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2 years ago

Find the point(s) of intersection between the quadratic function y = x + 4x + 4 and the linear function y = 2x+4.

Mathematics

1 answer:

Andrews [41]2 years ago

4 0

Answer:

(0, 4)

Step-by-step explanation:

To find the intersection of two lines, we want to find the value when they equal each other. To do this, we want to set the equations equal to each other.

First, let's simplify y = x + 4x + 4 by combining the x's.

y = 5x + 4

Now let's set the equations equal to each other. Since they both equal y, we can set the opposite sides equal to each other.

5x + 4 = 2x + 4

Now you want to combine the terms.

[subtract 4] 5x = 2x

[subtract 2x] 3x = 0

Now you want to isolate the x.

[divide by 3] x = 0

Now we want to find y by plugging x = 0 back into the equations.

y = 5(0) + 4

[multiply] y = 0 + 4

[add] y = 4

Check this with the other equation.

y = 2(0) + 4

[multiply] y = 0 + 4

[add] y = 4

Your answer is correct!

(0, 4)

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Answer:

Step-by-step explanation:

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3 years ago

Please help me with this problem

user100 [1]

Answer:

Keisha bought 3 sandwiches and 5 lemonades.

Equations: x + y = 8 2x + y = 11

Step-by-step explanation:

To solve a problem with two variables, you need to set up a system of equations comparing the two variables and solve using either substitution or elimination. If 'x' represents the number of sandwiches and 'y' represents the number of lemonades, then x + y = 8 because they bought a total of 8 items. Also, the cost of each item is given as well as the total amount of money spent. So, our second equation is: 2x + y = 11. We can use inverse operations to solve for 'y' in the first equation: x + y - x = 8 - x which simplifies to: y = 8 - x. We can then use this expression to substitute in for the variable 'y' in the second equation: 2x + 8 - x = 11.

Combine like terms: x + 8 = 11

Inverse Operations: x +8 - 8 = 11 - 8

Solve: x = 3, so Keisha bought 3 sandwiches

Solve for y: y = 8 - 3 = 5, so Keisha bought 5 lemonades

7 0

2 years ago

Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side

maria [59]

Answer:

cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = $-\frac{1}{3}$

cos(b) = $-\frac{1}{4}$

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = $-\sqrt{1-(-\frac{1}{3})^2}$ [Since, sin(a) = $\sqrt{(1-\text{cos}^2a)}$ ]

= $-\sqrt{\frac{8}{9}}$

= $-\frac{2\sqrt{2}}{3}$

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be negative.

sin(b) = $-\sqrt{1-(-\frac{1}{4})^2}$

= $-\sqrt{\frac{15}{16}}$

= $-\frac{\sqrt{15}}{4}$

By substituting these values in the identity,

cos(a + b) = $(-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})$

= $\frac{1}{12}-\frac{\sqrt{120}}{12}$

= $\frac{1}{12}(1-\sqrt{120})$

= $\frac{1}{12}(1-2\sqrt{30})$

Therefore, cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

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3 years ago

A bakery makes 260 donuts in 4 hours. At this rate, how many donuts can they make in 6 hours?

Yuri [45]

Answer:

385

Step-by-step explanation:

260 divided by 4 =65

65 + 65 + 260= 385

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3 years ago

The Sanchez family uses 2 3/4 tubes of tooth paste each month. How many tubes of toothpaste does the Sanchez family use each yea

Licemer1 [7]

2.75 * 12 = 33.

If the Sanchez family is using 2 3/4 (or 2.75) tubes of toothpaste and there are 12 months in a year, we use the equation above and get 33 as our answer.

8 0

3 years ago

Read 2 more answers

Find the point(s) of intersection between the quadratic function y = x + 4x + 4 and the linear function y = 2x+4.​

Find the point(s) of intersection between the quadratic function y = x + 4x + 4 and the linear function y = 2x+4.