Write the equation of the line through (2,15) and (-4,9)

The heaviest pack's maximum allowable weight is d = 46 - 39 = 7 kg.

Let the four packs each weight a, b, c, and d (with a <= b <= c <= d).

Using the given data, we can formulate the following six equations:

a + b = 34

a + c = 37

a + d = 39

b + c = 41

b + d = 43

c + d = 46

the fourth equation and the first equation added:

2a + 2b = 34 + 41 = 75

Solving for a, we get:

a = (75 - 2b) / 2

Substituting this into the first equation:

(75 - 2b) / 2 + b = 34

Multiplying both sides by 2:

75 - 2b + 2b = 68

Solving for b, we get:

b = 34 - (75 - 68) / 2 = 34 - 3.5 = 30.5

Substituting this value into the equation for a:

a = (75 - 2 * 30.5) / 2 = (75 - 61) / 2 = 7

The greatest possible weight of the heaviest pack is d = 46 - c. Since c <= 46 - a = 46 - 7 = 39,

The greatest possible weight of the heaviest pack is d = 46 - 39 = 7 kg.

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Answer:

P(Red) = [tex]\frac{12}{50}[/tex] = [tex]\frac{6}{25}[/tex]

P(not green)

= 1 - [tex]\frac{8}{50}[/tex]

= [tex]\frac{21}{25}[/tex]

P(Blue or yellow)

= P(Blue) + P(Yellow)

= [tex]\frac{7}{50}[/tex] + [tex]\frac{9}{50}[/tex]

= [tex]\frac{8}{25}[/tex]

Erika has 6.53 kilograms of apples, which is more than the 6 kilograms she needed for the recipe. Therefore, she has enough apples to make the recipe.

To determine if Erika has at least 6 kilograms of apples, we need to add the weight of all three bags of apples. The total weight of the apples is:

2.56 kg + 1.18 kg + 2.79 kg = 6.53 kg

Erika needs a certain amount of apples for a recipe, specifically 6 kilograms. She goes to the store and picks three different bags of apples - a 2.56-kilogram bag of red apples, a 1.18-kilogram bag of green apples, and a 2.79-kilogram bag of yellow apples. To determine if she has enough apples, she needs to add the weight of all three bags. The total weight of the apples comes out to be 6.53 kilograms. This means that Erika has more than the required 6 kilograms of apples and is sufficient to make the recipe. It's important to note that Erika has an excess of apples, which can be helpful in case she needs extra for the recipe or for future use. The combination of different types of apples can also add variety and flavor to the recipe.

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A graph which shows the new position of the rectangle after a translation include the following: B. Rectangle with coordinates: (0.5, 0), (0.5, 1), (3, 0), and (3, 1).

In Mathematics, a translation can be defined as a type of rigid transformation which moves every point of the object in the same direction, as well as for the same distance.

This ultimately implies that, a translation is a type of rigid transformation  that does not change the orientation of the original geometric figure (pre-image).

In this context, we can reasonably infer and logically deduce that a translation was applied to both rectangles.

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I'll do the first one for you.

Step-by-step explanation:

a)

First find the gradient using the coordinates given.

(-4, -2), (6, 8)

m = (y1 - y2)/(x1 - x2)

m = (-2 - 8)/(-4 - 6)

m = -10 / -10 = 1

Then use tanθ = m,

tanθ = 1

θ = tan -1(1)

θ = 45 degrees.

If you want to know why we use tanθ, refer to this -> https://amsi.org.au/ESA_Senior_Years/SeniorTopic1/1b/1b_2content_4.html

Answer:

22

Step-by-step explanation:

1 Simplify 14-6 to 8.

78-2^4 ÷ 8 × 28

2 Simplify 24 to 16.

78 - 68 ÷ 18 x 28

3 Simplify 16 ÷ 8 to 2.

78-2 × 28

4 Simplify 2 x 28 to 56.

78 - 56

5 Simplify.

22

A number which is 15 more than twice a number is 37 is 11.

Let the number be N.

Let's set up the equation.

A number which is given to us is 15 more than twice a number 37,

2N + 15 = 37

Let's subtract 15 from both sides.

