The sum of three consecutive integers is 1,628

Solve for 7/2x+7/9x=−17+2/56

kati45 [8]

Answer:

7/2x+7/9x-(-17+25/6)=0

4 0

3 years ago

HaAAAaAAaaaaAaaAaAaLp

Tamiku [17]

Answer:

D trust me look

Step-by-step explanation:

Hope This Helped

6 0

3 years ago

Read 2 more answers

Graph a line with a slope of - 3/4 that contains the point (2 3)

Savatey [412]

Answer:

Step-by-step explanation:

1. Graph point (2, 3)

2. Go down 3, 4 to the right or up 3 and 4 to the left

3. Repeat until you have about 3 to 4 points

4. Create a line

6 0

3 years ago

Please solve, answer choices included.

qaws [65]

4. To solve this problem, we divide the two expressions step by step:

$\frac{x+2}{x-1}* \frac{x^{2}+4x-5 }{x+4}$
Here we have inverted the second term since division is just multiplying the inverse of the term.

$\frac{x+2}{x-1}* \frac{(x+5)(x-1)}{x+4}$
In this step we factor out the quadratic equation.

$\frac{x+2}{1}* \frac{(x+5)}{x+4}$
Then, we cancel out the like term which is x-1.

We then solve for the final combined expression:
$\frac{(x+2)(x+5)}{(x+4)}$

For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:

$x-1\neq0$
$x+5\neq0$
$x+4\neq0$

Therefore, x should not be equal to 1, -5, or -4.

Comparing these to the choices, we can tell the correct answer.

ANSWER: $\frac{(x+2)(x+5)}{(x+4)}$ ; $x\neq1,-4,-5$

5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:

$\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r^{2}+ \pi r \sqrt{ r^{2} +h^{2} } }$

We can simplify this expression by factoring out the denominator and cancelling like terms.

$\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r(r+ \sqrt{ r^{2} +h^{2} } )}$
$\frac{ rh }{ 3(r+ \sqrt{ r^{2} +h^{2} } )}$
$\frac{ rh }{ 3r+ 3\sqrt{ r^{2} +h^{2} } }$

We then rationalize the denominator:

$\frac{rh}{3r+3 \sqrt{ r^{2} + h^{2} }} * \frac{3r-3 \sqrt{ r^{2} + h^{2} }}{3r-3 \sqrt{ r^{2} + h^{2} }}$
$\frac{rh(3r-3 \sqrt{ r^{2} + h^{2} })}{(3r)^{2}-(3 \sqrt{ r^{2} + h^{2} })^{2}}}=\frac{3 r^{2}h -3rh \sqrt{ r^{2} + h^{2} }}{9r^{2} -9 (r^{2} + h^{2} )}=\frac{3rh(r -\sqrt{ r^{2} + h^{2} })}{9[r^{2} -(r^{2} + h^{2} )]}=\frac{rh(r -\sqrt{ r^{2} + h^{2} })}{3[r^{2} -(r^{2} + h^{2} )]}$

Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:

$\frac{r*r(r -\sqrt{ r^{2} + r^{2} })}{3[r^{2} -(r^{2} + r^{2} )]}=\frac{ r^{2} (r -\sqrt{2 r^{2} })}{3[r^{2} -(2r^{2} )]}=\frac{ r^{2} (r -r\sqrt{2 })}{-3r^{2} }=\frac{r -r\sqrt{2 }}{-3 }=\frac{r(1 -\sqrt{2 })}{-3 }$

By examining the choices, we can see one option similar to the answer.

ANSWER: $\frac{r(1 -\sqrt{2 })}{-3 }$

8 0

4 years ago

In a bowl of fruit there are 10 bananas, 6 apples and 4 pears.

kobusy [5.1K]

Answer:

P(0,0) = 2/12 times 1/11 = 1/66

Step-by-step explanation:

For probability questions, think of each event happening separately, it makes the maths easier to understand. For example, in this question, do not think of the two boys taking a fruit at the same time - that makes the maths complicated

.

Let Daniel take a fruit first, then Sean can take a fruit. There are two parts to consider.

P

r

o

b

a

b

i

l

i

t

y

=

number of desirable outcomes

total number of possible outcomes

For Daniel: there are 12 different pieces of fruit in the bowl, he just takes one without choosing a specific fruit. (random)

The chance that Daniel takes an orange is

2

12

Of the 12 pieces of fruit. 2 are oranges.

Now Sean: the numbers of fruit in the bowl have changed. There are now only 11 pieces of fruit in the bowl, and only 1 is an orange.

The chance that Sean takes an orange is

1

11

4 0

4 years ago