A system of 3 linear equations in 3 variables is consistent and independent. How many solutions to the system exist

Answer:

[tex]\large\boxed{\text{The slope}\ m=-\dfrac{3}{2}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation of a line in the standard form:

[tex]6x+4y=8[/tex]

Convert to the slope-intercept form:

[tex]6x+4y=8[/tex]          subtract 6x from both sides

[tex]4y=-6x+8[/tex]           divide both sides by 4

[tex]y=-\dfrac{6}{4}x+\dfrac{8}{4}[/tex]

[tex]y=-\dfrac{3}{2}x+2[/tex]

Answer: Option D

Step-by-step explanation:

The equation of the line in slope intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b the y-intercept.

Solve for y from both equations:

[tex]5y=-3x+9\\y=\frac{-3}{5}x+\frac{9}{5}[/tex]

[tex]5y=-3x+15\\y=\frac{-3}{5}x+3[/tex]

As you can see, the slopes of the lines are equal, therefore, they are parallel.

If the lines are parallel then the system of equtions has no solution.

Answer:

Choice D  is correct answer.

Step-by-step explanation:

We have given a system of equations.

3x + 5y = 9                             eq(1)

3x + 5y = 15                          eq(2)

We have to find the description of the solution of equations.

y = mx+c is the slope-intercept of equation of line where m is slope and c is y-intercept.

Eq(1) can be written as:

y = -3/5x + 3 where slope is -3/5.

Eq(2) can be written as:

y = -3/5x+5 where slope is -3/5.

Equations with equal slopes are of parallel lines and parallel lines have no solution.Hence, system has no solutions.

Choice D  is correct answer.

Answer:

They need 57.5 more feet of rope

Step-by-step explanation:

Add all the lengths of rope together in feet ( so convert the yards to feet; 1 yd=   3 ft) and then subtract that number from 350!

Hope this helped! <3  

I think this is correct

Answer:

The school club needs additional 49.25 feet of rope.

Step-by-step explanation:

Total length of rope needed = 350 feet

Available lengths are :

4 pieces of rope that are each 14 yards in length. Total length = [tex]4\times14=56[/tex] yards

1 piece of rope that is 10.5 yards in length.

Total yards = [tex]56+10.5=66.5[/tex] yards

Now converting yards to feet as the final answer will be in feet.

1 yard = 3 feet

So, 66.5 yards = [tex]3\times66.5=199.5[/tex] feet

1 piece of rope that is 101.25 feet in length.

Total rope in feet = [tex]199.5+101.25=300.75[/tex] feet

As 350 feet of rope is needed, the club needs more rope of 350-[tex]300.75=49.25[/tex] feet

Therefore, the school club needs additional 49.25 feet of rope.

Answer:

The answers for your two question problem are:

a. He should  charge $7 dollars

b.   Maximum value : f(5) = 130

      Minimum value : f(2) = -32

Step-by-step explanation:

First problem

*When he charges $9 , the numbers of customers are an average of 1000

This means the revenue is

1000*$9  = $9000

*When he charges $7 , the numbers of customers are an average of 1500

This means the revenue is

1500*$7  = $10500

Since

$10500 > $9000

The owner should charge $7, to attract more customers and get higher revenue.

Second problem

f(x) = 2x^3 − 24x

To easily solve this problem, we can graph the equation using a calculator or any plotting tool.

Please, see attached picture

The highest point of the graph, in the interval [-3,5] corresponds to

f(5) = 130

and the lowest point :

f(2) = -32

Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In my opinion factoring is the better approach here

Given

x² + 6x - 7 = 0 ← in standard form

Consider the factors of the constant term (- 7) which sum to give the coefficient of the x- term (+ 6)

The factors are + 7 and - 1, since

7 × - 1 = - 7 and + 7 - 1 = 6, hence

(x + 7)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 1 = 0 ⇒ x = 1

Final answer:

Pairs B (y=2/3x-8 and y=-3/2x-8) and F (y=4/5x-8 and y=-5/4x+3) are the only ones with perpendicular lines, as their slopes multiply out to -1.

Explanation:

Lines are perpendicular if the product of their slopes is -1. The slopes (m) are derived from lines in the format y=mx+b.

Thus, the pairs B and F are the only ones that are perpendicular to each other.

Answer:the answer is c

Step-by-step explanation:

this question was on usatestprep and i got it wrong with the answer b that was given.

