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3 years ago

Draw the graph of the equation

Mathematics

1 answer:

guapka [62]3 years ago

6 0

9514 1404 393

Answer:

24 square units

Step-by-step explanation:

The triangle is a right triangle with legs 6 and 8. Its area is ...

A = 1/2bh = 1/2(6)(8) = 24 . . . . square units

_____

Additional comment

The equation for a line in intercept form is ...

x/a + y/b = 1

where 'a' and 'b' are the x- and y-intercepts, respectively. If we divide the given equation by 2, we get ...

x/6 +y/8 = 1

showing us that the x- and y-intercepts are 6 and 8. This is also clear on the graph.

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Find missing angles

yKpoI14uk [10]

Hey

The value of X is 35°

X and 35° are vertically opposite angles.

Vertically opposite angles are always equal.

Hope it helps

Good luck on your assignment

8 0

3 years ago

Present Value Hoew much shuold be deposited in an account paying 7.8% interest compounded monthly in order to have a balance of

Alisiya [41]

Answer: $15385 should be deposited.

Step-by-step explanation:

The principal was compounded monthly. This means that it was compounded 12 times in a year. So

n = 12

The rate at which the principal was compounded is 7.8%. So

r = 7.8/100 = 0.078

It was compounded for 4 years. Therefore,

t = 4

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. The total amount is given as $21000. Therefore

21000 = P (1+0.078/12)^12×4

21000 = P (1+0.078/12)^48

21000 = P (1+0.0065)^48

21000 = P (1.0065)^48

P = 21000/1.365

P = $15385

6 0

3 years ago

5 divided by 60 5/60 ??

mr Goodwill [35]

Answer:

1/12 or 0.08333333333

Step-by-step explanation:

5/60 can be factored to 1/12 because the two numbers are each divisible by 5.

6 0

3 years ago

Read 2 more answers

a rectangular prism with a volume of 10 cubic units is filled with cubes with side lenghts of 1/2 unit how many 1/2 unit cubes d

Pachacha [2.7K]

Answer:

Step-by-step explanation:

The volume of a cube is

V=s^3, we are told the volume is 10u^3 and that it will be filled with cubes having a side of 1/2 so

n(1/2)^3=10, where n will be the number of these small cubes

n(1/8)=10 upon multiplying each side by 8

n=80

So it will take 80 cubes of side length 1/2 to have a volume equal to 10u^3

6 0

3 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago