Please help me with this!!!

The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV

we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for  quadrant 2 and 3). Since we know cos² a + sin² a = 1

for α, cos² α + sin² α = 1

=> cos² α = 1 - sin² α

=> cos² α = 1 - 4/25

=> cos α = √21/25

same for β, cos² β + sin² β = 1

=> sin² β = 1 -cos² β

=> sin² β = 1 -1/9

= 8/9

=2√2/3

substituting the known values in the above formula for cos (α+β)

=>cos α cos β - sin α sin β

=√21/25 *1/3- 2/5*2√2/3

=√21/25- 4√2/15

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Answer:

d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]

Step-by-step explanation:

The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!

Have a lovely day!

Answer:

162.006

Step-by-step explanation:

Answer:

it is 18 mile

Step-by-step explanation:

12mile = 60 min

x = 90 min

we cris cross the equation and

we found x=18 mile

The length of the rectangular area is 800 yards and width is 800 yards

The perimeter of the rectangular area = 3200 yards

The perimeter of the rectangle = 2 (l + w)

Then the equation will be

2(l + w) = 3200

l + w = 3200 / 2

l + w = 1600 yards

w = 1600 - l

The area of the rectangular area = l × w

= l(1600 - l)

Since the area is maximizing the the rate of change of area will be zero

l × w = 0

1600 - 2l = 0

2l = 1600

l = 1600/2

l = 800 yards

Then

w = 1600 - l

Substitute the value of l in the equation

w = 1600 - 800

w = 800 yards

Hence, the length of the rectangular area is 800 yards and width is 800 yards

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Answer:

3

Step-by-step explanation:

45*64=2880

48*60=2880

444 students will climb the rock wall.

Given, that A class has 484848 students, one group of 242424 students chooses to play volleyball.

Then the teacher divides the remaining students into as many groups of 555 as possible to shoot baskets.

After that, the remaining students (not on a volleyball or basketball team) climb the rock wall.

Now, we are asked that the students who climb the rock wall

So, from a class of 484848 students if One group of 242424 students is made to play volleyball then there will be 242424 students remaining.

Now, to divide 242424 students into groups of 555 students,

we need to divide 242424 by 555, then we get

242424/555 = 436.8

Now there will be 436 groups of 555 students who will shoot basket and remaining 444 students who will climb the rock wall.

Hence, 444 students will climb the rock wall.

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The number of ways that a nine question true false quiz can be answered is; 512 ways

We are given;

Number of questions = 9

Options for each answer = 2 (True of false)

The power set is defined as the number of subsets of a set of n elements which is expressed as 2ⁿ

There are 2 ways to answer question 1 and as such it means that there are 2 ways to answer question 2.

For question 2; 2² = 4 ways

For question 3; 2³ = 8 ways

For question 4; 2⁴ = 16 ways

For question 5; 2⁵ = 32 ways

For question 6; 2⁶ = 64 ways

For question 7; 2⁷ = 128 ways

For question 8; 2⁸ = 256 ways

For question 9; 2⁹ = 512 ways

Thus we we conclude that, there are 512 ways to answer 9 true-false tests.

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Answer:

32.2222

Step-by-step explanation:

Answer: 32.22 degrees Celsius.

well, we know WXYZ is a kite, so is a quadrilateral, namely it has 4 sides, and it has two congruent angles, so

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 94+94+112+\measuredangle ZYW=360\implies \implies \measuredangle ZYW=60[/tex]

Check the picture below.

The least possible sum wen the integers, a and b, have a product of 20 is 9.

From the information given, two integers, a and b, have a product of 20. It should be noted that the values that an give a product of 20 will be:

1 × 20 = 20

2 × 10 = 20

4 × 5 = 20

Therefore, the sum of the factors will be:

1 + 20 = 21

2 + 10 = 12

4 + 5 = 9

The least possible sum is 9.

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a. Timothy is correct regarding the dilation, considering the vertices of each triangle.

b. The two triangles are similar, as they have congruent angle measures.

A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor.

The effects of a dilation are given as follows:

The vertices of each triangle in this problem are given as follows:

The scale factor is obtained by the division of any of the equivalent factors, hence:

k = 4.5/3 = 1.5.

Confirming that Timothy's statement regarding the scale factor of the dilation is correct.

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Answer:

11

Step-by-step explanation:

Distance formula is square root of (x2-x1)^2+(y2-y1)^2

square root of (6-(-5))^2+(7-7)^2

square root of (11)^2+(0)^2

square root of 121+0

square root of 121

11

distance is 11

Answer:

Yes.

Step-by-step explanation:

To decide if these triangles are similar, we need to check 2 criteria. The first is that the angles are all the same as their corresponding angles on the other triangle, which is true. The second is to check if the sides are all in the same proportional relationship. To do this, we need to put 40/50, 40/50, and 16/20 to see if they simplify to the same fraction (which is the proportion.) 40/50 and 40/50 simplify to the same fraction, 4/5. 16/20 also simplifies to 4/5, so the sides are all in the same proportion, which means the shapes are similar.

In order to find the sum to the indicated accuracy we need to add

5 terms  as the series is said to be convergent.

Given Series is Σ(-1/3)^n / n where error is less than 0.0005

      = Σ (-1)^n / n3^n

For this series, we will use ratio test

if [tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = L < 1 then series in convergent,

Let an = (-1)^n / n3^n ,  an+1 = (-1)^n+1 / (n+1)3^n+1

[tex]\lim_{n \to \infty} |an + 1 / an |[/tex]   =  [tex]\lim_{n \to \infty} | ((-1)^n+1 / (n+1)3^n+1)(n3^n/(-1)^n) |[/tex]

By solving we get,

[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = 1/3 < 1

Then given series is convergent.

By alternating series estimation theorem we have,

|Rn|=|S-Sn| <= an+1

an+1 <= 0.0005

1 / (n+1)3^n+1 <= 0.0005

(n+1)3^n+1 >= 2000

2 * [tex]3^{2}[/tex] >[tex]\neq[/tex] 2000 (n=1)

4 * [tex]3^{4}[/tex] >[tex]\neq[/tex] 2000 (n=3)

6 *  [tex]3^{6}[/tex] >= 200 (n=5)

So required terms is n=5

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Answer:

x-intercept(s): (−5,0)

y-intercept(s): (0,−5)

Explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Im also in K12 so Ez Good Luck

Hope this helped!

The height of the building after using proportion is  110.5 ft.

What is proportion ?

The main conceptual underpinnings on which proportion is described are ratio and fractions. When two ratios are written as a fraction using the formula a/b, ratio a:b, and then a proportion, they are equal. A and b in this situation can be any two integers. For grasping the myriad concepts in science and mathematics, the ratio and proportion are crucial constructing elements. With the right amount of proportion, a variety of problems in daily life, such as those encountered in the kitchen or in business when processing transactions, can be resolved. It facilitates comparison by establishing a relationship between two or more quantities.

Here House height = 13ft

Shadow of the house height = 20 ft

Shadow of the building height = 170ft

Noe using proportion ,

=> [tex]\frac{House height}{shadow of the house} = \frac{building height}{shadow of the building}[/tex]

=> [tex]\frac{13}{20} = \frac{x}{170}[/tex]

=> x=[tex]\frac{13*170}{20}[/tex] =110.5 ft.

Hence the height of the building is 110.5 ft tall.

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The answers are as follows -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given are the following relations -

3y = x

{(2,6),(3,9),(5,15)}

{(1,16),(2,8),(4,4)}

We can write -

x = 3y

as

y = (1/3)x

m = 1/3

Relation 3y=x represents direct variation.

For the relation - {(2,6),(3,9),(5,15)}, we can write -

We can write it as -

y = 3x

Relation {(2,6),(3,9),(5,15)} represents direct variation.

For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.

Therefore -

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Answer:

178 000

Step-by-step explanation:

178 383      8 is in the thousands place...if the number next to it (3) is ≥ 5 round it up by 1   o/w leave it alone

Answer:

178,000

Step-by-step explanation:

It's 178,000 because the number in front of the 8 in 178,383 was under five so the number dropped.

The correct statement regarding the proportional relationship c = 0.8w is given as follows:

The equation c = 0.8w is correctly represented by the graph.

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

When the two variables x and y are direct proportional, the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k, as follows:

y = kx.

