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3 years ago

Write the equation of the line that passes through (3, 4) and (2, –1) in slope-intercept form.

1 answer:

6 0

First find the slope. 4+1/3-2 = 5/1 or 5. Plug in your points to find b. 4=5(3)+b. 4=15+b. b=-11. SO the equation is y=5x-11.

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Pippi sold ten more cups of lemonade that cups of iced tea. She sold 120 cups in all. How many cups of lemonade did she sell?

Kamila [148]

Answer:

65 cups

Step-by-step explanation:

If she sold 10 more cups of lemonade than tea and sold 120 cups total. I first would subtract 10 cups from 120 =110. then I divide 110 /2 = 55 cups

The 55 cups makes it equal then I add the 10 cups back to the Lemonade to get 55+10 = 65

So your answer would be 65 cups of lemonade

7 0

3 years ago

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

3 years ago

17. Which of the following measures can be calculated for qualitative data? a. Mean b. Median c. Mode d. All of these

VLD [36.1K]

Answer: C. Mode

Step-by-step explanation:

Qualitative data applies to observable data such as reoccurring patterns (mode)

Quantitative data applies to numbers and numerical calculations (Mean, Median)

6 0

3 years ago

Find the value of z <br> 38 <br> 138 <br> 148 <br> 102

garri49 [273]

Answer:

Huatz no te entiendo wuey

6 0

2 years ago

Please please please please please please help me if u can tysmm

faltersainse [42]

Q55.
UTA+ATS=UTS
x+18+120=12x+17
x+138=12x+17
12x-x=138-17
11x=121
x=121/11
x=11

mUTA=x+18
put the value of x
11+18
mUTA=29

Q57.
AQP+RQA=RQP
9x+2+75=1+28x
9x+77=1+28x
28x-9x=77-1
19x=76
x=76/19
x=4

mRQP=1+28x
put the value of x
1+28(4)
1+112
mRQP=113

4 0

2 years ago