A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the diameter of the tank in feet to the nearest tenth

Answer:

∠1

Step-by-step explanation:

we know that

An inscribed angle in a circle is formed by two chords that have a common end point on the circle

The measure of the inscribed angle is half of measure of the intercepted arc

In this problem

∠1 is an inscribed angle

∠2 is an outer angle

∠3 is an interior angle

∠4 is an semi-inscribed angle ( angle formed by a chord and a tangent)

Answer:

1. Tangent ray: a ray that lies on a tangent line and contains the point of tangency;

2. Intercepted arc: an angle intercepts an arc if the endpoints of the arc lie on the sides of the angle and all points of the arc except the endpoints lie in the interior of the angle;

3. Secant ray: a ray that lies on a secant line and contains both points of intersection with the circle; and

4. Inscribed angle: an angle with sides containing the endpoints of an arc and with a vertex that is a point of the arc other than an endpoint of the arc.

Answer:

10 yards and 1 feet

Answer:

10 yards + 1 ft

Step-by-step explanation:

Conversion :

3 feet = 1 yard

or

30 feet = 10 yards

notice that 31 ft = 30 ft + 1 ft

                          = 10 yards + 1 ft

Answer:

Step-by-step explanation:

The angle adjacent to the 106 degree angle is 180 degrees - 106 degrees, or 74 degrees.  Next, the adjacent angle to the 145 degree angle is 35 degrees; in other words, the two bottom angles of this triangle are 35 degrees and 35 degrees.  That means that a 35 degree angle is vertical angle to x, and so x is also 35 degrees.

The sum of the three interior angles is 35 degrees + 74 degrees and

Check the picture below.

let's recall that vertical angles, angles across a junction, are equal, namely the angle across the "x" is also "x".

Answer:

false

Step-by-step explanation:

It could be equal because what if the proportions are something like 2/3=3/2

In this case the product of both sides is 6.

B. False

When I say that the proportion is 2 ratios that are equal to each other, It mean this in the sense of 2 fractions being equal to each other.

Proportions could be written as equivalent fractions and as = ratios. When we  can say that the ratios in the proportion are =, we mean that we could multiply and divide 1 ratio by some constant to result in the other.

It can be equal because what if the proportions are something such as

2/3=3/2

In this case the product of both sides is 6.

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Answer:

The answer is 142°

Step-by-step explanation:

Because 38° and m∠2 are corresponding angles, m∠2 = 38°. Also, m∠2 and m∠5 are supplementary angles, which means the sum of their angles adds up to 180°. We can create the equation 38° + m∠5 = 180°. By subtracting 38° on both sides, we get m∠5 = 142°.

ANSWER

[tex](2,-10.75)[/tex]

EXPLANATION

The given function is

[tex]y = {x}^{2} - 4x - 7[/tex]

We rewrite this function to obtain,

[tex](y + 11) = {( x- 2)}^{2} [/tex]

We now compare this function to

[tex](y - k) = 4p {( x- h)}^{2} [/tex]

We have

[tex]4p = 1[/tex]

This implies that,

[tex]p = \frac{1}{4} [/tex]

The vertex is (2,-11).

The focus is

[tex](2,-11+ \frac{1}{4} )[/tex]

[tex](2,- \frac{43}{4} )[/tex]

[tex](2,-10.75)[/tex]

Answer:

Part 1) The amount invested in the first account at 7% was $4,400

Part 2) The amount invested in the second account at 12% was $4,200

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x------> the amount invested in the first account at 7%

(8,600-x) -----> the amount invested in the second account at 12%

in this problem we have

[tex]t=1\ year\\ P1=\$x\\ P2=\$8,600-x\\ I=\$812\\r1=0.07\\r2=0.12[/tex]

substitute in the formula above

[tex]812=x(0.07*1)+(8,600-x)(0.12*1)[/tex]

[tex]812=0.07x+1,032-0.12x[/tex]

[tex]0.12x-0.07x=1,032-812[/tex]

[tex]0.05x=220[/tex]

[tex]x=\$4,400[/tex]

so

[tex]8,600-x=\$8,600-\$4,400=\$4,200[/tex]

therefore

The amount invested in the first account at 7% was $4,400

The amount invested in the second account at 12% was $4,200

Answer:

$4,400 at 7%

$4,200 at 12%

Step-by-step explanation:

Let the amount invested in 7% be x, so,

amount invested in 12% would be "8600 - x"

We can now write an equation and solve for x:

[tex]0.07(x)+0.12(8600-x)=812\\0.07x+1032-0.12x=812\\-0.05x=-220\\x=\frac{-220}{-0.05}=4400[/tex]

Thus, the amount invested in 12% is  8600 - 4400 = 4200

So,

$4,400 at 7%

$4,200 at 12%

Answer:

well it's 9/25 or 0.36% or (36%) only

Step-by-step explanation:

So you add all the numbers up it would be 25, divide the numerator by the denominator and get 0.36%, i can't remember if you divide .36 by 100 or not but anyway you get 36%.

