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3 years ago

The graph of y = x^2 has been translated 7 units to the left. The equation of the resulting parabola is _____.

Mathematics

2 answers:

Mumz [18]3 years ago

6 0

Answer:

$y=(x+7)^2$

Step-by-step explanation:

$y=x^2$ is the parent function.

Parent function is translated 7 units to the left

f(x)---> f(x-h), where f(x) is translated h units to the right

f(x)---> f(x+h), where f(x) is translated h units to the left

When the number is added with x then the graph will be translated to the left

Parent function is translated 7 units to the left

Add 7 with x

$y=x^2$

$y=(x+7)^2$

Marina86 [1]3 years ago

3 0

Move c units to left means add c to every x

move 7 so add 7 to every x

y=(x+7)^2

2nd option iis answer

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A factory sells backpacks for $40 each. The cost to make 1 backpack is $10.00. In addition to the costs of making backpacks, the

yKpoI14uk [10]

Answer:

x (40-10) -12000≥980

The factory must sell 433 backpacks to meet its weekly goal.

Hi, to answer this question we have to write an inequality.

So, since the backpacks (x) are sold by $40 and the cost of making one is $10, the revenue per bag is equal to 40x and the cost is 10x.

12,000 of operating expenses are also expenses.

So, for the profit:

Profit = revenue- cost

P = 40x-10x-12,000

P = x (40-10)-12000

The factory goal is to make a profit of at least $980 each week, so, the profit must be greater or equal than 980.

x (40-10) -12000≥980

Solving for x

30x-12000≥980

30x≥980+12000

30x ≥12980

x≥12980/30

x≥432.6

x≥433 (rounded, because if the sell 432 they will not meet the goal)

The factory must sell 433 backpacks to meet its weekly goal.

Step-by-step explanation:

4 0

3 years ago

Line l passes through point (3,−26) and line p is the graph of y−3=−5(x−2) .

uranmaximum [27]

Considering the definition of parallel line, the equation of line l is y= -5x -11.

<h3>Linear equation</h3>

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.
m is the slope.
b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

<h3>Parallel line</h3>

Parallel lines are two lines that are always at the same distance from each other.

Two lines are parallel if they have the same slope and different y-intercepts. This is, they have the same value of m and different value of b.

<h3>Equation of parallel line in this case</h3>

In this case, the line is y−3=−5(x−2) Expressed in the form y = mx + b, you get:

y−3=−5x−2×(-5)

y−3=−5x+ 10

y=−5x+ 10 + 3

where:

the slope is -5.
the y-intercept is 13.

Two lines are parallel if they have the same slope. So, the parallel line has a slope of -5 and has a form of: y= -5x + b

The line passes through the point (3, -26). Replacing in the expression for parallel line:

-26= -5× 3 + b

-26= -15 + b

-26 + 15 = b

Finally, the equation of parallel line is y= -5x -11.

Learn more about parallel line:

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1 year ago

What is the first quartile of this data set? {6, 47, 49, 15, 43, 41, 7, 36}

stepladder [879]

<span>The first quartile is the same as the median of the data which are less than the overall median. Same as the 25th percentile.
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I hope my answer has come to your help. God bless and have a nice day ahead!

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3 years ago

Translate the algebraic expression and simplify if possible.

tamaranim1 [39]

-2/(a+b)
Explanation: you are dividing negative two by the sum of a and b so you would put a+b in parentheses as the denominator and then put -2 as the numerator

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3 years ago

Which of the following angle measurements would you find in an equilateral triangle?

lesya692 [45]

Answer:

D. 60, 60, 60

Step-by-step explanation:

In an equilateral triangle, all sides are equal and equal to 180 when added together. because 60×3 is equal to 180, D is the right answer. I hope this helps you!

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2 years ago