For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?


A. 3/7

B. 7/3

C. 10

D. 21

Answer:

Answer: 23, 67, 90

Step-by-step explanation: The measures of the three angles are 23, 67, 90

I know you don’t care how I got the answer so enjoy it!

For this case we have by definition that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

We have as data that:

[tex]V = 324 \pi\\r = 12[/tex]

Substituting:

[tex]324 \pi = \pi * (12) ^ 2 * h[/tex]

We cleared h:

[tex]324 \pi = \pi * 144 * h\\324 = 144 * h\\h = \frac {324} {144}\\h = 2.25[/tex]

Thus, the height of the cylinder is 2.25 inches.

Answer:

[tex]h = 2.25[/tex]

Answer:

the anser is d

Step-by-step explanation:

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

If a transversal intersects two parallel lines, then _____ angles are supplementary.

Since the sum of interior angle on the same side is supplementary.

Supplementary angles are those angles whose sum is 180°.

Hence, Option 'c' is correct.

If a transversal intersects two parallel lines, then alternate interior angles are supplementary.

When a transversal intersects two parallel lines, alternate interior angles are formed. Alternate interior angles are pairs of nonadjacent interior angles located on opposite sides of the transversal and between parallel lines.

These angles have equal measures and are supplementary, meaning they add up to 180 degrees. This property holds true for any pair of parallel lines intersected by a transversal, providing a relationship between the angles that helps in solving geometric problems and proofs.

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Answer:

0,-2,-4,-6,-8, ...

Step-by-step explanation:

In order to find the sequence represented by the given explicit formula we have to plug in the values of n

Given formula is:

[tex]a_n=2-2n\\a_1=2-2(1)\\=2-2=0\\a_2=2-2(2)\\=2-4\\=-2\\a_3=2-2(3)\\=2-6\\=-4\\a_4=2-2(4)\\=2-8\\=-6\\a_5=2-2(5)\\=2-10\\=-8[/tex]

So the explicit sequence is:

0,-2,-4,-6,-8,..........

Answer:

kmkmlklm

Step-by-step explanation:

Answer:

It will take 8 hours to drive 400 miles

Step-by-step explanation:

The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.

Answer:

The answer is 8!

Step-by-step explanation:

It will take 8 hours to drive 400 miles

The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.

Answer and Step-by-step explanation:

Since we have given that

Time                Average age of a marriage

0                                  10

10                                 11.2

20                                13.9

30                                17.2

40                                29

We need to show that the above data indicated a non linear model.

For this it is enough to show that slope is different:

So, we consider the slope for first 2 points:

(0,10) and (10,11.2)

So, slope becomes

[tex]m_1=\dfrac{y_2y_1}{x_2-x_1}=\dfrac{11.2-10}{10-0}=\dfrac{1.2}{10}=0.12[/tex]

and similarly, (10,11.2) and (20,13.9)

[tex]m_2=\dfrac{y_2-y_}{x_2-x_1}\\m_2=\dfra{13.9-11.2}{20-10}=\dfrac{2.7}{10}=0.27[/tex]

so, [tex]m_1\neq m_2[/tex]

So, it becomes non linear model.

For this case we have by definition, that the electrical power is given by:

[tex]P = I ^ 2 * R[/tex]

Where:

P: It's the power

I: It's the current

R: It's the resistance

Clearing the current:

[tex]I ^ 2 = \frac {P} {R}\\I = \pm \sqrt {\frac {P} {R}}[/tex]

We choose the positive value:

[tex]I = \sqrt {\frac {500} {25}}\\I = \sqrt {20}\\I = 4.47A[/tex]

ANswer:

Option A

Answer: OPTION D.

Step-by-step explanation:

Rectangles have four right angles (angles of 90 degrees).

The point of intersection of the diagonals divides each one of them into two equal parts.

Knowing this, we can conclude that:

[tex]m\angle c=m\angle b=55\°[/tex]

(Observe the figure)

Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":

[tex]x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°[/tex]

Answer:

70 degrees

Step-by-step explanation:

55*2= 110

180-110=70

Answer:

98.5 degrees

Step-by-step explanation:

To find the angle measurement between two vectors use: cos(theta)=(u dot v)/(|u|*|v|)

The vectors are u=sqrt(5)i-8j and v=sqrt(5)i+1j .

So find the dot product of u and v.  u dot v=sqrt5*sqrt(5)+(-8)*(1)=5-8=-3.

Second step: Find the magnitude of both vectors.  So to find the magnitude of a vector, let's call it t when t=ai+bj, you just do |t|=sqrt(a^2+b^2).

|u|=sqrt(5+64)=sqrt(69) and |v|=sqrt(5+1)=sqrt(6)

Now multiply your magnitudes of your vectors: sqrt(69)*sqrt(6)=sqrt(414).

