How do I find the measure of the triangles? Help.

The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 150, hence:

Area = length × width = x × y

150 = xy

y = 150/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(150/x) = 2x + 450/x

To minimize the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2 = 450/x²

2x² = 450

x² = 225

x = 15 feet

Let's find the value of y.

y = 1350/x = 1350/15 = 10 feet

Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.

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Regarding the situation described, it is found that:

The total amount invested is of $25.

1. You start making a profit when 15x - 25 > 0.

2. You earned $215 with this work.

With the investment, you made money (option b).

The investment was as follows:

Hence the total amount invested was of:

10 + 15 = $25.

The profit is given by revenue subtracted by costs.

In the context of this problem, the revenue and the cost functions are given as follows:

Hence the profit function is:

P(x) = R(x) - C(x)

P(x) = 15x - 25.

You start making a profit when:

P(x) > 0.

15x - 25 > 0.

The amount you earned mowing 16 lawns is of:

P(16) = 15(16) - 25 = $215.

(positive profit, hence you made money).

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Answer:

Part A. (4,5)

Part B. (9,7)

Step-by-step explanation:

Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.

Answer:

10.53

Step-by-step explanation:

hope it helps :)

There are 126 blue marbles.

Total marbles in the bag=150

There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150

21 blue marbles appear 6 times for every 4 blue marbles

So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles

∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.

At the rate of variation of 50 days/pound the snake gain 1 pound.

The mathematical expression for the percentage difference change over a predetermined period is called the rate of variation, which also denotes the movement of a variable. It allows us to understand how 2 factors that are changing interact with one another.

A snake takes 25 ÷ 4 days to gain 1 ÷ 8 pounds of weight,

a) Gain 1 pound need take: (25 ÷ 4) × 8 = 50 days

b) In one year = 365 days

= (25 ÷ 4) × (1 ÷ 8)

= (25 ÷ 4) × 8

= 50 days/pound.

So, the snake gained(1 ÷ 50) pounds one day.

In one year: (1 ÷ 50) × 365 = 7.3 pound

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Answer:

0.64 feet

Step-by-step explanation:

make h the subject of this expression

[tex]t = \sqrt{ \frac{h}{16} } [/tex]

[tex] {t}^{2} = \frac{h}{16} [/tex]

[tex]h = 16 {t}^{2} [/tex]

then substitute in the value of t=0.2 into the equation of h:

h = 16 × (0.2)² = 0.64 feet(answer)

Answer:

answer: -35

Step-by-step explanation:

if it's not sorry

Answer:

-12

Step-by-step explanation:

5x+(-y)+8-6x+9y

Farmer A planted a greater ratio of green beans to corn

Ratio is defined as the comparison of two quantities (a and b) of the same units which indicates how much of one quantity is present in the other quantity. They are written a / b, where b does not equal 0

Given that:  Farmer A planted green beans and corn at a ratio of 5:3 and farmer B planted green beans and corn at a ratio of 3:2

To find the greater ratio treat the ratio as a fraction:

Farmer A => 5:3  and Farmer B => 3:2

5/3  and  3/2      (LCM of 2 and 3 is 6)

10/6 and 9/6

10:6 and 9:6

Since 10:6 is greater than 9:6. Therefore, Farmer A planted a greater ratio of green beans to corn

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Step-by-step explanation:

The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit of $3,365, what is the value of c?

$3,365 = 225(75) - (165(75) + c)

$3,365 = 16,875 - 165(75) - c

$3,365 = 16,875 - 12,375 - c

$3,365 = 4,500 - c

=1,135 =  - c

c = 1,135

The person from the 4 people that will reach his or her goal is Friend C.

Friend A: Works 6 hours per week at $13.90 per hour. The amount in 8 weeks will be:

= 6 × $13.90 × 8

= $667.2

b) Friend B: Works 7.5 hours per week at $11.70 per hour. The amount in 8 weeks will be:

= 7.5 × 11.70 × 8

= $702

c) Friend C: Works 9 hours per week at $10.50 per hour. The amount in 8 weeks will be:

= 9 × $10.50 × 8

= $756

d) Friend D: Works 5.5 hours per week at $15.60 per hour. The amount in 8 weeks will be:

= 5.5 × $15.60 × 8

= $686.40

In this case, C had $756 which is above the amount needed.

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Answer:

because there’s additional numbers to the equation

Step-by-step explanation:

it differs because of the -3 it’s -3 down

The cost of the appointment without insurance is $200. Isaiah has an insurance plan throw his employer with a $50 monthly premium and a $20 copay. then Isaiah will have to pay his doctor $ 20

Insurance co-pay is a pre-determined amount that a person with medical insurance pay every time they use medical services. The co-pay is a dollar amount and usually less than $25. Different insurance companies have varying co-pay amounts for different services, such as doctor visits and prescriptions.

Isaiah will pay $20 for a visit to the doctor, as stated in the policy document. The $50 premium is payable to the insurance company every month to maintain the insurance coverage.  

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Answer:$ 17.28

Step-by-step explanation:

The simplified equation is 14x+8 which has infinitely many solutions as given in the question.

