Kevin has a rectangular farm mapped on a coordinate plane. He wants to make a fence along one of the longer sides of the farm. What would be the length of the fence? A. 6 B. 10 C. 12 D. 8

Answer:

complex conjugates

Step-by-step explanation:

The factors (5 + i) and (5 – i) are called complex conjugates.

Answer:

complex conjugates

Step-by-step explanation:

Numbers of the form a+ bi and a - bi are complex conjugates.

Their product is real.

Any rectangle is also a parallelogram (but not the other way around). So AB is parallel to CD. The angles BAC and ACD are alternate interior angles that are congruent due to the parallel sides mentioned.

(angle BAC) = (angle ACD)

3x+4 = x+28

3x-x = 28-4

2x = 24

x = 24/2

x = 12

So,

angle BAC = 3x+4 = 3*12+4 = 40 degrees

and

angle CAD = 90 - (angle BAC) = 90 - 40 = 50 degrees

With any rectangle, the four interior angles are always 90 degrees. So that's why angles BAC and CAD add to 90.

[tex]\text{Solve for v:}\\\\4v-8\leq5v+5\\\\\text{Subtract 5v from both sides}\\\\-v-8\leq5\\\\\text{Add 8 to both sides}\\\\-v\leq13\\\\\text{Divide both sides by -1, while also flipping the inequality}\\\\\boxed{v\geq-13}[/tex]

Answer:

v>=-13

Step-by-step explanation:

4v-8<=5v+5

4v-5v-8<=5

-v-8<=5

-v<=5+8

-v<=13

v<=-13

v>=-13

Answer:

x-y is parallel, im confused on what your asking for and what you mean by "negative"

Step-by-step explanation:

The  equation of a line that is perpendicular to line g that contains (P, Q). is 3x − y = 3P − Q

The general form of the equation of a line with a slope m and passing through the point (x1, y1) is given as: y - y1 = m ( x- x1)

Further, this equation can be solved and simplified into the standard form of the equation of a line.

Given:

Line g passes through (3,6) and (0,5).

Slope of lone= y2 - y1/ (x2 - x1)

Perpendicular lines have opposite, reciprocal slopes, so negative change in x over change in y.

slope of line= -(-3 - 0)/(6 - 5)

                      = - -(-3)/1 =

slope of line = 3

Now, Two lines are perpendicular if they have the same slope.

Line parallel to line g has a slope of 1. Since it passes through (P, Q),

y - y1 = m ( x- x1)

y- Q =3 ( x- P)

y- Q = 3x- 3P

3x − y = 3P − Q

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Answer:

1.4a > 5+a

Step-by-step explanation:

If the number is increased by 40% of that number, then it multiplies by 1.4. So, the left side of the equation is 1.4a.

On the right side of the equation, if the number is increased by 5, then the equation is a + 5.

Since the left side of the equation is more than the right side of the equation, we add a greater than sign. So the expression is 1.4a > 5+a

Answer:

I think it is 32 hopes its right

Answer:

it is moved away in .625 seconds

Step-by-step explanation:

i did 5 divided by 8 though this question is weriod

Assuming the ladder is leaning against the wall and there are no spaces in between (that doesn't make sense sorry), it is still at a rate of 8 meters per second because it is standing straight up. It is moving at the same rate, since it is the same ladder.

Answer:

1. half circle: C = (2πr) / 2

a. C = (2π4) / 2 ≈ 12.566

2. triangle:

a. find slant / hypotenuse.

i. 4² + 10² = c²

ii. 16 + 100 = c²

iii. c² = 116

iv. c ≈ 10.770

b. add both slants to find triangular area

i. 10.77 + 10.77 ≈ 21.54

3. add:

a. 12.566 + 21.54 ≈ 34.106 cm

hope this helps :)

Answer:

Step-by-step explanation:

Since g(x) is the inverse of f (x) to find g(x) must first find f-¹(x)

To find f-¹(x) equate f(x) to y

That's

f(x) = y

y = 4x + 12

Next interchange the terms x becomes y and y becomes x

That's

x = 4y + 12

Next make y the subject

4y = x - 12

Divide both sides by 4

Therefore

Hope this helps you

Hi there! Hopefully this helps!

