(Algebra 1) please help

It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

We are given the first system of equations:

4x + y = 8

x + 3y = 8

thus 4/1 ≠ 1/3 = 1 is consistently independent.

The second system of the equation is;

-4x + 6y = 2

2x - 3y = 1

Therefore, -4/2 = -6/3 = 2 is inconsistent.

The third system of equations is;

5x - 2y = 4

5x - 2y = 6

Thus, 5/5 = -2/-2 ≠ 4/6 is consistent dependent.

Thus, It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

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Answer:

A

Step-by-step explanation:

36x = 535 - 31

36x = 504

36/36 x = 504/36

x = 14

[tex]{ \green{ \boxed{ \red{ \sf{x = 14}}}}}[/tex]

Step-by-step explanation:

[tex]{ \purple{ \tt{36x + 31 = 535}}}[/tex]

[tex]{ \purple{ \tt36x = 535 - 31}}[/tex]

[tex]{ \purple{ \tt{36x = 504}}}[/tex]

Divide both the sides by 36 then,

[tex]{ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = 14}}}}}[/tex]

Answer:

x = 6

Step-by-step explanation:

2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )

x = - 3 × - 2 = 6

x = 6

The dimensions that will minimize the cost is

h= 2.82876 and r = 1.06078

Given That, C₁ = $10 and C₂= $10 and C₃ = $15

lets multiply the top and bottom, we get,

C₁ × C₂ = $10 ×$ 20 = $ 30

The total cost is,

C = (2πr²) C₁ + (2πrh)C₂

Here,  r is base radius and h is the side length.

The volume is given by and the volume to 20 m³

∴ V = πrh² ⇒ πr²h = 20

So, h = 20/πr²

Now, the problem can be  stated as

minimum h, r C(h, r) restricted to V(h, r) = V₀

Using language multiplier it reads,

L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]

Solving for h, r, λ, we get,

h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)

λ = -2 ∛2πC₁C₂² /V₀

or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214

We know that is a minimum because,

(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r

d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³

and for the found solution has the value

d²/dr² (C₀V) (r) = 240 π > 0

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Answer:

(x - 3)

Step-by-step explanation:

4x² - 12x ← factor out 4x from each term

= 4x(x - 3)

the factors are 4x and (x - 3)

Measure of all angles must equal 180 degrees.

Therefore,
(4x+20) + (2x+34) + x = 180

6x + 54 + x = 180

7x + 54 = 180

7x = 126

x = 18

4(18)+20 = 92

Angle A = 92

2(18)+34 = 60
Angle C = 60 degrees

Unknown angle is 18 degrees because the "x" represents the third angle.

The value of [tex]\sqrt{13}[/tex] is between 3 and 4 on the number line.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

[tex]\sqrt{13}[/tex] = 3.60

The value 3.6 is going to be between 3 and 4 because it is seen to be more than 3 while the value is also seen to be less than 4.

Hence the solution to the problem is the locations are 3 and 4.

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Jamal need to invest $35838.77 in an account.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

As given Jamal wants to save $54,000 for a down payment on a home with 8.2% APR, compounding daily for 5 years.

The compound interest formula is,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here, A = $54000, r = 8.2% = 0.082, t = 5, n = 365

Plug the values in the above formula,

[tex]54000 = P(1+\frac{0.082}{365} )^(^3^6^5^)^(^5^)\\54000 = P(1.0002246575)^1^8^2^5\\54000= P(1.5067483068)\\P = \frac{54000}{1.5067483068} \\P = 35,838.766\\P = 35838.77[/tex]

Hence, Jamal need to invest $35838.77 in an account.

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Harold's solution for the given division problem is not valid because it is not accurate.

We are given two numbers. The numbers are given in scientific notation. The first number is 8.4×10^(-7). The second number is 3.6×10^(-2). We need to find the result of the division of the first number by the second number. Let the result of division be denoted by the variable "Q".

Q = [8.4×10^(-7)] ÷ [3.6×10^(-2)]

Q = [(8.4/3.6)×10^(-7 - (-2))]

Q = [(8.4/3.6)×10^(-7 + 2)]

Q = 2.33×10^(-5)

Harold solved this division problem by first rounding the numbers. His result is 2×10^(-5).

Harold's result differs a lot from the actual result. So, his result is not accurate. Hence, his solution is not valid.

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Protein intake, if he consumes 9 egg whites a day is 32.4 grams.

Given:

Candice eats six egg whites a day with a protein content of 21.6 grams.

6 egg white = 21.6 grams.

1 egg white = 21.6/6

= 216/10/6

= 216/10*6

= 216/60

= 3.6 grams.

