What are the dimensions of the rectangle shown on the coordinate plane?

9514 1404 393

Answer:

  (x, y) = (59/45, 11/15) ≈ (1.311, 0.733)

Step-by-step explanation:

A graphing calculator shows us the solution is not integer values, so we may find it easiest to solve these equations using the "cross-multiplication method."

Writing the equations in general form, we have ...

  3x -4y -1 = 0

  6x +7y -13 = 0

Then we can form an array of the coefficients, repeating the first column:

  [tex]\begin{array}{cccc}3&-4&-1&3\\6&7&-13&6\end{array}[/tex]

Forming differences of cross products involving adjacent pairs of columns gives ...

  d1 = (3)(7) -(6)(-4) = 45

  d2 = (-4)(-13) -(7)(-1) = 59

  d3 = (-1)(6) -(-13)(3) = 33

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

or

  x = d2/d1 = 59/45

  y = d3/d1 = 33/45 = 11/15

The solution is (x, y) = (59/45, 11/15) ≈ (1.311, 0.733).

_____

Additional comment

This takes longer to explain than to do. One reason we like it is that the number of math operations is slightly smaller than the number of math operations required for substitution or elimination. It is especially nice when the solution is not a pair of integers.

Answer:

R=3K/P

Step-by-step explanation:

P=3K/R

RP=3K

RP/P=3K/P

R=3K/P

Answer:

pythagorean theorem

18

Step-by-step explanation:

Answer:

v=9

Step-by-step explanation:

Given the right triangle is a 30-60-90 triangle, we can simply make the equation v√3=9√3 since the longest side of a 30-60-90 triangle is √3 times as big as its short side. Therefore, v=9.

Answer:

[tex]AB = 21.3[/tex]

Step-by-step explanation:

Given

[tex]\sin(25) = \frac{9}{c}[/tex]

See attachment

Required

Find AB

We have:

[tex]\sin(25) = \frac{9}{c}[/tex]

Make c the subject

[tex]c = \frac{9}{\sin(25)}[/tex]

[tex]c = 21.3[/tex]

From the attached triangle;

[tex]AB = c = 21.3[/tex]

Hence:

[tex]AB = 21.3[/tex]

Answer:

x = 11

Step-by-step explanation:

<4 and <5 are alternate interior angles and alternate interior angles are equal when the lines are parallel

<4 = <5

7x+5 = 5x+27

Subtract 5x from each side

7x+5-5x = 5x+27-5x

2x+5 = 27

Subtract 5 from each side

2x+5-5=27-5

2x =22

Divide by 2

2x/2 =22/2

x =11

I-moom equation is 12x+3

I-toons equation is 10x+9

Answer:

1.41

2.17

Hope this helps u

Explanation:

In Venn diagrams, similarities in both things are in the middle of the diagram, but we also have the others.

Therefore, there are 41 students who like tennis and swimming.

Students who don't like tennis like swimming, so that's 17.

Therefore, there are 17 students who don't like tennis.

I hope I helped!

Answer:

-x-6=y

Step-by-step explanation:

Perpendicular slope is -1

-1(-4)+b=-2

B=-6

Answer:

Determine the equation of the line perpendicular to the line y = –8 through the point (–4, –2).

The line y = –8 is

✔ horizontal

The line perpendicular to the line y = –8 is

✔ vertical

The equation of the line perpendicular to the line y = –8 through the point (–4, –2) is

✔ x = –4

Step-by-step explanation:

i got it right

Answer:

16 pages

Step-by-step explanation:

1 hour= 2 pages written of notes

so 8 hours of notes = 8x2=16 pages

Answer:

well, we only no that

2l + 2w is 80

(lengths and widths on all 4 sides

and that w * l is A

so the function should be w times what's left for l, but also expressed by something with w

2l + 2w = 80 | -2w

2l = 80 -2w | devide by 2

l = 80 - w

now we can substitute l in

A = w * l

so that we only need w's

A(w) = w * (80-w)

for any w it will give us the area, makes only sense for 0<w<80

Answer:

A

radius is 11

diameter is 22

B

radius is 15

diameter is 30

C

radius is 13

diameter is 26

D

radius is 7

diameter is 14

Answer:

Step-by-step explana

1- R == 11

D=2R = 22

2-D =30

R= 0.6D = 15

3- D = 26

R= 0.5D= 13

4 - R= 7

D= 2R = 14

Answer:

B

Step-by-step explanation:

0.3 is weakest

This is the same as 7.5pi

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

Explanation:

Refer to the previous post I answered a while back. It's a similar problem, just with different numbers.

