A doctor collected data on how many hours children of different ages slept in a day. Data for 5 participants are
shown below.

Answer:

[tex]-12x^2[/tex]

Step-by-step explanation:

Think of the box method as completing a chart or a multiplication table.

We can see that box B is in the second column of the first row. The second column is labeled by -4x. The first row is labeled by 3x. So, in order to fill out box B, you have to multiply -4x and 3x together.

To do so, multiply the terms' coefficients (the numbers in front of the variable). -4 times 3 makes -12. Then, multiply the variables - just keep the variable and add their exponents. x and x both have exponents of one, which makes [tex]x^1^+^1[/tex], resulting in [tex]x^2[/tex]. Put them together and the answer would be [tex]-12x^2[/tex].

Answer:

x= tm+5/4-t

Step-by-step explanation:

4x-5=t(x+5)

4x-5-=tx+tm   distributive

4x-5-tx=tm    substract tx from both sides

4x-tx=tm+5   add 5 to both sides

x * 4+ x(-t) =tm+5  factor x out 4x-tx

x(4-t)=tm+5   factor x out x*4 + x(-t)

x(4-t)/4-t= tm/4-t+ 5/4-t   divide each term in 4-t

x= tm/4-t + 5/4-t combine the numerators over the common denominator

x=tm+5/4-t

Answer:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = 1313.3[/tex]

Step-by-step explanation:

Given

Let x represent years and V represents the value.

So, we have:

[tex](x_1,v_1) = (0,2220)[/tex]

[tex](x_2,v_2) = (6,1540)[/tex]

Solving (a): The linear function

First, we calculate the slope (m)

[tex]m = \frac{v_2 - v_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{1540-2220}{6-0}[/tex]

[tex]m = \frac{-680}{6}[/tex]

[tex]m = -\frac{340}{3}[/tex]

The linear function is calculated using:

[tex]v - v_2 = m(x - x_2)[/tex]

Where:

[tex](x_2,v_2) = (6,1540)[/tex]

[tex]m = -\frac{340}{3}[/tex]

So, we have:

[tex]v - 1540 = -\frac{340}{3}(x - 6)[/tex]

Open bracket

[tex]v - 1540 = -\frac{340}{3}x +\frac{340}{3}* 6[/tex]

[tex]v - 1540 = -\frac{340}{3}x +680[/tex]

Make v the subject

[tex]v = -\frac{340}{3}x +680+1540[/tex]

[tex]v = -\frac{340}{3}x +2220[/tex]

So, the function is:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

Solving (b): When x = 8

Substitute 8 for x in [tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = -\frac{340}{3}*8 +2220[/tex]

[tex]V(8) = -\frac{340*8}{3} +2220[/tex]

[tex]V(8) = -\frac{2720}{3} +2220[/tex]

Take LCM

[tex]V(8) = \frac{-2720+2220*3}{3}[/tex]

[tex]V(8) = \frac{-2720+6660}{3}[/tex]

[tex]V(8) = \frac{3940}{3}[/tex]

[tex]V(8) = 1313.3[/tex]

Hence, its value after 8 years is 1313.3

Answer:

0.8

Step-by-step explanation:

that's the decimal.

Answer:

0.8

Step-by-step explanation:

Answer:

2 is the correct answer you know it also

Use the Pythagorean theorem

a^2 + b^2 = c^2

a^2 + 15^2 = 25^2

a^2 + 225 = 625

a^2 = 400

a = 20

Answer: 20 cm

Hope this helps!!

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Answer: h = 14.5 ft

Step-by-step explanation: Since it is given angles and side and it wants a side, let's use Law of Sines, which is formulated as

                                           [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

i.e., the ratio of a side and the sin of its opposite angle is constant.

So, for this triangle, height is

[tex]\frac{sin46}{h} =\frac{sin44}{14}[/tex]

[tex]h=\frac{14sin46}{sin44}[/tex]

[tex]h=\frac{10.07}{0.69}[/tex]

h = 14.51

Height of the main sail rounded to the nearest tenth is 14.5 ft.

Answer:

3x+9

Step-by-step explanation:

If it’s multiple choice the other one is

x +1+1+1+x +1+1+1+ x +1+1+1

I hope this helps!

Answer:

(a+b)(a-b)

Step-by-step explanation:

because (a+b)(a-b):

If you use FOIL it will work backwards

35, 42, 105 respectively

Answer:

32, 42, 105

Step-by-step explanation:

(32)^2 = 32×32

= 1225

(42)^2 = 42×42

= 1764

(105)^2 = 105×105

=11025

Answer:

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Answer:

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Answer:

[tex]y - 8 = \frac{5}{3}(x - 1)[/tex]

Step-by-step explanation:

1) Use the slope formula, [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex], and the given points to find the slope. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line must intersect, and [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point the line must also intersect:

[tex]\frac{(3)-(8)}{(-2)-(1)}[/tex]

= [tex]\frac{-5}{-3}[/tex]

= [tex]\frac{5}{3}[/tex]

2) Using the point-slope formula, [tex]y-y_1 = m (x - x_1)[/tex], use the slope you just calculated and substitute it for m. Choose any of the two points given (I chose (1,8)) and substitute its x and y values for [tex]x_1[/tex] and [tex]y_1[/tex]. Don't worry, the equation of the line is the same no matter which point you choose (unless the question specifies which one you need to choose):

[tex]y - 8 = \frac{5}{3}(x - 1)[/tex]

Answer:

321%

Step-by-step explanation:

hope I helped Kkkkkkkk

Answer:

[tex]r=9.0\:\mathrm{cm}[/tex]

Step-by-step explanation:

The volume of a sphere is given as [tex]\frac{4}{3}r^3\pi[/tex]. Therefore we have the following equation:

[tex]\frac{4}{3}r^3\pi=3026,\\r^3=\frac{3}{4}\cdot\frac{3026}{\pi},\\r^3=722.40428,\\r=\sqrt[3]{722.40428},\\r\approx \fbox{$9.0\:\mathrm{cm}$}[/tex].

