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3 years ago

Graph the function y=2 sqrt x+4 and state the transformation from the parent graph y= sqrt x

Mathematics

1 answer:

Darya [45]3 years ago

8 0

Answer:

Step-by-step explanation:

Please use parentheses so that there's no question about what constitutes the argument of the sqrt function:

y=2 sqrt x+4 → y = 2√(x + 4)

This result is obtained from y = √x by:

1) translating the graph of y = √x 4 units to the LEFT, and

2) stretching the resulting graph vertically by a factor of 2.

You might be interested in

Your friend Mel says he has an easier way to solve this problem. Here are the ﬁrst steps in his method.

damaskus [11]

Simplifying

2x2 + 6x + 4 = 24

Reorder the terms:

4 + 6x + 2x2 = 24

Solving

4 + 6x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:

4 + -24 + 6x + 2x2 = 24 + -24

Combine like terms: 4 + -24 = -20

-20 + 6x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0

-20 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.

2(-10 + 3x + x2) = 0

Factor a trinomial.

2((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying

-5 + -1x = 0

Solving

-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0

0 + -1x = 0 + 5

-1x = 0 + 5

Combine like terms: 0 + 5 = 5

-1x = 5

Divide each side by '-1'.

x = -5

Simplifying

x = -5

4 0

3 years ago

At the coffee shop, the ratio of cups of coffee sold to muffins was 2:7. If the shop sold 84 muffins, how many cups of coffee di

neonofarm [45]

Answer:

Step-by-step explanation:

84 divided by 7 equals 12.

12x2=24.

24 cups of coffe were sold.

8 0

2 years ago

Calculate the mean, median, mode, range, and 5 Number Summary of the following data set: 5,6,8,4,7,5,4,2,5,6,5,2,1,4

Artist 52 [7]

Answer:

mean = 4.57, median = 5 , mode = 5, range =7 ,

five number summary: Minimum value= 1 , First Quartile = 4, Median = 5

Third Quartile = 6, Maximum value = 8

Step-by-step explanation:

First arrange the data in ascending order.

1,2,2,4,4,4,5,5,5,5,6,6,7,8

Mean = sum of all numbers / total numbers

= 1+2+2+4+4+4+5+5+5+5+6+6+7+8 / 14

= 64 / 14

= 4.57

Median:

Since the given data is even number so, we can find median by taking mean of 2 middle numbers.

so the middle numbers are 7th and 8th data i.e, 5 and 5

Median =(5+5)/2

= 5

Mode:

The most repetitive number in the data set is mode

So Mode = 5

Range:

Range can be found by subtracting smallest number from largest number in the data set.

Smallest number = 1, Largest number = 8

Range= Largest number - Smallest number

= 8-1 = 7

Five no Summary

Minimum value= 1

First Quartile ( 25 % mark )= 4

Median = 5

Third Quartile (75 % mark) = 6

Maximum value = 8

First quartile can be found by : consider the data on left of the median and find median among them

Third quartile can be found by: consider the data on right of the median and find median among them

7 0

3 years ago

Segment BD is an altitude of triangle ABC. Find the area of the triangle. Triangle ABC with altitude BD is shown. Point A is at

pogonyaev

Where's the "triangle with alt. BD?" This problem can be solved without the diagram, but the solution would be easier with it.

BD is the altitude. Find the length of BD by finding the dist. between (-1,4) and (2,4); it is 2-(-1), or 3. |BD| = 3.

I've graphed the triangle myself and have found that the "base" of the triangle is the vertical line thru (2,1) and (2,6); its length is 6-1, or 5.

Thus, the area of this triangle is A = (b)(h) / 2, or A = (5)(3) / 2 = 10/3 square inches.

7 0

3 years ago

Read 2 more answers

PLEASE HELP. I need DE AND EF!!!

AlekseyPX

Answer:

DE = about 41.843 (rounded to nearest thousandth)

EF= 34.276 (rounded)

Step-by-step explanation:

For DE, we know that the shorter side (the opposite side) is 24, while the angle across form it is 35°. We can use trigonometry to figure this out. SinФ equals the opposite side (in this case, 24) divided by the hypotenuse. Set sinФ equal to a ratio of the sides like this:

sin(35) = $\frac{24}{x}$

x represents the hypotenuse length, which we don't know; 35 is the angle measure. Next, isolate x so that the equation looks like this:

$\frac{24}{sin(35)}$ = x

You will need a calculator for the next part. (and make sure you're in degree mode!). evaluate sin(35) and divide 24 by that value. That is DE's length. DE = about 41.843 (rounded to nearest thousandth)

For EF, we can just use Pythagorean theorem now that we know the other sides' values.

EF^2 + 24^2 = DE^2

*a calculator might also be useful for this part.

EF= 34.276 (rounded)

8 0

2 years ago