Find the distance between (4,5) and (-5,2).

Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

g,h,m

Step-by-step explanation:

All three of these line segments are perpendicular on n (which acts as the base).

Therefore , g,h,m are corresponding heights

Answer:

The range of values from one job is between $50 and $650.

Step-by-step explanation:

An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.

This means that his earnings in a job can be modeled by the following function:

\(y = 30x + 50\)

The electrician works maximum of 20 hours on any job. What is the range of values for one job?

Minimum, he works 0 hours, and earns:

\(y(0) = 30(0) + 50 = 50\)

Maximum, he works 20 hours, and earns:

\(y(20) = 30(20) + 50 = 650\)

The range of values from one job is between $50 and $650.

We have a sequence of number, the first number is 8 and the subsequent numbers are found by subtracting 9 from the previous, so:

The fifth number in the pattern is -28

Answer:

Cool

Step-by-step explanation:

Answer:

The median is going to be 7

9514 1404 393

Answer:

  one solution; (x, y) = (4/3, 11/3)

Step-by-step explanation:

The two lines described by the equations have different slopes, so there will be exactly one solution to the system of equations.

__

The slope of the line will be the coefficient of x when you solve for y. In the first equation, the slope is 2. In the second equation, you can solve for y by adding x, and dividing by 2. Then the slope of that line is found to be 1/2.

Lines with different slopes must intersect somewhere. That point of intersection is the (one) solution to the system of equations.

The first graph shows a system of equations that has a unique solution because the two linear graphs have a single point of intersection.

The second graph shows a system of equations with no solutions. This is because the two graphs are parallel to each other, and have no point of intersection.

The third graph has two linear equations that coincide at every point. This makes this system to have an infinite number of solutions.

The fourth graph shows two linear functions having a single point of intersection. This particular system of equations has a unique solution.

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Answer:

First two parts are right, last part is 8.2

Step-by-step explanation:

First two parts are right.

Last part is wrong.

Sin(ANGLE)=opp/hyp

sin(20)=W/24

0.34202014332=W/24

W=8.20848343982 or 8.2

The perimeter of the shape is 10 inches.

It's important to note that the perimeter of a shape or calculated by adding all the sides together.

In this case, this is a rectangle and the perimeter will be:

Perimeter = 2(length + width)

Length = 4 inches

Width = 1 inch

Perimeter = 2(length + width)

Perimeter = 2(4 + 1)

Perimeter = 10 inches.

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Answer:

\(V = \frac{4}{3} \pi {r}^{3} \\ \\ 3V = 4\pi {r}^{3} \\ {r}^{3} = \frac{3V}{4\pi} \\ \\ r = \sqrt[3]{ \frac{3V}{4\pi} } \)

Answer:

1. 3,077.2 cm³

2. 1,808.6 ft³

3. 602.9 in.³

4. 230.8 yd³

5. 191.8 m³

6. 70.3 in.³

Step-by-step explanation:

Recall: Volume of cylinder = πr²h

1. r = 7 cm

h = 20 cm

π = 3.14

Volume = 3.14*7²*20 = 3,077.2 cm³

2. r = 8 ft

h = 9 ft

π = 3.14

Volume = 3.14*8²*9 ≈ 1,808.6 ft³

3. r = ½(8) = 4 in.

h = 12 in.

π = 3.14

Volume = 3.14*4²*12 ≈ 602.9 in.³

4. r = 3½ yd = 3.5 yd

h = 6 yd

π = 3.14

Volume = 3.14*3.5²*6 ≈ 230.8 yd³

5. r = ½(5.3) = 2.65 m

h = 8.7 m

π = 3.14

Volume = 3.14*2.65²*8.7 ≈ 191.8 m³

6. r = 1.9 in.

h = 6.2 in.

π = 3.14

Volume = 3.14*1.9²*6.2 ≈ 70.3 in.³

Answer:4w-20

Step-by-step explanation:distribute

The new mixture contains 34% peanuts.

Using a weighted average approach.

