Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A: (2, -6) B: (5, -6) C: (5, -2) D: (2, -2). What is the perimeter of ABCD.

Answer:

System of equations:

L = 5W + 7

2W + 2L = P

L = 62 cm

W = 11 cm

Step-by-step explanation:

Given the measurements and key words/phrases in the problem, we can set up two different equations that can be used to find both variables, length and width, of the rectangle.  

The formula for perimeter of a rectangle is:  2W + 2L = P, where W = width and L = length.  We also know that the L is '7 more than five times its width'.  This can be written as:  L = 5W + 7.  Using this expression for the value of 'L', we can use the formula for perimeter and solve for width:

2W + 2(5W + 7) = 146

Distribute:  2W + 10W + 14 = 146

Combine like terms:  12W + 14 = 146

Subtract 14 from both sides:  12W + 14 - 14 = 146 - 14 or 12W = 132

Divide 12 by both sides:  12W/12 = 132/12 or W = 11

Put '11' in for W in the equation for 'L':  L = 5(11) + 7 or L = 55 + 7 = 62.

Answer:

5

Step-by-step explanation:

Scale factor = image/pre-image

Scale factor = - 15/-3 =5

Or

Scale factor = 45/9 = 5

\(3) \: y = \frac{ - 8}{2} ; \: y = - 4\) ✅

Step-by-step explanation:

\(2 \: y = - 8 \\ ⇢  y = \frac{ - 8}{2} \\ ⇢ y = - 4\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

Answer:

By 3.

Step-by-step explanation:

-12-3=-15

Hope this helps!

Answer:

-12 exceeds -15 by 3

Step-by-step explanation:

To find out by how much a exceeds b, subtract a - b.

For example, by how much does 8 exceed 6?

Here, a = 8 and b = 6.

a - b = 8 - 6 = 2

2 is correct since we know that 8 is 2 greater than 6.

Now we do this problem.

By how much does -12 exceed -15?

a = -12; b = -15

a - b = -12 - (-15) = -12 + 15 = 3

Answer: -12 exceeds -15 by 3

Let's use a diagram to represent the question below

using Pythagoras theorem we can find how high up the ladder reaches the wall.

The ladder reaches 24 ft up the wall.

Answer:

the answer = C (may be but not sure)

Answer:

The answer has to be A

Step-by-step explanation:

The trees have nothing changed about them, so they can be considered to be the control. In additon, placebo is given as a control in medical trials, so it cannot be correct. And, the students have nothing changed in D, so the answer to this question has to be A, where the patients are given a new drug.

The number of books bought by the school is 92.

Here it is given that the school spend $925 to buy new books for the library.

The cost of each book is $9.95

So we have to find the number of books that can be bought.

By dividing the total money spent by the cost of each book we get the number of books bought.

Let n be the number of books bought.

n × 9.95 = Total money spend on the books

As we know the total money spend on the books is $925.

So we get:

925 = n × 9.95

n = 925/ 9.95

= 92

Therefore the total number of books bought is 92.

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Total factor productivity. This term refers to the ratio of an organization's outputs to all of its inputs, including labor, capital, and other resources. This measurement is used to determine how efficiently an organization is using its resources to produce its desired outcomes.

An explanation of the other options is as follows:

- B. Total labor productivity refers only to the output of an organization divided by its labor inputs.
- C. Partial productivity measures the output of an organization relative to a single input factor, such as labor or capital.
- D. Total capital productivity measures an organization's output relative to its capital inputs.
- E. Efficiency ratio is a broader term that can refer to any ratio that measures an organization's efficiency in achieving its goals, but it does not specifically refer to the ratio of outputs to inputs.

total factor productivity is the most appropriate answer to the question as it measures the overall efficiency of an organization in using all of its resources to achieve its goals.

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The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.

Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.

The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.

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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.

One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.

In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.

Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.

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The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).

Given:  (a + 1)² - 4b²

Apply Perfect Square Formula, and we get

(a + b)² = a² + 2 a b + b²

(a + 1)² = a² + 2a1+1²

= a² + 2a1 + 1² - 4 b²

simplifying the equation, we get

a² + 2a1 + 1² = a² + 2a + 1

= a² + 2a + 1 - 4b²

Factor, a² + 2a + 1 = (a + 1)²

= (a + 1)² - 4 b²

Simplify 4 b² = (2 b)²

= (a + 1)² - (2b)²

Apply the Difference of Two Squares Formula, and we get

x² - y² = (x + y)(x - y)

(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)

simplifying the equation, we get

= ((a + 1) + 2b)(a + 1) - 2 b)

= (a + 1 + 2b)(a + 1 - 2b)

Therefore, the correct answer is (a+1+2b)(a+1-2b).

