Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0

Answer:

The amount invested at 8% was $11,000

The amount invested at 9% was $19,000

Step-by-step explanation:

Let the variable x represent the amount in $ invested at 8% and let y be the amount in $  invested at 9%

Total amount invested:
x + y = 30000   [1]

8% = 8/100 = 0.08

9% = 9/100 = 0.09

Interest at 8% on $x = 0.08x

Interest at 9% on $x = 0.09x

Total Interest :

0.08x + 0.09y = 2590  [2]

Using equations [1] and [2] we can solve for x and y

We have

x + y = 30000   [1]
0.08x + 0.09y = 2590  [2]

Multiply equation 1 by 0.08 to get
0.08x + 0.08y = 0.08(30,000)

0.08x + 0.08y = 2,400  [3]

Subtract [3] from [2] :

0.08x + 0.09y = 2590  
-
0.08x + 0.08y = 2400  
----------------------------------
       0x + 0.01y = 190

Divide both sides by 0.01
0.01y/0.01 = 190/0.01

y = = 19,000

Use [1] to get value of x

x + y = 30,000

x + 19,000 = 30,000

x = 30,000 - 19,000

x = 11,000

Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).

What does the triangle's angle relationship mean?

Angles and sides in relation to one another The biggest side and angle in any triangle are in opposition to one another. The smallest side and angle in every triangle are on opposing sides. The middle side and middle angle are always in opposition to one another in triangles.

A congruent triangle ,

if all of two triangles' sides match, then they are said to be congruent.

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Answer:

y = 3x + 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 5 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

to find c substitute (- 8, - 4 ) into the partial equation

- 4 = - 24 + c ⇒ c = - 4 + 24 = 20

y = 3x + 20 ← equation of parallel line

Answer:

Step-by-step explanation: From the given point,

The line is: -8x-4y=0

           viz, 2x+y=0

The line should be perpendicular to x = -4

x= -4 is a vertical line crossing the x axis at x= -4

The slope is undefined in x =-4

For an equation in slope intercept form, the general form is ;

y= mx + b where m is the slope and b is the y-intercept

So for any y value, x is always -4

Thus the slope for line x = -4 is not defined

A line perpendicular to x = -4 will thus be a horizontal line with slope 0

For the equation of this line

0= y--5/x-4

0 = y+5 /x-4

0{x-4} = y +5

0 = y+5

y= - 5

Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769

Proportion means a share from total set being discussed.

Data from the given case:

- The assembly has 769 team members.

- The assembly has 353 stations

- At each station, there are 2 shifts operations.

Assuming that 1 person is assigned to 1 shift operation, then there will:

353 x 2 = 706 person assigned.

The remaining team members that not assigned is:

769 - 706 = 63 person.

Therefore, the share or the proportion of unassigned team members is:

63/769

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The required probability is 0.852

Here, n=15

P(X ≤5) = P(X = 1)+...+ P(X = 5)

            = [(¹⁵₀)(0.25)⁰ (1-025)¹⁵⁻⁰ +...(¹⁵₅)(0.25)⁵ (1-0.25)¹⁵⁻⁵]

            = 0.01336+...+0.16515

            = 0.85163

            = 0.852  (Round to 3 decimal place)

Hence, the required probability is 0.852

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Note that a line whose equation is in the form :

has a slope of m

and a y-intercept of b

Slope is also equal to rise/run :

where rise is the number of vertical units between two points and run is the number of horizontal units between two points.

Note also that upward and right movement is positive, downward and left movement is negative.

From the figure, the vertical units between two given points is 3 units upward, so this is positive.

The horizontal units between them is 2 units to the right which is also positive.

The slope will be :

Next is to solve for b (y intercept).

y-intercept is the point where the line intersects the y-axis.

From the graph, the lines intersects at point (0, 2) on the y-axis

Therefore, the value of b is 2

Rewriting the equation, the answer is :

The equation is = because 1 makes a denominator equal zero and is a solution of the equation derived from cross multiplying. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.

An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation. A valid solution to a problem that vanished during the process of solving it is referred to as a missing solution.

We have to open the equation by using cross multiplication

10(3x - 3) = 15(x² - 1)

= 30x - 30 = 15x² - 15

we would have to factorize

30(x-1) = 15(x-1)(x+1)

We have to divide by 15(x-1)

2 = x + 1

take the like terms

2 -1 = x

x = 1

Hence the equation that has the extraneous solution is option a because the solution is 1.

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Answer:x>-11/2

search it for a better understanding of the understanding the question

Answer:

x > -11/2

Step-by-step explanation:

Given inequation,

→ 12(x + 3) > 4x - 8

Now the value of x will be,

→ 12(x + 3) > 4x - 8

→ 12x + 36 > 4x - 8

→ 12x - 4x > -8 - 36

→ 8x > -44

→ [ x > -11/2 ]

Hence, value of x is -11/2.

Answer:

23

Step-by-step explanation:

The p-value of the test corresponding to study a was found to be 0. 40. and the p-value for study b is 0.80

The entire area under the crucial range of values on both sides of the curve in a two-tailed test represents the likelihood of occurrence (negative side and positive side)

As a result, the connection below provides the probability values for a two-tailed test when compared to a one-tailed test.

Here

By replacing the supplied value in the previous equation, we obtain -

values of the probabilities for a two-tailed test

p-value = P (alpha/2) +  P (alpha/2)

p-value = 0.40 + 0.40

            =0.8

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Answer: the Equation is y-3=0.4(x-1) or y-5=0.4(x-6).

Step-by-step explanation: I hope this helps.

