Compare the integers.
-14
-23
A)
B)
> Greater than
O
= Equal to
D
Neither

Answer:

3/16

Step-by-step explanation:

Prove that sin 20 ×sin40 × sin60 × sin80 = 3/16.

We have to prove sin 20 × sin40 × sin60 × sin80 = 3/16.

Consider LHS

sin 20 × sin 40 × sin60 × sin80

Sin Values

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.

We know the trigonometric values of sin function

Proof

Consider LHS

sin 20 × sin 40 × sin60 × sin80

= sin60 [sin20 × sin40 × sin80]

= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]

= √3/2[sin 3(20)/4]

= √3/2[sin 60/4]

= √3/2[√3/2 × 4]

= √3/2 × √3/8 =  3/16

∴ LHS = RHS

Hence proved

Answer:

statements 2 & 5 are true

Step-by-step explanation:

1. False because is a quadratic nonlinear equation

2. True, 4 is the ordered to the origin

3. False, the rate not being linear is not constant

4. False, because when the input is -3 the output is 13

         [tex]y = (-3)^{2} +4=9+4=13[/tex]

5. True, y depends on x

Hope this helps

Step-by-step explanation:

[tex] \tan(31) = \frac{x}{33} \\ x = 33 \tan(31) \\ x = 19.82840042791 \\ x = 19.83[/tex]

Answer:

x = 19.8

Step-by-step explanation:

You want to use tangent, since you are trying to find the opposite side and know the adjacent side to the angle.

tan = opposite/adjacent

31tan = x/33

Multiply both sides by 33

33(31tan) = (33) x/33

33(31tan) = x

Find the tan of 31° using a scientific calculator.

tan 31° is about 0.6

Solve for x

33(0.6) = x

x = 19.83

rounded to the the nearest tenth

x = 19.8

Step-by-step explanation:

Here,let x = 1,2,3 and 4

Then,

Domain =(1,2,3,4)

Again,

f(1)= 3*1 + 5

=3 + 5

=8

f(2)=3*2 + 5

=6 + 5

=11

f(3)=3*3 + 5

=9 + 5

=14

f(4)=3*4 + 5

=12 + 5

=17

Therefore, Range=(8,11,14,17)

Answer:

So 18+-10=8, 18+-8=10. So the answer is 8 I guess.  

Tables A, B, and C.

The only non-linear graph is D. Do not overthink questions like this, this is where schools try to trick you. You are given plot points, plot them and see if they are straight lines (linear) on the graph. If there is a bend (non-linear or peyronie's disease).

Answer: 4 pounds

Step-by-step explanation:

      First, we will see how much the coffee cost by subtracting what was left by the total gift card.

             $90 - $59.64 = $30.36

      Now, we will divide how much the coffee cost by how much one pound costs. This will give us how many pounds she bought, and the answer to your problem

             $30.36 / $7.59 = 4

                 She bought four pounds of coffee.

Answer:

Minimum

Step-by-step explanation:

The zeros of a quadratic equation are the points at which the parabola intersects the x-axis.

[tex]\sf x=3 \implies x-3=0[/tex]

[tex]\sf x=7 \implies x-7=0[/tex]

[tex]\sf \implies y=a(x-3)(x-7)[/tex]   (for some constant a)

[tex]\sf \implies y=ax^2-10ax+21a[/tex]

The optimal value is the y-coordinate of the vertex.  

[tex]\sf \implies vertex=(x,-3)[/tex]

The x-coordinate of the vertex is the midpoint of the zeros:

[tex]\sf x=\dfrac{7-3}{2}+3=5[/tex]

[tex]\sf \implies vertex=(5,-3)[/tex]

Therefore, the vertex will be in Quadrant IV and so the parabola opens upwards into Quadrant I.  

So the optimal value is a MINIMUM since the vertex is the minimum point of the curve.

Additional Information to create the equation of the quadratic

Vertex form of quadratic equation:  [tex]\sf y=a(x-h)^2+k[/tex]

where (h, k) is the vertex

[tex]\sf \implies y=a(x-5)^2-3[/tex]

[tex]\sf \implies y=ax^2-10ax+25a-3[/tex]

To find the value of a, compare the constants of both equations:

[tex]\sf 21a=25a-3[/tex]

[tex]\sf \implies -4a=-3[/tex]

[tex]\sf \implies a=\dfrac34[/tex]

So the final equation is:

[tex]\sf factor \ form \implies y=\dfrac34(x-3)(x-7)[/tex]

[tex]\sf standard \ form\implies y=\dfrac34x^2-\dfrac{15}{2}x+\dfrac{63}{4}[/tex]

[tex]\sf vertex \ form \implies y=\dfrac34(x-5)^2-3[/tex]

Answer:

Step-by-step explanation:

Circumference is given by the formulas :

[tex]2\pi r[/tex] or [tex]\pi d[/tex]

Since we are given the diameter we can use the second one :

We are told to use 3.14 for π :

C = (3.14)×(16)

C = 50.24

Area of a circle is given by the formula:

[tex]\pi r^{2}[/tex]

To work out r we simply half the diamter:

16÷2 = 8

Now we put this into the area formula:

π(8)² = 64π

We are told to use 3.14 as pi so:

64π = 64×3.14 = 200.96

Answer:

Circumference = 50.24 in

Area = 200.96 in²

Step-by-step explanation:

First, let us find the circumference of the circle.

For that, let us use this formula.

C = π d

Given that,

d ⇒ diameter ⇒ 16 in

Let us find now.

C = π d

C = 3.14 × 16

C =  50.24 in

And now let us find the area of the circle.

Before that, let us find the radius.

d = 2r

16 = 2r

Divide both sides by 2.

8 in ⇒ radius

Let us use the below formula to find the area of the circle.

A = π r²

A = 3.14 × 8 × 8

A = 200.96 in²

Answer:

it would range between 11.28379... to 13.819765...

Step-by-step explanation:

the circle's area formula is pi * radius^2

so you make to equation, plugging the 100 and 150 into the circle's area

you get square root of (100/pi) which gets 11.28379... for the area of 100

you do the same with 150 to get square root of (150/pi) which gets 13.819765...

those are the diameter of the circle since the diameter is double the radius which i already multiplied afterwards. so if you need the radius divide the number ive given you

x=2

Step-by-step explanation:

y=7-2x -------(1)

6y=9x

y=9x/6 = 3x/2------(2)

Now,

Equation equation 1 and 2

7-2x= 3x /2

2(7-2x)=3x

14-4x=3x

14=4x+3x

14=7x

14/7=x

x=2

Answer: 495

Step-by-step explanation:

Since the foil covers the object and does not fill it, this problem is a matter of surface area rather than volume. Surface area is finding the area of all the faces, and adding them up.

Since we know the two triangular ends are not covered, this actually makes the problem easier.

Going with our definition of surface area above, we do:

(16.5 * 13) + (16.5 * 12) + (16.5 * 5) = 495

Our answer is 495

Answer:

C: 495ft²

Step-by-step explanation:

You need to calculate and add the surface area of the three rectangular faces of this prism. The two triangular ends are not covered in the foil as stated in the question. You find this like any other rectangle by multiplying the length by the width. (a = lw)

Let's start with the bottom rectangle, it has dimensions of 5x 16.5ft

5 * 16.5 = 82.5

Now the rectangle on the right side.

13 * 16.5 = 214.5

Now the left or back side rectangle.

12 * 16.5 = 198

Now add these values together

82.5 + 214.5 + 198 = 495ft²

Answer:

Eleanor has made an error in Step 1

She clearly intended to multiply both sides by 2, but forgot to multiply the [tex]-9x[/tex] part of the RHS.

Step 1 should be:   [tex]x+18=8(2x-6)-18x[/tex]

Correct solution

Given:   [tex]\dfrac12(x+18)=4(2x-6)-9x[/tex]

Step 1:  [tex]x+18=8(2x-6)-18x[/tex]

Step 2:  [tex]x+18=16x-48-18x[/tex]

Step 3:  [tex]x+18=-48-2x[/tex]

Step 4:  [tex]66=-3x[/tex]

Step 5:  [tex]x=-22[/tex]

Answer:

4 and 9

Step-by-step explanation:

Composite numbers are whole numbers that can have more than 2 factors.

Answer:

One triangle

Step-by-step explanation:

I hope this helps :)

Answer: A sequence is a type of function. Remember, a function is any formula that can be expressed in "f(x) = x" format, but a sequence only contains integers at or greater than zero.

Hope this helps! Have a good day! :)

Answer:

1.) 1169

2.) 7

3.) 167 students/year

4.) 1879

5.) 1879+167t

6.) 4050

Step-by-step explanation:

1.) Find the difference between the number of students in 2002 and 2009:

[tex]3382-2213=1169[/tex]

2.) Find the difference in the years:

[tex]2009-2002=7[/tex]

3.) To find the average growth, find the change between 2002 and 2009 and divide by 7.

[tex](3382-2213)/7=y\\1169/7=y\\167=y[/tex]

4.) To find the population of the students in the year 2000, we need to subtract the average growth time and the difference of years from 2213.

