14. Refer to the figure. Prove that AC is perpendicular to BC.

Answer: To find the total change in pounds of fruit in the basket, we need to subtract the amount taken out from the amount added.

First, let's convert all the fractions to decimals:

1 1/4 = 1.25

2 3/8 = 2.375

Now, we can subtract:

1.25 - 2.375 = -1.125

So, the total change in the fruit basket was -1.125 pounds, meaning the basket had 1.125 pounds less fruit after the removal.

Step-by-step explanation:

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Answer:

48

Step-by-step explanation:

the sequence of numbers alternates between adding 6 and 8.

6 + 6 = 12

12 + 8 = 20

20 + 6 = 26

26 + 8 = 34

34 + 6 = 40

40 + 8 = 48!

i hope this helps :)

Answer:48

Step-by-step explanation:The sequence adds 6 first then adds 8

The requried correct expression 3x - 1 + 5x + 10x = 5 1/2, and solution of the equation is x = 7.5/18

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The equation as written doesn't have a unique solution, as the left-hand side and right-hand side are not equal.

To correct the equation, you would need to provide more information about what you intended to do with the two equations and format the right-hand side of the equation properly. For example, if you meant to add the two equations, you could write,

3x - 1 + 5x + 10x = 5 + 2.5

18x = 7.5

x = 7.5/18

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The dot product a . b is -22

The dot product, also known as scalar product or inner product, is a binary operation that takes two vectors and returns a scalar (single-valued) quantity. The dot product of two vectors is equal to the product of the magnitude (length) of the vectors and the cosine of the angle between them.

Given two vectors, A and B, the dot product is defined as:

A ∙ B = |A| * |B| * cos(θ)

where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

a = <3, -2>

b = <-2, 8>

a . b = (3 * -2) + (-2 * 8)

a . b = -6 + - 16

a . b = -22

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Answer: Ray HF is opposite of Ray FH

Step-by-step explanation:

The number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

The probability of cookies sold in shape of dog is:

P = 35/85

The number of cookies sold that would be in the shape of the dog in the next 51 cookies is:

N = 51 (P)

N = 51 (35/85)

N = 21

Hence, the number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.

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The bakery made 384 donuts and 216 bagels

A bakery is a business that produces and sells baked goods, such as bread, cakes, pastries, and cookies.

Let's use the variable "x" to represent the number of bagels made.

From the problem, we know that:

The number of donuts made is 384 more than the number of bagels made, so the number of donuts is x + 384.

The bakery made 216 bagels.

We also know that the bakery made a total of 600 donuts. So, we can set up an equation to represent the total number of pastries made:

x + 384 + 216 = 600

Simplifying and solving for x:

x + 600 = 600

x = 600 - 600 + 384

x = 384

So, the bakery made 384 + 216 = 600 pastries in total.

Therefore, the bakery made 384 donuts and 216 bagels.

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The equation that represents the situation is q = 40 - 7

The formula for the perimeter of a quadrilateral is expressed as;

P = a + b + c + d

Where the sides, a , b , c and d are all the sides of the quadrilateral

From the information given, we have that;

The sides are a, the fourth is 7

The perimeter = 40 inches

Substitute the values

40 = 7 + q

collect the like terms, we get

q = 40 - 7

subtract the values

q = 33 inches

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The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:

d = 50 ft.

Olympic pool is a type of swimming pool that is used for competitive swimming and diving events. These pools typically have a uniform depth, a smooth and flat bottom and multiple lanes for swimmers to compete in.

The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:

d = 50 ft.

Where d is the depth of the pool. This expression simply states that the depth of the pool is equal to 50 ft.

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Answer:

[tex]x^{2}-4x-12[/tex]

Step-by-step explanation:

(x+2)(x-6)

STEP 1 - USE FOIL

(FOIL is a standard way of multiplying 2 fractions, just multiply in the following order):

Forward

Outside

Inside

Last

(x+2)(x-6) becomes this when you FOIL it:

[tex](x^{2} )(-6x)(2x)(-12)[/tex]

STEP 2 - COMBINE ALL THE TERMS

[tex]x^{2}[/tex] has to stay by itself because there are no other squares. [tex]-6x+2x=-4x[/tex] because you're adding two to -6 which effectively is 6 - 2 but you're adding a negative sign. And [tex]-12[/tex] stays the same because there are no x's  in it.

STEP 3 - WRITE THE SOLUTION

All in all, the final solution, once you put everything together, is:

[tex]x^{2} -4x-12[/tex]

Answer:

The nth term of an arithmetic sequence is given by an = a + (n – 1)d ... Step 1: First, calculate the difference between each pair of adjacent terms.

Step-by-step explanation:

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The probability of selecting the fair coin when a gambler has both a fair coin and a two-headed coin in his pocket is 50%.

This is because, when he selects one of the coins at random, it is equally likely that he has chosen either the fair coin or the two-headed coin. If he flips the coin and it shows heads, then the probability that it is the fair coin is still 50%, because either coin could have been selected and both would show heads.This is an example of a classical probability problem, which is based on the law of equal chances. This law states that when an event has multiple possible outcomes, each of those outcomes is equally likely to occur. In this case, there are two possible coins that could have been chosen, so each coin has a 50% chance of being selected. This means that the probability of selecting the fair coin is 50%.This also applies to events that have multiple outcomes which are not equally likely. For example, if a gambler has a fair coin, a two-headed coin, and a three-headed coin in his pocket, the probability of selecting the fair coin is still 50%. This is because the gambler has an equal chance of selecting any of the coins, regardless.

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Answer:

Step-by-step explanation:

This question of of Trigonometry

Tan means the ratio of sides which are opposite to the given angle divided by the adjacent side to the angle (NOT THE HYPOTENUSE)

So Tan(Unknown angle) = 5/14
Unknown angle = 19.6 Degrees

The arrow labeled C represents a transfer of chemical energy to mechanical energy. False, this is because, the gas released does not do any work.

The arrow labeled A represents a transfer of solar energy to chemical energy. True, chemical energy is stored in starch molecules

The arrows that represent the release of carbon dioxide is C. This is combustion and it occurs in nonliving things. The process involves the burning of carbon materials.

The conservation energy is demonstrated by arrow A since we can show it by a chemical reaction.

The carbon cycle is the process by which carbon atoms circulate through the Earth's atmosphere, oceans, and landmasses. In the carbon cycle, carbon is exchanged between the atmosphere, biosphere, hydrosphere, and geosphere. The main components of the carbon cycle include photosynthesis, cellular respiration, decomposition, and combustion.

In photosynthesis, plants take in carbon dioxide from the atmosphere and convert it into organic compounds, which serve as food for the plants and are stored in their tissues.

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The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then ∠FGN = ∠FJN.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The line segment GF = NJ and FN bisect the angle ∠GFJ.

In triangles ΔGFN and ΔJFN, then we have

GF = NJ                        (Given)

∠GFN = ∠JFN              (Given)

NF = NF                        (Common sides)

The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then we have

∠FGN = ∠FJN

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Answer: 28 (look at the image for the solution)

Step-by-step explanation:

Answer:

A = base x height

A = 7 x 4

A = 28

Have a wonderful day! :-)

The value of a in the equation a + 2 = 3 is 1.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

a + 2 = 3

Subtract 2 from both sides

a + 2 - 2 = 3 - 2

a = 1

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The first day after the autumn equinox that the solar panel generates 8400 kJ is approximately 39.2 days, or 0.107 radians, after the equinox.

To find the first day after the autumn equinox that the solar panel generates 8400 kJ, we need to solve the equation:

624sin(2π/365)t + 8736 = 8400

Simplifying the equation, we get:

sin(2π/365)t = 0.958

Taking the inverse sine of both sides, we get:

(2π/365)t = 1.296 or (2π/365)t = 3.846

Solving for t in each equation, we get:

t ≈ 78.97 or t ≈ 235.62

Since t is measured in radians, we need to convert it to days by dividing by 2π/365:

t ≈ 78.97 / (2π/365) ≈ 86.75 or t ≈ 235.62 / (2π/365) ≈ 256.73

Therefore, the first day after the autumn equinox that the solar panel generates 8400 kJ is either day 87 or day 257.

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Step-by-step explanation:

ABC and ADE are similar triangles.

that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.

so, we see that AB = 2, AD = 2+1 = 3

the scaling factor f from AB to AD is then

AB × f = AD

2 × f = 3

f = 3/2

the same scaling factor now applies between BC and DE (= x).

BC × f = x

1 × 3/2 = x

x = 3/2 = 1.5

Answer:

61 over 4 haircuts per day

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

A way to solve for the number of haircuts per day is to use this equation:

You could also use this fraction:

Inserting the numbers into the fraction::

Therefore, the rate for a ratio using the two different quantities is 61 over 4 haircuts per day.

Amount of iced-tea consumed during party was 92 cups, which is equivalent to 23 quarts. It's important to note difference between volume units such as cups and quarts, and the conversion factor between them.

To determine the number of cups of iced-tea that were consumed during the party, we need to subtract the amount that remained from the total amount that was in the drink dispenser at the start of the party.

One cup of iced tea is equal to 1/16 of a quart, so 7 cups is equal to

7 * (1/16) = 7/16 quarts.

Thus, the total amount of iced tea that was consumed during the party is 912 quarts -

7/16 quarts = 912 - 7/16

= 912 - 7 * (1/16)

= (912 * 16 - 7 * 1) / 16

= 1476 / 16

= 92.25 cups, rounded down to the nearest whole number, which is 92 cups.

It is important to note that the answer is given in cups and not quarts. Quarts is a unit of volume and cups is a unit of volume as well, but they are not equivalent. 1 quart is equal to 4 cups. If we wanted to express the amount of iced tea consumed in quarts, we would multiply the answer by 1/4.

In conclusion, the number of cups of iced tea consumed during the party is 92 cups, and if we express this in quarts it is equivalent to

92 * (1/4) = 23 quarts.

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The algebraic expression in simplified form representing the average is 3x + 1.

To solve this question, one must know the formula of average. It is as follows -

Average = sum of the numbers / quantity of numbers

Now, we see that there are 3 expressions in the question. Hence, quantity of numbers will be 3.

Sum of the numbers = 2x + 3 + x + 6x

So, keep the values in formula to find the expression -

Average = 2x + 3 + x + 6x/ 3

Simplifying the expression to find average

Average = 9x + 3/3

Performing division on Right Hand Side of the equation

Average = 3x + 1.

Hence, required algebraic expression is 3x + 1.

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The lines 4x+y=5 and 3x+12y=-6are neither parallel nor perpendicular

From the question, we have the following parameters that can be used in our computation:

4x+y=5 3x+12y=-6

Make y the subject in the equations

So, we have

y = -4x + 5

y = -1/4x - 1/2

The slopes of the lines are -4 and -1/4

These numbers are not equal and they are not opposite reciprocals

This means that the lines are neither parallel nor perpendicular

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To solve this system, we must first determine the number of available rooms in each city, as well as the per-night cost of hotel rooms. Without that information, we can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B.

Let's start by defining the variables we'll need to solve this problem:

Assume that x is the number of nights spent in City A.

Let y represent the number of nights in City B.

To determine whether the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, we must first determine whether the total cost of hotels and fuel for each scenario is less than or equal to $4200.

Given that the estimated cost of fuel is $200, the cost of hotels must be less than or equal to $4000.

The following equations calculate the cost of hotels for each scenario:

We also know that the club can only spend a total of 10 nights, so x + y must be less than or equal to 10.

Finally, we must ensure that the club can book four rooms each night. This means that the number of rooms required per night in each city is four times the number of nights. As a result, we must have:

When we combine all of these constraints, we get the following system of linear equations:

3x + 6y + 200 ≤ 4200 (cost constraint for spending 3 nights in city A and 6 nights in city B)

7x + 3y + 200 ≤ 4200 (cost constraint for spending 7 nights in city A and 3 nights in city B)

x + y ≤ 10 (total number of nights constraint) (total number of nights constraint)

A city with 4x available rooms (room constraint for city A)

4y rooms available in city B (room constraint for city B)

To solve this system, we must first determine the number of available rooms in each city as well as the cost of hotel rooms per night. We can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, without that information.

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Answer:  Yes, it's wrong.

Step-by-step explanation:

In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.

r = d/2 = 3/2 = 1.5 ft

[tex]A=\pi r^{2}\\[/tex]

   ≈ 3.14 x 1.5

   = 4.71

Step-by-step explanation:

This is a family of curves represented by the equation:

y = a (x + 4) (x − 2)

Different values of the a coefficient result in different quadratic functions.

The vertex of the parabolas is halfway between the zeros, at x = -1.

y = a (-1 + 4) (-1 − 2)

y = -9a

So to find the value of a, divide the y-coordinate of the vertex by -9. For example, curve A has a vertex at (-1, -3), so the value of the a coefficient is -3 / -9 = ⅓.

A. y = ⅓ (x + 4) (x − 2)

B. y = (x + 4) (x − 2)

C. y = 2 (x + 4) (x − 2)

D. y = -⅓ (x + 4) (x − 2)

E. y = -2 (x + 4) (x − 2)

Answer:

Step-by-step explanation:

y=2+x

1m per second.

2+1x=2+x=y

find the relational column formula.

Answer: 27

Step-by-step explanation: