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Zepler [3.9K]
3 years ago
10

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(1).

Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

\large\boxed{(h\circ g)(1)=8}

Step-by-step explanation:

(f\circ g)(x)=f\bigg(g(x)\bigg)\\===================\\\\(h\circ g)(1)=h\bigg(g(1)\bigg)\\\\g(1)-\text{put}\ x=1\ \text{to the equation of the function}\ g(x)=2x:\\\\g(1)=2(1)=2\\\\h\bigg(g(1)\bigg)=h(2)-\text{put}\ x=2\ \text{to the equation of the function}\ h(x)=x^2+4:\\\\h(2)=2^2+4=4+4=8

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Simplify the expression by combining like terms. 16+8a−3a+6b−9
Svetradugi [14.3K]
7+5a+6b is the answer because 16-9 is 7 and 8-3 is 5.
4 0
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A survey of an athletic shoe store’s customers showed that 8% of the customers run every day. The store has approximately 1900 c
dem82 [27]
Find 8% of 1900.

0.08 * 1900 = 152

So 152 customers run every day.
7 0
3 years ago
Simplify the following: a) [ -6 +22 – 6 + 8 ] ÷ ( -9 ) b) 400 ÷ { 40 – (-2) -3 – ( -1)} c) 40 x -23 + 40 x -17 d) 1673 x 99 – (-
oee [108]

Step-by-step explanation:

<h3> a) [ -6 +22 – 6 + 8 ] ÷ ( -9 )</h3>

[ -6 +22 – 6 + 8 ] = 18

18 ÷ (-9) = -2

<h3> b) 400 ÷ { 40 – (-2) -3 – ( -1)} </h3>

{40 – (-2) -3 – ( -1)} = { 40 + 2 -3 + 1} = 40

400 ÷ 40 = 10

<h3>c) 40 x -23 + 40 x -17 </h3>

(40 x 23) + (40 x -17)

920 + (-680)

= 240

<h3>d) 1673 x 99 – (-1673) </h3>

(1673 x 99) + 1673

1673 x 100

= 167300

<h3>e) 490 x 98 = 48020</h3>

Hope this helps ^-^

7 0
3 years ago
Consider the three points ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 ) . Let ¯ x be the average x-coordinate of these points, and let ¯ y
loris [4]

Answer:

m=\dfrac{3}{2}

Step-by-step explanation:

Given points are: ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 )

The average of x-coordinate will be:

\overline{x} = \dfrac{x_1+x_2+x_3}{\text{number of points}}

<u>1) Finding (\overline{x},\overline{y})</u>

  • Average of the x coordinates:

\overline{x} = \dfrac{1+2+3}{3}

\overline{x} = 2

  • Average of the y coordinates:

similarly for y

\overline{y} = \dfrac{3+3+6}{3}

\overline{y} = 4

<u>2) Finding the line through (\overline{x},\overline{y}) with slope m.</u>

Given a point and a slope, the equation of a line can be found using:

(y-y_1)=m(x-x_1)

in our case this will be

(y-\overline{y})=m(x-\overline{x})

(y-4)=m(x-2)

y=mx-2m+4

this is our equation of the line!

<u>3) Find the squared vertical distances between this line and the three points.</u>

So what we up till now is a line, and three points. We need to find how much further away (only in the y direction) each point is from the line.  

  • Distance from point (1,3)

We know that when x=1, y=3 for the point. But we need to find what does y equal when x=1 for the line?

we'll go back to our equation of the line and use x=1.

y=m(1)-2m+4

y=-m+4

now we know the two points at x=1: (1,3) and (1,-m+4)

to find the vertical distance we'll subtract the y-coordinates of each point.

d_1=3-(-m+4)

d_1=m-1

finally, as asked, we'll square the distance

(d_1)^2=(m-1)^2

  • Distance from point (2,3)

we'll do the same as above here:

y=m(2)-2m+4

y=4

vertical distance between the two points: (2,3) and (2,4)

d_2=3-4

d_2=-1

squaring:

(d_2)^2=1

  • Distance from point (3,6)

y=m(3)-2m+4

y=m+4

vertical distance between the two points: (3,6) and (3,m+4)

d_3=6-(m+4)

d_3=2-m

squaring:

(d_3)^2=(2-m)^2

3) Add up all the squared distances, we'll call this value R.

R=(d_1)^2+(d_2)^2+(d_3)^2

R=(m-1)^2+4+(2-m)^2

<u>4) Find the value of m that makes R minimum.</u>

Looking at the equation above, we can tell that R is a function of m:

R(m)=(m-1)^2+4+(2-m)^2

you can simplify this if you want to. What we're most concerned with is to find the minimum value of R at some value of m. To do that we'll need to derivate R with respect to m. (this is similar to finding the stationary point of a curve)

\dfrac{d}{dm}\left(R(m)\right)=\dfrac{d}{dm}\left((m-1)^2+4+(2-m)^2\right)

\dfrac{dR}{dm}=2(m-1)+0+2(2-m)(-1)

now to find the minimum value we'll just use a condition that \dfrac{dR}{dm}=0

0=2(m-1)+2(2-m)(-1)

now solve for m:

0=2m-2-4+2m

m=\dfrac{3}{2}

This is the value of m for which the sum of the squared vertical distances from the points and the line is small as possible!

5 0
3 years ago
Item 6 A bowl contains blueberries and strawberries. There are a total of 20 berries in the bowl. The ratio of blueberries to st
Fiesta28 [93]

Answer:

there are 5 strawberries

Step-by-step explanation:

4 x 5 =20 so that is 20 blue berries  

and there are 4 blue berries for every one strawberry

and there are 5 groups of 4 blue berries which equals 5 strawberries

5 0
3 years ago
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