In the equation y = 2x + 6
If x= 2, then what is y equal to?

Answer:

u = [tex]\sqrt{6}[/tex].

Step-by-step explanation:

This is a 45-45-90 triangle.

That means that there are two side lengths with lengths of x, and a hypotenuse with a length of xsqrt(2). We can then set up a proportion.

[tex]\frac{1}{\sqrt{3} } =\frac{\sqrt{2} }{u}[/tex]

1 * u = [tex]\sqrt{3} * \sqrt{2}[/tex]

u = [tex]\sqrt{6}[/tex].

Hope this helps!

Answer:

1/19

Step-by-step explanation:

Let's say there are x yellow cubes.

That means there are 3x blue cubes.

Therefore, there must be 15x green cubes.

In total: we have 19x cubes.

Therefore the probability of a cube being yellow is x / 19x

which simplifies to 1/19

Answer:

1/19

Step-by-step explanation:

Solution:-

- First we will define the distribution of colors in the bag.

- We will use variable:

                     x: the number of yellow cubes in bag

- The following color distribution can be made by using the data given in the question:

                   Color                     Number of cubes

                   Yellow                               x

                   Blue                                  3*x = 3x

                   Green                               3x*5 = 15x

          ======================================

                  Total                                 19x

          ======================================

- Sarah is to draw a cube from the bag. We are to determine the probability that the randomly picked cube would be yellow. We will denote our event as randomly picking a yellow cube from the bag with a defined finite distribution.

         p ( Picks Yellow cube ) = [ Number of yellow cubes ] / [ Total cubes ]

         p ( Picks Yellow cube ) = [ x ] / [ 19x ]

         p ( Picks Yellow cube ) = 1 / 19   .... Answer

Solve each equation with (0, 3)

y = -x + 3

3 = -0 + 3

y = 3 (correct since y = 3 in (0, 3))

y = 2x - 3

3 = 2(0) - 3

3 = 0 - 3

3 = -3 (incorrect since it isn't equal)

So... No, because it does not check in the second equation.

Best of Luck!

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:

(g + f) (x) = (2^x + x – 3)^1/2

Step-by-step explanation:

The following data were obtained from the question:

f(x) = 2^x/2

g(x) = √(x – 3)

(g + f) (x) =..?

(g + f) (x) can be obtained as follow:

(g + f) (x) = √(x – 3) + 2^x/2

(g + f) (x) = (x – 3)^1/2 + 2^x/2

(g + f) (x) = (x – 3)^1/2 + (2^x)^1/2

(g + f) (x) = (x – 3 + 2^x)^1/2

Rearrange

(g + f) (x) = (2^x + x – 3)^1/2

Answer:

Amount of solution = 15 liter

Step-by-step explanation:

Given:

One third of solution is acid

Amount of acid = 5 Liter

Find:

Amount of solution

Computation:

Amount of solution = Amount of acid (1 / One third of solution is acid)

Amount of solution = Amount of acid (3)

Amount of solution = (5)(3)

Amount of solution = 15 liter

Answer: Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

We must work with linear equations, remember that the general shape is:

y = a*x + b

where a is the slope and b is the y-intercept.

Ok, first we want to find the rate of change (or the slope) of the graphed line:

We know that for a line that passes through the points (x1, y1) and (x2, y2)

The slope is:

a = (y2 - y1)/(x2 - x1)

Then for the graphed function, we can see that it passes through the points:

(0, -2) and (4, 0)

Then the slope is:

a = (0 -(-2))/(4 - 0) = 2/4 = 1/2

Now, the slope of the second line is 15/4.

Let's calculate the difference between the slopes:

15/4 - 1/2 = 15/4 - 2/4 = 13/4

(notice that we are calculating slope2 - slope1)

Then the correct option is:

Function 2 has a greater rate of change by 13/4

Answer:

B) Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

Answer:

144 units²

Step-by-step explanation:

Surface area of a traingular prism is given as:

Area = 2(B.A) + P*L

Where,

B.A = base area of the triangular prism = ½*b*h

b = base of the triangular base = 4 units

h = height of the triangular base = 3 units

Base Area (B.A) = ½*4*3 = 2*3 = 6 units²

P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units

L = length or height of prism = 11 units

Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L

[tex] Area = 2(6) + 12*11 [/tex]

[tex] = 12 + 132 [/tex]

[tex] Surface Area = 144 [/tex]

Surface area of the triangular prism = 144 units²

Answer:

15w - 10x + 30.

