Prove:Sinx-2sin3x+sin5x=2sinx(cos4x-cos2x)
​

Answer:

l = 7 in; w = 3 in

Step-by-step explanation:

The formula for the area of a rectangle is

A = lw

Data:

A = 21 in²

l = w + 4

Calculation:

                 21 = (w + 4) × w

                 21 = w² + 4w

w² + 4w - 21 = 0

(w + 7)(w - 3) = 0

w + 7 = 0     w - 3 = 0

      w = -7         w = 3

We reject the negative value, so w = 3 in.

21 = l × 3

l = 7

The rectangle is 7 in long and 3 in wide.

Answer:

51

Step-by-step explanation:

Process exponents and division before performing addition, that is

49 + 64 ÷ 32 ← perform division

= 49 + 2 ← finally addition

= 51

Answer:

the image of the dilation a reduction or an enlargement of the original figure

Step-by-step explanation:

The scale factor will be within the figure

Answer:

Reduction, 1/2

Step-by-step explanation:

We can already see that the prime figure is smaller, so we can justify that it is a reduction.

We can look at the points of the original figure and if we divide them by 2, we get the prime figure coordinates so we can conclude that the scale factor is 1/2.

Answer:

pie

Step-by-step explanation:

since line CT passes through point A (center) it is doameter (straight line)

its measure is 180° = pie radian

Answer:

Refer to step-by-step.

Step-by-step explanation:

12.  x = 28

BC = x

AB = 96

AC = 100

We use the Pythagorean theorem to find the value of x.

a² + b² = c²

x² + 96² = 100²

x² + 9216 = 10000

x² = 10000-9216

x² = 784

√x² = √784

x = 28

13. x = 64

a² + b² = c²

48² + x² = 80²

2304 + x² = 6400

x² = 6400 - 2304

x² = 4096

√x² = √4096

x = 64

14. YES and 25 = 25

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

So this means that AB is tangent to the circle.

15. NO and 45 ≠ 49

a² + b² = c²

3² + 6² = 7²

9 + 36 = 49

45 = 49

So this means the AB is not tangent to the circle.

16. x = 4.5 and P = 52

To find the value of x, we need to determine the value of our hypotenuse.

QU is congruent to QT, therefore, QT = 4

UR is congruent with SR, therefore, UR = 13

PS is congruent to AB, therefore:

2x = 9

Divide both sides by 2

x = 4.5

The perimeter of a triangle is:

P = a + b + c

a = 9 + 4 or 13

b = 2(4.5) + 13 or 22

c = 4 + 13 or 17

P = 13 + 22 + 17

P = 52

17. x = 13 and P = 72

TJ is congruent to UJ, therefore, TJ = 13

x = 13

The perimeter of a parallelogram is:

P = 2(a+b)

a = HR + RK

b = KU + UJ

a = 13 + 5 or 18

b = 5 + 13 or 18

P = 2(18 + 18)

P = 2(36)

P = 72

18. x = 8 and P = 80

We know that part of the whole of 26 is 18 because one side is congruent to 18.

to find the value of the other half, we simply subtract 18 from 26.

26 - 18 = 8

x is congruent to 8, therefore x = 8

The line segment 14 is congruent to the opposite segment of x, therefore making the value 14.

So then we have:

a = 8 + 14 or 22

b = 26

c = 18 + 14 or 32

P = a + b + c

P = 22 + 26 + 32

P = 80

19. x = 6 and P = 52

Now we have the case of x + 2 is congruent to 8.

x + 2 = 8

Combine like terms.

x = 8 - 2

x = 6

Now that we have the value of x, we can simply look for the value of the line segment attached to it.

4 is congruent to the line segment attached to x + 2, therefore the value is 4.

To find the perimeter we have to add all sides together.

P = (8+5)+(5+9)+(9+4)+(8+4)

P = 52

20. x = 5, y = 2, z =10, and P = 68

Let's take this one step at a time.

First we look for x.

2x + 2 = 3x - 3

Combine like terms.

2x - 3x = -3 - 2

-x = -5

Divide both sides by -1.

x = 5

Now let's get the value of y.

5y - 2 = 3y + 2

Combine like terms.

5y - 3y = 2 + 2

2y = 4

Divide both sides by 2.

y = 2

Now let's look for z.

34 - 2z = z + 4

Combine like terms.

-2z - z = 4 - 34

-3z = -30

Divide both sides by -3.

z = 10

Now that we have the values of x, y, and z. We can substitute them to find the values of our segments.

2x + 2

2(5) + 2 = 12

3x - 3

3(5)-3 = 12

5y - 2

5(2) - 2 = 8

3y + 2

3(2) + 2 = 8

z + 4

10 + 4 = 14

34 - 2z

34 - 2(10)

34 - 20 = 14

Now that we have our values let's look for our perimeter.

P = a + b + c

P = (12 + 8) + (12 + 14) + (14 + 8)

P = 20 + 26 + 22

P = 68

Amanda could eat 3/8 of her pizza and Lauren could eat 2/3 of her pizza.

To find out how much pizza Amanda and Lauren each eat, let's start with Cami who eats 1/2 of her pizza. Since Amanda eats less than Cami, we can represent her fraction as a fraction smaller than 1/2. For example, Amanda could eat 3/8 of her pizza. On the other hand, since Lauren eats more than Cami, we can represent her fraction as a fraction larger than 1/2. For example, Lauren could eat 2/3 of her pizza.

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A real life use of Surface area is when we need to figure out how much paint is needed to paint something. Paint can only cover so much surface area so we must figure out Surface area before it is painted.

Another example is in fashion when making clothes. You need to know the surface area of fabric so that there is enough cloth to fit a model and make a garment.

Answer:

Finding the area of a yard/centimeter.

Step-by-step explanation:

A house or let's say a building can be used as an example.

How to find the answer:

You would times length times width. (Up and bottom) Decimal or not, you would get your answer.

Answer:

540 oranges

Step-by-step explanation:

360 Oranges=40L

40*3/2=60

360*3/2=540

Answer:

540

Step-by-step explanation:

First you have to divide 360 by 40. 360/40 = 9. So that means 9 oranges are needed to make 1 L of fresh squeezed juice.

Now since you know how many oranges are needed for 1 L, you have to find out how many are for 60. To do that you need to multiply 60 and 9. 60*9 = 540.

540 is your answer.

Hope this helped.

Answer:

x = -10

Step-by-step explanation:

You're looking for a number that gives -1000 when cubed. In other words, you're looking for the cubic root of -1000.

In fact, cubic root and cube are one the opposite of the other, meaning that

[tex] a^3=b \iff \sqrt[3]{b}=a[/tex]

So, you have

[tex]x^3=-1000 \iff x = \sqrt[3]{-1000} = -10[/tex]

To find the area of circle

formula

[tex]a = \pi \: r {}^{2} \\ [/tex]

So,

Diameter is 26

to make radius

26÷2=13

Now we got the radius 13

Apply in the formula

[tex]a = \pi \: (13) {}^{2} \\ a =530.92 [/tex]

The answer is 530.92

if you wana Round it 530.93

Hope this Help:))

Answer:

The answer is C.

Step-by-step explanation:

Think about it as substitution.

The equation given to you is 15n=10.

They are telling you that n is equal to 2/3.

So now, this is where you do the substitution.

1. Substitute 2/3 in for n.

  15(2/3)=10

2. Determine if true.

  15·2/3=10

3. Are they the same?

  10=10

So now you know your answer is C. :)

Answer:

25 mph

Step-by-step explanation:

Weren't there several possible answer choices?

175 miles

--------------- = 25 mph

  7 hrs

Answer:

a= 1/2p-b

Step-by-step explanation:

p=2a+b

divide by 2 on both sides

1/2 p = a+b

subtract b from both sides

1/2 p - b = a

flip equation (not needed, just personal preference)

a= 1/2p-b

(Sorry if I didn't understand well enough and got it wrong)

Answer:

[tex]y = -\frac{1}{3}x - 5[/tex]

Step-by-step explanation:

To write the equation of a line use the point slope formula [tex]y - y_1 = m(x-x_1)[/tex]. Find m by using the slope formula with the points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{1--3}{-5-7} =\frac{4}{-12} =-\frac{1}{3}[/tex]

Since the line is parallel, it will have the same slope.

Substitute m = -1/3 and (-3,-4).

[tex]y --4 = -\frac{1}{3}(x --3)\\y + 4 = -\frac{1}{3}(x+3)\\y +4 = -\frac{1}{3}x - 1\\y = -\frac{1}{3}x - 5[/tex]

Final answer:

The equation of the line that passes through the point (-3, -4) and is parallel to a given line is y = -1/3x - 5. This is found by calculating the slope of the given line and then using the point-slope form to find the equation for the parallel line.

