Which equation represents a line which is perpendicular to the line 4x
y = -2?

Answer:

30

Step-by-step explanation:

200 x .15   (1-.85 = .15)

30

Hello!

3x + 4 = 1

3x + 4 - 4 = 1 - 4

3x = -3

3x/3 = -3/3

x = -1

The solution of the equation 3x + 4 = 1 is -1.

The answer is:

C) x = -1

Work/explanation:

To solve this equation, I subtract 4 from each side:

\(\sf{3x+4=1}\)

Subtract :

\(\sf{3x=-3}\)

Divide each side by 3:

\(\sf{x=-1}\)

Hence, C is correct.

Answer:

Verified

Area = 13.12 square units.

Step-by-step explanation:

Let the given points / vertices of the parallelogram be represented as follows:

A(2,-1,1),

B(5, 1,4),

C(0,1,1),

D(3,3,4)

In vector notation, we can have;

A = 2i - j + k

B = 5i + j + 4k

C = 0i + j + k

D = 3i + 3j +4k

One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.

(i) Now, let's find the various sides of the assumed parallelogram. These sides are:

AB = B - A = [5i + j + 4k] - [2i - j + k]            open the brackets

AB = 5i + j + 4k - 2i + j - k                            collect like terms and solve

AB = 5i - 2i + j  + j - k + 4k

AB = 3i + 2j+ 3k

BC = C - B = [0i + j + k] - [5i + j + 4k]            open the brackets

BC = 0i + j + k - 5i - j - 4k                             collect like terms and solve

BC = 0i - 5i + j  - j + k - 4k

BC = -5i + 0j - 3k

CD = D - C = [3i + 3j +4k] - [0i + j + k]            open the brackets

CD = 3i + 3j + 4k - 0i - j - k                             collect like terms and solve

CD = 3i - 0i + 3j  - j + 4k - k

CD = 3i + 2j + 3k

DA = A - D = [2i - j + k] - [3i + 3j +4k]            open the brackets

DA = 2i - j + k - 3i - 3j - 4k                             collect like terms and solve

DA = 2i - 3i  - j  - 3j + k - 4k

DA = - i - 4j - 3k

AC = C - A = [0i + j + k] - [2i - j + k]            open the brackets

AC = 0i + j + k - 2i + j - k                             collect like terms and solve

AC = 0i - 2i  + j  + j + k - k

AC = - 2i + 2j +0k

BD = D - B = [3i + 3j + 4k] - [5i + j + 4k]            open the brackets

BD = 3i + 3j + 4k - 5i - j - 4k                             collect like terms and solve

BD = 3i - 5i  + 3j  - j + 4k - 4k

BD = - 2i + 2j + 0k

(ii) From the results in (i) above, it has been shown that;

AB is equal to CD, and that implies that AB is parallel to CD. i.e

AB = CD => AB || CD

Also,

AC is equal to BD, and that implies that AC is parallel to BD. i.e

AC = BD => AC || BD

(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.

(B) Now let's calculate the area of the parallelogram.

To calculate the area, we find the magnitude of the cross product between any two adjacent sides.

In this case, we choose sides AC and AB.

Area = | AC x AB |

Where;

\(AC X AB = \left[\begin{array}{ccc}i&j&k\\-2&2&0\\3&2&3\end{array}\right]\)

AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)

AC X AB = 6i + 6j - 10k

|AC X AB| = \(\sqrt{6^2 + 6^2 + (-10)^2} \\\)

|AC X AB| = \(\sqrt{36 + 36 + 100} \\\)

|AC X AB| = \(\sqrt{172} \\\)

|AC X AB| = 13.12

Therefore the area is 13.12 square units.

PS: The diagram showing this parallelogram has been attached to this response.

As a result, $17.55 should be chosen as the selling price to sell 480,000 units for a profit of $1,500,000.

We must add the desired net profit of $1,500,000 to the total cost of producing the 480,000 units to determine the selling price.

You can determine the overall cost as follows:

Total cost equals fixed costs plus. (Variable costs per unit x Number of units)

Total expense equals $984,000 plus ($14.50 x 480,000)

Cost in total is $7,224,000.

To reach a net profit of $1,500,000, we must add the following sum to the whole expense:

Selling price is calculated as Total Cost + Desired Net Profit / Units Sold.

($7,224,000 + $1,500,000) / 480,000 = selling price

Price to Sell: $17.55

As a result, $17.55 should be chosen as the selling price to sell 480,000 units for a profit of $1,500,000.

