Write and Y varies directly as x. y 20 when x graph the direct variation function.

Answer:

a.) is 36 square meters

b.) 400 square meters

Step-by-step explanation:

to find the Volume you must multiply the length, width, and the hight. so to find a.) V = lwh

6 x 2 x 3 = 36

36 square meters.

and you can use the same formula for b.)

Hope this helps!

Please mark as brainliest! Thanks!

Volume of a) 36 cubic meter

Volume of b) 400 cubic feet

Let, Length of the rectangular solid = l unit

Width of the rectangular solid = w unit

And height of the rectangular solid = h unit

Then volume of rectangular solid = l × w × h cubic unit

Given, Length of the rectangular solid = 6 meters

Width of the rectangular solid = 2 meters

And height of the rectangular solid = 3 meters

∴ Volume of the rectangular solid = (6×2×3) cubic meter

                                                        = 36 [tex]m^{3}[/tex]

Given, Length of the rectangular solid = 5 feet

Width of the rectangular solid = 10 feet

And height of the rectangular solid = 8 feet

∴ Volume of the rectangular solid = (5×10×8) cubic feet

                                                        = 400 cubic feet

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Answer:

Step-by-step explanation:

(1/4) (2-5x+6)

=(1/4)(8-5x)

= 8/4 - 5x/4

=1/2 - 5x/4

Final answer:

To factor the expression 3x² - 19x + 20, we find two numbers that multiply to 60 and add up to -19, which are -4 and -15. The expression can then be rewritten and factored by grouping to obtain the factors (x - 5)(3x - 4).

Explanation:

The question asks to factor the quadratic expression

3x² - 19x + 20

To factor this expression, we need to find two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 20), and at the same time, add up to give the coefficient of x (which is -19). The two numbers that satisfy these conditions are -4 and -15, as (-4) * (-15) = 60 and (-4) + (-15) = -19.

Now, we can rewrite the expression by splitting the middle term:

3x² - 4x - 15x + 20

Factor by grouping: x(3x - 4) - 5(3x - 4)

The factors are: (x - 5)(3x - 4)

Answer:

35 ft²

Step-by-step explanation:

We set up a system of linear equations describing this rug and then solve it:

Perimeter:  P = 2L + 2W

L = (1  2/5)W = 1.4W

Going back to the Perimeter equation, and knowing that P here is 24 ft, we have:

24 ft = 2(1.4W) + 2W, or 2.8W + 2W, or 4.8W.

Solve for W (width) by dividing both sides of this equation by 4.8:

W = 24 ft  / 4.8  = 5

The width of the rug is 5 ft; the length is 1.4(5 ft), or 7 ft.

Thus the area of the rug is A = L * W, or A = (7 ft)(5 ft) = 35 ft²

Answer:

[tex]S.A=96\pi m^2[/tex]

Step-by-step explanation:

The surface area of a right circular cylinder is given by the formula;

[tex]S.A=2\pi r(r+h)[/tex]

where [tex]h=8m[/tex] is the height of the cylinder and

[tex]r=4m[/tex] is the radius of the cylinder.

We plug in these values into the formula to obtain;

[tex]S.A=2\pi \times4(4+8)[/tex]

[tex]S.A=8 \times12 \pi[/tex]

[tex]S.A=96\pi m^2[/tex]

[tex]AB\: is \:the \:diameter\Rightarrow \widehat{ACB}=90°\Rightarrow \widehat{ABC}=180°-90°-30°=60° \: (1) \\ \bigtriangleup OBC \: has \: OB=OC=R\Rightarrow \bigtriangleup OBC \: is \: an \: isosceles \: triangle \: (2) \\ (1),(2)\Rightarrow \bigtriangleup OBC \: is \: an \: equilateral \: t riangle \Rightarrow \widehat{COB} =\widehat{COD} = 60° \\ CD \: tangents \: (O) \: at \: C\Rightarrow OC\perp OD \: at \: C\Rightarrow \widehat{OCD}=90° \\ \widehat{CDO}=180°-\widehat{OCD}-\widehat{COD}=180°-90°-60°=30° \\ In\: \bigtriangleup ACD,\widehat{CAD}=\widehat{CDA}=30°\\\Rightarrow \bigtriangleup ACD\: is\: an\: isosceles\: triangle\: at\: C[/tex]

Triangle ACD is an isosceles triangle, with AC = AD.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Let O be the center of the circle, and let E be the point where the tangent line to the circle at point C intersects diameter AB.

Since OC is perpendicular to CE (tangent line at C), and OD is perpendicular to AB, angle ECD and angle OAD are alternate angles, and hence congruent.

Now,

Since the measure of the angle between diameter AB and chord AC is 30°, the measure of angle AOC is 60°.

The measure of angle OAD is also 60°.

Now,

Since angles ACD and OAD are congruent, and angle AOC is 60°,

we have:

angle ACD = angle OAD = 60°

Also,

Since OC is perpendicular to AC (radius of the circle),

we have angle OCA = 90°.