Step-by-step explanation:

-5(2x - 3w - 6)

= (-5 * 2x) + (-5 * -3w) + (-5 * -6)

= -10x + 15w + 30

= 15w - 10x + 30.

Hope this helps!

Answer:

Step-by-step explanation:

[tex] - 5(2x - 3w - 6)[/tex]

Multiply each term in the parentheses by -5

[tex] - 5 \times 2x - 5 \times ( - 3w) - 5 \times ( - 6)[/tex]

Calculate the product

[tex] - 10x - 5 \times ( - 3x) - 5 \times ( - 6)[/tex]

Multiplying two negatives equals a positive [tex]( - ) \times ( - ) = ( + )[/tex]

[tex] - 10x + 5 \times 3w - 5 \times ( - 6)[/tex]

Calculate the product

[tex] - 10x + 15w - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex] - 10x + 15w + 30[/tex]

Hope this helps..

Best regards!!

Answer:

32 remainder 2

Step-by-step explanation:

To divide 162 by 5, we simply do the following:

5 goes into 16 => 3

Multiply 5 by 3 => 3 × 5 = 15

Subtract 15 from 16 => 16 – 15 = 1

Put the 1 before 2 => 12

5 goes into 12 => 2

Multiply 5 by 2 => 5 × 2 = 10

Subtract 10 from 12 => 12 – 10 => 2

In summary,

162 divided by 5 => 32 remainder 2

Please see attached photo for further details.

Answer:

The common difference is -5/4

T(n) = T(0)  - 5n/4,

where T(0) can be any number. d = -5/4

Assuming T(0) = 0, then first term

T(1) = 0 -5/4 = -5/4

Step-by-step explanation:

T(n) = T(0) + n*d

Let

S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240

S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220

S2 - S1

= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)

= (5+6+7+8 - 1 -2-3-4)d

= 4(4)d

= 16d

Since S2=220,  S1 = 240

220-240 = 16d

d = -20/16 = -5/4

Since T(0) has not been defined, it could be any number.

Answer:

53.076923

Step-by-step explanation:

130% as a decimal is 1.3

Divide 69 by 1.3:

69 /1.3 = 53.076923

Answer:

30

Step-by-step explanation:

The unknown number is x.

Start with x.

To increase x by 130%, you need to add 130%of x to x.

x + 130% of x

The sum equals 69.

x + 130% of x = 69

x + 130% * x = 69

1x + 1.3x = 69

2.3x = 69

x = 30

Answer: The number is 30.

Answer:

Sine angle of <ACB = 38.68°

Step-by-step explanation:

Hello,

To solve this problem, we need a good representation of the sides and the angle.

See attached document for better illustration.

Assuming it's a right angled triangle,

AC = hypothenus

AB = opposite

BC = adjacent

AC = 40

BC = 25

AB = 25

From trigonometric ratios

Sinθ = opposite/ hypothenus

Sinθ = AB / AC

Sinθ = 25 / 40

Sinθ = 0.625

θ = sin⁻¹0.625

θ = 38.68°

Sine angle of <ACB = 38.68°

Answer:

[tex]\boxed{\sf 27 \ and \ 29}[/tex]

Step-by-step explanation:

Let the first consecutive odd integer be [tex]\sf x[/tex].

Let the second consecutive odd integer be [tex]\sf x+2[/tex].

The sum of the two numbers is 56.

[tex]\sf x+x+2=56[/tex]

[tex]\sf 2x+2=56[/tex]

[tex]\sf 2x=54[/tex]

[tex]\sf x=27[/tex]

Put x as 27 for the second consecutive odd integer.

[tex]\sf 27+2=29[/tex]

The two numbers are 27 and 29.

Answer:

i believe a=105, b=29, and c=45

Answer:

12π inches

Step-by-step explanation:

s = rθ

s = (21) (4π/7)

s = 12π

The length of the arc will be;

⇒ Arc = 37.68 inches

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The central angle = 4π/7

And, A circle has a radius of 21 inches.

Now,

We know that in circle;

⇒ Arc = Radius × Angle

Substitute all the values, we get;

⇒ Arc = 21 × 4π/7

⇒ Arc = 3 × 4 × 3.14

⇒ Arc = 37.68 inches

Thus, The length of the arc will be;

⇒ Arc = 37.68 inches

Learn more about the circle visit:

https://brainly.com/question/1294687

#SPJ2

Answer:

R = 21.8° to the nearest tenth

Step-by-step explanation:

To find Angle R we use tan

tan ∅ = opposite / adjacent

From the question

The opposite is 2

The adjacent is 5

So we have

tan R = 2/5

R = tan-¹ 2/5

Hope this helps you

[tex](-a+3)(a+4)=-a^2-a+12[/tex].

