The area of a rectangular garden is 3927cm . If the width of the garden is 51 m , what is its length?

Answer:

x ≈ 23.31

Step-by-step explanation:

We can use the law of cosines because we know 2 sides and 1 angle.

The general formula  for the law of cosines if the triangle sides are a, b,c and α is the angle between sides a and b. c is the missing side.

[tex]c = \sqrt{a^{2} +b^{2} -2*a*b* cos \alpha }[/tex]

In our problem the law of cosines is

x = [tex]\sqrt{21^{2} +13^{2} - 2*21*13 *cos 83}[/tex]

x ≈ 23.31

[tex](x - 3)(2x {}^{2} - 5x + 1)[/tex]

[tex]2x {}^{3} - 5x {}^{2} + x - 6x {}^{2} + 15x - 3 [/tex]

[tex]2x {}^{3} - 11x {}^{2} + 16x - 3[/tex]

Answer:

d = st, d = 100 x 3

Step-by-step explanation:

distance = speed x time

distance = 100 x 3, therefore, distance = 300, but if you just want the equation, it is d = 100 x 3 or d = st

Step-by-step explanation:

d = 100 x 3.

d= 100n

where n = time the journey took.

Hey there!

Let's solve this equation!

The first step is to use the Distributive Property.

7(5-5y)=9y-4-357

35-35y=9y-361

Combine Like Terms:

-35y-9y=-361-35

-44y=-396

Divide both sides by -44:

y=9

Hence, the answer is:

[tex]\boxed{\boxed{\bold{y=9}}}[/tex]

Hope everything is clear.

Let me know if you have any other questions; if so, please comment.

#LearningDoesn'tEnd

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Answer:

Step-by-step explanation:

Because a square has 4 equal sides:

P = 4x

A = [tex]x^{2}[/tex]

[tex]P=\frac{4x^2+4}{x^2-2x+1}[/tex]                              (original P equation)

[tex]4x=\frac{4x^2+4}{x^2-2x+1}[/tex]                             (substitute P = 4x)

[tex]4x(x^2-2x+1)={4x^2+4}[/tex]         (multiply denominator on both sides)

[tex]4x^3-8x^2+4x={4x^2+4}[/tex]          (distribute 4x)

[tex]4x^3-12x^2+4x-4=0[/tex]            (combine like terms, set = to 0)

[tex]4(x^3-3x^2+x-1)=0[/tex]             (factor)

Continue using quadratic formula to find x

Hope this helps! Cannot finish answer right now, so sorry

side=Perimeter/4

side:-

[tex]\\ \rm\Rrightarrow \dfrac{4(x^2+1)}{4(x^2-2x+19}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{x^2+1}{x^2-2x+19)}✓/tex]

Area=side ²

[tex]\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x^2-2x+19}\right)^2[/tex]

Percentage Calculator: What is the percentage increase/decrease from 72 to 63? = 12.5.  

Answer:

-1/4

Step-by-step explanation:

14x - 2x + 3 = 0
12x + 3 = 0
12x = -3
12x/12 = -3/12
x = -1/4

1 foot = 12 inches

56 inches / 12 inches = 4.66 feet = 4 feet and 8 inches

Answer:

4 feet and 8 inches

Step-by-step explanation:

To convert a high number of inches to feet you divide it by 12 since 12 inches makes 1 foot.

So 56÷12 = 4 reminder 8

The remainder we keep it as inches

So our answer is 4 feet and 8 inches.

Answer:

B) 203 grams

Step-by-step explanation:

19.4 * 1.308 = 25.3752

25.3752 * 8 = 203.0016

Step-by-step explanation:

See the solution for each part

1)

2)

3)

4)

5)

Now

Answer:

A. 0.125 foot per square feet

Step-by-step explanation:

When finding average rate of change, use the formula

ΔY/ΔX

The ΔY, or Y final - Y initial would be 1.5-1.0, which is equal to 0.5.

The ΔX, or X final - X initial would be 7-3, which is equal to 4.

Plug these values into the equation ΔY/ΔX to get 0.5/4.

