The of the matrix whose columns are vectors which define the sides of a parallelogram one another is the area of the parallelogram?

To prove that: (2cosA+1) (2cosA-1) = 2cos2A+1

We try to solve one side of the equation to get the other side of the equation.

In this case, we'll solve the right hand side (2cos2A + 1) of the equation with the aim of getting the left hand side of the equation  (2cosA + 1)(2cosA - 1)

Solving the right hand side: 2cos2A + 1

i. We know that cos2A = cos(A+A) = cosAcosA - sinAsinA

Therefore;

cos2A = cos²A - sin²A

ii. We also know that: cos²A + sin²A = 1

Therefore;

sin²A = 1 - cos²A

iii. Now re-write the right hand side by substituting the value of cos2A as follows;

2cos2A + 1 = 2(cos²A - sin²A) + 1

iv. Expand the result in (iii)

2cos2A + 1 = 2cos²A - 2sin²A + 1

v. Now substitute the value of sin²A in (ii) into the result in (iv)

2cos2A + 1 = 2cos²A - 2(1 - cos²A) + 1

vi. Solve the result in (v)

2cos2A + 1 = 2cos²A - 2 + 2cos²A + 1

2cos2A + 1 = 4cos²A - 2 + 1

2cos2A + 1 = 4cos²A - 1

2cos2A + 1 = (2cosA)² - 1²

vii. Remember that the difference of the square of two numbers is the product of the sum and difference of the two numbers. i.e

a² - b² = (a+b)(a-b)

This means that if we put a = 2cosA and b = 1, the result from (vi) can be re-written as;

2cos2A + 1 = (2cosA)² - 1²

2cos2A + 1 = (2cosA + 1)(2cosA - 1)

Since, we have been able to arrive at the left hand side of the given equation, then we can conclude that;

(2cosA + 1)(2cosA - 1) = 2cos2A + 1

Answer:

[tex]\boxed{\sf LHS = RHS }[/tex]

Step-by-step explanation:

We need to prove that ,

[tex]\sf\implies (2 cosA +1)(2cosA-1) = 2cos2A+1[/tex]

We can start by taking RHS and will try to obtain the LHS . The RHS is ,

[tex]\sf\implies RHS= 2cos2A + 1 [/tex]

We know that , cos2A = 2cos²A - 1 ,

[tex]\sf\implies RHS= 2(2cos^2-1)-1 [/tex]

Simplify the bracket ,

[tex]\sf\implies RHS= 4cos^2A - 2 +1 [/tex]

Add the constants ,

[tex]\sf\implies RHS= 4cos^2-1 [/tex]

Write each term in form of square of a number ,

[tex]\sf\implies RHS= (2cos^2A)^2-1^2 [/tex]

Using (a+b)(a-b) = a² - b² , we have ,

[tex]\sf\implies RHS= (2cosA+1)(2cosA-1) [/tex]

This equals to LHS , therefore ,

[tex]\sf\implies \boxed{\pink{\textsf{\textbf{ RHS= LHS }}}} [/tex]

Hence Proved !

Answer:

1300

Step-by-step explanation:

Given that :

Number of sections = 8

Number of seats per section, x ;

150 ≤ x ≤ 200

The possible Number of seats in the auditorium :

Number of seats per section * number of sections

150 * 8 ≤ x ≤ 200 * 8

1200 ≤ x ≤ 1600

The possible Number of seats will lie within 1200 and 1600

From the options, only 1300 lie within this range

Answer:

144 people

Step-by-step explanation:

88% = 0.88

We multiply the total number with 0.88 to see how many people went in the water:

1200(0.88) = 1056

To find the number of those who did NOT go in the water, we subtract the product from the total number:

1200 - 1056 = 144

Answer:

144 people DID NOT go in the water

Step-by-step explanation:

We know that there at 1,200 ppl at the beach and 88% of them DID go into the water.

So the percent of people that DID NOT go into the water is 12%, because

100% - 88% = 12%

12% is the same as 0.12

Multiply 0.12 and 1,200 and you get: 144

Hope it helps (●'◡'●)

Answer:

The center of the circle is found at h,k

These values represent the important values for graphing and analyzing a circle.

Center: 0,0

And also,

Algebra Graph x^2+y^2=25 x2 + y2 = 25 x 2 + y 2 = 25 This is the form of a circle.

And also,

Simple and best practice solution for X2+y2=25 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework. If it's not what You are looking for type in the equation solver your own equation and let us solve it.

And also,

Match the values in this circle to those of the standard form. The variable r r represents the radius of the circle, h h represents the x-offset from the origin, and k k represents the y-offset from origin. The center of the circle is found at (h,k) ( h, k).

And also,

Ox (0) 6°x= 1) 6x ** + y = 25 SOLUTION (a) Since f(x) = 25 - x2 0, we can interpret this integral as the area under the curve y = 25 - x2 from 0 to 5 . But since y2 = 25 - x2 , we get x2 + y2 = 25, which shows that the graph of fis a quarter-circle with radius 5 in the top figuer

And also,

(3x2y2)3 Final result : 32x2y2 Reformatting the input : Changes made to your input should not affect the solution: (1): "y2" was replaced by "y^2".

And thats all!

Solution graph is image 2.

We first graph [tex]x^2+y^2=25[/tex]. This is a circle with center = (0,0) and radius = [tex]\sqrt{25} =5[/tex].

For [tex]x^2+y^2<25[/tex], we'll shade inside the circle.

[tex]y^2=6x[/tex] is a parabola.

we make a table for it.

x   -1   0   1

y   -6  0   6

For [tex]y^2<6x[/tex] we'll shade inside the parabola.

So the graph will be image 1.

So the solution region is image 2.

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Answer:

<LKJ = 115°

Step-by-step explanation:

<LKJ = <LKD + <DKJ

<LKJ = 60°+55°

<LKJ = 115°

Answered by GAUTHMATH

Answer:

[tex] \large{ \tt{✺ \: m \: \angle \: LKJ= m \: \angle} \: LKD \: + \: m \: \angle \: dKJ}[/tex]

[tex] \large{ \tt{⟶ \: m \: \angle \: LKJ= 60 \degree + 55 \degree}}[/tex]

[tex] \large{ \boxed{ \tt{⟶ \: m \: \angle \: LKJ = 115 \degree}}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

$40,000

Step-by-step explanation:

this the workings above

Answer:

x = 1/2; y = 1/3

Step-by-step explanation:

2x + 3y = 2     Eq. 1

-6x + 12y = 1     Eq. 2

Eq. 1

2x + 3y = 2

2x = -3y + 2

x = -3/2 y + 1

Eq. 2

-6x + 12y = 1

De Eq. 1 sabemos que x = -3/2 y + 1

-6x + 12y = 1

-6(-3/2 y + 1) + 12y = 1

9y - 6 + 12y = 1

21y - 6 = 1

21y = 7

y = 7/21

y = 1/3

Eq. 1

2x + 3y = 2

2x + 3(1/3) = 2

2x + 1 = 2

2x = 1

x = 1/2

Respuesta: x = 1/2; y = 1/3

Answer: [tex]y=7\dfrac{1}{3}[/tex].

Step-by-step explanation:

[tex]\dfrac{y}{9} =\dfrac{44}{54} \\\\y \times 54=44 \times 9\\\\54y=396\\\\54y \div 54=396 \div 54\\\\y=7\dfrac{1}{3}[/tex]

Answer:

1) x = 2

Step-by-step explanation:

Hope it helps. I'll try to solve the second one too

9514 1404 393

Answer:

Step-by-step explanation:

1. Substitution can work for this.

  2x +3(4x -5) = 13

  14x = 28 . . . . . add 15

  x = 2 . . . . . . . divide by 14

__

2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...

  x + y + 6 = 5

  x + y = -1

Only the 3rd choice satisfies this equation.

  (x, y, z) = (-5, 4, 6)

Answer:

Step-by-step explanation:

that alot of work shhheeshhh

Answer:

0.001

Step-by-step explanation:

(0.0001)^-3/4=((0.1)⁴)^-3/4

(0.1)^4×-3/4

0.1^‐3

0.001

Answer:

 B and D are polynomial

Step-by-step explanation:

An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.

A)

If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex]   , then it is a polynomial.

But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial

Answer:

A = 16 ft^2

P = 20 ft

Step-by-step explanation:

P = perimeter

A = area

STEP 1: divide the shape into rectangles

Rectangle 1: 2ft*3ft

Rectangle 2: 2ft*5ft

STEP 2: Find the area of each rectangle

Equation for area of a rectangle = bh

Rectangle 1: b = 2, h = 3

Rectangle 2: b = 2, h = 5

(2 * 3) + (2 * 5)

6 + 10

16 ft^2

Now, we have to find the perimeter

STEP 1:  Find the unknown side lengths.

To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.

The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.

STEP 2: Add up all the side lengths

P = 2 + 5 + 5 + 2 + 3 + 3

P = 20 ft

Don't forget to label your answers!!

I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.

Step-by-step explanation:

[tex]G(t) =\displaystyle \int (4 + t + t^2)dt[/tex]

[tex]\:\:\:\:\:\:\:=4t + \frac{1}{2}t^2 + \frac{1}{3}t^3 + C[/tex]

Check:

[tex]\dfrac{d}{dt}(4t + \frac{1}{2}t^2 + \frac{1}{3}t^3+C)= 4 + t + t^2 =g(t)[/tex]

Answer:

3x^2 + 10x

Step-by-step explanation:

If u wrote it correctly it would be ((x+4+2)+4)(x)

Answer:

The p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Step-by-step explanation:

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before.

At the null hypothesis, we test if the two means are equal, that is, the subtraction of them is 0.

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, we test if the two means are different, that is, the subtraction of them is different of 0. So

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.2789.

Considering a standard significance level of 0.02789, the p-value is 0.2789 > 0.05, which means that the appropriate conclusion is that the students do not score differently.

Answer:

1 hour

Step-by-step explanation:

J = 50 mph by 2 hours

S = 50 mph by 1 hour

2-1 = 1

Answer:

The first one (90, 90) is supplimentary, the next two (54, 36. and 45, 45) are complimentary, and the last two are supplimentary.

Step-by-step explanation:

A complimentary angle is two angles that add up to 90, and supplimentary is two angles that add up to 180! :)

Answer:

1st picture at the top would be a supplementary angle because a supplementary angles always add to 180 degrees.

the 54 and 36 one is a complementary angle

the 45 and 45 would be complementary angle

the last two on the bottom would both be supplementary angles.

High hopes-

Barry

Answer:

x = -1 and y = 1

Step-by-step explanation:

5x + 2y = -3 . . . . . . . (i)

x + 5y = 4 . . . . . . . (ii)

x + 5y = 4

x = 4 - 5y

5(4 - 5y) + 2y = -3

20 - 25y + 2y = -3

-23y = - 23

y = 1

5x + 2(1) = -3

5x + 2 = -3

5x = - 5

x = -1

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Put the x-value in the equation and do the arithmetic.

For example, ...

  for x = -5,

  y = -10(-5) +3 = 50 +3 = 53

Answer:

Step-by-step explanation:

The equation in slope-intercept form:  y = mx + b

y + 2 = -2(x - 5)

y + 2 = -2x + 10              {subtract 2 from both sides

y = -2x + 8

Answer:

me too

Step-by-step explanation:

me too

Answer:

A. Q and R

Step-by-step explanation:

The x-axis is the horizontal line. The y-axis is the vertical line.

On the x-axis, go to the left, all the way to -5.

Look at the line that goes through -5 vertically. You will see that that line intersects with both Q and R.

This means that Q and R have equal x-coordinates, -5.

They're x and y coordinates would be

Q- (-5, 6)

R- (-5, -7)

I hope this helps!

Answer: Q and R

Step-by-step explanation:

See since in the photo the Q coordinate(Q) is directly above the R coordinate(R), that can only mean that they have the same X coordinate(X) or else it wouldn't be possible for Q to be right above R. The reason Q is right above R is because their Y coordinates(Y) are different, not because of X.

I hope this helps!

Answer:

Step-by-step explanation:

There are only 2 angle values  that <1 to <8 can be. The two values add up to 180

In this case <6 and <7 are equal.

<6 = 4x - 15

<7 = x + 30

4x - 15 = x + 30             Subtract x from both sides

4x-x - 15 = 30                Add 15 to both sides

3x = 30 + 15

3x = 45                         Divide by 3

x = 45 / 3                          

x = 15

<6 = 4x - 15

<6 = 4*15 - 15

<6 = 60 - 15

<6 = 45

Answer:

y = 75.5

Step-by-step explanation:

Reference angle (θ) = 49°

Hypotenuse = 100

Opposite = y

Apply trigonometric function, SOH. Which is:

Sin θ = Opp/Hyp

Plug in the values

Sin 49 = y/100

100*Sin 49 = y

y = 75.5 (nearest tenth)

Answer:

0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean number of miles between services is 4959 miles, with a standard deviation of 448 miles

This means that [tex]\mu = 4959, \sigma = 448[/tex]

Sample of 43:

This means that [tex]n = 43, s = \frac{448}{\sqrt{43}}[/tex]

What is the probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles?

p-value of Z when X = 4959 + 111 = 5070 subtracted by the p-value of Z when X = 4959 - 111 = 4848, that is, probability the sample mean is between these two values.