2N = 22

Divide both sides by 2, and you get

N = 11

So, the number which we needed is 11.

It is a type of mathematical notation that consistently expresses the numbers in a set using digits or other symbols. It provides each number with a unique representation and specifies the arithmetic and algebraic structure of the numbers. Additionally, we may use it to carry out mathematical operations like addition, subtraction, multiplication, and division.

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The probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is 0.4

We can calculate the probability by finding the number of favorable outcomes, i.e., the number of ways that Sergio can choose a number that is larger than the sum of the two numbers chosen by Tina, and dividing it by the total number of possible outcomes, which is

5C2 * 10C1 = (5!/(2! * 3!)) * 10

= 100

Tina's sum   Sergio's favorable outcomes  

3           7

4           6

5           5

6           4

7           3

8           2

9           1

For example the sum 5 can be achieved by two ways, that is 1+4 and 2+3. So

Tina's sum   Number of ways to achieve that sum

3           1

4           1

5           2

6           2

7           2

8           1

9           1

The number of favourable outcomes is

= 1*7 + 1*6 + 2*5 + 2*4 + 2*3 + 1*2 +1*1

= 40

So probability is

= 40/ 100

= 0.4

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Answer:102

Step-by-step explanation: add 2

Answer:

102

Step-by-step explanation:

=2+100

=102

So the answer is.. 102

Answer:

x+2=11

Step-by-step explanation:

77/7=11

And x=9

11-2=9

A line must have a 2 1/2 slope in order to be perpendicular to the line whose equation is 6x + 15y = 225.

A line's slope is determined by its inclination.

M is used to signify it.

m = (y₂ - y1)/(x₂ -x₁).

Consider Point 1 and Point 2 as the two points on a line.

The coordinates for Point 1 are (x1,y1), while the coordinates for Point 2 are (x2,y2).

The line equation was provided to us as follows:

⇒ 6x + 15y = 225

⇒ 15y = -6x + 255

⇒ y = -6/15 x + 255/15

The slope, m = -6/15

The angle of perpendicularity = -1/m

⇒ -1/(-6/15)

Reciprocal the term of denominator, and we get    

⇒ 15/6  = 2 1/2

Therefore, a line must have a 2 1/2 slope in order to be perpendicular to the line whose equation is 6x + 15y = 225.

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Answer:

To solve for x in the equation AX - B = 4, if A does not equal 0, we can isolate x by adding B to both sides and then dividing both sides by A:

AX - B + B = 4 + B

AX = 4 + B

X = (4 + B) / A

So, the solution for x is given by: X = (4 + B) / A, where A is not equal to 0.

Step-by-step explanation:

The amount of time they rest in 8 hours is 40 minutes.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

In the problem, it is stated that a couple rests for 25 minutes in 5 hours during a dance-a-thon. We can use this information to find out how long they rest each hour. To do this, we simply divide the total amount of time they rest (25 minutes) by the number of hours (5 hours). That is:

rest time in 1 hour = 25 minutes / 5 hours = 5 minutes.

So, if they dance for 8 hours, the amount of time they rest will be:

8 hours * 5 minutes/hour = 40 minutes.

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Answer:

Quadrilateral

Step-by-step explanation:

Quadrilateral = 4 sides

Answer:

ΔGAS ≅ ΔIOLby AAS

Step-by-step explanation:

We can prove congruence by the AAS Theorem

AAS Theorem

By definition, AAS congruence rule states that if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle, the two triangles must be congruent

In triangles ΔGAS and ΔIOL

We have:
∠G ≅ ∠I
m∠A ≅ m∠O

AS ≅ OL

AS is the non-included side of ΔGAS and OL is the non-included side of ΔIOL

Therefore we have two corresponding angles congruent and the non-included side of each of these triangles also congruent

Therefore by the AAS (Angle-Angle-Side) theorem, the two triangles are congruent

ΔGAS ≅ ΔIOL by AAS

Answer:

ΔGAS ≅ ΔIOL by AAS

Step-by-step explanation:

From the dashes on the angles and sides of the given triangles:

Therefore, the two triangles have two corresponding congruent angles and a congruent corresponding non-included side.  This means we can show that the triangles are congruent by the AAS congruence Theorem.

