Find the distance between the points A(-6,8) and B(12, - 7) by using the distance formula or Pythagorean Theorem. Leave your answer under the radical unless it is a a perfect square. Or, round your decimal answer to the nearest tenth.

Answer:

[tex]SA(x) = x^2 + \frac{12}{x}[/tex]

Step-by-step explanation:

Given

[tex]V = 3m^3[/tex] --- volume

[tex]x \to base\ length[/tex]

[tex]y \to height[/tex]

Required

The surface area as a function of base length

The volume (V) is calculated as:

[tex]V = Base\ Area * Height[/tex]

[tex]V = x*x*y[/tex]

[tex]V = x^2*y[/tex]

Make y the subject

[tex]y = \frac{V}{x^2}[/tex]

Substitute 3 for V

[tex]y = \frac{3}{x^2}[/tex]

The surface area of the open box is:

[tex]SA = x^2 + 2xy+2xy[/tex]

[tex]SA = x^2 + 4xy[/tex]

Substitute: [tex]y = \frac{3}{x^2}[/tex]

[tex]SA = x^2 + 4x*\frac{3}{x^2}[/tex]

[tex]SA = x^2 + 4*\frac{3}{x}[/tex]

[tex]SA = x^2 + \frac{12}{x}[/tex]

Hence, the function is:

[tex]SA(x) = x^2 + \frac{12}{x}[/tex]

Answer:

Correct.

Step-by-step explanation:

It looks good to me.

Good job!

Answer:

20 feet

Step-by-step explanation:

Volume = length x width x height

1200 = 10 x 6 x h

1200 = 60h

h = 1200/60

height = 20

The rectangular bin is 20 feet deep.

A cuboid is a three-dimensional shape in which all sides are rectangles. A cuboid has 6 faces, 8 vertices, and 12 edges. All the angles formed at the vertices of a cuboid are right angles. The opposite edges are parallel to each other.

For the given situation,

A rectangular bin is in the shape of a cuboid.

Volume of the rectangular bin,V = 1200 cubic feet

Length of the rectangular bin,l = 10 feet

Width of the rectangular bin,w = 6 feet

Let the height of the rectangular bin be h.

The formula of volume of cuboid is

[tex]V=lwh[/tex]

Now substitute the above values,

⇒ [tex]1200=(10)(6)h[/tex]

⇒ [tex]h=\frac{1200}{60}[/tex]

⇒ [tex]h=20[/tex]

Hence we can conclude that the rectangular bin is 20 feet deep.

Learn more about cuboid here

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Answer:

-3/4

Step-by-step explanation:

From point (0,3), to get to point (4,0) you would need to go down 3 units, and right 4 units.

Hope this helps

Answer:

a. m<B = 100°

b. m<L = 55°

c. Scale factor = 9/11

Step-by-step explanation:

a) Similar triangles have their three corresponding angles congruent to each other, while the ratio of their corresponding sides are proportional to each other.

Since ∆ABC ~ ∆GLJ, therefore,

<A = <G,

<B = <J

<C = <L

m<J = 100° (given)

Therefore,

m<B = m<J = 100°

m<B = 100°

b) m<A = m<G

m<A = 25° (given)

Therefore,

m<A = m<G = 25°

m<G = 25°

m<L = 180° - (m<J + m<G)

Substitute

m<L = 180° - (100° + 25°)

m<L = 55°

c) scale factor of smaller triangle to the larger = side length of smaller triangle / corresponding side length of bigger triangle

Scale factor = AB/GJ

Substitute

Scale factor = 18/22

Simplify

Scale factor = 9/11

Answer:

Mean: 44

Step-by-step explanation:

1. 24 + 36 + 52 + 48 + 64 + 40 = 264

2. 264 divided by 6 = 44

(I divided it by 6 because there are 6 numbers (data points).)

Answer:

[tex]\begin{array}{cccc}{Scores} & {f} & {LB} &{CF} & {39-41} & {6} & {39} &{6} & {36-38} & {7} & {36} &{13}& {33-35} & {9} &{33}&{22}& {30-32} & {13}&{30} &{35} & {27-29} & {22} &{27}&{57} & {24-26} & {10} &{24}&{67} & {21-23} & {9} &{21} &{76}& {18-20} & {7} &{18}&{83}& {15-17} & {8} &{15}&{91}& {12-14} & {4} &{12}&{95}& {9-11} & {2} &{9}&{97}& {6-8} & {1} &{6}& {98}&{3-5} & {1} &{3}&{99} \ \end{array}[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Fill in the blanks

First, we fill in the lower boundary (LB).

This is done by writing out the lower boundary of each class

So, we have:

[tex]\begin{array}{ccc}{Scores} & {f} & {LB} & {39-41} & {6} & {39} & {36-38} & {7} & {36} & {33-35} & {9} &{33}& {30-32} & {13} &{30}& {27-29} & {22} &{27}& {24-26} & {10} &{24}& {21-23} & {9} &{21}& {18-20} & {7} &{18}& {15-17} & {8} &{15}& {12-14} & {4} &{12}& {9-11} & {2} &{9}& {6-8} & {1} &{6}& {3-5} & {1} &{3} \ \end{array}[/tex]

Next, is to fill the CF column

This is done by adding the current with the previous cumulative frequency.