But I hope i have helped you in anyway.

Answer:

(x - 2) (x - 6)

Step-by-step explanation:

Factor the following:

x^2 - 8 x + 12

The factors of 12 that sum to -8 are -2 and -6. So, x^2 - 8 x + 12 = (x - 2) (x - 6):

Answer:  (x - 2) (x - 6)

The factors of the given polynomial are (x-6) and (x-2).

The given polynomial is x²-8x+12.

The factors are the polynomials which are multiplied to produce the original polynomial.

By splitting middle term method, we get

x²-6x-2x+12

x(x-6)-2(x-6)

(x-6)(x-2)

Therefore, the factors of the given polynomial are (x-6) and (x-2).

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Answer:

Option C is correct.

Step-by-step explanation:

Let x be the original width

then x+2 will be the length (consecutive odd integer)

if length is increased by 5 feet , length will be: (x+2)+5 = x+7

Area = 60 square ft.

Area = length * width

60 = (x+7) *x

60 = x^2 +7x

Rearranging

x^2 + 7x -60 = 0

Solving quadratic equation to find the value of x

using Quadratic formula

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

a=1, b =7, c=-60

[tex]x=\frac{-7\pm\sqrt{(7)^2-4(1)(-60)}}{2(1)}\\x=\frac{-7\pm\sqrt{49+240}}{2}\\x=\frac{-7\pm\sqrt{289}}{2}\\x=\frac{-7\pm17}{2}\\x=5 \,\, and \,\, x = -12\\[/tex]

Since width can be positive so x=5

length of original rectangle = x+2 = 5+2 =7

Area of original rectangle = Length * Width

Area of original rectangle = 5 * 7

Area of original rectangle = 35 ft^2

So, Option C is correct.

Final answer:

The width of the original rectangle is 5 feet, and the length is 7 feet, making the area 35 square feet. We determined this by setting up an equation for the area of the enlarged rectangle and solving for the odd integer width.

Explanation:

We are given that a rectangle has dimensions of consecutive odd integers and if the length is increased by 5 feet, the resulting area is 60 square feet. Let's denote the width as w feet (an odd integer) and the length as w + 2 feet (the next consecutive odd integer), since consecutive odd integers are two units apart.

After increasing the length by 5 feet, the new dimensions are w feet and w + 7 feet. The area can be calculated as the product of these dimensions:

w × (w + 7) = 60

Solving this quadratic equation: w² + 7w = 60

Subtracting 60 from both sides gives: w² + 7w - 60 = 0. Factoring this, we get: (w + 12)(w - 5) = 0

Considering the positive value that fits the condition of being an odd integer, we find that w = 5 feet. This makes the width 5 feet and the length 7 feet (5 + 2) for the original rectangle.

Thus, the area of the original rectangle is 5 feet × 7 feet = 35 square feet.

Therefore, the correct answer is C. 35 ft².

Answer:

The base of the cone is a circle of radius r. The height of the cone is the length h of the straight line from the cone's tip to the center of its circular base. Both ends of a cylinder are circles, each of radius r. ... For example, the volume of a cube is the area of one side times its height.

Step-by-step explanation:

Hope this helps! Please mark brainliest!

Answer:

The volume of a cone is one-third the volume of a cylinder.

Step-by-step explanation:

[tex]

L=25,W=105 \\

P=2L+2W=2(L+W)\Rightarrow P=2(25+105) \\

P=2\cdot130=\boxed{260}

[/tex]

Hope this helps.

r3t40

Answer:

