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3 years ago

3x+5y=78 2x-y=0 the point of intersection of the lines has an x-coordinate of what

1 answer:

4 0

In order to find where these two lines intersect you must solve them simultaneously x

3x +5y = 78.... (1)

2x - y = 0 ........(2)

by multiplying eq (2) by 2 and adding it to eq (1)
5(2x - y = 0) ..... (3)
10x - 5y = 0 ..... (3)

eq(3) + eq (1) : 10x + 3x +5y - 5y = 78 + 0
⇒ 13x = 78
⇒ x = 6

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A dog weighs 2 pounds less than 3 times the weight of a cat. The dog weighs twenty two more pounds than the cat

Nesterboy [21]

Complete Question

A dog weighs 2 pounds less than 3 times the weight of a cat. The dog weighs twenty two more pounds than the cat.

Write and solve an equation to find the weights of the cat and the dog.

Answer:

Weight of cat = x = 12 pounds

Weight of Dog = y = 34 pounds

Step-by-step explanation:

Let's represent:

Weight of cat = x

Weight of Dog = y

A dog weighs 2 pounds less than 3 times the weight of a cat.

y = 3x - 2........ Equation 1

The dog weighs twenty two more pounds than the cat

y = x + 22....... Equation 2

The equation is given as:

y = y

3x - 2 = x + 22

Collect like terms

3x - x = 22 + 2

2x = 24

x = 24/2

x = 12 pounds

Solving for y using any of the equations:

y = 3x - 2

y = 3 × 12 - 2

y = 36 - 2

y = 34 pounds

Therefore:

Weight of cat = x = 12 pounds

Weight of Dog = y = 34 pounds

6 0

2 years ago

James has 21 cups of flour. He will pour the flour equally into 4 containers. How many cups of flour will be in each container?

e-lub [12.9K]

Answer:

5.25 cups of flour

Step-by-step explanation:

4 containers - 21 cups of flour

1 container - 21 cups of flour ÷ 4 = 5.25 cups of flour

7 0

2 years ago

Read 2 more answers

Find the x- and y- intercepts of parabola y=5x^2-16x+10

____ [38]

Y-INTERCEPT

$y = 5x^2 - 16x + 10$

The y-intercept is where the equation/curve/parabola cosses the y-axis.

The y-axis is where x = 0. (The x-axis is where y = 0)

To find the y-intercept:

$\text{y-axis} \rightarrow \text{x = 0} \rightarrow y = 5(0)^2 -16(0) + 10 = 10$

The y-intercept must be at (0, 10)

X-INTERCEPT (ROOTS/SOLUTIONS)

$y = 5x^2 - 16x + 10\\\text{make it equal 0}\\y = 0\\\therefore 5x^2 - 16x + 10 = 0$

We need to use the quadratic formula

The quadratic formula helps us find what values of $x$ make the equation = 0

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-16) + \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\\x = \frac{16 + \sqrt{256-200}}{10}\\x = \frac{16 + \sqrt{56}}{10}\\x = \frac{16 + 2\sqrt{14}}{10}\\x = \frac{8 + \sqrt{14}}{5}\\\\\\x=\frac{-(-16) - \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\text{doing the same thing...}\\\text{end up with...}\\x = \frac{8 - \sqrt{14}}{5}\\$

The x-intercepts are at:

$(\frac{8 + \sqrt{14}}{5}, 0)\\(\frac{8 - \sqrt{14}}{5}, 0)$

5 0

2 years ago

Multiple and convert to simplest form

Lady bird [3.3K]

Answer:

1)4

2)28

3)18.3

4)38.5

5)22.5

6)19.25

7)25.5

8)69.666

9)6.5

10)22.666

Step-by-step explanation:

To do this first you should convert the mix numbers into inproper fractions and then solve.

1)8/5*5/2=4

2)21/5*20/3=7*4

=28

3)33/4*20/9=11*5/3

=55/3

=18.33...

=18.3

4)35/6*33/5=7*11/2

=77/2

=38.5

5)22/8*90/11=45/2

=22.5

6)11/3*21/4=11*7/4

=77/4

=19.25

7)34/5*15/4=34*3/4

=25.5

8)22/3*57/6=11*19/3

=209/3

=69.666

9)39/8*4/3=13/2

=6.5

10)17/2*8/3=17*4/3

=68/3

=22.666

Hope you got this

If you have any doubt please ask me

If you need this in fraction form just check the attachment

5 0

3 years ago

Please please please please help me someone

Shtirlitz [24]

Answer:

That incorrect

Step-by-step explanation:

Yes

3 0

2 years ago