Let x be the percentage of peanuts in the new mixture. Then we can set up the following equation:

(0.16)(4) + (0.40)(12) = x(4 + 12)

simplifying the equation, we get:

0.64 + 4.8 = 16x

5.44 = 16x

x = 0.34 or 34%

Therefore, the new mixture contains 34% peanuts.

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Answer:

bnvc43

Step-by-step explanation:

Answer:

d 9 years, 11 months

Step-by-step explanation:

Rachel deposited $5,960.32 into a savings account with an interest rate of 4.2% compounded twice a year.

P = $5,960.32

Rate = 4.2%

Number of years = x

Final amount=$9000

Number of times compounded= x/2

A= p(1+r/n)^(nt)

9000= 5960.32(1+(0.042*2)/x)^(x/2 *x)

9000= 5960.32(1+0.084/x)^x²/2

2(9000/5960.32)=(1+0.084/x)^x²

3.019972=((x+0.084)/x)^x²

On trial an error

The value of x is found to be approximately 9 year, 11 months

Answer:

they can make 6 batches

Step-by-step explanation:

1/2 = 2/4 1 = 4/4

so if one batch is 1/4, and 4+2 is 6, they can make 6 batches

Answer:

6 Batches

Step-by-step explanation:

Answer:

8π/5

Step-by-step explanation:

Length of an arc, L

L = θ / 360° * (2πr)

r = Radius = 4 ; θ = 72

Hence,

L = 72/360 * (2π4)

L = 1/5 * 8π

L = 8π/5

To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.

A relation represents a function when each input value is mapped to a single output value.

In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.

The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.

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Answer:

15-18

Step-by-step explanation:

The IQR is the middle 50% of a set of numbers

There are 8 numbers, so its the middle 4

The middle 4 consists of 15,15,16,18

The range is 15-18

Answer:

29/60

Step-by-step explanation:

probability of playing is 290/600 which when simplified is29/60

Answer:

No.

Step-by-step explanation:

4 tenths is \(\frac{4}{10}\). 4 sixteenths is \(\frac{4}{16}\). These are two different numbers/fractions.

Hope it helps!

Answer:

nope :D

Step-by-step explanation:

Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given : Sue covered 2.4 km distance and

bike wheel rotated 1225 times.

Thus,

To find the value of diameter of the wheel

=>2400=2πr*1225

=> 2400/2 = πr*1225

=> 1200 = πr*1225

=>r=31

Diameter = 2*31 = 62cm

Therefore , the solution of the given problem of circle comes out to be

the diameter is 62 cm.

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The soccer ball is above 15 feet between 0.25 seconds and 1 second.

To determine when the soccer ball is above 15 feet, we need to find the values of t that satisfy the inequality h(t) > 15.

Given the quadratic function h(t) = -16t² + 20t + 11, we can rewrite the inequality as follows:

-16t² + 20t + 11 > 15

Subtracting 15 from both sides:

-16t² + 20t - 4 > 0

Simplifying further:

-16t² + 20t - 4 = -4(4t² - 5t + 1) = -4(t - 1)(4t - 1) > 0

Now, we can solve for t by finding the values that make the inequality true. We have two factors: (t - 1) and (4t - 1).

Setting each factor greater than zero and solving for t:

t - 1 > 0 => t > 1

4t - 1 > 0 => 4t > 1 => t > 1/4

So, we have t > 1 and t > 1/4. To satisfy both conditions, t must be greater than the maximum of 1 and 1/4, which is 1.

Therefore, the soccer ball is above 15 feet for t > 1 second.

The correct answer is:

C. The soccer ball is above 15 feet between 0.25 seconds and 1 second.

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The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint.

Let 'x' be the amount of blue paint and 'y' be the amount of red paint. Then the equations are given as,

x / y = (1/2) / (1/3)

x / y = 3/2                        ...1

x + y = 5                          ...2

From equations 1 and 2, then we have

(3/2) y + y = 5

(5/2) y = 5

y = 2 quart

Then the value of 'x' is given as

x + 2 = 5

x = 3 quart

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

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