The correct diagram that shows ∠1 and ∠2 as vertical angles is Option C.

Vertical angles are formed when two lines intersect. They are opposite angles and have equal measures.

If we consider the diagram given, option C shows two intersecting line, ∠1 and ∠2 are opposite angles formed by the intersecting lines, so they are vertical angles.

∠1 = ∠2 (because they are vertically opposite angles)

Thus, the correct diagram that shows ∠1 and ∠2 as vertical angles is option C.

Learn more about Vertical angles here:

https://brainly.com/question/24460838

#SPJ2

The missing diagram is in the image attached

You can factor 12 from both terms to get

[tex]24x+12 = 12(2x+1)[/tex]

Answer:

-1/3

Step-by-step explanation:

The slope of the line has the form y = mx + b where m is the slope. Here the slope is m = 3. A line perpendicular to it will have a negative reciprocal slope. The negative reciprocal of 3 is -1/3.

Answer:

[tex]\boxed{\bold{57 \ Ft.}}[/tex]

Step-by-step explanation:

Area of whole rectangle including triangle: 66 Feet

(6 * 11 = 66)

Area of Triangle: [tex]\bold{\frac{1}{2}Base \ \cdot \ Height }[/tex]

Height: 3

Base: 6 (Solved by using this: (11 - 2 + 3))

Half of base: 3

3 * 3 = 9

66 - 9 = 57

Answer: b=14.7

Step-by-step explanation:

Answer: b=7.5

Step 1: Cross-multiply.

7/5 = 10.5/b

7*b=(10.5)*(5)

7b=52.5

Step 2: Divide both sides by 7.

7b/7 = 52.5/7

Therefore:

b=7.5

Please give me a brainlist :)

Answer:

C.

Step-by-step explanation:

The answer is C since the y intercept is 20.

Answer:

Statement C is true.

Step-by-step explanation:

In this question we will go through each statement.

(A). The equipment starts producing items after about 25 minutes of warning up -  False

Because machine takes 20 minutes to produce the items.

(B). Each item requires about 12 minutes of production time - False

(C). The equipment starts producing items after about 20 minutes of warming up - True

(D) Each item requires about 3 minutes of production time. - False

Answer:

C) J' (-3, 4), N' (1, 4), M' (1, 1), P' (-2,-1)

Step-by-step explanation:

The rule (x, y)→(x - 4, y + 4), means to translate the figure four points to the left and four points up. If we apply this rule to each vertex of the figure, the resulting coordinates are J' (-3, 4), N' (1, 4), M' (1, 1), P' (-2,-1).

Irrational numbers just means that it isn’t rational so this means that A is true. If you look up a chart with irrational,rational,real, and integer it will show that all whole numbers are integers so this means B is true. C is false. Same thing about B proves that D is true. SHORT ANSWER: C is false. I hope this helps.

In  the given statement D is false.

What is Rational number ?

In mathematics, a rational number is any number that can be written as a fraction, in which the numerator (the top number) and the denominator (the bottom number) are both integers, and in which the numerator is not equal to zero. In other words which can be written in p/q form.

It is rational to consider integers as rational numbers, not as irrational, because all integers, whether positive or negative, or zero can be written as p/q, for example, 2, 3 and 5 are rational because they can be written as 2/1, 3/1 and 5/1 respectively.

Due to the fact that the rational numbers as well as the irrational numbers can be added together, we can derive real numbers. This means that all real numbers are not rational numbers, since they contain irrational numbers as well.

Hence, the given statement D is false.

Read more about Rational number here :

https://brainly.com/question/24398433

#SPJ2

Since p = 60 we can plug 60 into the equation.

so instead of (p / 20) x 4 it's (60 / 20) x  4 which equals 12 minutes.

Hope this helped!

Answer:

5/8 of a pizza

Step-by-step explanation:

Answer:

The % is 33.3%

Step-by-step explanation:

Due to:

If 600 is the 100%, then 200 what  % is?

600 ---> 100%

200 ---> %?

% = [(200)*(100)]/[600]

% = 33.3%

Best regards

g mowed 5 lawns and earned $150

Nate mowed 40 lawns and Gabe mowed 34 lawns for the equal earn of money. The value of x is 34.

It is a system of an equation in which the highest power of the variable is always 1. It is a combination of infinite points side by side.

Given

Gabe charges $30 to mow a lawn.

Nate charges $25 to mow a lawn.

Their total combined revenue one summer was $2020.

