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Ymorist [56]
2 years ago
14

Please help due in 6 minutes!!!!

Mathematics
1 answer:
luda_lava [24]2 years ago
4 0

Answer:

hi

Step-by-step explanation:

Sorry u gonna fail cause I to dumb.

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Carly's family traveled 3/10 of the distance to her grandmother's house on Saturday. They traveled 3/7 of the remaining distance
polet [3.4K]

Answer:

3/10 of the total distance to her grandmother's house was traveled on Sunday

Step-by-step explanation:

Carly's family traveled distance of Saturday = \frac{3}{10}

Remaining distance =1-\frac{3}{10}=\frac{7}{10}

They traveled 3/7 of the remaining distance on Sunday.

So, Distance traveled on Sunday =\frac{3}{7}(\frac{7}{10})

Distance traveled on Sunday =\frac{3}{10}

Fraction of the total distance to her grandmother's house was traveled on Sunday =\frac{3}{10}

Hence 3/10 of the total distance to her grandmother's house was traveled on Sunday

5 0
3 years ago
Joy wants to buy strawberries and raspberries to bring to a party. Strawberries cost $1.60 per pound and raspberries cost $1.75
zimovet [89]

Answer: 1.60x + 1.75y is less than or equal to 10

Step-by-step explanation:

Since the strawberries cost $1.60 per pound, it would be x pounds times $1.60 for the total cost of strawberries. Since the raspberries cost $1.75 per pound, it would be y pounds times $1.75 for the total cost of the raspberries. The total cost of both, or 1.60x + 1.75y, must be equal to or less than 10 because she cannot spend over 10 dollars.

5 0
3 years ago
Find the integral using substitution or a formula.
Nadusha1986 [10]
\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx

Derivative of the denominator:
\rm (x^2+2x+5)'=2x+2

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx

and then split the fraction,

\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx

Based on our previous test, we know that a simple substitution will work for the first integral: \rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx

So the first integral changes,

\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx

integrating to a log,

\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2

So we have this going on,

\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx

Bringing all that stuff together as a single square,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx

Making the substitution: \rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx

giving us,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du

simplying a lil bit,

\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du

and hopefully from this point you recognize your arctangent integral,

\rm ln|x^2+2x+5|+\frac52arctan(u)

undo your substitution as a final step,
and include a constant of integration,

\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c

Hope that helps!
Lemme know if any steps were too confusing.

8 0
3 years ago
What is the product?<br> (-2x- 9y2 )(-4x-3)
lara [203]

Answer:

36xy^2 + 8x^2 + 27y^2 + 6x

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: -2x * -4x = 8x^2

Outside terms: -2x * -3 = 6x

Inside terms: -9y^2 * -4x = 36xy^2

Last term in each binomial: -9y^2 * -3 = 27y^2

Now, rearrange the terms correctly. 36xy^2 + 8x^2 + 27y^2 + 6x

This is our final answer, since it can not be simplified any more.

4 0
3 years ago
Whats the best expansion for (x+5a+5b)(x+a-b) ​
jeka57 [31]

Answer:

x² + 6ax + 4bx + 5a² - 5b²

Step-by-step explanation:

(x+5a+5b )(x+a-b) ​

x² +a x -bx +5ax + 5a² -5ab + 5bx + 5ab -5b²

x² + 6ax + 4bx + 5a² - 5b²

4 0
2 years ago
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