X = 5070

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5070 - 4959}{\frac{448}{\sqrt{43}}}[/tex]

[tex]Z = 1.62[/tex]

[tex]Z = 1.62[/tex] has a p-value of 0.9474

X = 4848

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{4848 - 4959}{\frac{448}{\sqrt{43}}}[/tex]

[tex]Z = -1.62[/tex]

[tex]Z = -1.62[/tex] has a p-value of 0.0526

0.9474 - 0.0526 = 0.8948

0.8948 = 89.48% probability that the mean of a sample of 43 cars would differ from the population mean by less than 111 miles

Answer:

ok so its is 5 dollars for a pencil and 420 dollars for a pen(dang)

a40+2100=2140

now

b6 pencil 462 pen

60+3696=3756

Hope This Helps!!!

(a) Afua paid ¢44,500.00 for 8 pencils and 5 pens.

(b) Afua will pay ¢71,400.00 for 10 pencils and 8 pens after the price increase.

(a) To find how much Afua paid altogether for 8 pencils and 5 pens, we need to calculate the total cost for each item and then add them together.

Given:

Cost of a pencil, [tex]Pencil_{cost}[/tex] = ¢500.00

Cost of a pen, [tex]Pen_{cost}[/tex] = ¢42,000.00

Number of pencils bought, [tex]n_{pencils}[/tex] = 8

Number of pens bought, [tex]n_{pens}[/tex] = 5

Total cost of pencils,

[tex]Total_{pencil}_{cost} = Pencil_{cost} * n_{pencils}[/tex]

                      = ¢500.00 × 8

                      = ¢4,000.00

Total cost of pens,

[tex]Total_{pen}_{cost} = Pen_{cost} * n_{pens}[/tex]

                   = ¢42,000.00 × 5

                   = ¢210,000.00

Altogether, [tex]Total_{cost} = Total_{pencil}_{cost} + Total_{pen}_{cost}[/tex]                                      

                                  = ¢4,000.00 + ¢210,000.00

                                  = ¢214,000.00.

Therefore, Afua paid ¢214,000.00 for 8 pencils and 5 pens.

(b) Now, let's calculate the new total cost after the price increase.

The price of a pencil increased by 20%, which means the new pencil cost is:

[tex]New_{pencil}_{cost}[/tex] = [tex]Pencil_{cost}[/tex]+ (20% × [tex]Pencil_{cost}[/tex])

                                  = ¢500.00 + (0.20 × ¢500.00)

                                  = ¢500.00 + ¢100.00

                                  = ¢600.00

Similarly, the price of a pen increased by 10%, which means the new pen cost is:

[tex]New_{pen}_{cost}[/tex] = [tex]Pen_{cost}[/tex] + (10% × [tex]Pen_{cost}[/tex])

                          = ¢42,000.00 + (0.10 × ¢42,000.00)

                          = ¢42,000.00 + ¢4,200.00

                          = ¢46,200.00

Now, we can find the total cost for 10 pencils and 8 pens with the increased prices:

Number of pencils to be bought, [tex]n_{pencils}_{new}[/tex] = 10

Number of pens to be bought, [tex]n_{pens}_{new}[/tex] = 8

Total cost of pencils with new prices,

[tex]Total_{pencil}_{cost}_{new}[/tex] =[tex]New_{pencil}_{cost}[/tex] × [tex]n_{pencils}_{new}[/tex]

                                        = ¢600.00 × 10

                                        = ¢6,000.00

Total cost of pens with new prices,

[tex]Total_{pen}_{cost}_{new}[/tex] = [tex]New_{pen}_{cost}[/tex] × [tex]n_{pens}_{new}[/tex]

                                    = ¢46,200.00 × 8

                                    = ¢369,600.00

Altogether, [tex]New_{total}_{cost}[/tex] = [tex]Total_{pencil}_{cost}_{new}[/tex] + [tex]Total_{pen}_{cost}_{new}[/tex]

                                               = ¢6,000.00 + ¢369,600.00

                                               = ¢375,600.00

Therefore, Afua will pay ¢375,600.00 for 10 pencils and 8 pens with the increased prices.

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Answer:

[tex]y= -x^{2} -2x+15[/tex]

Step-by-step explanation:

[tex]y= -x^{2} -2x+15[/tex]