Evaluate and simplify the expression
when x = 1 and y = 2.
3(x + 2y) − 2x + 10

Answer:

Step-by-step explanation:

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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The value of n(AUB) i.e. union of A and B is 53.

What are Intersections and Unions in Probablity?

The union of two sets results in a new set that contains all of the items from both sets. The union is abbreviated as A∪B or "A or B." The intersection of two sets yields a new set containing all of the members from both sets. The junction is denoted by the letters A∩B or "A and B."

Solution:

Given that,

n(A) = 14

n(B) = 51

n(A∩B) = 12

We know that thee formula is n(AUB) = n(A) + n(B) - n(A∩B)

Putting the values,

n(AUB) = 14 + 51 - 12 = 53

So, the answer for the value of n(AUB) = 53

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Answer:

1) = 32.02

2) = 18

Step-by-step explanation:

1) 20^2 + 25^2 = 1025

sq rt 1025 = 32.02

2) 30^2 - 24^2 = 324

sq rt 324 = 18

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Step-by-step explanation:

Just multiply the two dimensions to get m^2  area

7.2 m * 11 m = 79.2 m^2

Answer:

\(Probability = \frac{27}{80}\)

Step-by-step explanation:

Given

\(Blue =9\)

\(Yellow = 7\)

Required

Determine the probability that one of the balls is blue while others is yellow

The order of selection may be any of these three:

Yellow, Yellow, Blue or Yellow, Blue, Yellow or Blue, Yellow, Yellow

Solving Yellow, Yellow, Blue

\(Probability = P(Y_1) * P(Y_2) * P(B)\)

\(Probability = \frac{7}{16} * \frac{6}{15} * \frac{9}{14}\)

\(Probability = \frac{1}{8} * \frac{1}{5} * \frac{9}{2}\)

\(Probability = \frac{9}{80}\)

Solving Yellow, Blue, Yellow

\(Probability = P(Y_1) * P(B) * P(Y_2)\)

\(Probability = \frac{7}{16} * \frac{9}{15} * \frac{6}{14}\)

\(Probability = \frac{9}{80}\)

Solving Blue, Yellow, Yellow

\(Probability = P(B) *P(Y_1) * P(Y_2)\)

\(Probability = \frac{9}{16} * \frac{7}{15} * \frac{6}{14}\)

\(Probability = \frac{9}{80}\)

Hence:

The required probability is:

\(Probability = \frac{9}{80} + \frac{9}{80} + \frac{9}{80}\)

\(Probability = \frac{27}{80}\)

Answer:

40.6

Step-by-step explanation:

Use the pythagorean theorem a^2+b^2=c^2

25^2+32^2=1649

The square root of 1649 is 40.607

Answer:

D) 40.6

Step-by-step explanation:

When finding the hypotenuse, you square the two leg values (in this case, 25 and 32). Then, you add them together and find the square root of the sum. Use the Pythagorean theorem: a²+b²=c²

Answer:

C

Step-by-step explanation:

Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

We can see here that the probability that the password does not have repeated letters, expressed to the nearest tenth of a percent is = 9.8%.

Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

The probability of an event can be calculated using the following formula:

Probability = Favorable Outcomes / Total Outcomes

The number of possible passwords is:

26 × 26 × 26 × 26 × 26 × 26  = 308,915,776.

The number of passwords with no repeated letters is

26P6 = 30,260,000.

The probability of a password having no repeated letters is

= 30,260,000 / 308,915,776 = 0.09779 = 9.78%.

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In a table is given the number of lcd television consumers have bought from a retail chain over five years. We are asked to estimate the average rate of lcd television sold by the retail chain between 2006 and 2008.

To estimate this average we will consider only the following three numbers

They correspond to the Tv's sold in 2006,2007 and 2008 respectively , we use the following formula for the average rate

Making the calculations we find that:

Looking at the options for this question, we found that the correct one is the option C

Answer:

d

Step-by-step explanation:

The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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Answer:

40%

Step-by-step explanation:

20 cherry + 10 lemon + 4 blueberry + 16 apple = 50 total pies

20 cherry pies/50 total pies is the same ratio as 40/100, which means that 40% of the pies are cherry

The value of x or the expression 56 = -4x + 2 is -27/2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

56 = -4x + 2

Solve for x.

56 = -4x + 2

Subtract 2 on both sides.

56 - 2 = -4x

54 = -4x

Divide -4 into both sides.

-54/4 = x

x = -54/4

x = -27/2

x = -13(1/2)

Thus,

The value of x is -27/2.

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Answer:

the area of compound shapes is the amount of space inside a shape composed of basic shapes put together (cm²,m²,mm²)

The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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Answer:

A' = (0,0)

B'=(8,0)

C'=(8,2)

D'=(0,2)

It is not a rigid motion.

Step-by-step explanation:

To use the mapping rule, substitute the original x and y values in it.

The coordinates of A are (0,0).

