Answer:
23
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of hours required to tutor to have enough money to pay for the trip is 23 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of days for the summer vacation = 6
Savings = $840
Earnings per hour = $45
Airfare cost = $525
Food and sightseeing = $780
Hotel cost per night = $95
Number of hours = x
We can make an expression.
525 + 780 + 6 x 95 = 840 + 95x
525 + 780 + 570 = 840 + 45x
1875 = 840 + 45x
1875 - 840 = 45x
1035 = 45x
1035/45 = x
x = 23
This means 23 hours.
Thus,
The number of hours required to tutor to have enough money to pay for the trip is 23 hours.
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Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x=-3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Never mind I got it. mtan=6x+4. Sub in x values, for x=-2, take 6(-2)+4 = -8, and for x=1.5. 6(1.5)+4=13.
Complete Question
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for [tex] x = 3[/tex] and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Answer:
The generally expression for the slope of [tex]y = 2x^2 + 4x[/tex] is [tex]y' = 4x +4[/tex]
The graph is shown on the first uploaded image
The generally expression for the slope of [tex]y=2x^2+4[/tex] is [tex]y' = 4x[/tex]
Step-by-step explanation:
From the question we are told that
The equation of the curve is [tex]y = 2x^2 + 4x[/tex]
First we differentiate the equation
So
[tex]y' = 4x +4[/tex]
Therefore the generally expression for the slope tangent to the curve [tex]y=2x^2+4x[/tex] is [tex]y' = 4x +4[/tex]
The next step is to substitute for x = 3 and x = 0.5
So for [tex]x_1 = 3 [/tex]
[tex]y' = 4(3) +4[/tex]
[tex]y' =m_1= 16[/tex]
And for [tex]x_2 = 0.5[/tex]
[tex]y' = 4(0.5) +4[/tex]
[tex]y' =m_2= 6[/tex]
Here m_1 and m_2 are slops of the curve
Next we obtain the coordinates of the tangent lines
So at [tex]x_1 = 3 [/tex]
[tex]y_1 = 2(3)^2 + 4(3)[/tex]
[tex]y_1 = 21[/tex]
So the coordinate for the first tangent line is
[tex](x_1 , y_1 ) = (3 , 21)[/tex]
At [tex]x_2 = 0.5 [/tex]
[tex]y_2 = 2(0.5)^2 + 4(0.5)[/tex]
=> [tex]y_2 = 2.5[/tex]
So the coordinate for the second tangent line is
[tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex]
Next we obtain the equation for the tangent lines
So generally the slope is mathematically represented as
[tex]m = \frac{y - y_1 }{x-x_1}[/tex]
For [tex](x_1 , y_1 ) = (-3 , 21)[/tex] and [tex]y' =m_1= 16[/tex]
[tex] 16 = \frac{y -21 }{x-3)}[/tex]
=> [tex]y = 16x - 27[/tex]
For [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex] and [tex]y' =m_2= 6[/tex]
[tex] 6 = \frac{y -2.5 }{x-0.5}[/tex]
[tex]y = 6x -0.5[/tex]
Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows
[tex]y' = 4x[/tex]
198,500 round to ten thousand
Answer:
200,000
Step-by-step explanation:
Whats the three numbers between 813 930
The numbers between 813-930 are 870,880,925.
It is required to find the three numbers.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given:
We have to find the three numbers between 813 to 930.
Numbers between 813-930 are 870,880,925.
Therefore , the numbers between 813-930 are 870,880,925.
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When x=-2, the value of y is
Answer:
emaybe
Step-by-step explanation:
e hopeA train traveled at a constant speed for six hours and traveled a distance of 408 miles. What is the best estimate of the number of miles the train could travel in 2.5 hours? *A train traveled at a constant speed for six hours and traveled a distance of 408 miles. What is the best estimate of the number of miles the train could travel in 2.5 hours? *A train traveled at a constant speed for six hours and traveled a distance of 408 miles. What is the best estimate of the number of miles the train could travel in 2.5 hours? *A train traveled at a constant speed for six hours and traveled a distance of 408 miles. What is the best estimate of the number of miles the train could travel in 2.5 hours? *
someone help me on this please
Answer:
✓ The data for store 1 shows greater variability.
✓ The mean of the data for store 1 is greater than the mean of the data for store 2.
Use the given conditions to write an equation in slope-intercept form. passing through (-2, 0) & (0, 2)
Answer:
Step-by-step explanation:
(2 - 0)/(0 + 2)= 2/2= 1
y - 0 = x + 2
y = x + 2
If a=2b then a:b= what ???
Answer:
[tex]2:1[/tex]
Step-by-step explanation:
[tex]a:b\\---\\\ 2b:b\\2:1[/tex]
A school bus requires 40 liters of fuel per week. If your school district runs 5,000 school buses, how many liters of fuel will the buses consume in 52 weeks? A. 15 million liters B. 10 million liters C. 10.4 million liters D. 200 million liters
Answer:
C. 10.4 million liters.
Step-by-step explanation:
1. First, you want to create an equation to help you solve this. You know that there are 5,000 school buses and they use 40 liters of fuel per week. So, you know that 5,000 · 40x would be the amount of fuel for x weeks (where x is the number of weeks).
2. To figure out how many liters would be used in 52 weeks, simply put 52 in for x. So, the expression is 5,000·40(52).
3. Multiply 40(52) to get 2,080. Your expression now looks like this: 5,000·2,080
4. Multiply 5,000(2,080) to get your answer of 10,400,000 liters.
Hope this helps! :) If you could give me Brainliest that would be super helpful!
Find the distance between a point (6, 9) and a horizontal line at y = 5. A) 4 B) 11 C) 15 D) 14
Answer: A.) 4
Step-by-step explanation:
Given the following:
Horizontal line y = 5
Point (6, 9)
Distance between point (6, 9) and horizontal line y = 5
For point (6,9) ; x1 = 6, y1 = 9
Horizontal line : y = 5
Hence, distance between the two points will be the difference between the the y values :
y1 - y = 9 - 5 = 4
Hence, the distance between a point (6, 9) and a horizontal line at y = 5 is 4
which expression represents exponential decay
A. Y=1/100 (31)x
B. Y=1/10 (3.1)x
C. Y=10(0.13)x
D. Y=100(1.03)x
Given:
The exponential equations in the options.
To find:
The equation which represents exponential decay.
Solution:
The general exponential equation is
[tex]y=ab^x[/tex]
where, a is initial value and b is growth rate.
If b<1, then it is an equation of exponential decay.
If b>1, then it is an equation of exponential growth.
In option A, b=31>1, i.e., exponential growth.
In option B, b=3.1>1, i.e., exponential growth.
In option C, b=0.13<1, i.e., exponential decay.
In option D, b=1.03>1, i.e., exponential growth.
Only [tex]y=10(0.13)^x[/tex] represents exponential decay.
Therefore, the correct option is C.
5+5 you get 39 points
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Use a calculator to find this or simply use your figers and count 5 more starting from 5.
HELP WILL GIVE BRAINLIEST!!Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
12 + 0.60 x less-than-or-equal-to 50
What is the greatest number of bracelets she could buy?
Answer:
The greatest number of bracelets she can buy is 63.
Step-by-step explanation:
12 + 0.60x ≤ 50
Since we already have the inequality, we have to start picking random numbers(until there are no more solutions):1.) 12 + 0.60(63) ≤ 50
12 + 37.8 ≤ 50
49.8 ≤ 50
Since 49.8 ≤ 50 is always true, there are infinitely many solutions.
Now we know that she can buy 63 bracelets, we have to figure out if she can buy more:2.) 12 + 0.60(64) ≤ 50
12 + 38.4 ≤ 50
50.4 ≤ 50
Since 50.4 ≤ 50 is false, there is no solution.
Answer:
63
Step-by-step explanation:
did the test on edge
A positive number divided by a negative number will result in a ___ quotient.
Answer:
a negative quotient.
Evaluate the expression and enter your answer in the box below.
[(8 + 10) /3] +3 • (7-3)
Answer:
38.6
Step-by-step explanation:
3(x+5) = -6x+6 two column proof
Answer:
- 1
Step-by-step explanation:
Step 1:
3x + 15 = - 6x + 6
Step 2:
9x + 15 = 6
Step 3:
9x = - 9
Answer:
x = - 1
Hope This Helps :)
In your part-time job, your hours vary each week. One week you worked 22 hours, the next 25 hours, the third 14 hours, and the fourth 19 hours. Your gross pay for the entire month was $960. How much money did you bring home during the second week?
Answer:
$300
Step-by-step explanation:
1 month =4 weeks
1 week=22 hrs
2 week= 25 hrs
3 week = 14 hrs
4 week = 19 hrs
Total of hrs in the month is 80 hrs
80 hrs = $960
25 hrs = ?
960×25÷80=300
Answer =$ 300
Does the following number belong to the interval (1.5, 2.4) ?
Square root of 2
Square root of 3
Square root of 5
Square root of 6
Yes or no
Answer:
Square root of 2: No
Square root of 3: Yes
Square root of 5: Yes
Square root of 6: No
Step-by-step explanation: Verified by RSM
Problem Solving Skills
Answer the questions below. Use the Problem Solving Skills that we discussed in class.
Look back in your notebook if you need a reminder.
7) Suppose that x and y are rational numbers such that x >y. Which of the following
inequalities must be true?
A. (x/>ly/
B. X'>y'
C. x+y > 0
D. X-y> 0
Answer:i think the answer is A(x/.ly/
Step-by-step explanation:
Answer:
D. x - y > 0
Step-by-step explanation:
Given:
x > y
Solution:
x - y > y - y . . . . . subtract y from both sides
x - y > 0 . . . . matches choice D
Please answer fast will make brainlest
Answer:
C
Step-by-step explanation:
SOMEONE HELP I NEED THE ANSWERS TO THIS PROBLEM
Answer:
Step-by-step explanation:
∠6 = 45 {Vertically opposite angles are equal}
∠6 + 5x + 35 = 180 {Co interior angles}
45 + 5x + 35 = 180 {add like terms}
80 + 5x = 180
5x = 180 - 80
5x = 100
x = 100/5
x = 20
5x + 35 = 5*20 + 35 = 100 + 35 = 135
∠8 = 5x + 35 { Corresponding angles}
3) ∠8 = 135
4) ∠ 3 = ∠6 {Alternate interior angles are equal}
∠3 = 45
5) ∠6 = 45
HELP PLEASE MY WORK HAS TO BE DUE IN A FEW MINUTES PLEASE HELP
Given: 2/3 every 30 seconds
If we cut 2/3 in half, we get 1/3. This would also mean we cut the time in half 30 / 2 = 15 seconds
Therefore, 1/3 of the length every 15 seconds.
15 + 15 + 15 = 45 seconds to go the full length of the path
please help me fr tho
Answer: y=2x+1
Step-by-step explanation:
To solve for y, we want to use our algebraic properties to isolate y.
16x+9=9y-2x [add both sides by 2x]
18x+9=9y [divide both sides by 9, divide to each term]
2x+1=y
Now, we know that y=2x+1.
Answer:
no thx and thx for the points
Step-by-step explanation:
357,335 rounded to the nearest ten
Answer:
357,340
35 is the tens place, and if it is 5 or larger we round up to in this case, 40
Answer:
357340
Step-by-step explanation:
Find the equation of the line that is perpendicular to -x+2y=11 and passes through the point (6,-5).
Step-by-step explanation:
m=-2
y+5=2(x-6)
y+5=2x-12
y=2x-17
Answer:
Step-by-step explanation:
2y = x + 11
y = 1/2x + 11/2
perp. -2
y + 5 = -2(x - 6)
y + 5 = -2x + 12
y = -2x + 7
Two points (p, q) on a linear supply function are ($2.55, 98,000) and ($6, 195,500).
⦁ Determine the supply function q = f(p).
⦁ What price would result in supplier offering 145,000 units for sale?
⦁ Interpret the slope of the function.
⦁ Determine the p intercept.
⦁ Sketch f(p)
Answer:
q ≈ 28270p +25935$4.21 will give a supply of 145,000slope is the supply increase per dollar of pricep-intercept is about -$0.92a graph is attachedStep-by-step explanation:
The two-point form of the equation of a line is useful for this.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
q = (195500 -98000)/(6.00 -2.55)(p -2.55) +98000
q = 97500/3.45(p -2.55) +98000
q ≈ 28269.9p +25934.8
__
For a supply of 145000, the price would need to be ...
145000 = 28269.9p +25934.8
119065 = 28270p
119065/28270 = p = 4.21
A price of $4.21 will result in a supply of $145,000.
__
The slope is the additional amount supplied for each dollar increase in price.
__
The price value that results in a supply of zero is ...
0 = 28270p +25935
-25935 = 28270p
-25935/28270 = p ≈ -0.92
The p-intercept is about -$0.92.
Juan baked 5 dozens of cupcakes which cost her a total of PHP 2675.How much should she sell each cupcake if she wants to get a 25% profit?
Step-by-step explanation:
5 cupcakes = PHP 2675
25% profit =
25/100 × 2675 = 668.75
Selling price for 25% profit = 2675 + 668.75 = 3343.75
Cost of each cupcake for 25% profit = 3343.75/5
= 668.75
You have a summer job detailing cars. You charge $5 to wash a car, $25 to wax a car, and $2 to vacuum a car. What algebraic expression models the total amount you can earn? If you wash 8 cars, wax 2 cars, and vacuum 6 cars, how much will you earn in all?
5x+25x+2x, $102
Step-by-step explanation:
5x+25x+2x
5(8)=40
25(2)=50
2(6)=12
add what's behind the equal signs to get $102 in all
I need help with part 2 please
Answer:
$65
Step-by-step explanation:
So we already determined that the total cost C to drive m miles is:
[tex]C=0.25m+40[/tex]
And we want to find the total cost of driving 100 miles.
So, substitute 100 for m and solve for C:
[tex]C=0.25(100)+40[/tex]
Multiply:
[tex]C=25+40[/tex]
Add:
[tex]C=\$ 65[/tex]
Therefore, it will cost $65 to drive 100 miles.
a man whose income is rupees 576 a year spends rupees 432 a year what percentage of his income does he save
Answer:
He save 25% of his income.
Step-by-step explanation:
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lets take 576 as 100% so 576=100432=xfollowing unitary methodx=43200/576x=75%now saving %= 100%-75%= 25%Answer:
25%
Step-by-step explanation:
576-432=144
576=100%
144=?
144×100÷576=25%
The midpoint of AB is M(1, -3). If the coordinates of A are (4, -7), what are the
coordinates of B?