in a system of equations why is the intersection the solution

Answers

Answer 1

9514 1404 393

Answer:

  It satisfies both equations.

Step-by-step explanation:

The points on the graph of an equation are the values of the variables that satisfy the equation (make it true).

In a system of equations, you're generally looking for values of the variables that satisfy all of the equations in the system. That is, the solution will be a point on the graph of every equation in the system.

For a point to be on more than one graph, it must lie at a point of intersection of the graphs. If all of the graphs of a system go through the point of intersection, that point satisfies all of the equations, so is a solution of the system of equations.


Related Questions

Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center at the origin;
passes through (4, 6)

Answers

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]

which of the following points lies on the line 2x-y=12

Answers

Answer:

You forgot something

Step-by-step explanation:

"which of the following points "

no points follow?????

Sets L and J are defined as follows: L = { g , h , i , j , k } J = { i , l , m , n , o } Find the intersection of L and J .

Answers

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

Find the area of following rhombuses. Round your answers to the nearest tenth if necessary.

Answers

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

Which explicit formula is equivalent to a1 = 1, an=
4an-1?
A. an = 1(4)^n-1
B. an = 4(4)^n-1
C. an = 4(1)^n–1
D. an = 1 + (n - 1)4

Answers

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.

Find the 7th term of the geometric sequence: 4, 14, 49, ...

Answers

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]

PLEASE HELP FAST!!!!!

Answers

BAnswer:

Step-by-step explanation:

A cheetah can run at a speed of 70 miles per hour. Which representation shows the distance a cheetah can travel
at this rate?

I’ll give brainliest

Answers

B, because the first graph shows a rate of 35 mph. We don’t want that. Answer c states, that the rate is constant however that is not true. B is the only equation showing that if you plug in any x for the number of hours, you will get your answer. Therefore b is your answer! Hope this helps

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:

Is this the correct answer?

Answers

Answer:

Correct.

Step-by-step explanation:

It looks good to me.

Good job!

which of the following is not an appropriate method of proving triangles congruent. A] .asa B].sas C]ssa. D] sss.

Answers

C. Ssa. This is me writing for 20 characters

dennis and christine scored 32 and 23, respectively, in the national career assessment examination

Answers

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).

The function f(x) = x2 - 4x + 5 is shown on the graph.



Which statement about the function is true?

1. The domain of the function is all real numbers less
than or equal to - 2.

2. The domain of the function is all real numbers less
than or equal to 9.

3. The range of the function is all real numbers less than
or equal to -2.

4. The range of the function is all real numbers less than
or equal to 9.

Answers

Answer:

4. The range of the function is all

real numbers less than or equal to 9.

About 7% of the population has a particular genetic mutation. 800 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 800.

Answers

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.

Can y’all help me? Thanks :)

Answers

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

Help me please I’m down baddddd

Answers

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

Help me out thanks !!!!!!!!!!

Answers

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

Question 14
Find the perimeter.

Answers

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

Write the equation of a line that is perpendicular to y =(1/2)x - 5 and passes through point (-6,2)

Answers

Answer: y=-2x-10

Work:
m=(1/2)
m perpendicular= -2
2=-2(-6)+b
b=-10

Explanation: the standard form of the equation of a line is y=mx+b, find the y-int and perpendicular slope.

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 :)

Calculate the arithmetic mean 24, 36, 52, 48, 64, 40.

Answers

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).)

52 words in 2minutes and 39 words in 90 seconds?
(Show your work)

Answers

Answer: Proportion: (52/120)=(39/90)

Explanation: Since there is no given question, I assumed that the question asks for an proportion. So, 2 minutes=120 seconds and set up the proportion where (words/seconds).

You should get, (52/120)=(39/90).

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.

When does two ratios form a 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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A number z is greater than 3 and is less than or equal to 8

Answers

Answer:

z > 3

z <_8

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

What is the slope of the line in the graph? Enter answer without spaces

Answers

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

What is the GCF of the terms of 8c3 + 12c2 + 10c

Answers

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

is it possible to make a triangle with measure of 3mm 9mm and 5mm​

Answers

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! :)

Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April. The box shows her data for March. Select all true statements about the data.

Answers

Answer:

I think it's the first obtion

A rectangular bin, completely filled, holds 1,200 cubic feet of grain. If the bin is 6 feet wide and 10 feet long, how deep is it ?

Answers

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.

What is a cuboid?

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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A pair of dice was rolled many times and the results appear below. Based upon these results, what is the experimental probability of rolling a multiple of 3?
Outcome
2 3 4 5 6 7 8 9 10 11 12
Frequency
3 6 8 11 14 16 15 12 9 5 1 The percent probability is = [ ? ]%
Round to the nearest percent.

Answers

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%.

What is probability?

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 the following questions
1. 2 2/3 divided by 1 1/6.
2. 6 2/3 divided by 2 6/7.
3. 4 1/6 divided by 10.
4. 6 1/2 divided by 3/4.
5. 3 3/4 divided by 5 5/8

Answers

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]1. \: \: 2 \frac{2}{3} \div 1 \frac{1}{6} [/tex]

[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]2. \: \: 6 \frac{2}{3} \div 2 \frac{6}{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]3. \: \: 4 \frac{1}{6} \div 10[/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]4. \: \: 6 \frac{1}{2} \div \frac{3}{4} [/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]5. \: \: 3 \frac{3}{4} \div 5 \frac{5}{8} [/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]

Hope it is helpful...

HELP PLSS I WILL GIVE BRAINLYEST
I SUCK AT MATH

Answers

Answer:

W=11

Step-by-step explanation:

Just trust me with this one :3

What is the scale factor from abc to def?

Answers

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

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