Consider the system of equations shown in the box.
y = 3x + 1
y = 2x - 4
What is the x-coordinate in the solution of the system?

Answer:

Linear expression is linear equations

Step-by-step explanation:

Answer:

[tex]x = 2.5[/tex]

Step-by-step explanation:

Given

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

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

[tex]BC = 2\sqrt{7[/tex]

[tex]\angle A = 60^{\circ}[/tex]

Required

Find x

To find x, we make use of cosine formula which states:

[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]

In this case:

[tex]BC^2 = AB^2 + AC^2 - 2*AB*BC*CosA[/tex]

Substitute values

[tex](2\sqrt{7})^2 = (2x + 1)^2 + (2x-1)^2 - 2*(2x + 1)*(2x - 1)*Cos(60^{\circ})[/tex]

Evaluate all exponents

[tex]4*7 = (4x^2 + 4x + 1)+(4x^2 - 4x + 1) - 2(4x^2 - 1)*cos(60^{\circ})[/tex]

Open brackets

[tex]28 = 4x^2 + 4x + 1+4x^2 - 4x + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]

Collect Like Terms

[tex]28 = 4x^2 +4x^2+ 4x - 4x+ 1 + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]

[tex]28 = 8x^2+ 2 - (8x^2 - 2)*cos(60^{\circ})[/tex]

Substitute 0.5 for cos(60)

[tex]28 = 8x^2+ 2 - (8x^2 - 2)*0.5[/tex]

Open bracket

[tex]28 = 8x^2+ 2 - 4x^2 + 1[/tex]

Collect Like Terms

[tex]8x^2- 4x^2 + 2 + 1 - 28 = 0[/tex]

[tex]4x^2 -25 = 0[/tex]

Collect Like Terms

[tex]4x^2 =25[/tex]

Divide both sides by 4

[tex]x^2 =\frac{25}{4}[/tex]

[tex]x^2 =6.25[/tex]

Take positive square root of both sides

[tex]x = \sqrt{6.25[/tex]

[tex]x = 2.5[/tex]

Answer:

768 in.

Step-by-step explanation:

Answer:

I don't get the question

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

The mode is the number that occurs the most in a data set, and 88 is the only number that occurs twice.

Answer:

30 mild wings

Step-by-step explanation:

Answer:

m=2

Step-by-step explanation:

5-1/3-1

4/3-1

4/2

2

I hope this helps

Answer:

2a=3b

Step-by-step explanation:

b/a=2/3 not b/a =3/2

b/3=a/2 not b/2=a/3

2a/3=b not 3a/2=b

hope it's helpful ❤❤❤

THANK YOU

Answer:

1.3 & 1/3

Step-by-step explanation:

Answer:

The t-statistic for a hypothesis test that is designed to answer the question is 2.4.

Step-by-step explanation:

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the saple and n is the size of the sample.

A store manager designs a new accounting system that will be cost effective if the mean monthly charge account balance is more than $50.

This means that [tex]\mu = 50[/tex]

A sample of 100 accounts is randomly selected. The sample mean balance is $56 and the sample standard deviation is $25.

This means that [tex]X = 56, s = 25, n = 100[/tex]. So

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

[tex]t = \frac{56 - 50}{\frac{25}{\sqrt{10}}[/tex]

[tex]t = \frac{6}{2.5}[/tex]

[tex]t = 2.4[/tex]

The t-statistic for a hypothesis test that is designed to answer the question is 2.4.

Answer: False

Step-by-step explanation:

it’s usually 20%

Answer:

False

Step-by-step explanation:

1. Normally it is 20%.

2. Move yous decimal one place to the left

3. Round this number to the next easy coin amount

4. Double that number

That is roughly 20%

Answer: 48

Step-by-step explanation: all you have to do is subtract $128 by 80% that will equal 48

Your welcome!

Answer:

39 tickets were given to the employees

Step-by-step explanation:

1. Approach

First, list the given information, then form an equation based on the given information. Finally, solve the equation with simplification and inverse operations.

2.Given

A total of 234 tickets were given away

5 times as many tickets were given away to listeners compared to employees

-Call the number of tickets given away to employees (x)

3. Form an equation

(Tickets_given_to_employees) + (Tickets_given_to_listeners) = (Total_tickets)

Substitute,

x + 5x = 234

Simplify,

6x + 234

Inverse operations,

6x = 234

/6      /6

x = 39

Answer:

78

Step-by-step explanation:

Ratio of left-footed teachers to right-footed teachers = 3:13

18 left-footed teachers; 3x6 = 18 (3:13 is a simplified ratio and to get 18, you have to multiply 3 by 6)

13x6 = 78 (whatever you do to one side, you have to do the other)

78 right-footed teachers

The are 78 teachers are right footed.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The ratio of the number of left footed teachers: the number of right footed teachers = 3:13

Total left footed teachers = 18

let the Common ratio be x.