Rounding this to the nearest tenth of a centimeter, the radius of the sphere is approximately 14.0 cm.

Volume refers to the amount of space occupied by an object or substance. In mathematics, it is usually measured in cubic units (e.g. cubic meters, cubic centimeters).

The volume of an object can be calculated using its dimensions and specific formulas that depend on the shape of the object.

For example, the volume of a cube is calculated by multiplying its length, width, and height, while the volume of a sphere is calculated using the formula [tex](4/3)\pi r^3[/tex], where r is the radius of the sphere.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere and π (pi) is a mathematical constant approximately equal to 3.14159.

We can rearrange this formula to solve for r:

r = [tex](3V/4\pi)^{(1/3)[/tex]

Substituting the given volume V = 3026 [tex]cm^3[/tex], we get:

r = [tex](3(3026)/(4\pi))^{(1/3)[/tex] ≈ 14.0 cm

Thus, the radius of the sphere is approximately 14.0 cm, rounded to the nearest tenth of a centimetre.

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Answer:

Step-by-step explanation:

the student buys a total of 8 magazines for $14.00

x+y = 8

x = 8-y

2x+1.6y = 14

2(8-y)+1.6y = 14

16-2y+1.6y = 14

16-0.4y = 14

0.4y =16-14 = 2

y = 2/0.4 = 5

x = 8-y = 3

The correct equation best represents the situation is,

⇒ x + y = 8

And, 2x + 1.60y = 14.00

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A student buys (x) fashion magazines and (y) sports magazines.

And, Each fashion magazine costs $2.00 and each sports magazine costs $1.60.

Here, The student buys a total of 8 magazines for $14.00.

Hence, We can formulate;

⇒ x + y = 8

And, 2x + 1.60y = 14.00

Thus, The correct equation best represents the situation is,

⇒ x + y = 8

And, 2x + 1.60y = 14.00

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Step-by-step explanation:

Cost of each golf ball = $9.31 / 18

≈ $9 / 18 = $0.5.

Answer: 0.5172222222222222

Step-by-step explanation: divide 18 by 9.31

Answer:

m∠C = 66°

Step-by-step explanation:

Given

m∠ A = 33°

m∠ B = 81°

To determine

m∠C = ?

We know that sum of angles of a triangle is 180°.

so using the equation

m∠ A + m∠ B +  m∠C = 180°

substituting m∠ A = 33°, and m∠ B = 81° in the equatio

33° + 81°+m∠C= 180°

114° + m∠C = 180°

m∠C = 180° - 114°

m∠C = 66°

Therefore,

Hey there!

I believe the answer to your question is 24.

If it's being reduced by 1/3, you are being left with 2/3, so we can take 2/3 of 9 and you get 6. Perimeter is adding up all the side lengths. Thus, we do 6 + 6 + 6 + 6, and that is 24.

Sorry for any confusion before, I didn't understand the problem before. Hope it helps! Have a great day, and sorry if it's late.

Answer:

-5 1/2

The first one is right.

Step-by-step explanation:

k12 right ?

The solution of the given expression if p = 1, r= -7, and s = -2 will be; -5 and 1/2

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE have been given an expression as

-3p-2r / 6+4s

We have to substitute the value p = 1, r= -7, and s = -2 to find the solution.

Plug the values;

-3p-2r / 6+4s

-3 (1) -2 (-7) / 6+4(-2)

-3 + 14 / 6 - 8

11 / -2

Hence, the solution of the given expression if p = 1, r= -7, and s = -2 will be; -5 and 1/2

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Answer:

Any real number strictly larger than 9 and strictly less than 21.

Step-by-step explanation:

By triangle inequality, the sum of the lengths of any two sides are greater than the length of the third side.

We therefore could set up three inequalities.

x+6>15, x+15>6, 15+6>x

Solving these, we get x>9, x>-9, x<21 i.e. 9 < x < 21.

Answer:

C

Step-by-step explanation:

Answer:

...

against the wind, an airplane travels 3640 km in 7 hours.

with the wind, the same plane travels 6000 km in 6hrs.

...

let speed of plane in still air be x mph

speed of wind be y mph.

..

t=d/r

..

against wind speed = x-y mph

with wond speed = x=y mph

...

3640/(x-y)=7

3640 = 7x-7y

/7

520=x-y.....................1

...

6000/x+y = 6

6000 = 6x+6y

/6

1000=x+y.....................2

...

Add (1) & (2)

2x=1520

/2

x=760 mph speed of plane in still air

...

plug value of x in 2

1000=760+y

100-760=y

240 = y

240 mph speed of wind

Answer:

Y=−3x2+6x+9

Step-by-step explanation: