What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?

The solution of the inequality is as follows;

x > 4 or x < -3

The inequality can be solve as follows:

5x - 3 > 17 or -2x + 2 > 8

Let's solve the first inequality,

5x - 3 > 17

add 3 to both sides of the inequality

5x - 3 + 3 > 17 + 3

5x > 20

divide both sides by 5

5x / 5 > 20 / 5

x  > 4

-2x + 2 > 8

subtract 2 from both sides

-2x + 2 - 2 > 8 - 2

-2x > 6

divide both sides by -2

-2x / -2 > 6 / -2

x < -3

Therefore, x > 4 or x < -3

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[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]

Multiply both sides by [tex]\frac1{x^2}[/tex].

[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]

Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].

[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]

[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]

Separate the variables.

[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]

[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]

Integrate both sides

[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]

On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].

[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]

[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].

[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]

[tex]w = e^C e^{\ln|x^{-1}|}[/tex]

[tex]w = Cx^{-1}[/tex]

[tex]1 + v^2 = Cx^{-1}[/tex]

[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]

[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]

Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)

You incorrectly combine the fractions on the left side.

[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]

Answer:

7,647.4?

Step-by-step explanation:

Answer:

268.08

Step-by-step explanation:

Answer:

803.84 m³

Step-by-step explanation:

The formula to find the volume of a sphere is:

V = 4 π r³

Given that,

radius ⇒ 4m

Let us find the volume now.

V = 4 π r³

V = 4 π × ( 4 )³

V = 4 π × 64

V = 4 π × 64

V = 12.56 × 64

V = 803.84 m³

Answer:

Dependent variable: time(months) or [tex]t[/tex]

Independent variable: 6

Step-by-step explanation:

[tex]h=24+6t[/tex]

(h=height)

Step-by-step explanation:

The value of b will be 43° as it is vertically opposite angle.. !!

Step-by-step explanation:

sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2

sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha

1+ 2sin alpha* cos alpha

1+sin2 alpha

The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)

The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.  

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example, The number 5 x 10³ is equivalent to 500

Paper produced in the second year = paper produced in the first year x 5.6

(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]

4.704 x [tex]10^{9 + 1}[/tex]

= 4.704 x [tex]10^{10}[/tex]

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By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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Answer:

B. 1

Step-by-step explanation:

-1*2 = -2

-2+1 = -1

-1+1 = 0

0+1 = 1

The system of equations has one solution (-1, 1)

From the question, we are to graph the given system of equations.

The given system of equation is

y + 2x = −1

3y − x = 4

The graph of the given system of equations is shown below.

From the graph, we can observe that the solution to the given system of equation is given by two lines that intersect at the point (-1, 1).

Hence, the system of equations has one solution (-1, 1)

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I think the answer is A. The first one

The standard deviation for the number of people with the genetic mutation is 3.77

The given parameters are:

Sample size, n = 300

Proportion that has the particular genetic mutation, p = 5%

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation = √np(1 - p)

Substitute the known values in the above equation

Standard deviation = √300 * 5% * (1 - 5%)

Evaluate the product

Standard deviation = √14.25

Evaluate the exponent

Standard deviation = 3.77

Hence, the standard deviation for the number of people with the genetic mutation is 3.77

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Based on the given parameters in the question, the value of the probability of A and D is 0.30

The given parameters from the tree diagram are:

The probability P(A and D) is calculated using the following probability formula

P(A and D) = P(A) × P(D)

Substitute the known values in the above equation

P(A and D) = 0.5 × 0.6

Evaluate the product of 0.5 and 0.6

P(A and D) = 0.30

Hence, the value of the probability of A and D is 0.30 based on the given parameters in the question

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Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]

Using the Factor Theorem, the equation of h(x) is given as follows:

h(x) = -2(x³ - 2x² - 5x + 6)

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:

[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]

Then the rule is:

h(x) = a(x + 2)(x - 1)(x - 3)

h(x) = a(x² + x - 2)(x - 3)

h(x) = a(x³ - 2x² - 5x + 6)

The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:

6a = -12

a = -12/6

a = -2.

