Find the equation of the plane passing through the lines of intersection of the planes :
2x - 7y + 4z = 3 , 3x - 5y + 4z + 11 = 0 and the point ( -2 , 1 , 3 ).

Answer:

C

Step-by-step explanation:

input y=x+3 into the second equation and solve for x

-2x+y=1

so -2x +x+3 =1

solve for x

x = 2

y= 5

This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:

5x + y = 10

x + y = 6

x + 4y = 12

The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.

To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.

For example, using the first and second equations, you can solve for x in terms of y as follows:

x = 6 - y (from the second equation)

y = 10 - 5x (from the first equation)

Substituting y = 10 - 5x into the third equation, you get:

x + 4(10 - 5x) = 12

Simplifying this equation, you get:

-19x + 40 = 0

Solving for x, you get:

x = 40/19

Using x = 40/19 and the equation x + y = 6, you can solve for y as:

y = 6 - x = 6 - 40/19 = 94/19

Therefore, the minimum value of 3x + 2y subject to the given constraints is:

3(40/19) + 2(94/19) = 222/19

And the values of x and y that minimize this expression are:

x = 40/19 and y = 94/19.

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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:

5x + y = 10

x + y = 6

x + 4y = 12

The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.

To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.

For example, using the first and second equations, you can solve for x in terms of y as follows:

x = 6 - y (from the second equation)

y = 10 - 5x (from the first equation)

Substituting y = 10 - 5x into the third equation, you get:

x + 4(10 - 5x) = 12

Simplifying this equation, you get:

-19x + 40 = 0

Solving for x, you get:

x = 40/19

Using x = 40/19 and the equation x + y = 6, you can solve for y as:

y = 6 - x = 6 - 40/19 = 94/19

Therefore, the minimum value of 3x + 2y subject to the given constraints is:

3(40/19) + 2(94/19) = 222/19

And the values of x and y that minimize this expression are:

x = 40/19 and y = 94/19.

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The Volume of stock solution needed = 1 mL

Molarity of stock solution (M1) = 1.50 M

The volume of stock solution needed (V1) = to be calculated

Molarity of diluted solution (M2) = 0.0750 M

The volume of diluted solution (V2) = 20 mL

M1V1 = M2V2

Volume of stock solution (V1) = M2V2 / M1 = (0.075 M x 20 mL) / (1.5 M) = 1 mL

So; the Volume of stock solution needed = 1 mL

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Answer:  Maria is 12 years old, Jonas is 6 years old, and Franklin is 3 years old.

Step-by-step explanation:  Let's start by assigning variables to represent the ages of Maria, Jonas, and Franklin.

Let's use the variable "M" to represent Maria's age.

Let's use the variable "J" to represent Jonas's age.

Let's use the variable "F" to represent Franklin's age.

From the problem statement, we know that:

Maria is twice the age of Jonas: M = 2J

Jonas is twice the age of Franklin: J = 2F

Franklin is 2 years less than half of Maria's age: F = 0.5M - 2

We can use these equations to solve for the ages of Maria, Jonas, and Franklin.

First, we can substitute J = 2F into the equation M = 2J to get M = 2(2F) = 4F.

Next, we can substitute this expression for M into the equation F = 0.5M - 2 to get F = 0.5(4F) - 2, which simplifies to 2F = 6 and therefore F = 3.

Now that we know Franklin's age, we can use the equation J = 2F to find Jonas's age: J = 2(3) = 6.

Finally, we can use the equation M = 2J to find Maria's age: M = 2(6) = 12.

Therefore, Maria is 12 years old, Jonas is 6 years old, and Franklin is 3 years old.

Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40 points.

A percentage is a means to represent a piece of 100 as a ratio or percentage. The sign for it is % (percent), which stands for "per hundred." If you state, for instance, that 50 out of 100 people like chocolate, then means that 50 out of 100 people, or 0.5 (50/100), like chocolate overall. In several disciplines, including finance, business, mathematics, and statistics, percentages are frequently used.

