Mr. Hayes has 111 straw bundles to use for bedding in his horse stalls.What is the greatest number of stalls he can fill if each stall holds exactly 4 bundles of straw?

We have

v = (-7, 9) - (4, 3) = (-7 - 4, 9 - 3) = (-11, 6)

which as a linear combination of the i and j unit vectors is

v = -11i + 6j

Answer:

Step-by-step explanation:

Answer:

[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]

Step-by-step explanation:

1. Approach

One is given the following information:

[tex]cos(2\theta)=-\frac{2}{5}[/tex]

One can rewrite this as:

[tex]cos(2\theta)=-0.4[/tex]

Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.

Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]).  Substitute the given information into the ratio and simplify.

2. Solve for [tex](cos(\theta))[/tex]

Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).

[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]

Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).

[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]

[tex]-0.4=2(cos^2(\theta))-1[/tex]

Inverse operations,

[tex]-0.4=2(cos^2(\theta))-1[/tex]

[tex]0.6=2(cos^2(\theta))[/tex]

[tex]0.3=cos^2(\theta)[/tex]

[tex]\sqrt{0.3}=cos(\theta)[/tex]

Since this angle is found in the third quadrant its value is actually:

[tex]cos(\theta)=-\sqrt{0.3}[/tex]

3. Solve for [tex](sin(\theta))[/tex]

Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).

[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]

Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).

[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]

[tex]-0.4=1-2(sin^2(\theta))[/tex]

Inverse operations,

[tex]-0.4=1-2(sin^2(\theta))[/tex]

[tex]-1.4=-2(sin^2(\theta))[/tex]

[tex]0.7=sin^2(\theta)[/tex]

[tex]\sqrt{0.7}=sin(\theta)[/tex]

Since this angle is found in the third quadrant, its value is actually:

[tex]sin(\theta)=-\sqrt{0.7}[/tex]

4. Solve for [tex](tan(\theta))[/tex]

One can use the following identity to solve for [tex](tan(\theta))[/tex];

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

Substitute the values on just solved for and simplify,

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]

Rationalize the denominator,

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]

[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]

[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]

[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]

Answer:

[tex]y = - 2x - 4[/tex]

Step-by-step explanation:

Slope intercept eqn:

[tex]y - y1 = m(x - x1)[/tex]

P = (-4,4) and Q = (-3,2)

Let (x1, y1) = (-4,4) and (x2, y2) = (-3,2).

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{ 2 - 4}{ - 3 - ( - 4)} = \frac{ - 2}{1} = - 2[/tex]

Therefore the equation of the line in slope-intercept form :

[tex]y - 4 = - 2(x - ( - 4)) \\ y - 4 = - 2(x + 4) \\ y - 4 = - 2x - 8 \\ y = - 2x - 8 + 4 \\ y = - 2x - 4[/tex]

Step-by-step explanation:

square cube 214

I think this was your answer

Answer:

1,100

Step-by-step explanation:

200 + 200 + 200 + 200 + 100 + 200

Total amount after rounding off will be : 900

Rounding off a number to the nearest hundred means that you have to look or find the hundred which is closest to the given number and then write that as   the rounded-off number .

Rounding off each number in the table to the nearest hundred :

1) 223  ( since , we have 223 and 223 < 250 . Since, 223 is closest to 200 as compared to 300 , after rounding it off we will get 200 instead of choosing 300) = 200

2) 189 =200

3) 210 = 200

4) 164 = 200

5) 148 = 100

6) 206 = 200

Total amount after rounding of numbers will be = 200 + 200 + 200 + 100 + 200

                                                                = 900

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The range of the function  g(x) = |x + 2|– 1 is (-1,∞) and domain of the function is (-∞,∞).

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Given the function  g(x) = |x + 2|– 1

The minimum value of the function

At x = -2 ⇒ |-2+ 2|– 1 = -1

The maximum value of the function

At x = ∞ ⇒ |∞+ 2|– 1 = ∞

So,

The range will be (-1, ∞)

Now,

We can put x as -∞ and ∞ so the domain will be (-∞,∞).

Hence "The range of the function  g(x) = |x + 2|– 1 is (-1,∞) and domain of the function is (-∞,∞)".

For more details about the range and domain of the function,

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Answer:50 degree

Step-by-step explanation:

It is an isosceles triangle so two sides and angles are equal. The first line is facing the first angle so the second angle ( m<DEF) = 65 degrees because both angles are equal.

This implies that m<FED =

65 + 65+ <FED= 180( sum of angle in a triangle)

130 + <FED=180

<FED= 180- 130

<FED= 50 degree

Answer:

"How many times does 81 divide into 547?"