Now,

angle ACB

= angle OCA - angle AC0

= 90° - 30°

= 60°

Since angle ACD is equal to angle ACB, and angle AOC is also equal to 60°,

We have:

angle ACD = angle ACB = 60°

angle AOC = 60°

Therefore,

Triangle ACD is an isosceles triangle, with AC = AD.

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Answer:

[tex]x \geq -56[/tex]

Step-by-step explanation:

You can solve inequalities the same way as equations as long as whenever you multiply or divide by a negative number, or flip fractions, you change the direction of the sign.

We don't have to do that here, here is the worked solution:

[tex]-12 \leq 44 + x[/tex]

[tex]-56 \leq x[/tex]

[tex]x \geq -56[/tex]

Answer:

x ≥ -56

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Hope this helps,

Davinia.

Answer:

2

Step-by-step explanation:

Answer: (-1, -4) and (4, 6)

Step-by-step explanation:

The pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equations:

y = 2x - 2

y = x² - x - 6

Equate both equations:

2x - 2 = x² - x - 6

x² - 3x - 4 = 0

Solving using the quadratic formula:

[tex]\rm x_{1,\:2}=\dfrac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]

x = 4, -1

y = 6, -4

Thus, the pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

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To round 7/11 to three decimal places, you divide 7 by 11 to get 0.63636..., and then round the result to 0.636 since the fourth decimal place is 6, which mandates rounding up.

To convert 7/11 as a decimal rounded to 3 decimal places, you can either use a calculator or do long division. After dividing 7 by 11, you will get a result that must be rounded to maintain only three digits after the decimal point. To round off a decimal number, look at the digit after the place you want to round to. In this case, if you want to round to three decimal places, you will look at the fourth place after the decimal. If this digit is 5 or higher, you round up the third-place digit. If it's lower than 5, you leave the third-place digit as it is.

So, converting 7/11 into a decimal, you get approximately 0.63636... Looking at the fourth decimal place, we see that the digit is 6, which means we round up the third decimal place. So, 7/11 rounded to three decimal places is 0.636.

C is the one you're looking for

Answer:

x + y = -1

Step-by-step explanation:

To write the equation of a line, find the slope and use it with a point in the point slope form.

You can find the slope using the slope formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{5--3}{-6-2} = \frac{8}{-8}=-1[/tex]

Substitute m = -1 and the point (2,-3) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y --3 = -1(x-2)\\y+3=-1(x-2)[/tex]

Convert to standard form by applying the distributive property and rearranging the terms.

y+3 = -1(x-2)

y + 3 = -x + 2

x + y + 3 = 2

x + y = -1

Answer:

it is 5/6

Step-by-step explanation:

it's easy. There are 5 numbers that are greater than 2.

Answer: the answer is 2/3 i took the test

Answer:

1. Area = 113.1 square units

2. Area = 28.27 square units

3. Area of Shaded = 22.27 square units

Step-by-step explanation:

1.

Area of the circle is given by the formula   [tex]A=\pi r^2[/tex]

where A is the area and r is the radius

In our case the radius is 6 units, thus we have:

[tex]A=\pi r^2\\A=\pi (6)^2\\A=\pi *36\\A=113.1[/tex]

Area = 113.1 square units

2.

When we have the angle given in radians, the area of sector is given by the formula   [tex]A=\frac{1}{2}r^2\theta[/tex]

Where  [tex]\theta[/tex]  is the central angle ( in our case [tex]\theta = \frac{\pi}{2}[/tex] and r is the radius (it is 6)

Plugging in these info into the formula we have area of sector:

[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(6)^2(\frac{\pi}{2})\\A=\frac{1}{2}*36*\frac{\pi}{2}\\A=28.27[/tex]

Area = 28.27 square units

3.

Area of shaded region = Area of Sector - Area of Triangle

We know area of sector is 28.27

Since the angle is 90 degrees, we have a right triangle, we can use the pythagorean theorem to find the height of the triangle, CE.

Thus

[tex]DC^2+CE^2=DE^2\\3^2+CE^2=5^2\\9+CE^2=25\\CE^2=25-9\\CE^2=16\\CE=4[/tex]

The area of triangle is  [tex]A=\frac{1}{2}bh[/tex]

where b is the base (in our case it is DC = 3 ) and h is the height (in our case it is CE, which is 4). Plugging into the formula we have the area of triangle as:

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(3)(4)\\A=6[/tex]

Area of Shaded = 28.27 - 6 = 22.27 square units

Answer:

Plane = 441 mi/h; wind =  63 mi/h

Step-by-step explanation:

distance = rate × time

 Let p = the plane's speed in still air

and w = the wind speed . Then,

p + w = speed with wind

 p - w = speed against wind

We have two conditions:

(1)  756 = (p - w) × 2

(2) 756 = (p + w) × 1.5

Distribute the constants                  (3)    756 = 2p - 2w

                                                          (4)   756 = 1.5p + 1.5 w  

Multiply Equation (3) by 3                (5) 2268 = 6p  -  6w

Multiply Equation (4) by 4                (6) 3024 = 6p + 6w

Add Equations (5) and (6)                     5292 = 12p

Divide each side by 12                     (7)        p = 441 mi/h

Substitute (7) into Equation(3)                 756 = 882 - 2w

Add 2w to each side                      2w + 756 = 882

Subtract 756 from each side                    2w = 126

Divide each side by 2                                 w = 63 mph

The plane's speed in still air is 441 mi/h.