So now we have:

cos(theta)=-3/sqrt(414)

Now arccos( ) or cos^(-1) to find the angle theta.

theta=cos^(-1)[-3/sqrt(414)] which is approximately 98.5 degrees.

Answer:

Ans 1) The correct option is B) 98.5

Ans 2) The correct option is C) [tex]\sqrt{5}[/tex]

Step-by-step explanation:

The angle measurement between two vectors by:

[tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]

Magnitude of vector t=ai+bj, calculated by:

[tex]|t|=\sqrt{a^{2}+b^{2}}[/tex]

The given vectors are [tex]u=\sqrt{5}i-8j[/tex] and [tex]v=\sqrt{5}i+1j[/tex]

First find the dot product of u and v;

[tex]u.v=(\sqrt{5}i-8j)(\sqrt{5}i+1j) = 5-8= - 3[/tex]

Now,  Find the magnitude of both vectors u and v.  

[tex]|u|=\sqrt{(\sqrt{5})^{2}+8^{2}}[/tex]

[tex]|u|=\sqrt{5+64}[/tex]

[tex]|u|=\sqrt{69}[/tex]

and

[tex]|v|=\sqrt{(\sqrt{5})^{2}+1^{2}}[/tex]

[tex]|v|=\sqrt{5+1}[/tex]

[tex]|v|=\sqrt{6}[/tex]

Now, put the all values in  [tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]

[tex]cos(\theta)=\frac{-3}{\sqrt{69} \times \sqrt{6}}[/tex]

[tex]=\frac{-3}{414}[/tex]

take arc cos both the sides,

[tex]\theta=cos^{-1} \frac{-3}{\414}[/tex]

[tex]\theta=98.5 \degree[/tex]   (approx)

Therefore, the correct option is B) 98.5

Ans 2)  calculate IvI by

If t= ai +bj then magnitute is [tex]\sqrt{a^{2}+b^{2}}[/tex]

Given : v = (-2,-1)

it means v = -2i -1 j

[tex]|v| =\sqrt{(-2)^{2}+(-1)^{2}}[/tex]

[tex]|v| =\sqrt{4+1}[/tex]

[tex]|v| =\sqrt{5}[/tex]

Therefore, the correct option is C) [tex]\sqrt{5}[/tex]

Answer:

  7 days

Step-by-step explanation:

We assume that "by day 4" means "at the end of day 3." Since Curtis had run 9 miles in 3 days, his average rate is 9/3 = 3 miles per day.

It will take Curtis ...

  (21 mi)/(3 mi/day) = 7 days

to run 21 miles at that rate.

_____

Comment on the question

There is nothing in the problem statement to suggest that the number of miles run each day is the same. A different assumption than the one we have made will give a different answer.

Answer:4

Step-by-step explanation: 6 times 6 divide by 9

Multiply the denominators across and Multiply the numerators across

x/6= 6/9

9x= 36

x= 4

Check answer by using substitution method

x/6= 6/9

4/6= 6/9

Divide by 2 for 4/6

Divide by 3 for 6/9

2/3= 2/3

Answer is x= 4

Answer:

x=6.6 cm

Step-by-step explanation:

The angle force at the point where the tangent touches the circle is 90° hence the  triangle is a right angle triangle . We can apply the Pythagorean relationship in this case

Given the hypotenuse as x+ 8.45  and the base as x and height as 13.5 then;

a²+b²=c²  .................where a=x  , b= 13.5 and c x+8.45

x² +13.5²= (x+8.45)²

x²+182.25=x²+8.45x+8.45x+71.4025

x²+182.25=x²+16.90x+71.4025-----------------collect like terms

x²-x²+ 182.25-71.4025=16.90x

110.8475=16.90x-------------------divide by 16.90 to remain with x

110.8475/16.90 = x

x=6.5590

x= 6.6 cm

Answer:

The probability that the dart lands inside the triangle is 0.25

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes ÷ Total

  number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- P(A) < 1

* Lets solve the problem

- A rectangular dartboard has an area of 648 cm²

- The triangular part of the dartboard has an area of 162 cm²

- A dart is randomly thrown at the dartboard

- The dart lands in the rectangle

∴ The area of the rectangle is the set of all possible outcomes n(S)

- The probability P(A) that the dart lands inside the triangle

∴ The area of the triangle is set of favorable outcomes of an

   event n(E)

∵ P(A) = n(E) ÷ n(S)

∴ P(T) = area of the triangle ÷ area of the rectangle

∵ Area of the rectangle is 648 cm²

∴ n(S) = 648

∵ The area of the triangle is 162 cm²

∴ n(E) = 162

∴ P(T) = 162 ÷ 648 = 1/4 = 0.25

* The probability that the dart lands inside the triangle is 0.25

Answer:

  about 26 min

Step-by-step explanation:

Let x represent the time spent rowing distance d upstream. Then the time spent rowing downstream is ...

  time = distance/speed . . . . speed × time = distance

  downstream time = (4.5 km/h)(x)/(5.5 km/h)

So, the total time in both directions is ...

  x + 4.5/5.5x = 48 min

  x(1 + 9/11) = 48 min

  x = (48 min)/(20/11) = 26.4 min

Rounded to the nearest minute, Toni spent about 26 minutes rowing upstream.