Part A:

Say we decide to set the number of points gained on the quiz at 40. The following formula is used to determine your percentage score if the quiz was worth a total of 40 points and you received 34 of them:

(Points earned / Total Points) x 100% is the percentage score.

Score in percentage: (34 / 40) x 100%

Score in percentages: 85%

Your percentage score would be 85% if you completed the quiz and received 34 out of a possible 40.

Part B:

You would receive a B on the specified grading scale based on the percentage score of 85%. The percentage score gained in section A falls within the range required for a B grade on the grading scale, which is awarded for percentage scores between 80% and 89%.

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The theoretical probabilities are: 0.15, 0.15, and 0.05 respectively

Probability is a branch of mathematics concerned with the analysis of random phenomena

The given parameters that will help us to get the probabilities are

25% are stakeholders

20% have dark hair

The probability of being stakeholders 20%/25%

= 0.20/0.25 = 0.

b)  1-0.8 * 1.0.25

0.2 * 0.75 = 0.15

c.  0.2 * 0.75 = 0.15

d.  Has light hair and is a stakeholder

0.20 * 0.25

= 0.05

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Some poetic elements found in the poem are:

Poetic elements are described as  the devices used that characterize a piece of writing as a poem and  are integral to categorise a piece of writing as poetry, such as poetic meter and rhyme scheme.

In the poem, the author uses Imagery which is described as use of sensory details to create vivid mental images in the reader's mind.

The author made use of metaphor as a  comparison between two things that are not alike, in order to create an image or deepen understanding.

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Answer:

In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.

A = (1/2)Pa

= (1/2)(2)(8/√3)(6)(8)

= (384√3)/3 = 128√3 = 221.7 units^2

Chloe can travel 4.4 miles less than Jin on one gallon of gas.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

Chloe travels 93 miles on 5 gallons of gas, hence the constant is given as follows:

k = 93/5

k = 18.6 miles per gallon.

Jin's ratio is of 23 miles per gallon, hence he can travel more and the difference is given as follows:

23 - 18.6 = 4.4 miles per gallon.

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Answer:

A) 5x+32=67

Rebecca is 7, Mary is 15, and Jill is 45

Step-by-step explanation:

Rebecca is x years old.

If Mary is 8 years older than Rebecca, Mary's age is 8 more than x.

We can write Mary's age as:

x+8

Jill is three times older than Mary.

This means that Jill's age is equal to three times x+8.

We can write Jill's age as:

3(x+8)

Use the distributive property.

3(x+8)=

3x+24

So, Jill's age (in terms of x) is 3x+24.

The sum of their ages is 67, so if we add all of their ages, we will get 67.

x+(x+8)+(3x+24)=67=

5x+32=67

Not sure if you want this solved, but here it is:

5x+32=67=

5x=35=

x=7

Let's find Mary's age.

x+8=

7+8=

15.

Now, let's find Jill's age.

3x+24=

3(7)+24=

21+24=

45.

So, Rebecca is 7, Mary is 15, and Jill is 45.

Answer:

1.x=7 or x=-7

2.x=root of 65 or x=-root of 65

Step-by-step explanation:

I have put what I mean by root 65

A rational number between 8/10 and 1/8 is 37/80.

We know that a rational number between two rational numbers can be given by finding the average of the two given numbers:

The numbers are 8/10 and 1/8.

Let's simplify the fractions first:

8/10 = 4/5 (dividing both numerator and denominator by 2)

1/8 = 1/8 (already in simplest form)

Average = [tex](\frac{4}{5} + \frac{1}{8})/2[/tex]

              = [tex](\frac{(4*8) + (5*1)}{40} )/2[/tex]

             = [tex](\frac{37}{40}) /2[/tex]

             = [tex]\frac{37}{80}[/tex]

So, the rational number halfway between 8/10 and 1/8 is 37/80.