This will give you 0.125.

Answer:

$8.96

Step-by-step explanation:

Since 6 hot dogs are $6.72, 1 hot dog would be that divided by 6, which is $1.12. Now we want the cost of 8 of those hot dogs, so we have to multiply by 8. Hence the answer is $1.12 * 8 = $8.96.

Answer:

For the outside square, the diagonal is 7√2, or about 9.9 units.

For the inside square, the diagonal is 5√2, or about 7.1 units.

Answer:78.6[tex]ft^{2}[/tex]

Step-by-step explanation:

Area=π[tex]r^{2}[/tex]

Area=[tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex]

=[tex]\frac{22}{7}[/tex] x 25

=78.6[tex]ft^{2}[/tex]

Answer:

9

Step-by-step explanation:

twice the value of 4.5 equals 9

Using translation concepts, it is found that the correct statement about h(x) is:

The function is decreasing on the interval (0, ∞).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is:

[tex]f(x) = \sqrt{x}[/tex]

Which is increasing on (0, ∞).

After the translation, the function is:

[tex]h(x) = -2\sqrt{x}[/tex]

It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).

More can be learned about translation concepts at https://brainly.com/question/4521517

[tex]\rightarrow[/tex]Radius(r) of sphere = 3m

[tex]\rightarrow[/tex] Volume of the sphere.

[tex]\rightarrow[/tex]Volume of sphere = [tex]\sf{\frac{4}{3}πr^3}[/tex]

[tex]\rightarrow[/tex]Volume of sphere = [tex]\sf{\frac{4}{3}πr^3}[/tex](putting the value of r(radius) from the above given and pie(π) = [tex]\sf{\frac{22}{7}}[/tex])

[tex]\rightarrow[/tex][tex]\sf{=\frac{4}{3}×\frac{22}{7}×3^3}[/tex]

[tex]\rightarrow[/tex][tex]\sf{=\frac{4}{3}×\frac{22}{7}×27}[/tex]

[tex]\rightarrow[/tex][tex]\sf{=\frac{2,376}{21}}[/tex]

[tex]\rightarrow[/tex][tex]\sf{=113.14m^3}[/tex]

Therefore, the volume of the sphere [tex]\sf{=113.14m^3}[/tex], which can be rounded off to it's nearest tenth as [tex]\sf{113.1m^3}[/tex]

____________________________________

Hope it helps you:)

Answer:

b. translation, rotation

Step-by-step explanation:

When a shape is translated, that just means nothing about it has changed except it's location on the coordinate plane. This is that happened with shape 1 - it was translated, and that created shape 2.

When a shape is rotated, that just means it is turned (or rotated) at a specific point. This is what happened to shape 2 that changed it to shape 3.

The other two transformations that aren't shown in this specific example are dilation, which means that the shape either shrinks or grows, and reflection, which means that the shape is reflected across the y-axis or the x-axis.

I included a picture with all four transformation examples in it. I hope this helps! Have a lovely day!! :)

Answer: i dont knpw how to do tht can u tell me where to draw im just getting points

Step-by-step explanation:

The standard form of a polynomial is: ax^n+ bx^n-1 + cx^n-2  + ......... + d

The standard form of the polynomial is 4x^3 + 2x^2  + 3x - 6

The polynomial is given as:

(4x^3 - 2x - 9) + (2x^2 + 5x + 3)

Remove the bracket

4x^3 - 2x - 9 + 2x^2 + 5x + 3

Collect like terms

4x^3 + 2x^2 - 2x + 5x - 9 + 3

Evaluate the like terms

4x^3 + 2x^2  + 3x - 6

Hence, the standard form of the polynomial is 4x^3 + 2x^2  + 3x - 6

Read more about polynomials at:

https://brainly.com/question/4142886

Answer:

Min = 4

Q1 = 9.5

Median = 13

Q3 = 16

Max = 19

Step-by-step explanation:

4, 6, 9, 10, 11, 12, 13, 13, 14, 15, 17, 17, 19

          Q1             Q2               Q3

Min (minimum value) = 4

Q1 (middle value of values before Q2) = (9 + 10) / 2 = 9.5

Median (middle value) = 13

Q3  (middle value of values after Q2) = (15 + 17) / 2 = 16

Max (maximum value) = 19

Answer:

x = -3

Step-by-step explanation:

A vertical line has an equation of the form

x = a

where a is the x-coordinate of every point on the line.

Every point on the line has x-coordinate -3, so the equation is

x = -3

Answer:

Rs. 480

Step-by-step explanation:

Per month interest amount = 2000 x 0.02 = Rs.40

One total interest cost =Rs. 40 x 12 ( 12months i. e. 1 year)

= Rs. 480

Answer:

Step-by-step explanation:

Try to get all the numbers and variables on one side of the =

X^2 - 8x - 24 = 0

I think solving this equation via factorisation would be difficult so you should use the quadratic formula which I have attached.

Given:

⇒ Probability of happening of an event = 45%

To Find:

⇒ Probability of event

Now, probability of happening of an event is 45% means non happening event is 100 - 45 = 55%.

⇒ Probability of happening event = 45/100

⇒ Probability of happening event = 0.45

⇒ Probability of non happening event = 55/100

⇒ Probability of non happening event = 0.55

Hence, the correct option is (c) 0.45.

Extra Info:

Probability is the likelihood /chances of a given event's occurence which is expressed as a number between 1 and 0.

Answer:

a cone with a radius of 4 units

Step-by-step explanation:

when rotating something, this involves a circle. so, the result will always be round and never edgy. therefrom the first option is wrong.

and we are rotating a triangle. the result will have a wide base and a pointed tip. so, the third option is wrong.

the rotation does not make the basic shape smaller. so, the second option is wrong.

yes, the fourth option is correct.

The average rate of change of the height function is slope of the height function

The model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.

The height function is given as:

[tex]H(V) = 2.69\sqrt[3]{V}[/tex]

When V = 512, the function becomes

[tex]H(512) = 2.69\sqrt[3]{512}[/tex]

[tex]H(512) = 21.52[/tex]

Similarly;

When V = 1000, the function becomes

[tex]H(1000) = 2.69\sqrt[3]{1000}[/tex]

[tex]H(1000) = 26.9[/tex]

The average rate of change is then calculated as:

[tex]H' = \frac{H(1000) - H(512)}{1000 - 512}[/tex]

This gives

[tex]H' = \frac{26.9 - 21.52}{1000 - 512}[/tex]

[tex]H' = \frac{5.38}{488}[/tex]

Evaluate the quotient

[tex]H' = 0.01102459016[/tex]

Approximate

[tex]H' = 0.011[/tex]

Hence, the model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.

Read more about average rate of change at:

https://brainly.com/question/8728504

Answer:

The model’s height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.

Step-by-step explanation:

Plato/Edmentum

Answer:

The key to this question is converting all the mass units to the same unit and adding them all up.

The only value that isn't consistent with the other units is 450 gm or grams.

Recall that 1 gram is equal to 0.001 kilo grams. So if you want to convert grams to kilograms you would multiply that amount by 0.001 or 1/1000

[tex]450gm * \frac{1}{1000} = 0.45kg[/tex]

Now let's add up all the masses.

[tex]53.6kg + 0.45kg + 4.5kg = 58.55 kg\\[/tex]

(Now a few footnotes here, that I considered but wasn't sure about. The answer asks for weight, but you're only given mass to work with. That would be fine, if the question asked you to convert it to SI weight units like Newtons, but there's no mention of that. And also I'm not sure if the question requires significant digits. But I'll continue the answer if you think so)

To convert this into weight in Newtons, multiply by 9.81 m/s^2

[tex]58.55kg*9.81m/s^2 = 574.3755 N\\\\= 5.7 * 10^2 N[/tex]

Answer:

the answer is A

Step-by-step explanation:

If Eugene is at a cash-only restaurant he must withdraw cash out of his bank account (linked to debit card.)