Write the equation of the line with the two given points. (-4, -2) and (4, 0)
First, find the slope using the given points.
Slope formula: y2-y1/x2-x1
0-(-2)/4-(-4)
2/8
1/4
Second, find the y-intercept with the slope and one point.
-2 = 1/4/(-4) + b
-2 = -1 + b
-1 = b
Third, put everything we know into the equation.
y = 1/4x - 1
Best of Luck!
The area of a rectangular wall of a barn is 216 square feet. Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn
Answer:
Length is 24 feet and width is 9 feet.
Step-by-step explanation:
It is given that length of a rectangular wall is 6 feet longer than twice its width.
Let x feet be the width of wall.
Length = 2x+6 feet
Area of rectangle is
[tex]A=length \times width[/tex]
[tex]A=(2x+6)\times x[/tex]
[tex]A=2x^2+6x[/tex]
It is given that area of a rectangular wall of a barn is 216 square feet.
[tex]2x^2+6x=216[/tex]
[tex]x^2+3x=108[/tex]
[tex]x^2+3x-108=0[/tex]
Splitting the middle term, we get
[tex]x^2+12x-9x-108=0[/tex]
[tex]x(x+12)-9(x+12)=0[/tex]
[tex](x+12)(x-9)[/tex]
[tex]x=-12,9[/tex]
Width can not be negative. So width is 9 feet.
Length [tex]=2(9)+6=18+6=24\text{ feet}[/tex]
Therefore, length is 24 feet and width is 9 feet.
Please Help!!! What is the end behavior of function h? h(x)=2(x-3)^2 As x approaches negative infinity, approaches negative infinity, positive infinity, or a constant . As x approaches positive infinity, approaches negative infinity, positive infinity, or a constant .
Answer:
Step-by-step explanation:
Function to be graphed is,
h(x) = 2(x - 3)²
Function 'h' is a quadratic function.
Since, the coefficient of the leading term (term with the highest power) is positive, parabola will open upwards.
Both the ends of the parabola will be upwards (towards positive infinity).
As x approaches to negative infinity, h(x) approaches to positive infinity.
As x approaches to positive infinity, h(x) approaches to positive infinity.
A) As x approaches negative infinity, h(x) approaches positive infinity.
B ) As x approaches positive infinity, h(x) approaches positive infinity.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
Function to be graphed is,
h(x) = 2(x - 3)²
Function 'h' is a quadratic function.
Since the coefficient of the leading term (a term with the highest power) is positive, the parabola will open upwards.
Both the ends of the parabola will be upwards (towards positive infinity).
Therefore As x approaches negative infinity, h(x) approaches to positive infinity. As x approaches positive infinity, h(x) approaches to positive infinity.
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What is 80,023 written in scientific notation?
Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change? Distance Carol Traveled while Cross-Country Skiing Minutes Distance Traveled (miles) 2 StartFraction 1 Over 6 Endfraction 3 StartFraction 17 Over 48 EndFraction 4 StartFraction 13 Over 24 EndFraction 5 StartFraction 35 Over 48 EndFraction 6 StartFraction 11 Over 12 EndFraction
Answer:
3/16 miles/minute
Step-by-step explanation:
A rate of change describes how an output quantity changes relative to the change in the input quantity.
Points given:
Input Output
2 1/6
3 17/48
4 13/24
5 35/48
6 11/12
Here input values describe the time in minutes from 2 to 6 and output values describe the distance in miles from 1/6 to 11/12
Calculating the rate of change using the first two pairs of input-output values
Relative change = change in distance/change in time(17/48 - 1/6)/(3-2) = (17/48 - 8/48) /1 = 9/48 = 3/16 miles/minuteWe will get the same result if we take any other ordered pair of input and output values.
Answer:
it is 3/16 miles per minute
Step-by-step explanation:
...
C (x) = x^2 - 10x+27
Answer:
C(x) = (x-5)^2 + 2
................
Answer
[tex]5+2\sqrt{x} 13=12.211[/tex] or 5−2 this is where the square root would go 13=−2.211
Step-by-step explanation:
1.1 Factoring x2-10x-27
The first term is, x2 its coefficient is 1 .
The middle term is, -10x its coefficient is -10 .
The last term, "the constant", is -27
Step-1 : Multiply the coefficient of the first term by the constant 1 • -27 = -27
Step-2 : Find two factors of -27 whose sum equals the coefficient of the middle term, which is -10 .
-27 + 1 = -26
-9 + 3 = -6
-3 + 9 = 6
-1 + 27 = 26
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
2.1 Find the Vertex of y = x2-10x-27
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 5.0000
Plugging into the parabola formula 5.0000 for x we can calculate the y -coordinate :
y = 1.0 * 5.00 * 5.00 - 10.0 * 5.00 - 27.0
or y = -52.000
Hannah is asked to convert the number 0.00000305 to scientific notation. Her answer is 3.05 x 106.
Which statement best describes her answer?
Answer:
Hanna converted the number:
0.00000305
to:
3.05x10^6.
Now, when we have:
Ax10^n
This will "move" the value of A n times to the left, adding zeros when the decimals of A run over.
if we have
Ax10^-n
This will move A n times to the right.
Then the number:
3.05x10^6 = 3050000
This is clearly not the number that Hannah wanted to write.
The problem is that the exponent should be negative, if we have instead:
3.05x10^-6
We move our number 6 times to the right, adding zeros when necessary.
3.05x10^-6 = 0.00000305.
So Hannah is incorrect, she should wrote 0.00000305 = 3.05x10^-6
Answer: D. Hannah is not correct because the exponent should be -6.
Hope this helps!
Nancy has to find the reflection of a point across the x-axis. How can she find the new coordinates without graphing the point? Is there a rule that she can apply to find it?
Answer:To find the reflection of a point across the x-axis without graphing it, Nancy can change the sign of the y-coordinate and keep the sign of the x-coordinate the same.
Step-by-step explanation:
(x, y) transforms into (-x, y) is the rule that she can apply to find reflection.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that Nancy has to find the reflection of a point across the x-axis
We need to find how can Nancy find the new coordinates without graphing the point
Let us find the rule that she can apply to find it
When we do a reflection over a given axis, the distance between the initial point to the axis must be the same as the distance of the reflected point to the axis.
We do a reflection over the y-axis, then the value of y must be fixed.
Start with the point (x, y), the only other point that is at the same distance from the y-axis is the point (-x, y)
So the rule is, the y value remains equal and the x changes of sign.
(x, y) transforms into (-x, y)
Hence, (x, y) transforms into (-x, y) is the rule that she can apply to find reflection.
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Elena works at the ticket booth of a local play house. On the opening night of the play, tickets are $10 each. The playhouse has already sold $300 worth of tickets during a presale. How many tickets must Elena sell In order for the play house to make a total of $900?
Answer:
Elena needs to sell 60 tickets
Answer:
Elena must sell 90 tickets to earn $900
Step-by-step explanation:
Divide the total money needed by how much each ticket costs:
900 ÷ 10 = 90
If you're talking about how many more tickets are needed:
Subtract the total tickets needed by how many tickets Elena already sold
90 - 30 = 60 more tickets needed
I hope this helped!
What is the Value of X?
Answer:
x = 27
Step-by-step explanation:
4x+7 = 5(x-4)
4x + 7 = 5*x + 5*-4
4x + 7 = 5x - 20
7 + 20 = 5x - 4x
27 = x
Check:
4*27 + 7 = 5*(27-4)
108 + 7 = 5 * 23 = 115
Answer: x = 27
Step-by-step explanation:
These angles are congruent to each other so we well put an equal sign in between the two degrees.
Distribute the 5 by multiplying x and the -4 by 5 to get, 5x - 20
4x + 7 = 5x - 20
add 20 to the 7
subtract 4x from the 5x
27 = 1x
Solve the equation!!?!
Answer:
The correct answer is "B"
Step-by-step explanation:
m=-1/4
Hope this help!
have a nice day!
Answer:
B
Step-by-step explanation:
So we have the equation:
[tex]\frac{3m-3}{5}=\frac{2m-1}{2}[/tex]
First, let's get rid of the fractions. Multiply both sides by the LCM of 5 and 2, which is 10:
[tex]10(\frac{3m-3}{5})=10(\frac{2m-1}{2})[/tex]
On the left, the 10 gets reduced to 2. On the right, the 10 gets reduced to 5. Thus:
[tex]2(3m-3)=5(2m-1)[/tex]
Distribute:
[tex]6m-6=10m-5[/tex]
Subtract 6m from both sides:
[tex]-6=4m-5[/tex]
Add 5 to both sides:
[tex]-1=4m[/tex]
Divide both sides by 4:
[tex]m=-\frac{1}{4}[/tex]
And we're done!
The answer is B.
José stood on a 4 foot high still, then jumped into a 1 foot deep hole. Which applies to his action
I'm going to assume that you are asking how deep he jumped. He jumped from 4 feet high into a 1 foot deep hole, so, we need to add.
4 + 1 = 5
Therefore, Jose jumped a total of 5 feet.
Best of Luck!
Q: Evaluate -3(-10)
Answer:
[tex] - 3( - 10) \\ = + 30[/tex]
Step-by-step explanation:
- and - =+
that's why when we multiply -3 with -10 then product is positive i.e +30
hope it helped you:)
thanks!
Which transformation creates similar polygons?
a. dialation
b. translation
c. rotation
d. reflection
Answer: Translation
Step-by-step explanation: One-to-one correspondence between two sets of points.
A rectangle has length 2x+3 and width 7x+9. Write a polynomial in standard form that represents the perimeter of the rectangle. You MUST combine like terms.
Answer:
18x+21
Step-by-step explanation:
First multiply each equation by 2 since there is 2 sides for both the length and width.
2(2x+3) 2(7x+9)
4x+3 14x+18
Then combine like terms
4x+14x 3+18
18x 21
(-5q^2 + 6q + 7) - (-q^2 + 4q)
Steps to solve:
(-5q^2 + 6q + 7) - (-q^2 + 4q)
~Distribute the left side
-5q^2 + 6q + 7 + q^2 - 4q
~Combine like terms
-4q^2 + 2q + 7
Best of Luck!
Answer:
-4q^2+2q+7
Remove unecessary parenthesis
-5q^2+6q+7-(-q^2+4q)
when there is a - in front of an expression in parenthesis, change the sign of each term in the expression
-5q^2+6q+7+q^2-4q
collect like terms -5q^2 and q^2
-4q^2+6q+7-4q
-4q^2+2q+7
Help please!!! Thxxxxxx
Answer:
40 degrees
Step-by-step explanation:
Angle ACO = 80 ( 180 - 100)
Angle CAO = 60 (180 - 120)
Angle AOC = 40 (180 - 80 - 60) (TOTAL DEGREES OF A TRIANGLE IS 180)
For the equation 17h + 6 = 40, select the appropriate property of equality to move the constant term to the right
side of the equation. (1 point)
O Subtraction Property of Equality to subtract 6 from both sides
O Addition Property of Equality to add 6 to both sides
O Division Property of Equality to divide both sides by 6
O Multiplication Property of Equality to multiply both sides by 6
Answer:
Subtraction Property of Equality to subtract 6 from both sides
Step-by-step explanation:
By subtracting, you cancel out 6 on the left and you move the constant over to 40. 17h = 34
Right and solve an equation to find the number N
Six times the sum of a number and 15 is -42
Answer:
N=-22
Step-by-step explanation:
We first highlight all the information that is important and make an equation based on that. From that, we get 6(N+15)=-42. From there, we divide both sides by 6 to get N+15=-7. We subtract 15 from both sides to get N =-22, which is our answer.
4
Solve for n.
11(n − 1) + 35 = 3n
O n = -6
The answer is n=-3
Answer:
[tex]\boxed{n=-3}[/tex]
You should be correct.
Step-by-step explanation:
[tex]11(n-1) + 35 = 3n\\\\11n-11+35=3n\\\\11n+24=3n\\\\11n+24-24=3n-24\\\\11n=3n-24\\\\11n-3n=3n-3m-24\\\\8n=-24\\\\\frac{8n=-24}{8}\\\\ \boxed{n=-3}[/tex]
Hope this helps.
The value of n in the expression is,
⇒ n = - 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Expression is,
⇒ 11(n − 1) + 35 = 3n
Now, We can simplify as;
⇒ 11(n − 1) + 35 = 3n
⇒ 11n - 11 + 35 = 3n
⇒ 11n - 3n = - 24
⇒ 8n = - 24
⇒ n = - 3
Thus, The value of n in the expression is,
⇒ n = - 3
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Which is NOT a correct statement about variables?
A) variables are letters or symbols
B) variables can represent unknown quantities
C) variables can appear in numerical expressions
D) variables can represent quantities that change depending on the situation
Answer:
The answer would be C, since numerical expressions only contain numbers.
Answer:
The answer is A even though variables are letters they are not symbols like %,$,# etc. All the other ones are correct besides C. Hope this helps
Step-by-step explanation:
7. Da'Quan is reading a 532-page book for English. His teacher says that each student must have read at least half of the book by the end of the 1st week. If Da'Quan reads each of the 7 nights, write and solve an inequality to represent the number of pages he should read each night to meet the teacher's requirements.
Answer: x > 38
Step-by-step explanation:
Easy
Da'Quan must read more than 38 pages each night.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
The Number of pages in the Quran = 532
The Number of nights in a week = 7
Target is to read more than half by the end of the first week
In other to meet up, Let number of pages to be read per night = r
Hence, the equality goes ;
Pages read per night × 7 > pages of the Quran / 2
7× r > 532 / 2
7r > 266
r > 266/7
r > 38
Hence, Da'Quan must read more than 38 pages each night.
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How much of the original 250 U.S. dollars does Phelan have now?
Answer:
After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? A. 44.70 US dollars.
Point V is on line segment UW. Given VW = x, UV = 3x – 1, and
UW = 5x – 5, determine the numerical length of VW.
Answer:
4 units
Step-by-step explanation:
Since V lies on UW,
UV + VW = UW
[tex]3x - 1 + x = 5x - 5 \\ 5x - x - 3x = 5 - 1 \\ x = 4[/tex]
Therefore, VW = 4 units
Two times the sum of half a number and six is four. Find the number.
Answer:
The number is:
-8
Step-by-step explanation:
2(a/2 + 6 ) = 4
2*a/2 + 2*6 = 4
2a/2 + 12 = 4
a + 12 = 4
a = 4-12
a = -8
Check:
2(-8/2 + 6) = 4
2(-4+6) = 4
2*2 = 4
Lue! 576 x 8 help me
Answer:
4,608
Step-by-step explanation:
hopefully this helps you :)
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Find the diffrence of 159 - 88.99
Answer:
70.01.
Step-by-step explanation:
159 - 88.99
= 159 - 90 + 1.01
= 69 + 1.01
= 70.01.
Solve for A.
F = m a
Answer:
F/m = a
Step-by-step explanation:
F = ma
Divide each side by m
F/m = ma/m
F/m = a
11-(3x-6)+2(4x+5)-x simplify
Answer:
HOPE THAT WILL HELP YOU
Two people share £700 in the ratio 3:2
Answer:
420:280
Step-by-step explanation:
first you add 3:2 up which comes to 5.
700 divided by 5 = 140.
3:2 means that 3 will get 3 lots of 140 and 2 will get 2 lots of 140.
3x140= 420.
2x140= 280
the ratio is 420:280