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Answer:

--------------------------

To determine the selling price, we first need to calculate the total  variable cost:

Now calculate the required revenue:

Find the required selling price per unit:

Total number of slices = 12

No. of slices eaten by Kesh = 2

No. of slices eaten by Jorge = 3

No. of slices left

= Total number of slices - (No. of slices eaten by Kesh + No. of slices eaten by Jorge)

= 12 - (2 + 3)

= 12 - 5

= 7

Fraction of the pizza left

= No. of slices left/Total number of slices

= 7/12

Answer: 7/12

Find the total amount of pizza eaten.

Kesh = 2 slices

Jorge = 3 slices

Total eaten: 5/12

Subtract 5/12 from 12/12.

12/12 - 5/12 = 7/12

Answer = 7/12

Hope this answer helped!

Answer:

A. 32 sq. units

Step-by-step explanation:

To find the area of a parallelogram, multiply the base by the height.

In this case, the base is 8.

However, the height is unknown.

According to the word problem, the height is HALF the base.

To find half of the base, we divide it by 2.

8 / 2 = 4

4 is the height.

Lastly, multiply as usual.

Base ⋅ height:

8 x 4 = 32.

Therefore, the area of the parallelogram is 32 sq. units.

Answer:

Parallel

Step-by-step explanation:

The have equal slopes

Answer:

15

Step-by-step explanation:

5x - 6 = 4x + 9

    +6         + 6

    5x = 4x + 15

  -4x     - 4x

x = 15

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer: (3, 1)

Step-by-step explanation: Plug in (3,1) to get -2x3 -1 to get -7≤-4, and -7 is less than -4

The additional information is required in order to know that the triangle are congruent is, GW ≅ WX.

What is congruent triangles?

If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.

We have to show that the the triangles ΔVWX and ΔEWG are congruent by using the AAS (angle, angle, side) criteria.

From the given reasons,

∠V ≅ ∠E

∠VWX ≅ ∠EWG

From this the AA criteria is satisfied.

We want sides of the triangle are congruent.

From the figure, GW ≅ WX

Therefore, by AAS the two triangles ΔVWX and ΔEWG are congruent.

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Answer:  Let me explain

Step-by-step explanation:

So if the percents of the cookies all together is 100% and you only have 70%

that means you sold 30% of the trefoils which is equal to 30/100

then simplify the answer

30/10

100/10

3/10 is your final answer

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

4/25

Step-by-step explanation:

4/5 ÷ 5 = 4/5 × 1/5 = 4/25

Answer:

Your correct answer is 31/50 + -4/25 i

Step-by-step explanation:

5+4i/6+8i = 31/50 + -4/25 i

Answer:

Joey needs 9 boxes.

Step-by-step explanation:

You will use the fact that a dozen is 12 cookies. You're trying to find how many dozen are in 100.

Something like:

12b = 100

or if you're studying inequalities:

12b >= 100

Divide by 12 to solve. See image. Interpret the results. See image.

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.

The volume of a solid is the three dimensional space the solid occupies.

The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;

Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³

Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³

70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³

The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0

The number of times Johnny needs to use the wheelbarrow is about 41 times

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Answer:

1.75 * 0.84

Step-by-step explanation:

1.74 * 0.84 = 1.4616

1.79 * 0.69 = 1.2351

Answer:

1.74 x 0.84 is greater

Step-by-step explanation:

1.74 x 0.84 = 1.4616

while

1.79 x 0.69 = 1.23509

Answer: Evaluation : 6x^2  +37x+38           Factor: 6(x − - √ 457-37/12  )(x−  √ 457-37/12)

Step-by-step explanation: Evaluation: (6x ^2 +36x+33)+(x+5)

Combine 36x and x to get 37x.

6x  ^2 +37x+33+5

Add 33 and 5 to get 38.

6x  ^2  +37x+38

Factor: Its pretty long

Answer:

\(246.22\ \text{inches}^2\)

Step-by-step explanation:

\(r_1\) = Radius of arm = 15 inch

Length of blade = 11 inches

\(r_2\) = Radius of point at which the blade is mounted = 4 inches

\(\theta\) = Angle of the sector = \(135^{\circ}\)

The required area is ABDE

\(ABDE=ACE-BCD\\\Rightarrow ABDE=\dfrac{\theta}{360^{\circ}}\pi r_1^2-\dfrac{\theta}{360^{\circ}}\pi r_2^2\\\Rightarrow ABDE=\dfrac{\theta}{360^{\circ}}\pi(r_1^2-r_2^2)\\\Rightarrow ABDE=\dfrac{135^{\circ}}{360^{\circ}}\pi(15^2-4^2)\\\Rightarrow ABDE=246.22\ \text{inches}^2\)

The area which is swept clean is \(246.22\ \text{inches}^2\)

\(-21x^{2}-588\)

let me know if anything is unclear, I'm happy to help!