Solve the system of equations graphically. Then classify
the system as consistent or inconsistent and the
equations as dependent or independent.
5x - y = 7
5x+6y= -7

Solve The System Of Equations Graphically. Then Classifythe System As Consistent Or Inconsistent And

Answers

Answer 1

Answer:

They are consistent and independent

Step-by-step explanation:

Consistency

If two lines have an intersection point, they are said to be consistent. For example, two parallel lines do not have an intersection and therefore they are inconsistent.

In the problem, the two lines intersect at (1, -2) so they have a unique solution and therefore consistent.

Dependency

Two lines are said to be independent if one of them cannot be written as an integer multiple of the other. Or, in other words, if the slope-intercept form of both equations have different slope and y intercept

Note: slope-intercept form of an equation is y = mx + c where m is the slope and c the y intercept

Line 1: 5x - y = 7 can be written as y = 5x - 7 which has slope +5 and y intercept -7

Line2 : 5x + 6y = -7 can be re-written as y = (-5/6)x - (7/6). This has slope -5/6 and y intercept -7/6

Since slope and intercepts of both lines are different they form a system of independent equations


Solve The System Of Equations Graphically. Then Classifythe System As Consistent Or Inconsistent And

Related Questions

Find the next two terms in this
sequence.
20, 32, 42, 50, 56, [?

Answers

Answer:

so the next 2 sequences would be 60 and 62

Step-by-step explanation:

The next two terms in the given arithmetic sequence are 60 and 62.

The arithmetic sequence is given as follows:

20, 32, 42, 50, 56, ?

To find the next two terms in the sequence, let's analyze the pattern:

The sequence increases by the following increments:

12, 10, 8, 6

We can observe that the increments are decreasing by 2 each time.

To find the next two terms, we can continue this pattern:

Increment: 4 (6 - 2)

Increment: 2 (4 - 2)

Adding the increments to the previous terms:

56 + 4 = 60

60 + 2 = 62

Therefore, the next two terms in the arithmetic sequence are 60 and 62.

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Solve this pls explain all steps for 22.5 = 1.5x

Answers

22.5 = 1.5x

x = 22.5/1.5

x = 15

hope it helps...!!!

Answer:

x = 15

Step-by-step explanation:

1.5x = 22.5

x = 22.5/1.5

assuming your finding x

NEED HELP ON THIS

If z=-1-i, find z^10 in rectangular form.

The polar form of this problem is 3cis90degrees, what’s the rectangular form?

Answers

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Let [tex]z=r(\cos\theta+i\sin\theta)[/tex] be a complex number, where [tex]n[/tex] is an integer and [tex]n\geq 1[/tex]. By DeMoivre's Theorem, if [tex]z^n=r^n(\cos\theta+i\sin\theta)^n[/tex], then [tex]z^n=r^n(\cos n\theta+i\sin n\theta)[/tex].

Hence, we must first convert from rectangular to polar form:

[tex]z=-1-i\\\\r=\sqrt{a^2+b^2}\\\\r=\sqrt{(-1)^2+(-1)^2}\\\\r=\sqrt{1+1}\\\\r=\sqrt{2}[/tex]

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)\\\\\theta=\tan^{-1}\biggr(\frac{-1}{-1}\biggr)\\ \\\theta=\tan^{-1}(1)\\\\\theta=45^\circ[/tex]

Therefore, the rectangular form for the complex number is [tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)[/tex], and now we can apply DeMoivre's Theorem to raise the complex number to the 10th power:

[tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)\\\\z^{10}=\sqrt{2}^{10}(\cos45^\circ+i\sin45^\circ)^{10}\\\\z^{10}=2^5(\cos10\cdot45^\circ+i\sin10\cdot45^\circ)\\\\z^{10}=32(\cos450^\circ+i\sin450^\circ)\\\\z^{10}=32(0+i)\\\\z^{10}=32i[/tex]

Therefore, [tex]z^{10}=32i[/tex] in rectangular form.

Problem 2

[tex]3\:\text{cis}\:90^\circ=3(\cos90^\circ+i\sin90^\circ)=3(0+i)=3i[/tex]

Therefore, [tex]3\:\text{cis}\:90^\circ=3i[/tex] in rectangular form.

PLEASE HELP For what value of x is the parallelogram a rectangle. The arrows point to the entire diagonal, not just a segment.

Answers

Step-by-step explanation below

Respond

1. Describe a real-life situation that can be modeled by a function (a relation in which every input
value corresponds to only one output value). The situation must be different from the examples
provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your
relation does, in fact, represent a function.


2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example.


3. Identify the domain and range of your function, using proper mathematical notation.


4. Cite any sources you may have used in
formulating your response.

Answers

A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

What is a function?

It should be noted that a function simply means an expression that shows the relationship between the variables.

In this case, a real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

The function will be:

= 20 + 5w

where w represents the number of weeks.

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Increase £180 by 25%
please thank you so much!!!

Answers

Answer:

£225

Step-by-step explanation:

[For percentage increase, add the percentage with 100, for percentage decreases substract the percentage from 100.]

100 + 25 = 125%

[tex]\frac{125}{100}[/tex] × 180 = £225

PLEASE HELP ME ANSWER THIS AAAA

Answers

Volume of a Rectangular Prism = length x width x height

Volume = 20

Length = 2

Width = 2

Height = d

20 = 2 x 2 x d

20 = 4 x d

d = 5

Answer: d = 5 centimeters

Hope this helps!

Answer:

d = 5 cm

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

L = 2 cmW = 2 cmH = d cmV = 20 cm³

Substitute the values above into the formula:

V = L*W*H

20 = 2*2*d

20 = 4d

/4    /4

5 = d

Therefore, the value of d is 5 cm.

Hope this helps!

[tex](sinx^{2} theta)\frac{x}{y}(1+costheata)[/tex]

Answers

The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

How to evaluate the expression?

The expression is given as:

[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]

Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].

So, we have:

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]

Open the bracket

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Express 1 as cos°(Ф)

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

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The average score for the statistics exam was a 75 with a standard deviation of 8. A student was told that they received a
score 1.45 standard deviations below the mean. What was their score?

Answers

A mean is an arithmetic average of a set of observations. The score of the student is equal to 63.4.

What is Mean?

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given the mean score was 75, while the standard deviation was 8. Therefore, the score of the student is,

Scre of the student = μ - 1.45σ = 75 - 1.45(8) = 63.4

Hence, the score of the student is equal to 63.4.

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Composition of the functions is
commutative.

Answers

Answer:

The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).

Julia has 42 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 180 square meters. List each set of possible dimensions (length and width) of the field.

Answers

The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.

Area of a rectangle

area of rectangle = lw

where

l = lengthw = width

Therefore,

perimeter = 2w+ l

42 = 2w + l

l = 42  - 2w

Hence,

area = w(42 - 2w)

180 = 42w - 2w²

-2w² + 42w - 180 = 0

-w² + 21w - 90 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1b = 21

w = - 21 / 2 ×  -1

w = 10.5 meters

Then,

l = 42  - 2w

l = 42 - 2(10.5)

l = 21 meters

Therefore, the dimensions are 10.5 meters and 21 meters.

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Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.

Answers

Answer:
it’s C. To send to college recruiters

Reason:
You use technology to asses performance so you can better your technique, change up your training program to focus on the things you’re doing wrong and you can also see if you’ve made improvement.
To send to college recruiters

The sum of four consecutive even numbers is 60. Find the smallest of the four number.

Answers

Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

Rewrite the equation below so that it does not have fractions:

3/4x - 2 = 5/12

Do not use decimals in your answer.

Answers

Answer:

Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]

First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2

Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]

Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29

—-

Have a nice day!!

Factor the polynomial completely. 14a^4 b^2 - 21a^3 b^2

Answers

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

The price of a tv was decreased by 20% to £1440. What was the price before the decrease?

Answers

Answer:

€ 1800

Step-by-step explanation:

x - 20% of x = 1440

x - 20x/100 = 1440

x - x/5 = 1440

(5x - x)/5 = 1440

4x/5 = 1440

therefore x = 1440 × 5/4 [ transpose 4/5 to right hand side ]

x = 360 × 5

= € 1800

is -0.25 rattional or irrational

Answers

The answer is rational

1.156÷106
Please help
Will give 20 points whoever gets this right
Thank you :)

Answers

Answer:

0.0109056604

that is the answer, I used a calculator

SOMEONE PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer:

75.96°

Step-by-step explanation:

[tex] \angle A = \tan^{-1}\bigg(\frac{8}{2}\bigg)[/tex]

[tex] \angle A = \tan^{-1}(4)[/tex]

[tex] \angle A =75.963756532\degree[/tex]

[tex] \angle A \approx 75.96\degree[/tex]

A population about which we want to get some information is called?​

Answers

A population about which we want to get some information is called the sample.

