Prove: The product of the slopes of lines AC and BC is -1.

Answer:

-1/2

Step-by-step explanation:

[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]m = \dfrac{0 - 5}{10 - 0} = \dfrac{-5}{10} = -\dfrac{1}{2}[/tex]

Answer: slope = -1/2

Answer:

The perimeter of the parallelogram is 2πr

Step-by-step explanation:

The area of the circle should be the same as the area of the parallelogram. Therefore, the area of the circle cannot equal the area of the parallelogram.

Hope this helps. (:

Answer:

Step-by-step explanation:

First, we will find the midpoint for the x - coordinate first.

Midpoint (x) = [tex]\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5[/tex]

Now we will find the midpoint for the y - coordinate.

Midpoint (y) = [tex]\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5[/tex]

Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)

Answer:

Step-by-step explanation:

The ratio is 1 : 3, so we multiply the numbers by 3

4 * 3 = 12

3 * 3 = 9

So, the length is 12 and the width is 9.

12 * 9 = 108

So the area is 108

Hope this helps!

Answer:

The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

Let’s assume the speed of the plane =x miles/hr

And let the speed of wind =y miles/hr

So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr

Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr

We know that, distance=speed×time

Then according to the given conditions, we have

3300=(x+y)×(3+(18/60))

here convert 18mins to hour by dividing by 60 and add to 3hrs.

⇒x+y= 3300/3.3

⇒x+y=1000 … (i)

And,

3300=(x-y)×(4+(24/60))

here convert 24mins to hour by dividing by 60 and add to 4hrs.

⇒x-y= 3300/4.4

⇒x-y=750 … (ii)

Adding equation (i) and (ii), we get

2x=1750

⇒x= 1750/2

=875

Substituting the value of x in equation (ii), we get

875−y=750

⇒y=875-750

⇒y=125

Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

2/40 = 1/20.
We are able to simplify by dividing 2 and 40 by the greatest common factor (GCF), which was 2. We know this because 2 and 40 can be divided by 2.
2cm is 1/20th of 40cm.

The amount of money invested at 12% was $4327 while $1442 was invested at 7%.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount invested at 12% and y represent the amount invested at 7%, hence:

x + y = 5679   (1)

Also:

0.12x = 0.07y + 407.5   (2)

From both equations:

x = 4327, y = 1442

The amount of money invested at 12% was $4327 while $1442 was invested at 7%.

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The correct rectangular equivalence of 3sqrt(2)·cis(7pi/4 ) is:

3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 )  =  3 - 3i.

David mistakenly interchanged the Sin function and the Cos function when he was calculating the problem.

Hence the correct rectangular equivalence is:

3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 )  =  3 - 3i.

An equation is rectangular in form when it is comprised of Variables like X and Y and can be represented on a Cartesian Plane.

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The interval notation for all real numbers between -3 and 8 is:

[-3, 8].

There are an infinite number of real numbers between a and b, hence we list all them in interval notation, as follows:

In this problem, we include -3 and 8, hence the notation is:

[-3, 8].

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The notation "t(x)" represents the statement t is a function of x

The notation is given as:

t(x) = ....

The above notation is a function notation, and it used to relate one element  to another

For instance:

f(x) means f is a function of x

Similarly, "t(x)" represents the statement t is a function of x

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Answer: 3/11

The question is just asking you to select three people out of the group of eleven. And because we don't know there ages, the probability they are the oldest three in the group would be 3/11 or 3 out of 11.

Answer:

Exact Form:

1/243

Decimal Form:

0.00411522…

Step-by-step explanation:

if I understand your comment correctly, then you need the mean value of the lifetime of these light bulbs.

1. get the midpoint of each interval.

2. multiply each frequency with its midpoint.

3. sum all frequencies.

4. sum all multiplication results if 2. (of frequencies and midpoints).

5. divide 4. by 3.

lifetime midpoints :

(25 + 50)/2 = 75/2 = 37.5

(50 + 100)/2 = 150/2 = 75

(100 + 150)/2 = 250/2 = 125

(150 + 200)/2 = 350/2 = 175

(200 + 250)/2 = 450/2 = 225

(250 + 300)/2 = 550/2 = 275

(300 + 350)/2 = 650/2 = 325

multiply frequencies with their midpoints :

37.5 × 47 = 1762.5

75 × 86 = 6450

125 × 45 = 5625

175 × 36 = 6300

225 × 0 = 0

275 × 37 = 10175

325 × 50 = 16250

sum all frequencies

47+86+45+36+0+37+50 = 301

sum all multiplication results of 2.

1762.5+6450+5625+6300+0+10175+16250 = 46,562.5

divide 4. by 3.

the mean value is

46,562.5 / 301 = 154.692691... hours ≈

≈ 154.69 hours

False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².