(a) 38 inches (b) 374 inches (c) 3564 inches (d) 6273767 square inches

Step-by-step explanation:

a) 2 ft 5 inches + 9 inches

Convert to inches

1 feet = 12 inches

2 feet = 12 x 2 inches = 24 inches

24 inches + 5 inches + 9 inches = 38 inches

b) 4 yards 8 inches + 6 yards 6 inches

Convert to inches

1 yard = 36 inches

4 yards = 36 x 4 = 144 inches

144 inches + 8 inches = 152 inches

6 yards = 36 x 6 = 216 inches

216 inches + 6 inches = 222 inches

152 inches + 222 inches = 374 inches

c) 29 yard 2 feet 11 inches + 55 yard 1 feet 10 inches + 13 yard 1 feet 3 inches

Convert to inches

29 yard 2 feet 11 inches

1 yard =  36 inches

29 yards = 36 x 29 = 1044 inches

1 feet = 12 inches

2 feet = 12 x 2 = 24 inches

1044 + 24 + 11 = 1079 inches

55 yard 1 feet 10 inches

1 yard = 36 inches

55 yards = 26 x 55 = 1980 inches

1 feet = 12 inches

1980 + 12 + 10 = 2002 inches

13 yard 1 feet 3 inches

1 yard = 36 inches

13 yards = 13 x 36 = 468 inches

1 feet = 12 inches

468 + 12 + 3 = 483 inches

1079 + 2002 + 483 = 3564 inches

d) 4,839 sq yard 8 sq feet 139 sq inches + 7 sq feet 124 sq inches

Convert to square inches

4,839 sq yard 8 sq feet 139 sq inches

1 square yard = 1296 square inches

4839 x 1296 = 6271344 square inches

1 square feet = 144 square inches

8 x 144 = 1152

6271344 + 1152 = 6272635 square inches

7 sq feet 124 sq inches

7 x 144 = 1008

1008 + 124 = 1132 square inches

1132 + 6272635 = 6273767 square inches

!!

Answer:

6

Step-by-step explanation:

2+6=8

8+6=14

14+6=20

20+6=26

Answer:

The inputs to this formula are:

The equation of this line in point-slope form will be:

[tex]y - 4 = -2(x +11)[/tex].

Step-by-step explanation:

The general form of a 2D line in its point-slope form is:

[tex]l:\; y - y_0 = m(x - x_0)[/tex].

This form of the equation of a line takes two pieces of information:

For this line, the point [tex](x_0, y_0)[/tex] is [tex](-11, 4)[/tex].

The slope of this line is [tex]-2[/tex]. In other words,

Apply the point-slope formula for a 2D line:

[tex]l:\; y - 4 = -2 (x - (-11))[/tex].

[tex]l:\; y - 4 = -2 (x +11 )[/tex].

Answer:

3

Step-by-step explanation:

f(x) = 18x + 3x^2

f(x) =  3x^2+18x

Factor out a 3

     = 3(x^2 +6x)

Take the coefficient of x, divide by 2 and then square

6/2 = 3 3^2 =9

Remember the 3 out side 3*9 =27 so we are really adding 27

3(x^2+6x+9) -3*9

The number inside the parentheses added to x is b/2  or 6/2

3(x+3)^2 -27

Answer:

[tex]f(x)=3(x+3)^{2}-27[/tex]

Step-by-step explanation:

In the last step is missing the number 3 which is the second term of the binomial squared expression.

Basically, the complete step is

[tex]f(x)=3(x+3)^{2}-27[/tex]

As you can see, the three inside the parenthesis is the missing part in the last step.

Answer:

39

Step-by-step explanation:

The short answer is 39.

Every triangle has 180 degrees. There are no exceptions to this rule.

Since a triangle has 3 angles, all three together must add up to 180o

A right angle = 90 degrees always.

You are given 51 degrees as your second angle

The third one is x

x + 51 + 90 = 180                   Total of three angles must be 180

x + 141 = 180                           The left has been added to give 141

x = 180 - 141                            Subtract 141 from both sides

x = 39                                     The third angle = 39    

The calculated value of the variable A from the table of values is -3x²

How to determine the value of the variable A

From the question, we have the following parameters that can be used in our computation:

The contingency table

The cell A is in the row -x and the column 3x

This means that

A = 3x * -x

When the product is evaluated, we have

A = -3x²

Hence, the value of the variable A is -3x²

Answer:

table d is the proportional relationship

Step-by-step explanation:

Answer:

-1/2 , 0 , 3/2

Step-by-step explanation:

Given equation is:

[tex]4x^3-5x = |4x|[/tex]

We know that [tex]|x|=a\\The\ solution\ will\ be:\\x=a\ and\ x=-a\\[/tex]

So, from given equation,we will get two solutions:

[tex]4x^3-5x = 4x\\4x^3-5x-4x=0\\4x^3-9x=0\\x(4x^2-9) = 0\\x = 0\\and\\4x^2-9 = 0\\4x^2=9\\x^2 = \frac{9}{4} \\\sqrt{x^2}=\sqrt{\frac{9}{4} }\\[/tex]

x= ±√3/2 , 0

and

[tex]4x^3-5x = -4x\\4x^3-5x+4x=0\\4x^3-x=0\\x(4x^2-1) = 0\\x = 0\\and\\4x^2-1 = 0\\4x^2=1\\x^2 = \frac{1}{4} \\\sqrt{x^2}=\sqrt{\frac{1}{4} }[/tex]

x= ±1/2 , 0

We can check that 1/2 and -3/2 do not satisfy the given equation.

