What is the exact value of cos 45º ?
Enter your answer, as a simplified fraction, in the box.

A

Step-by-step explanation:

A is a midpoint and so is O, giving reason to why the distances are the same

Answer:

The bird is approximately 9 ft high up in the tree

Explanation:

The required diagram is shown in the attached image

Note that the tree, the cat and the ground form a right-angled triangle

Therefore, we can apply special trigonometric functions

These functions are as follows:

[tex]sin(\alpha)=\frac{opposite}{hypotenuse} \\ \\ cos(\alpha)=\frac{adjacent}{hypotenuse} \\ \\tan(\alpha)=\frac{opposite}{adjacent}[/tex]

Now, taking a look at our diagram, we can note the following:

α = 25°

The opposite side is the required height (x)

The adjacent side is the distance between the cat and the tree = 20 ft

Therefore, we can use the tan function

This is done as follows:

[tex]tan(\alpha)=\frac{opposite}{adjacent}\\ \\ tan(25)=\frac{x}{20}\\ \\x=20tan(25) = 9. 32 ft[/tex] which is 9 ft approximated to the nearest ft

Hope this helps :)

Answer:

D

Step-by-step explanation:

The n th term ( explicit formula ) of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

The recursive formula allows us to find the next term from the previous term by adding d to it

Given

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 ⇒ d = - 3

Hence

[tex]a_{n}[/tex] = 9 + (n - 1)(- 3) ← explicit formula → D

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The general formula is a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The general formula for an arithmetic sequence is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.

For example, in the given sequence 1, 3, 5, 7, 9, the first term a1 is 1, and the common difference d is 2. Using the formula, we can find the nth term by replacing n with the position of the term we want to find. For instance, to find the 5th term, we substitute n = 5:

a5 = 1 + (5-1)2 = 1 + 8 = 9

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Answer:

(x - 3)(4x² + 6x + 9)

Step-by-step explanation:

This is a difference of cubes which factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

8x³ = (2x)³ ⇒ a = 2x

27 = 3³ ⇒ b = 3

Hence

8x³ - 27

= (2x)³ - 3³

= (2x - 3)( (2x)² + (2x × 3) + 3²)

= (2x - 3)(4x² + 6x + 9)

Answer: W = 700 divided by a+18

Step-by-step explanation:

a) We can plug in $358 into A(w), since A(w) represents the amount of money Dale needs. So,

358 = 700 - 18w

Subtract: -342 = -18w

Divide: w = 19 weeks

b) We can plug in 6 into w, since w represents the number of weeks Dale saves money. So,

A(w) = 700 - 18(6)

Multiply: A(w) = 700 - 108

Subtract: A(w) = $592

Answer:

(3a-1)(3a+1)

Step-by-step explanation:

We can quickly see with this problem that it is the difference of two squares as 9a^2 is (3a)^2 and 1 is 1^2 and therefore can factorise quickly using this rule.

x^2-y^2 = (x-y)(x+y) where x = 3a and y = 1

ANSWER

[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]

EXPLANATION

We want to simplify completely:

[tex]9 {a}^{2} - 1[/tex]

We express the two terms as difference of two squares;

[tex] {(3 {a})^{2} } - {1}^{2} [/tex]

Recall and apply the following identity;

[tex]{x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

We apply this identity to obtain:

[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x^2+y^2=16&(1)\\y+4=x^2&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\(y+4)+y^2=16\\y^2+y+4=16\qquad\text{subtract 16 from both sides}\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\iff y+4=0\ \vee\ y-3=0\\\\y+4=0\qquad\text{subtract 4 from both sides}\\\boxed{y=-4}\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}[/tex]

[tex]\text{Put the values of y to (2)}:\\\\\text{for}\ y=-4\\x^2=-4+4\\x^2=0\to x=\sqrt0\to\boxed{x=0}\\\\\text{for}\ y=3\\x^2=3+4\\x^2=7\to x=\pm\sqrt{7}\\\boxed{x=-\sqrt7\approx-2.65}\ \vee\ \boxed{x=\sqrt7\approx2.65}[/tex]

Answer:

out of the 4 people who had a sister, 2 also had a brother

Step-by-step explanation:

a pex

The P(B| A) = 0.50 mean in terms of the Venn diagram is of the 4 people who have a brother, 2 of them also have a sister.