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Therefore:

The problem can be written as:

x/(5 - 4) = 12

which simplifies to:

x/1 = 12

x = 12

Therefore, the number is 12.

Answer: 5

Step-by-step explanation:

1st piece = x

2nd piece = 2x

3rd piece = 2x + 2

All of these pieces add up to 27, which means =>

5x + 2 = 27

5x = 27 - 2 = 25

x = 5

Answer:

x= the square root of 7 and the negative square root of 7

Step-by-step explanation:

basically

x^2=7

can be converted into

x=7^1/2 (^1/2 is another way to say square root or represent square root)

x= 2.645751311 or -2.645751311

negative is included as a negative value to the power of 2 gives a positive value

hope this helps

The value of adding x² and y² results to

(-20√7 + 84√3) / 416

In the problem it was given that

1/x = √7 - √3 and

1/y = √7 + √3

hence we can get x and y to be

x = 1/(√7 - √3)

y = 1/(√7 + √3)

rationalization of surd

x

=  1/(√7 - √3) *  (√7 - √3) /(√7 - √3)

= (√7 - √3)/(7 - 42 + 3)

= (√7 - √3)/(-32)

y

=  1/(√7 + √3) *  (√7 + √3) /(√7 + √3)

= (√7 + √3)/(7 + 42 + 3)

= (√7 + √3)/(52)

adding the parameters

x² + y² = (√7 - √3)/(-32) + (√7 + √3)/(52)

= (-52√7 + 52√3 + 32√7 + 32√3) / 416

= (-20√7 + 84√3) / 416

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Answer: a. The area of the rectangular base of the bale of hay is 2 feet * 3 feet = 6 square feet.

The area of the circular base of the bucket is π * (diameter/2)^2, where the diameter is 3 feet, so the area is π * (3/2)^2 = π * (9/4) = 9π/4 square feet.

Since π is approximately equal to 3.14, the area of the circular base is approximately 9 * 3.14 / 4 = 6.935 square feet, which is less than the area of the rectangular base.

So the rectangular base of the bale of hay is larger in area.

b. The volume of the bale of hay is 2 feet * 3 feet * 5 feet = 30 cubic feet.

The volume of the bucket is π * (diameter/2)^2 * height, where the diameter is 3 feet and the height is 5 feet, so the volume is π * (3/2)^2 * 5 = π * (9/4) * 5 = 45π/4 cubic feet.

Since π is approximately equal to 3.14, the volume of the bucket is approximately 45 * 3.14 / 4 = 34.65 cubic feet, which is less than the volume of the bale of hay.

So the bale of hay is larger in volume.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression "15/18 - 7/36" can be simplified as follows:

Step 1: Find a common denominator for the two fractions. In this case, the least common denominator is 36.

Step 2: Convert both fractions to have a denominator of 36.

15/18 can be converted to 30/36 by multiplying both the numerator and denominator by 2.

7/36 can be expressed as 7/36.

Step 3: Subtract the two fractions to simplify the expression:

30/36 - 7/36 = 23/36

So the expression simplifies to 23/36.

P' would have coordinates  d. (8, -5).

What is Reflection across a line?

It is discovered using reflections principles that:

1) When a function is reflected across the x-axis, the x-coordinates remain unchanged, however the y-coordinates have the opposite signal.

2) When a function is reflected across the y-axis, the y-coordinates remain unchanged, whereas the x-coordinates have the opposite signal.

Given that,

      Triangle is reflected across the dashed line with coordinates of P' if P(8, 5).

Reflection across a line means taking a shape and flipping it over the line so that it appears as its mirror image.

In the case of the point P(8,5), reflecting it across the dashed line would result in a new point P' whose y-coordinate is the opposite of the y-coordinate of P.

Therefore, P' would have coordinates (8, -5).

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Answer:

C = 24 inches

Step-by-step explanation:

the fraction of the circumference (C) that the arc AB subtends is

[tex]\frac{45}{360}[/tex] = [tex]\frac{1}{8}[/tex]

thus C is 8 times length of arc AB

C = 8 × 3 = 24 inches

The below points can be plotted on the graph to show the relationship between the number of cases of cereal boxes shipped and the number of cereal boxes in those cases.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

A graph can be plotted with the number of cases of cereal boxes on the x-axis and the number of cereal boxes in those cases on the y-axis.

