radius and then multiply the figure by 2

volume of a cylinder = nr^2h

n = 22/7

r = radius

903 = 11.5 x r^2 x 3.14

r^2 = 903 / (3.14 x 11.5)

r = 5 cm

diameter = 10cm

Given the method given to calculate an outlier, the method does not identify 7.5 miles as an outlier.

An outlier is either very much larger or smaller than the rest of the data in the dataset.  In this dataset: 1, 2, 1000. 1000 is an outlier.

Outlier = 1.5 x interquartile range

Interquartile range = q3 - q1

1.5 x (3.8 - 2.6) = 1.8

To learn more about outliers, please check: https://brainly.com/question/27197311

Answer:

2 inches

Step-by-step explanation:

If 10 inches of snow fell each hour, then you divide that by five hours to get your average, which then equals 2.  So your answer is 2 inches per hour.

I hope this answered your question and helped you :)

Answer:

Looking at the graph it looks like 5 inches in 2 1/2 hours

Hope this helps :)

Answer: 3p

Step-by-step explanation: The reason is because -3 + 6 = 3, therefore -3p + 6p = 3p. I hope this helped! If I did anything wrong then please let me know! :)

[tex] - 3p + 6p[/tex]

first you'll have to combine light terms, both are light terms so,

[tex] - 3p + 6p[/tex]

[tex] =3p[/tex]

Answer:

65%

Step-by-step explanation:

set a porportion

245 =x

377  100

245x100= 24500/377  = 64.9 rounded = 65%

Considering the situation described, it is found that Ashton was born on August 8.

It means that August 31 was on Monday, hence the same is valid for August 24, August 17, August 10 and August 3.

Hence, the first Saturday was August 1, and the second August 8.

A similar problem, involving the interpretation of a situation, is given at https://brainly.com/question/25537936

Answer:

Quadrant III

Step-by-step explanation:

sin and cos are both less than zero thus negative

the x and y axis are both negative in QIII

sorry if the explaination is wrong but I know the answer is right bc I took the test

Hello! Mikosan here to help doll!

The Answer is: Quadrant 3

I hope this helps doll!

Have a great day love~

Answer:

Step-by-step explanation:

Cost = 2.49 * y

You really should spend the time. Math is used everywhere.

Step-by-step explanation:

please mark me brilliant

Step-by-step explanation:

5. θ = 60°

→ To find the value of y ,

Cos θ = b/h

putting the values in terms of cos

Cos 60° = y/16

1/2 = y/16

16/2 = y

y = 8 unit

→ To find the value of x ,

Sinθ = P/h

putting the values in terms of sin

Sin60° = x/16

√3/2 = x/16

16×√3/2 = x

16×1.73/2 13.84 unit

6. θ = 30°

→ To find the value of y

tanθ = p/b

putting the values in terms of tan

tan 30° = 2/y

1/√3 = 2/y

2×√3 = y

3.46 unit = y

→ To find the value of x

Sin θ = p/h

putting the values in terms of sin

Sin 30° = 2/x

1/2 = 2/x

4 unit = x

Answer:

9

Step-by-step explanation:

Since Area = L × W

Thus,

Area = (x + 2)(2x - 5) = 56

x^2 +4x - 5x - 10 = 56

x^2 - x - 10 = 56

x^2 - x - 66

Using the quadratic formula:

a = 1

b = - 1

c = - 66

Solving:

[tex]\frac{x = (-b) +/- sqrt(b^2 - 4ac)}{2a}[/tex]

[tex]\frac{x = 1 + /- sqrt(1^2 - 4(1)(-66)}{2(1)}[/tex]

[tex]\frac{1 +/- sqrt (265)}{2}[/tex]

17.279/2

8.639

Round = 9

~Lenvy~

Answer:

249 centimeters squared

Step-by-step Explanation:

The area of the rectangle: l x w, where l is the length and w is the width.

= 15.5 x 18

= 279

Area of the smaller rectangle: l x w, where l is the length and w is the width.

= 4 x 7.5

= 30

We do not need this 30.

Area of the shaded region:

= 279 - 30

= 249 cm²

Answer: 15ft or 7(2)

Step-by-step explanation:

The opposite side or the side standing up is the "x" side the hypotenuse is double the size of the opposite in a 30-60-90.