MATHEMATICS HIGH SCHOOL

1)If (x-2) is a factor of x2+ 3ax -2a, then find the value of a

Answers

Answer 1
Answer:

Answer:

x - 2 => x = 2

x² + 3ax - 2a

=> 2² + 3 × a × 2 - 2 × a

=> 4 + 6a - 2a

=> 4 + 4a

=> 4 ( 1 + a )

★ 1 + a = 0

a = -1

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If the tax rate is 6.5%, what is the tax on $80?

Answers

Multiply 80✖️.065 and you'll get 8.80 Then add it to the total which is 80 +8.80 Which the answer is 88.80

Answer: 5.2

Step-by-step explanation:

Antoine is on vacation with his family. They have a vacation budget of $1,400. Antoine predicts they will spend $110 each night on the hotel, $80 a day on food, and $100 a day on activities. They will also spend $120 on gasoline for the entire trip. Write an inequality to find how many nights, n, they afford to stay on vacation. What is the longest vacation they can take?

Answers

Answer:

290n + 120 ≤ 1400

4 days

Step-by-step explanation:

Given that:

Vacation budget = $1400

Cost on hotel = $110 per night

Cost on food = $80 per day

Cost on activities = $100 per day

Cost on gas = $120 for entire trip

Number of nights they can afford to stay

Let the Number of nights they can afford = n

((110 + 80 + 100) * number of nights) + 120 ≤ vacation budget

290n + 120 ≤ 1400

290n ≤ 1400 - 120

290n ≤ 1280

n ≤ 1280 / 290

n ≤ 4.4137

Hence, longest vacation they can take is 4 days

Final answer:

The family can afford up to 4 nights for their vacation, as per the inequality 290n + 120 ≤ 1400, where 'n' stands for the number of nights.

Explanation:

Let's first define the total expenses per day as the sum of the hotel costs ($110), food costs ($80), and the daily amount for activities ($100). This adds up to $290 per day. So for 'n' nights, the family will be spending $290n. In addition, there's a $120 onetime expense for gasoline. Hence, the inequality representing their spending will be: 290n + 120 ≤ 1400.

To find the longest vacation this family can afford, we simply need to solve this inequality. Pay attention as we do this: 290n ≤ 1280 (subtracting 120 from both sides), and then n ≤ 4.41 (dividing both sides by 290).

Since the number of nights 'n' should be a whole number, the family can afford up to 4 nights on their vacation.

Learn more about Vacation budgeting here:

brainly.com/question/36787192

#SPJ3

Slope for -8,18 and -14,-3

Answers

(\stackrel{x_1}{-8}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{-14}~,~\stackrel{y_2}{-3}) \n\n\n \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{18}}}{\underset{\textit{\large run}} {\underset{x_2}{-14}-\underset{x_1}{(-8)}}} \implies \cfrac{ -21 }{-14 +8} \implies \cfrac{ -21 }{ -6 } \implies \cfrac{7}{2}

How tall would I  be if i were 54 inches

 

How tall would I be if i were 58 inches?

 

How tall would i be if Iwere 59 inches?

Answers

So the question is how tall would a person be in three cases, 54 inches, 58 inches and 59 inches. Since the height measure are feet and inches and one feet has 12 inches, this is the first case: 54 inches = 4*12 inches + 6 inches = 4 feet and 6 inches = 4'6''. Second case: 58 inches= 4*12 + 10 inches= 4 feet and 10 inches = 4'10'' and third case: 59 inches= 4*12 inches + 11 inches= 4 feet and 11 inches = 4'11''.

Peyton has a goal to walk 10,000 steps each day. On Tuesday afternoon,Peyton walked 7,338 steps. She averages 2.5 feet per step

Answers

Please consider the complete question.

Peyton has a goal to walk 10,000 steps each day. On Tuesday afternoon, Peyton walked  7,338 steps. She averages 2.5 feet per step.

How many more feet does Peyton need to walk to reach her goal of 10,000 steps?

First of all we will find the steps Peyton needs to walk to reach her goal.

\text{Steps Peyton needs to walk}=10000-7338

\text{Steps Peyton needs to walk}=2662

Since Peyton averages 2.5 feet per step, so to find number of feet in 2662 steps, we will multiply 2662 by 2.5 as:

\text{Distance that Peyton needs to walk to reach her goal}=2662* 2.5\text{ ft}

\text{Distance that Peyton needs to walk to reach her goal}=6655\text{ ft}

Therefore, Peyton needs to walk 6655 feet to reach her goal.

If David bought 12 pencils for $3.00. How much did 1 pencil cost?

Answers

Step-by-step explanation:

get the cost of 12 pencil and divide by those 12 pencils to get the cost of 1 pencil

Answer:
$.65

We divide $3.00 by 12 which gets us $.65.

Hope you understand!
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