Suppose y varies directly with x. Write a direct variation equation that relates x and y when y = 6 and x = 12

Answer:

\(\frac{3}{5}\)

Step-by-step explanation:

Probability is the chance of an event happening. One finds the probability of an event by using the following general formula,

\(\frac{desired}{total}\)

In this case, the desired outcome is pulling whether a red or blue marble from the bag, the desired equals the sum of the number of red and blue marbles.

(red) + (blue)

= 10 + 5

= 15

The total number of marbles is the sum of all the number of marbles in the bag.

(red) + green)  + (yellow) + (blue)

= 10 + 3 + 7 + 5

= 25

Now substitute these values into the formula to find the probability, then simplify,

\(\frac{15}{25}\)

Divide both the numerator and denominator by (5),

\(\frac{3}{5}\)

9514 1404 393

Answer:

  1.  see the first attachment for a graph; quadrants I, II, III; vertex (-3, -4); x-intercepts -5, -1; graph is dashed line, shaded inside the parabola, which opens up

  2.  see the second attachment for a graph; all quadrants; vertex (1, 2); x-intercepts 1±√2; graph is a solid line, shaded outside the parabola, which opens down; (-7, 0) is a solution

Step-by-step explanation:

1. The boundary expression is in vertex form, so the vertex can be read directly.

  y = (x -h)^2 +k . . . . . . parabola with vertex (h, k)

  y > (x +3)^2 -4 . . . . .  (h, k) = (-3, -4)

The leading coefficient is +1, a positive number, so the parabola opens up. The relation is y > ( ), so values of y above the dashed line will be shaded. Those values are inside the parabola. The points (0, 0) and (-7, 0) are not in the shaded area, so are not solutions.

__

2. Again, the boundary expression is in vertex form, so the vertex can be read directly.

  y ≥ -(x -1)^2 +2 . . . . . (h, k) = (1, 2)

The x-intercepts are found by solving for x when y=0:

  0 = -(x -1)^2 +2

  x -1 = ±√2

  x = 1±√2

The leading coefficient is -1, so the parabola opens downward. The relation is y ≥ ( ), so y-values above the solid line will be shaded. Those values are outside the parabola. Point (0, 0) is not a solution. Point (-7, 0) is a solution.

_____

Additional comment

As with the graph of any inequality, the boundary line is solid when the "or equal to" case is part of the relation. If the relation is strictly "greater than" or "less than", then the boundary line is dashed.

The zeros of the polynomial function are x = -1 and x = 5

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

y = x⁴ - 4x³ - 4x² - 4x - 5

To calculate the zeros of the polynomial function, we create a graph of the polynomial

The point where the graph intersect with the x-axis are the zeros of the polynomial function

using the above as a guide, we have the following:

Zeros: x = -1 and x = 5

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Answer:

y=3x+6

Step-by-step explanation:

the equation of a line in

slope-intercept form

is.

xy=mx+b

The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

In a circle

Diameter (d) = 22 cm

radius (r) = d / 2 = 22 /2 = 11 cm

Hope it will help :)

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

Step 1

Draw the image of triangl ABC.

Answer: The instructor randomly selects one student to record for the group and another student to spy on the other groups.

\(\color{yellow}{}\)

Answer:

-12

Step-by-step explanation:

3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =

= 3/5 * (1 + 4)^2 - (3)^3

= 3/5 * (5)^2 - 27

= 3/5 * 25 - 27

= 15 - 27

= -12

Answer: Use “Desmos”.

Step-by-step explanation:

Desmos can show you how the numbers look when they are graphed, but not how to graph them.

Answer:

The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.

The cruise ship's will need 2.425 hours for its upstream journey.

Step-by-step explanation:

The total time of the cruise (\(t\)), in hours, is the sum of the times for the upstream (\(t_{u}\)) and downstream journeys (\(t_{d}\)), in hours. Let suppose that both river and cruise ship travel at constant velocity, the cruise ship travels against the current in its upstream journey, whereas it is in favor of the current in the downstream journey, meaning that:

\(t = t_{u} + t_{d}\)

\(t = \frac{x}{v_{S/C} - v_{C}} + \frac{x}{v_{S/C} + v_{C}}\) (1)

Where:

\(v_{C}\) - Speed of the current, in kilometers per hour.

\(v_{S/C}\) - Speed of the cruise ship relative to the current, in kilometers per hour.

If we know that \(t = 4\,h\), \(x = 18\,km\) and \(v_{C} = 2\,\frac{km}{h}\), then we have the following expression:

\(4\,h = (18\,km)\cdot \left(\frac{1}{v_{S/C} - 2\,\frac{km}{h} } + \frac{1}{v_{S/C}+2\,\frac{km}{h} }\right)\)

\(\frac{2}{9} = \frac{1}{v_{S/C}-2} + \frac{1}{v_{S/C}+2}\)

\(\frac{2}{9} = \frac{2\cdot v_{S/C}}{v_{S/C}^{2}-4}\)

\(2\cdot v_{S/C}^{2} - 8 = 18\cdot v_{S/C}\)

\(2\cdot v_{S/C}^{2}-18\cdot v_{S/C}-8 = 0\)

The roots of the second order polynomial are, respectively:

\(v_{S/C,1} \approx 9.424\,\frac{km}{h}\), \(v_{S/C,2} \approx -0.424\,\frac{km}{h}\). Since the speed is the magnitude of the velocity, a realistic solution must be a positive quantity and the solution is:

\(v_{S/C} \approx 9.424\,\frac{km}{h}\)

The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.

And the time needed for the upstream journey is:

\(t_{u} = \frac{x}{v_{S/C}- v_{C}}\) (2)

If we know that \(x = 18\,km\), \(v_{S/C} \approx 9.424\,\frac{km}{h}\) and \(v_{C} = 2\,\frac{km}{h}\), then time for the upstream journey is:

\(t_{u} = \frac{18\,km}{9.424\,\frac{km}{h}-2\,\frac{km}{h} }\)

\(t_{u} = 2.425\,h\)

The cruise ship's will need 2.425 hours for its upstream journey.

Answer:

hello attached below is the sketch of the missing diagram

a) h = 2

b) cos^-1 ( 2 ) = ∞

c ) θ ≈ 215°

Step-by-step explanation:

a) The length ( h ) to the right of the circles center

= h^2 = ( -1.15)^2 + ( -1.64)^2

∴ h = 2

b) cos^-1 ( 2 ) = ∞

c) The value gotten from b does not give us the value of θ

AB = - 1.64

BC = -1.15

AC = 2

sin^-1 ( - 1.64 / -1.15 )

cos^1 ( -1.15 / 2 ) gives us the value of θ

tan^-1 ( -1.64 / -1.15 )

∴ θ ≈ 215°

Answer: u need to send a pic of the angle

Step-by-step explanation:

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

so the ratio is what? to me I think it's 15 iguanas to 5 dogs

Step-by-step explanation:

have a great day :)

Answer:

Step-by-step explanation:

\(\frac{2}{5} : \frac{1}{15}\\\)

LCM of the denominator = LCM ( 5 , 15 ) = 15

∴ Now we have to multiply LCM by both the fractions , we get ,

\(\frac{2}{5}.15 : \frac{1}{15}.15\\ 6 : 1\)

Answer: B) 2000

Step-by-step explanation:

Sale Price: The cost following a discount applied to the initial cost.

Cost Price: The cost price is what we pay to purchase a good.

Discount Price : A price that is lower than the usual price.

Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).

So, The sale price is Rs 1600 after discount.

Discount =20%

Selling price of the skates = Rs 1600

Discount price = 100/80 × 1600= Rs 2000

Discount price = Rs 2000

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The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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Answer: The most important aspect in doing algebra is having a pen/pencil and paper in hand. It'll give you a better understanding of the question being posed.

Answer:

The value of a is 8.

Step-by-step explanation:

In the expression, x² + 16x + 64, 64 is a perfect square of 8 so if you factorize it, you will get :

x² + 16x + 64

= x² + 8x + 8x + 64

= x(x + 8) + 8(x + 8)

= (x + 8)²

(x + a)² = (x + 8)²

a = 8

Answer:

Step-by-step explanation:

A. Directrix: y = 4-6 = -2

:::::

B. Axis of symmetry: x = 6

Axis of symmetry intersects directrix at (6,-2)

:::::

C . Vertex is halfway between focus and directrix, at (6,1)

:::::

D. The focus lies above the directrix, so the parabola opens upwards.

:::::

E. Focal length p = 1/(4×0.5)

:::::

F. p = 0.5

::::

G. y = 0.5(x-6)² + 1

Answer:

the one above is correct

Step-by-step explanation:

h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).

Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.

The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).

The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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Answer:

(3, 4.5)

Step-by-step explanation:

x = \(\frac{0 + 6}{2}\) = 3

y = \(\frac{3+6}{2}\) = 4.5

The correct answers are

1)  2x^2 + 12

2) Option C.

3) Option B.

1. You must apply the Distributive property as following:

(-5x^2 - 2x +4) + (8x^2 -x -1) - (x^2 -5x + 2x -10)

2. Now, you must distribute the negative sign, then you have:

3. Finally, you must add the like terms. Then you obtain the polynomial:

2x^2 + 13

4. By definition, a polynomial that has two terms is classified as a binomial. Therefore, the answer is the option C.

5. The degree of a polynomial is determined by highest exponent of the variable. So, it is a polynomial of degree 2 (option B).

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Answer:

y = 4/3

Step-by-step explanation:

the expression can be written as,

(x^8)^1/3 divided by (x^4)^ 1/3

so by using the rules of powers we can deduce y = 4/3

The rules are,

1. (x^y)^z = X^y*z

2. x^y * x^z = x^ y+z

3. x^y / x^z = x^ y-z

Hence,

8/3 -4/3 = 4/3

Answer:

See below

Step-by-step explanation:

\(\displaystyle \frac{\sec x\sin x}{\tan x+\cot x}\\\\=\frac{\frac{1}{\cos x} \sin x}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}}\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin x \sin x}{\cos x \sin x} + \frac{\cos x \cos x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin^2 x}{\cos x \sin x} + \frac{\cos^2 x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x}}{\frac{\sin^2 x+\cos^2 x}{\cos x \sin x} }\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{1}{\cos x \sin x} }\)

\(=\frac{\sin x}{\cos x}\cdot \sin x \cos x\\ \\=\frac{\sin x \sin x \cos x}{\cos x}\\ \\=\sin^2x\)

Thus, the identity is proven. Match the options up accordingly to my step-by-step process.

4

divide 16 by 4, which equals 4

Answer:

4 goes into 16 4 times

Step-by-step explanation:

4 x 4=16

Hope this helps!

Answer:

The resistance is 484 ohm.

Step-by-step explanation:

An incandescent lamp has the following data inscribed on its bulb. U= 220 V and P = 100 W. Knowing the relations U = R. i and P = U. i , it can be stated that the value of the resistance R of the lamp during operation is, in omhs:

P = 100 W

V = 220 V

Let the current is I.

P = V I

100 = 220 I

I = 0.45 A

Now,

V = I R

220 = 0.45 x R

R = 484 ohm

The resistance is 484 ohm.