You have 900 feet of fencing to enclose a rectangular plot that borders on
a river. If you do not fence the side along the river, find the length and
width of the plot that will maximize the area. What is the largest area that
can be enclosed?
The width, labeled x in the figure, is
(Type an integer or decimal.)
feet.
X
River
900-2x
x

Answer:

x = 1 or x =3

Step-by-step explanation:

2x² + 4x = 3 + 3x²

2x²-3x²+4x -3 = 0

-x² + 4x -3 = 0

by calculator:

x = 1 or x =3

Anwser is 18

I used a website

Answer: x = 18

Isolating a variable: rearranging the equation to make the variable on side of the equation and the others on the other side

1. Collect like terms

2. Inverse operations to isolate

3. simplify if necessary

Calculations:

[tex]3x -14 +3x +9= 103[/tex]

Collect like terms: [tex]6x -5 =103[/tex]

Inverse operations:

[tex]6x = 103 +5[/tex]

[tex]6x= 108[/tex]

[tex]\frac{6x}{6}=\frac{108}{6}[/tex]

∴ [tex]x= 18[/tex]

The given equation is

5(x - 3) = x + 13

We want to test if x = 6 is a solution. We would substitute x = 6 into the equation. We have

5(6 - 3) = 6 + 13?

5(3) = 6 + 13?

15 = 19?

Since both sides of the equation is not equal, then

x = 6 is not a solution of the equation

It takes Phindi to run almost 22 tracks to cover 12kms

Given that,

First you have to figure out the length of the track whihc is circumference of circle ,

r is the radius  of circular track which is 88m

The athlete has to run 12km on the track

Circumference of circle = 2πr

Solving circumference will give length of the circular track which is,

Circumference of circle = 2(3.14)(88)

                                          =552.6 meters

If she covers 552.6 m whe runs one circular track then,

1 circular track -------- 552.6 meters

? circular track -------- 12000 meters or 12 kilometers

No of circular tracks = 12000/552.6 = 21.7 tracks

Therefore, It takes Phindi to run almost 22 tracks to cover 12kms

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Answer:

11.4 m

Step-by-step explanation:

2m / 5 cm   * 28.5 cm = 11.4 m

Answer:

  -8k -2

Step-by-step explanation:

You want the simplified form of -2(k+1)-6k.

The process of simplifying an algebraic expression includes ...

Parentheses are removed using the distributive property. The factor outside parentheses multiplies each term inside.

  -2(k +1) -6k

  = (-2)(k) +(-2)(1) -6k = -2k -2 -6k

Terms with the same variable content can be combined by adding their coefficients. (The distributive property is involved here, too.)

  = (-2 -6)k -2 = -8k -2

The simplified expression is -8k -2.

The distance that member of the cross country team ran is 6.2 miles yesterday.

Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage.

The cross-country team ran 1.772 hours yesterday, today they ran 1.49 hours Each member of the team ran 3.5 miles every hour.

The number of miles attained by each member of the team yesterday can be calculated as follows:

3.5 × 1.772= 6.2

Hence for yesterday each member of the team ran for 6.2 miles.

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After doing some mathematical operations we can conclude that there are 11 servings in a fruit can.

So, servings in a fruit can:

Now, solve the following as follows:

Therefore, after doing some mathematical operations we can conclude that there are 11 servings in a fruit can.

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SOLUTION

Line 1 is given as

let's find the equation of line 2, it passes through points (2, 3) and (4, 4)

The slope is

The slope of line 2 is 1/2

If the two lines are perpendicular, then the product of their slope will be = -1, that is

Since the product of their slope = -1

Hence Line 1 and Line 2 are perpendicular

Firstly, congruent angles are equal

The three statements are

1. Triangle PTW = Triangle HGD

2. Triangle WPT = Triangle DHG

3. Triangle TWP = Triangle GDH

From the figures, it was observed that they are similar

When you look at the figures very well

You will observed that Triangle PTW is Similar to triangle HGD

They both have similar properties

The measures of the angles are given as follows:

1. p = 67º.

2. q = 27º.

To solve item 1, first we have to consider that the sum of the internal angles of a triangle is of 180º, hence we find angle x, which is the interval angle of angle p.

Hence:

x + 35 + 32 = 180

x + 67 = 180

x = 113º.

An angle and it's respective external angle are supplementary, meaning that the sum of it's measures are of 180º, hence:

p + x = 180

p + 113 = 180

p = 67º.

The internal angles are given as follows:

The sum of their measures is of 180º, hence we can simply solve for q as follows:

q + 128 + 25 = 180

q + 153 = 180

q = 27º.

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Answer:

The measures of the angles are given as follows:

1. p = 67º.

2. q = 27º.

Step-by-step explanation:

But you didn't have to cut me off

Make out like it never happened and that we were nothing (aah-ooh)

And I don't even need your love (ooh)

But you treat me like a stranger, and that feels so rough (aah)

No, you didn't have to stoop so low (ooh)

Have your friends collect your records and then change your number (aah)

I guess that I don't need that, though

Now you're just somebody that I used to know

a) From the exercise we can identify 3 unknowns from the 3 funds

• Large Growth = ,LG

• Small Growth = ,SG

• Large Value = ,LV

b)

Answer:

1

5

Step-by-step explanation:

y = mx + b

b = -5 (the y-intercept)

m = 1/1 = 1

y = x - 5

The equation is 10x=2x+60

 x=15/2

∠CFH=75

∠CBD= 75

We are dealing with parallel lines, which are the lines that are equidistant to each other and never meet,  will never meet, when such lines are crossed by another line called the transversal creates many angles such as corresponding angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive angles.

