Solve the equation. 25-3(2w + 1) = 10w-3(10+w)

1 answer:

3 0

25 - 3(2w + 1) = 10w - 3(10 + w)
Distribute
25 - 6w - 3 = 10w - 30 - 3w
Combine liked terms
22 - 6w = -30 + 7w
+30 on both sides
52 - 6w = 7w
+6w on both sides
52 = 13w
/13 on both sides
w = 4

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Nora ordered a set of purple and green pins. She received 50 pins, and 70% of them were

Paladinen [302]

Answer:

Nora received <u>35</u> purple pins.

Step-by-step explanation:

If Nora received 50 pins, and 70% of the pins were purple, to calculate the number of purple pins Nora received, we must find 70% of 50.

To find 70% of 50, we can multiply 50 by the decimal form of 70%:

$50 * .7=35$

Therefore, we can conclude that since 70% of the 50 pins Nora received were purple, and 70% of 50 is 35, Nora received 35 purple pins.

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3 years ago

Use these functions to answer the questions.

Elenna [48]

Part A
We have $f\left(x\right)=\left(x+3\right)^2-1$ . To solve for the x-intercept, we set f(x) equal to 0. That is
$\left(x+3\right)^2-1=0$

$\left(x+3\right)^2=1$

Take the square root of both sides,
$x+3=1$

$x=-2$

The x-intercept is (-2,0).

To solve for the y-intercept, we set x=0. That is
$y=\left(0+3\right)^2-1=3^2-1=9-1=8$

The y-intercept is (0, 8)

The coordinates of the optimum point are actually the vertex which can be easily seen from the vertex form equation given above. The minimum point is (-3, -1).

Part B.
We have $g\left(x\right)=-2x^2+8x+3$ .
Factor out -2
$=-2\left(x^2-4x\right)+3$

Complete the square
$=-2\left(x^2-4x+4\right)+3-2\left(4\right)$

Simplify
$g(x)=-2\left(x-2\right)^2-5$

Part C
We have $h\left(t\right)=-16t^2+28t$ .
The maximum height is 12.25 feet after 0.875 seconds from the time of the jump. The dolphin will be back in the water after 1.75 seconds. The graph of the jump is shown in the photo.