Nate mowed 6 more lawns than Gabe.

Let the number of lawns mowed by Gabe be [tex]\rm x[/tex].

Then the number of lawns mowed by Nate be [tex]\rm x + 6[/tex].

Then the equation will be

[tex]\rm 30x + 25(x+ 6) = 2020[/tex]

On simplifying, we have

[tex]\begin{aligned} \rm 30x + 25x + 150 &= 2020\\\\\rm 55x &= 1870\\\\\rm x &= 34\end{aligned}[/tex]

Thus, Nate mowed 40 lawns and Gabe mowed 34 lawns for the equal earn of money. The value of x is 34.

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer:

Please refer to step-by-step.

Step-by-step explanation:

Let's solve all of these one at a time.

15. -2x - y = -5

To find the x-intercept, we need to equate the value of y to 0.

-2x - 0 = -5

[tex]\dfrac{-2x}{-2}=\dfrac{-5}{-2}[/tex]

[tex]x=2.5[/tex]

To find the y-intercept, we need to equate the value of x to 0.

-2(0) - y = -5

Now since we cannot have a negative value, we need to divide both sides by -1.

[tex]\dfrac{-y}{-1}=\dfrac{-5}{-1}[/tex]

[tex]y=5[/tex]

To find the slope form, we can simply transpose the value of -2x to the other sides of the equal sign.

-y = 2x - 5

Now we cannot have a negative value for the slope, we need to divide both sides by -1, leaving us with.

y = -2x + 5

16. 6x + 3y = -9

Let's start with the x-intercept.

6x + 3y = -9

6x + 3(0) = -9

[tex]\dfrac{6x}{6}=\dfrac{-9}{6}[/tex]

[tex]x=1.5[/tex]

Now we solve for the y-intercept.

6x + 3y = -9

6(0) + 3y = -9

[tex]\dfrac{3y}{3}=\dfrac{-9}{3}[/tex]

[tex]y = -3[/tex]

Now for the slope.

3y = -6x - 9

Now we need to divide all our variables by 3 to get y.

[tex]\dfrac{3y}{3}=\dfrac{-6x}{3}-\dfrac{9}{3}[/tex]

[tex]y=-2x-3[/tex]

17. x - y = 4

Let's start with the x-intercept.

x - y = 4

x - 0 = 4

[tex]x=4[/tex]

Now we solve for the y-intercept.

x - y = 4

0 - y = 4

-y=4

[tex]\dfrac{-y}{-1}=\dfrac{4}{-1}[/tex]

[tex]y = -4[/tex]

Now for the slope.

x - y = 4

-y = -x + 4

We need to divide all our variables by -1 to get y.

[tex]\dfrac{-y}{-1}=\dfrac{-x}{-1}+\dfrac{4}{-1}[/tex]

[tex]y=x-4[/tex]

18. 3x + 4y = 12

Let's start with the x-intercept.

3x + 4y = 12

3x + 4(0) = 12

[tex]\dfrac{3x}{3}=\dfrac{12}{3}[/tex]

[tex]x=4[/tex]

Now we solve for the y-intercept.

3x + 4y = 12

3(0) + 4y = 12

[tex]\dfrac{4y}{4}=\dfrac{12}{4}[/tex]

[tex]y = 3[/tex]

Now for the slope.

3x + 4y = 12

4y = -3x + 12

[tex]\dfrac{4y}{4}=-\dfrac{3x}{4}+\dfrac{12}{4}[/tex]

[tex]y=-\dfrac{3x}{4}+3[/tex]

19. -7x + 2y = -16

Let's start with the x-intercept.

-7x + 2y = -16

-7x + 2(0) = -16

[tex]\dfrac{-7x}{-7}=\dfrac{-16}{-7}[/tex]

[tex]x=-2\dfrac{2}{7}[/tex]

Now we solve for the y-intercept.

-7x + 2y = -16

-7(0) + 2y = -16

[tex]\dfrac{2y}{2}=\dfrac{-16}{2}[/tex]

[tex]y=-8[/tex]

Now for the slope.