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Answer:18

Step-by-step explanation:18

Okay, let's break this down step-by-step:

* Circle O has chords AB and CD that intersect at E

* AE = 3 inches

* BE = 8 inches

* CE is 2 inches longer than DE

So we know:

AE = 3 inches

BE = 8 inches

CE = DE + 2 inches

To find DE, we can use the Pythagorean theorem for any right triangle:

a^2 + b^2 = c^2

In this case:

3^2 + 8^2 = c^2

9 + 64 = 73

c = 8 inches

So the hypotenuse AE forms a right triangle with leg BE of length 8 inches.

Now we have the length of one leg (BE = 8 inches) and the hypotenuse (AE = 8 inches).

We can use the relation between leg, hypotenuse and sine to calculate the other leg (DE):

sin(A) = DE / 8

DE = 8 * sin(A)

Without knowing the angle A, we can make an estimate:

sin(A) ≈ A (for small A)

So DE ≈ 8A inches

Now we know:

CE = DE + 2 inches

And DE ≈ 8A inches

So: 8A + 2 = DE

=> DE = 10A

And since A is small, we can say: DE ≈ 10 * A inches

To summary, if AE = 3 inches and BE = 8 inches,

then DE ≈ 10 * A inches

DE is approximately 10 times some small angle A.

Does this make sense? Let me know if you have any other questions!

Step-by-step explanation:

See image

a) The area of the triangle is 13.3 square units.

b) The area of the rectangle is 57.4 square units.

Let's start with the triangle. The area of a triangle can be calculated by multiplying its base and height and then dividing the result by 2. In your case, the base of the triangle is 7 units and the height is 3.8 units. Therefore, the area of the triangle can be calculated as:

Area of triangle = (Base × Height) ÷ 2

= (7 × 3.8) ÷ 2

= 13.3 square units

Now, let's move on to the rectangle. The area of a rectangle can be calculated by multiplying its length and width. In your case, the width of the rectangle is 7 units and the height is 8.2 units. Therefore, the area of the rectangle can be calculated as:

Area of rectangle = Length × Width

= 8.2 × 7

= 57.4 square units

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Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=[tex]\frac{122}{3}[/tex]≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

The other angle that is congruent to  ∠DFA is: ∠BFC

Congruent angles are defined as two or more angles that are said to be identical to each other. This means that the measure of these angles is equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.

Now, we want to find the angle that is congruent to ∠DFA.

By inspection, we can see that ∠BFC is an opposite angle to ∠DFA.

We know that Opposite angles are the two angles opposite each other when two lines cross. They can also be called vertical angles due to sharing a vertex, which is the point where the two lines connect. Opposite angles always have the same measurement, making them congruent.

Thus, ∠BFC is congruent to  ∠DFA.

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Okay, let's break this down step-by-step:

* There are 2 white shirts, 5 black shirts, and 3 gray shirts in the drawer.

* That's a total of 2 + 5 + 3 = 10 shirts.

* We want to find the probability that the chosen shirt is NOT white.

* So there are 5 + 3 = 8 shirts that are NOT white.

* Probability = (Number of favorable outcomes) / (Total possible outcomes)

* So in this case, Probability = 8/10 = 4/5

Therefore, the probability that the chosen shirt is NOT white is 4/5.

Answer:

25

Step-by-step explanation:

range = largest number - smallest number

38-13=25

Answer:

t = 4

Step-by-step explanation:

Use the quadratic formula to find the zeros of the function, when h(t) equals 0 that means the ball is touching the ground, giving the maximum time it took for the ball to hit the ground.

[tex]\frac{-b\frac{+}{-} \sqrt{b^2-4*a*c} }{2*a} \\\frac{-14\frac{+}{-} \sqrt{14^2-4*-4*8} }{2*-4} \\t = -0.5,4[/tex]

It takes 4 seconds, since time can not be negative

Answer: The actual car length is 12ft.