The wind speed is 63 mph.

Check:

(1) 756 = (441 - 63) × 2     (2) 756 = (441 + 63) × 1.5

   756 = 378 × 2                   756 = 504 × 1.5

   756 = 756                         756 = 756

The speed of the plane in still air is 420 miles per hour and the wind speed is 84 miles per hour.

To solve Dave and Sandy Hartranft's problem, we set up two equations for flying into and with the wind. For Dave and Sandy flying into the wind, we use the formula speed equals distance over time: P - W = 756 miles / 2 hours. This represents the plane's speed minus the wind speed equaling the distance traveled divided by the time taken. We denote P as plane's speed and W as wind speed.

On the return trip, with the wind behind them, we calculate plane's speed plus the wind speed based on the same formula: P + W = 756 miles / 1.5 hours. Solving these two equations, you get: P = 420 miles per hour (plane's speed in still air) and W = 84 miles per hour (wind speed).

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Answer:

The inequality is

6+4r>17

The miminum number of runs per inning is  

3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) = - 4x + 3

x = - 5

f(- 5) = - 4.(- 5) + 3

f(- 5) = 20 + 3

f(- 5) = 23

Alternative D

I hope I helped you.

Answer:

the answer is D

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

slope is equal to:       y2-y1

                                _______ =

                                   x2-x1

  6-2            4

______ = _____ = -2

-7-(-5)          -2

The solution to the number 8000 in scientific notation is 8  * 10³

From the question, we have the following parameters that can be used in our computation:

Number = 8000

Multiply the number by 1

So, we have

Number = 8000 * 1

Express 1 as 1000/1000

So, we have the following representation

Number = 8000 * 1000/1000

Next, we have

Number = 8 * 1000

Express 1000 as 10³

So, we have

Number = 8 * 10³

Hence, the solution is 8  * 10³

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Answer:

All are True

a) 30a^6-24a^2=3à^2(10a^4-8)

b) 24a^4+18=6(4a^⁴+3)

c) 16a^5-20a^3=4a^3(4a^2-5)

D) 12a^3+8a=4(3a^3+2a)​

Step-by-step explanation:

a) 30a^6-24a^2=3à^2(10a^4-8)

since; 3à^2(10a^4-8)

        = 30a^6 - 24a^2

b) 24a^4+18=6(4a^⁴+3)

Since; 6(4a^⁴+3) opening the brackets

           = 24a^4 + 18

c) 16a^5-20a^3=4a^3(4a^2-5)

Since; 4a^3(4a^2-5) , opening the brackets we get

         = 16a^5 - 20^3

D) 12a^3+8a=4(3a^3+2a)​

Since;4(3a^3+2a)​, opening the bracket we get;

        = 12a^3 + 8a

Answer:

c)Q3

Step-by-step explanation:

In the third quadrant, tangent and cotangent are positive while cosine and thus secant are negative. Therefore, the solution is C. Q3

Answer:

C

Step-by-step explanation:

Answer:

Although variables wouldn't really fit for this problem, if you were to graph it, the pizza types would be on the x axis and the cost would be on the y axis since the cost of the pizzas technically "depend" on the type of pizza.

Answer:

your answer would be: x=1±√11 all divided by 2

Hope this helps

~QueenSupreme AKA Trinity

Answer:   [tex]\bold{\dfrac{1\pm \sqrt{11}}{2}}[/tex]

Step-by-step explanation:

[tex]x^2-x-\frac{5}{2}=0\quad \text{multiply by 2 to get:}\\\\2x^2-2x-5=0\quad \rightarrow \quad a=2,\ b=-2,\ c=-5\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(2)(-5)}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{40}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{44}}{2(2)}\\\\\\.\ =\dfrac{2\pm 2\sqrt{11}}{2(2)}\\\\\\.\ =\boxed{\dfrac{1\pm \sqrt{11}}{2}}[/tex]

Answer:

You can make one triangle with these lengths

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify if the lengths satisfy the triangle inequality theorem

1) 2+1 > 2

3 > 2 ------> is true

2)2+2 > 1

4 > 1 -----> is true

so

The lengths  satisfy the triangle inequality theorem

therefore

You can make one triangle with these lengths

Answer:B.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

it is C because A, B, and D are triangular prisms.

Answer:

Approx. 39.7%

Step-by-step explanation:

All you have to do is

17,892÷45,128

Answer:

40 %

Step-by-step explanation:

Percent = Responses/total surveys × 100 %

             = 17 892/45 128 × 100 %

             ≈ 40 %

Approximately 40 % of people responded to the survey.

The Answer is hundredths

The car would be about 90 ft

Answer:

radius=3.5 Diameter=7 Circumference=21.99 area=38.48

Step-by-step explanation: These are the answers, hope you found them helpful :)