Which of the following would be an acceptable first step in simplifying the expression
sinx/1- cosx?

A. sinx - sinx/1- cos x
B. 1/cscx - cosx
C. Cannot be simplified further
D. sin x(1+cosx)/(1-cosx)(1+cosx)

The count of numbers in the list a, a+1, a+2.... b is b - a + 1

The list of numbers is given as:

a, a+1, a+2.... b

From the above list, we can see that the numbers are consecutive numbers.

This means that, the count of numbers in the list is

Count = Highest - Least + 1

Where

Highest = b

Least = a

Substitute the known values in the above equation

Count = b - a + 1

Hence, the count of numbers in the list a, a+1, a+2.... b is b - a + 1

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Answer:

-20

Step-by-step explanation:

Use the distributive property to get [tex]2xy-14[/tex] (you multiply both xy and -7 by 2.) Now plug in the x and y values to get: [tex]2(-1)(3)-14[/tex]. This gets you [tex]-6-14[/tex] which is [tex]-20[/tex].

Answer:

  a. no

  b. yes

  c. yes

  d. no

Step-by-step explanation:

To test a solution, put the values where the variables are, and simplify to the point where you can tell whether the statement is true.

Each ordered pair is (x, y), so the first value gets substituted for x; the second value gets substituted for y.

  11 < 13 -2 = 11 . . . . no

  8 ≤ 16 -3 = 13 . . . . yes

  20 > 18 -4 = 14 . . . . yes

  9 ≥ 15 -5 = 10 . . . . no

Answer:

c subtract 5 from both sides

Answer:

Percent increase is 70%.

Step-by-step explanation:

The original price was $110. That will go on the bottom (denominator) in our calculation. On the top (numerator) we put the change in the dollar amount. The new price is $187. So we'll subtract:

187 - 110

= 77

The change in price was $77.

change/original

= 77/110

= 0.7

Change the decimal answer to a percent by multiplying by 100.

0.7 × 100

= 70%

The percent increase is 70%.

The only ordered pair that is a solution to the given system of equations is (-2, -6)

From the question, we are to determine if each ordered pair is a solution to the given system of equations

The given system of equations is

-9x + 2y = 6

5x - 3y = 8

That is,

x = 7, y = 9

Putting the values into the first equation

Is -9(7) + 2(9) = 6

-63 + 18 = 6

-45 ≠ 6

Thus, (7,9) is not a solution

That is,

x = 0, y = 3

Putting the values into the first equation

Is -9(0) + 2(3) = 6

0 + 6 = 6

6 = 6

The ordered pair satisfies the first equation

Testing for the second equation

Is 5(0) - 3(3) = 8

0 - 9 = 8

-9 ≠ 8

Thus, (0, 3) is not a solution

That is,

x = 5, y = -4

Putting the values into the first equation

Is -9(5) + 2(-4) = 6

-45 - 8 = 6

-53 ≠ 6

Thus, (-5,4) is not a solution

That is,

x = -2, y = -6

Putting the values into the first equation

Is -9(-2) + 2(-6) = 6

18 - 12 = 6

6 = 6

The ordered pair satisfies the first equation

Testing for the second equation

Is 5(-2) -3(-6) = 8

-10 + 18 = 8

8 = 8

The ordered pair satisfies the second equation

∴ The ordered pair that is a solution to the system of equations is (-2, -6)

Hence, the only ordered pair that is a solution to the given system of equations is (-2, -6)

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Answer:

y = [tex]\frac{24}{\sqrt{x} }[/tex]

Step-by-step explanation:

given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is

y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation

to find k use the condition y = 8 when x = 9 , then

8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

24 = k

y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation

Step-by-step explanation:

"congruent" for lines simply means they are equally long.

15. yes. AB = EF = 3

16. yes. BD = DF = 8

17. no. AC = 5, CD = 6

18. yes. AC = DE = 5

19. no. BE = 13, CF = 14

20. no. CD = 6, DF = 8

Answer:

  x-intercept: (4, 0)

  y-intercept: (0, 3)

Step-by-step explanation:

The intercepts of the equation can be found by setting each variable to zero and solving for the other. The graph will be a line through the intercept points.

Setting x=0 and solving for y, we have ...

  4y -12 = 0   ⇒   y = 12/4 = 3

Setting y=0 and solving for x, we have ...

  3x -12 = 0   ⇒   x = 12/3 = 4

The intercepts are ...

  x-intercept: (4, 0)

  y-intercept: (0, 3)

The line will go through these intercept points.

The time at which the break started is 10 : 30 am.