Given:

a = 2√3 ft,

c = 4 ft,

Lengths of the sides of a right triangle = a and b

Hypotenuse= c

Hence:

c²=a²+b²

4²=(2√3)²+b²

16=12+b²

4=b²

b=2

Area of triangle

A=1/2×a×b

A=1/2×2√3×2

A=4√3÷2

A=2√3 sq.ft

The Area of the triangle is 2√3 ft².

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[tex]x = 12.9[/tex]

Note:

The following is sin formula:

[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]

1) Using the sin formula

[tex]sin(59) = \frac{x}{15} [/tex]

2) Multiply both sides by 15

[tex]15 \sin(59) = \frac{x}{15} \times 15[/tex]

3) Divide both sides by sin(59)

[tex] \frac{15 \sin(59) }{ \sin(59) } = \frac{x}{ \sin(59) } [/tex]

4) Find the value of x

[tex]x = 15 \sin(59) [/tex]

[tex]x = 12.9[/tex]

Taking into account the rule of three, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.

The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following expression must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: [tex]x=\frac{cxb}{a}[/tex]

On October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos. So, you can apply the following rules of three:

1 dollar ⇒ 13.65 Mexican pesos

81.35 dollars ⇒ x

So: [tex]x=\frac{81.35 dollarsx13.65 Mexican pesos}{1 dollar}[/tex]

Solving:

x= 1110,4275 Mexican pesos

13.65 Mexican pesos ⇒ 1 dollar

91.03 Mexican pesos ⇒ x

So: [tex]x=\frac{91.03 Mexican pesosx 1 dollar}{13.65 Mexican pesos}[/tex]

Solving:

x= 6.67 dollars

In summary, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.

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The amount of interest that the principal in each account had earned is as follows:

Raul Avila = $167.12

Samuel Griffin = $364.91

The compound interest can be calculated using the compound interest formula:

A = P(1 + \frac{r}{n})^{nt}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

It can also be computed using an online finance calculator as follows:

N (# of periods) = 110 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

FV = $10,167.12

Total Interest = $167.12

N (# of periods) = 120 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $20,000

PMT (Periodic Payment) = $0

Results:

FV = $20,364.91

Total Interest = $364.91

Thus, using the online finance calculator, the compound interests for each principal have been computed as $167.12 and $364.91, respectively.

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n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.

Since these are solutions

x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.

We have (x-2)(x-5i)(x+5i) = 0

Now,

f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.

f(-1) = (-3)(26) = -78.

But -78 x -2 = 156, so our polynomial becomes

Y= -2x (x - 2 ) x (x to the power of 2 + 25) = 0

Answer:

[tex]f(x)=2x^4-12x^3+50x^2-56x-120[/tex]

Step-by-step explanation:

Complex Conjugate Theorem

For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs.  So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.

Given zeros:

-1, 3, and (2 + 4i)

As one of the given zeros is a complex number, (2 - 4i) is also a zero.

Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:

[tex]\begin{aligned}f(x) & =a(x+1)(x-3)(x-(2+4i))(x-(2-4i))\\& = a(x+1)(x-3)(x-2-4i)(x-2+4i)\\& = a(x+1)(x-3)(x^2-2x+4ix-2x+4-8i-4ix+8i-16i^2)\\& = a(x+1)(x-3)(x^2-4x+4-16i^2)\end{aligned}[/tex]

Remember that [tex]i^2=-1[/tex], therefore:

[tex]\begin{aligned}f(x)&=a(x+1)(x-3)(x^2-4x+4-16(-1))\\&=a(x+1)(x-3)(x^2-4x+4+16)\\&=a(x+1)(x-3)(x^2-4x+20)\end{aligned}[/tex]

To find the value of the leading coefficient (a), use the given [tex]f(1)=-136[/tex] :

[tex]\begin{aligned}f(1) & = -136\\\implies a(1+1)(1-3)(1^2-4(1)+20) & = -136\\a(2)(-2)(17) & = -136\\-68a & = -136\\\implies a & = 2\end{aligned}[/tex]

Therefore, the polynomial in factored form is:

[tex]f(x)=2(x+1)(x-3)(x^2-4x+20)[/tex]

Finally, expand the brackets:

[tex]\begin{aligned}f(x) & =2(x+1)(x-3)(x^2-4x+20)\\& =2(x^2-2x-3)(x^2-4x+20)\\& =2(x^4-4x^3+20x^2-2x^3+8x^2-40x-3x^2+12x-60)\\& =2(x^4-4x^3-2x^3+20x^2+8x^2-3x^2-40x+12x-60)\\& =2(x^4-6x^3+25x^2-28x-60)\\& =2x^4-12x^3+50x^2-56x-120\end{aligned}[/tex]

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Answer:

C.

Step-by-step explanation:

The function that correctly returns grades from 60 percent to a 100 percent is f(x) = [[(x - 50)/10]]

The question tells us that the students do not fail and they do not get a 100 percent score either.

Hence there is no need for worry if the grade is at 5.0 or less than 1.

