Which geometric object is defined as the set of all points in a plane equidistant from a single point and a single line

Answer:

Part a) [tex]V=1,000\ ft^{3}[/tex]

Part b) [tex]h=5\ ft[/tex]

Part c) [tex]=718\ gal[/tex]

Step-by-step explanation:

Part a) What is the volume of your friend's swimming pool?

we know that

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

substitute the values

[tex]V=(25)(8)(5)=1,000\ ft^{3}[/tex]

Part b) Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool?

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]V=1,000\ ft^{3}[/tex]

[tex]r=16/2=8\ ft[/tex] ----> the radius is half the diameter

substitute and solve for h

[tex]1,000=\pi (8)^{2} h[/tex]

[tex]h=1,000/(64 \pi)[/tex]

[tex]h=1,000/(64*3.14)=5\ ft[/tex]

Part c) While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool?

remember that

[tex]1\ ft=12\ in[/tex]

so

[tex]6\ in=6/12=0.5\ ft[/tex]

Find the volume of water  for [tex]h=5-0.5=4.5\ ft[/tex]

[tex]V=(3.14)(8)^{2}(4.5)=904.32\ ft^{3}[/tex]

so

the volume of water evaporated is equal to

[tex]1,000\ ft^{3}-904.32\ ft^{3}=95.68\ ft^{3}[/tex]

convert to gallons

remember that

[tex]1\ ft^{3}=7.5\ gal[/tex]

so

[tex]95.68\ ft^{3}=95.68*7.5=718\ gal[/tex]

a. The volume of the rectangular prism is 1000 cubic feet. b. The height of the cylindrical pool is 4 feet. c. About 750 gallons of water evaporated from the pool.

a. The volume of the rectangular prism can be found by multiplying the length, width, and height. So, the volume is 25 * 8 * 5 = 1000 cubic feet.

b. Since the two pools have the same volume, we can use the formula for the volume of a cylinder (V = πr²h) to find the height of the cylinder. We know the diameter is 16 feet, so the radius is half of that, which is 8 feet. Plugging it into the formula, 1000 = 3.142 * 8² * h. Solving for h, we find h = 4 feet.

c. To find the gallons of water evaporated, we need to convert the units. 6 inches is 0.5 feet. The volume evaporated is 25 * 8 * 0.5 = 100 cubic feet. Since 1 cubic foot is equal to 7.5 gallons, the amount evaporated is 100 * 7.5 = 750 gallons.

Answer:

126.

Step-by-step explanation:

This is the number of combinations of 4 cards  from 9 cards:

= 9C4

= 9! / 4! 5!.

A quick way of calculating this is  

9*8*7*6

----------- =   9*2*7   =    126 combinations.

4*3*2*1

There are 126 different 4-card combinations possible when selecting 4 cards from a shuffled stack of 9 different cards.

To find out how many different 4-card combinations are possible from a stack of 9 different cards when 4 cards are turned face up, we need to use combinatorial mathematics. The formula needed here is the combination formula, which for selecting r items from a set of n items is given by C(n, r) = n! / (r!(n-r)!), where '!' denotes factorial.

Substituting the given values, we get C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9×8×7×6) / (4×3×2×1) = 3024 / 24 = 126. So, there are 126 different combinations of 4 cards that can be turned face up from a shuffled stack of 9 different cards.

Answer

Please see attached image for full understanding of the solution

If we plot the function we can see that it has a discontinuity at x = 1.

Also,

If we evaluate at x = -9, we see that the values of the piecewise function in both cases are completely different.

Therefore, x = -9 is also a discontinuity.

The right answer is option a

(discontinuity at x = 1 and x = -9)

Answer:

C

Step-by-step explanation: EDGE 2020

Answer:

1 3/16

Step-by-step explanation:

5/16 + (7/8= 14/16)

14/16 + 5/16= 19/16

16/16 = 1

3 LEFT OVER

1 3/16

Answer:

He caught 1 3/16 pounds of fish.

Minimum weight = 13/16 pounds.

Step-by-step explanation:

So far he caught 5/16 + 7/8

= 5/16 + 14/16 = 19/16

= 1 3/16 pounds.

Minimum wight of the third fish = 2 - 1 3/16

=  32/16 - 19/16

= 13/16 pounds.

Answer:

Congrats! you are correct, the answer is C.) This is because if you look at the line, it intercects with the points you recieved.

C is correct because the y intercept is 1 and the slope is going down 4 for every next x value

is there anything else that you didn't include in this problem?

Answer: 321.4167 or about 322 boxes

Step-by-step explanation:

20 picks in total .

Answer:

30 degrees

Step-by-step explanation:

Answer:  Measure of ∠BAM is 30°.

Step-by-step explanation:

As given in the question, points A and B split the circle with center O into two arcs in the attached figure below. Major of the minor arc is 150°. And, the point M splits the major arc in the ratio 2 : 5.

We are to find the measure of ∠BAM.

Since the measure of minor arc AB is 150°, so the measure of major arc AB will be

360° - 150° = 210°.

Also, point M divides the major arc AB in the ratio 2 : 5, so we have

[tex]arc~BM:arc~MA=2:5.[/tex]

Therefore, the measure of ∠BOM is given by

[tex]m\angle BOM=\dfrac{2}{2+5}\times210^\circ=\dfrac{2}{7}\times 210^\circ=60^\circ.[/tex]

We know that

the measure of the angle subtended at the center by an arc is equal to twice the measure of the angle subtended at the circumference by the same arc.

That is, on arc BC, we get

[tex]m\angle BOM=2\times m\angleBAM\\\\\Rightarrow m\angle BAM=\dfrac{m\angle BOM}{2}\\\\\\\Rightarrow m\angle BAM=\dfrac{60^\circ}{2}\\\\\Rightarrow m\angle BAM=30^\circ.[/tex]

Thus, the measure of ∠BAM is 30°.

Answer:

This would probely be 266.

Step-by-step explanation:

There are three kids so I would divide them by three. Or multiply 266 by three. Of course there would still be 2$ left.

Answer:

Share of Eli, Freda and Geoff will be $180, $260, $360 respectively.

Step-by-step explanation:

Eli, Freda and Geoff were given $800 to share in the ratio of their age.

Their ages were 9 years, 13 years and 18 years respectively.

Ratio of their ages will be 9 : 13 : 18

Now share of Eli will be = [tex]\frac{9}{9+13+18}\times 800[/tex]

= [tex]\frac{9\times 800}{40}[/tex]

= $180

Share of Freda will be = [tex]\frac{13}{9+13+18}\times 800[/tex]

                                     = $260

Share of Geoff will be = [tex]\frac{18}{9+13+18}\times 800[/tex]

                                     = $360

Therefore, share of Eli, Freda and Geoff will be $180, $260, $360 respectively.

Answer:

4 students are working on fractions

Step-by-step explanation:

The lion runs 50 miles per hour which is 20 more than a house cat. 20 mph + house cat mph = 50 → house cat mph = 30mph

You just have to calculate the difference.

50-20=c

c=30

Answer:

A) p = 2x - 4  for the expression. B) Your team scored 44 points.

Step-by-step explanation:

Let P represent the points your team made.

Since the question says "Your basketball team scored 4 fewer than twice as many points as the other team." this is how I came up with the expression.

p = 2x - 4 ( our points = 2 times more then the other teams points minus 4.

Using this expression and the given information that the other team made 24 points, I solved B.

44 = 2(24) - 4.

The expression for given statement can be found by system equation. We can create the system equation as per the statement.

(a) The expression for the number points your team scored is [tex]P=2x-4[/tex].

(b) Your team score 44 points.

Given:

Other team score [tex]x[/tex].

Let the [tex]P[/tex] is points scored by your team.

As per the statement, your basketball team scored 4 fewer than twice as many points, [tex]x[/tex] as the other team.

Convert the above statement in form of expression.

[tex]P=2x-4[/tex]

Thus, the expression for the number points your team scored is [tex]P=2x-4[/tex].

Substitute 24 for [tex]x[/tex] in above expression.

[tex]P=2\times 24-4\\P=44[/tex]

Thus, your team score 44 points.

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We have a right triangle 9,12,15 which is 3,4,5 scaled.

So OG=15 and OH=9 (the radius) so x = 15-9 = 6

Answer: 6

The length of EF is 3.8. Option A

To determine the value of the side, we have to make use of the sine rule, this rule is represented as;

sin A/a = sin B/b

Such that;

Now, substitute the values, we have;

sin 75/EF = sin 50/3

cross multiply the values, we get;

EF = 3sin 75/sin 50

find the values

EF = 3(0.96)/0.766

EF = 2.88/0.766

Divide the values

EF = 3. 8

Answer:

[tex]\log_{81}(27)=\frac{3}{4}[/tex]

Step-by-step explanation:

The given logarithm is

[tex]\log_{81}(27)[/tex]

Let us change to base 3.

[tex]\log_{81}(27)=\frac{\log_3(27)}{\log_3(81)}[/tex]

[tex]\log_{81}(27)=\frac{\log_3(3^3)}{\log_3(3^4)}[/tex]

[tex]\log_{81}(27)=\frac{3\log_3(3)}{4\log_3(3)}[/tex]

[tex]\log_{81}(27)=\frac{3(1)}{4(1)}[/tex]

[tex]\log_{81}(27)=\frac{3}{4}[/tex]

Answer:

3/4 ( or 0.75).

Step-by-step explanation:

let y = log81 27, then:

27 = 81^y     ( by the definition of a logarithm).

27 = 3^3 and 81 = 3^4

So 27 =  81 ^3/4

so y = log81 27 = = 3/4.

The line parallel to the equation 2x + 3y = 12 can be expressed in the form y = -2/3x + c, where c is any arbitrary constant. This is because parallel lines share the same slope.

In mathematics, parallel lines have the same slope. To find an equation that is parallel to an existing line, we need to find the slope of the existing line and use that same slope for the parallel line. We know that your line equation is 2x + 3y =12. Let's rewrite this in the y = a + bx form, where a is the y-intercept and b is the slope.

So, subtract 2x from both sides to get the equation in the form of 3y = -2x +12. Now, divide the entire equation by 3 to isolate y. You get y = -2/3x + 4. Here, the slope (b) is -2/3. Any line parallel to this one must also have a slope of -2/3.

Thus, the parallel line is y = -2/3x + c, where c is any arbitrary constant.

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To find a line parallel to 2x + 3y = 12, you must use the same slope, which is -2/3. Any line of the form y = (-2/3)x + b, where b is any number, will be parallel to the original line.

To find an equation for a line parallel to the given line 2x + 3y = 12, we need to find a line with the same slope. First, we rearrange the given equation into slope-intercept form (y = mx + b), where m represents the slope, and b represents the y-intercept.

The original equation can be rewritten as:

3y = -2x + 12

y = (-2/3)x + 4

The slope of this line is -2/3. Any line parallel to this line will have the same slope, -2/3. The general form of the equation for any parallel line will be:

y = (-2/3)x + b

where b can be any real number.

Here are a couple of examples of lines that are parallel to the original:

Both have the same slope (-2/3) as the original line but different y-intercepts.

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Answer:

56 divided by 8 would equal p.

Step-by-step explanation:

If you want to find how many packs there are, it would be 56 divided by 8 would equal p.

Brainiest Please :D

Answer:

The equation is [tex]p*8=56[/tex]

Step-by-step explanation:

The neighbors buy a number of packs (p) of hot dogs and each one has 8 hot dogs. To calculate the number of hot dogs resulting we have to multiply the packs (p) by the number of hot dogs in each pack (8), this is:

[tex]p*8=56[/tex]

Then to calculate p we have to clear it:

[tex]p=\frac{56}{8} =7[/tex]

The number of packs bought were 7.

Answer:

[ -9(x^2 - 16)] / [4(x^2 + 5x + 6)]  = 0

Step-by-step explanation:

Ok this will be a rational function with denominator (x + 2)(x + 3)  - to give the vertical asymptotes.

The numerator  will be a(x + 4)(x - 4)  to give the x-intercepts . The a is some constant.

As the y intercept is  (0,6) we have:

6 =   a(0-4)(0+4) /  (0+2)(0+3)

6 =  -16a / 6

-16a = 36

a = - 36/16 = -9/4.

So our equation is -9(x^2 - 16)/ 4(x^2 + 5x + 6)  = 0.

Answer:

E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.

Step-by-step explanation:

A z score tells us how many standard deviations away from the mean a given value is.

The higher the z-score, the farther above the mean the value is.  Since we are referring to the score on a test, we want the value to be as far above the mean as possible; this means that our best choice out of those given is 2.00, since it is 2 standard deviations above the mean.

Answer:

It will take 5 years for the population to reach 1,944. Option D is correct.

Step-by-step explanation:

Initial population = I = 8

Final population = F = 1944

number of years = x

As given, the population is tripled every year that can be calculated using:

F = I*3^x

By putting values in this equation, we get

1944 = 8*3^x

1944/8 = 3^x

243 = 3^x

3^x = 243

3^x = 3^5

x = 5 bases are same so powers can be simplified.

Therefore, it will take 5 years for the population to reach 1,944. Option D is correct.

Answer:

8 • 3^y = R

Step-by-step explanation:

...................

Answer:

Step-by-step explanation:

can you explain a little bit more ?

Answer:

B.

Step-by-step explanation:

You are given the double inequality

[tex]1<x\le 6.[/tex]

This means that x is greater than 1 and less than or equal to 6.

Thus, point 1 must be excluded (with bracket "(") and 6 must be included (with bracket "]").

Hence, the correct answer is [tex](1,6].[/tex]

Answer:

b. [tex](1,6][/tex]

Step-by-step explanation:

The given inequality is [tex]1\:<\:x\le6[/tex].

We use the parenthesis [tex]()[/tex] to represent an open interval < or >.

We use the square brackets [tex][][/tex] to represent a closed interval [tex]\le[/tex] or [tex]\ge[/tex].

[tex]1\:<\:x\le6[/tex] represents [tex](1,6][/tex].

The correct choice is B.

➷ Find the total number of cards:

24 + 18 + 18 = 60

Find the total number of cards that aren't green:

24 + 18 = 42

The probability would be 42/60

This could be simplified to 7/10

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

710

Step-by-step explanation:

7/10

Answer:

[tex]{x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]

Step-by-step explanation:

To write a polynomial in descending order means writing the polynomial in decreasing powers of x.

The given polynomial expresion is

[tex] - 4 {x}^{5} + 4 {x}^{3} + {x}^{7} - 10 + 2 {x}^{4} [/tex]

We start from the term with the highest degree and end with term with the least degree.

[tex] {x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]

Therefore the given polynomial written in descending order is

[tex]{x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]

The distance between the parallel lines 3x - 5y = 1 and 3x - 5y = -3 is 4/√34 units.

To find the distance between two parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3, we need to use the formula for distance between two parallel lines in a coordinate plane. This formula is:

Distance = |C2 - C1| / sqrt(A^2 + B^2)

In this case, your A coefficient is 3, the B coefficient is -5, and the constants (C1 and C2) are -1 and 3 respectively (from the given equations). Substituting these values into the formula gives:

Distance = |3 - (-1)| / sqrt(3^2 + (-5)^2)

Distance = 4 / sqrt(9 + 25)

Distance = 4 / sqrt(34)

So, the distance between parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3 is 4/sqrt(34) units.

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Final answer:

The distance between the parallel lines described by the equations 3x-5y=1 and 3x-5y=-3 is calculated using a standard formula for the distance between parallel lines, resulting in a distance of 4 / √34.

Explanation:

The distance between two parallel lines can be calculated using a formula once the equations of the lines are in standard form. The equations 3x-5y=1 and 3x-5y=-3 are indeed in standard form and clearly show that the lines are parallel because they have the same coefficients for x and y. To find the distance between these parallel lines, one can use the formula involving the absolute difference of the constants in the equations and the square root of the sum of squares of the coefficients of x and y.

The formula for the distance d between two parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by:

d = |C2 - C1| / √(A² + B²)

Applying this to our equations, we have:

A = 3, B = -5, C1 = 1, and C2 = -3.

Thus,

d = |-3 - 1| / √(3² + (-5)²) = 4 / √(9 + 25) = 4 / √34

Distance between parallel lines, standard form, and formula are essential in solving this problem.

Answer:

Step-by-step explanation:

The diagonals in the parallelogram intersect by dividing in half.

Therefore we have the equation:

2y + 22 = 79 - y                 subtract 22 from both sides

2y = 57 - y              add y to both sides

3y = 57              divide both sides by 3

y = 19

The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).

Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3

Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3

Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3

The tank holds 641 gallons since the volume of the tank is 85.66 cubic feet. The tank has a cylindrical part and two hemispheres.

The volume of the cylinder is V=Bh or V=2πrh.

Where B is the base area, h is the height of the cylinder and r is the radius.

The formula for the volume of a hemisphere: V = (2/3)πr³

Where r is the radius of the hemisphere.

The tank has a cylindrical part and two hemispheres.

So, the volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)

Finding the volume of the cylinder:

The height of the cylinder is h=5'9'' and the diameter is 3'6''.

(1 feet = 12 inches)

So, the diameter = 3 feet 6 inches = 3+(6/12) feet = 3.5 feet

Then, the radius r = 3.5/2 = 1.75 feet and

The height h=5 feet 9 inches = 5 + (9/12) feet = 5.75 feet

The volume of the cylinder = 2πrh

                                             = 2π×1.75×5.75

                                             = 63.22 cubic feet

Finding the volume of the hemisphere:

The diameter of the sphere is 3'6'' i.e., 3.5 feet

So, radius r = 1.75 feet

Then the volume of a hemisphere:

V = (2/3)πr³

  = (2/3)π×(1.75)³

  = 11.22 cubic feet

So,

The volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)

⇒ Volume of the tank = 63.22 + 2×11.22 =85.66 cubic feet.

Since it is given that for 1 cubic ft it holds 7.48 gallons then for 85.66 cubic ft it holds 85.66 × 7.48 = 640.73 gallons

Rounding to the nearest gallon. So, it holds 641 gallons.

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where are the options??