Experimental probability is a probability that is determined on the basis of a series of experiments.

Events are defined as follows.

Event A: The selected person has a sister

Event B: The selected person has a brother

The conditional probability of A given B is the probability that the selected person also has a sister since he has a brother.

[tex]\rm P(A|B)=\dfrac{P(A\ and \ B)}{P(B)}[/tex]

P(B) is the probability that the selected person has a brother. Notice that there are 4 people who have a brother.

P(A and B) is the probability that the selected person has a brother and also a sister. Notice that there are 2 people who have a brother and a sister.

So P(A| B) = 0.5 means that of the 4 people who have a brother, 2 of them also have a sister.

Hence, the P(B| A) = 0.50 mean in terms of the Venn diagram is of the 4 people who have a brother, 2 of them also have a sister.

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Answer:

The slope is 7/8

Step-by-step explanation:

Use the equation: (Y2 - Y1) / (X2 - X1)

[3 - (-4)] / [4 - (-4) = 7/8

The slope is 7/8

it's important that you should remember this formula, so you know the slope of the line:

slope formula: [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

usually i would label the points, like the picture shown below

then, you plug in the points into the equation:

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

m = [tex]\frac{7}{8}[/tex]

hope this helps!

The mean, or average, of the data set is 3 defective toys per sample group. Therefore set 0.3 and 0.5 are the most accurate representations.

Option C) 0.3

Answer:

80%

Step-by-step explanation:

(54-30)/30 *100 = 80%

Answer:

4.8 hr, or 4 hr 48 min

Step-by-step explanation:

Let '1' represent 'the whole house-painting job.'

Then perform a dimensional analysis:

    1 whole house job

 -------------------------------- = 12 hours.   →This restates the obvious:  Jim can

          1 job/ 12 hrs                                     paint a house in 12 hours.

Now if both people work together, the total time required to paint the house is:

              1 house job                         1 house job

-----------------------------------------  =  ------------------------------  =  t for whole job

         1 job               1 job               8 job-hr + 12 job-hr        with both people

      ------------    +    ------------          -----------------------------       working

      12 hours           8 hours                        96 hr

This turns out to be:

              1

--------------------------  =  96/20 hr  = 4.8 hr, or 4 hr 48 min

      20/96

It would take Jim and Alex 4.8 hours to paint the house together if they both work at their individual rates.

Now, Let's start by finding the individual rates of Jim and Alex in terms of the fraction of the house they can paint per hour.

Jim can paint a house in 12 hours, so his rate is 1/12 of the house per hour.

Similarly, Alex can paint the same house in 8 hours, so his rate is 1/8 of the house per hour.

Now, let's suppose they work together for t hours to complete the job.

During this time, Jim will be able to paint t/12 of the house and Alex will be able to paint t/8 of the house.

The sum of their individual rates is equal to the combined rate at which they can paint the house together.

So we can set up the following equation:

t/12 + t/8 = 1

Solving for t, we get:

t = 4.8 hours

Therefore, it would take Jim and Alex 4.8 hours to paint the house together if they both work at their individual rates.

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Answer:

Perimeter of triangle JKL: [tex]2 \sqrt{17} + 2\sqrt{34}[/tex].

Area of triangle JKL: 17.

Step-by-step explanation:

None of the three sides of triangle JKL is parallel to either the x-axis or the y-axis. Apply the Pythagorean Theorem to find the length of each side.

[tex]\rm JK = \sqrt{(3 - (-5))^{2} + (4- 6)^{2}} = \sqrt{8^{2} + (-2)^{2}} = \sqrt{68} = 2\sqrt{17}[/tex].

[tex]\rm JL = \sqrt{(-2 - (-5))^{2} + (1- 6)^{2}} = \sqrt{3^{2} + (-5)^{2}} = \sqrt{34}[/tex].

[tex]\rm KL = \sqrt{(-2 - 3)^{2} + (1-4)^{2}} = \sqrt{(-5)^{2} + (-3)^{2}} = \sqrt{34}[/tex].

The perimeter of triangle JKL will be:

[tex]\rm JK + JL + KL = 2\sqrt{17} + \sqrt{34} + \sqrt{34} = 2 \sqrt{17} + 2\sqrt{34}[/tex].

In case you realized that [tex]\rm JK : JL : KL = \sqrt{2} : 1 : 1[/tex], which makes JKL an isosceles right triangle:

Area of a right triangle:

[tex]\begin{aligned}\displaystyle \rm Area &= \frac{1}{2} \times \text{First Leg} \times \text{Second Leg}\\ &=\frac{1}{2} \times \sqrt{34}\times\sqrt{34}\\&= 17\end{aligned}[/tex].

Alternatively, apply the Law of Cosines to find the cosine of any of the three internal angles. This method works even if the triangle does not contain a right angle.

Taking the cosine of angle K as an example:

[tex]\displaystyle\begin{aligned}\rm \cos{K}&=\frac{(\text{First Adjacent Side})^{2} + (\text{Second Adjacent Side})^{2}-(\text{Opposite Side})^{2}}{2\times (\text{First Adjacent Side})\times(\text{Second Adjacent Side})}\\&\rm =\frac{(JK)^{2} + (JL)^{2} -(KL)^{2}}{2\times JK \times JL}\\&=\frac{(2\sqrt{17})^{2}+(\sqrt{34})^{2}-(\sqrt{34})^{2}}{2\times\sqrt{34} \times(2\sqrt{17})}\\ &=\frac{2^{2}\times 17}{2\times \sqrt{2}\times\sqrt{17}\times 2\times \sqrt{17}}\\&=\frac{1}{\sqrt{2}}\end{aligned}[/tex].

Apply the Pythagorean Theorem to find the sine of angle K:

[tex]\displaystyle \rm \sin{K} = \sqrt{1 - (\cos{K})^{2}} = \sqrt{1 - \left(\frac{1}{\sqrt{2}}\right)^{2} } = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}[/tex].

The height of JKL on the side JK will be:

[tex]\displaystyle \rm KL \cdot \sin{K} = \sqrt{34} \times \frac{\sqrt{2}}{2} = \frac{\sqrt{68}}{2} = \frac{2\sqrt{17}}{2} = \sqrt{17}[/tex].

What will be the area of JKL given its height [tex]\sqrt{17}[/tex] on a base of length [tex]2\sqrt{17}[/tex]?

[tex]\displaystyle \rm Area = \frac{1}{2} \times Base\times Height = \frac{1}{2}\times (2\sqrt{17})\times \sqrt{17} = 17[/tex].

if segments OX = OC and perpendicular to those chords, then AB = YZ, the chords are also equal.

Answer:

[tex]9y^2-4x^2-36y+16x-16=0[/tex]

Step-by-step explanation:

The given hyperbola has equation:

[tex]\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1[/tex]

We multiply through by 36 to get:

[tex]9(y-2)^2-4(x-2)^2=36[/tex]

We expand to get:

[tex]9(y^2-4y+4)-4(x^2-4x+4)=36[/tex]

[tex]9y^2-36y+36-4x^2+16x-16=36[/tex]

[tex]9y^2-36y-4x^2+16x-16=0[/tex]

The equation of the hyperbola in general form is:

[tex]9y^2-4x^2-36y+16x-16=0[/tex]

Answer:

If you're asking for the formula to find the area of a triangle, its:

1/2bh

b = base

h = height

there are two pieces, both divided in 10 equal segments.

so each piece is 10/10, or namely 1 whole.

two pieces, 10/10 each, is 20/10 for the whole thing, but there are only 11 shaded, so if we take 20 to be the 100%, what is 11 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 20&100\\ 11&x \end{array}\implies \cfrac{20}{11}=\cfrac{100}{x}\implies 20x=1100\\\\\\ x=\cfrac{1100}{20}\implies x=55[/tex]

He can fit 4 boxes along the wall

Answer:

No solution

Step-by-step explanation:

Rearrange into quadratic form: 3x² + 0x - 3 = 0

Quadratic formula: when ax² + bx + c = 0: x = (-b ± √(b² - 4ac))/2a

Plug in: x = 0 ± √(0 - 4*3*3))/2a

From this, we can conclude that this equation has no solution, as 0 - 4*3*3 will definitely be negative, and a negative number can not be square rooted.

Answer:

maybe you add then all up

A would be your best option. Choice A properly displays the equation, 5x+6=4x+(-3), using words. Let me know if you want an explanation of why the other options are invalid. :)

Answer:

A is correct.

Step-by-step explanation:

Which is the correct way to model the equation 5x+6=4x+(-3) using algebra tiles?  

5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side.

5 positive x-tiles = 5x

6 positive unit tiles = 6

4 positive x-tiles = 4x

3 negative unit tiles = -3

-----------------------------------------------------------------------

B - There are 5 x tiles but its given 6 x tiles.

C  - There is 6 positive unit tile and its given 6 negative,

D - There is 3 negative unit tile but here its given positive.

Answer:

D. 12

Step-by-step explanation:

Answer:

D 12

Step-by-step explanation:

8h > 64

Divide each side by 8

8h/8 > 64/8

h > 8

H must be greater than 8

The only value in your list greater than 8 is 12

Answer:

[tex]y=\tan \frac{1}{2} \pi[/tex]

Step-by-step explanation:

The given graph has a period of [tex]2\pi[/tex], because the graph repeats after every [tex]2\pi[/tex] units.

The formula for finding the period of a tangent function is

[tex]T=\frac{\pi}{b}[/tex]

We substitute the period to get;

[tex]2\pi=\frac{\pi}{b}[/tex]

This implies that;

[tex]b=\frac{\pi}{2\pi}[/tex]

Therefore[tex]b=\frac{1}{2}[/tex]

Hence the function represented by the graph is

[tex]y=\tan \frac{1}{2} \pi[/tex]

Answer:

2

Step-by-step explanation:

Given Data:

total distance= 850 miles

gas tank holds gas= 15 gallons

mileage = 72/3.2 miles/gallon

if

72 miles uses= 3.2 gallon

then

850 miles uses= x gallons

by cross-multiplication we get

72x=3.2(850)

x=37.778

i.e. 850 miles will use 37.7778 gallon of gas

Asgas tank holds 15 gallons

number of times gas tank is used up= 37.3/15

                                                            = 2.518

rounding off

number of times gas tank is used up=3

As they filled the gas tank at the start of the road trip, hence 3-1=2

ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION =2 !

Let's call trade balance b, exports e and imports i.

We now construct formula.

[tex]b=\Delta{ei}=e-i[/tex]

Put in the data from last year.

[tex]b=968-1658=\boxed{-690}[/tex]

U.S trade balance for that year is -690 billion dollars.

The answer is:

Answer: 34

Units: Joules

[tex]KE=34J[/tex]

The kinetic energy is the work needed to accelerate an object to a determined speed.

The kinetic energy can be calculated using the following equation:

[tex]KE=\frac{1}{2}mv^{2}[/tex]

Where,

m, is the mass of the object.

v, is the speed of the object.

So, we are given the information:

[tex]mass=17kg\\\\v=\frac{2m}{s}[/tex]

Then, substituting and calculating we have:

[tex]KE=\frac{1}{2}mv^{2}[/tex]

[tex]KE=\frac{1}{2}*17kg*(\frac{2m}{s})^{2}[/tex]

[tex]KE=8.5kg*(\frac{4m^{2}}{s^{2}})[/tex]

[tex]KE=34\frac{kg.m^{2}}{s^{2}}=34J[/tex]

Have a nice day!

Answer:

16 and 46

Step-by-step explanation:

Lowest number = left of the number line

1 , 2 , 3 , 4 , 5 , 6 , 7

Answer:

Step-by-step explanation:

a) 17 is further to the left on the number line than 305.

b) 187  .... than 900.

c) 16  ... than 46.

d) 149,984 is further to the left than 157,019.

Answer:

see explanation

Step-by-step explanation:

The length of the arc is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{90}{360}[/tex] ← r = 1

      = 2π × [tex]\frac{1}{4}[/tex] = [tex]\frac{\pi }{2}[/tex] ≈ [tex]\frac{3.14}{2}[/tex] = 1.57

Answer:

D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

The line gets smaller left to right so that means the line is negative. Since the line is negative x must be negative. The line is also touching the y-axis at 6. We are going to use the formula y=mx+b. So our equation is going to be y=6-x.