What is a sample in a population study?

This is a portion of a population that is known to contain several parts of the population. The information that is gotten from the sample would be used to draw conclusion about the entire information.

Therefore from the definition above the answer to the question is the population sample.

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help will mark Brainliest​

Answers

Answer:

4.03 < 16.5

Step-by-step explanation:

Four and three hundreths = 4.03

sixteen and five-tenths = 16.5

4.03 < 16.5

A box contains 14 books & 7 pieces of dusters. Each piece of duster weighs 0.2 pounds each book weighs 1.1 pounds. The box & its contents together weigh 18.25 pounds. How much does the empty box weigh?

Answers

Answer:

1.45

Step-by-step explanation:

weight of all books= 14×1.1= 15.4

weight of all duster=7×0.2= 1.4

weight of books and duster= 15.4+1.4=16.8

weight of the empty box = 18.25-16.8=1.45

Select the correct answer.
The graph of function fis shown.
Which statement correctly compares the two functions?
OA. They have the same end behavior as x approaches -
B. They have the same end behavior as x approaches -
OC. They have different end behavior as x approaches -

Answers

Answer A

They have the same x-intercept but different end behavior as x approaches ∞ :)

The product of a number and 7 less than the number is 260. Find the numbers.

Answers

Answer: 20,-13

Step-by-step explanation:

We can rewrite the problem as an equation. This equation is x(x-7)=260 (x being the mystery number). We can simply this into x^2 -7x=260. We can then rewrite this as x^2 -7x -260=0. We need to find the roots of this quadratic, which are -13 and 20. You can find this by factoring the quadratic.

when A complete 1/3 part of any work B can complete 1/4 part of that same work. Similarly when B complete 1/5 part of that work C can complete 1/2 part of that same work. if A can complete that work in 20 hours, then in how many hours can C complete that work.

Answers

Answer:

10.672hrs ( maybe)

Step-by-step explanation:

A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs

B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs

B can complete the 1/5 part of work in 26.67/5=5.336hrs

according to question C can complete 1/2part of work in same time then the whole work can complete in

2*5.336=10.672hrs

165 divided by 11 =
154 divided by 14 =
306 divided by 17 =
322 divided by 14 =

Answers

Answer:

165 divided by 11 = 15

154 divided by 14 = 11

306 divided by 17 = 18

322 divided by 14 = 23

The rule for a pattern is subtract 4. The first number of the pattern is 41. Which choice is true about this pattern?
A.The numbers in the pattern are even.
B.The numbers in the pattern are odd.
C. The numbers alternate between even and odd. ​

Answers

Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

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given the right triangle ABC, find tan A​

Answers

The tangent is the ratio of the perpendicular and the base of the right triangle. Then tan A will be x/y.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The right-angle triangle ΔABC is given.

The angle ∠C is 90°.

And the perpendicular is x, the base is y, and the hypotenuse is z.

Then the value of the tangent of angle ∠A will be

The tangent is the ratio of the perpendicular and the base of the right triangle.

tan A = x/y

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a) Fill in the gaps below to describe the transformations.
clockwise/anticlockwise about (-1,0) to give
triangle A'.
Triangle A' is then reflected in the line
to give triangle A".
b) What type of single transformation maps triangle A onto triangle A"?
A"
Triangle A is rotated
O
-4
A

Answers

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.

Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

Given,

Triangles A , A' , A'' .

Here,

The triangles are rotated and reflected to get different triangles .

Firstly ,

Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .

To get A'' triangle A' is reflected from horizontal axis.

Triangle A maps into triangle A'' by rotation .

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Help me out with this math problem for 50 points!!!

Answers

Hope that helps!! If it’s asking to simplify it, you can’t simplify it anymore. I don’t get what it means by possible solutions, but maybe put what the numbers are on the number line? I really hope that helps have a great day!!

Answer:

see attached for a graph-1, -2.6, -497

Step-by-step explanation:

The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.

__

Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.

The graph will be a solid dot at x=-1, and shading to its left.

__

Possible solutions are any values less than or equal to -1. Some are ...

  -1

  -1.073

  -429

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