which of the following equations is an example of inverse variation between the variables x and y?

Answer:

x = 31.12

Step-by-step explanation:

First find the base (hypotenuse) of the smaller triangle (the isosceles triangle):  Its three sides are 11, 11 and b.  b can be found using the Pythagorean Theorem:  b^2 = 11^2 + 11^2 = 242.  Then b = √242, or b = approximately 15.56.

b (which is approximately 15.56) is the shorter leg of the large (right) triangle.  The trig function needed to solve for x is the cosine:

                               adjacent side

cos 60 degrees = ----------------------

                                  hypotenuse,

                                       15.56

which becomes (1/2) = ------------

                                            x

Solving this for x, we get:  x = 2(15.56) = 31.12

Answer:

Step-by-step explanation: 10 meters/3 meters =x/4.5 meters

Where x = the maximum distance the projector can be placed that can produce an image 4.5 meters high

3x = 10 (4.5)

3x = 45

X= 45/3

X= 15 meters

So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

Answer:The integer represented by H is -2

Step-by-step explanation:

Answer:

(- 3, 2 )

Step-by-step explanation:

Given the 2 equations

x + 3y = 3 → (1)

- 2x + 3y = 12 → (2)

Subtract (1 ) from (2) term by term to eliminate y

- 2x - x + (3y - 3y) = 12 - 3

- 3x = 9 ( divide both sides by - 3 )

x = - 3

Substitute x = - 3 into either of the 2 equations and solve for y

Substituting into (1)

- 3 + 3y = 3 ( add 3 to both sides )

3y = 6 ( divide both sides by 3 )

y = 2

solution is (- 3, 2 )

Answer:

64

Step-by-step explanation:

(x-8)^2

derived from the middle term divided by 2

Answer:

64

Step-by-step explanation:

x^2 − 16x + ___

Complete the square

Take the coefficient of the x term

-16

Divide by 2

-16/2 = -8

Then square it

(-8)^2 = 64

Explanation:

The number -1/2 is rational as it is a fraction or ratio of two integers (-1 and 2). We can never have 0 in the denominator. Since it is rational, it means the number is not irrational. Recall that "irrational" means "not rational", so it is the opposite of rational.

-1/2 = -0.5 is not a whole number as it has a fractional or decimal portion. This means -1/2 is not an integer either, nor is it a natural number. The negative portion is another reason to exclude -1/2 from the list of whole numbers and natural numbers.

But we can say that -1/2 = -0.5 is a real number. Any number you encountered so far is a real number until you get to the complex numbers.

Answer:

Step-by-step explanation:

The given trigonometric expression is :

11 cos^2 x +3 sin^2 x+6sinx cosx +5

or, we can write it as,

(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5

Again, after rearranging the terms, we can write the whole expression as,

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

Then if you factor the following underlined section as you would with a polynomial:

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

You get:

(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5

Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.

So, now the whole expression becomes,

(3 cos x + sin x)^2 +7

Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),

The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.

So, I've attached a screenshot from a relevant document below:

Here, a=3 and b=1,

So, R= √10

As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.

Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.

i.e., in our case between (-√10) to √10.

Again, coming back to our original expression,

(3 cos x + sin x)^2 +7

The value of the term in bracket will lie between (-√10) and √10.

But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.

So, the minimum value will be,

(0)^2 + 7=7

and the maximum value will be,

(√10)^2 +7 = 17

Answer:

6.71cm

Step-by-step explanation:

a²+b²=c²

6²+3²=x²

sqrt(6²+3²)=6.71

Answer:

[tex]\Large \boxed{\sf 6.71 \ cm}[/tex]

Step-by-step explanation:

The triangle is a right triangle. We can use Pythagorean theorem to solve for the hypotenuse.

a² + b² = c²

a and b are the lengths of the legs. c is the length of the hypotenuse.

6² + 3² = x²

Evaluate.

36 + 9 = x²

45 = x²

Take the square root of both sides.

√(45) = √(x²)

6.7082039325... = x

Answer:

the missing values is 5

I hope it's helps you

Answer:

From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.

Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).

Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).

Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.

Answer:

2y + 16 +2y +30 +4y –13 +3y - 21

11y + 12

I hope I helped you^_^

Hi there! :)

Answer:

[tex]\huge\boxed{V = 359.01 mm^{3} }[/tex]

Use the formula V = 1/3(bh) to solve for the volume of the cone where b = πr² where π ≈ 3.14:

Find the area of the base:

b = π(7)²

b = 49π

b = 153.86 mm²

Find the volume:

V = 1/3(153.86 · 7)

V = 1/3(1077.02)

V = 359.006 ≈ 359.01 mm³.

Answer:

45 * 3/5 = 135/5 = 27

Step-by-step explanation:

The best value for each of the characteristics of the parabola are presented in the following table;

The table of best values of parabola characteristics

[tex]\begin{array}{lcccc}\mathbf{Characteristic&\mathbf{r}&\mathbf{ (\pi \cdot r)}&(2 \cdot \pi \cdot \mathbf{r})& ( \pi \cdot \mathbf{r^2})\\\\\mathbf{Base \ of \ parallelogram} & &\checkmark &&\\\\\mathbf{Height \ of \ parallelogram}& \checkmark &&&\\\\\mathbf{Area \ of \ parallelogram}&&&&\checkmark \end{array}}[/tex]

The process of obtaining the above values is shown as follows;

The given parameters are;

To justify the area of a circle, the argument Yvonne wants to use = The dissection argument

The shape to which the reassembled figure tends to approximate = A parallelogram

Description of the of the reassembled figure

The horizontal parallel sides of the parallelogram formed = The arcs of the circle

The other pair of parallel sides = The radius of the circle

The best values of the characteristics of the parallelogram given in the table are therefore found as follows;

(a) The base of the parallelogram = (1/2) the total sum of the arcs in a circle = (1/2) the circumference of the circle = π·r

∴ The base of the parallelogram = π·r

(b) The height of the parallelogram = The perpendicular distance from the tip of one of the sectors to the midpoint of the arc of the sector = The radius of the circle = r

∴ The height of the parallelogram = r

(c) The area of the parallelogram, A = The sum of the area of the sectors

A = (n × θ/360) × π·r²

Where;

n × θ = 360°

Therefore;

A = (n × θ/360) × π·r² = (360/360) × π·r² = π·r²

We have;

The area of the parallelogram, A = π·r²

The table showing the best value of each characteristics of the parallelogram is therefore presented as follows;

[tex]\begin{array}{lcccc}\mathbf{Characteristic&\mathbf{r}&\mathbf{ (\pi \cdot r)}&(2 \cdot \pi \cdot \mathbf{r})& ( \pi \cdot \mathbf{r^2})\\\\\mathbf{Base \ of \ parallelogram} & &\checkmark &&\\\\\mathbf{Height \ of \ parallelogram}& \checkmark &&&\\\\\mathbf{Area \ of \ parallelogram}&&&&\checkmark \end{array}}[/tex]

Learn more about geometric figures (circles, and parallelogram) here;

https://brainly.com/question/16663192

https://brainly.com/question/24054192

Answer:

3/12 as a decimal is 0.25

2/9 as a decimal is 0.2 reapeted

Answer:

Answer written below

Step-by-step explanation:

Divide 3 by 12 and 2 by 9 using long division solve like normal long division if your divisor is bigger than your dividend add a zero on top and add a zero to the dividend.

Decimal form of  3/12:0.25

Decimal form of  2/9:0.22223

Answer: Acid concentration will be 25%.

Step-by-step explanation:

Solution 1: 2 quarts(=4 pints) of a 30% acid

concentration = 0.3*4 = 1.2

Solution 2: 4 pint of a 20% acid

concentration = 4*0.2 = 0.8

Final solution: total volume = 4 pints + 4 pints = 8 pints

Final Concentration:

[tex]\frac{1.2+0.8}{8}[/tex] = 0.25

In the resulting mixture, the concentration is 25% of acid solution.

Answer:

6

Step-by-step explanation:

5

Answer:

k = 10

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

2x(2x + kx) = 3x(3x + 5x)

4x² + 2kx² = 3x × 8x = 24x² ( subtract 4x² from both sides )

2kx² = 20x² ( divide both sides by 2x² )

k = 10

[tex]\\ \sf\longmapsto 1\dfrac{1}{2}+2\dfrac{3}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{2}+\dfrac{11}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{6+11}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{4}[/tex]

2:-

[tex]\\ \sf\longmapsto 4\dfrac{3}{7}+6\dfrac{1}{5}[/tex]

[tex]\\ \sf\longmapsto \dfrac{31}{7}+\dfrac{31}{5}[/tex]

[tex]\\ \sf\longmapsto \dfrac{155+225}{35}[/tex]

[tex]\\ \sf\longmapsto \dfrac{380}{35}[/tex]

[tex]\\ \sf\longmapsto 12[/tex]

3:-

[tex]\\ \sf\longmapsto 4\dfrac{2}{5}+5\dfrac{2}{6}[/tex]

[tex]\\ \sf\longmapsto \dfrac{22}{5}+\dfrac{32}{6}[/tex]

[tex]\\ \sf\longmapsto \dfrac{132+160}{30}[/tex]

[tex]\\ \sf\longmapsto \dfrac{292}{30}[/tex]

4:-

[tex]\\ \sf\longmapsto 3\dfrac{7}{7}+3\dfrac{1}{3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{28}{7}+\dfrac{10}{3}[/tex]

[tex]\\ \sf\longmapsto 4+\dfrac{10}{3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{12+10}{3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{22}{3}[/tex]

[tex] \bf \large \longrightarrow \: \: 1 \frac{1}{2} \: + \: 2 \frac{3}{4} \: = \: \\ [/tex]

[tex] \bf \large \longrightarrow \: \: \frac{3}{2} \: + \: \frac{11}{4} \\ [/tex]

[tex] \bf \large \longrightarrow \: \: \frac{6 \: + \:11 }{4} \\ [/tex]

[tex] \bf \large \longrightarrow \: \: \frac{17}{4} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: 4 \frac{3}{7} \: + \: 6 \frac{1}{5} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{31}{7} \: + \: \frac{31}{5} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{155 \: + \: 217}{35} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{372}{35} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: 4 \frac{2}{5} \: + \: 5 \frac{2}{6} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{22}{5} \: + \: \frac{32}{6} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{132 \: + \: 160}{30} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{292}{30} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: 3 \frac{7}{7} \: + \: 3 \frac{1}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{28}{7} \: + \: \frac{10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \cancel\frac{28 ^{4} }{7 \: ^{1} } \: + \: \frac{10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{4}{1} \: + \: \frac{10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{12 \: + \: 10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{22}{3} \\ [/tex]

Answer:

[tex]\sqrt{52}[/tex]

Step-by-step explanation:

[tex]a^{2} + b^{2} =c^{2}[/tex]

Here, a = 4, and b = 6.  So if you square a, you get 16.  If you square b, you get 36.

16+36 = 52 = [tex]c^{2}[/tex]

Take the square root of 52 and [tex]c^{2}[/tex] and you get that c = [tex]\sqrt{52}[/tex]

This can be simplified further.  c = [tex]\sqrt{52} = \sqrt{13*4} = 2\sqrt{13}[/tex]

Answer:

The rule of the transformation is 6 units up and 3 units to the right [tex]T_{(3, \ 6)}[/tex] and an horizontal dilation of 2 as well as a vertical dilation of 4.

Step-by-step explanation:

The given coordinates of EFG and E'F'G' from the chart are;

E(3, 2)

F(9, 5)

G(9, 2)

E'(6, 8)

F'(18, 20)

G'(18, 8)

Therefore, we have, given that the y-coordinates of E and G are the same, the length of segment EG = 9 - 3 = 6 units

Similarly, given that the x-coordinates of F and G are the same, the length of segment FG = 5 - 2 = 3 units

The length of segment FE =  [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex] which gives;

Length from E(3, 2) to F(9, 5) = [tex]l = \sqrt{\left (5-2 \right )^{2}+\left (9-3 \right )^{2}} = 3 \cdot \sqrt{5}[/tex]

For similarly oriented E'F'G', we have;

E'G' = 18 - 6 = 12

F'G' = 20 - 8 = 12

E'F' = 12·√2

Therefore, the transformation is 6 units up and 3 units to the right and an horizontal dilation of 2 as well as a vertical dilation of 4.

Answer: no real solutions

Step-by-step explanation:

8n^2-7n+7=0

a=8, b=-7, c=7

b^2-4ac=(-7)^2-4*8*7=49-224=-175

-175<0

no real solutions

Answer:

Substitute 6 for the variable, n, using parentheses. Then simplify by multiplying 8 and 6. 8(6) = 48. So you have 56 = 48, which is not a true statement. 6 is not a solution to the equation.

Step-by-step explanation:

hope it helps

Answer:

x = 30

b = 30

a = 90

Step-by-step explanation:

So first let's find the 'X'

we already know one angle - 30 degrees

i think you should know the straight equals 180 so we minus 180 to 30

- 180 - 30 = 150

then we know there is 2x and 3x, which is unknown so in this we actually divide 150 with 5 cause 2 + 3 = 5, to get the x value

so x = 30

____________________________________________________

so you know the progress so I will write the answers now

x = 30

b = 30

a = 90

___

so just to check the answers I will add all the numbers to equal it to 360

30 + 90 + 60 + 30 + 60 + 90 = 360

Answer:

Step-by-step explanation:

30 + 2x + 3x = 180   {Straight line angles}

30 + 5x = 180     {Combine like terms}

5x = 180 - 30  {Subtract 30 from both sides}

5x = 150

x = 150/5           {divide both sides by 5}

x = 30

30 + 3x + a = 180  {Straight line angles}

30 + 3*30 + a  = 180

30 + 90 + a = 180

   120 +  a = 180      

{Subtract 120 from both sides}

             a = 180 - 120

             a = 60

b + 2b + a = 180  {Straight line angles}

 3b + a = 180

   3b + 60 = 180

       3b  = 180 - 60      {Subtract 60 from both sides}

      3b = 120

         b = 120/3

b = 40

Answer:

Area: x^2+x-6

Perimeter: 4x+2

Step-by-step explanation:

Area: multiply x+3 and x-2 and combine the like terms

Perimeter: multiply the length and width by two, then combine the like terms.

Answer:

I think that the answer is 1 to1

Answer:

[tex]SU=18[/tex]

Step-by-step explanation:

The segments ST and TU make up the line segment SU. Add the values to find SU:

[tex]ST+TU=SU\\\\13+5=18[/tex]

The length of SU is 18.

The length of SU is 18 units.

We have a point T is between S and U.

We have to determine the length SU.

According to the question -

ST = 13 units

TU = 5 units

Now -

SU = ST + TU = 13 + 5 = 18 units

Hence, the length of SU is 18 units.

To solve more questions on Line Segments, visit the link below-

brainly.com/question/19569734

#SPJ2

Answer:

El ancho de la superficie = 444,44 my el largo = 200 m

La superficie de la superficie de la presa = 88888,89 m²

Step-by-step explanation:

Los parámetros dados son;

La altura del agua en la presa = 225 m

El volumen de agua en la presa, d = 20 millones de m³

La longitud de la base = 200 m

Sea el ancho de la presa = x

El volumen viene dado por la relación;

200 × 225 × x = 20 millones de m³

x = 20.000.000 / (200 × 225) = 444,44 m

Por tanto, las dimensiones de la superficie son ancho = 444,44 my largo = 200 m

El área de superficie de la superficie de la presa = 444.44 × 200 = 88888.89 m².

Answer:

D 1,433.25

Step-by-step explanation:

1/2(10)(7)=35

35*13=455

455*3.15=1,433.25

Answer:

D

Step-by-step explanation:

You need to find the volume of the attic (I would find the surface area myself -- but this is math. You just have to obey the rules of the question no matter how silly).

The Volume is found by V = B * h1

The base is a triangle.

b = 7 m

h1 = 10 m

Area = 1/2 * 7 * 10

area = 35 m^2

The volume of the attic is

V = B * h

V = 35 * 13

V = 455 m^3

The cost = cost /m^3  * m^3

m^3 = 455

Cost = 3.15 * 455

Cost = 1433.25

Answer:

92 is the smaller even integer

Step-by-step explanation:

x = first even integer

x+2 = second even integer

(x) + (x+2) = 186

Combine like terms

2x+2 = 186

Subtract 2 from each side

2x+2-2 =186-2

2x = 184

Divide by 2

2x/2 = 184/2

x = 92

x+2 = 94

Step-by-step explanation:

let,two even consecutive number be x and x+2

now,according to the question

x+x+2=186

or, 2x=186-2

or, 2x= 184

or, x= 184/2

:- x= 92

Hence,

x=92 and x+2= 94

two even consecutive numbers are 92 and 94

Step-by-step explanation:

u just need to imagine it was x^2-17X+16 in the beginning and add square onto the x after u factorise. then solve the x. hope it helps

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.

The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:

[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]

Combine like terms so we can get a simpler equation:

[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]

Now let's solve for x!

[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]

So [tex]x = 15[/tex].

Hope this helped!

Answer:

15

Step-by-step explanation:

3x + 6x + 45 = 180

9x = 135

x = 15