Using the mapping rule, the x coordinate of A' = 2x0 = 0

Using the mapping rule, the y coordinate of A' = (1/2)x0=0

So A' will not change locations. The image will be at (0,0).

The coordinates of B are (4,0)

Using the mapping rule, the x-coordinate of B' = 2x4 = 8

Using the mapping rule, the y-coordinate of B' = (1/2)x0=0

Therefore the image of B' will be located at coorindate (8,0)

The coorindates of C are (4,4).

Using the mapping rule, the x-coordinate of C' = 2x4=8

Using the mapping rule, the y-coordinate of C' = (1/2)x4=2

Therefore the image of C' will be located at coordinate (8,2)

The coordinates of D are (0,4)

Using the mapping rule, the x-coordinate of D' = 2x0 = 0

Using the mapping rule, the y-coordinate of D' = (1/2)x4=2

Therefore the image of D' will be located at coordinate (0,2)

Is the transformation a rigid motion?

NO, this transformation is not a rigid motion because the relative distance between the points does not stay the same after they have been transformed. The transformation is not a translation , rotation, reflection, nor glide reflection.

Young adults might value credit in case of an emergency for several reasons. Firstly, credit provides financial flexibility, allowing them to access funds quickly when unexpected expenses arise.

This can be essential for covering costs related to medical emergencies, car repairs, or other unforeseen events that may strain their limited savings. Secondly, young adults often have less established financial safety nets than older individuals. They may not have significant savings, insurance policies, or support from family members to fall back on during emergencies. Credit, in this case, acts as a temporary financial cushion, enabling them to manage immediate needs without resorting to high-interest loans or further jeopardizing their financial stability.

Thirdly, responsible use of credit can help young adults build a positive credit history. Demonstrating responsible borrowing and repayment habits will make it easier for them to access more favorable credit terms in the future, such as lower interest rates or higher credit limits. This can prove valuable when making significant purchases, like buying a home or financing higher education.

Lastly, having access to credit can also provide young adults with a sense of financial independence and empowerment. Knowing they have the means to handle emergencies without relying on others can boost their confidence in managing personal finances and help them make more informed financial decisions as they navigate adulthood.

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The farmer's market originally had 400 peaches on hand.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.

Let's use x to represent the original number of peaches the farmer's market had on hand.

We know that the farmer's market sold 35% of its produce, which means it sold 0.35x peaches. The remaining number of peaches can be calculated by subtracting the number of peaches sold from the original number of peaches:

remaining peaches = x - 0.35x

We also know that there are 260 peaches remaining, so we can set up an equation:

260 = x - 0.35x

Simplifying this equation, we can combine like terms:

260 = 0.65x

To solve for x, we need to isolate the variable by dividing both sides by 0.65:

x = 260 / 0.65

x = 400

Therefore, the farmer's market originally had 400 peaches on hand.

To explain how we used equivalent ratios, we used the fact that the farmer's market sold 35% of its produce. This can be represented as a ratio of 35/100 or 0.35. We then used this ratio to find the number of peaches sold, which is 0.35x. We also used the fact that the remaining peaches are the original peaches minus the peaches sold, or x - 0.35x. Finally, we set up an equation using the remaining peaches and solved for x to find the original number of peaches.

Hence, the farmer's market originally had 400 peaches on hand.

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Answer:

15.19 cm

Step-by-step explanation:

The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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Answer:3000

Step-by-step explanation:

You need to find the LCM of 500 and 600

Answer: D

Step-by-step explanation:

This is actually a really easy question. I have three ways to solve this:

1) 180- (54+64)=62, 180-62=118, like the solution

2. Since 54+64+c=180 and 180-c= d, d=54+64, which equals 118.

3. Deduction! d is not a straight line, cannot be more than 180 degrees, and can't be smaller than 90 degrees, so halfway through solving by 1), you've already got the answer!

Answer:

Total weight in lb = 10 lb

The weight of wooden pencils is 10 pounds.

Step-by-step explanation:

We are given that an office supply company is shipping a case of wooden pencils to a store.

There are 64 boxes of pencils in the case.

The weight each box of pencils is 2.5 ounces (oz)

We are asked to find the weight of wooden pencils in pounds.

Step 1: Find the total weight of pencils in ounces

Since there are 64 pencils and each pencil weighs 2.5 ounces,

Total weight in oz = 64×2.5

Total weight in oz = 160 oz

Step 2: Convert the total weight of pencils into pounds

We know that 1 pound has 16 ounces so we have to divide the total weight of the pencils by 16 to get the weight in pounds

Total weight in lb = 160/16

Total weight in lb = 10 lb

Therefore, the weight of wooden pencils is 10 pounds.

Answer:

It will take 4 hours for the two vehicles to meet

Step-by-step explanation:

Answer: (13, -8)

Step-by-step explanation:

Subtract 5 from -3

Add 5 to 8