Then , number of left footed teachers= 3x

and, number of right footed teachers= 13x

So, 3x= 18

x= 6

Hence, there are 78 teachers are right footed.

Learn mor about algebra here:

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9514 1404 393

Answer:

  A

Step-by-step explanation:

Using m=3, n=5, x2=2, x1=-14, the only match is the first one.

The correct expression for the point on the line is [tex]M=\frac{3}{3+5} (2-(-14))+(-14)[/tex]

The formula for expressing the midpoint of a line is expressed as:

[tex]M=\frac{m}{m+n} (x_2-x_1)+x_1[/tex]

Given the following parameters

m=3,

n=5,

x2=2,

x1=-14,

Substitute

[tex]M=\frac{3}{3+5} (2-(-14))+(-14)[/tex]

This given the correct expression for the point on the line

Learn more on midpoint here: https://brainly.com/question/18315903

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Answer:

y=-49

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A transversal line is a line that intersects two or more lines. Since line C is intersecting two lines, it is transversal.

The required line C is a transversal of lines a and b.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
The line which intersects two or more lines is said to be a transversal line.
So as of the given figure, line C intersects line a and line b so Line C is a transversal line.

Thus, the required line C is a transversal of lines a and b.

Learn more about lines here:

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Answer:

7.07 in^2 is what i got

Answer:

In 3 months the total cost of each health club will be the same.

The total cost for each health club will be $_60_.

Step-by-step explanation:

Answer:

h + 3

Step-by-step explanation:

Since Raj is 3 inches taller than Howard (h), Raj would be h + 3 inches taller than Raj, giving you your answer.

Answer:

h + 3

Step-by-step explanation:

h + 3

3 = they are 3 inches TALLER which means you need to add 3

h = Howards height

So all you would need to do is add Howards age by 3, and you will get Raj's height. They said that " Raj is 3 inches taller than Howard", so that means when you get Howard (h) you would need to add it by 3 (3 inches taller), and you will be able to get Raj's height.

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

4

Step-by-step explanation:

x must equal 2 and 2 to the power of 2 is 4

Answer:

4

Step-by-step explanation:

Original equation: 3x-1=5

Add 1 on both sides: 3x=6

Divide by 3 on both sides: x=2

If x=2, then x^2 = 4.

Let me know if this helps!

Answer:

6/65

Step-by-step explanation:

using the proper calculator, and through solving.

Answer:

v=-5 and v=3

Step-by-step explanation:

We are given that

[tex]v^2-15=-2v[/tex]

We have to find  two solutions of quadratic equation.

[tex]v^2+2v-15=0[/tex]

Using addition property of equality

[tex]v^2+5v-3v-15=0[/tex]   (By using factorization method)

[tex]v(v+5)-3(v+5)=0[/tex]

[tex](v+5)(v-3)=0[/tex]

Substitute each factor equal to 0

[tex]v+5=0[/tex] and [tex]v-3=0[/tex]

[tex]v=-5[/tex] and [tex]v=3[/tex]

Hence, two solutions of quadratic equation are

v=-5 and v=3

Answer:

The proportion of this group that likes chocolate is 0.625.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Likes sprinkles

Event B: Likes chocolate

25% of your friends who like Chocolate (C) also like sprinkles (S).

This means that [tex]P(A \cap B) = 0.25[/tex]

40% of your friends like sprinkles (S) topping.

This means that [tex]P(A) = 0.4[/tex]

Of the friends who like sprinkles, what proportion of this group likes chocolate

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.25}{0.4} = 0.625[/tex]

The proportion of this group that likes chocolate is 0.625.

Answer:

He will earn $6 in interest in 9 months.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

Initial deposit of $400.

This means that [tex]P = 400[/tex]

2% annual interest

This means that [tex]I = 0.02[/tex]

How much interest will he earn in 9 months?

An year has 12 months, this means that [tex]t = \frac{9}{12} = \frac{3}{4} = 0.75[/tex]

This is E. So

[tex]E = P*I*t = 400*0.02*0.75 = 6[/tex]

He will earn $6 in interest in 9 months.

Answer:

1

Step-by-step explanation:

SAS is one of the methods to define congruent triangles. When two sides and the angle between these two sides are specified, the triangle has been defined certainly.

Answer:

1

Step-by-step explanation:

becasue