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Answer:

Volume of he shed = 142.50 \(m^{3}\)

Step-by-step explanation:

Volume of cuboid = l x w x h

Here;

Vol. = 5 x 6 x \(\frac{19}{4}\)

= 30 x \(\frac{19}{4}\)

=30 x 4.75

=142.50 \(m^{3}\)

Answer:

142.5

Step-by-step explanation:

The variable that can be used for the number of brownies sold is x

The variable that can be used for Kate's profit is y

The equation that can be used to describe the pattern is y = 2x

A variable is quantity or symbol that may assume any one of a set of values.

Let

Kate's profit = Number of brownies sold × profit earned per brownies sold

If kate earned $8 as profit and sold 4 brownies

Kate's profit = Number of brownies sold × profit earned per brownies sold

8 = 4 × z

8 = 4z

divide both sides by 4

z = 8/4

z = 2

The equation:

Kate's profit = Number of brownies sold × profit earned per brownies sold

y = x × 2

y = 2x

Therefore, the equation that can be used to represent the situation is y = 2x

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Answer: The slope is 15/4.

Step-by-step explanation:

Riboflavin is similar to thiamin in that option d: both riboflavin and thiamin serve as coenzymes in energy metabolism.

Riboflavin is similar to thiamin in that both serve as coenzymes in energy metabolism. Coenzymes are molecules that assist enzymes in carrying out their biological functions. In the case of riboflavin and thiamin, they play vital roles in the conversion of carbohydrates, fats, and proteins into usable energy for the body.

Riboflavin, also known as vitamin B2, is an essential nutrient found in various foods such as dairy products, meat, eggs, and leafy green vegetables. It is a water-soluble vitamin, meaning it dissolves in water and is not stored in the body to a significant extent. Therefore, it needs to be regularly replenished through the diet.

Thiamin, also called vitamin B1, is another water-soluble vitamin that plays a crucial role in energy metabolism. It is involved in converting glucose into energy and is found in foods like whole grains, legumes, nuts, and seeds.

Both riboflavin and thiamin work as coenzymes by participating in specific enzymatic reactions. They assist enzymes in catalyzing chemical reactions necessary for energy production. Riboflavin, in the form of its coenzyme derivatives flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN), acts as a carrier of hydrogen atoms in metabolic reactions. Thiamin, on the other hand, is converted into its active form, thiamin pyrophosphate (TPP), which plays a crucial role in the metabolism of carbohydrates.

Now, let's address the options mentioned in the question to understand how riboflavin is similar to thiamin:

a. both are easily destroyed by heat: While it is true that riboflavin and thiamin can be degraded by heat, riboflavin is more sensitive to heat than thiamin. Riboflavin is easily destroyed when exposed to high temperatures, such as during cooking or food processing. Thiamin, although also susceptible to heat, is relatively more stable.

b. both are easily destroyed by ultraviolet light: This statement is incorrect. Riboflavin is indeed sensitive to ultraviolet (UV) light, which is why it is often stored in opaque containers to protect it from light exposure. However, thiamin is not particularly affected by UV light.

c. though rare, both can be toxic when consumed in high amounts: While excessive intake of any nutrient can potentially be harmful, toxicity from riboflavin and thiamin is rare. These vitamins are considered safe for consumption in recommended amounts, and any excess is typically excreted in the urine.

d. both serve as coenzymes in energy metabolism: This statement is correct, as explained earlier. Both riboflavin and thiamin are essential coenzymes involved in energy metabolism.

e. both are found in abundant amounts in pork: While pork is a source of several nutrients, neither riboflavin nor thiamin is found in exceptionally high amounts in pork. Riboflavin is more commonly found in dairy products, while thiamin is abundant in whole grains and legumes.

In summary, the correct answer is option d: both riboflavin and thiamin serve as coenzymes in energy metabolism. They play important roles in converting food into energy and are essential for overall health and well-being.

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Answer:

Step-by-step explanation:

44 = 2 * 2 * 11

    = 2² *11

Since the events A and B are equal, the probability P(A and B) is the same P(A).

The outcomes that are greater than or equal 6 are 6 and 7, and the probability of each one is: P(6) = 0.14 and P(7) = 0.13

So we have that:

Answer:

y = -2x + 12

Step-by-step explanation:

Parallel = Same Slope         Perpendicular = Opposite Reciprocal of Slope

How to find "b" or y intercept:

y = mx + b       (3,6)        slope = m: -2

plug in the corresponding values for the variables

6 = -2(3) + b

12 = b

Answer: 8.7 m

Step-by-step explanation:

This is a right angled triangle question.

a^2 + b^2 = c^2

a^2 + 5^2 = 10^2

a^2 + 25 = 100

a^2 = 100-25 = 75

a = √75 = 8.7

Answer:

8.7

Step-by-step explanation:

Using the Pythagorean Theorem (a^2 + b^2 = c^2), we get:

a^2 + 5^2 = 10^2

a^2 = 10^2 - 5^2

= 100 - 25

a^2 = 75

Taking square roots on both sides of the equation, we get:

a = 8.7

Hope this helps!

