Answer:
<u>5/8</u>
Step-by-step explanation:
So, let's do the first one first.
You want to make the fraction have the same denominator (bottom number). So, in this case, we have 3/8 and 3/4. If we want them to have the same bottom number, we keep 3/8 how it is, and multiply 2/2 by the 3/4 to get 6/8. So, now we have 3/8 + 6/8. 3/8 + 6/8 = 9/8.
Now, we have 1/3 + 1/6. So, we are going to do the same thing, keep the 1/6, and multiply 1/3 by 2/2, so that the bottom number is equal to the other fraction's bottom number. So, 1/3 x 2/2 = 2/6. Now, we have the equation 2/6 + 1/6. 2/6 + 1/6 = 3/6.
Now, we have this final equation: 9/8 - 3/6. So, now we need to find the denominator that both of them can deal with. So, in this case, we can do 24.
9/8 x 3/3 = 27/24
3/6 x 4/4 = 12/24
Now, we subtract:
27/24
- 12/24
_______
15/24.
Now, we simplify.
15 divided by 3 = 5.
24 divided by 3 = 8
So, <u>5/8</u> is our final answer.
Answer:
x = 0 and x = 1
Step-by-step explanation:
When x = 0 and x = 1 both f(x) and g(x) have the same value, that is
f(0) = g(0) = 1 and
f(1) = g(1) = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
The solution to f(x) = g(x) is x = 0 and x = 1
Answer:
Robert will have $481 more in his account than Cooper.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Continuous compounding:
Similar to compound interest:
![A(t) = P(1 + r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20r%29%5Et)
Cooper:
Cooper invested $3,100 in an account paying an interest rate of 2% compounded quarterly. This means that ![P = 3100, r = 0.02, n = 4](https://tex.z-dn.net/?f=P%20%3D%203100%2C%20r%20%3D%200.02%2C%20n%20%3D%204)
After 12 years is A(12). So
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![A(12) = 3100(1 + \frac{0.02}{4})^{4*12}](https://tex.z-dn.net/?f=A%2812%29%20%3D%203100%281%20%2B%20%5Cfrac%7B0.02%7D%7B4%7D%29%5E%7B4%2A12%7D)
![A(12) = 3938.5](https://tex.z-dn.net/?f=A%2812%29%20%3D%203938.5)
Cooper will have $3938.5 in his account.
Robert:
Robert invested $3,100 in an account paying an interest rate of 3 % compounded continuously. So
.
After 12 years.
![A(t) = P(1 + r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20r%29%5Et)
![A(12) = 3100(1 + 0.03)^{12}](https://tex.z-dn.net/?f=A%2812%29%20%3D%203100%281%20%2B%200.03%29%5E%7B12%7D)
![A(12) = 4419.9](https://tex.z-dn.net/?f=A%2812%29%20%3D%204419.9)
Robert will have $4419.9 in his account.
How much more money would Robert have in his account than Cooper, to the nearest dollar?
4419.9 - 3938.5 = 481.4
To the nearest dollar, Robert will have $481 more in his account than Cooper.
Answer/Step-by-sep explanation:
1. Given:
∆NMK ≅ ∆TRP
![\overline{NM} = 20](https://tex.z-dn.net/?f=%20%5Coverline%7BNM%7D%20%3D%2020%20)
![\overline{MK} = 15](https://tex.z-dn.net/?f=%20%5Coverline%7BMK%7D%20%3D%2015%20)
![\overline{KN} = 25](https://tex.z-dn.net/?f=%20%5Coverline%7BKN%7D%20%3D%2025%20)
![\overline{TR} = 3x - 1](https://tex.z-dn.net/?f=%20%5Coverline%7BTR%7D%20%3D%203x%20-%201%20)
a. To complete the congruent statement, thus: ∆MNK ≅ ∆RTP
b. The side that is congruent to
is
. Thus:
≅ ![\overline{NM}](https://tex.z-dn.net/?f=%20%5Coverline%7BNM%7D%20)
c. Since
≅
, therefore:
![\overline{TR} = \overline{NM}](https://tex.z-dn.net/?f=%20%5Coverline%7BTR%7D%20%3D%20%5Coverline%7BNM%7D%20)
(substitution)
Add 1 to both sides
![3x = 20 + 1](https://tex.z-dn.net/?f=%203x%20%3D%2020%20%2B%201%20)
![3x = 21](https://tex.z-dn.net/?f=%203x%20%3D%2021%20)
Divide both sides by 3
![x = \frac{21}{3}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B21%7D%7B3%7D%20)
![x = 7](https://tex.z-dn.net/?f=%20x%20%3D%207%20)
2. a. Slope of LK = ![\frac{rise}{run} = \frac{4}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7Brise%7D%7Brun%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20)
Slope of LM = ![\frac{rise}{run} = -\frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7Brise%7D%7Brun%7D%20%3D%20-%5Cfrac%7B3%7D%7B5%7D%20)
b. ✍️Length of LK is the distance between L(-7, 4) and (-4, 8):
![Lk = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20Lk%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
![Lk = \sqrt{(-4 -(-7))^2 + (8 - 4)^2}](https://tex.z-dn.net/?f=%20Lk%20%3D%20%5Csqrt%7B%28-4%20-%28-7%29%29%5E2%20%2B%20%288%20-%204%29%5E2%7D%20)
![Lk = \sqrt{(3)^2 + (4)^2}](https://tex.z-dn.net/?f=%20Lk%20%3D%20%5Csqrt%7B%283%29%5E2%20%2B%20%284%29%5E2%7D%20)
![Lk = \sqrt{9 + 16}](https://tex.z-dn.net/?f=%20Lk%20%3D%20%5Csqrt%7B9%20%2B%2016%7D%20)
![Lk = \sqrt{25}](https://tex.z-dn.net/?f=%20Lk%20%3D%20%5Csqrt%7B25%7D%20)
![Lk = 5](https://tex.z-dn.net/?f=%20Lk%20%3D%205%20)
✍️Length of LM is the distance between L(-7, 4) and (-2, 1):
![LM = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20LM%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
![LM = \sqrt{(-2 -(-7))^2 + (1 - 4)^2}](https://tex.z-dn.net/?f=%20LM%20%3D%20%5Csqrt%7B%28-2%20-%28-7%29%29%5E2%20%2B%20%281%20-%204%29%5E2%7D%20)
![LM = \sqrt{(5)^2 + (-3)^2}](https://tex.z-dn.net/?f=%20LM%20%3D%20%5Csqrt%7B%285%29%5E2%20%2B%20%28-3%29%5E2%7D%20)
![LM = \sqrt{25 + 9}](https://tex.z-dn.net/?f=%20LM%20%3D%20%5Csqrt%7B25%20%2B%209%7D%20)
![LM = \sqrt{34}](https://tex.z-dn.net/?f=%20LM%20%3D%20%5Csqrt%7B34%7D%20)
(nearest tenth)
∆KLM is not an isosceles ∆ because it does not has two equal side lengths. This we can see because LK and LM are not equal.
Therefore, Anthony is incorrect. Am isosceles ∆ has two equal sides.
![\frac{4*4}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%2A4%7D%7B5%7D%20)
=
![\frac{16}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B16%7D%7B5%7D%20)
Then you divide the numerator(top) by the denominator(bottom). 16÷5=
![3 \frac{1}{5}](https://tex.z-dn.net/?f=3%20%5Cfrac%7B1%7D%7B5%7D%20)
Your answer is