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2 years ago

Answer for brainliest asap

Mathematics

1 answer:

V125BC [204]2 years ago

3 0

Answer:

$x = 8 \\ y = 9$

Step-by-step explanation:

$2y = x + 10 \\ y = 2x - 7 \\$

since they gave us a value for y in the second equation, we can input it into the first equation. so...

$2(2x - 7) = x + 10 \\ 4x - 14 = x + 10 \\ 4x - x = 10 + 14 \\ 3x = 24$

$\frac{3}{3} x = \frac{24}{3} \\ x = 8$

Since x is 8 we can find y by substituting 8 for x

$y = 2x - 7 \\ y = 2(8) - 7 \\ y = 16 - 7 \\ y = 9$

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Simplify and answer in scientific notation (3.5*10^4) (4*10^5)

Studentka2010 [4]

Answer: 14 x 10^9

Step-by-step explanation:

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \

Kisachek [45]

Answer:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2$

Step-by-step explanation:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?$

We can use Part I of the Fundamental Theorem of Calculus:

$\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}$

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

$\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}$

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

$\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

$\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}$

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

$\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

$\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]$
where u represents any function other than a variable

For the first term, replace $\text{t}$ with $2x$ , and apply the chain rule to the function. Do the same for the second term; replace

$\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)$

Simplify the expression by distributing $2$ and $2x$ inside their respective parentheses.

$[-(8x^2 +2)] + (2x^5 + 2x)$
$-8x^2 -2 + 2x^5 + 2x$

Rearrange the terms to be in order from the highest degree to the lowest degree.

$\displaystyle2x^5-8x^2+2x-2$

This is the derivative of the given integral, and thus the solution to the problem.

6 0

3 years ago

For a club gathering you were having, you bought a total of 50 burgers, and spent $90. You paid $2 per turkey burger, and $1.50

Sedaia [141]

Answer:

No. You would have to cut the number of veggie burgers in more than half.

Explanation:

1. Model the situation with a system of equations

a) Name the variables:

number of turkey burgers: t
number of veggie burgers: v

b) Number of burgers:

50 = t + v

c) Cost of the 50 burgers:

$90 = 2t + 1.50v

2. Solve that system of equations:

a) System

50 = t + v

90 = 2t + 1.50v

b) Mutliply the first equation by 2 and subtract the second equation

100 = 2t + 2v
90 = 2t + 1.50v

10 = 0.5v

v = 20 ⇒ t = 50 - 20 = 30

c) How much would you spend if the next year you buy the double of 20 turkey burgers (40) and the half of 30 veggie burgers (15)

$2(40) + $1.50(15) = $80 + $22.50 = $102.50

Then, you if you double the number of turkey burgers, and cut the number burgers in half, you would spend more than $90 ($102.50).

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3 years ago

Hey guys! Need help asap! Pls help! Will give brainliest!!!

AVprozaik [17]

Answer:

The answer for 1 = B for second one it is D

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2 years ago

A 12 ounce bottle of shampoo lasts Juan 16 weeks. Assuming he uses the same amount each week, write an equation relating the oun

trasher [3.6K]

He uses one and one third ounces of shampoo per week.

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3 years ago