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2 years ago

If the common difference in an arithmetic sequence is 4, and the 20th term is 36, what is the first term?

1 answer:

8 0

4 difference, subtract 20 point - 1st point, =19, 19 places x difference of 4= 76 more or less than 36. More would be 112, less would be -40. A and C are both 40 while choice B = the difference so I'd say it's supposed to be 1 of the 40's but it's missing the negative sign

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Write 2.3181818... as a mixed number

JulsSmile [24]

Let x= 2.3181818...

then

10x=23.181818... and

1,000x=2,318.1818...

1,000x-10x=2,318.1818...-23.181818...

990x = 2,318 - 23
990x = 2295

x=2295/990

dividing by 5 both numerator and denominator:

x= 459/198

now, x= 198 + 198+ 63

so $x= 2\frac{63}{198}$

Answer: $x= 2\frac{63}{198}$

7 0

2 years ago

Alan wears his coat when the temp is colder than -4.c

denis23 [38]

Answer:

T<-4.c

Step-by-step explanation:

If it’s “less than” then the stated number is the highest number that you can have

4 0

2 years ago

84. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value

Yakvenalex [24]

Answer:

a) 1/27

b) 16

c) 1/8

Step-by-step explanation:

a) $x^{-3/2}$

One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

$x^{-3/2}=\frac{1}{x^{3/2} }$

And now, solving for x = 9 we have:

$\frac{1}{x^{3/2}}=\frac{1}{9^{3/2} } =\frac{1}{27}$

b) $y^{4/3}$

This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

$y^{4/3}=8^{4/3}=16$

c) $z^{-3/4}$

Using the same property we used in a) we have:

$z^{-3/4}=\frac{1}{z^{3/4} }$

And now, solving for z = 16 we have:

$\frac{1}{z^3/4} } =\frac{1}{16^{3/4} } =\frac{1}{8}$

4 0

3 years ago

Which of the following equations represents the perpendicular bisector of WX graphed below?

kotykmax [81]

The coordinates of the 2 given points are W(-5, 2), and X(5, -4).

First, we find the midpoint M using the midpoint formula:

$\displaystyle{ M_{WX}= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )= (\frac{-5+5}{2}, \frac{2+(-4)}{2} )=(0, -1).$

Nex, we find the slope of the line containing M, perpendicular to WX. We know that if m and n are the slopes of 2 parallel lines, then mn=-1.

The slope of WX is $\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{2-(-4)}{-5-5}= \frac{6}{-10}= -\frac{3}{5}$ .

Thus, the slope n of the perpendicular line is $\displaystyle{ \frac{5}{3}$ .

The equation of the line with slope $\displaystyle{ n= \frac{5}{3}$ containing the point M(0, -1) is given by:

$\displaystyle{ y-(-1)=\frac{5}{3}(x-0)$

$\displaystyle{ y+1= \frac{5}{3}x$

$\displaystyle{ 3y+3=5x$

$\displaystyle{ 5x-3y-3=0$

Answer: 5x-3y-3=0

8 0

3 years ago

A rectangular room is 12.5 feet wide and 14 feet long. How many linear feet of baseboards are needed to trim the room?

QveST [7]

If you do width times length you will get 30. Good luck

8 0

3 years ago