The first step is to convert the time between  10:00 a.m. - 11:15 a.m. to minutes.

The time  between  10:00 a.m. - 11:15 a.m. is 1 hour 15 minutes

In order to convert hours to minutes, multiply hour by 60

1 x 60 = 60 minutes

60 minutes +  15 minutes =  75 minutes

The second step is to subtract the time from the break from the duration of the golf lesson

75 minutes -  15 minutes = 60 minutes

The third step is to divide 60 minutes into equal halves by dividing 60 by 2

60 / 2 = 30 minutes

The last step is to add 30 minutes to the time the lesson started : 10 : 00 am + 30 minutes = 10 : 30 am

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Answer:

x = 6

Step-by-step explanation:

the tangent- tangent angle UVW is half the difference of the intercepted arcs, that is

∠ UVW = [tex]\frac{1}{2}[/tex] (UW - WU ) , then

5x + 17 = [tex]\frac{1}{2}[/tex] (37x + 5 - (23x - 5) ) ← multiply both sides by 2

10x + 34 = 37x + 5 - 23x + 5

10x + 34 = 14x + 10 ( subtract 14x from both sides )

- 4x + 34 = 10 ( subtract 34 from both sides )

- 4x = - 24 ( divide both sides by - 4 )

x = 6

Answer: 111

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees, so:

[tex]121+58+70+x=360\\\\x=111[/tex]

Answer:

111

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 360:

121 + 58 + 70 + x = 360 add like terms

249 + x = 360 subtract 249 from both sides

x = 111 is the measure of the angle represented with x

The examples of insurable interest is an employer under certain arrangements.

Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to  mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.

Examples of insurable interest are:

Hence the examples of insurable interest is an employer under certain arrangements.

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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.

If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.

Step-by-step explanation: Edmentum

Answer:

converge

Step-by-step explanation:

the reason is : the individual terms of the series get smaller and smaller towards 0, and therefore the sum converges to a certain limit.

why do I know that the individual terms get smaller and smaller ?

because the terms are ultimately (with n getting very large the constant factors added constants become irrelevant)

n / (n^(3/2))

as sqrt(n³) = n^(3/2)

and n^(3/2) progresses much faster and stronger than n (or n¹), as 3/2 is larger than 1.

so, the denominator (bottom) of that fraction grows stronger than the numerator (top), and the terms go therefore against 0 with larger and larger n.

Answer:

Step-by-step explanation:

3.5805

Considering the asymptotes of the function, the equation that represents the graph is:

[tex]y = \frac{1}{x + 2} + 3[/tex]

This function, from the graph, has a vertical asymptote at x = -2, hence the denominator is given by:[tex]y = \frac{1}{x + 2} + 3[/tex]

x + 2, as x + 2 = 0 -> x = -2.

The horizontal asymptote is of y = 3, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]

Which means that the function is described by the following rule:

[tex]y = \frac{1}{x + 2} + 3[/tex]

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Step-by-step explanation:

x+x+10+50=180

2x+60=180

2x=180-60

2x=120

x=120/2

x=60

Answer:

250 - 6 - 3n

Step-by-step explanation:

Let n equal the number of students.

[tex]number \: of \: movies = 3 \\ permutations = 2 \\ \\ c( \gamma ) = 2! \times 1 = 2 \: ways[/tex]

[tex]g(1) \: \: \: \: g(2) \: \: \: \: nc(17) \\ g(2) \: \: \: \: g(1) \: \: \: \: nc(17)[/tex]

Question 14

Part (a)

[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]

Part (b)

[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]

Answer:

Raphael's tomato sauce has too much garlic.

Step-by-step explanation:

We can use ratios to solve

Emily:

15 cloves

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

6L

2.5 Cloves per Liter

Raphael

25 cloves

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

9 L

2.7777(repeating) cloves per liter

Raphael has more garlic per liter

Answer:

B

Step-by-step explanation:

perfect tomato sauce

15 cloves → 6 L ( multiply both parts by 1.5 )

22.5 cloves → 9 L← Raphael's tomato sauce

since he used 25 cloves of garlic , then

Emily would think Raphael's sauce has too little garlic

Answer:

