solve 0.7cos(x)-sin(x)=r for x

where r is a real number

show all steps (if you don't show steps, I'll report the answer)

Answer:

x = 15

Step-by-step explanation:

When figures are similar, the lengths of corresponding sides are in the same ratio.

In the figure, the side measuring 8 corresponds to the side measuring 20. The ratio of the lengths of those two corresponding sides is 8/20.

The side measuring 6 corresponds to the side measuring x. The ratio of the lengths of those two corresponding sides is 6/x.

Since the quadrilaterals are similar, the ratio 8/20 must equal the ratio 6/x.

We use that fact to write an equation, and then we solve for x.

8/20 = 6/x

Reduce the fraction on the left side.

2/5 = 6/x

Cross multiply.

2x = 5 * 6

2x = 30

x = 15

[tex]210^{o} and 260^{o}[/tex] are not quadrantal angles.

A quadrantal angle is formed by two lines which lie on x-axis and y-axis.

For this reason, angles like;

[tex]0^{o},90^{o},180^{o},270^{o} and also -90^{o},-180^{o},-270^{o}[/tex] are quadrantal.

However, on the other hand,

[tex]210^{o} and 260^{o}[/tex] are not quadrantal because these angles are not formed by lines lying along x-axis and y-axis.

Answer:

210 and 260 degrees are not quadrantal angles

Step-by-step explanation:

quadrantal angles are angles that directly fall on the x or y axis. They're also multiples of 90 degrees. Quadrantal angles are 0, 90, 180, 270 degrees. hope this helps!

there is enough acres to support 3 cattle on their farmland .

Michael's family's 210-acre farmland can support 630 cattle, with each cow needing 1/3 acre for grazing.

To find out how many cattle Michael's family's farmland can support, you would divide the total acreage by the amount of land each cow needs for grazing.

Given:

- Michael's family has 210 acres.

- Each cow requires 1/3 acre for grazing.

You can calculate it like this:

[tex]\[ \text{Number of cattle} = \frac{\text{Total acreage}}{\text{Acreage per cow}} \][/tex]

[tex]\[ \text{Number of cattle} = \frac{210 \, \text{acres}}{\frac{1}{3} \, \text{acre/cow}} \][/tex]

To divide by a fraction, you multiply by its reciprocal:

[tex]\[ \text{Number of cattle} = 210 \, \text{acres} \times \frac{3}{1} \, \text{cow/acre} \][/tex]

[tex]\[ \text{Number of cattle} = 630 \, \text{cows} \][/tex]

So, Michael's family's farmland can support 630 cattle.

Answer:

B) y = 10x

Step-by-step explanation:

It should not be too hard for you to determine that every number on the bottom row is the same as the number on the top row with a zero appended.

Appending a zero to a number is the same as multiplying it by 10. For example, ...

... 90 = 10·9

... y = 10x

_____

In case that observation doesn't work out for you, you can always solve the given equation for k, then choose values from the table to fill in.

... y = kx

... k = y/x . . . . . divide by the coefficient of k, which is x

Fill in values from the table

... k = 20/2 = 10 . . . . . . from the second column

Now put this value where k is in the equation. After you do that, you know ...

... y = 10x

slope = (30 - 20)/(3 - 2) = 10 /1 = 10

equation

y = 10x

Answer

B) y = 10x

Answer:

The error is the exponent in the answer should be 11.

Step-by-step explanation:

When you move the decimal place one spot as they do in the final step to move it from a base 10 to a base 1, we have to add a exponent on. Therefore, it should go from 10 to 11.

Answer:

m = kg

Step-by-step explanation:

125 = 5k   , k = 25  where k is the constant of variation.

175 = 7k,  k = 25

Direct variation m = kg

Answer:

[tex]m=kg[/tex]  direct variation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem

Let

m------> the number of miles traveled

g------> the number of gallons used

we have that

[tex]\frac{125}{5}\frac{miles}{gallons}=25\frac{miles}{gallons}[/tex]

[tex]\frac{175}{7}\frac{miles}{gallons}=25\frac{miles}{gallons}[/tex]

The linear direct variation that represent the situation is equal to the equation

[tex]\frac{m}{g}=k[/tex]  or [tex]m=kg[/tex]

where

k is the constant of proportionality

In a direct variation the constant k is equal to the slope m of the line, and the line passes through the origin

[tex]k=25\frac{miles}{gallons}[/tex]

substitute

[tex]m=kg[/tex] -------> [tex]m=25g[/tex]

Your answer would be

10330.9

answer:  3767.74

work:

(1.18 × 103) ⋅ (9.1 × 10 − 6)

121.54 ⋅  (91 − 60)

121.54 ⋅  31

3767.74

hope this helps! comment if the problems seems wrong :) ❤ from peachimin

Hey there!!

