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lisabon 2012 [21]
2 years ago
12

Determine the vertex form of g(x) = x^2 + 2x – 1. Which graph represents g(x)?

Mathematics
1 answer:
nataly862011 [7]2 years ago
3 0

Answer:

Graph D

Step-by-step explanation:

Move the constant to the opposite side of the equation and group terms that include the same variable.

g(x) + 1 = x^2 + 2x

Finish the square. Remember to keep the equation balanced by using the same constants on both sides.

g(x) + 1 + 1 = x^2 + 2x + 1

g(x) + 2 = x^2 + 2x + 1

Rewrite as perfect squares

g(x) + 2 = (x + 1)^2

Equation in vertex form:
g(x) = (x + 1)^2 - 2

The vertex:

(-1, -2)

* This a minimum *

  • <em>(Parabola open upward)</em>
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Y = 2x + 4 <br> 16x + 4y = 40
Dafna11 [192]
<span>Y = 2x + 4 
16x + 4y = 40

substitute </span>Y = 2x + 4  into <span>16x + 4y = 40

</span><span>16x + 4y = 40
</span>16x + 4(2x + 4) = 40
16x + 8x + 16 = 40
24x  = 40 - 16
24x = 24
x = 1

Y = 2x + 4 
Y = 2(1) + 4 
Y = 6

answer (1, 6)
6 0
2 years ago
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Write an equation of the line below.
iVinArrow [24]

(0,-2)

(5,-7)

hope it helps u

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2 years ago
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90 hazelnuts have a mass of 125 g. Hazelnuts have 630 calories per 100 g. work out the number of calories per hazelnut
jenyasd209 [6]

90 hazelnuts = 125g

Therefore, the mass of one hazelnut is this...

90 / 90 = 125 / 90

1 hazelnut = 25/18 grams


630 calories = 100 grams

100 divided by 25/18 = 72

Therefore...

630 / 72 = 1 hazelnut

AND THE ANSWER IS

8.75 calories = 1 hazelnut

8 0
3 years ago
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Help me with this problem?<br> 15 points
kobusy [5.1K]

Answer:

See explanation

Step-by-step explanation:

Since 12 is 3 times greater than 4, you simply need to divide all of the ingredients by 3.

Cactus chunks: 4 1/2 divided by 3 is 3/2 or 1 1/2

Crushed Tumbleweed: 8/3 is just 8/3 or 2 2/3

Cactus Juice: 10/4 or 2 1/2

Lizard eggs: 4

Crumbled Flower Petals: 7/4 or 1 3/4

Water: 10/3 or 3 1/3

Hope this helps!

5 0
3 years ago
For women aged 19-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation
Mrac [35]

Answer: p = 0.00714

Step-by-step explanation:

Since the population standard deviation of the distribution is known, the z test ( which produces the z score) is the perfect test for finding the probability of the data set in the question.

From the question,

Population mean (u) = 114.8

Sample mean (x) = 121.5

Population standard deviation (σ) = 13.1

Sample size (n) = 23

The z score formulae is given below as

Z = x - u/σ/√n

Z = 121.5 - 114.8/(13.1/√23)

Z = 6.7/(13.1/√23)

Z = 6.7/2.731

Z = 2.45.

The question is interested in knowing the probability of mean systolic blood pressure greater than 121.5.

This implies that we are looking for the probability at which our z score is greater than 2.45: P(z>2.45)

The z score (z=2.45) has divided the distribution into two regions, z< 2.45 ( area to the left of the distribution) and z>2.45 ( area to the right of distribution).

Hence, p(z>2.45) + p(z<2.45) = 1

To get a the probability, we have to use a standard normal distribution table.

The table we have here gives probability of the distribution to the left ( that's area towards the left), hence we need to find p(z<2.45) first

From the table p(z<2.45) = 0.99286

But p(z>2.45) = 1 - p(z<2.45)

p(z>2.45) = 1 - 0.99286

p(z>2.45) = 0.00714

8 0
3 years ago
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