Answer:

119.93

Step-by-step explanation:

I will assume the total of the cost of the movies will be the total.

the total  = 4*14.99 + 3*19.99

total = 119.93

Answer:

The choose C.3√34

Step-by-step explanation:

15²+9²=c²

225+81=c²

306=c²

C= 3√34

I hope I helped you^_^

Let numbers be x and 2x

ATQ

[tex]\\ \rm\longmapsto \dfrac{x+7}{2x+7}=\dfrac{3}{5}[/tex]

[tex]\\ \rm\longmapsto 5(x+7)=3(2x+7)[/tex]

[tex]\\ \rm\longmapsto 5x+35=6x+21[/tex]

[tex]\\ \rm\longmapsto 6x-5x=35-21[/tex]

[tex]\\ \rm\longmapsto x=14[/tex]

Expression represent the area of the sandbox is a² + 3a

GIven that;

Length of sandbox is three feet longer than its width

Find:

Expression represent the area of the sandbox

Computation:

Assume;

Width of sandbox = a feet

So,

Length of sandbox = (a + 3) feet

[tex]Area\ of\ rectangle = Length \times Width[/tex]

So,

Area of the sandbox = Length of sandbox × Width of sandbox

Area of the sandbox = (a + 3) × a

Area of the sandbox = a² + 3a

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Answer:

your answer is 24 in

I hope it's helps you

The length of the diagonal is 24 inches

From the given diagram, the length of the diagonal is twice the length EA

Mathematically;

EH = 2EA

Given the parameter:

EA = 12in

EH = 2(12)

EH = 24 in

Hence the length of the diagonal is 24 inches

Laern more on rectangle here: https://brainly.com/question/24438517

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 5y = - 10 ( subtract 2x from both sides )

5y = - 2x - 10 ( divide the terms by 5 )

y = - [tex]\frac{2}{5}[/tex] x - 2 ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex] and y- intercept c = - 2

Answer:

m = (3/4) n

Step-by-step explanation:

4m + 2n = 5n

The subtraction property of equality states that we can subtract 2n from both sides to isolate the m and its coefficient to get

4m = 3n

The division property of equality states that we can divide 4 from both sides to isolate only the m (we divide by 4 because anything divided by itself equals 1) to get

m = (3/4) n

Answer:

B

Step-by-step explanation:

look at where the line reaches on the y-axis

Answer:

A radius is a line segment with one endpoint at the center of the circle and the ... is called the midpoint, and arc PQ ≅ arc PR if and only if PQ ≅ PR.

Step-by-step explanation:

brainliest please

Answer:

A radius is a line segment with

Answer:

Step-by-step explanation:

I take it that what you are asking is which one of the three choices gives f(5) = 2.

It is not the table. When you try adding 5 in the x column, you get a much larger result than 2 for y.

And it is not the scattered points of the graph. x = 5 gives 5 on the y axis, not 2.

It is the first choice on the left.

f(5) = x - 3

f(5) = 5 - 3

f(5) = 2

Answer:

Fifteen feet is the closest to the side length of the frame, have a good day

Answer:

B

Step-by-step explanation:

22/7 X 14 squared

--------------------------------  =308

           2

406-308= 98cm ^2

Answer:

the value of X is 3 and y is 6 .

Answer:

not proportional

Step-by-step explanation:

We can check using cross products

18/73  = 4/16

18*16 = 73*4

288=292

Since this is not equal, this is not proportional

Answer:

a point

Step-by-step explanation:

because it really seems like a point I dunno

Answer:

Sorry I don't really understand your question, but 28-19 is 9 therefore 9 is more than 0

9 >0

Answer:

25°

Step-by-step explanation:

20°--5°=

20°+5°=

25°

Answer: fell 25 degrees

Step-by-step explanation: 20-25= -5

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Answer:

[tex] \frac{ - 4 + 4i}{ - 3 - 6i} \\ multiply \: and \: divide \: by \: - 3 + 6i \\ \frac{ - 4 + 4i}{ - 3 - 6i} \times \frac{ - 3 + 6i}{ - 3 + 6i} \\ = \frac{ ( - 4 + 4i)( - 3 + 6i)}{ ( - 3 - 6i)( - 3 + 6i)} \\ = \frac{12 - 24i - 12i + 24 {i}^{2} }{ {( - 3)}^{2} - {(6i)}^{2} } \\ = \frac{12 - 24 - 36i}{9 + 36} \\ = \frac{ - 12 - 36i}{45} \\ \frac{ - 36i}{45} + \frac{ - 12}{45} \\ thank \: you[/tex]