[tex]4x^3-5x = |4x|\\Put\ x=1/2\\4(\frac{1}{2})^3 - 5(\frac{1}{2}) = |4 * \frac{1}{2}|\\   4 * (\frac{1}{8)} - \frac{5}{2} = |2|\\ -2 = 2\\Put\ x=-\frac{3}{2} \\4(\frac{-3}{2})^3 - 5(\frac{-3}{2}) = |4 * \frac{-3}{2}|\\-6 = 6\\[/tex]

So, 1/2 and -3/2 will not be the part of the solution ..

So, the solutions in increasing order are:

-1/2 , 0 , 3/2 ..

Answer:

[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]

Step-by-step explanation:

We are given that an equation

[tex]4x^3-5x=\mid x\mid[/tex]

We have to find the solution of given equation and arrange the solution in increasing order.

[tex]4x^3-5x=4x[/tex]  when x >0

and [tex]4x^3-5x=-4x[/tex] when x < 0

because [tex]\mid x\mid =x when x > 0 [/tex]

                                     =-x when x < 0

[tex]4x^3-5x-4x=0[/tex]

[tex]4x^3-9x=0[/tex]

[tex]x(4x^2-9)=0[/tex]

[tex]x(2x+3)(2x-3)=0[/tex]

Using identity [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]x=0,2x+3=0,2x-3=0[/tex]

[tex]2x=3\implies x=\frac{3}{2}=1.5[/tex]

[tex]2x=-3 \implies x=-\frac{3}{2}=-1.5[/tex]

[tex]4x^3-5x=-4x=0[/tex]

[tex]4x^3-5x+4x=0[/tex]

[tex]4x^3-x=0[/tex]

[tex]x(4x^2-1)=0[/tex]

[tex]x(2x+1)(2x-1)=0[/tex]

[tex]x=0,2x+1=0[/tex]

[tex]2x-1=0[/tex]

[tex]2x-1=0[/tex]

[tex]2x=1 \ilmplies x=\frac{1}{2}=0.5[/tex]

[tex]2x+1=0[/tex]

[tex]2x=-1 \implies x=-\frac{1}{2}=-0.5[/tex]

When we substitute x=[tex]\frac{1}{2}[/tex]

[tex]4(\frac{1}{2})^3-\frac{5}{2}=\frac{1}{2}-\frac{5}{2}=\frac{1-5}{2}=-2[/tex]

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

[tex]-2\neq 2[/tex]

Hence, [tex]\frac{1}{2}[/tex] is a not solution of given equation.

When substitute [tex]x=\frac{-3}{2}[/tex]

[tex]4(\frac{-3}{2})^3+\frac{15}{2}=\frac{-27}{2}+\frac{15}{2}=\frac{-27+15}{2}=-6[/tex]

[tex]\mid 4(-\frac{3}{2}\mid=6[/tex]

[tex]-6\neq 6[/tex]

Hence, [tex]\frac{-3}{2}[/tex] is not  a solution of given equation.

Substitute x=[tex]-\frac{1}{2}[/tex] in the given equation

[tex]4(-\frac{1}{2})^3+\frac{5}{2}=-\frac{1}{2}+\frac{5}{2}=2[/tex]

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

[tex]2=2[/tex]

Hence, [tex]-\frac{1}{2}[/tex] is   a solution of given equation.

Substitute [tex]x=\frac{3}{2}[/tex] in the given equation

[tex]4(\frac{3}{2})^3-\frac{15}{2}=\frac{27-15}{2}=6[/tex]

[tex]\mid 4(\frac{3}{2})\mid =6[/tex]

[tex]6=6[/tex]

Hence, [tex]\frac{3}{2}[/tex] is a solution of given equation.

Answer:[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]

The index of a radical is the number indicating what root of a given number should be taken. In the expression '4 radical 8', '4' is the index of the radical, meaning the expression represents the fourth root of 8.