-7x + 2y = -16

2y = -7x - 16

[tex]\dfrac{2y}{2}=-\dfrac{7x}{2}-\dfrac{16}{2}[/tex]

[tex]y=-\dfrac{7x}{2}-8[/tex]

20. x - 5y = 55

Let's start with the x-intercept.

x - 5y = 55

x - 5(0) = 55

x = 55

Now we solve for the y-intercept.

x - 5y = 55

0 - 5y = 55

[tex]\dfrac{-5y}{-5}=\dfrac{55}{-5}[/tex]

[tex]y=-11[/tex]

Now for the slope.

x - 5y = 55

-5y = x + 55

[tex]\dfrac{-5y}{-5}=-\dfrac{x}{-5}+\dfrac{55}{-5}[/tex]

[tex]y=-\dfrac{x}{5}-11[/tex]

Twelve divided by the sum of x and 2 equals the quotient of 4 and the difference of x and 2 , the value of x is 4

Given

Twelve divided by the sum of x and 2 equals the quotient of 4 and the difference of x and 2

we need to write the given expression in equation

Twelve divided by the sum of x and 2 is written as  [tex]\frac{12}{x+2}[/tex]

quotient of 4 and difference of x  and 2 can be written as

[tex]\frac{4}{x-2}[/tex]

Now make them equal and solve for x

[tex]\frac{12}{x+2} =\frac{4}{x-2} \\12\left(x-2\right)=\left(x+2\right)\cdot \:4\\12x-24=4x+8\\12x=4x+32\\8x=32\\x=4[/tex]

So the value of x is 4

Learn more : brainly.com/question/2574967

To solve the given equation 12 / (x + 2) = 4 / (x - 2), we cross multiply, simplify and solve for x, the solution is x=4.

The equation given in this problem translates to the following algebraic equation: 12 / (x + 2) = 4 / (x - 2)

To solve for x, we first cross multiply to remove fractions: 12 * (x - 2) = 4 * (x + 2) which simplifies to 12x - 24 = 4x + 8

Then, subtract 4x from both sides: 8x - 24 = 8 and finally add 24 to both sides: 8x = 32. Therefore, solving for x by dividing both sides with 8, we get x = 4.

https://brainly.com/question/953809

#SPJ11

Answer:

Time to highest point: 5/2, or 2.5 seconds

Ordered pair: (5/2, 50)

Step-by-step explanation:

Find the vertex of h(t). This will be the highest point of the ball

Find the x coordinate of the vertex with the formula: x = -b/(2a)

x = -40/[2(-8)] = -40/-16 = 5/2

to find the y value, plug 5/2 into the equation and solve

h(5/2) = -8(5/2)² + 40(5/2)

   h(5/2) = -8(25/4) + 200/2

          h(5/2) = -200/4 + 100

             h(5/2) = 50

So the ball reached a maximum height of 50 feet

Final answer:

It takes 2.5 seconds for the ball to reach its highest point. The ordered pair representing the highest point is (2.5, 50), where the ball reaches a height of 50 meters.

Explanation:

The equation h = -8t^2 + 40t describes the height of a ball thrown into the air over time, where h is the height above the ground and t is time in seconds. To find how many seconds it takes for the ball to reach the highest point, we find the time at which the vertex of the parabola occurs since the vertex represents the maximum height.

We know that the ball will reach its highest point halfway between the times when it is at ground level (i.e., when h = 0). Factoring the quadratic equation 0 = -8t^2 + 40t gives us:

0 = t(-8t + 40)

0 = t(0, -8t + 40)

Setting each factor equal to zero gives us two values of t:

t = 0 s (when the ball is first thrown)

-8t + 40 = 0 => t = 5 s (when the ball hits the ground again)

Thus, the time to reach the highest point is halfway between 0 s and 5 s, which is 2.5 seconds.

The ordered pair representing the highest point is found by substituting t = 2.5 s into the original equation:

H = -8(2.5)^2 + 40(2.5)

H = -50 + 100

H = 50 meters.

Therefore, the ordered pair representing the highest point the ball reaches is (2.5, 50).

Answer:

[tex]\large\boxed{C.\ (1.5,\ -4)}[/tex]

Step-by-step explanation:

The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):

[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points P(-6, 3) and Q(9, -11).

Substitute:

[tex]M_{PQ}(x,\ y)\\\\x=\dfrac{-6+9}{2}=\dfrac{3}{2}=1.5\\\\y=\dfrac{3+(-11)}{2}=\dfrac{-8}{2}=-4[/tex]

Answer:

(-1.5, -1)

Step-by-step explanation:

Answer:

[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

Step-by-step explanation:

Given: [tex]A=\frac{1}{2}(b_{1} +b_{2})h[/tex]

We need to completely isolate [tex]b_{1}[/tex] to solve.