Given equation :

... 3 ( 2k - 9 ) + 4 = 5 - 2 ( k + 7 )  

Using the distributive property :

... 6k - 27 + 4 = 5 - 2k - 14

Combining the like terms :

... 6k - 23 = -2k - 9

Adding 2k on both sides :

... 8k - 23 = -9

Adding 23 on both sides :

... 8k = 24

Dividing by 8 on both sides :

... k = 24 / 8

... k = 3

The required answer is 3.

Hope my answer helps!!

If you look at the graph, the x axis the the number of hats and y axis is the cost.

So 8 hats will cost $60

Answer

D. The cost of 8 hats is $60

Answer: The cost of 8 hats = $60.

Step-by-step explanation:

In the given graph , the x-axis is representing the number of hats and y-axis is representing the cost of hats ( in dollars $).

To find the cost of 8 hats , just look at the x-axis and search for point x=8 on it .

Then , draw a straight line vertically passing through x=8 or just look at the dot marked above x=8 on the graph.

Then check the y-value associated with that dot or draw a horizontal line from that point , you will get y= 60

It means, the cost of 8 hats = $60.00.

See attachment below.

32 mm = length × 100

(32 mm)/100 = length . . . . . divide both sides by 100

0.32 mm = length

The actual length of the organism is 0.32 mm.

Let L be the actual length.  Then 100 L = 32 mm, and so L = 3 1/8 mm or 3.125 mm.

Answer:

The answer would be C) $3.55

Step-by-step explanation:

$26.30-$22.75=3.55

The gas in Huntsville is $3.55 more expensive than in Centerville for 19 gallons, so the correct answer is C) $3.55.

To determine how much more the gas cost in Huntsville than in Centerville, you need to subtract the cost of gas in Centerville from the cost of gas in Huntsville. In math terms, the operation is as follows:

Huntsville cost ($26.30) - Centerville cost ($22.75) = Additional cost.

When you perform this subtraction, the result is $3.55. Therefore, the gas in Huntsville is $3.55 more expensive than in Centerville for 19 gallons.

So, the correct choice is C) $3.55.

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Since the answer choices differ in their first coordinate, it is sufficient to determine that one. The 2:5 ratio means the distance from A to the point is 2/(2+5) = 2/7 of the total distance A to B.

The x-distance from A to B is 20 -1 = 19 units. 2/7 of that is (2/7)·19 = 38/7 = 5 3/7. Adding this value to the x-coordinate of A gives the x-coordinate of the point of interest: 1 +5 3/7 = 6 3/7.

The appropriate answer choice is ...

... (6 3/7, 12 2/7)

Answer:

(6 3/7, 12 2/7)

Step-by-step explanation: because I got it right

Final answer:

To prove that triangle ABC is isosceles, we can use the fact that the altitudes from vertex B and C intersect at point M and BM = CM. Since BM = CM and the two triangles share the side BM, we can conclude that ΔBMC and ΔBMA are congruent by Side-Side-Side Congruence (SSS). Therefore, the corresponding angles and sides of the two triangles are congruent, meaning that AB = AC, and triangle ABC is isosceles.

Explanation:

To prove that triangle ABC is isosceles, we can use the fact that the altitudes from vertex B and C intersect at point M and BM = CM.

When the altitudes from vertex B and C intersect at point M, it creates two right triangles, ΔBMC and ΔBMA.

Since BM = CM and the two triangles share the side BM, we can conclude that ΔBMC and ΔBMA are congruent by Side-Side-Side Congruence (SSS).

Therefore, the corresponding angles and sides of the two triangles are congruent, meaning that AB = AC, and triangle ABC is isosceles.

[tex]\frac{41}{24}[/tex] and - [tex]\frac{2}{3}[/tex]

calculate the slope m using the gradient formula

m = ( y₂ - y₁ )/ (x₂ - x₁ )

with (x₁, y₁ ) = (12, 1 ) and (x₂, y₂ ) = (36, 42 )

m = [tex]\frac{42-1}{36-12}[/tex] = [tex]\frac{41}{24}[/tex]

repeat with (x₁ y₁ ) = (- 1, - 8 ) and (x₂, y₂ ) = (- 7, - 4 )

m = [tex]\frac{-4+8}{-7+1}[/tex] = [tex]\frac{4}{-6}[/tex] = - [tex]\frac{2}{3}[/tex]

The slope of a line passing through the points (1, 0.1) and (7, 26.8) is found by subtracting the y-coordinates and the x-coordinates and then dividing the former by the latter, resulting in a slope of approximately 4.45, which is option 'b'.

To find the slope of a line passing through two points, you use the formula: slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Lets calculate the slope for the points (1, 0.1) and (7, 26.8).

The slope of a line passing through these two points is therefore approximately 4.45, which matches option b.

You can start with the 2-point form of the equation for a line:

... y = (y₂ -y₁)/(x₂ -x₁)·(x -x₁) +y₁

Filling in the given values, you get

... y = (0 -7.5)/(-1 -2)·(x -(-1)) +0

... y = 2.5(x +1) . . . . . simplify a bit

... y = 2.5x +2.5 . . . . slope-intercept form

First you find the slope with the 2 points: (2, 7.5) and (-1, 0)

y1-y2/x1-x2 so  7.5-0/2-(-1) which equals 2.5

Next you solve the slope intercept form equation to get b

y=m*x+b (m is the slope and b is the intercept)

7.5=2.5*2+b

b=2.5

So the equation is y=2.5x+2.5

height = 15 cm

the volume (V) of a cylindrical can is

V = πr²h ( r is the radius and h the height )

here d = 8 cm ⇒ r = 4 cm

π × 4² × h = 753.6

16πh = 753.6 ( divide both sides by 16π )

h = 753.6 / 16π = 14.99 ≈ 15 cm

Solution: The given random experiment follows Binomial distribution with [tex]n=10,p=0.44[/tex]

Let [tex]X[/tex] be the number of adults who use their smartphones in meetings or classes.

Therefore, we have to find:

[tex]P(X<3)[/tex]

We know the binomial model is:

[tex]P(X=x)=\binom{n}{x} p^{x} (1-p)^{n-x}[/tex]

[tex]\therefore P(X<3) = P(X=0)+P(X=1) +P(X=2)[/tex]

                       [tex]=\binom{10}{0}0.44^{0}(1-0.44)^{12-0}+\binom{10}{1}0.44^{1}(1-0.44)^{10-1}+\binom{10}{2}0.44^{2}(1-0.44)^{10-2}[/tex]

                       [tex]=1 \times 1 \times 0.0030 + 10 \times 0.44 \times 0.0054 + 45 \times 0.1936 \times 0.009672[/tex]

                       [tex]=0.0030+0.0238+0.0843[/tex]

                       [tex]=0.1111[/tex]

Therefore, the probability that fewer than 3 of them is 0.1111

1.) Translation to the right increases the x-coordinate value.

... (x+10, y)

2.) Translation up increases the y-coordinate value.

... (x, y+10)

100

let the number of football cards be x then she has 5x baseball cards

the total cards she has is 120, hence

x + 5x = 120

6x = 120 ( divide both sides by 6 )

x = 20

Allison has 20 football cards and 5 × 20 = 100 baseball cards

b=baseball cards

f=football cards

b=5f    she has 5 times as many baseball cards as football cards so we multiply the football cards by 5 to make them equal

b+f=120   there are 120 football and baseball cards total

5f+f = 120  substitute 5f everywhere you see a b

6f = 120  combine like terms

f=20  divide by 6

there are 20 football cards

b=5f

b=5(20)

there are 100 baseball cards

Answer:

C.No because two of the y values are the same

Step-by-step explanation:

Answer: A. No, because one x-value corresponds to two different y-values.

Step-by-step explanation:

We take input variable as 'x' and output variable as 'y'.

In the given table, it can be seen that one input value corresponds to two two different output values.

i.e. 8 is the input value corresponding to 5 and 8 both.

It  contradicts the definition of the function.

Hence, the given table doesn't represent any function.

The require line is passing through the points [tex](-6,-5)[/tex] and [tex](-4,-3)[/tex].

We can use the following formula to find the equation of the line passing through a pair of points:

[tex]y-y_1=m(x-x_1)[/tex] .................equation (1)

Where 'm' is slope of the line which is defined as:

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

Now, lets say point [tex](x_1, y_1)[/tex] is [tex](-6,-5)[/tex] and point [tex](x_2,y_2)[/tex] is [tex](-4,-3)[/tex].