Hence the function is given by:

h(x) = -2(x³ - 2x² - 5x + 6)

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Using it's concept, your percentage for the month was of 94.12%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, your goal was of 85, with a grade of 80, hence the percentage is:

P = 80/85 x 100% = 94.12%.

Hence, your percentage for the month was of 94.12%.

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Answer:

C...........................

If Ama and her son Brandon's average age is currently 36 years. then

Brandon's age is 38 years.

Two or more expressions with an equal sign is called as Equation.

Let the Brandon age be x

Ama was 34 years old

Ama and her son Brandon's average age is currently 36 years

(34 + x)/2= 36

Use cross multiplication

34 + x = 72

x=72-34

x = 38

So  Brandon's average age is 38.

Hence Brandon is 38 years old.

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Answer: C

Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.

Separating variables, we have

[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]

Integrate both sides.

[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]

[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]

Given that [tex]y(0)=-1[/tex], we find

[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]

Then the particular solution is

[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]

[tex]y^2 = x^2 + 1[/tex]

[tex]y = \pm\sqrt{x^2 + 1}[/tex]

and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.

[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]

\cos (\tan \left( -1\right) (\frac{x}{2}))

c

o

s

(

t

a

n

(

−

1

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(

2

)

)

Simplify

1

Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

c

o

s

(

t

a

n

(

−

1

)

⋅

2

)

\cos (\frac{\tan \left( -1\right) x}{2})

c

o

s

(

t

a

n

(

−

1

)

2

)

Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

c

o

s

(

t

a

n

(

−

1

)

2

)

Answer:

Step-by-step explanation:

[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]

Answer:

X = 17√3

Y = 34

Step-by-step explanation:

TO calculate the values of X and y we use SOHCAHTOA.

tan 30 = opposite/adjacent

tan30 = 17/X

Cross multiply

tan30 ×X = 17

Divide bothsides by tan30

X = 17/1/√3

X=17√3

X = 29 ( approximately)

[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]

[tex]sin30 \times y = 17[/tex]

[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]

Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Assuming the following parameters for triangle ABC:

For the slope of BC, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2.

For the slope of CA, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3.

For the slope of AB, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4.

Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.

Since side AB is perpendicular to side QC, we have:

m₁ × m₂ = -1

Slope of AB × Slope of QC = -1

Slope of QC = (k - 4)/(h - 2)

4 × (k - 4)/(h - 2) = -1

(4k - 16)/(h - 2) = -1

4k - 16 = -h + 2

4k + h = 18    .......equation 1.

Similarly, we have the following:

Slope of BC × Slope of AH = -1

-3/2 × (k)/(h + 2) = -1

3k/(2h + 4) = 1

3k = 2h + 4

3k - 2h = 4     .......equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

8k + 2h = 36

3k - 2h = 4

11k = 40

k = 40/11.

For the value of h, we have:

h = -4k

h = -4 × (40/11)

h = -160/11

Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).

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Answer:

c

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

19*2 = 38 + 2 = 40

Answer:

Step-by-step explanation:

we have to get k by itself on one side of the equal sign. To do that we have to get rid of 3. To get rid of 3 we have to do the opposite. The opposite of +3 is -3 so we -3 on both sides. 19 - 3 = 16. So k = 16

k+3=19

 -3  -3

   k=16

Answer:

-24 would be the temperature

Answer:

-24 BECAUSE I did all the math.

The ski club has 44 members in all

What is population?

Population refers to the total number of items or individuals that form a group.

In this case, the population means the total  number of all members in the  Mogul Runners ski club.

What is sample?

Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.

We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.

25% of club members=11 members

divide both sides by 25%

25%/25% of club members=11/25% members

club members=44 members

The ski club has 44 members altogether as computed above.

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Step-by-step explanation:

Use this sort of layout, but where x will be an odd number, do not shade it. there should be a pattern of shaded segments followed by unshaded segments repeating

Answer:

7.....gggggggggggggggh