[tex]2213-167(2002-2000) = y\\2213-334=1879[/tex]

5.) Taking the equation above, and changing it to match the requirements, we get:

[tex]P = 1879+167t[/tex]

6.) Now find the difference between 2013 and 2000, and substitute for t to get:

[tex]P = 1879+167(2013-2000)\\P = 1879+167*13\\P = 4050[/tex]

Answer:

Angle BFC is complimentary to AFB. Its measure is 12.

Step-by-step explanation:

Complementary angles add up to 90 degrees. When these two angles combine, it adds up to 90. 90-78 = 12. This angle's measure is 12.

Look at the diagram for the answer

Hope that helps!

Answer:

x²+14x+33<0.

Step-by-step explanation:

1) according to the condition x=-11 and x=-3 are zeros of the function y=ax²+bx+c;

2) if -3;-11 are zeros, then (-3)*(-11)=c ( already a=1; b=14). Then

3) x²+14x+33<0.

Answer:

12/13

Step-by-step explanation:

P(not a queen) = 48/52 = 12/13

Answer:

48/52

Step-by-step explanation:

Out of a 52 card deck there are 4 queens

there is  a 48/52 propability you will not be drawn a queen or 92.31% you will not be drawn a queen

Answer:

960 cm²

Step-by-step explanation:

Area of trapezoid: (a + b)(h)/2

A = (20 + 40)(32)/2

A = 60(32)/2

A = 1920/2

960 cm²

Answer:

  A, D

Step-by-step explanation:

You want to know the bound for the values of Sn and Tn, given their definitions as ...

  [tex]\displaystyle S_n=\sum_{k=1}^n{\dfrac{n}{n^2+kn+k^2}}\\\\T_n=\sum_{k=1}^{n-1}{\dfrac{n}{n^2+kn+k^2}}[/tex]

All we need to do to determine the correct answer choices is evaluate the sums for some value of n.

For n=2, the value of S2 is ...

  S2 = 2/(4+2+1) +2/(4+4+4) = 2/7 +2/12 = 19/42 ≈ 0.4524

For n=2, the value of T2 is ...

  T2 = 2/(4+2+1) = 2/7 ≈ 0.2857 . . . . . 1/(3n) less than the value of Sn

Both of these values are less than π/(3√3) ≈ 0.6046.

The correct answer choices are ...

  A) Sn < π/(3√3)

  D) Tn < π/(3√3)

__

Additional comment

For the purpose here, it is not necessary to determine the limiting value of either Sn or Tn. It is only necessary to demonstrate which side of the given value the terms of either sequence lie.

<95141404393>

Answer: the answer is 45

Step-by-step Step-by-step explanation:

so it says a pilot goes from 0 to 8 and then two images above so you add to to eat and then you add 5 to 2:30 for me to 522 the artistic 24 + 27 + 5 then you answer 8 + 2028 and then you add 5 + 1 + 2 + 2 + 4 + 3 + 3 + 4 + 1 + 5 + 16 + 18 and you get 45

Answer:

A, A, B, B

Step-by-step explanation:

Answer:

The power is 32 because that is what 2 to th 5 is , 2 is the base as its the number being multiplied 5 times which leaves 2 as the exponent.

Answer:

see explanation

Step-by-step explanation:

the area (A) of a trpezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

b₁, b₂ are the parallel bases and h the perpendicular height between them

(1)

b₁ = 12, b₂ = 8 , h = 5

A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 8) = 2.5 × 20 = 50 cm²

(2)

b₁ = 6 , b₂ = 4 , h = 3

A = [tex]\frac{1}{2}[/tex] × 3 × (6 + 4) = 1.5 × 10 = 15 cm²

(3)

b₁ = 7 , b₂ = 4 , h = 4

A = [tex]\frac{1}{2}[/tex] × 4 × (7 + 4) = 2 × 11 = 22 cm²

Answer:

see explanation

Step-by-step explanation:

the area (A) of a trpezoid is calculated as

A = \frac{1}{2}21 h (b₁ + b₂ )

b₁, b₂ are the parallel bases and h the perpendicular height between them

(1)

b₁ = 12, b₂ = 8 , h = 5

A = \frac{1}{2}21 × 5 × (12 + 8) = 2.5 × 20 = 50 cm²

(2)

Answer:

25

Step-by-step explanation:

Answer:

50.24 square yards

Step-by-step explanation:

Area of the circle

it goes through the point (2, 10), has a vertex at (5, 1) and goes through the point (8, 10)

Answer:

140% increase

Step-by-step explanation:

Percent increase = [(final - initial) ÷ initial] · 100

[(228 - 95) ÷ 95] · 100

[133 ÷ 95] · 100

1.4 · 100

140

Answer:

See below ↓↓↓↓↓↓

Step-by-step explanation:

5.

6.

7.

8.

9.

10.