Answer:

First answer is obtuse

The second answer is scalene

Step-by-step explanation:

Obtuse is when an angle is over 90

Scalene since all the angles are different, all the side lengths are different.

the answer is 5896. . . . . . ... . . . . . ......................

Hello!

When multiplying 67 x 88, the correct answer would be 5896.

Hope this helped!

There are 264 red marbles in a bag.

What is Marbles?

A marble is a tiny, sphere-shaped object that is frequently fashioned of agate, glass, clay, steel, or plastic. They come in a variety of sizes, but the most have a diameter of about 13 mm (12 in). These toys can be made into works of art or utilized in a variety of marble-based activities. They can also be used in races or runs. They are frequently collected for their pleasing colors and nostalgic appeal.

Let x = Number of red marbles

y = Number of black marbles.

A bag contains 275 marbles.

So, x + y = 275             ..(1)

There are 24 red marbles for every black marble.

x = 24y       ..(2)

Plug value of x in equation (1).

24y + y = 275

25y = 275

y = 11

Put y = 11 in equation (2),

x = 24(11)

x = 264

Hence, there are 264 red marbles in the bag.

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Given:

Required:

To find the quotient and remainder using synthetic division.

Explanation:

Consider

Here the quotient is

And the remainder is

Final Answer:

Quotient :

Remainder : -9.

   y - 5 = -1 ( x + 3 )  is Equation of a Lin in slope intercept form,.

What is in slope-intercept form?

Slope between the points M(-3, 5) and N(2, 0).

       m = 0 - 5/2 + 3

       m = -5/5  = -1

the equation of   point-slope form

    y - y₁ = m ( x - x₁ )

   y - 5 = -1 ( x - ( -3 ))

   y - 5 = -1 ( x + 3 )

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Answer:

==============================

[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]                                              Given

[tex]3(ax+b)=4(x+c)[/tex]                                     Cross-multiply

[tex]3ax + 3b=4x+4c[/tex]                                       Distribute

[tex]3ax-4x=4c-3b[/tex]                                       Collect terms with x

[tex]x(3a-4)=4c-3b[/tex]                                       Factor out x

[tex]x=\cfrac{4c-3b}{3a-4}[/tex]                                                   Divide both sides by 3a - 4

The all possible zeros predicted by the Rational Zero Theorem individually and separated by commas are  ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.

P(x) = 11x³ + 2x² + x + 10

The factors of the constant term 10 is  ±1, ±2, ±5, ±10 (=p)

The factors of leading coefficient are ±1, ±11 (= q)

The possible rational zeros are p/q : ±1/1, ±1/11, ±2/1, ±2/11, ±5/1, ±5/11, ±10/1, ±10/11.

After simplification the possible roots are  ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.

Therefore, ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11. are the all possible zeros predicted by the Rational Zero Theorem individually and separated by commas.

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Based on the amount you have received in grants, and the amount the boss wants to increase it to, the increase the new amount represents over the previous amount is $15,000 or 33.3%.

Your boss wants to increase the grants to $60,000 from the current amount of $45,000.

This means that the new amount will represent an increase over the previous amount by:
= 60,000 - 45,000

= $15,000

In percentage terms this is:
= Increase over previous amount / Previous amount x 100%

= 15,000 / 45,000 x 100%

= 33.3%

In conclusion, the difference between the grants applied for in the past 5 years and the amount the boss is asking for, gives the increase of $15,000.

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Answer:2 is the scale factor

Step-by-step explanation:

Answer:

The answer is |-3|

Step-by-step explanation:

The absolute value of a negative number will always be the same number but positive. Like the absolute value of |-4| will be 4.

The height of plant will be 7.56cm tall after 2 weeks

The original height of the plant is 6.2cm

The height increases by 11% each week

= 11/100

= 0.11

The increase of the plant in a week

= 0.11 × 6.2

= 0.682

The height of the plant after two weeks can be calculated as follows

= 0.682 + 0.682

= 1.364

= 6.2 + 1.364

= 7.56

Hence the height of the plant after 2 weeks is 7.56cm

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1) Area of patio = 1/2 base x height

Height = 3.1ft

base = 7 + 10 =17 ft

Area = 1/2 x 3.1 x 17

Area of patio = 26.35 square ft

1 yard = 3 ft

1 square yard = 9 square ft

so the area of the patio in yard is

26.35/9 = 2.927777778 square yard

2) Cost of concrete = $10/square yard poured 1/9 yard deep+ $60 delivery fee

for 2.9277777778 square yard it will cost 1/9($10 x 2.9277777778) + $60 =$

3)

We can define the percent error as the difference between the estimated value and the actual value, divided by the actual value.

In this case, the estimated value (what Jimmy thought he had purchased) is 7 and the actual value is 6.

Then, the percent error is:

The percent error is 16%.

Given:

Principal (p) =$3,000

Time (T) = 48 months = 4 years

Interest rate = 4.5%

Required :

Ending balance = ?

The simple interest :

Ending balance :

Ending balance = $ 3540

Step-by-step explanation:

you don't a type your question. so if it correct i will be happy to help you

the size of the wedge for aqua pencils is 43°

Given:

A table showing the pencil collection

To find:

the portion that represents the aqua pencils in degree

The total number of pencils = 23 + 106 + 62 + 47 + 32

The total number of pencils = 270

In degrees:

Total angle in a circle = 360°

Size of the wedge for aqua = number of aqua pencils/total pencils × 360°

To the nearest degree, the size of the wedge for aqua pencils is 43°

√12

Explanation:

though it may not be a simplification,

2√3

can be shown as

√12

.

2=√4