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Question: "Prove that a^{4} + b^{4} + c^{4} > abc(a + b + c) , where a, b, c are different positive real numbers."

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From the AM and GM inequality, we have:

a^4 + b^4 ≥ 2a^2b^2

b^4 + c^4 ≥ 2b^2c^2

c^4 + a^4 ≥ 2a^2c^2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From adding the inequalities we have above and dividing by 2, we have:

a^4 + b^4 + c^4 ≥ a^2b^2 + b^2c^2 + c^2a^2......1

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now we need to repeat the process of a^2b^2, b^2c^2, and c^2a^2 to get:

a^2b^2 + b^2c^2 ≥ 2b^2ac

b^2c^2 + c^2a^2 ≥ 2c^2ab

c^2a^2 + a^2b^2 ≥ 2a^2bc

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, we add from what we have above and divide by 2 to get:

a^2b^2 + b^2c^2 + c^2a^2 ≥ (b^2ac + c^2ab + a^2bc) or abc(b + c + a).....2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So, from (1) and (2) it follows:

a^4 + b^4 + c^4 ≥ abc( a + b + c)

Answer:

0.5

Step-by-step explanation:

a+b+c=0—(1)  

a2+b2+c2=1—(2)  

We know that:

(a+b+c)2=a2+b2+c2+2ab+2bc+2ca—(3)  

Substituting  (1)  and  (2)  in  (3) ,  0=1+2(ab+bc+ca)  

=>ab+bc+ca=−0.5—(4)  

Squaring:  (ab+bc+ca)2=0.25  

=>a2b2+b2c2+c2a2+2ab2c+2bc2a+2a2bc=0.25  

=>a2b2+b2c2+c2a2+2abc(a+b+c)=0.25  

Since  a+b+c=0 ,

a2b2+b2c2+c2a2=0.25—(4)  

squaring  (2) :

(a2+b2+c2)2=12

=>a4+b4+c4+2a2b2+2b2c2+2c2a2=1  

=>a4+b4+c4+2(a2b2+b2c2+c2a2)=1—(5)

Substituting (4) in (5),

a4+b4+c4+2(0.25)=1

=>a4+b4+c4=0.5

Hope this helps :D

Answer:

9 1/5

Step-by-step explanation:

3 2/7 * 2 4/5

Change to improper fractions

( 7*3+2)/7  * ( 5*2+4)/5

23/7 * 14/5

Rewriting

14/7 * 23/5

2 * 23/5

46/5

Changing back to a mixed number

5 goes into 45 9 times with 1 left over

9 1/5

The product of 3 2/7 and 2 4/5 is 9 1/5 in simplest form as per the concept of simplifying fractions.

To multiply the mixed numbers 3 2/7 and 2 4/5, we need to convert them to improper fractions and then perform the multiplication.

First, convert 3 2/7 to an improper fraction:

3 2/7

= (3 x 7 + 2) / 7

= 23/7

Next, convert 2 4/5 to an improper fraction:

2 4/5

= (2 x 5 + 4) / 5

= 14/5

Now, multiply the two improper fractions:

(23/7) x (14/5) = (23 x 14) / (7 x 5)

                      = 322/35

To simplify the resulting fraction, we find the greatest common divisor (GCD) of the numerator (322) and the denominator (35), which is 7. Divide both the numerator and the denominator by the GCD:

322/35

= (322/7) / (35/7)

= 46/5

Now, express the improper fraction as a mixed number:

46/5 = 9 1/5

Therefore, the product of 3 2/7 and 2 4/5 is 9 1/5 in simplest form.

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Area of a quarter of circle

A = 1/4 * π * R²

A = 1/4 * π * 12²

A = 36 * π cm²

Perimeter of a quarter of circle

P = 1/4 * 2 * π * R²

P = 1/4 * 2 * π * 12²

P = 72 * π cm

Area of a right triangle

A = b * h / 2

A = 12 * 12 / 2

A = 72 cm²

Length of hypotenuse

L = 12√2 cm

Area of blue

A = 36 * π - 72

Perimeter of blue

Hope it helps

xxx

Answer:

e) 75

Step-by-step explanation:

Given the following :

Total length of cable = 60 foot

Length of each stripe = (4/5) of a feet

Number of stripes = ( total cable length / length of each stripe)

Number of stripes = ( 60 / (4/5))

Number of stripes = 60 ÷ 4/5

Number of stripes = (60 * (5/4)

= (60 * 5) / 4

= 300 / 4

= 75

Number of stripes made = 75

Answer:

[tex]\boxed{r=3}[/tex]

Step-by-step explanation:

We can use SAS ≅ SAS congruence to validate that the triangles are similar (both share the same side, have another congruent side, and have a congruent angle).

Because the sides are congruent, set them equal to each other and solve for r.

18 - 2r = 4r

18 = 6r

3 = r ⇒ [tex]\boxed{\bold r = 3}[/tex]

Therefore, the answer is D.

Answer:

r = 3

Step-by-step explanation:

Here Triangle ALR is divided precisely in half by the vertical side LU.  The two triangles thus formed are therefore congruent.

Thus, 18 - 2r = 4r, and 6r = 18.  Then r = 3.

Answer:

a=4

Step-by-step explanation:

When going from degrees to radians, 180 degrees is always going to equal π radians

That means 2π would be 360 degrees, and 4π would be 720

And since we're trying to find a in aπ when it's a 720 degree angle, we can conclude that a=4

Answer:

4

Step-by-step explanation:

We know that:

Then:

The value of a:

Answer:

24.43

Step-by-step explanation:

first find the price of One sachets

next Find the no. of sachets consumed for four weeks..

and at last the product of the price of one sachet and no. of sachets consumed will give the answer...

Mathematical operation are above...

Answer:

132

Step-by-step explanation:

If US bisects the angle then

BUS = SUL

2x+10 = 3x-18

Subtract 2x from each side

2x+10 -2x = 3x-18-2x

10 = x-18

Add 18 to each side

10+18 =x

28 =x

We want to find BUL

BUL = BUS + SUL

      2x+10 + 3x-18

     5x-8

    5*28 -8

   140-8

   132

Answer:

m<BUL=132

Step-by-step explanation:

Since US bisects <BUL, we know that <BUS ≅ <SUL

This is based on the angle bisector definition.

Hence, we can set up an equation to solve for x.

<BUS≅<SUL

2x+10=3x-18

Subtract 10 from both sides

2x+10-10=3x-18-10

2x=3x-28

Subtract 3x from both sides

2x-3x=3x-3x-28

-x=-28

Divide both sides by -1

x=28

m<BUL is the sum of m<BUS and m<SUL

m<BUL=m<BUS+m<SUL

m<BUS=2x+10

m<SUL=3x-18

Plug it in

m<BUL=2x+10+3x-18

Combine like terms

m<BUL=5x-8

Plug in 28 for x

m<BUL=5(28)-8

m<BUL=140-8

m<BUL=132

Answer:

  2 triangles

Step-by-step explanation:

The given angle is opposite the shorter of the given sides, so the number of triangles is 2. (30/25·sin(42°) ≈ 0.8 < 1)

_____

Additional comment

For the case where the shorter given side is opposite the given angle, there is the possibility that the triangle could be a right triangle (1 solution) or that there may be no solutions. You can tell the difference by computing ...

  (long side)/(short side) × sin(given angle)

If this result is exactly 1, the triangle is a right triangle. If it is greater than 1, the triangle cannot exist (no solutions). Since the sines of most angles are irrational, it is unlikely you will see this result be exactly 1 (except for a 30°-60°-90° right triangle).

These observations are a consequence of the Law of Sines, which tells you ...

  sin(A) = (a/b)sin(B)

For real angles, sin(A) ≤ 1.

Answer:

Step-by-step explanation:

The rate at which distance is increasing between the birds is ...

  r = d/t = (402 mi)/(6 h) = 67 mi/h

This is the sum of the speeds of the two birds, so is 15 mph more than double the speed of the slower bird. That bird's speed is then ...

  (67 -15)/2 = 26 . . . miles per hour

The faster bird is 15 mph faster so is 26+15 = 41 mph.

The slower bird's speed is 26 mph; the faster bird's speed is 41 mph.

Answer:

6

Step-by-step explanation:

If a number and a variable were together in a term, the number would the the coefficient. The coefficient would multiply the variable.

In '6x', the number '6' is the coefficient. '6' would be multiplying 'x'.

The correct answer should be 6.  

