(08.01) Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point

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:

It is ASA congruence rule as the 2 angles and the included side of the triangle are equal

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

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

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:

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.

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. 945 m^3

Step-by-step explanation:

We just need to find the volume of the big box and the small box and find the difference.

To find the volume of a box, we multiply length, width, and height

Big box:

15.3x7x10=1071

1071

Small box:

4.2x3x10=126

126

1071-126=945

945 m^3

Answer:

b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The area of triangle PQR which is an SAS triangle, to the nearest tenth, is: A. 24.1 m²

The area of an SAS triangle = ½ × bc × sin(A).

Given the following:

Area of triangle PQR = ½ × (14)(6) × sin(35)

Area of triangle PQR = 24.1 m²

Learn more about the area of an SAS triangle on:

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Answer:

35

Step-by-step explanation:

The median is the middle number in the data

The middle is the line in the middle of the box

Median is 35

In a box plot, the median can be found by looking the middle dot in the rectangle.

As we can we, the middle dot represents 35 and the median.

Best of Luck!

Answer:

48-20

Step-by-step explanation:

The distance of the surveyor from the bottom of the building is  125.1 feet.

You look straight parallel to the ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called the angle of elevation.

Assume the distance of the surveyor from the bottom of the building is represented by x.

First, we have to know that the Tan of 48° is equal to 1.11.

The equation to get the distance will then be;

tan(48) = 50/h

h = 45.05  feet

Now, tan(20) = 45.05  /x

x = 45.05  / 0.36

x = 125.1 feet

The distance of the surveyor from the bottom of the building is  125.1 feet.

Learn more about trigonometric;

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Answer:

For those who achieve a year of sobriety, less than half will relapse. If you can make it to 5 years of sobriety, your chance of relapse is less than 15 percent.

So A

Answer:

2

Step-by-step explanation:

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:

[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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I'll do the first two to get you started

===============================================

Problem 1

A = 3 = starting value

B = 10 = ending value

C = percent change

C = [ (B - A)/A ] * 100%

C = [ (10-3)/3 ] * 100%

C = (7/3) * 100%

C = 2.3333333 * 100%

C = 233.33333%

C = 233.3%

The positive C value means we have a percent increase. If C was negative, then we'd have a percent decrease.

===============================================

Problem 2

A = 9 = start value

B = 20 = end value

C = percent change

C = [ (B - A)/A ] * 100%

C = [ (20-9)/9 ] * 100%

C = (11/9)*100%

C = 1.2222222222*100%

C = 122.22222222%

C = 122.2%

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:

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:

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

Step-by-step explanation:

R is 4 times so the equation will be

32 = 4r

32/4 = r

8 = r

Answer:

A. 0

Step-by-step explanation:

In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices.  Since four is the smallest number, the other two must have four left as well.  That means Donavan drank 1 spoiled milk and 2 flat sodas.  Therefore, he drank 0 purified water.

Answer: Speed  of first bird =41 mph

Speed of second bird = 26 mph

Step-by-step explanation:

Let x be the speed of the second bird, then the speed of first bird will be x+15.

After 6 hours ,

Distance covered by first bird= (x+15)(6)      [Distance = speed × time]

= 6x+90

Distance covered by second bird= (x)(6) = 6x

After 6 hours the two birds are 402 miles apart.

[tex]\Rightarrow\ 6x+90+6x=402\\\\\Rightarrrow\ 12x=402-90\\\\\Rightarrow\ 12x=312\\\\\Rightarrow\ x=\dfrac{312}{12}\\\\\Rightarrow\ x=\dfrac{312}{12}=26[/tex]

Speed of second bird = 26 mph, Speed  of first bird = 26+15 = 41 mph.

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:

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:

[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]

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.

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:

I think it is 32 hopes its right

Answer:

  all real numbers

Step-by-step explanation:

The function f(x) = 3|x +4| +1 is defined for all values of x. Its domain is all real numbers.

Answer:

16$ per shirt

Step-by-step explanation:

60% of 10 is 6

10 + 6 = 16