Step-by-step explanation:

Actual car length = 3cm x 4ft/cm = 12ft

The statement that shows equivalent measurements is "4.5 meters = 0.0045 kilometers".

How to solve the problem?

To convert meters to kilometers, we need to divide by 1000, since there are 1000 meters in a kilometer. Therefore, 4.5 meters is equal to 4.5/1000 = 0.0045 kilometers.

The other statements are incorrect:

4.5 meters is not equal to 0.045 centimeters, since there are 100 centimeters in a meter, so 4.5 meters is equal to 450 centimeters.

4.5 meters is not equal to 0.45 decimeters, since there are 10 decimeters in a meter, so 4.5 meters is equal to 45 decimeters.

4.5 meters is not equal to 45 decameters, since there are 10 meters in a decameter, so 4.5 meters is equal to 0.45 decameters.

It is important to be able to convert between different units of measurement in order to make accurate comparisons and calculations. In this case, the correct conversion factor was used to convert meters to kilometers, resulting in an equivalent measurement.

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Billie made the error in the second step of the equation

Billie made an error in Step 2. She added 9 to one sides of the equation, but she should have added 9 to the left side only. The correct steps are as follows:

Step 1: x^2 + 6x = 16

Step 2: x^2 + 6x + 9 = 16 + 9

Step 3: (x + 3)^2 = 25

Step 4: x + 3 = ±√25

Step 5: x = -3 + 5, x = -3 - 5

Step 6: x = 2, x = -8

So, the correct solutions are x = 2 and x = -8.

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The May raw materials purchases for May in Rensing Ltd., in dollars terms, is $32,620.

The cost of raw materials purchased in May is determined by computing the required production units and multiplying the result by 2 units and the unit raw material cost.

                                     April     May      June

Sales                           2,520   2,440   2,390

Ending inventory       2,280    2,170    2,330

Goods available for

 sale                          4,800    4,610    4,720

Beginning inventory              2,280    2,170

Production units                     2,330

Raw materials purchases      4,660 (2,330 x 2)

Raw materials price per unit = $7

Total purchases of Raw Materials for May = $32,620 (4,660 x $7)

Thus, we can conclude that in May Rensing Ltd. purchased raw materials worth $32,620.

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The expression for the area of the compound shape in cm² is 2x^2 + 11x - 6.

To find the expression for the area of the compound shape, we need to first calculate the individual areas of Shape A and Shape B, and then add them together.

The area of Shape A is given by multiplying its length and width:

Area of Shape A = (x + 3) * (x + 2)

The area of Shape B is given by multiplying its length and width:

Area of Shape B = (x + 6) * (x - 2)

Now, we can add the two areas together to get the expression for the area of the compound shape:

Area of compound shape = Area of Shape A + Area of Shape B

= (x + 3) * (x + 2) + (x + 6) * (x - 2)

Expanding the above expression, we get:

= x^2 + 2x + 3x + 6 + x^2 + 6x - 12

= 2x^2 + 11x - 6

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The equivalent speed in still water for the boat is 30.26 km/h.

The equivalent speed of the boat in still water is calculated as follows;

The boat needs to travel North at 30 km/h,

The speed of the wave = 4 km/h

The equivalent speed of the boat in still water is calculated by applying Pythagoras theorem;

v² = (4 km/h)² + (30 km/h)²

v = √ [(4 km/h)² + (30 km/h)²]

v = 30.26 km/h

Thus, the equivalent speed of the boat is calculated by applying vector addition principle.

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Answer:   y=4

Step-by-step explanation:

The Parent function [tex]y=a^{x}[/tex]  has a horizontal asymtote at y=0

because the function approaches 0 but never touches it no matter how small the number you input.  See image.  Asymtotes are like a boundary that is not passed

Your curve has been shifted up 4 so y=4

See image

Extra info:   y-intercept = 3000

shifted right 2