Answer:

hello

3.32 > 3.18

Step-by-step explanation:

Answer: 26.46cm

Step-by-step explanation:

The formula of a diagonal of a square is square root 2 a(a is not under the square root though)

So just substitute the a (area) with 350 and solve the equation.

Answer:

26.46cm

Step-by-step explanation:

Because you are dealing with a square, take the square root of the area and then use pythagoras theorem to calculate the diagonal.

Answer:

Step-by-step explanation:

root 9 looks like

\(\sqrt{9}\)

maybe you can solve it now?

3*3 = 9

so root 9 = 3

mark 3 on the number line

Answer:

52°

Step-by-step explanation:

360 - 33 - 165 - 20 - 90 = x

x = 52

Answer:

Step-by-step explanation:

Let's find the size of angle x

The angle in a complete turn add up to 360°

\( \mathsf{x + 20 + 165 + 33 + 90 = 360}\)

Add the numbers

\( \mathsf{x + 308 = 360}\)

Move constant to R.H.S and change it's sign

\( \mathsf{x = 360 - 308}\)

Calculate the difference

\( \mathsf{x = 52}\) °

Hope I helped!

Best regards!

Answer:

34.69 feet

Step-by-step explanation:

First, you would set up a proportion using the person's measurements and the measurements you do have from the building. You would put your actual value on top of one of the proportions, 6, then put its shadow value, 3.2, on the bottom. Then, you would add 18.5 to the bottom of your other fraction.

Next, you would cross multiply and divide. If you don't know what that means, you will multiply 18.5 by 6, and get 111. Then, divide this number by 3.2. This should make you get 34.6875, so then you round to the nearest hundredths place to get 34.69.

As, Michael completed a 6.2-mile race in 2 hours and 30 minutes. Using the inverse proportionality between time and speed, we can determine Michael's speed. The calculation shows that Michael's speed was approximately 2.48 miles per hour.

In an inverse proportion, two variables are related in such a way that an increase in one variable leads to a decrease in the other variable, and vice versa. In this case, the time taken to finish the race (t) is inversely proportional to the speed of the runner ($). Mathematically, this relationship can be expressed as t = k/$, where k is a constant.

To determine Michael's speed, we can plug in the given values into the equation. The race length is given as 6.2 miles, and the time taken is 2 hours and 30 minutes. First, we convert the time into hours by dividing 30 minutes by 60: 30/60 = 0.5 hours. So, the total time in hours is 2 + 0.5 = 2.5 hours.

Now we can substitute the values into the equation: 2.5 = k/$. To isolate $, we can multiply both sides of the equation by $ and divide by 2.5: $ = 2.5k. Since we are looking for the speed in miles per hour, we can express it as miles per hour = 6.2 miles / 2.5 hours. Simplifying the expression gives us approximately 2.48 miles per hour as Michael's speed.

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The volume of the hexagonal is 9√3a² where 'a' is the side of the prism

The volume of the prism is calculated by multiplying the base area and height of the prism. A six-sided polygon with a hexagon-shaped base and tip is called a hexagonal prism.

The formula for the volume of the prism is given by

Where a side and h are the height of the prism

Here we have

The height of the prism is 6 inches

Let 'a' be the side of the prism

Using the formula

Volume of the hexagonal prism = [(3√3)/2]a²(6)  

= [ (18√3)a²/2 ]

=  9√3a²

Hence,

The volume of the hexagonal is 9√3a² where 'a' is the side of the prism

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Substitution is the replacing the variables in an algebraic expression with their numerical values. It involves substituting the value of any one of the variables.

How to determine this

When an adult ticket costs  £7.50

A child ticket costs  £3.50.

Let x represent the number of adult tickets

And let y represent the number of child tickets

When Brooke sold tickets for her show

i.e x + y = 100 ----  (1)

From the equation, by making y the subject of the formula

y = 100 - x ----  (2)

7.50x + 3.50y = 590  ---- (3)

By substituting equation 2 into 3

7.50x + 3.50(100 - x) = 590

Open bracket

7.50x + 350 - 3.50x = 590

Collect like terms

7.50x - 3.50x = 590 - 350

4x = 240

Divides through by 4

4x/4 = 240/4

x = 240/4

x = 60

When y = 100 - x

x = 60

So, y = 100 - 60

y = 40

Therefore, the amount she sold for adult tickets to child tickets is 60 tickets to 40 tickets respectively

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Answer:

42 degrees

Step-by-step explanation:

Find opposite side of 132 degrees which is 48. Add 48 and 90 because of right angle to get 138. Then do 180-138 to get 42 degrees for remaining angle

Answer:

Step-by-step explanation:

132 is the exterior angle, which is the sum of the two non-adjacent interior angles:

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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Answer:

he is a -168

Step-by-step explanation:

-5.6*30=-168