help really quick .​

Answer:  see both proofs below

Step-by-step explanation:

Use Difference Identity: tan (A - B) = (tan A - tan B)/(1 + tanA · tanB)

Use Unit Circle to evaluate: tan (π/4) = 1

Use Tangent Identity: tanA = (sinA)/(cosA)

Use Half-Angle Identities:

[tex]\cos \dfrac{A}{2}=\sqrt{\dfrac{1+\cos A}{2}}\\\\\\\sin \dfrac{A}{2}=\sqrt{\dfrac{1-\cos A}{2}}[/tex]

Part 1   Proof LHS → Middle

LHS:                                [tex]\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)[/tex]

Difference Identity:        [tex]\dfrac{\tan (\frac{\pi}{4})-\tan(\frac{A}{2})}{1+\tan(\frac{\pi}{4})\cdot \tan(\frac{A}{2})}[/tex]

Unit Circle:                      [tex]\dfrac{1-\tan(\frac{A}{2})}{1+ \tan(\frac{A}{2})}[/tex]

[tex]\text{Tangent Identity:}\qquad \qquad \dfrac{\frac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}}}{\frac{\cos\frac{A}{2}+\sin\frac{A}{2}}{\cos\frac{A}{2}}}[/tex]

Simplify:                             [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}[/tex]

LHS = Middle:  [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}=\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}\qquad \checkmark[/tex]

Part 2   Proof  Middle → RHS

Middle:                                     [tex]\dfrac{\cos\frac{A}{2}-\sin\frac{A}{2}}{\cos\frac{A}{2}+\sin\frac{A}{2}}[/tex]

[tex]\text{Half-Angle Identity:}\qquad \qquad \dfrac{\sqrt{\frac{1+\cos A}{2}}-\sqrt{\frac{1-\cos A}{2}}}{\sqrt{\frac{1+\cos A}{2}}+\sqrt{\frac{1-\cos A}{2}}}[/tex]

Simplify:                               [tex]\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}+\sqrt{1-\cos A}}[/tex]

Rationalize Denominator:  [tex]\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}+\sqrt{1-\cos A}}\bigg(\dfrac{\sqrt{1+\cos A}-\sqrt{1-\cos A}}{\sqrt{1+\cos A}-\sqrt{1-\cos A}}\bigg)[/tex]

                                          [tex]=\dfrac{1+\cos A-2\sqrt{1-\cos^2 A}+1-\cos A}{1+\cos A-(1-\cos A)}[/tex]

Simplify:                                [tex]\dfrac{2-2\sqrt{1-\cos^2 A}}{2\cos A}[/tex]

                                         [tex]=\dfrac{2-2\sqrt{sin^2 A}}{2\cos A}[/tex]

                                         [tex]= \dfrac{2-2\sin A}{2\cos A}[/tex]

Factor:                                   [tex]\dfrac{2(1-\sin A)}{2(\cos A)}[/tex]

Simplify:                               [tex]\dfrac{1-\sin A}{\cos A}[/tex]

Expand:                                [tex]\dfrac{1-\sin A}{\cos A}\bigg(\dfrac{1+\sin A}{1+\sin A}\bigg)[/tex]

                                          [tex]=\dfrac{1-\sin^2 A}{\cos A(1+\sin A)}[/tex]

Simplify:                                 [tex]\dfrac{\cos^2 A}{\cos A(1+\sin A)}[/tex]

                                          [tex]=\dfrac{\cos A}{1+\sin A}[/tex]      

Middle = RHS:   [tex]\dfrac{\cos A}{1+\sin A}=\dfrac{\cos A}{1+\sin A}\qquad \checkmark[/tex]            

Answer:

2

Step-by-step explanation:

Answer:

if you round the 13 to fifteen and the 49 to 50, your best estimate answer would be 750. Hope this is what you were looking for and that it helps!

Step-by-step explanation:

The best estimate of the product of 13 and 49 is 600.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The two given numbers are 13 and 49.

The product of 13 and 49 is

13×49 =637

So, 637 is estimated to 600

Therefore, the best estimate of the product of 13 and 49 is 600.

Learn more about the multiplication here:

https://brainly.com/question/1562995.

