2X-3Y=4
X+Y=6
please explain each step

if h(x) = 2x² - 5x + 7

h(-3) = 2(-3)² - 5(-3) + 7

= 18 + 15 + 7

= 40

The lengths of the sides of the rectangular field should be 244.95 m in order to minimize the cost of the fence.

Let the dimensions of a rectangular field be;

Length = l

Width = w

We know that the formula for perimeter of a rectangle is;

P = 2(l + w)

And the formula for area of the rectangle is;

A = lw

⇒ w = A/l

Subtitute w = A/l in the formula of perimeter of rectangle.

P = 2l + 2(A/l)

P = 2L + 2A/l

We differentiate above equation with respect to l,

dP/dl = 2 - 2A/l²

when dP/dl = 0 we get,

2 - 2A/l² = 0

l = √A

Substitute l = √A in the area equation,

A = w√A

w = A/√A

w = √A

This means, l = w = √A

Since length is equal to width, then it is a square.

We have been given that the area is 60,000 m²

So, l = w = √(60,000)

l = w = 244.95 m

Therefore, the lengths of the sides of the rectangular field should be 244.95 m

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Answer:

a. 10 km

b. 25 km

c. 35 km

Step-by-step explanation:

You are given the rate running = 5 km per 0.5 hr and the rate for biking = 20 km per 0.8 hr. Set up a proportion to get from 0.5 hr to 1 hr multiply by 2, so multiply 5 km by 2 = 10 km. Do the same for biking 0.8 hr to 1 hr is multiplied by 1.25, so multiply 20 by 1.25 = 25 km. Add those two values together for c to get 35 km. See attached image

Answer:

62.92

Step-by-step explanation:

The required number is 0.0556, which is 1.03 times of 0.054.

Given that,
To determine the number which is 1.03 times of 0.054.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
According to the question,
1.03 times of 0.054 = 1.03 ×0.054
                              = 0.0556

Thus, the required number is 0.0556, which is 1.03 times of 0.054.

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Answer: -41

Step-by-step explanation:

-7x - 6

-7(5) - 6

-35 - 6

-41

Answer:39.9

Step-by-step explanation:1 kilogram is 0.453592 kilograms so if you multiply that number by 88 you will get 39.9

True. In a probability​ model, the sum of the probabilities of all outcomes must equal 1.

This is incomplete question

Complete question is this:

True or False​: In a probability​ model, the sum of the probabilities of all outcomes must equal 1.

Answer in true or false.

Now, According to the question:

Let's know:

What is Probability Model?

A probability model is a mathematical representation of a random phenomenon. It is defined by its sample space, events within the sample space, and probabilities associated with each event. The sample space S for a probability model is the set of all possible outcomes.

Now, According to the above statement is:

Hence, True. In a probability​ model, the sum of the probabilities of all outcomes must equal 1.

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True. In a probability model, the sum of all outcomes' probabilities must equal 1.

Probability Model

A probability model is a mathematical model that represents a random phenomenon. Its sample space, events within the sample space, and probabilities associated with each event define it. A probability model's sample space S is the set of all possible outcomes.

As a result, the statement given here is true. In a probability model, the sum of all outcomes' probabilities must equal 1.

One advantage of using an explicit mathematical model rather than simply applying a set of rules to probability situations is that the intuitive approach to probability has significant limitations when analysing tricky or sophisticated phenomen.

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Step-by-step explanation:

remember :

when multiplying terms with the same base, we add the exponents.

when dividing terms with the same base, we subtract the exponent of the denominator from the exponent of the numerator.

when putting exponent on exponent, we multiply the exponents.

a negative exponent means 1/...

e.g. 6^-4 = 1/6⁴

1/6^-4 = 1 / 1/6⁴ = 6⁴

so,

1.

(3^-4 × 3²)/3 = 3^-2 × 3^-1 = 3^-3 = 1/3³ = 1/27 =

= 0.037037037...

2.

(4²)^-1 × 4² = 4^-2 × 4² = 4⁰ = 1

3.

(2^-4 / 2^-2)^-1 = (2^-4 × 2²)^-1 = (2^-2)^-1 = 2² = 4

4.

(3^-3)² / (3²)^-1 = 3^-6 / 3^-2 = 3^-6 × 3² = 3^-4 =

= 1/3⁴ = 1/81 = 0.012345679...

The number of children and adults using the swimming pool is x=318, and y=235 respectively.

Given that,

Swimming pool on a certain hot summer day 553 people use the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1085.25.