Here is an example of how the points for 4, 8, 10, 14 and 16 cases can be plotted:

For 4 cases: (4, 4 x 144 = 576)

For 8 cases: (8, 8 x 144 = 1152)

For 10 cases: (10, 10 x 144 = 1440)

For 14 cases: (14, 14 x 144 = 2016)

For 16 cases: (16, 16 x 144 = 2304)

These points can be plotted on the graph to show the relationship between the number of cases of cereal boxes shipped and the number of cereal boxes in those cases.

The graph will be a straight line, showing that the number of cereal boxes is directly proportional to the number of cases shipped.

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When a restaurant goes bankrupt the probability it purchased organic food is 0.04

By using the formula for Probability:

[tex]P(B|A) = \frac{P(AB)}{P(A)}[/tex]

In which

P(B|A) is the likelihood that event B will occur in the absence of event A.

P(A/B) is the likelihood that both A and B will occur.

P(A) denotes the likelihood that A will occur.

Event A: Goes bankrupt

Event B: Purchase organic food.

Probability it goes bankrupt:

59% of 4%(purchases organic food)

60% of 96%( don't purchase organic food).

So,

P(A) = 0.59*0.04 + 0.6*0.96

P(A) = 0.5996

Bankrupt when purchases organic food. So

59% of 4%

P(A|B) = 0.59*0.04 = 0.0236

The likelihood that a restaurant bought organic food before it went out of business

[tex]P(B|A) = \frac{P(AB)}{P(A)}[/tex]  = 0.0236/0.5996 = 0.0393

When a restaurant goes bankrupt the probability it purchased organic food is 0.04.

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Based on the above, it can be inferred that the arrow is expected to stop on the number 3 space at least 13 times in the 104 shots.

To calculate how many times the arrow will stop at number 3 we must perform the following mathematical operation:

1 / 8 = 0.125

0.125 is equivalent to 12.5% of the pitches.

Therefore, we must make a rule of three.

According to the above, the arrow must stop at least 13 times at the number 3.

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Taylor had $788.50 left over from her paycheck after making the house payment and the car payment.

Let's calculate the amount spent on the house payment first:

$1575 * 0.30 = $472.50

Now, let's calculate the amount that was left after the house payment:

$1575 - $472.50 = $1102.50

Next, let's calculate the amount spent on the car payment:

$1102.50 - $314 = $788.50

Here's a step by step breakdown of the calculation:

Taylor received a paycheck of $1575.

She spent 30% of her paycheck on the house payment, which is $1575 * 0.30 = $472.50.

After making the house payment, Taylor had $1575 - $472.50 = $1102.50 left. She then spent $314 on the car payment, leaving her with $1102.50 - $314 = $788.50.

So, Taylor had $788.50 left over from her paycheck after making the house payment and the car payment.

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Answer:

  C.  17 units

Step-by-step explanation:

You want the hypotenuse of a right triangle with legs 8 and 15.

The Pythagorean theorem tells you the relation between the sides of a right triangle is ...

  c² = a² +b² . . . . . . where c is the hypotenuse, and a, b are the legs

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17 . . . . units

The missing side length is 17 units.

__

Additional comment

A set of integers that satisfies the Pythagorean theorem is called a "Pythagorean triple." Perhaps the first one you run across is {3, 4, 5}. Other triples commonly seen are {5, 12, 13}, and {7, 24, 25}. This one, {8, 15, 17} also shows up in algebra and trig problems. It can be worthwhile to remember a few of these.

Their multiples are also seen. For example, {6, 8, 10} is the {3, 4, 5} triple times 2.

The cost of the computer in Mexican pesos would be 839,779 Mexican pesos.

To convert an amount in American dollars to Mexican pesos, we can multiply by the exchange rate of 18.4398 Mexican pesos per American dollar.

That is, 18.4398 in Mexican peso is equal to one American dollar.

So, if an order of American computer hardware costs $45,000, the cost in Mexican pesos would be $45,000 * 18.4398 = 839,779 Mexican pesos.

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