1.f(x)=2x-5

i will take the set {-2,-1,0,1,2}

f(-2)=2(-2)-5

=-4-5

=-9

f(-1)=2(-1)-5

=-2-5

=-7

f(0)=2(0)-5

=-5

f(1)=2(1)-5

=-3

f(2)=2(2)-5

=-1

so the coordinates of the function is {-9,-7,-5,-3,-1}

2.f(x)=-3x+6

i will the take the set {-2,-1,0,1,2} too

f(-2)=-3(-2)+6=6+6=12

f(-1)=-3(-1)+6=3+6=9

f(0)=-3(0)+6=6

f(1)=-3(1)+6=-3+6=3

f(2)=-3(2)+6=-6+6=0

{12,9,6,3,0}

3.f(x)=2/3.x+4

{-2,-1,0,1,2}

f(-2)=2/3(-2)+4=-4/3+4=(-4+12)/3=8/3

f(-1)=2/3(-1)+4=-2/3+4=(-2+12)/3=10/3

f(0)=2/3(0)+4=4

f(1)=2/3(1)+4=2/3+4=(2+12)/3=14/3

f(2)=2/3(2)+4=4/3+4=(4+12)/3=16/3

{8/3,10/3,4,14/3,16/3}

you're can graph those coordinates

actually you can take other coordinates...

CMIIW

,

The least number of colors needed to correctly color in the sections of the given picture so that no two touching sections have the same color is 5.

Let's say we begin with a single triangle. This triangle will be the first of a series of seven subsequent triangles, none of which will have any portions contact. If a square were the initial shape, then there are five shapes—three of which are squares and the other two are triangles—that don't have any touching portions. Given that a square takes up twice as much room, this value is probably lower, but location also matters. Therefore, for the given figure, the least number of colored areas you can color in that yet meet the required criteria is 5.

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The cross-section perpendicular to the base of a right rectangular prism is a rectangle.

A shape or a solid that has three dimensions that is length, width and height is called a 3D shape. 3D shapes have faces, edges, and vertices. Examples are cylinder, cone, prism, pyramid.

A shape that has two dimensions is called a 2D shape. 2D shapes have breadth and length.

The cross-section perpendicular to the base of a right rectangular prism is a rectangle.

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Answer:

cos(x)

Step-by-step explanation:

(1 + cos(x))(1 - cos(x)) = 1 - cos²(x) = sin²(x)

sqrt(sin²(x)) = sin(x)

sin'(x) = cos(x)

The exponential equation modeling this relationship is given as follows:

f(x) = 8(0.5)^x.

An exponential equation is modeled by:

f(x) = a(b)^x

In which:

For this problem, we have that when x = 0, y = 8, hence a = 8. Then:

f(x) = 8(b)^x.

When x = 1, y = 4, hence b is found as follows:

f(x) = 8(b)^x.

4 = 8b

b = 0.5.

Hence the equation is:

f(x) = 8(0.5)^x.

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The length of the new base is 26.56 inches or [tex]26\frac{14}{25}[/tex] inches. Using the area of a right triangle, the required base is calculated.

The area of the right triangle is given by

A = [tex]\frac{1}{2}[/tex] × b × h sq. units

Where A -area; b -base; h -height;

It is given that,

The right triangle has a base of length b = 8 1/2 = 8.5 inches and a height of length h = 12 1/2 = 12.5 inches.

So, its area is

A = [tex]\frac{1}{2}[/tex] × 8.5 × 12.5 = 53.125 sq. inches

When the height of the right triangle is reduced to 4 inches,

53.125 = [tex]\frac{1}{2}[/tex] × b × 4

⇒ b = 53.125/2

∴ b = 26.56 or [tex]26\frac{14}{25}[/tex] inches

Thus, the length of the new base is 26.56 or [tex]26\frac{14}{25}[/tex] inches.

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144π cm²

Answer:

Solution given:

diameter (d)= 12cm

radius (r)=12/2=6 cm

slant height(l)=18cm

Now

Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²

Step-by-step explanation:

there is a nice formula for the height in a right-angled triangle :

h = sqrt(p×q)

h being the height to the 90° angle, p and q being the segments (left and right of the height) of the Hypotenuse.

so, in our case

x = sqrt(25×144) = 5×12 = 60

Answer:

[tex]\sf 2\dfrac{1}{4}\ cups \ of \ sugar[/tex]

Explanation:

Let the full batch be x

Here given:

3/4 cup of sugar required to make 1/3 batch of cookies

Build equation:

[tex]\sf \rightarrow \dfrac{1}{3}x = \dfrac{3}{4} \ cup \ of \ sugar[/tex]

Solve:

[tex]\sf \rightarrow x = \dfrac{3(3)}{1(4)}[/tex]

[tex]\sf \rightarrow x = \dfrac{9}{4}[/tex]

[tex]\rightarrow \sf x = 2\dfrac{1}{4}[/tex]

Answer:

2 2\3 cups of sugar.

Step-by-step explanation: