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Anna11 [10]
3 years ago
14

F the graph of y=ax+b/x+c has a horizontal asymptote y=2 and a vertical asymptote x=-3 then a+c=?

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
3 0
Correct answer is E.

y= \frac{ax+b}{x+c}
\\
\\  \lim_{x \to \infty} \frac{ax+b}{x+c}=2
\\
\\ \lim_{x \to \infty} \frac{ \frac{ax}{x} + \frac{b}{x} }{ \frac{x}{x} + \frac{c}{x} }=2
\\
\\ \lim_{x \to \infty} \frac{a + \frac{b}{x} }{ 1 + \frac{c}{x} }=2
\\ \frac{a + 0}{ 1 + 0 }=2
\\
\\  \frac{a}{1} =2
\\a=2
\\
\\x+c=0
\\-3+c=0
\\c=3
\\
\\a+c=2+3=5



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5 0
3 years ago
Solve this
sesenic [268]

A sandwich store charges a delivery fee to bring lunch to an office.

Delivery cost - D

Meatball sandwich cost  - M

One office pays $40.50 for 5 meatball sandwiches.

40.50 = 5M + D

Another office pays $66.50 for 9 meat ball sandwiches

66.50 = 9M + D

A. How much does each meatball sandwich add to the cost of delivery?

D = 40.50 - 5M = 66.50 - 9M

40.50 - 5M = 66.50 - 9M

9M - 5M = 66.50 - 40.50

4M = 26.00

M = 6.50

B. What is the delivery fee

D = 40.50 - 5M = 40.50 - 5(6.50) = 40.50 - 32.50 = 8.00

Check

66.50 = 9M + D = 9(6.50) + 8 = 58.50 + 8.00 = 66.50

3 0
3 years ago
In ΔRST, t = 4.1 inches, r = 7.1 inches and ∠S=45°. Find the length of s, to the nearest 10th of an inch.
dem82 [27]

Answer:

The length of s is 5.1 inches to the nearest tenth of an inch

Step-by-step explanation:

In Δ RST

∵ t is the opposite side to ∠T

∵ r is the opposite side to ∠R

∵ s is the opposite side to ∠S

→ To find s let us use the cosine rule

∴ s² = t² + r² - 2 × t × r × cos∠S

∵ t = 4.1 inches, r = 7.1 inches, and m∠S = 45°

→ Substitute them in the rule above

∴ s² = (4.1)² + (7.1)² - 2 × 4.1 × 7.1 × cos(45°)

∴ s² = 16.81 + 50.41 - 41.1677568

∴ s² = 26.0522432

→ Take √ for both sides

∴ s = 5.10413981

→ Round it to the nearest tenth

∴ s = 5.1 inches

∴ The length of s is 5.1 inches to the nearest tenth of an inch

3 0
3 years ago
Read 2 more answers
Can the polynomial equation have exactly 1 real solution, including any repeated solutions? (Use the Fundamental Theorem of Alge
Kryger [21]

yes, there are infinitety many polynomial that have exactly one real root just like your example, to determine the real root first let the real root is a, and the complex roots are b±ic the polynomial satisfy

-9x³ + 19x² + 17 = -(x - a)(x - b - ic)(x - b + ic)

9x³ - 19x² - 17 = (x - a)(x - b - ic)(x - b + ic)

5 0
3 years ago
Tickets to a school basketball game cost $4 for students and $7 for adults. At the end of the night, 168 tickets are sold for a
stepan [7]
4s+7a=861
s+a=168

This can be solved using either elimination or substitution. I am going to use substitution.

Solve s+a=168 for s
s=168-a

Replace 168-a for s in 4s+7a=861
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Solve for a
672+3a=861
3a=189
a=63

Substitute 63 for a in s=168-a
s=168-63=105

So, s=105 student tickets and a=63 adult tickets
3 0
3 years ago
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