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3 years ago

Determine whether the pair of figures are similar and explain why.

Mathematics

2 answers:

s344n2d4d5 [400]3 years ago

6 0

The answer should be D because all the side remain the same as they increase. each side is increased by times 2.

marin [14]3 years ago

5 0

C and D- The bigger triangle is exactly twice as large

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A rectangle has an area of 72 swaure units. The width of the rectangle is 9 units. The length of the rectangle is 2x + 4. What i

vichka [17]

Answer:

8 units

Step-by-step explanation:

Area of a rectangle = Width multiplied by Length

Substitute in all the known numbers into this formula to get

72 = (9) × $(2x+4)$

Solve the equation for x, to find out the length

$9(2x+4)=72$

$2x+4=72/9$

$2x+4=8$

$2x=8-4$

$2x=4$

$x=4/2$

$x=2$

Length of the rectangle = $(2x+4)$

$2(2)+4$

$4+4=8$

5 0

3 years ago

If f(3) = 3(x+5+2, what is f(a+ 2)?

Mamont248 [21]

Solution:

f(3) = 3(x + 5 + 2)

f(3) = 3(3 + 5 + 2)

f(3) = 3(10)

f(3) = 30

Substitute 30 for a:

f(30 + 2)

f(32)

Best of Luck!

8 0

3 years ago

Approximate area under the curve f(x) =-x^2+2x+4 from x=0 to x=3 by using summation notation with six rectangles and use the the

bekas [8.4K]

Answer:

Summation notation:

$\frac{1}{2}\sum_{k=1}^6f((.5k))$

or after using your function part:

$\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)$

After evaluating you get 11.125 square units.

Step-by-step explanation:

The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.

The distance between x=0 and x=3 is (3-0)=3.

We want to divide that length of 3 units by 6 which gives a length of a half per each base length.

We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).

The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).

The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).

The fourth rectangle will have a height of f(2-.5)=f(1.5).

The fifth one will have a height of f(1.5-.5)=f(1).

The last one because it is the sixth one will have a height of f(1-.5)=f(.5).

So to find the area of a rectangle you do base*time.

So we just need to evaluate:

$\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)$

or by factoring out the 1/2 part:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

To find f(3) replace x in -x^2+2x+4 with 3:

-3^2+2(3)+4

-9+6+4

To find f(2.5) replace x in -x^2+2x+4 with 2.5:

-2.5^2+2(2.5)+4

-6.25+5+4

2.75

To find f(2) replace x in -x^2+2x+4 with 2:

-2^2+2(2)+4

-4+4+4

To find (1.5) replace x in -x^2+2x+4 with 1.5:

-1.5^2+2(1.5)+4

-2.25+3+4

4.75

To find f(1) replace x in -x^2+2x+4 with 1:

-1^2+2(1)+4

-1+2+4

To find f(.5) replace x in -x^2+2x+4 with .5:

-.5^2+2(.5)+4

-.25+1+4

4.75

Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

$\frac{1}{2}(1+2.75+4+4.75+5+4.75)$

$\frac{1}{2}(22.25)$

$11.125$

Okay now if you wanted the summation notation for:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

is it

$\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))$

or after simplifying a bit:

$\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))$

$\frac{1}{2}\sum_{k=1}^6f((.5k))$

If you are wondering how I obtain the .5+.5(k-1):

I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)

6 0

3 years ago

Show how decimals are used in money

Illusion [34]

Answer:

Ex: $12 is dollars .25 would be cents = $12.25

Step-by-step explanation:

8 0

3 years ago

Maddie climbed 48 mountain in 12 month. find her climbing rate in mountain per month

mina [271]

4 mountains per month, 48/12

4 0

3 years ago