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3 years ago

If you scale an object with a scale factor greater than one it will get bigger.

1 answer:

4 0

True 1, it results in an enlargement. And if the absolute value of the scale factor is equal to 1, that results in a congruent image and preimage.

You might be interested in

A 12 oz bag of birdseed cost $3.12. A 16 oz bag of birdseed cost $3.84. Which is the better deal? How much money per ounce would

lidiya [134]

The better deal would be the 16 oz bag since it costs .24 cents an ounce.
You would be saving .2 cents on each ounce you buy.

6 0

3 years ago

The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?

Lena [83]

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

$a(n)=ar^{n-1}$

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

Given, 5th term is 40, we can write:

$ar^{5-1}=40\\ar^4=40$

Given, 7th term is 10, we can write:

$ar^{7-1}=10\\ar^6=10$

We can solve for a in the first equation as:

$ar^4=40\\a=\frac{40}{r^4}$

Now we can plug this into a of the 2nd equation:

$ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}$

Let's solve for a:

$a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640$

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:

$ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80$

possible values of 4th term is 80 & - 80

3 0

4 years ago

if pentagon abcd was reflected over the axis y-axis, reflected over the x-axis, and rotated 180, where would be point A' lie

frez [133]

A reflection over the x axis coupled with another reflection over the y axis leads to a rotation of 180 degrees.

In other words,

Start with point A. Reflect over the x axis to get point B. Reflect B over the y axis to get point C. To go from A to C, we can rotate A 180 degrees about the origin.

----------------

So this means that if we do those reflections and then do the rotation, then we end up back where we started. Wherever point A is located, the point A' will also be located at the same position with the same coordinates.

4 0

3 years ago

Please help me!!!!!

chubhunter [2.5K]

Answer:

y = - $\frac{2}{5}$ (x - 5)² + 7

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (5, 7 ) , then

y = a(x - 5)² + 7

To find a substitute (10, - 3 ) into the equation

- 3 = a(10 - 5)² + 7 ( subtract 7 from both sides )

- 10 = 5²a = 25a ( divide both sides by 25 )

$\frac{-10}{25}$ = a , that is

a = - $\frac{2}{5}$

y = - $\frac{2}{5}$ (x - 5)² + 7 ← in vertex form

8 0

3 years ago

Based on a study of population projections for 2000 to 2050, the projected population of a group of people (in millions) can b

Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

$A(t) = 11.19(1.009)^t$

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, $t=0$ and in 2014, $t=14$ . Mathematically,

$\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}$

$A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107$

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm $y=a^x$ (where $a$ is a constant) is $\dfrac{dy}{dx}=a^x\ln a$ . Let's use in this in finding the derivative of $A(t)$ .

$A\prime(t) = \dfrac{A}{t}=11.19\cdot1.009^t\ln1.009$

In the year 2014, $t=14$ .

$A\prime(14) =11.19\cdot1.009^14\ln1.009=0.114$

6 0

3 years ago