Hope this helps.

Answer:

-a²-a+12

Step-by-step explanation:

-a²+3a-4a+12

-a²-a+12

Answer:

Step-by-step explanation:

The given equation is expressed as

(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12

Simplifying the right hand side of the equation, it becomes

[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)

x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)

(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)

4x/(x - 1)(x + 1)

Therefore,

4x/(x - 1)(x + 1) = 7/12

Cross multiplying, it becomes

4x × 12 = 7(x - 1)(x + 1)

48x = 7(x² + x - x - 1)

48x = 7x² - 7

7x² - 48x - 7 = 0

Applying the quadratic formula,

x = - b ± √(b² - 4ac)]/2a

from our equation,

b = - 48

a = 7

c = - 7

Therefore

x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)

x = [48 ± √(2304 + 196]/14

x = (48 ± √2500)/14

x = (48 ± 50)/14

x = (48 + 50)/14 or x = (48 - 50)/14

x = 98/14 or x = - 2/14

x = 7 or x = - 1/7

Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7

Step-by-step explanation:

Answer:

Mode: 100

Mean: 46.94444...

Median: 29.5

Range: 150

Step-by-step explanation:

Mode: most occurring number: 100

Mean: Plus everything and divide by how many number there is: 845/18=46.94....

Median: The middle number, but you need to line it from smallest to greatest.

0, 0, 0, 1, 3, 4, 5, 12, 29, 30, 40, 50, 100, 100, 100, 100, 121, 150

29 and 30 is in the middle. In this case, you plus 29+30 and divide by 2. =29.5

Range: Largest number-Smallest number. You also need to line it from smallest to largest: 150-0=150

Hope this helps, BRAINLIEST would really help me:)

Answer:

The standard form of the equation is y = -x/2 -2

Step-by-step explanation:

The standard form of equation of this line is expressing the line in the form;

y = mx + c

So let’s make a rearrangement to what we have at hand;

y + 7 = -1/2(x-10)

2(y + 7) = -1(x-10)

2y + 14 = -x + 10

2y = -x + 10 -14

2y = -x -4

divide through by 2

y = -x/2 -2

Answer:

288π

Step-by-step explanation:

V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.

Answer: Jennifer didn't randomly assign participants to the control and experimental group.

Step-by-step explanation: In the scenario discussed above, Jennifer failed to perform a random assignment of the participants who took part in the survey, that is the experimental group, those who receive the treatment and the control group, those who don't. Random assignment is required in other to address the issue of bias in our experiment. She was supposed to perform a random assignment of the participants to the two groups instead of asking them to make a choice.

Answer:

BHF

Step-by-step explanation:

Definition of inscribed

Answer:

2/13

Step-by-step explanation:

In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.

Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.

Hope this helps!

Answer:

17 cans

Step-by-step explanation:

18 cans

7 are taken away

18-7 =11

Then we put 6 back on

11+6 = 17

There are now 17 cans

Answer:

[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]

[tex]\bold{METHOD\ 2}[/tex]

[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]

[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]

Answer:

The information given are;

[tex]r(V)=\sqrt[3]{\dfrac{V}{6\cdot \pi ^{2}}}[/tex]

Where;

r(V) = The radius of the doughnut (cm)

V = The volume of the doughnut (cm³)

The data are;

V,          r(V)

-30,     -0.8

-20,     -0.7

-10,      -0.55

0,          0

10,         0.55

20,        0.7

30,        0.8

From the table of values, the identified key features are;

a) There is a direct relationship between the radius and the volume of the doughnut

b) The correlation between the data increases to direct proportionality from the volume of 20 cm³ and above

c) The data values are symmetric and continuous about the y and x-axis

2) There is a direct linear relationship between radius, r and the volume V at end ends of the data between r and  V where V = -30 and-20 at one end and 20 and 30 at the other end

b) The x and y-intercept are

The x -intercept = (0, 0)

The x -intercept = (0, 0)

c) The pivot point is the point about which change occurs, therefore, the pivot point is the (10, 0.55)

d) The domain is a member of the set of real numbers, R while the range is also a member of the set of real numbers, R

Step-by-step explanation:

Answer:

1. 2.997

2. 29.93

Step-by-step explanation:

1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.

2. Same thing, gotta multiply all given values