In the expression '4 radical 8', '4' is referred to as the index of the radical. The index of a radical is the number that denotes what root of the number is to be taken. For example, an index of 2 (which is often not written) refers to a square root, an index of 3 refers to a cube root, and so on. In this case, since the expression is '4 radical 8', it means we are looking at the fourth root of 8.

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In 4 radical 8, the given index of the radical 4, means we are looking for a number that, when raised to the power of 4, gives us 8.

The index of a radical is the number that is written just above and to the left of the radical symbol. In your problem, 4 radical 8, the number 4 is the index of the radical. So, the index of the radical in 4 radical 8 is 4. This means that we are looking for a number that, when raised to the power of 4, gives us 8.

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Answer: x = 2

Step-by-step explanation:

3x2 - 6 = 10 - x2

       +6   +6

3x2 = 16 - x2

+x2         +x2

4x2 = 16

4/4     16/4

x2 = 4

√x2 = √4

x = 2

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[tex]\bf \cfrac{2}{5}\div\cfrac{7}{9}=N\implies \cfrac{2}{5}\cdot \cfrac{9}{7}=N\implies \cfrac{18}{35}=N\implies 0.514\approx N \\\\[-0.35em] ~\dotfill\\\\ \boxed{0}\rule[0.35em]{10em}{0.25pt}\stackrel{N}{0.514}\rule[0.35em]{9em}{0.25pt}\boxed{1}[/tex]

Hello There!

WHAT WE KNOW  Levi reads 280 words in 2 minutes. We need to find out how many words he can read in 5 minutes

To find out how many words Levi can read in 5 minutes, it will first be easier to find out how many words Levi can read in 1 minute. To find this, we will divide 280 by 2 and that will give us the number of words per minute.

Next, once we divide we will get a quotient of 140.

Finally, we take 140 and multiply it by 5 and we get a product of 700

Therefore, Levi reads 700 words in 5 minutes

Answer:

[tex]2x^2+7x-4[/tex]

Answer:

2x² + 7x - 4

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x + 4) - 1(x + 4) ← distribute both parenthesis

= 2x² + 8x - x - 8 ← collect like terms

= 2x² + 7x - 8

Answer:

4th option

Step-by-step explanation:

Solve and rearrange the second equation for y

y= 2 +3

y =5

The substitute y in first equation to get x

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes, hence

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line.

To find c substitute (- 8, - 18) into the partial equation

- 18 = - 6 + c ⇒ c = - 18 + 6 = - 12

y = [tex]\frac{3}{4}[/tex] x - 12 ← equation of parallel line

Answer:

Step-by-step explanation:

The equation of a linear function in point-slope form is y – y1 = m(x – x1)

The point is A (x1 , y1)  

the slope is : m     the line that is parallel to the given line so : m = 3/4

passes through the given point (-8 -18)

so :  x1 = - 8   and y1 = -18

an equation is : y +18= 3/4(x +8)

Using the Pythagorean theorem a^2 + b^2 = c^2, where a and b are the sides and c is the hypotenuse, we can find the length needed.

6^2 + 8^2 = c^2

Simplify:

36 + 64 = c^2

100 =c^2

Take the square root of both sides:

c = √100

c = 10

The hypotenuse is 10 meters.

Answer:

It is just right

Step-by-step explanation:

Kermit's fav = 15 tea bags every 2 liters = 15/2 = 7.5 teabags per liter

Peggy made 90 teabags in 12 liters = 90/12 = 7.5 teabags per leter

Hence peggy used the same teabags per liter than kermit's favorite. It is just right.

edit: calculation error. corrected.

Your answer would be C:Just right.

Because:

2 liters of water = 15 tea bags

15/2 = 7.5 tea bags

Peggy needs to make 12 liters

12 x 7.5 = 90 tea bags

Conclusion:

Peggy's 12-liter batch of iced tea with 90 tea bags is JUST RIGHT.

Hope helps!-Aparri

lcd 210

1/5=42/210

1/7=30/310

3/21=30/210

42+30+30=102/210

reduced 51/105

The sum of the fractions 1/5, 1/7 and 3/21 is 17/35. This was achieved by finding the least common denominator (LCD), converting the fractions to have the LCD, adding them, and then simplifying the result.

To add or subtract fractions, it's essential to find the least common denominator (LCD). The LCD in this case would be the least common multiple (LCM) of 5, 7, and 21, which is 105. Once we have the LCD, we can rewrite the fractions as an equivalent fraction with the LCD as the denominator:

Now all the fractions have the same denominator, and we can combine the numerators: 21/105 + 15/105 + 15/105 = 51/105. However, this can be simplified to 17/35 by dividing both numerator and denominator by 3.

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