9 eggs white = 9 * 3.6

= 9 * 36/10

= 324/10

= 32.4 grams.

Therefore protein intake, if he consumes 9 egg whites a day is 32.4 grams.

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The quadrilateral with the given vertices is a Rhombus , the correct option is (C) .

In the question ,

it is given that ,

the vertices of the quadrilateral are (0,2), (6,0), (0,-2), (-6,0)

let us rename , the coordinates as A(0,2) , B(6,0) , C(0,-2) , D(-6,0) .

the distance between two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula

d = √(x₂ - x₁)² + (y₂ - y₁)²

distance between A(0,2) and B(6,0) is

AB = √(6 - 0)² + (0 - 2)²

AB = √(6² + (-2)²)

AB = √(36+4)

AB = √40

distance between B(6,0) and C(0,-2) is

BC = √(0 - 6)² + (-2 - 0)²

BC = √((-6)² + (-2)²)

BC = √(36+4)

BC = √40

distance between C(0,-2) and D(-6,0) is

CD = √(-6 - 0)² + (0 - 2)²

CD = √((-6)² + (-2)²)

CD = √(36+4)

CD = √40

distance between D(-6,0) and A(0,2) is

DA = √(0 -(-6))² + (2 - 0)²

DA = √(6² + 2²)

DA = √(36+4)

DA = √40

we see that the length of all the sides  is √40 ,

all the sides are same in Square and Rhombus ,

But from the graph below, we see that the quadrilateral formed is in the shape of the Rhombus .

Therefore , The quadrilateral with the given vertices is a Rhombus .

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Value of tan90 is 1/0 which is undefined

Let AB, BC, AC be the base(adjascent side), side opposite to θ, hypotenuse of a right angled triangle respectively.

Now as per sine, cosine and tangent formulas, we have here:

It is seen from these formulaes that

Now, other formulas for trigonometry ratios are:

The other way of representing trigonometric values formulas are:

Therefore, value of tan90 is undefined.

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The fraction value of tan90° after using trigonometric value is 1/0 that is undefined.

What is trigonometric ratio?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan 90°

Tan 90 degrees in radians is written as

=>tan (90° × π/180°)

=> 1/0 = undefined.

Hence the fraction value of tan 90° is 1/0 that is undefined.

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The equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.

Given: A line is perpendicular to line y = 4x – 7  and passes through point A (8, 2).

We know that,

Slope of line perpendicular to another line is negative reciprocal of its slope.

So, m(slope) = -1/4

Equation of line is given as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 8)

y + (1/4)x = 4

Therefore, the equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

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A linear graph with a negative slope indicates that as the independent variable decreases, the dependent variable increases.The line with a negative slope is sloping down to the right.

This relationship is represented by a line sloping down to the right. A line with a negative slope indicates that there is a negative correlation between the two variables. This means that as one variable decreases, the other variable increases.

This is because the line is going down from left to right, which means that the y-value is increasing as the x-value decreases. This relationship is known as a negative correlation.It is also known as an inverse relationship. In an inverse relationship, the two variables move in opposite directions. As one variable decreases, the other variable increases.

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Explanation:

To isolate the Y from y - 3 = 2/5 (x+4), you need to add 3 from both sides to move it to the right side of the equation:

y - 3 = 2/5 (x+4)

+3         +3

y = 2/5 (x+4) + 3

Answer:

add 3 to both sides

or move 3 across the equal sign, which will change its sign from - to +

= y = 2x + 8 / 5 +

Answer: Angles 6,2,3 are the same and are all 112 degrees.

Angles 1,4,5,8 are the same and are all 68 degrees.

Step-by-step explanation:

Angles 6,2,3 are all 112 degrees because of diagonal angle rule.

Angles 1,4,5,8 are 180-112=68 degrees because we can use 180 degree angle rule.

Hope this helped, If you have any questions or clarifications, comment below!

Please rate!

x² + (y – 3)² = 36 and x² + (y + 8)² = 36 are equations that represent circles having a diameter of 12 units and a center that lies on the y-axis

Given : x² + (y – 3)² = 36, x² + (y – 5)²= 6, (x – 4)² + y² = 36, (x + 6)² + y² = 144 and x² + (y + 8)² = 36

and x² + (y + 8)² = 36

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Let's compare the given equations with the standard equation:

x² + (y – 3)² = 36 can be written as:

(x-0)² + (y – 3)² = 6²

This has a center (0, 3), radius r = 6 and diameter = 12 units

x² + (y – 5)²= 6 can be written as:

(x-0)² + (y – 5)² = (√6)²

This has a center (0, 5), radius r = √6 and diameter = 2√6 units

(x – 4)² + y² = 36 can be written as:

