in a system of equations why is the intersection the solution

Answer:

The GCF of the terms is 2c

Step-by-step explanation:

Greatest common factor:

To find the gcf of the expression, we find the gcf separately for the numbers and for the powers of c, and then multiply them.

Numbers:

8, 12 and 10.

Dividing them all by prime factors:

8 - 12 - 10|2

4 - 6 - 5

5 is not divisible by 2, so we stop there, and the gcf of the numbers is 2.

Powers of c:

Powers of c are 1, 2 and 3. The gcf of 1,2,3 is 1, as there is not a number that is divisible by all of 1,2,3 other than 1. So the gcf for the powers of c is c^1 = c.

GCF of the expression:

2*c = 2c

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:

W=11

Step-by-step explanation:

Just trust me with this one :3

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:

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:

[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]

BAnswer:

Step-by-step explanation:

Answer:

I think it's the first obtion

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

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:

You forgot something

Step-by-step explanation:

"which of the following points "

no points follow?????

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:

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:

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:

z > 3

z <_8

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

Proportion form of the given problem is (52/120)=(39/90). They both are equivalent to each other which gives the same value of 4.33 after solving the proportion.

Two ratios form a proportion if simplified form of both the ratios comes out as same ratio.

Using above method to find out whether the given ratios are forming proportion or not.

The question asks for an proportion.

So, 2 minutes = 120 seconds and set up the proportion

where it will be in the form of (words/seconds).

It is given that 52 words in 2minutes and 39 words in 90 seconds

Now, the proportion form will be;

(52/120) = (39/90).

They both are equivalent to each other which gives the same value of 4.33 after solving the proportion.

Learn more about directly inversely proportional relationship variable here:

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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:

-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:

Step-by-step explanation:

Soooo, by looking at the picture we can tell that it is a right trapezoid

The formula for the area is

(b1+b2)/2*h

(Base 1+ Base 2)/ 2 * height

Now we can plug in the numbers:

(5+15)/2*6

20/2*6

10*6

=60

1 gallon of paint per sq. foot

So Isha needs 60 gallons of paint

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:

Step-by-step explanation:a

Answer:

The answer is L∩J= {i}

Step-by-step explanation:

I just took a quiz and this was the correct answer

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:

Correct.

Step-by-step explanation:

It looks good to me.

Good job!

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.

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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:

4. The range of the function is all

real numbers less than or equal to 9.

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:

Step-by-step explanation:

[tex]a_2=a_1*r=>14=4*r=>r=\frac{7}{2}\\a_n=a_1*r^{n-1}=>a_7=a_1*r^{7-1}=4*(\frac{7}{2})^6=\frac{117649}{16}\\\\a_7=\frac{117649}{16}[/tex]