A flower bed is in the shape of a triangle with one side twice the length of the shortest side and a third side is 22 more than the length of the shortest side. Find the dimensions if the perimeter is 182 feet.

9514 1404 393

Answer:

  x = 2 or x = 9

Step-by-step explanation:

To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).

  2(3) +4(3(x -3)) = (x +4)(x -3)

  6 +12x -36 = x² +x -12

  x² -11x +18 = 0

Using the quadratic formula to find the solutions, we have ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]

The solutions are x=2 and x=9.

Answer:

[tex]C=27inch\ by\ 27inch[/tex]

Step-by-step explanation:

Squares [tex]h=4inch[/tex]

Volume [tex]v=1444in^3[/tex]

Generally the equation for Volume of box is mathematically given by

 [tex]V=l^2h[/tex]

 [tex]1444=l^2*4[/tex]

 [tex]l^2=361[/tex]

 [tex]l=19in[/tex]

Since

Length of cardboard is

 [tex]l_c=19+4+4[/tex]

 [tex]l_c=27in[/tex]

Therefore

Dimensions of the piece of cardboard is

[tex]C=27inch\ by\ 27inch[/tex]

Answer:

6

Step-by-step explanation:

Of 4 options, Janet has to choose 2. This is combinations as A and B is the same as B and A.

Combinations formula gives us 4!/ 2!2! , or 6.

Answer:

Let x = the number. Then you have:

2x + 14x = 48 Collect like terms

16x = 48 Divide both sides by 16

x = 3

PLEASE MARK AS BRAINLIEST ANSWER

The number that satisfies the given statement is 3.

We are given that twice a number increased by the product of the number and 14 results in 48.

We will find the value of the number that we used in the given above statement.

Increased means addition.

Product means multiplication.

Results mean equal to sign.

Let's write the given statement in equation form.

Consider P = the number

Twice a number = 2P

Increased =  +

Products of the number and 14 =  P x 14

Results in 48 = equals 48.

Combining all the above we get,

2P + P x 14 = 48

2P + 14P = 48

16P = 48

P = 48 / 16

P = 3

Thus the number that satisfies the given statement is 3.

Learn more about similar problems here:

https://brainly.com/question/17618748

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Answer:

25.40

Step-by-step explanation:

tickets  ( 2 at 10.95 each) = 2* 10.95 = 21.90

popcorn ( 1 at 7.50)         = 7.50

Total cost before discount

21.90+7.50=29.40

subtract the discount

29.40-4.00 =25.40

Answer:

Yep! That's correct!

Step-by-step explanation:

We know that Marilyn and her sister are each getting a ticket that cost $10.95. They are also getting a $7.50 popcorn to share. Let's add those values up.

(10.95 * 2) + 7.50 {Multiply 10.95 by 2 to get 21.90.}

21.90 + 7.50 {Add 7.50 to 21.90 to get 29.40}

$29.40 (without the credit) in toal

A credit on a movie reward card functions as a discount, so what we need to do next is subtract 4 from 29.40. That will get us $25.40 as the total cost.

After doing the math, I can deduce that your answer is correct!

Answer:

good luck

.............

Answer: the third one. filled circle for 4 ,5,6,7,8,9, open circle 10

Step-by-step explanation:

Answer:

1/8 is less than

Step-by-step explanation:

i dont see any fractions below gona have to edit your answer

Answer:

n is 13

Step-by-step explanation:

[tex] {n}^{2} = {12}^{2} + {6}^{2} - (2 \times 12 \times 6) \cos(90 \degree) \\ {n}^{2} = 180 \\ n = 13.4[/tex]

Answer:

n is 13

Step-by-step explanation:

Answer: 9 miles I think but I dont know where her house is exactly.

Answer:

A=3.1

B=4.2

C=2.7

Step-by-step explanation:

Answer:

2.665 < σ < 3.379

Step-by-step explanation:

Given :

s = 2.97

Sample size, n = 60

α = 80%

χ² Critical value (two - tailed), df = (60-1) = 59

χ² = 45.577 ; χ² = 73.279

The 80% confidence interval for the standard deviation :

s * √(n - 1) / χ² critical

2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577

2.665 < σ < 3.379

Answer:

[tex]y = -7x -13[/tex]

Step-by-step explanation:

Given

Perpendicular to

[tex]7y = x -4[/tex]

Passes through

[tex](-2,1)[/tex]

Required

The equation

First, we calculate the slope of:

[tex]7y = x -4[/tex]

Divide through by 7

[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]

A linear function is:

[tex]y=mx + c[/tex]

Where;

[tex]m \to slope[/tex]

So:

[tex]m = \frac{1}{7}[/tex]

For the perpendicular line; the slope is:

[tex]m_2 = -\frac{1}{m}[/tex]

So, we have:

[tex]m_2 = -\frac{1}{1/7}[/tex]

[tex]m_2 = -7[/tex]

The equation is:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = -7(x - -2) + 1[/tex]

[tex]y = -7(x +2) + 1[/tex]

Open bracket

[tex]y = -7x -14 + 1[/tex]

[tex]y = -7x -13[/tex]

Answer:

279+x

Step-by-step explanation:

Emily + Yani + Joyce=3209 stickers

how many stickers does Emily have than Joyce:

(279+2x)-(x)

279+2x-x

=279+x

Answer: 6 con ga

Step-by-step explanation:

So ga ca 2 ban mua la:

2+4=6 (con ga)

Answer:

chash greatly ta 45uerywryrsyrsyrs

Answer:

it's too much for me im a child u know

Answer:

I think it is twenty seven

Answer:

A

Step-by-step explanation:

f(-1)=7, f(0)=2, f(1)=-3

Answer:

Answer:

Hello,

Answer 31

Step-by-step explanation:

[tex]3*log_2(x+1)-2=13\\\\3*log_2(x+1)=13+2\\\\log_2(x+1)=5\\\\\\x+1=2^5\\\\x=32-1\\\\\boxed{x=31}\\[/tex]

Answer:

y-0 = 1/2(x-0)

y = 1/2(x)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-0 = 1/2(x-0)

y = 1/2(x)

Answer:

The third side is increasing at an approximate rate of about 0.444 meters per minute.

Step-by-step explanation:

We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.

Let the angle between the two given sides be θ and let the third side be c.

Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.

First, convert the degrees into radians:

[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]

Hence, dθ/dt = π/90.

From the Law of Cosines:

[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]

Since a = 13 and b = 19:

[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]

Simplify:

[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]

Take the derivative of both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]

We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:

[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]

Solve for dc/dt:

[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]

Evaluate. Hence:

[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]

The third side is increasing at an approximate rate of about 0.444 meters per minute.

9514 1404 393

Answer:

  0.444 m/min

Step-by-step explanation:

I find this kind of question to be answered easily by a graphing calculator.

The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...

  c = √(a² +b² -2ab·cos(C))

Since C is a function of time, its value in degrees can be written ...

  C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest

Using a=13, and b=19, the length of the third side is ...

  c(t) = √(13² +19² -2·13·19·cos(60° +2t°))

Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...

  0.443855627418 m/min ≈ 0.444 m/min

_____

Additional comment

At that time, the length of the third side is about 16.823 m.

__

c(t) reduces to √(530 -494cos(π/90·t +π/3))

Then the derivative is ...

  [tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]

Answer:

A child who weighs 84 pounds should be given 94.5 milligrams of the drug.

Step-by-step explanation:

Givens:

1kg=2.5 milligrams of dosage

Weight of child = 84 pounds

1 pound = 0.45 kg

Solution:

Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg

Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.

Answer:

multiples of 2 2,4,6,8,10,12,14,16,18,20

multiples of 3 3,6,9,12,15,,18,21,24,27,30

Step-by-step explanation:

Lcm is 6

Answer:

117.8

Step-by-step explanation:

Surface area = πr²+πrl (whee r = radius and l = slant height)

= π×3²+π×3×9.5

= 75π/2

= 117.8

Answer:

12 x^5y^12

Step-by-step explanation:

3x^2y^5 * 4x^3y^7

Multiply the constants

3*4 = 12

Multiply the x terms

x^2 * x^3

We know a^b* a^c = a^(b+c)

x^(2+3) = x^5

Multiply the y terms

y^6 * y^7 = y&(5+7) = y^12

Put them back together

12 x^5y^12

Answer:

Consider the following identity:

Let a = 2, b = 1/2

Use the algebraic identity given below

[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]

[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]

[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

8(-2x+1) =0

Divide each side by 8

-2x+1 = 0

Add 2x to each side

-2x+1+2x = 2x

1 = 2x

Divide by 2

1/2 = 2x/2

1/2 =x

Answer:

1/2

Step-by-step explanation:

8(-2x+1)=0

Use distributive property first

-16x+8=0

Subtract 8 on both sides

-16x=-8

Divide both sides by -16 to get x by itself

x=0.5

Which is also equal to 1/2

Therefore, x is equal to 1/2

Answer:

-7/25

Step-by-step explanation:

1/5 ÷ (-5/7)

Copy dot flip

1/5 * -7/5

-7/25

Answer:

117.8

Step-by-step explanation:

surface area = πr²+πrl, where r = radius and l = slant height

so,

πr²+πrl

= π×3²+π×3×9.5

= 75π/2

= 117.8 (rounded to the nearest tenth)