We will calculate the slope of the line now:

[tex]m=\frac{-3-(-5)}{-4-(-6)} =\frac{-3+5}{-4+6} =\frac{2}{2} =1[/tex]

So, the slope of the required line is 1.

Now, plugging the value of the slope in equation 1, we get:

[tex]y-(-5)=1(x-(-6))[/tex]

[tex]y+5=x+6[/tex]

[tex]y=x+6-5[/tex]

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

Therefore, the equation of the line passing through the points [tex](-6,-5)[/tex] and [tex](-4,-3)[/tex] is [tex]y=x+1[/tex].

To verify if the equation of line is correct or not, you can plug in any of the points in the equation and compare both the sides:

Lets plug in  (-6,-5) in the equation:

[tex]-5=-6+1=-5[/tex]

Hence, the equation of the line is correct.

Answer:

(a) 1825 = 2.25x + (2.25-1)(x -108)

(b) 560 mi/h

Step-by-step explanation:

(a) distance = speed·time

The first plane's speed is x. The distance it travels in 2.25 hours is 2.25x.

The second plane's speed is x-108. It travels only 1.25 hours (since it started an hour later). The distance it travels is then (2.25 -1)(x -108).

The problem statement tells us the total of the distances traveled by the two planes is 1825 miles, so we can write the equation ...

... 1825 = 2.25x + (2.25 -1)(x -108)

(b) Simplifying the equation gives ...

... 1825 = 3.50x -135

To solve this 2-step equation, we add 135, then divide by 3.50.

.. 1960 = 3.50x

... 1960/3.50 = x = 560

The first airplane's speed is 560 mph.

Check

In 2.25 hours, the first plane travels (560 mi/h)·(2.25 h) = 1260 mi.

In 1.25 hours, the second plane travels (452 mi/h)·(1.25 h) = 565 mi.

Then 2.25 hours after the first plane leaves, the planes are 1260 +565 = 1825 miles apart, as given in the problem statement.

The first plane's average rate is 560 mph. The equation that can be used to solve this problem is 2.25x + 1.25(x - 108) = 1825

To solve this problem, we need to set up an equation based on the information given.

Simplifying the equation gives us:

2.25x + 1.25x - 135 = 1825

3.5x - 135 = 1825

Adding 135 to both sides:

3.5x = 1960

Dividing by 3.5:

x = 560

Therefore, the first plane's average rate was 560 mph.

Let us assume Doreen rate = x miles per hour.

Sue travels 19 miles per hour faster than Doreen.

Therefore,

Rate of Sue = (x+19) miles per hour.

We know time, rate and distance relation as

Time = Distance / rate.

Therefore, time taken by Doreen to travel  42 miles at the rate x miles per hour =

[tex]\frac{42}{x}[/tex].

And time taken by Sue to travel  100 miles at the rate (x+19) miles per hour =

[tex]\frac{100}{(x+19)}[/tex].

Sue takes 3 hours less time than it takes Doreen.

Therefore,

[tex]\frac{42}{x}-\frac{100}{(x+19)}=3[/tex]

We need to solve the equatuion for x now.

[tex]\frac{42}{x}-\frac{100}{\left(x+19\right)}=3[/tex]

[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x,\:x+19:\quad x\left(x+19\right)[/tex]

[tex]\mathrm{Multiply\:by\:LCM=}x\left(x+19\right)[/tex]

[tex]\frac{42}{x}x\left(x+19\right)-\frac{100}{x+19}x\left(x+19\right)=3x\left(x+19\right)[/tex]

[tex]42\left(x+19\right)-100x=3x\left(x+19\right)[/tex]

[tex]-58x+798=3x^2+57x[/tex]

[tex]3x^2+57x=-58x+798[/tex]

[tex]3x^2+57x-798=-58x+798-798[/tex]

[tex]3x^2+57x-798=-58x[/tex]

[tex]\mathrm{Add\:}58x\mathrm{\:to\:both\:sides}[/tex]

[tex]3x^2+57x-798+58x=-58x+58x[/tex]

[tex]3x^2+115x-798=0[/tex]

[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}[/tex]

[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-115+\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad 6[/tex]

[tex]x=\frac{-115-\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad -\frac{133}{3}[/tex]

[tex]x=6,\:x=-\frac{133}{3}[/tex]

We can't take rates as negative numbers.

So, the rate of Doreen (x) = 6 miles per hour.

Rate of Sue = x+19 = 6+19 = 25 miles per hour.

Time taken by Doreen @ 6 miles per hour to cover 42 miles = 42/6 = 7 hours.

Time taken by Sue @ the rate 25 miles per hour to cover 100 miles = 100/25 = 4 hours.

For this case we have the following equation:

[tex]y + 6 = -3y + 26[/tex]

To clear the value of and we have the following steps:

1st step:

We subtract 6 on both sides of the equation:

[tex]y + 6-6 = -3y + 26-6\\y = -3y + 20[/tex]

2nd step:

We subtract "y" from both sides of the equation:

[tex]y-y = -3y-y + 20\\0 = -4y + 20[/tex]

3rd step:

We add [tex]4y[/tex] to both sides of the equation:

[tex]0 + 4y = -4y + 4y + 20\\4y = 20[/tex]

4th step:

We divide between 4 sides of the equation:

[tex]\frac{4y}{4}=\frac{20}{4}\\y = 5[/tex]

Thus, the value of y is 5.

Answer:

[tex]y = 5[/tex]

Option C

Answer:

Step-by-step explanation:

5

[tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]

solve cosx = 0

x = [tex]cos^{-1}[/tex](0) = [tex]\frac{\pi }{2}[/tex], [tex]\frac{3\pi }{2}[/tex]

The solutions to the trigonometric equation: 0.5π radians, 1.5π radians.

In this question we find the case of a trigonometric equation whose solution must be found:

cos (2π · x / T) = 0

Solution:

2π · x / T = cos⁻¹ 0

2π · x / T = 0.5π + i · π, where i is an integer.

2π · x = π · T · (0.5 + i)

[tex]x = \frac{T\cdot (0.5 + i)}{2}[/tex]

Where T is the period of the trigonometric equation.

If we know that T = 2π, then the solutions to the trigonometric equations are:

x = π · (0.5 + i)

x₁ = 0.5π, x₂ = 1.5π

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When solving a problem like this you will need to break down the equation. The answer is actually really simple and easy.

For Kim's age we will use X as the variable. For her sister we will use Y.

y*3=x  and   X+Y=40 and that will get us our answer.

Now we are going to break it down. Kim is three times the age of her sister. So what number under 40 can be evenly distributed into 3 parts since we need to find a number three times greater than another number that can be added one time to itself to equal 40.

The answer to that question would be x=10.

Which means her younger sister is going to be 10

So taking that and plugging it into our equation we will get the following;

10*3(y*3) = (x)30

Which now means Kim's age is 30.

Now we check to make sure. Does 30 + 10 = 40? If so then that's your answer explained and in depth.

Try this option:

According to the properties of the quadratic equation the sum of its roots is '-b', in other words x₁+x₂= -b

Answer: -b

if we were to use the quadratic formula, we would get that the roots are

[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

or that the 2 seperate roots are

[tex]\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

if we sum these, then the [tex]\sqrt{b^2-4ac}[/tex] bits will cancel and we wil be left with

[tex]\frac{-b-b}{2a}[/tex] or [tex]\frac{-2b}{2a}[/tex] or [tex]\frac{-b}{a}[/tex]

the sum of the solutions is [tex]\frac{-b}{a}[/tex]

Answer:

D. 36

Step-by-step explanation:

The square of half the x-coefficient must be added. That value is (12/2)² = 36.

_____

You're trying to create a trinomial of the form ...

... (a + b)² = a² +2ab +b²

where a = x, and 2b = 12.

The number you need to add is b² = (2b/2)² = (12/2)² = 36.

Answer:

D. 36 is the answer .. (ap ex)

Step-by-step explanation:

I would say K and M

By eye this looks like the line would pass through points with approximately an equal amount of points above and below the line of best fit

K and M are  pair of points which should be used to find the line of best-fit for the scatterplot, option d is correct.

To choose the pair of points that should be used to find the line of best fit, we look for two points on the scatterplot that are representative of the general trend and capture the spread of the data.

The pair of points K and M should be used.

By selecting these two points, we can establish a line that best approximates the overall relationship between the variables.

These points are typically chosen from the extremes of the scatterplot or from points that are evenly distributed across the range of the data. Choosing K and M allows us to incorporate a range of data points, providing a more accurate representation of the overall trend.

By using these two points, we can calculate the slope and intercept of the line of best fit using various regression techniques, such as linear regression.

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