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jasenka [17]
3 years ago
9

In the arithmetic sequence, -12, -17, -22, -27... which term has a value of -68?​

Mathematics
1 answer:
RSB [31]3 years ago
7 0

Answer:

-68 is not a term in the given sequence

Step-by-step explanation:

The given sequence is -12, -17, -22, -27...

There is a common difference of d=-17--12=-5

The explicit rule for this sequence is f(n)=-12-5(n-1)

Or f(n)=-5n-7

To find the term that has a value of -68 we equate the explicit formula and solve for n.

 -68=-5n-7

 \implies -68+7=-5n

 \implies -61=-5n

n=\frac{61}{5} =12.2

The position should be a natural number.

Since n is a decimal, it tells us that -68 is not a term in the given sequence

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What is the equation of a line that passes through the point?
Artist 52 [7]
<h3>Answer: 3x-2y = 5 (choice A)</h3>

=====================================================

Explanation:

The given graph passes through (0,2) and (2,5)

The slope of this line is

m = (y2 - y1)/(x2 - x1)

m = (5-2)/(2-0)

m = 3/2

Since the y intercept is b = 2, we go from y = mx+b to y = (3/2)x+2, which is the equation of the graphed line shown.

Any parallel line will have the same slope, but a different y intercept.

-------------------

The parallel line must pass through (x,y) = (3,2). We'll use these coordinates along with m = 3/2 to find the y intercept b

y = mx+b

2 = (3/2)(3)+b

2 = 9/2+b

2-9/2 = b

4/2 - 9/2 = b

-5/2 = b

b = -5/2 ... is the new y intercept

The equation of the parallel line is y = (3/2)x-5/2, which is in slope intercept form

-------------------

Let's convert to standard form

y = (3/2)x-5/2

2y = 3x-5 .... multiply everything by the LCD 2 to clear out fractions

2y+5 = 3x

3x = 2y+5

3x-2y = 5 ... is the equation in standard form of the parallel line

-------------------

As a check, we can plug (x,y) = (3,2) into that last equation above to get

3x-2y = 5

3*3-2*2 = 5 ... replace x with 3, replace y with 2

9-4 = 5

5 = 5

Confirming that (x,y) = (3,2) is on the line.

3 0
3 years ago
Scott bought a pen and received change of $4.75 in 25 coins, all dimes and quarters. How many of each kind did he receive?
dangina [55]

Answer:

He received 10 dimes and 15 quarters.

Step-by-step explanation:

Dimes = $0.10

Quarters = $0.25

Variable x = dimes

Variable y = quarters

Create a pair of linear equations:

0.10x + 0.25y = 4.75

x + y = 25

Isolate any variable, using an equation of your choice:

x + y = 25

x = 25 - y

Plug in this new value of x into the other equation:

0.10(25 - y) + 0.25y = 4.75

Use the distributive property:

2.5 - 0.10y + 0.25y = 4.75

Combine like terms:

2.5 + 0.15y = 4.75

Isolate variable y:

0.15y = 2.25

y = 15

Plug in the value of y into any equation:

x + y = 25

x + 15 = 25

Isolate variable x:

x = 10

7 0
2 years ago
Arbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks sh
pashok25 [27]
If ice tea is lets say y (ice tea = y) and water is x (water = x) then the answer is 
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the error is that she forgot the second variable(y).
8 0
3 years ago
PLEASE NEEED HEELPP
krok68 [10]
There are many systems of equation that will satisfy the requirement for Part A.
an example is y≤(1/4)x-3 and y≥(-1/2)x-6
y≥(-1/2)x-6 goes through the point (0,-6) and (-2, -5), the shaded area is above the line. all the points fall in the shaded area, but
y≤(1/4)x-3 goes through the points (0,-3) and (4,-2), the shaded area is below the line, only A and E are in the shaded area. 
only A and E satisfy both inequality, in the overlapping shaded area.

 
Part B. to verify, put the coordinates of A (-3,-4) and E(5,-4) in both inequalities to see if they will make the inequalities true. 
 for y≤(1/4)x-3: -4≤(1/4)(-3)-3
-4≤-3&3/4 This is valid.
For y≥(-1/2)x-6: -4≥(-1/2)(-3)-6
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Part C: the line y<-2x+4 is a dotted line going through (0,4) and (-2,0)
the shaded area is below the line
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3 years ago
Solve for x: You must show your work (how you got your answer).<br><br> 8x + 5 = 35
valentinak56 [21]

Answer:

3.75 or 15/4

Step-by-step explanation:

8x+5=35

Subtract 5 from the left side to cancel it out, do the same thing to 35.

8x=30

Divide 8x by 8 to get x alone, do the same thing to 30.

x=3.75, or once you simplify 30/8, you get 15/4.

6 0
3 years ago
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