For example we have

x = 82.976

f(82.976) =[[(82.976-50)/10]

This would then be 3.29

This is then = 3.0

This function is not an odd function and it is not an even function. This is because the domain does not have negative values.

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Answer:

Height is 40√2 m or 56.57 m

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are the legs and 'c' is the hypotenuse

Here given:

Substitute values:

(20)² + (h)² = 60²

400 + h² = 3600

h² = 3600 - 400

h² = 3200

h = √3200

h = 40√2

h = 56.6 meter

Answer:

Your answer is -2/-3

The formula to calculate slope is y2-y1/x2-x1

I think it will help you

The numbers are:

What is number system?

A number system is defined as a system of writing to express numbers.

First, the number between 8,500 and 8,800.

So, the thousands place digit is 8.

Second, When multiplied by 8, the result is a whole number.

So, multiplying by 8, the decimal has to end in 5.

Because there is no zeroes in the decimal place..

options are:

8 times 0.5

8 times 0.25

8 times 0.125

Now, The digit in the hundredths place is 200% of the digit in the tenths place

considering digit in the hundreds place is ¾ the digit in the thousands place.

So, choose 0.125.

Now, The digit in the hundreds place is 3/4 the digit in the thousandths place.

Digit in Thousandth Place = 5

Digit in Hundreds place=3/4*2=6

Our number now is:86_ _.125

As, The sum of all the numbers is 26

8+6+1+2+5=22

26-22=4

The possible numbers are:

8,640.125

8,604.125

8,622.125

8,613.12

8,631.125

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The amount of heavy-duty fencing to be used is 2000 ft for $9000 and the amount of standard fencing to be used is 3000 ft for $9000 in order to make a total cost of $18000.

The area of the rectangular plot is denoted by the length multiplied by the width.

Let us assume that the length = x and the width = y.

Then, for two opposite with heavy fencing for $4.50 a foot and the standard fencing for $3 a foot, we have:

2x (4.50) + 2y(3) = 18000  ---- (1)

⇒ 9x + 6y = 18000

Make (y) the subject, we have:

[tex]\mathbf{y = \dfrac{18000-9x}{6}}[/tex]

Replace the value of y with the area of the rectangle, and we get:

[tex]\mathbf{Area =x(\dfrac{18000 - 9x}{6})}[/tex]

Area = x(3000 - 1.5x)

Area = 3000x - 1.5x²

For the area to be maximum, we take the differentiation of the Area:

dA/dx = 0

dA/dx = 3000 - 3x

x = 3000/3

x = 1000 ft

From equation (1)

2x (4.50) + 2y(3) = 18000  

x (4.50) + y(3) = 9000  

1000(4.50) + 3y = 9000

3y = 9000 -4500

y = 4500/3

y = 1500 ft

So, there are (1000× 2)ft = 2000ft heavy duty fencing for $9000, and (1500 ×2)ft = 3000ft standard fencing for $9000 to make a cost of $18000.

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A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

The area of AEDC is 25 cm². Therefore,

AEDC = AC²

25 cm² = AC²

AC = 5 cm

In ΔABC,

AB² + BC² = AC²

Since AB=BC,

2(AB²) = AC²

AB² = 25/2

AB = 5/√2 cm

Hence, the length of side AB is 5/(√2) cm.

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The total surface area of a cylinder with radius 4 and height 8 is 96π.

It follows from the task content that the total surface area of the cylinder is to be determined. The total surface area of the cylinder is given by the formular;

S=2πr(r+h)

S=2πr(r+h)

= 2 × π × 4(4 + 8)

= 2 × π × 4(12)

= 2π × 48

= 96π

Hence, the total surface area of the cylinder in terms of π is; 96π.

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Answer:

19/24

Step-by-step explanation:

3/8=36/96

5/12=40/96

36/96+40/96=76/96

76/96=19/24

The equation of the function is the graph of line.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The function is given below.

f(x) = (3/4)x – 2

The function is an equation of line.

The graph of the function is given below.

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Answer:

150

Step-by-step explanation:

Mean is average, so adding any number above the original mean would increase the mean.

Answer: A

Step-by-step explanation:

Following the first two steps of the sequence of transformations,

[tex]A(-4,-2) \longrightarrow (-2,-1) \longrightarrow (-2,1)[/tex]

We need to map this onto D(1,1), which involves a translation 3 units right.

In the similarity transformation of ΔABC to ΔDFE, ΔABC was dilated by a scale factor of [1/2 ], reflected across the [x-axis ], and moved through the translation [(X+3, Y+0)].

So, correct option is: A.

Here, we have,

from the given fugre we get,

A =( -4, -2)

Following the first two steps of the sequence of transformations,

Dilated by a factor of 1/2 => A' = ( -2, -1)

reflected across the X-axis => A''=( -2, 1)

and moved through the translation becomes D = ( 1,1)

We need to map this onto D(1,1), which involves a translation 3 units right.

so, translation=> ( -2 + 3, 1+0) => (X+3, Y+0)

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