[tex]A=\frac{1}{2}(b_{1} +b_{2})h[/tex]

[tex]A=(\frac{1}{2}b_{1} +\frac{1}{2} b_{2})h[/tex]

[tex]A=\frac{1}{2}b_{1} h+\frac{1}{2}b_{2}h[/tex]

[tex]-\frac{1}{2}b_{1}h+A=\frac{1}{2}b_{2}h[/tex]

[tex]-\frac{1}{2}b_{1}h=-A+\frac{1}{2}b_{2}h[/tex]

[tex]-\frac{1}{2}b_{1}=\frac{-A}{h}+\frac{1}{2}b_{2}[/tex]

Finally, multiply both sides by -2 to completely isolate [tex]b_{1}[/tex].

[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

The right option is D

See the image

Answer:

x = 6

Step-by-step explanation:

Complementary angles = angles that add up to 90 degrees.

Therefore 8x - 30 + 5x + 42 = 90

13x + 12 = 90

Subtract 12 from both sides and then divide each side by 13.

x = 6

10.54cm2

Answer:

the answer is 10.54 cm2

Step-by-step explanation:

Answer:

The correct answer is 15x⁶ - 20x⁵ + 10x⁴

Step-by-step explanation:

The given expression is  -5x⁴ (-3x² + 4x - 2)​

Points to remember:

xᵃ * x ᵇ = xᵃ⁺ᵇ

To find the simplified expression

-5x⁴ (-3x² + 4x - 2)​ = (-5x⁴ * -3x²)  + (-5x⁴  *  4x ) - (-5x⁴  * 2)​

 = 15x⁴ ⁺² - 20x⁴ ⁺ ¹ + 10x⁴

 = 15x⁶ - 20x⁵ + 10x⁴

Therefore -5x⁴ (-3x² + 4x - 2)​ = 15x⁶ - 20x⁵ + 10x⁴

Answer:

15x⁶-20x⁵+10x⁴ is the simplification of this expression.

Step-by-step explanation:

We have given the expression:

-5x⁴(-3x²+4x-2)​

We have to simplify this expression.

-5x⁴(-3x²+4x-2)​

-5x⁴(-3x²)+(-5x⁴)(4x)+(-5x⁴)(-2)

15x⁴⁺²-20x⁴⁺¹+10x⁴

15x⁶-20x⁵+10x⁴

15x⁶-20x⁵+10x⁴ is the answer.

Step-by-step explanation:

By using the distributive formula, you can solve this:

-a(b - c + d) = -ab + ac - ad

-3(4x - 5y + 6) + 8x - 9

Use distributive property:

-12x + 15y - 18 + 8x - 9

Add/Subtract by the common terms:

-12x + 8x = -4x

-18 - 9 = - 27

Plug it back into an equation:

= -4x + 15y - 27

That is your answer!!

Hope that helped

~A̷l̷i̷s̷h̷e̷a̷♡

Answer:

-4x + 15y - 27

Step-by-step explanation:

-3 (4x -5y + 6) = -3*4x, -3* -5y and -3*6

-3*4x= -12x

-3*-5y= 15y

-3*6= -18

-12x + 15y -18 +8x - 9

Combine like terms (-12x + 8x) and (-18 - 9)

12-8 = 4 and 18+9 = 27 now flip the signs, add the variables back on (the letters) and carry down what was remaining (15y)

-4x + 15y -27

answer is

= 1.312.53 ft²

Answer:

John = $1220.19

Cayden = 1161.62

Step-by-step explanation:

To find how much they'll both get, we can use the formula:

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

First let's start with John.

P = 1000

r = 4% or 0.04

t = 5

n = 4 (Quarterly)

[tex]A=1000(1+\dfrac{0.04}{4})^{4(5)}[/tex]

[tex]A=1000(1+0.01)^{20}[/tex]

[tex]A=1000(1.01)^{20}[/tex]

[tex]A=1220.19[/tex]

Now let's compute for Cayden's.

P = 1000

r = 3% or 0.03

t = 5

n = 12 (Monthly)

[tex]A=1000(1+\dfrac{0.03}{12})^{12(5)}[/tex]

[tex]A=1000(1+0.0025)^{60}[/tex]

[tex]A=1000(1.00.25)^{60}[/tex]

[tex]A=1161.62[/tex]

The monthly compounding gets more yield compared to the quarterly compounding due to the number of times the amount of times it increases per year.