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3 years ago

Given that (-3,7) is on the graph of f(x), find the corresponding point for the function f(x + 5).

Mathematics

1 answer:

natulia [17]3 years ago

8 0

Given transformation is f(x+5) which is similar to f(x+h).

f(x+h) shifts the graph "h" units to the left side.

so that means f(x+5) will shift the graph "5" units to the left side.

Left or right movement is done using x-coordinate only so -3 will change in (-3,7)

-3+5=2

so the new coordinate of the point will be (2,7)

Hence final answer is (2,7).

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Noah gathered data at his school among 7th and 8th graders to see if there was an association between grade level and handedness

mash [69]

Answer: 4) 157

Step-by-step explanation:

We know that there is no association between the grade level and the andedness, then we should find that the ratio between left handeds and right handed is the same for both grades.

In 7-th grade we have:

Left handed : 11

Right handed: 72

The ratio is 11/72 = 0.14

Then, the ratio for the 8-th graders must be about the same:

Left handed: 24

Right handed: X

Ratio: 24/X

Let's start with the bigger option, X = 157.

24/157 = 0.15

Ok, we now see that with the bigger option we obtained almost the same ratio (if we use the smaller values for X, we will get a ratio bigger than 0.15, so 0.15 is the better aproximation that we can find to the 0.14 of the 7-th graders)

Then the correct option is 4) 157

4 0

2 years ago

What is the equation of this graphed line?

Veseljchak [2.6K]

Answer:

Slope Intercept form of the equation is $y = \frac{1}{3} x - 9$

Step-by-step explanation:

Here, the two point line are given as is A(-6,-3) and B(6,-7)

The slope of the line AB = $m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-7-(-3)}{6-(-6)} = \frac{-7 + 3}{6 + 6} = \frac{4}{12} \\\implies m = \frac{1}{3}$

⇒ the slope of AB is m = (4/3)

By SLOPE INTERCEPT FORMULA:

The equation of a line with slope m and a point (x0, y0) is given as

(y-y0)= m (x-x0)

⇒ The equation of line with point (6,-7) is:

$y + 7 = \frac{1}{3} (x-6) \implies 3y + 21 - x + 6 - 0\\or, -x + 3y + 27 = 0$

Now, the given equation is -x + 3y = -27

Convert it in the SLOPE INTERCEPT FORM y = mx + c

We get, 3y = x - 27

or, $y = \frac{1}{3} x - \frac{27}{3} \\\implies y = \frac{1}{3} x - 9$

Hence, the Slope Intercept form of the equation is $y = \frac{1}{3} x - 9$

3 0

2 years ago

What property is shown in the following equation? 17 + 8 + 3 = 17 + 3 + 8

ss7ja [257]

Answer:

The Commutative Law of Addition.

Step-by-step explanation:

Basically, this law says we can swap numbers over and still get the same number when we add. This has demonstrated exactly that.

Hope this helped!

3 0

2 years ago

Read 2 more answers

A line passes through the points (0, 9) and (9, 19). What is its equation in slope-intercept form?

STatiana [176]

Answer:

y = 10/9x + 9

Step-by-step explanation:

To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).

Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:

$m = \frac{y2 - y1}{x2 - x1}$

Let (x1, y1) = (0, 9)

and (x2, y2) = (9, 19)

Substitute these values on the formula:

$m = \frac{y2 - y1}{x2 - x1} = \frac{19 - 9}{9 - 0} = \frac{10}{9}$

Therefore, the slope (m ) = 10/9.

Next, the y-intercept is the point on the graph where it crosses the y-axis, and has the coordinates, (0, b ). It is also the value of the y when x = 0.

One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.

Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9

3 0

2 years ago

Josh has been running for 6 min and completes a lap in 7 min. Gabe has been running for 2 min and completes a lap in 9 min.

Amanda [17]

So j completed 6/7 of a lap
gabe has completed 2/9 lap
so
1 j lap=7 mins s o
7j
j=num of laps
1 g lap=9 mins so
9g
g=num of laps
then 6+j
and g+2

so
when will the times be equal
7j+6=9g+2
subtract 2 from both sides
7j+4=9g
divide both sides by 9
7/9j+4/9=g
so to get a whole number of laps, we must subsitute a number when it is multiplied by 7 then add 4, we get a multiplue of 9
so if j=2
7/9(2)+4/9=g=14/9+4/9=g=18/9=g=2
so josh and gabe must run 2 lap each because
6+(2 times 7)=2+(9 times 2)
6+14=2+18
20=20
true so

the answer is 2 laps

3 0

3 years ago

Read 2 more answers