Answer:

  -6/5

Step-by-step explanation:

The slope is computed from ...

  slope = (change in y)/(change in x)

  = (-2 -4)/(3 -(-2)) = -6/5

Answer:

[tex]-\frac{6}{5}[/tex]

Step-by-step explanation:

We are given the points (-2,4) and (3, -2).

We want to find the slope (m) of this line.

The slope can be found using the following formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.

Even though we are already given the points, we can label the values of them to avoid confusion and mistakes.

[tex]x_1=-2\\y_1=4\\x_2=3\\y_2=-2[/tex]

Now, substitute the values of the points into the formula. Remember that we have negative numbers.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-2-4}{3--2}[/tex]

[tex]m=\frac{-6}{3+2}[/tex]

[tex]m=\frac{-6}{5}[/tex]

The slope of the line is [tex]-\frac{6}{5}[/tex].

Answer:

8 inches

Step-by-step explanation:

Area (A) of a triangle = [tex]\frac{1}{2}[/tex] × base (b) × height (h)

72 square inches = [tex]\frac{1}{2}[/tex] × 18 × h

9h = 72

h = 8 inches

Follow below steps:

The area of a triangle: A = 1/2 * base * height. Given area = 72 sq in and base = 18 in, we can calculate the height:

72 = 1/2 * 18 * height

height = 8 inches

Answer: B. 36

The complete square is (x+6)^2. It's missing the third term, which is 36 because 6 x 6 is 36.

ANSWER

B. 36

EXPLANATION

The given quadratic expression is:

[tex] {x}^{2} + 12x = 16[/tex]

To complete the square we add the square of half the coefficient of x.

The coefficient of x is 12.

Half of it is 6.

The square of 6 is 36.

Therefore we add 36 to both sides of the equation to complete the square.

The correct answer is B.

Answer:

Option D) x = 2

Step-by-step explanation:

(4-2)(x-2) = 4x - 8

Distribute and simplify 4-2

2(x-2) = 4x - 8

2x-4 = 4x -8

Subtract 2x on both sides and add 8 on both sies

4x - 8 = 2x-4

2x= 4

Divide 2 on both sides

x = 2

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Answer: Graph D

Step-by-step explanation:

in slope intercept form, the equation is y</= 1/2x-6

Since it's </=, the line is solid instead of dashed

The graph that matches the inequality is:

                         Graph D

We are given a inequality as:

[tex]y+4\leq \dfrac{1}{2}x-2[/tex]

i.e. it could also be represented in the form:

[tex]y\leq \dfrac{1}{2}x-2-4\\\\i.e.\\\\y\leq \dfrac{1}{2}x-6[/tex]

The graph of this inequality is a straight solid line ( since the inequality is not strict i.e. it is a inequality with a equality sign) that passes through (0,-6) and (12,0) .It also passes through (4,-4) and the shaded region is away from the origin.

Hence, the graph which satisfies all the above property is:

                           Graph D

Answer:

x = 16

Step-by-step explanation:

From the first statement, we can say that:

Angle A is equal to angle D,

Angle B is equal to and E.

Since measure of Angle B and E are given and they are equal, we equate them and solve for x.

[tex]B=E\\x+15=6x-65\\15+65=6x-x\\80=5x\\x=\frac{80}{5}\\x=16[/tex]

Hence x = 16

Answer: Option d

They are opposites and parallel.

Step-by-step explanation:

Although they have the same magnitude, one can not say that a and b are equal because they have opposite directions.

If we know that both vectors have opposite directions then necessarily a and b must be parallel.

So what we know about a and b is that they are parallel and opposite.

The correct answer is the option d

Answer:

guy above is right

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

The mean of the first graph comes to be the point at which the graph reaches its highest point.

The mean of the blue graph is: μ = 30

The mean of the blue graph is: μ = 45

The difference of the means of the distributions is: 45 - 30 = 15

Answer:

15

Step-by-step explanation:

The answer is:

The correct option is:

D. 40 feet.

To solve the problem and calculate the width of the river, we need to assume that the distance from A to B and the angle formed between that distance and the distance from A to the other point (C) is equal to 90°, meaning that we are working with a right triangle, also, we need to use the given angle which is equal to 34°. So, to solve the problem we can use the following trigonometric relation:

[tex]Tan\alpha =\frac{Opposite}{Adjacent}[/tex]

Where,

alpha is the given angle, 34°

Adjacent is the distance from A to B, which is equal to 60 feet.

Opposite is the distance from A to C which is also equal to the width of the river.

So, substituting and calculating we have:

[tex]Tan(34\°) =\frac{Width}{60ft}[/tex]

[tex]Width=60ft*Tan(34\°)=60ft*0.67=40.2ft=40ft[/tex]

Hence, we have that the correct option is:

D. 40 feet.

Have a nice day!

Answer: OPTION D

Step-by-tep explanation:

Observe the figure attached.

You can notice that the the width of the river is represented with "x".

To calculate it you need to use this identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

In this case:

[tex]\alpha=34\°\\opposite=x\\adjacent=60[/tex]

Now you must substitute values:

 [tex]tan(34\°)=\frac{x}{60}[/tex]

And solve for "x":

[tex]60*tan(34\°)=x\\\\x=40.4ft[/tex]

[tex]x[/tex]≈[tex]40ft[/tex]

Answer:

A

Step-by-step explanation:

it has to do with the people's ethnics or standard or values.

The statement is not ambiguous so it has no language barrier

Answer:

  C.  use of language

Step-by-step explanation:

The descriptor "childish" will likely influence results. Most Grade 9 students prefer not to be thought of as "childish."

Answer:

(1/2, 0)

Step-by-step explanation:

The solution to a system of equations graphically is where they intersect on the graph.  In a coordinate, the x is first and the y is second.  Where our lines cross is ON the x-axis.  This means that y = 0 here.  Because we are to the right of the origin, we are in positive x values.  Because we are between x = 0 and x = 1, the best estimate from our choices is x = 1/2.  The coordinate for the solution is best represented by (1/2, 0)

Answer:

  C.  postulate; theorem

Step-by-step explanation:

While a "given" is taken as true without proof, and a "problem" sometimes involves an assertion that can be proven, the answer choices involving these terms are not correct here.

The dictionary definitions of "postulate" and "theorem" apply. It is useful to learn the meaning of these terms so you can understand problems and descriptions that use them.

Answer:

  x +2y = 12

Step-by-step explanation:

Try the given points in the given equations and see what works.

  -2x + 5y at (2, 5) is -2(2) +5(5) = 21 ≠ 12

) +)   2x + y at (2, 5) = 2(2) +(5) = 9 ≠ 12

  x + 2y at (2, 5) = 2 +2(5) = 12 . . . . . goes through first point

  x + 2y at (4, 4) = 4 + 2(4) = 12 . . . . goes through second point

__

You know the answer at this point, so the next check is just for "completeness." It is not necessary to properly answer the question.

  -x +2y at (2, 5) = -(2) +2(5) = 8 . . . . goes through first point

  -x +2y at (4, 4) = -(4) + 4(4) = 4 ≠ 8 . . . does not go through second point

The hole which was initially 8 feet deep and then extended by 3 more feet got partially filled by 4 feet of dirt by a tractor, resulting in a total remaining depth of 7 feet.

Your question is a simplifying numerical values scenario. First, you dug a hole that was 8 feet deep. Next, you dug an additional 3 feet, so you would add these two values together to get a total depth of 11 feet (8 + 3). Finally, a tractor accidentally filled 4 feet of the hole with dirt. Subtracting this from the total depth of the hole means your hole is now 7 feet deep (11 - 4).

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Answer:

  one solution: (x, y) = (1, 0)

Step-by-step explanation:

See below for a graph with the one solution identified.

Answer:

The system has one solution at (1,0).

Step-by-step explanation:

Consider the provided system of equations

y=-6x+6

Substitute x = 0 in above equation.

y=-6(0)+6

y=6

The coordinate is (0,6)

Now substitute y=0 in the above equation.

0=-6x+6

-6=-6x

x=1

The coordinate is (1,0)

Now use the coordinates (0,6) and (1,0) in order to draw the graph.

The graph of y= -6x + 6 is shown in figure 1.

Similarly, consider the second equation y= 3x - 3

Substitute x = 0 in above equation.

y=3(0)-3

y=-3

The coordinate is (0,-3)

Now substitute y=0 in the above equation.

0=3x-3

3=3x

x=1

The coordinate is (1,0)

The graph of y= 3x - 3 is shown in figure 2.

Now draw the graph of both equation as shown in figure 3.

By observing the graph it can be concluded that the system has one solution at (1,0)

Hence, the system has one solution at (1,0).