So, we have:

[tex]\begin{array}{cccc}{Scores} & {f} & {LB} &{CF} & {39-41} & {6} & {39} &{6} & {36-38} & {7} & {36} &{6 + 7 = 13}& {33-35} & {9} &{33}&{13+9 = 22}& {30-32} & {13}&{30} &{22+13=35} & {27-29} & {22} &{27}&{35+22=57} & {24-26} & {10} &{24}&{57+10=67} & {21-23} & {9} &{21} &{67+9=76}& {18-20} & {7} &{18}&{76+7=83}& {15-17} & {8} &{15}&{83+8=91}& {12-14} & {4} &{12}&{91+4=95}& {9-11} & {2} &{9}&{95+2=97}& {6-8} & {1} &{6}& {97+1=98}&{3-5} & {1} &{3}&{98+1=99} \ \end{array}[/tex]

Thia is the complete table of filling the values of LB(lower boundaries) and <cf (less than commulative frequency).

Answer:

y=-2x-10

Step-by-step explanation:

Let us start with a general slope-intercept equation, y=mx+b, where m represents the slope, b represents the y-intercept, and the y and x represents the coordinates the line passes through.

Therefore, the slope of our line

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

is 0.5

We also know that the perpendicular slope is simply the negative reciprocal of the current slope. We know have:

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

Now, let us find the y intercept. We can plug in the x and y values using the given coordinate (–6,2).

[tex]y=-2x+b\\2=-2*(-6)+b\\2=12+b\\b=-10[/tex]

Now, we can write our equation:

[tex]y=-2x-10[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

4. The range of the function is all

real numbers less than or equal to 9.

Answer:

505.4 in²

Step-by-step explanation:

½d2= 19×tan 35° = 19×0.7 = 13.3 in

d2 = 2×13.3 = 26.6 in

d1 = 2×19=38 in

the area of Rhombus =

½×38×26.6 = 505.4 in²

Answer:

W=11

Step-by-step explanation:

Just trust me with this one :3

Answer:

A. an = 1(4)^n-1

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio, and the sequence is given by:

[tex]a_n = a_1(q)^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term and q is the common ratio.

We are given the following sequence:

[tex]a_1 = 1[/tex]

[tex]a_n = 4a_{n-1}[/tex]

So

[tex]a_2 = 4a_1 = 4[/tex]

[tex]a_3 = 4a_2 = 16[/tex]

[tex]a_4 = 4a_3 = 64[/tex]

That is, the quotient between consecutive terms is 4, so [tex]q = 4[/tex].

The first term is already given, [tex]a_1 = 1[/tex]. So

[tex]a_n = a_1(q)^{n-1}[/tex]

[tex]a_n = 1(4)^{n-1}[/tex]

And thus, the correct answer is given by option A.

Answer:

The exponential probability should be 33%.

Step-by-step explanation:

[tex]4 \div 12 = .33 \\ [/tex]

[tex].33 \times 100 = 33\%[/tex]

The experimental probability of rolling a multiple of 3 will be 33%.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

A pair of dice was rolled many times and the results appear below. Based upon these results.

Outcome      2     3     4     5     6     7     8     9     10     11     12

Frequency    3    6     8     11     14   16    15    12     9      5      1

Then the experimental probability of rolling a multiple of 3 will be

Favorable events = 6 + 14 + 12 + 1 = 33

Total events = 100

Then the probability will be

P = (33 / 100) x 100

P = 0.33 x 100

P = 33%

More about the probability link is given below.

https://brainly.com/question/795909

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Answer:

Sorry if this is wrong, but seeing the question I think the best answer following the question would be answer B, because for A it shows that 1 hour is 35 miles when it says 70 miles in 1 hour, not C because as the time rises so does the distance, and I checked D and it's wrong.

Step-by-step explanation:

Answer:

B I think because i did my math

Step-by-step explanation:

Answer: No

Step-by-step explanation: if you mean the measure of a is 3, the measure of b is 9 and the measure of c is 5, c being the hypotenuse then the answer is no because the the sides of a and b must be less than the measure of c. If 5 wasn’t the hypotenuse then the answer would be different.

(KEEP IN MIND THAT IF 9 IS THE HYPOTENUSE THEN THE ANSWER IS YES)

Hope this helps! :)

Answer:

(32 ÷4) +8

Step-by-step explanation:

More than means it comes after

quotient of 32 and 4

32÷ 4

8 more than

(32 ÷4) +8

Answer:

x= 55

Step-by-step explanation:

Answer:

x is 55 degrees

Step-by-step explanation:

since it is a right angle set up the equation

20+x+15=90

then solve to get 55

Answer:

The standard deviation is of 7.22 people.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have the mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

About 7% of the population has a particular genetic mutation.

This means that [tex]p = 0.07[/tex]

800 people are randomly selected.

This means that [tex]n = 800[/tex]

Find the standard deviation for the number of people with the genetic mutation in such groups of 800.

