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In-s [12.5K]
3 years ago
13

At what point do the lines y = 6x – 18 and y=8x – 32 intersect?

Mathematics
1 answer:
anzhelika [568]3 years ago
4 0

Answer:

(7, 24)

Step-by-step explanation:

Solve the system:

6x - 18 = 8x - 32

2x = 14

x = 7

y = 6(7) - 18

y = 24

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Can y’all help me answer these questions
cupoosta [38]

2. f(x)=\dfrac18\left(\dfrac14\right)^{x-2}

Domain: (-\infty,\infty), because any value of x is allowed and gives a number f(x).

Range: (0,\infty), because a^x>0 for any positive real a\neq0.

y-intercept: This is a point of the form (0, f(0)). So plug in x=0; we get f(0)=\frac18\left(\frac14\right)^{-2}=\frac{4^2}8=2. So the intercept is (0, 2), or just 2. (Interestingly, you didn't get marked wrong for that...)

Asymptote: This can be deduced from the range; the asymptote is the line y=0.

Increasing interval: Going from left to right, there is no interval on which f(x) is increasing, since 1/4 is between 0 and 1.

Decreasing interval: Same as the domain; f(x) is decreasing over the entire real line.

End behavior: The range tells you f(x)>0, and you know f(x) is decreasing over its entire domain. This means that f(x)\to+\infty as x\to-\infty, and f(x)\to0 and x\to+\infty.

3. f(x)=\left(\dfrac32\right)^{-x}-7

Domain: Same as (2), (-\infty, \infty).

Range: We can rewrite f(x)=\left(\frac23\right)^x-7. \left(\frac23\right)^x>0 for all x, so \left(\frac23\right)^x-7>-7 for all x. Then the range is (-7,\infty).

y-intercept: We have f(0)=\left(\frac32\right)^0-7=1-7=-6, so the intercept is (0, -6) (or just -6).

Asymptote: y=-7

Increasing interval: Not increasing anywhere

Decreasing interval: (-\infty,\infty)

End behavior: Similar to (2), but this time f(x)\to+\infty as x\to-\infty and f(x)\to-7 as x\to+\infty.

5 0
3 years ago
Sara has $65 and wants to buy the following items from a store. Board game: $14.95 Building blocks: $25.49 Art kit: $35.79 At th
valina [46]

The correct statement is Sara can afford to purchase the items because the final price of the items is $60.

The first step is to determine the total cost of the items Sara wants to buy. The total cost can be determined by adding the cost of the items together.

Total cost = $14.95 + $25.49 + $35.79 = $76.23

The second step is to determine the cost of the items after the discount.

Price of the items = total cost x (1 - discount)

= total cost x (1 - 1/4)

total cost x 3/4

$76.23 x 3/4 = $57.17

The third step is to determine the cost of the items after tax.

Cost = (1.05) x $57.17 =$60.03

Please find attached the complete question. To learn more about taxes, please check: brainly.com/question/25311567

4 0
2 years ago
(10-i)-(12+6i)<br> .............
sergeinik [125]

Answer:

-2 - 7 i

Srry If Im wrng but Hope this helped :)

5 0
3 years ago
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Determine whether the given linear equations are parallel, perpendicular, or neither.
ladessa [460]

Answer:

A. Perpendicular

Step-by-step explanation:

Lines are perpendicular if their slopes are opposite reciprocals of each other. Opposite, meaning if positive, the other slope is negative, and if negative, the other slope is positive. Reciprocal meaning, the number is flipped upside down, turning fractions into whole numbers and vice versa.

1/9  

-1/9

-9

The slopes are perpendicular

4 0
3 years ago
Ratios equivalent to 5:1
Virty [35]
Ratios equivalent to 5:1 are
10:2 
15:3      
5 0
3 years ago
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