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Answer:

28.3 square meters.

Step-by-step explanation:

So we know that the radius of the circle is 3 meters. With that, we can figure out the area of the circle.

The area of a circle is given by the formula:

[tex]A=\pi r^2[/tex]

Plug in 3 for r:

[tex]A=\pi (3)^2[/tex]

Square the number:

[tex]A=9\pi[/tex]

Use a calculator. Approximate:

[tex]A\approx28.2743\approx28.3[/tex]

Therefore, the area of the circle is approximately 28.3 square meters.

Answer:

28.3 m²

Step-by-step explanation:

The area of a circle can be found using the following formula.

[tex]a=\pi r^2[/tex]

We know the radius of the circle is 3 meters. We can substitute 3 m in for the variable, r.

[tex]a= \pi (3m)^2[/tex]

Evaluate the exponent.

(3m)² = 3m * 3m= 9 m²

[tex]a= \pi (9 m^2)[/tex]

Multiply pi and 9 meters squared.

9 m² * π = 28.2743339 m²

[tex]a=28.2743339 m^2[/tex]

Round to the nearest tenth. The 7 in the hundredth place tells us to round the 2 in the tenth place to an 3

[tex]a\approx 28.3 m^2[/tex].

The area is approximately 28.3 square meters.

Answer:

63°

Step-by-step explanation:

a = 27°

b = 180° - (a + 27°)

b = 180° - (27° + 27°)

b = 180° - 54°

b = 126°

By inscribed angle theorem:

c = 1/2 b = 1/2 * 126°

c = 63°

Answer:

D

Step-by-step explanation:

This would be a discrete graph  ( points) not a solid line.

This eliminates A and C

1 copy costs 20 cents

8 copies costs 1.60

The number of copies is the independent variable, so it should be plotted on the x axis

Answer:

The answer is D in this question, if you are on plato it may be different so just make sure the graph on choice d on here matches on your test

Step-by-step explanation:

Answer:

Volume of the hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]

Step-by-step explanation:

It's a picture of a globe and a globe of the Earth is in the shape of a sphere.

We know equator divides the earth into two equal halves and these equal halves are called as "hemisphere".

Therefore, a line joining the two extreme points of the diameter of the Earth divides the Earth into two hemispheres.

If the radius of the Earth is 'r',

Volume of the hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]

Answer: C 165

Step-by-step explanation:

30(5)+15= 165

You need to find the GCF (greatest common factor) of 96 and 36. The GCF of 96 and 36 is 12.

12 times what gets you 36?

12 times 3 gets you 36.

12 times what gets you 96?

12 times 8 gets you 96.

So the third answer has 12 as the GCF.

The answer is 12(8+3) = 96+36 = 132

♡ Hope this helped! ♡

❀ 0ranges ❀

Answer: A: hours per acre. B. 4 1/8÷2 3/4 C. 4 1/8÷2 3/4=33/8÷11/4

Step-by-step explanation:

The domain is {x∈R| x≠−2}

The range is {y∈R| y≠−5}

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

Explanation:

Using the function, we can factor the numerator to get

x^2-x-6 = (x-3)(x+2)

Then the (x+2) terms cancel out leaving x-3 only

Therefore, f(x) simplifies to f(x) = x-3.

This produces the straight line graph that is shown. But there's a hole at (-2,-5)

Why is this? It's because plugging x = -2 into the original equation (before you simplify) leads to a division by zero error.

The denominator x+2 becomes -2+2 = 0 and we can't divide by zero.

If we plugged x = -2 into the simplified version of f(x), then we have

f(x) = x-3

f(-2) = -2-3

f(-2) = -5

Showing why the hole is at (-2,-5)

There is no way that x can equal -2, so this is why we kick it out of the domain. Similarly, there's no way to get to y = -5, and this value is kicked out of the range.

The notation x∈R means that x is in the real number set. Saying  {x∈R| x≠−2} means x is any real number but -2. The range is a similar story but we kick out -5 instead.

Answer:

[tex]\Huge \boxed{\mathrm{52\°}}[/tex]

Step-by-step explanation:

Complementary angles add up to 90 degrees.

There are two angles in this case.

Let the first angle be x.

Let the second angle be x+14.

The sum of these two angles is 90.

x + x + 14 = 90

Combine like terms.

2x + 14 = 90

Subtract 14 from both sides.

2x = 76

Divide both sides by 2.

x = 38

Let x = 38 for the second angle.

38 + 14 = 52

The two angles are 52 degrees and 38 degrees.

52 degrees is 14 degrees more than complementary angle.

Answer:

[tex]\huge\boxed{ Angle = 52\ degrees}[/tex]

Step-by-step explanation:

Complementary angles add up to 90 degrees

So, Let the first angle be x then the second angle will be x + 14

Given condition is:

x + x + 14 = 90

2x + 14 = 90

Subtracting 14 to both sides

2x = 90 - 14

2x = 76

Dividing both sides by 2

x = 38

So, the second angle that is 14 degrees more than 38

=> Second Angle = 38 + 14

=> Second Angle = 52 degrees

Answer:

242.52 cubic inches

Step-by-step explanation:

Volume of the cake pan = Length × Width × Height

From the about question, we have the following dimensions for the cake pan

8 inches wide = Width

11 inches long = Length

7 cm deep = Height

We are asked to find the maximum volume in inches. Hence all the dimensions have to be in inches.

Converting Height in cm to inches

From the question,

2.54 cm = 1 inch

7cm = x inch

Cross Multiply

2.54 × x = 7 × 1

x = 7/2.54

x = 2.7559055118 inches

Volume of the cake pan =

8 × 11 × 2.7559055118

= 242.51968504 cubic inches

Approximately, the volume of the cake pan = 242.52 cubic inches

What is the maximum volume, in cubic

inches, the cake pan can hold is 242.52 cubic inches

Answer:

The amount of discount is Rs.5,000

Step-by-step explanation:

The given parameters are;

The amount the shopkeeper sold her goods = Rs. 16,950

The percentage discount allowed = 25%

The VAT included in the sale = 13%

Therefore, we have;

Sale amount = Discounted price + VAT percentage × Discounted price

Discounted price = (100 - Percentage discount)/100×Display price

Sale amount = The amount the shopkeeper sold her goods = Rs. 16,950

Let the display price = X;

We have;

Discounted price = (100 - 25)/100×X = 0.75·X

Therefore;

Sale amount = 0.75·X+ 13/100 × 0.75·X

Rs. 16,9504 = 0.8475·X

X = Rs. 16,950/0.8475 = Rs.20,000

Therefore, the display price = Rs.20,000

The amount of discount = Percentage discount × Display price

The amount of discount = 25/100 × Rs.20,000 = Rs.5,000

The amount of discount = Rs.5,000.

Answer:8.26402

Step-by-step explanation:

Answer:

15 bicycles and 6 skateboards.

Step-by-step explanation:

x+y = 21, since there are 21 total items in the shop

Answer:

The answer is going to be A. Equality property

Answer:

A.-8

Step-by-step explanation:

The greater the slope the steeper the line.

In order to determine which line is closer to vertical, we have to consider the absolute values, because the slope can be positive or negative.

Therefore, the steepest is -8.

Answer:

a. 5 represents the number of calories that come from other ingredients.

b. Neither 8 nor 3 satisfy the given equation, so neither 8 nor 3 can be the solution to the equation.

c. c = 5.5

Step-by-step explanation:

We are given the equation:

[tex]4c + 5 = 27[/tex]

Where [tex]c[/tex] represents the grams of carbohydrates

27 is the total number of calories that are received by the granola bite.

4 is the number of calories from 1 gram of carbohydrates and

5 is the number of calories that are received from other ingredients.

Answer of Part a:

5 is the number of calories that are received from other ingredients.

Part b:

Let us take left hand side (LHS) and put values of c = 8 and 3 one by one.

So, LHS becomes:

4 \times 8 + 5 = 37 [tex]\neq RHS\ i.e.\ 27[/tex]

4 \times 3 + 5 = 17 [tex]\neq RHS\ i.e.\ 27[/tex]

So, Priya is correct that neither 8 or 3 could be solution.

Part c:

[tex]4c + 5 = 27\\\Rightarrow 4c = 22\\\Rightarrow \bold{c = 5.5}[/tex]

So, solution to the equation is: c = 5.5

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

Explanation:

The portion below the x axis is when f(x) is negative. This happens on the interval [tex]-5 < x < 3[/tex]. Note how -5 and 3 are the x intercepts or roots. So because f(x) is negative when [tex]-5 < x < 3[/tex] we can say f(x) is negative over the interval (-5, 3). This is interval notation and not ordered pair notation.

----------

The function f(x) is positive in two places. When x < -5 and when x > 3. This is where the purple parabola is above the x axis.

The x < -5 portion converts to the interval notation (−∞,−5)

The x > 3 portion converts to the interval notation (3,∞)

The function is positive over the interval (3,∞) and interval (−∞,−5) while negative over interval (−5,3) so options (B),(C), and (D) will be correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

If we look at the graph

The value of graph is positive after x = 3 and it is positive before x = -5

Let's say the graph is going infinitely in both directions.

Then the function is positive over the interval (3,∞) and interval (−∞,−5).

The function is negative from x = -5 to 3 so it will be negative over that.

Hence "The function is positive over the interval (3,∞) and interval (−∞,−5) while negative over interval (−5,3)".

For more information about the graph of a function

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Answer: 65

Step-by-step explanation: Just divide the numbers, It's simple. 3835 divided by 59 equals 65

Hope this helps^^

Answer:

65 :)

Step-by-step explanation:

Answer:

12/(15+12+15+18)

12/60=0.2=20%

B 20%

please mark as brainliest

Answer:

Step-by-step explanation:

Convert mixed fraction to improper fraction.

[tex]1\frac{5}{8}*2\frac{2}{3}=\frac{13}{8}*\frac{8}{3}\\\\\\=\frac{13}{3}\\\\\\=4\frac{1}{3}[/tex]

Answer:

4 1/3

Step-by-step explanation:

1 5/8 × 2 2/3

First we turn it into an improper fraction:

1 5/8 × 2 2/3 = 13/8 × 8/3

Now we multiply them across:

13/8 × 8/3 = 104/24

Now we simplify:

104/24 = 13/3

because 3 × 8 = 24 and 13 × 8 = 104

Now we simplify again because we can't leave it as an improper fraction. So we turn it into a mixed fraction:

13/3 = 4 1/3

4 1/3 is answer

Answer:

handle your brain its easy

Answer:

3/2

Step-by-step explanation:

To get x we need to isolate it

First, subtract both sides by 4 1/3

-x=2 3/4- 4 1/4

Find LCD

-x= 2 9/12- 4 3/12

Multiply both sides by -1

x=-2 9/12 +4 3/12

x=1 1/2 or 3/2

Answer: 137

Step-by-step explanation:

The given expression: [tex]7x^2 +8x-7[/tex]

We need to find the value of the expression when x=4.

So we just use the substitution property and substitute the value of x= 4 in the given expression , we get

[tex]7(4)^2+8(4)-7\\\\= 7(16)+32-7\\\\= 112+25\\\\=137[/tex]

Hence, the value of the expression at x=4 is 137.

Answer:

The answer is 35.

46-11=35

Answer:

35

Step-by-step explanation:

x-11

46-11

35

Answer:

C

Step-by-step explanation:

Let's find the area of each of the two circles.

First Circle:

The first circle has a diameter of 10 inches. That means the radius is 5 inches. So, its area is:

[tex]A=\pi r^2\\A=\pi (5)^2\\A=25\pi[/tex]

Second Circle:

The second circle has a diameter twice that of the first. So, the diameter is 20 inches. This means that the radius is 10 inches. Find the area:

[tex]A=\pi r^2\\A=\pi (10)^2\\A=100\pi[/tex]

Now, find the ratio between them by dividing:

[tex]\frac{\text{Smaller}}{\text{Larger}}=\frac{25\pi}{100\pi}[/tex]

Simplify:

[tex]\frac{\text{Smaller}}{\text{Larger}}=\frac{1}{4}[/tex]

1/4 is the same as 1:4

So, our answer is C      :)