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.07*0.93} = 7.22[/tex]

The standard deviation is of 7.22 people.

Answer:

below

Step-by-step explanation:

perimeter of a semicircle

½*2πr

=πr

=3.142*3

=9.42 ft

Answer:

A

Step-by-step explanation:   6  5  17  17

the perimeter is a semi-circle PLUS the diameter   d = 6 ft

so

      C = 2π r        semi-circle   C/2  = π r        r = d/2  = 3 ft

total perimeter is

      perimeter   =  C/2 + d

                         =  π r  + d

                         =  3π  + 6

                         =  3(3.14) + 6

                         =  15.425 ft

Answer:

1/3

Step-by-step explanation:

Considering the triangles are similar the side lengths would be proportional too

like AB is similar to DE so 5/15 = 1/3

Answer:

1. [tex]2 \frac{2}{7} [/tex]

2. [tex]2 \frac{1}{3} [/tex]

3. [tex] \frac{5}{12} [/tex]

4. [tex]8 \frac{2}{3} [/tex]

5. [tex] \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] \frac{8}{3} \div \frac{7}{6} [/tex]

[tex] \frac{8}{3} \times \frac{6}{7} [/tex]

[tex]8( \frac{2}{7} )[/tex]

[tex] \frac{8 \times 2}{7} [/tex]

[tex] \frac{16}{7} [/tex]

[tex]2 \frac{2}{7} [/tex]

[tex] \frac{20}{3} \div \frac{20}{7} [/tex]

[tex] \frac{20}{3} \times \frac{7}{20} [/tex]

[tex] \frac{1}{3} \times 7[/tex]

[tex] \frac{7}{3} [/tex]

[tex]2 \frac{1}{3} [/tex]

[tex] \frac{25}{6} \div \frac{10}{1} [/tex]

[tex] \frac{25}{6} \times \frac{1}{10} [/tex]

[tex] \frac{5}{6} \times \frac{1}{2} [/tex]

[tex] \frac{5}{6 \times 2} [/tex]

[tex] \frac{5}{12} [/tex]

[tex] \frac{13}{2} \div \frac{3}{4} [/tex]

[tex] \frac{13}{2} \times \frac{4}{3} [/tex]

[tex]13( \frac{2}{3} )[/tex]

[tex] \frac{13 \times 2}{3} [/tex]

[tex] \frac{26}{3} [/tex]

[tex]8 \frac{2}{3} [/tex]

[tex] \frac{15}{4} \div \frac{45}{8} [/tex]

[tex] \frac{15}{4} \times \frac{8}{45} [/tex]

[tex] \frac{1}{4} \times \frac{8}{3} [/tex]

[tex] \frac{2}{3} [/tex]

Answer:

Parallel means that the lines never intersect. If the equation of the new line is y=ax+b , then the system

y=ax+b

y=2x+5

needs to have no solutions. Subtracting the equations gives us

(a−2)x+(b−5)=0

In order for this to ever be 0 we need either a≠2 or b=5 , so to stop this from happening, we will require both a=2 and b≠5 .

Since our line now has the form y=2x+b , and (4,5) is on the line, then the equation

5=2⋅4+b

should be true. Since this implies that b=−3 , we have that the parallel line going through (4,5) has equation

y=2x−3

What is an equation of a line that goes through point (4,-5) and is parallel to y=2x+8?

Which line is parallel to the line y = 2x -4?

What is an equation for a line parallel to y = 5 x -5 and passing through the point (4,19)?

What is an equation for the line that is parallel to y= -4x

Answer:

[tex]x^2 + y^2 = 52[/tex]

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Equation of a circle:

The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r has the following format:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Center at the origin;

This means that [tex]x_0 = 0, y_0 = 0[/tex]

So

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 0)^2 + (y - 0)^2 = r^2[/tex]

[tex]x^2 + y^2 = r^2[/tex]

Passes through (4, 6)

The radius is the distance from this point to the center. So

[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]r = \sqrt{(4-0)^2+(6-0)^2}[/tex]

[tex]r = \sqrt{16+36}[/tex]

[tex]r = \sqrt{52}[/tex]

So

[tex]r^2 = 52[/tex]

Then

[tex]x^2 + y^2 = r^2[/tex]

[tex]x^2 + y^2 = 52[/tex]

Answer:

16.8 [tex]m^{3}[/tex]

Step-by-step explanation:

Find your answer by using the formula of a cone (v= [tex]\frac{1}{3}[/tex]π[tex]r^{2}[/tex]h)

r= 2 (half of your diameter, which is 4)

h= 4

By inserting your radius and height, you get v= [tex]\frac{1}{3}[/tex]π([tex]2^{2}[/tex])4.

Put that into a calculator and you get 16.75516, which rounds to 16.8.

Answer:   0.8

Step-by-step explanation:

Answer:

I would tell you but you do not have a picture

9514 1404 393

Answer:

  (b)  93°

Step-by-step explanation:

Assuming the line containing YT is a diameter, the measure of angle UYT is ...

  180° -87° = 93° = m∠UYT

BAnswer:

Step-by-step explanation: