EXPLANATION
Since the two planes are 3400 miles apart, and their speed differs by 80 mph, we can apply the following relationship:
2660 / 4 = 665 mph
Assuming that x is the speed of the slower plane and y is the speed of the faster, we have:
(1) x + 65 = y
(2) x + y = 665 [Combined speed of both planes]
Plugging in (1) in (2):
x + (x + 65) = 665
Removing the parentheses:
x + x + 65 = 665
Adding like terms:
2x + 65 = 665
Subtracting -50 to both sides:
2x = 665 - 65
Subtracting numbers:
2x = 600
Dividing both sides by 2:
x = 300
Plugging in x=315 into (1):
300 + 65 = 365
In conclusion, the speed of both planes is:
Slower plane = 300 mph
Fastest plane = 365 mph
What is the least common denominator of 1/7 and 7/8?
Answer:
72/24. Solution: Rewriting input as fractions if necessary: 3/2, 3/8, 5/6, 3/1. For the denominators (2, 8, 6, 1) the least common multiple ( LCM) is 24. LCM (2, 8, 6, 1) Therefore, the least common denominator ( LCD) is 24. Calculations to rewrite the original inputs as equivalent fractions with the LCD: 1 1/2.
Step-by-step explanation:
The expression -7y is a ____. (20 Points!!) (Please help!)
Term
Constant
Variable
Answer:
constant
Step-by-step explanation:
-7y is a contant
Circle O has a center of (-1,5) and passes through the point (2,9) write the equation in center radius form and standard form
Firstly, calculate the radius r of the circle using distance between two points
[tex]\begin{gathered} r\text{ = }\sqrt[]{(2-(-1))2+(9-5)^2} \\ r=\text{ }\sqrt[]{(2+1)^2+(4)^2} \\ r=\sqrt[]{3^2+4^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=\text{ 5} \end{gathered}[/tex]Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle
[tex]\begin{gathered} r^2=(x-h)^2+(y-k)^2 \\ 5^2=(x-(-1))^2+(y-5)^2 \\ 5^2=(x+1)^2+(y-5)^2 \end{gathered}[/tex]The center radius form is
[tex]5^2=(x+1)^2+(y-5)^2[/tex]The standard form is
[tex]\text{ 25}^{}=(x+1)^2+(y-5)^2[/tex]PLEASE HELP 3x^2 - 3x - 18
Answer: 3(x-3)(x+2) is the solution
Step-by-step explanation:
Common factor
Use the sum-product pattern
Common factor from the two pairs
Rewrite in factored form
Answer:
x1,2= 3;-2
Step-by-step explanation:
3x^2 - 3x - 18=0
Counting discriminant: (-3)^2-4*3*-18=225
X1,2= 3+-√225/2*3= 3+-15/6=3;-2
X1=3, x2=-2
Simplify the equation 3( m- 5 ) + m
Answer:
4m-15 is the answer
Step-by-step explanation:
Hope this helps!!
Naomi opened a savings account 7 years ago. the account earns 8% interest compounded monthly if the current balance is 1,000.00 how much did she despoit initially
Manuel took a total of 20 quizzes over the course of 2 weeks. How many weeks of school will Manuel have to attend this quarter before he will have taken a total of 90 quizzes? Assume the relationship is directly proportional.
Manuel will attend the quarter in 9 weeks.
Given,
In the question:
Total taken quizzes is 90
Manuel took a total of 20 quizzes over the course of 2 weeks.
To find the how many weeks of school will Manuel have to attend this quarter ?
Now, According to the question:
Based on the given conditions :
Formulate:
Let the no. of weeks be x
Total quizzes = 90
Here, The relationship is directly proportional.
20/2 = 90/x
If the fraction is defined, the denominator cannot be equal 0.
Solve the equation:
10 = 90/x
10x = 90
x = 9
Hence, Manuel will attend the quarter in 9 weeks.
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There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.
The total number of pages they read by the end of November is 2916 pages.
As the question, Chapter 1 has 35 pages, Chapter 2 has 38 pages and Chapter 3 has 35 pages. All these pages are read by all 27 students by the end of November.
⇒ Total number of pages in Three chapters [tex]=35+38+35[/tex]
[tex]=108[/tex]
⇒ Total number of pages in all three chapters read by one student = 108
⇒ Total number of pages read by 27 students
[tex]= total number of pages in three chapters * 27[/tex]
[tex]=108*27[/tex]
[tex]=2916[/tex]
Therefore, The total number of pages 27 students read by the end of November = 2916.
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The full question is
There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.
the scatter plot below was constructed using data on length and inches (x) of several alligators and weight in pounds (y)right if you sent this describing the relationship between weight and length for these alligators
Answer
We are told that the relationship describing the weight and length, for alligators.
The length in inches is presented on the x-axis and the weight in pounds is presented on the y-axis.
The observations about this include
- From the scatterplot, we can see that the more the length of the alligator (that is, as x increases), the weight of the alligator also increases (that is, y increases too).
- This points to a direct relationship between the length of alligator and the weight of the alligator.
- Small alligators weigh light weights and longer alligators are heavy.
Hope this Helps!!!
Pls do this for me asap
a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.
b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.
How to build and interpret an inequality associated to the area of an rectangle
The area of a rectangle (A) is described by the following formula:
A = b · h
Where:
b - Base of the rectangleh - Height of the rectanglea) If we know that b = 2 · x and h = 3, then the area of the rectangle is:
A = (2 · x) · 3
A = 6 · x
And the inequality is:
12 ≤ 6 · x ≤ 36
b) And the solutions for the values of x are represented by the following inequality:
2 ≤ x ≤ 6
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What did I do wrong? Need help with this equation
Solve the system
[tex]\begin{bmatrix}y=4x-8 \\ y=2\mleft(x-3\mright)^2-2\end{bmatrix}[/tex]Subtract the equations
[tex]\begin{gathered} y-y=4x-8-\mleft(2\mleft(x-3\mright)^2-2\mright) \\ 0=4x-8-2(x-3)^2+2 \\ 0=4x-8-2(x^2-6x+9)+2 \\ 0=4x-8-2x^2+12x-18+2 \\ 0=16x-24-2x^2 \\ 0=-2x^2+16x-24 \end{gathered}[/tex]Solve quadratic equation
[tex]\begin{gathered} 0=-2(x^2-8x+12) \\ 0=-2(x-2)x-6) \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \\ \text{For y} \\ y=4(2)-8=8-8=0 \end{gathered}[/tex]And
[tex]\begin{gathered} x-6=0 \\ x-6+6=0+6 \\ x=6 \\ \text{For y } \\ y=4(6)-8=24-8=16 \end{gathered}[/tex]Answer:
(2,0)
(6,16)
Can someone please help me answer this?
Answer:
sol y=5x+15 (see photo for calc)
Question 3 of 30
sin 0=/941 and cos 0 =-40/41. Find tan 0.
O A. 40/9
OB. 9/40
C. -40/9
D. - 9/40
Answer:
answer Is -9/40
Step-by-step explanation:
the formula Is
tan0= sin0/cos0
tan0= (9/41)/(-40/41)
tan0=(9/41)*(-41/40)
tan0= -9/40
How do you divide x by a fraction, or an example of dividing x by a fraction.
SOLUTION
Now this is how I can divide x by a fraction.
Let's divide x by
[tex]\frac{2}{3}[/tex]So
[tex]x\text{ divided by }\frac{2}{3}[/tex]Now to do this, change division to multiplication. When you do this, the fraction reverses. That is the number up will come down and the number down will go up.
So, this becomes
[tex]\begin{gathered} x\text{ divided by }\frac{2}{3} \\ x\times\frac{3}{2} \end{gathered}[/tex]x on its own means x over 1, that is
[tex]\begin{gathered} x\times\frac{3}{2} \\ \frac{x}{1}\times\frac{3}{2} \\ m\text{ultiplying we have } \\ \frac{3x}{2} \end{gathered}[/tex]So this is how to divide x by a fraction.
Calculate the difference between 7.841 and 3.733
You have to subtract each value from rigth to left.
[tex]\begin{gathered} 007.841 \\ -03.733 \\ \text{ 4.107} \end{gathered}[/tex]The result for 7.841 minus 3.733 is 4.107
3. Evaluate:
Suppose you want to buy something for $60, and you have
$15 saved up so far. Then your grandmother calls and says she
will chip in for your purchase. She doesn't tell you the amount
of money she will give you yet, so you just consider it x
dollars. Write the expression that represents the equation.
The expression that represents the equation is x + 15 = 60
The total money needed to buy something is $60
And the saved up amount is $15
The amount of money that the Grandmother contributes is x
The saved up amount and the grandmothers contribution is equal to the total amount required to purchase
We need to write the expression that represents the equation.
x + 15 = 60
Therefore, the expression that represents the equation is x + 15 = 60
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Lina picks a 4 digit number.
The number is more than 5000.
The number is odd.
The second digit is a prime number.
How many different possible numbers could Lina pick?
Answer:
1000
Step-by-step explanation:
The easiest way to go about this is by turning our number into ABCD.
A will be in the 1000th spot, B 100th, C 10th, and D 1st.
A has to be ≥ 5. So 5, 6, 7, 8, 9.
B has to be a prime number. 2, 3, 5, 7.
C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Since the number is odd, D has to be 1, 3, 5, 7, 9.
A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000
What are the domain and range of g(x) = −4?
Answer:
look at attached image!
Step-by-step explanation:
Mr. March sells popcorn at his theater. He uses 3 3/4 cups of unpopped corn to make 15 bags of popped corn. Write an equation for the number of bags of popcorn b that can be made with c cups of unpopped corn.
The equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
Given, Mr. March sells popcorn at his theater.
He uses 3(3/4) cups of unpopped corn to make 15 bags of popped corn. We have to write an equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn.
Now, according to the question
3(3/4) cups = 15 bags
15/4 cups = 15 bags
1 cup = 4 bags
So, in 'c' cups he will make, 4c bags
therefore, 4c = b
Hence, the equation for the number of bags of popcorn 'b' that can be made with 'c' cups of unpopped corn is
b = 4c.
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BD bisects ABC, m/ABD = 2(3x), and m/ABC = 42°.
What is the value of x?
In the given triangle ABC where BD bisects ABC and according to the values of the given angles, the value of x is found out to be 3.5.
It is given to us that -
BD bisects ABC.
m/ABD = 2(3x) ----- (1)
and, m/ABC = 42 ------- (2)
We need to find out the value of x.
Since BD bisects triangle ABC,
The angles created with respect to the bisector are equal.
=> m/ABD = m/CBD ----- (3)
Also, it is also known that -
m/ABD + m/CBD = m/ABC ----- (4)
Substituting equation (3) in equation (4),
m/ABD + m/CBD = m/ABC
=> m/ABD + m/ABD = m/ABC
=> 2 m/ABD = m/ABC ----- (5)
Substituting the values of m/ABD and m/ABC from equation (1) and (2) in equation (5), we get
2 m/ABD = m/ABC
=> 2*2(3x) = 42
=> 12x = 42
=> x = 3.5
Thus, according to the values of the angles of the triangle, the value of x is 3.5.
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A driver accelerates her car from rest to a velocity of 35.9 mi/hr in 8.2 seconds. What is the acceleration of the car?
The acceleration of the car will be 0.002 m / s².
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The velocity of the car = 35.9 m/hr
The time take by car = 8.2 seconds
Now,
Since, We know that;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.
So, Initial velocity = 0
And, Final velocity = 35.9 m / hr
= (35.9 / 3600) m/s
= 0.01 m / s
So, We get;
⇒ Acceleration = (Final velocity - Initial velocity) / Time
⇒ Acceleration = (0.01 - 0) / 8.2
⇒ Acceleration = 0.01 / 8.2
⇒ Acceleration = 0.002 m / s²
Thus, The acceleration of the car will be 0.002 m / s².
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Two different squares have an areas of 36m° and 49m°
What is the difference of the lengths of their sides?
The difference of the length of two different squares having area of 36 square meters and 49 square meters is 1 m.
According to the question,
We have the following information:
Two different squares have an area of 36 square meters and 49 square meters.
We know that the following formula is used to find the area of square:
Area = side*side
Side*side = 36
Side = √36
Side = 6 m
Now, side of the another square:
Side*side = 49
Side = √49
Side = 7 m
Now, the difference in the length of the sides of these two squares:
7-6
1 m
Hence, the difference of the length of two different squares having area of 36 square meters and 49 square meters is 1 m.
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Which is the smallest ratio? 2 3 to 4, 3, 10:12, 2 to 1 03 to 4 em O 10:12 2 to 1
Answer:
2/3
Explanation
Given the following:
3 to 4, 2/3, 10:12 and 2 to 1
First let us express them as percentage. The smallest percentage will be the smallest ratio;
3 to 4 = 3/4 * 100
3 to 4 = 75%
2/3 = 2/3 * 100
2/3 = 66.7 %
10:12 = 10/12 * 100
10:12 = 1000/12
10:12 = 83.3%
2 to 1 = 2/1 * 100
2 to 1 = 200%
Since the lowest percent id 66.7%, hence the smallest ratio will be 2/3
Someone please Help!! 30 Points
There are currently 1,250 pine trees on Judy's plot of land. The number of pine trees on her land is currently decreasing at a rate of 14% per year.
Which of the following graphs shows the number of pine trees, Np, on Judy's land x years from now?
Answer: we would need to see the graphs to address this question fully, but you should look for the graph that starts at x = 0, 1250 and decreases by 14% compared to the previous year
so for example, x = 1, the y value should be 1250 - (0.14)(1250)
Step-by-step explanation:
help me please , for 20 points
Answer:
A
Step-by-step explanation:
First off we can see that there are 46 pencils - and 7 students - so we can divide the two
46/7 is not a whole number, so we need to find a number that can be multiplied by 7, and is right below 46.
If you multiply 7 by 6, you get 42, which is the highest you can get with multiply by 7, which is also below 46.
Now that we know that each student gets 6 pencils, we need to find out how many are left.
We can do 46 (total pencils) minus 42 (pencils given) to get a leftover of 4 pencils, so the answer is A.
I’m confused because I don’t know how to answer this question
SOLUTION:
We are to find the domain of the given exponential function shown;
The domain of exponential functions is all real numbers.
So the correct option is D
survey of 100 shoppers, were asked whether they have access to a computer at home. and if they have a personal email account. A) what % of shoppers have an email account?B) what % of shoppers do NOT have computer access at home?
Answer:
A). 34%
B). 62%
Explanation:
Part A:
How many shoppers have an email account?
The answer is 32 + 2 = 34 shoppers have an email account.
What percent of the total shoppers are 34 shoppers?
We know the there are 100 shoppers in total ( 32 + 2 + 6 + 60 = 100); therefore, 34 shoppers is
[tex]\frac{34}{100}\times100\%=34\%[/tex]Hence, 34% of the shoppers have an email account.
Part B:
How many shoppers do not have computer access at home?
The answer is 2 + 60 = 62 shoppers do not have computer access at home.
Now, what percent of the total number of shoppers is 62 shoppers?
The answer is
[tex]\frac{62}{100}\times100\%=62\%[/tex]Meaning, 62% of the shoppers do not have computer access at home.
Hence, to summerise
A). 34%
B). 62%
Question 3 Part B (2.02, 2.04): The table of values represents a linear function
(x), where x is the number of weeks that have passed and g(x) is the balance
n the bank account.
Write the equation of the line in point slope form (1 point):
Write the equation of the line in slope-intercept form (1 point):
Write the equation of the line in standard form (1 point):
X
0
5
10
g(x)
$1,250
$750
$250
The point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
What is equation of line?
The algebraic form of representing set of points is known as the equation of line.
The point slope form is as follows:
[tex]y-y_{1}=m(x-x_{1})[/tex] ... (1)
Here, [tex]y_{1}[/tex] is [tex]y[/tex] co-ordinates, [tex]x_{1}[/tex] is [tex]x[/tex] co-ordinates, and [tex]m[/tex] is the slope.
Also, slope is given by the following expression:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Hence, equation (1) can be written as follows:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex] ... (2)
Consider the following points:
[tex](g(x_{1}),x_{1})=(1250,0)\\(g(x_{2}),x_{2})=(750,5)[/tex]
substitute values in equation (2).
[tex]y-1250=\frac{750-1250}{5-0}(x-0)\\y-1250=-100x[/tex]
On comparing the above equation with equation (1), the value of slope [tex]m=-100[/tex]
Now, calculate the slope intercept form.
The following form is known as the slope intercept form:
[tex]y=mx+c[/tex]
Here, [tex]c[/tex] is the [tex]y[/tex] intercept that the value of [tex]y[/tex] when [tex]x=0[/tex] .
Substitute the value of slope that is -100 and value of g(x) when x =0 that is 1250 for [tex]c[/tex] in the above equation.
[tex]y=-100x+1250[/tex] ... (3)
Standered form of a line is as follows:
[tex]Ax+By=C[/tex]
Here, A,B, and C are integeres.
Rearrange equation (3) as follows:
[tex]y=-100x+1250\\100x+y=1250[/tex]
Hence, the point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
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Answer:
Step-by-step explanation:
3(2y + 3) + 6(3y – 1) = 1 – 7y
Answer:
y = - [tex]\frac{2}{31}[/tex]
Step-by-step explanation:
3(2y + 3) + 6(3y - 1) = 1 - 7y ← distribute parenthesis and simplify left side
6y + 9 +18y - 6 = 1 - 7y
24y + 3 = 1 - 7y ( add 7y to both sides )
31y + 3 = 1 ( subtract 3 from both sides )
31y = - 2 ( divide both sides by 31 )
y = - [tex]\frac{2}{31}[/tex]
A group of students was asked, "How many hours did you watch television last week?" Here are their responses. 15,14,20,17,6,11. Find the mean number of hours for these students.
The mean of these numbers is 13.83 hours (14 hours to the nearest whole number)
Here, we want to calculate the mean number of hours
To do this, we simply add all the numbers and divide by the count of the numbers
The count of the numbers is 6
Thus, we have the calculation as follows;
[tex]\frac{(15+14+20+17+6+11)}{6}\text{ = }\frac{83}{6}\text{ = 13.83}[/tex]