Explanation:

The student has asked for the equation of a line that passes through point
(-3, -4) and is parallel to another line. First, we need to find the slope of the given line that passes through points (-5, 1) and (7, -3). The slope (m) is calculated by using the difference in y-coordinates over the difference in x-coordinates (rise over run), which is:

m = (y2 - y1) / (x2 - x1) = (-3 - 1) / (7 - (-5))

m = (-4) / (12) = -1/3

Since parallel lines have the same slope, our new line will also have a slope of -1/3. Using the point-slope form of a line's equation, y - y1 = m(x - x1), and substituting the point (-3, -4) and the slope -1/3, we get the equation of the parallel line:

y - (-4) = -1/3(x - (-3))

y + 4 = -1/3(x + 3)

To write it in slope-intercept form (y = mx + b), we distribute the slope and simplify:

y + 4 = -1/3x - 1

y = -1/3x - 5

Therefore, the equation of the line parallel to the given line and passing through the point (-3, -4) is y = -1/3x - 5.

There is no solution for the given equation |x+5|=−3.

Two or more expressions with an Equal sign is called as Equation.

The equation |x+5| = -3 has no solutions in the real number system because the absolute value of any real number is always non-negative, and can never be negative.

Therefore, there are no values of x that make the left-hand side of the equation equal to -3, and the equation has no solutions.

Graphically, this means that there is no point on the number line where the distance from that point to -5 is equal to -3.

The solution set for the equation |x+5| = -3 is the empty set .

Hence, for the given equation |x+5|=−3 has no solution.

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9514 1404 393

Answer:

  1400 km/hour to the east

Step-by-step explanation:

We assume the jet is flying directly toward US airspace, so is flying east. The speed is ...

  speed = distance/time

  speed = ((8400 km)/3)/(2 h) = 1400 km/h

The jet's velocity is 1400 km per hour to the east.

Final answer:

The velocity of the supersonic jet traveling one-third of the way to U.S. airspace is 1400 km/h to the east, calculated by dividing the distance covered (2800 km) by the time taken (2 hours).

Explanation:

The supersonic jet's velocity can be determined by calculating the distance it flew and the time taken to cover that distance. The jet started 8400 km west of U.S. airspace and flew one-third of that distance, which is 2800 km (8400 km / 3). It took 2 hours for the jet to cover this distance. So, to find the velocity, we use the formula velocity = distance / time.

V = 2800 km / 2 hours = 1400 km/h to the east.

Each part is 1/4 of a whole. There are 12/4 in all. 12/4=3

Each part is 1/4 of a whole and there are 12/4 in all which is if the models show wholes and parts.There are 3 wholes,each divided into fourths.​

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The model is given in the picture.

The models show wholes and parts.There are 3 wholes,each divided into fourths.​

From the data given in the question:

Each part is 1/4 of a whole.

There are 12/4 in all.

= 12/4

= 3

Thus, each part is 1/4 of a whole and there are 12/4 in all which is if the models show wholes and parts.There are 3 wholes,each divided into fourths.​

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Answer:

h = 20 cm

Step-by-step explanation:

The volume (V) of a square based prism is

V = area of base × h ( h is the height )

area of square base = 9 × 9 = 81 cm²

Hence

81h = 1620 ← equation to be solved

Divide both sides by 81

h = 20 cm

Answer:

166

Step-by-step explanation:

5/2=2.5

415/2.5

=166

Answer:  Interval Notation (0, 6)

               Graph: 0 o--------------o 6

Step-by-step explanation:

[tex]\dfrac{2}{x}>\dfrac{4}{12}\implies \dfrac{2}{x}>\dfrac{1}{3}\\\\\text{Restriction: Since the denominator cannot be zero, }x\neq 0\\\\\text{First, set the left side EQUAL to the right side and solve:}\\\dfrac{2}{x}=\dfrac{1}{3}\quad \text{cross multiply}\rightarrow 2(3)=x\quad \rightarrow \quad 6=x\\\\\\\text{Next, choose your test points}\\\bullet \text{to the left of 0: I choose -1}\\\bullet \text{between 0 and 6: I choose 1}\\\bullet \text{to the right of 6: I choose 8}[/tex]

[tex]\text{Now, plug each of the test points into the inequality to see which one(s)}\\\text{make a true statement.}\\\\\dfrac{2}{-1}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE\\\\\\\dfrac{2}{1}>\dfrac{1}{3}\implies 2>\dfrac{1}{3}\quad \boxed{TRUE!}\\\\\\\dfrac{2}{8}>\dfrac{1}{3}\implies -2>\dfrac{1}{3}\quad FALSE[/tex]

So, the solution is: every value between 0 and 6

2/x > 4/12

We can plug each of the numbers given in to verify.

2/4 = 4/8 = 6/12 > 4/12 √ this is correct

2/6 = 4/12 > 4/12 × this is incorrect

2/12 > 4/12 × this is incorrect

2/24 = 1/12 > 4/12 × this is incorrect

Your answer is A

Answer:

First, you have to calculate the angles.

3x-2 + 4x +2x -12  + 2x  + 3x + 10

14x -4 = 360

14x = 364

x = 26

So, the angles are:

3x -2 = 76

4x = 104

2x -12 = 40

2x = 52

3x + 10 = 88

Step-by-step explanation:

Answer:

The measure of angle ALO = 35°

Step-by-step explanation:

* Lets talk about the tangents to a circle drawn from a point

 outside the circle:

- They are equal in length

- They are perpendicular to the radii at the point of tang-ency

- If we join the points of tang-ency withe the center of the circle

 and join the outside point with center of the circle, we

 formed two congruent triangles

* Now lets check our problem

- AL and LB are two tangents to the circle O ant points A and B

∴ LA = LB ⇒ (1)

- OA and OB are radii in circle O

∴ OA = OB ⇒ (2)

∴ OA ⊥ AL and OB ⊥ BL ⇒ radius and tangent

∴ m∠OAL = 90° , m∠OBL = 90

∴ m∠OAL = m∠OBL ⇒ (3)

* From (1) , (2) , (3)

- The two triangles LAO and LBO are congruent ⇒ SAS

- SAS is one case of congruence

∵ The lengths of two sides and the measure of the including

  angle between them in one triangle equal to the

  corresponding sides and angles in the second triangle,

  then the two triangles are congruent

∴ m∠LOA = m∠LOB

∵ m∠AOB = 110°

∴ m∠LOA = m∠LOB = 110/2 = 55°

* In ΔLAO

∵ m∠ LAO = 90° , m∠LOA = 55°

∴ m∠ALO = 180 - (90 + 55) = 180 - 145 = 35°

* The measure of angle ALO = 35°

[tex]\bf \textit{volume of a right-circular cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ V=471 \end{cases}\implies 471=\pi r^2(6)\implies \cfrac{471}{6\pi }=r^2 \\\\\\ \sqrt{\cfrac{471}{6\pi }}=r\implies \stackrel{diameter = 2\times radius}{d=2\left( \sqrt{\cfrac{471}{6\pi }} \right)}\implies d\approx 9.997[/tex]

180 - 11 = 169

So b = 169 degrees.

Answer:

- 2

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 7 ] and from the graph

f(b) = f(7) = 2

f(a) = f(3) = 10, hence

average rate of change = [tex]\frac{2-10}{7-3}[/tex] = [tex]\frac{-8}{4}[/tex] = - 2

Answer:

not

Step-by-step explanation:

Negation is turning a positive statement into a negative one. The positive form of the sentence is: It is raining.

Adding the word 'not' makes it negative (not positive): It is NOT raining.

The negation of the given statement is It is raining.

In Mathematics, the negation of a statement is the opposite of the given mathematical statement. If “P” is a statement, then the negation of statement P is represented by ~P. The symbols used to represent the negation of a statement are “~” or “¬”.

Given statement

P : It is not raining.

~P : It is raining

Hence, The negation of the given statement is It is raining.

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You're correct, t represents seconds

Answer:

[tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

This is a recurring decimal.

Let x = 4.666666...                 ⇒ (1)

  10x = 46.66666...                     ⇒ (2)

Subtract equation (1) from equation (2)

    10x = 46.66666..

   -  x = 4.666666...  

     9x = 42.0000.....

9x = 42

  x =  42/9

      = 14/3

       =[tex]4\frac{2}{3}[/tex]

Answer:

to not over eat an get the right amount of servings

Step-by-step explanation:

Answer:

same

Step-by-step explanation:

Answer:

11, 13 and 15.

Step-by-step explanation:

Let's say that the odd number is "x". If x is for example 15, then the next ODD number would be 15+2=17 and the one after that would be 15+2+2=15+4=19.

Applying that here, we get:

Odd number* the next odd number*the next odd number=2145

x*(x+2)*(x+4)=2145

x*(x^2+4x+2x+8)=2145

x^3+6x^2+8x=2145

By solving the polynomial, you get x=11.

Which makes our three numbers: 11, 13 and 15.

11*13*15=2145. The answer checks.

Final answer:

To find the three consecutive odd numbers whose product is 2,145, set up and solve an equation for n, the first odd number. The solution is n = 11, so the three consecutive odd numbers are 11, 13, and 15.

Explanation:

To find the three consecutive odd numbers whose product is 2,145, we can set up an equation and solve for n, the first odd number:

Let n be the first odd number

Then, the next two consecutive odd numbers would be n + 2 and n + 4

We can write the equation as: n x (n + 2) x (n + 4) = 2,145

Expanding this equation, we have: n³ + 6n² + 8n - 2,145 = 0

By factoring or using a numerical method, we can find that n = 11

So, the three consecutive odd numbers are 11, 13, and 15.