(x-4)² + (y – 0)² = 6²

This has a center (4, 0), radius r = 6 and diameter = 12 units

(x + 6)² + y² = 144 can be written as:

(x+6)² + (y – 0)² = 12²

This has a center (6, 0), radius r = 12 and diameter = 24 units

x² + (y + 8)² = 36 can be written as:

(x+0)² + (y + 8)² = 6²

This has a center (0, -8), radius r = 6 and diameter = 12 units

Therefore, the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36

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The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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Answer:

Step-by-step explanation:

so,  I was just commenting about word problems to another person and here is a great example of a word problem that is too complex.  They are using the term  "function rule"  that is too broad.  They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about.  We need to understand what "function rule"  really means.   They have also used the varible "s"  which is mostly reserved for  Laplace /  Fourier  transformations.  This is just a really badly written question.   Don't feel bad if  you don't get what it's asking.  it's messy at best.   t(s) is then name of our function,  it's rule ( the function rule)  is 40/s  it's constant of proportionality is 40  ,  This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH  , which is obviously not correct.   There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH,  this function rule is probably not accurate after some time.  the speed probably starts out fast,   slows down till the close to the very end of the race... they jumps up dramatically to the finish.   Watch the Tour de France writer of this question.  :D   The riders slow down as the race progress according to this function rule.  But I don't think that's at all accurate for a real bike race.   they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH  :0

60 seconds long will it take for the planes to reach the same altitude.

Given that,

Two planes are being monitored by an air traffic controller. Plane A is initially at an altitude of 3500 feet, while Plane B is initially at a height of 1970 feet. The altitude of Plane A is increasing at a rate of 40.25 feet per second, while Plane B is doing so at a rate of 65.75 feet per second.

We have to find how long will it take for the planes to reach the same altitude.

Let us take x as the number of seconds in time.

We get,

3500+40.25x for Plan A.

1970+65.75x for Plan B.

Take,

3500+40.25x=1970+65.75x

3500-1970=65.75x-40.25x

1530=25.5x

x=1530/25.5

x=60

Therefore, 60 seconds long will it take for the planes to reach the same altitude.

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Answer:

Step-by-step explanation:

y + 8= 2(x-1)

y+8=2x-2

y=2x-10

Slope equals 2

a. The discount amount of the exercise machine is $3.39.

b. The exercise machine's sale price will be $561.61

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since the exercise machine with an original price of $565 is on sale at 6% off. The discount will be:

= Discount percentage × Price

= 6% × $565

= $3.39

The exercise machine's sale price will be:

= Original price - Discount

= $565 - $3.39

= $561.61

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Answer:

  4x² +4x -20

Step-by-step explanation:

You want the difference between 6x² -5x -12 and 2x² -9x +8.

The difference is found by subtraction. This is the same as adding the opposite.

  (6x² -5x -12) - (2x² -9x +8)

  = 6x² -5x -12  -2x² +9x -8

  = (6 -2)x² +(-5 +9)x +(-12 -8)

  = 4x² +4x -20

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The different proportional relationship is given by:

Relationship B.

The justification is:

Since graph B has a different constant of proportionality and different equation, it is different than other three graphs.

The definition of a proportional equation is given as follows:

y = kx.

Which means that the output variable y is obtained with the multiplication of the constant of proportionality k and the input variable x.

The constant is obtained as the division of y by x of a point (x,y) different of the origin, as follows:

k = y/x.

Hence, for each relationship, the constant is given as follows:

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Answer:

Okay, sorry for answering a few minutes late!

Step-by-step explanation:

So, for data in a table to be a function, the input must only have one output.

Short and sweet answer, hope this helps!

Yes, r=5 is a solution of inequality r<11.

Given the inequality is r<11

Given the value of r is, r=5

Since 5<11

So yes r=5 is the solution of the inequality r<11.

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Proved that the length of AB ≅ the length of CD

The conditions are given that

The line BC and the line AD are parallel lines

The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other

Similarly

The measure of angle BAD is equal to the measure of angle DCB

If angle BAD = angle DCB, then we can say that the given shape is a parallelogram

In the parallelogram the opposite sides will be equal

Then the length of the length of AB equal to the length of CD

Hence, proved that the length of AB ≅ the length of CD

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Answer:

[tex]y=3x-13[/tex]

Step-by-step explanation:

Parallel lines have the same slope. So, the equation is:

[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]

The value of the inequality X + 3 < 6 is x < 3.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information given, the inequality will be illustrated thus:

x + 3 < 6

Collect like terms

x < 6 - 3

x < 3

The value is x < 3.

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