1.Remove parenthesis and combine like terms to simplify either side of the equation.

2.Isolate the variable term on one side of the equation using addition or subtraction.

3.To find the variable, use multiplication or division.

Given equation is:

12x-x+8+ 3x

= 11x+3x+8

=14x+8

Therefore, the simplified equation is 14x+8 which has infinitely many solutions.

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(y + 7) = -2/3(x - 1) is the point-slope form of the equation of a line passing through (1, -7) and having a slope of -2/3.

The query revealed information include

a slope of -2/3

point (1, -7)

Those functions with exponents of 1 are known as linear functions.

The form represents the equation of a line in point-slope form.

(y - y₁) = m (x - x₁)

Variables in the y direction are described by  (y and y₁).

variables in the x direction are described by (x and x₁).

m = slope

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".

A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.

Here,

The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.

=(1+2+3+4+5+6+7+8)/2

=18

Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.

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A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.

Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.

A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.

Perpendicular bisector: A line that bisects a line segment in two equal parts.

Median: The middle number; found by ordering all data points and picking out the one in the middle.

Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.

Therefore, a police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.

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Answer:

45

Step-by-step explanation:

The 27 red cars make up 60% of the total collection, here is the equation

to be solved:

         27 = 60% of C                         C is the total cars in the collection

         27 = .60 C

         27 / .60 = C

         45 = C

Hope this helps! :)

The solution to the variable x is 12 and the measure of ∠B is 48°.

∠A = 5x−12°

∠B = 2x+24°

Angle A and Angle B are congruent angles.

Congruent angles are angles with the same or equal measures.

So,

∠A = ∠B

5x - 12 = 2x + 24

5x - 2x = 24 + 12

3x = 36

divide both sides by 3

x = 36/3

x = 12

So therefore,

∠A = 5x−12°

= 5(12) - 12

= 60 - 12

= 48°

∠B = 2x+24°

= 2(12) + 24

= 24 + 24

= 48°

Therefore, since ∠A and ∠B are congruent, the measure of ∠A and ∠B is 48° respectively.

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The length of AC which is the hypothenuse is equal 15.5mm

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.

In this question, triangle ABC forms a right-angle triangle at angle B and this makes it possible to use Pythagoras theorem.

Using the formula;

AC² = AB²  + BC²

AC²  = 7²  + 13.8²

AC = 15.5mm

The length of the hypothenuse is 15..5mm

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Answer:

31

Step-by-step explanation:

x+10+2x+20+2x-5=180

5x+25=180

5x=155

x=31

Answer: calculate these equations

Step-by-step explanation: if you have times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form. If we substitute what is in the ( ) with a variable like t, then the original equation will become a quadratic equation.

The value of the variable r in 6r+ r- 4 will be 4/7.

Given,

To solve the polynomial,

6r + r- 4,

and find the value of the variable r,

we have to convert the polynomial in to a quadratic equation by equating it with 0, or, in other words, making the polynomial equal to zero.

So, the quadratic equation will be,

6r + r- 4 = 0

=> (6r+ r) -4 =0

=> 7r -4 = 0

=> 7r = 4

=> r = 4/7.

Thus, the value of the variable r in the polynomial 6r + r -4 will be 4/7.

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Slope equals the change in the vertical (Y value) divided by the change in the horizontal (X value), the slope of a horizontal line is zero and equation of line is Y =12. So option C is correct.

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept.

Here,

Since the Y-axis is vertical, a line perpendicular to it would be horizontal..  The slope of a horizontal line is zero, because slope is the change in the vertical (Y value) divided by the change in the horizontal (X value), and the vertical coordinate does not change from the -3 of the point given.

If we start with the slope-intercept form of an equation of a line

Y = mX + b,

we can write Y = 0X + (12)

Y =12

Slope is the vertical change (Y value) divided by the horizontal change (X value); the slope of a horizontal line is zero, and the equation of the line is Y =12.

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a) Sample mean of set is 36.375.

b) Standard deviation of sample is 6.66208.

The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.

Given,

a) Mean

Total number of values = 16

= Sum/Total number of values

=  34 +45+ 27 +33 +38+ 41+ 45 +29 +30+ 39 +34 +40 +28 +33 +36+ 50/16

= 582/16

= 36.375

Sample mean of set is 36.375.

b) Sample standard deviation

S² = ∈ (x i - x)²/N-1

S² = 666.75/16-1

S² = 44.383333

S = √44.38333

S = 6.66208

Standard deviation of sample is 6.66208.

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Answer:

360 sq feet

Step-by-step explanation:

The width of the room is given in the question, 12 feet.

We don't know the length. Let's call the length x.

x = length

We were also given the perimeter, 81, that's the distance around the sides...

all the sides added up.



Use x for the long wall.

Use x-3 for the wall with the door in it.

x + 12 + x-3 + 12 = 81

combine like terms

2x + 21 = 81

subtract 21

2x = 60

divide by 2

x = 30

The room is 30 feet long by 12 feet wide.

Area =

length × width

= 30 × 12

= 360

The area of the room is 360sq feet.