Answer:

D. -4

Step-by-step explanation:

Using the general formula, [tex] m = \frac{f(b) - f(a)}{b - a} [/tex] , average rate of change for the quadratic function from x = 1 to x = 3, can be calculated as shown below:

Where,

[tex] a = 1, f(1) = -2 [/tex]

[tex] b = 3, f(3) = -10 [/tex]

Plug in the above values in the average rate of change formula:

[tex] m = \frac{-10 - (-2)}{3 - 1} [/tex]

[tex] m = \frac{-10 + 2}{2} [/tex]

[tex] m = \frac{-8}{2} [/tex]

[tex] m = -4 [/tex]

Average rate of change is D. -4

Answer:

B) The vertex will shift down.

Step-by-step explanation:

In the equation of a parabola, (y - k)² = 4p(x - h), (h, k) is the vertex.

The original parabola's vertex was (3, -2).

In the new parabola, the y-coordinate changed to -10, making the new vertex (3, -10).

So, the parabola's vertex shifted down 8 units from -2 to -10.

Answer:

Step-by-step explanation:

To match each number with its place in order from smallest (1st) to largest (6th).

1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48

First we write all numbers:  -56, 90, -84, 59, -80, 48

In Ascending order ( from smallest to largest): -84, -80,-56, 48, 59, 90

Here, the required arrangement:

C)

Because if you choose some points for example x = 0 and x = 3.14 (≈ pi)

you will see that there's only one match.

Answer:

Option C. y = cos x -2

Step-by-step explanation:

Answer:

[tex]x= \sqrt{503}-3[/tex]

Step-by-step explanation:

Hypotenuse = 32 feet

Short leg = x

Long leg = x+6

We will use Pythagoras theorem

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]32^2=x^2+(x+6)^2[/tex]

[tex]1024=x^2+x^2+36+12x[/tex]

[tex]2x^2+12x-988=0[/tex]

[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]

Since the distance cannot be negative

So,[tex]x= \sqrt{503}-3[/tex]

Answer:

Step-by-step explanation:

To the nearest tenth:  53.2

To the nearest thousandth:  53.185

To the nearest whole number:  53

Answer:

y=¾(4x-20)

y=3x-15

Final answer= y - 3(x+12)

=y - 3x-36

=3x-15-3x-36

= -51

Answer:

The answer is -51

Step-by-step explanation:

Table Given in the question :

Open = HT 111 = 8

Side = 1111 = 4

Side = HT 111 = 8

Answer:

The probability of landing on the open end is greater.

Step-by-step explanation:

Given the experimental probability distribution :

Open = HT 111 = 8

Side = 1111 = 4

Side = HT 111 = 8

The experimental probability is the ratio of the number of times an event occurs and the total number of trials.

P(A) = number of times A occurs / total number of trials

Where A is defined event.

COMPARING the probabilities of open and closed events

P(open) = 8 / 20 = 2 / 5

P(closed) = 4 / 20 = 1/5

2/5 > 1/5

P(open) > P(closed)

Answer:5,3,7

2,4,9

3,6,4

Step-by-step explanation:he determinant of a 2 x 2 matrix A,

EVALUATING A 2 X 2 DETERMINANT,

DETERMINANT OF A 3 X 3 MATRIXFINDING THE DETERMINANT OF' A MATRIX,

FINDING THE COFACTOR OF AN ELEMENT,                                          ,EVALUATING A 3 X 3 DETERMINAN,

EVALUATING A 4 X 4 DETERMINANT

voila

Answer: The answer is 15. You can use the calculator in Edge2020

Step-by-step explanation:

Edg2020

Answer:

$2.25/km

Step-by-step explanation:

The cost charged for a total taxi ride of [tex]14\frac{2}{9}\ km[/tex] was $32. To get the cost per km, we divide the cost charged for the total taxi ride by the total distance that was traveled by the taxi. The cost per km is given by:

Cost per km = [tex]\frac{Cost \ of\ money\ charged}{Total\ distance}=\frac{\$ 32}{14\frac{2}{9} \ km}=\frac{32}{\frac{128}{9} }= \$2.25/km[/tex]

Therefore the cost per kilometer is $2.25 per kilometer. Each kilometer traveled by the taxi cost $2.25.