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creativ13 [48]
3 years ago
10

Find a quadratic function that includes the set of values below.

Mathematics
1 answer:
timurjin [86]3 years ago
3 0
Plug in points to general form of quadratic function:
y=ax²+bx+c

(0,7)
7 = c
(2,13)
13 = 4a +2b + c
(4,3)
3 = 16a + 4b + c

Now solve the system of equations in two unknowns.

Substitute the value of 7 for c in the second equation:
13 = 4a + 2b + 7
6 = 4a + 2b
3 = 2a + b
b = 3 - 2a

Substitute this into third equation:
3 = 16a + 4(3-2a) + 7
3 = 16a + 12 - 8a + 7
3 = 8a + 19
-16 = 8a
a = -2

b = 3-2a = 3 - 2(-2) = 7

a = -2, b =7. c = 7
The quadratic function is y= -2x² + 7x +7
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Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor
jonny [76]

Answer:

12

trust me it works i just took the test.

5 0
3 years ago
Find the value of 15.0 N in pounds. Use the conversions 1slug=14.59kg and 1ft=0.3048m .
Sliva [168]

The value of 15.0 N in pounds = 3.375 lb

<h3><em>Further explanation </em></h3>

The derivative magnitude is a quantity derived from the principal amount

7 main quantities have been determined based on international standards, namely:

  • 1. Length, meters (m)
  • 2. Time, second (s)
  • 3. Mass, kilograms (kg)
  • 4. Temperature, kelvin (K)
  • 5. Light intensity, candela (cd)
  • 6. Electric current, ampere (A)
  • 7. Amount of substance, mol (m)

Newton (N) is one unit of force (F) which is a quantity derived from mass (m), length (l) and time (s)

Newton can be expressed in terms of Kg m / s²

Formula used:

F = m. a

N = kg. m / s²

In the British system there are units of slug, feet, and pounds so that the unit of force becomes:

F = m. a

Lb = slug. ft / s²

The relationship between the two-unit systems above is:

1 kg = 0.0685 slug

1 slug = 14.59 kg

1 newton = 0.225 lb

1 lb = 4,448 newtons

1 ft = 0.3048 m

So if we change 15 N to lb by using slug and ft

15 N = 15 * (1 / 14.59) slug * (1 / 0.3048) ft / s²

15 N = 3,375 slug ft / s ²

15 N = 3,375 lb

or we convert directly:

15 N = 15 * 0.225 lb

15 N = 3,375 lb

<h3><em>Learn more </em></h3>

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the quantity 0.0075 meters expressed in centimeters

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A vineyard has 145 acres of Chardonnay grapes

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Keywords: slug, Newton, feet, kg, pound

6 0
3 years ago
A rectangle has a length of (x + 4) centimeters and a width of 12x centimeters. If the perimeter is 26 centimeters, what is the
STALIN [3.7K]

Answer:

The width of rectangle is W=\frac{108}{13}\ cm  or  8\frac{4}{13}\ cm

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

P=2(L+W)

where

L is the length of rectangle

W is the width of rectangle

we have

P=26\ cm\\L=(x+4)\ cm\\W=12x\ cm

substitute

26=2(x+4+12x)

solve for x

26=2(13x+4)

26=26x+8

26x=26-8

26x=18

x=\frac{18}{26}

simplify

x=\frac{9}{13}

<em>Find the width of rectangle</em>

W=12x\ cm

substitute the value of x

W=12(\frac{9}{13})=\frac{108}{13}\ cm

Convert to mixed number

\frac{108}{13}\ cm=\frac{104}{13}+\frac{4}{13}=8\frac{4}{13}\ cm

7 0
3 years ago
Please help and explain the question is in the picture
Digiron [165]

Answer: 123 square feet

Step-by-step explanation: The question is a little odd, but I can break it down easily. It wants us to find the area of a three foot border around his room.

First, the whole area of his room is 20 x 24 = 480

Next, we have to make the measurements 3 feet smaller on each wall, so 17 x 21 = 357

Finally, to find the area of the border, we simply do 480 - 357 = 123

He needs to buy 123 square feet of carpeting

Hope this helps!

8 0
3 years ago
Read 2 more answers
Fimd the angles marked with letters <br>Please help! ​
damaskus [11]

Answer:

a=64° alternating angles

b=40° corresponding angles

3 0
3 years ago
Read 2 more answers
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