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3 years ago

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The graph of g(x) resembles the graph of f(x)=x^2, but it has been changed. Which of these is the equation of g(x)?

1 answer:

siniylev [52]3 years ago

7 0

Answer:

A.

Step-by-step explanation:

Anwer A has the following equation:

$g(x)=\frac{3}{5}x^2-3$

In this equation, we can calculated the intercept replacing x by 0, as:

$g(x)=\frac{3}{5}0^2-3=-3$

if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.

Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:

$0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236$

It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.

So, the answer is A, $g(x)=\frac{3}{5}x^2-3$

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7900 dollars is placed in an account with an annual interest rate of 5.5%. How much will be in the account after 11 years, to th

Lady bird [3.3K]

Answer:

$\$12,679.50$

Step-by-step explanation:

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=11\ years\\ P=\$7,900\\r=5.5\%=5.5/100=0.055$

substitute in the formula above

$A=7,900(1+0.055*11)$

$A=7,900(1.605)$

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3 years ago

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Which equation shows the quadratic formula used correctly to solve 7x2 = 9+ x for x?

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Answer:

x = (1 + sqrt(253))/14 or x = (1 - sqrt(253))/14

Step-by-step explanation:

Solve for x:

7 x^2 = x + 9

Subtract x + 9 from both sides:

7 x^2 - x - 9 = 0

x = (1 ± sqrt((-1)^2 - 4×7 (-9)))/(2×7) = (1 ± sqrt(1 + 252))/14 = (1 ± sqrt(253))/14:

Answer: x = (1 + sqrt(253))/14 or x = (1 - sqrt(253))/14

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4 years ago

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What is the inequaliity of 3<-5n+2n and how do you put it on a number line

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The inequality would be the negative factor, because -5n+2n is 3n. You would write it on a number line like this.....
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4 years ago

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A chocolate factory made 708.6 pounds of dark chocolate in 6 days. How much dark chocolate, on average, did the factory make per

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Answer:

118.1

Step-by-step explanation:

You need to divide 708.6 by 6 to get the amount of chocolate in one day

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3 years ago

Learning Task 3

ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. $Distance = 3682km$

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. $L < 38m$

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

$Perimeter = 160$

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

$Perimeter = x + x + 1 + x + 2 + x + 3$

This gives:

$160 = x + x + 1 + x + 2 + x + 3$

Collect Like Terms

$160 -1-2-3= x+x+x+x$

$154= 4x$

Divide both sides by 4

$38.5 = x$

$x =38.5$

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: $Inzo = 10 + Miz$

Five years ago: $Miz - 5= \frac{1}{3} * (Inzo-5)$ --- (Missing from the question)

Required: Determine their present ages

Substitute $10 + Miz$ for Inzo in the second equation

$Miz - 5 = \frac{1}{3} * (10 + Miz - 5)$

$Miz - 5 = \frac{1}{3} * (Miz + 5)$

Multiply both sides by 3

$3Miz - 15 = Miz + 5$

Collect Like Terms

$3Miz -Miz = 15 + 5$

$2Miz= 20$

Divide both sides by 2

$Miz = 10$

Substitute 10 for Miz in $Inzo = 10 + Miz$

$Inzo = 10 + 5$

$Inzo = 15$

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

$Speed = 100kph$

$Time = t$

Local Train:

$Speed = 45kph$

$Time = t + 45$

Required: Determine the distance between A and B

Distance is calculated as:

$Distance = Speed * Time$

For the express train:

$Distance = 100 * t$

For the local train

$Distance = 45 * (45 + t)$

Distance between both stations are equal; So,

$100 * t = 45 * (45 + t)$

$100 t = 2025 + 45t$

Collect Like Terms

$100 t -45t= 2025$

$55t= 2025$

Divide by 55

$t = 36.82$

Substitute 36.82 for t in $Distance = 100 * t$

$Distance = 100 * 36.82$

$Distance = 3682km$

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: $n + n + 2 > 24$

Sum less than 60: $n + n + 2 < 60$

So, we have:

$n + n + 2 > 24$

$2n + 2 > 24$

Collect Like Terms

$2n > 24-2$

$2n > 22$

$n > 11$

$n + n + 2 < 60$

$2n + 2< 60$

Collect Like Terms

$2n < 60-2$

$2n < 58$

Divide by 2

$n$

So, we have:

$n > 11$ and $n < 29$

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

$Perimeter < 152m$

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

$Perimeter =4 * L$

$Perimeter =4 L$

So, we have:

$4L < 152m$

Divide through by 4

$L < 38m$

Hence, length is less than 38m (e.g. 37m)

5 0

3 years ago