In this problem, the equation is given as follows:

c = 0.8w.

In which:

For a input of 2, the output is given as follows:

c = 0.8 x 2 = 1.6.

Hence point (1,0.8) is in the graph, along with point (2,1.6).

The statements are given as follows:

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Yes. The residuals' distribution pattern resembles a haphazard dispersion around the horizontal line at 0.

The horizontal plot in this instance comprises points that are unstructured and randomly dispersed around the horizontal mean line.

These are also points below the mean above the mean. This shows that some points in the distribution of data points are above and some are below the least square line, which crosses through the distribution.

The least-square line model would not produce adequate results if, in a residual plot, the majority of the data points are located roughly in a straight line or on either side of the horizontal line.

A residual plot must have data points randomly distributed on both sides of the horizontal mean line in order to produce good results.

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COMPLETE QUESTION:

if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at 0. is this the case for the residual plot?

The value of x is 10.6 which is equivalent to 11.

In the given triangle

the triangle is divided into two triangles which are both right angled

However in the bigger triangle

we would use the Pythagoras Theorem

( y + 6 )² = x² + 100 ---------- equation 1

In the smaller triangle;

x² = y² + 64 --------------equation 2

Thus substituting the value of x in equation 1

Thus the equation becomes

( y + 6 )² = y² + 64 + 100

y² + 36 + 12x = y² + 164

Cancelling y² on both sides we will get

36 + 12x = 164

12x = 164 - 36

this implies 12 x = 128

x = [tex]\frac{128}{12}[/tex]

x = 10.6 ≈ 11

Thus the required value of x is 10.6 or 11

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Answer:

I believe the answer is number 2, which is 20 degrees.

Step-by-step explanation:

When I plugged that number in for x for both of them I got the numbers 81 and 99. Added them together ad they made 180 degrees. Which makes them supplementary.

(-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

As, we know that the Tangent function is neither an One-One nor Onto function. So, the domain should be restricted to obtain the inverse function of the Tangent function.

Domain of the tangent function be, R - {(2n+1)π/2}

Range of the tangent function be, R

Now, to build the inverse tangent function we have to restrict the domain so that, the function will be one-one and onto both.

So, the restricted domain be (-π/2 , π/2).

In the domain (-π/2 , π/2), the tangent function is one-one and onto both and hence, we can build the inverse tangent function i.e. arctangent.

So, (-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

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Answer:

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

Answer:

3/5

Step-by-step explanation:

Given problem,

→ (1/10) + (1/2)

Let's solve the problem,

→ (1/10) + (1/2)

→ (1/10) + (5/10)

→ 6/10

→ 3/5 {simplest form}

Thus, answer is 3/5.

Answer:

============

Answer:

Range:  [tex]\text{y} \ge 0[/tex]

Domain: [tex]\text{x} \ge 0[/tex]

Both involve "greater than or equal to 0".

==============================================

Explanation:

The domain is the set of allowed inputs (x). The smallest input allowed in this case is x = 0, as it corresponds to the left-most point (0,0) on the blue graph. There is no largest x value since it stretches forever to the right.

Either x = 0 or x > 0 which condenses to [tex]\text{x} \ge 0[/tex] and this is the domain as an inequality.

--------

The range will have us look at the possible y values or possible outputs. We have y = 0 as the smallest output possible, which corresponds to the lowest point (0,0).

There is no largest y value since the blue graph goes forever upward.

Either y = 0 or y > 0 to give us the range of [tex]\text{y} \ge 0[/tex]

Answer:

Slope:   [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The slope-intercept form is y = m x + b , where m is the slope and b is the y-intercept.

The expression given is already in slope intercept form. In this case [tex]m=\frac{1}{2}[/tex]

Therefore the slope is [tex]\frac{1}{2}[/tex]

Answer:

slope = [tex]\frac{1}{2}[/tex]

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 )

y = [tex]\frac{1}{2}[/tex] x + 4 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Answer:

(a-5)(a+4)

Step-by-step explanation:

[tex]a^{2}[/tex]-a-20

[tex]a^{2}[/tex]+4a-5a-20

a(a+4) -5(a+4)

(a-5)(a+4)