All categories

3 years ago

1 with 1 over 3 and 2 over 3

Mathematics

1 answer:

Alex_Xolod [135]3 years ago

4 0

Answer:

The answer is 2

Step-by-step explanation:

If you add these two together, you get 2. First you add the fractions together.

1/3 + 2/3 = 1

And then you add the whole number.

1 + 1 = 2

You might be interested in

judy got 117 problems right on a math test in her night school class. She got a score of 78% right. How many problems were on th

scZoUnD [109]

You would set this up as Part÷Whole=Percent÷100
Part=117
Whole= X
Percent=78
117÷X=78÷100
Set these up as fractions and cross multiply. You will get 117×100=78X
117×100=11,700
Divide both sides by 78 and you get x=150
There were 150 problems

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

Which choice is equivalent to the expression √20 + √80

salantis [7]

Answer:

13.41

Step-by-step explanation:

Hope it helps!

7 0

3 years ago

Read 2 more answers

Find the unknown side length x write your answer in simplest radical form

Sauron [17]

Answer:

(B) $4\sqrt{37}$

Step-by-step explanation:

First, we determine the height of the triangle which we label as y.

Using Pythagoras Theorem.

$25^2=7^2+y^2\\y^2=25^2-7^2\\y^2=576\\y=\sqrt{576}\\y=24$

In the smaller right triangle with hypotenuse, x

Base = 7-3 =4 Units

Height, y= 24 Units

Therefore, applying Pythagoras Theorem.:

$x^2=24^2+4^2\\x^2=592\\x=\sqrt{592}\\ x=4\sqrt{37}$

5 0

3 years ago

WILL MARK BRAINLIEST!!!!!!MUST BE CORRECT!

ExtremeBDS [4]

Hi there! The answer is 9 square units

To find the area of a triangle we use the following formula:
Area = 0.5 * base * height.

The base of this triangle:
AC = 6

The height of this triangle:
BD = 3

Filling in this formula gives us:
Area = 0.5 * 3 * 6 = 9

Therefore, the answer is 9 square units

7 0

3 years ago

Read 2 more answers