Here,
let the number of children be x and the number of adults be y,
According to the conditions,
x + y = 553,  - - - - - - (1)
1.75x + 2.25y = 1085.25 - -- - - - - -(2)
Solving the above equations by substitution of x from 1 in equation 2.
1.75[y - 553] + 2.25y = 1085.25
x = 318
Now,
x = 553 - 318
x = 235

Thus, the number of children and adults using the swimming pool is x=318, and y=235 respectively.

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Answer:

y-10=   1/2(x-2) --- point slope form

Step-by-step explanation:

Point slope form is:

y- y1=m(x-x1)

y1= 10

m= y2-y1/x2-x1

y2= 6

x2= -10

x1= -2

Using point slope form and defining the variables using the given coordinates, the equation can be written.

Answer:

y-6 = -1/3(x-10)

Step-by-step explanation:

Let's use point slope form! The form of this is y-y1 = m(x-x1) where m is the slope.We have points to use, so let's find the slope.

The slope is rise over run, so we take the difference in y and divide it by the difference in x. This gives us [tex](10-6)/(-2-10)[/tex], which simplifies to -1/3. Now we plug in a point, say (-2, 10) for x1 and y1, and -1/3 for the slope, which gives us y-6 = -1/3(x-10)

Another way you could approach this is to plug in both the points to solve for m. Plug in both the y-values(10, 6) for y and y1 and both the x-values(-2, -10) for x and x1.

This gives us [tex]10-6 = m(-2-10)[/tex], which simplifies to [tex]4 = -12m[/tex]. Dividing both sides by -12 gives m = -1/3, which is the slope. Whichever way makes most sense works!

I hope this helps!

The expression 17n+11 represents the perimeter of a triangle, which is the sum of the lengths of the three sides of the triangle. Therefore, we can use this expression to determine the length of the third side of the triangle.

Since the perimeter of the triangle is equal to 17n+11, we know that the sum of the lengths of the three sides is equal to 17n+11. We can write this as:

a + b + c = 17n+11

where a, b, and c are the lengths of the three sides of the triangle.

To determine the length of the third side, we need to know the lengths of the other two sides. However, since the question does not provide this information, we cannot determine the length of the third side with certainty. In general, there are many different triangles that could have a perimeter of 17n+11, and the length of the third side could vary depending on the specific lengths of the other two sides.

Without additional information about the lengths of the other two sides, it is not possible to determine the length of the third side of the triangle.

The ratio shows how many times one value is contained in another value.

The fraction of the bracelets from the total items is 6/13.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of earrings, bracelets, and necklace is 13:24:15.

This means,

Earrings = 13x

Bracelets = 24x

Necklace = 15x

The fraction of the bracelets from the total items.

= 24x / (13x + 24x + 15x)

= 24x / 52x

= 24/52

= 12/26

= 6/13

Thus,

The fraction of the bracelets from the total items is 6/13.

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Answer:

2i[tex]\sqrt{6[/tex]

Step-by-step explanation:

So, for right now, ignore the negative. Consider the factors of 24. Both 6 and 4 multiply to 24. This means that [tex]\sqrt{24} = \sqrt{6}[/tex] x [tex]\sqrt{4}[/tex]. [tex]\sqrt{4}[/tex] can simplfy down to just 2. Now let's remember the negative. When taking a negative square root, you need to add an 'I' to the number you take out of the root. So right now you have 2i. Then [tex]\sqrt{6}[/tex] does not have any additional square roots to take out. So your final answer is 2i[tex]\sqrt{6[/tex].

Please give me brainiest if this helped.

Answer:

8 years old

Step-by-step explanation:

Make Nick's age = x

Caroline's age = x + 12

Mark's age = x - 4

So,

x + (x + 12) + (x - 4)

Remove brackets:

x + x + 12 + x - 4 = 44

Collect like terms:

3x = 44 - 12 + 4

3x = 36

x = 12 

Mark is 8 yrs old

Nick is 12 yrs old

Caroline is 24 yrs old

Youngest is Mark = 8 years old.

Hope this helps :-)

The inequality that is different is C. X is no less than 12

Inequalities are created through the connection of two expressions. It should be noted that the expressions in inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

An inequality is created when two or more algebraic expressions are compared using the symbols. They represent mathematical expressions where neither side is equal.

p ≠ q means that p is not equal to q

p < q means that p is less than q

p > q means that p is greater than q

p ≤ q means that p is less than or equal to q

p ≥ q means that p is greater than or equal to q

It should be noted that x is no less than 12 isless than the other inequalities that are given. Therefore, the correct option is C.

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The average increase in flower count is 42.

The average is the ratio created by dividing the total number of figures in a set by the number of elements

Fowers pollinated in this instance is f(x), where x is the number of days. The nunumber of figures.The number of flmber of flowers that were pollinated between days 4 and 10 as well as on those days must first be determined.

F(4) = 3(4^2) = 3*16 = 48

F(5) = 3(5^2) = 3*25 = 75

F(6) = 3(6^2) = 3*36 = 108

F(7) = 3(7^2) = 3*49 = 147

F(8) = 3(8^2) = 3*64 = 192

F(9) = 3(9^2) = 3*81 = 243

F(10) = 3(10^2) = 3*100 = 300

The average of the day-to-day variations will be

[(75-48)+(108-75)+(147-108)+(192-147)+(243-192)+(300-243] in order to obtain the average increase.

=(27+33+39+45+51+57)/6=42

There the average increase in the number of flowers pollinated per day is 42

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Answer:

Step-by-step explanation:

if you're looking for an+1 it might be an=3

because the an represents the first term in the sequence

If an IR signal has a percent transmittance of 45%, then the sample absorbed 55% of the IR light

The percent transmittance of an IR signal = 45%

The equation of percent transmittance is

Percent transmittance = ( I / Io ) × 100

Where Io is the intensity of the IR signal entering the sample

I is the intensity of the IR signal leaving the sample

If the Io = I, then the percent transmittance is 100% that means the sample did not absorb any light and if Io= 0 then the the percent transmittance is 0% then sample absorbed all the light

Here, the percent transmittance is 45%, that mean the 55% of light absorbed by the sample

Therefore, the sample absorbed 55% of the IR light

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Answer:x>1

Step-by-step explanation:

The equivalent expression of the expression given as (m−2n−4)−4 is m − 2n − 8

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

(m−2n−4)−4

Remove the brackets

So, we have the following representation

This gives

(m−2n−4)−4 = m − 2n − 4 −4

Evaluate the like terms in the above expression

So, we have the following representation

(m−2n−4)−4 = m − 2n − 8

The above expression cannot be further simplified

Hence, the solution is m − 2n − 8

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Answer:

x = 45

Step-by-step explanation:

Answer:

It would have saved 445$

Explanation: because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 280$ and the he saved 175$ on the fifth week because 7/8 of 200 is 175 so 280+175 is 445

Step-by-step explanation:

Answer:

6+18

Step-by-step explanation:

Use PEMDAS, or standard order of operations for basically all levels of math.

In order from first to last, solve:

Parenthesis

Exponents/Roots

Multiplication/Division

Addition/Subtraction

Exponents, Multiplication, or Addition are not to be prioritized over Roots, Division,  or Subtraction. Solve left to right in that situation.

Because 6+18 is in parenthesis, solve that first.

John has the greater total change in the amount of detergent in their bottle.

Given that, Brenda pours laundry detergent from a bottle into the cap and then into the washing machine.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 L. She fills the cap 314 times in all.

Now, the volume of bottle =314×0.26

= 81.64

≈ 82 L

Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 L. He fills his cap 256 times in all.

Here, the volume of bottle =256×0.21

= 53.76

≈ 54 L

Hence, John has the greater total change in the amount of detergent in their bottle.

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The range of horn lengths for the middle 99.7% is  (46.5 , 73.5) inches .

In the question ,

it is given that ,

the horn lengths of Texas cattle are Normally Distributed ,

the mean of the horn spread is = 60 inches ,

the standard deviation of horn spread is = 4.5 inches ,

we know that the range for the middle 99.7% is (μ ± 3σ) ,

So , substituting the values in the range formula ,

we get ,

Range = (μ ± 3σ)

= (μ - 3σ , μ + 3σ)

= (60 - 3*4.5 , 60 + 3*4.5)

= (60 - 13.5 , 60 [tex]+[/tex] 13.5)

= (46.5 , 73.5)

Therefore , the range is (46.5 , 73.5) inches .

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Eve made 56 free throws for every 30missed throws in her practice

What is ratio?

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

From the question;

The ratio of misses would be: 7:3

If she missed 24 free throws, the new ratio would be: x:24

To do this, we would need to find how many times did 3 go into 24.

3 goes into 24 8 times. We do the same thing to the 7.

We multiply 7x8, which is 56.

The new ratio is: 56:24

So, Eve made 56 free throws.

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