Instead of following that exact route, I'll use a more direct route this time. I'll use the formula below

S = (x/360)*pi*r^2

where S is the area of the sector (aka pizza slice), x is the angle of the sector, and r is the radius.

Notice the x/360 portion represents taking a fractional part of the full circle area pi*r^2

-----------------------

Plugging in the given values leads us to...

S = (x/360)*pi*r^2

S = (108/360)*pi*5^2

S = (3/10)*pi*25

S = (3/10)*25*pi

S = 75pi/10

S = 15pi/2

This is the same as 7.5pi because 75/10 = 15/2 = 7.5

I'll leave it as a fraction since the previous answer I wrote was in fraction form.

-------------------------

Side note: if the angle x is in radian mode, then you'll use this formula

S = (x/2)*r^2

Answer:

7.5π square meters

Step-by-step explanation:

The formula for the area of a sector (when angle is given in degrees) is: [tex]A=\frac{\theta}{360}\pi r^{2}[/tex]

Where r is the radius, and [tex]\theta[/tex] is the angle of the sector in degrees.

We are given the information that the radius = 5m, and [tex]\theta[/tex] = 108 degrees. So now we can just substitute these values into the equation to solve for A:

[tex]A=\frac{108}{360}\pi 5^{2}\\\\A=0.3\pi * 25\\A = 7.5\pi[/tex]

(OR approx. 23.56 square meters)

Hope this helped!

Answer:

3

Step-by-step explanation:

Express the numbers as a product of their primes.

42 = 2 × 3 + 7

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Identify the prime factors common to all 3 numbers.

common prime factor = 3 , thus

GCF = 3

Answer: 3

Step-by-step explanation: The factors of 30 are 1. 2. 3. 5. 6. 10, 15, 30

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 45 are 1, 3, 5, 9, 15, 45

As you can see they all share the factors of 1 and 3. Since 3 is the greatest number of the factors all of them share it is the greatest common factor.

Answer:

r = 3 in

Step-by-step explanation:

The volume (V) of a sphere is calculate as

V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )

Here V = 36π , then

[tex]\frac{4}{3}[/tex]πr³ = 36π ( multiply both sides by 3 to clear the fraction )

4πr³ = 108π ( divide both sides by 4π )

r³ = [tex]\frac{108\pi }{4\pi }[/tex] = 27 ( take the cube root of both sides )

r = [tex]\sqrt[3]{27}[/tex] = 3

Step-by-step explanation:

hope the picture above help u to understand:)

Answer:

222 yds^3

Step-by-step explanation:

First find the volume of the back rectangular prism

V = l*w*h = 9* 6*3 =162

Then find the volume of the front rectangular prism

V = 5*4*3 = 60

Add them together

V total = 162+60 =222 yds^3

Answer:

A

Step-by-step explanation:

Area of rectangle  = length x width

length = 5x - 2

width = x

area = (5x - 2) × x

100 = 5x² - 2x

the width would be less than the area of the rectangle, thus the inequality sign to be used is <

5x² - 2x < 100

Answer:

Step-by-step explanation:

x-3=0mod 4 means

if x-3 is divided by 4 ,remainder is zero.

[tex]\frac{x-3}{4} =m(say)\\x-3=4m\\x=4m+3[/tex]

where m is an integer.

Answer:

m∠RUT=1/2 m∠RST

=1/2(68)

=34°

m∠RUT=34°

Answer:

1/2 or 50% or .5

Step-by-step explanation:

She hits at .500 that's pretty good. I'd take her on my fantasy team.

Answer:

Second one

Step-by-step explanation:

Integers are any whole numbers ( can be negative or positive )

The only answer choice that contains only whole numbers is the second one

Answer:

18.0

Step-by-step explanation:

The three lines form a right triangle where 10 and 15 are the two legs of the triangle. You can use the pythagorean theorem to solve for the length of x.

x = [tex]\sqrt{15^{2} + 10^{2} }[/tex]

x = 18.028 (approximately 18)