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3 years ago

Choose the equation of the line that has a slope of zero and passes through the point (6, -3).

Mathematics

1 answer:

olga2289 [7]3 years ago

7 0

Answer:

y= -3

Step-by-step explanation:

Since there is no slope, there is no mx in y=mx+b. Because the line has to go through point (6,-3), the y-intercept is -3.

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In m + 8, the variable m can have any value. Tell whether each statement is true or false. Then explsin your reasoning.

mote1985 [20]

M can have any value because M can represent any number because it is the unknown.

4 0

3 years ago

Mike completed an online course that contained 20 core topics in a total of

romanna [79]

Answer:

6 hours

Step-by-step explanation:

What you have to do is find the unit rate, which would be 20/40 which is .5 ( half an hour, 30 mins ) . Then you would do 30 x 12 = 360 ( 6 hours ).

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4 years ago

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.

Arisa [49]

Answer: $S_n=5(1-\dfrac{1}{n+1})$ ; 5

Step-by-step explanation:

Given series : $[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]$

Sum of series = $S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]$

Consider $\dfrac{1}{n\cdot(n+1)}=\dfrac{n+1-n}{n(n+1)}$

$=\dfrac{1}{n}-\dfrac{1}{n+1}$

⇒ $S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]$

Put values of n= 1,2,3,4,5,.....n

⇒ $S_n=5(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......-\dfrac{1}{n}+\dfrac{1}{n}-\dfrac{1}{n+1})$

All terms get cancel but First and last terms left behind.

⇒ $S_n=5(1-\dfrac{1}{n+1})$

Formula for the nth partial sum of the series :

$S_n=5(1-\dfrac{1}{n+1})$

Also, $\lim_{n \to \infty} S_n = 5(1-\dfrac{1}{n+1})$

$=5(1-\dfrac{1}{\infty})\\\\=5(1-0)=5$

4 0

3 years ago

If a shoebox measures 6 cm high, 7 cm wide, 20 cm long, what is its volume?

Talja [164]

Answer:

420cm cubed

Step-by-step explanation:

8 0

3 years ago

Carmen can buy bottles of paint for $2.00 each and boxes of colored pencils for $3.50 each. She can spend no more than $42 on ar

Lemur [1.5K]

Answer:

Step-by-step explanation:

Let x = the number of bottles of paint that Carmen can buy

Let y = the number of boxes of colored pencils that Carmen can buy

A bottle of paint costs $2

A box of colored pencils costs $3.50

She can spend no more than $42 on art supplies. This means

She can buy bottles of paint worth 2×x = $2x

She can buy boxes of colored pencils

worth 3.5 × y = $3.5y

Since the total amount she can spend cannot exceed $42, the equation becomes

2x + 3.5y lesser than or equal to 42

This is shown in the attached photo

b) three different solutions to the inequality would be three different possible values that x and y can take. These are

x = 7 while y = 8

x = 10 while y = 6

x = 14 and y = 4

3 0

4 years ago