Since, angle CBD and angle CFH are the corresponding angles and they are equal to each other, we are given CBD=2x+60 and CFH = 10x

therefore , 10x=2x+60

=>10x-2x=60

=>8x=60

x=15/2

So, the angle CBD= 2x+60= 2(15/2)+60=  75

and the angle CFH = 10x= 10(15/2)= 75

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Step-by-step explanation:

Since area = 27cm²

area = 3 × (x + 4)

27 = 3(x + 4)

expand the right side

27 = 3x + 12

move 12 to the left side and subtract it with 27

15=3x

then divide both sides with 3

x=5

Answer: 6

Step-by-step explanation: .

Answer:

x=12.92

cube root of 9 Is 2.08 so you minus 15-2.08=12.92

900km is less than the perimeter of the of Bhutan about 1075km.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.

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Answer:

17 * 2= 34

therefore, 17 and 2 are the factors of 34

Step-by-step explanation:

According to the solving the space between Arthur and Jamie are 39.1 meters.

A coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

The length of the line segment bridging two locations in a plane is known as the distance between them. d=√((x2 – x1)² + (y2 – y1)²).  is a typical formula for determining the separation between two places. Any two sites on an x-y plane or coordinate plane can have their distance between them calculated using this equation.

location of Arthur is (20, 30)

location of Jamie is (45, 60)

Let's apply the rule of distance to determine how far away they are because we know that :

d = √((X₂ - X₁)² + (Y₂ - Y₁)²)

let substituting the value we get:

d = √((X₂ - X₁)² + (Y₂ - Y₁)²)

d = √((45 - 20)² + (60 - 30)²)

=   √(25)² + (30)²)

= 39.1

According to the solving the space between Arthur and Jamie are 39.1 meters.

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The probability of drawing a consonant from the given set of cards is 0.66.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The given letters are  M, A, T, H, I, S, F, U and N.

Total number of letters are 9.

The number of vowels is 3.

Then, the number of consonants is 9 - 3 =6.

Now, the probability for choosing consonant is given as follows,

P(Consonant) = Number of Consonants ÷ Total letters

⇒ 6/9 = 0.66

Hence,  the probability of randomly drawing a consonant is given as 0.66.

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Answer: 6/10 is answer

Step-by-step explanation:

Just trust please

Simplify both sides of the inequality.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3x-21 } \end{gathered}$} }[/tex]

Subtract 3x from both sides.

Subtract 6 from both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{0 < -27} \end{gathered}$} }[/tex]

Answer:

0 < - 27

Step-by-step explanation:

1. Distribute

3x + 6 < 3(x-7)

3x + 6 < 3x - 21

2. Subtract 6 from both sides

3x + 6 <  3x - 21

3x + 6 - 6 < 3x - 21 - 6

3. Simplify

   subtract

    3x + 6 - 6 < 3x - 21 - 6

    3x <  3x - 21 - 6

   subtract

     3x < 3x - 21 - 6

     3x < 3x - 27

4. Subtract 3x from both sides

3x < 3x - 27

3x - 3x < 3x - 27 - 3x

5. Simplify

    combine like terms

     3x - 3x < 3x - 27 - 3x

     0 < 3x - 27 - 3x

     0 < 3x - 27 - 3x

      0 < -  27

And that is how you get your answer

Assuming the question is : How much does x liters/milimeters of oil weigh?

First, we calculate how much mass did the bottle of oil lose : 590 - 400 = 190 (grams)

Since it loses 190 grams after Sophia uses 200 milimeters of oil, 200 milimeters of oil weighs 190 grams (yes.)

-> 1 milimeter of oil weighs : 190/200 = 0.95(grams)

So, to calculate the mass of x *liters* of oil, we take 0,95 x 1000 times x.

For example : To calculate the mass of 22,5 liters of oil, we take 0,95 x 1000 x 22,5 = 21375 (g) or 21.35(kg).

A segment that is both an altitude and a median of a triangle is a perpendicular bisector.

A median is a segment from a vertex to the midpoint of the opposite side. There are of course three medians of a triangle; they’re concurrent, meeting at a point called the centroid.

An altitude is a segment through a vertex that’s perpendicular to the opposite side; the foot of the altitude (at the point of perpendicularity) either on the side or on the line resulting from extending the side. The three altitudes of a triangle are also concurrent, meeting at a point called the orthocenter.

And when both the altitude and a median of a triangle are the same, then it is called a perpendicular bisector.

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Answer: 28.75 cm

Step-by-step explanation:

           Using the formula for the area of a rectangle, we can plug in our known values and solve for the height.

A = B * H

(345 cm²) = (12cm) * H

28.75 cm = H

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MFM (option A)

Outcome could be male or female

At least two male means the minimum of number of men that we would have in the sample space outcome is 2.

The outcome that satisfies this are:

MMM, MMF, MFM, FMM

From the above, the one in the options is MFM (option A)

The equation of S in terms of N is S(N) = 2200 + 40N

From the question, the given parameters are

Monthly salary = $2200

Additional earnings = $40 per copy of Math fun sold

The equation that relates S to N is then calculated as

Total = Monthly salary + Additional earnings x Number of copy of Math fun sold

Substitute the known values in the above equation

So, we have

S(N) = 2200 + 40N

So, the equation is S(N) = 2200 + 40N

See attachment for the graph

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Find out the total number of animals

25+12=37 animals

Compare the number of birds to the total number of animals

number of birds=25

so

25/37

or

25:37

or

25 to 37