Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (2, -2) and (4, -1).
Substitute:
[tex]m=\dfrac{-1-(-2)}{4-2}=\dfrac{-1+2}{2}=\dfrac{1}{2}[/tex]
Put the value of a slope and the coordinates of the point (2, -2) to the equation of a line:
[tex]-2=\dfrac{1}{2}(2)+b[/tex]
[tex]-2=1+b[/tex] subtract 1 from both sides
[tex]-3=b\to b=-3[/tex]
Finally:
[tex]y=\dfrac{1}{2}x-3[/tex]
Through a given point not on a line, there exists exactly one _____ to the given line
There exists exactly one parallel line that can be drawn through a given point not on the original line. This line will have the same slope but a different y-intercept as the original line.
Explanation:The answer to your question, 'Through a given point not on a line, there exists exactly one ___ to the given line' is Parallel Line.
In geometry, a line is said to be parallel to another if they are at the same plane and they never intersect, no matter how far they are extended. This principle also applies to lines on the graph of a linear equation such as y = a + bx which represents a straight line.
For example, assume we have a line graph that uses x and y as its axes where y = 3x + 9. Now let's say there's a point on the graph that is not on this line. You can draw exactly one line through this point that would be parallel to the original line of y = 3x + 9. This line would have the same slope as the first line, but a different y-intercept, and thus, would never intersect the original line.
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PLEASE HELP I WON'T PASS THIS CLASS
What is the slope of a line that contains
the point (-0.5, 4) and has a y-intercept
of -5?
Answer:
The slope of line that contain the points ( - 0.5 , 4 ) and has y- intercept of - 5 is -18
Step-by-step explanation:
Given as :
The points that satisfy the line is ( - 0.5 , 4 )
The y - intercept = - 5
The equation of line is
y = m x + c
Where m is the slope of line
∵ For y- intercept , c = - 5
Now, points on the line is ( - 0.5 , 4 ) and y intercept c = - 5 is
y = m x + c
or, 4 = m × ( - 0. 5 ) + ( - 5 )
Or, 4 = - 0. 5 m - 5
or, 4 + 5 = - 0.5 m
Or, 9 = - 0. 5 m
∴ m = [tex]\frac{-9}{0.5}[/tex]
So, Slope = m = - 18
Hence the slope of line that contain the points ( - 0.5 , 4 ) and has y- intercept of - 5 is -18 Answer
Final answer:
The slope of a line that contains the point (-0.5, 4) and has a y-intercept of -5 is -18. This is calculated using the slope formula, resulting in a negative slope.
Explanation:
To find the slope of a line with a given point and a y-intercept, we can use the slope formula slope = (y2 - y1) / (x2 - x1), where (x1, y1) is the given point and (x2, y2) is the y-intercept point. Since the y-intercept is at a point where x = 0, the second point is (0, -5).
The given point is (-0.5, 4), so after substituting into the slope formula we get: slope = (-5 - 4) / (0 - (-0.5)) = (-9) / (0.5) = -18. The slope of the line is -18, indicating a negative slope meaning the line will move downwards on the graph as the x-value increases.
Suppose that F(x) = x2 and G(X) = 2/3 x^2. Which statement best compares the graph of G(x) with the graph of F(x)?
Step-by-step explanation:
Given that [tex]F(x)=x^{2}[/tex] and [tex]G(x)=\frac{2}{3}x^{2}[/tex]
[tex]F(x)[/tex] is always positive because [tex]x^{2}[/tex] is always positive.
[tex]G(x)[/tex] is always positive because [tex]\frac{2}{3}x^{2}[/tex] is always positive.
So,both are always positive.
So,there is no flipping over x-axis.
In [tex]F(x)[/tex],the height of a point at [tex]x_{0}[/tex] is [tex]x_{0}^{2}[/tex]
In [tex]G(x)[/tex],the height of a point at [tex]x_{0}[/tex] is [tex]\frac{2}{3}x_{0}^{2}[/tex]
So,height of any point has less height in [tex]G(x)[/tex] than [tex]F(x)[/tex]
So,the graph of [tex]G(x)[/tex] is the graph of [tex]F(x)[/tex] compressed vertically.
Answer:
C.
Step-by-step explanation:
In this figure, AB || CD and mZ6 = 75"
What is mZ3?
Enter your answer in the box.
Answer:
105
Step-by-step explanation:
Theorem:
If parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Lines AB and CD are parallel, and angles 3 and 6 are same-side interior angles, so by the theorem above, angles 3 and 6 are supplementary. That means that the sum of their measures is 180 deg.
m<3 + m<6 = 180
m<3 + 75 = 180
Subtract 75 from both sides.
m<3 = 105
Answer: 105 degrees
HELP!!! WILL MARK BRAINLIEST!!! ASAP.
What was the original number if after an increase of 40%, it became 420.
Answer:
300
Step-by-step explanation:
Let x be the initial number. Initially, this number was 100%.
After an increase of 40%, it became 420 and 100% + 40% = 140% in percent.
So,
x - 100%
420 - 140%
Write a proportion:
[tex]\dfrac{x}{420}=\dfrac{100\%}{140\%}[/tex]
Cross multiply:
[tex]140\cdot x=420\cdot 100\\ \\140x=42,000\\ \\14x=4,200\\ \\x=\dfrac{4,200}{14}=\dfrac{600}{2}=300[/tex]
Answer:
Just going to create this answer so the other person can get brainliest.
Step-by-step explanation:
:) :D <3
sales tax in Philadelphia is 8.5%. what is the price of your items before taxes if your final price is $162.75
Answer:
177.87
Explanation:
162.75 * 100 = 177.87
91.5
177.87 * 0.915 = 162.75
Answer:
177.87 is the correct answer. Really hope that this helped :)
Step-by-step explanation:
Please please answer this correctly
Answer:
63 Inches.
Step-by-step explanation:
2 yards - 9 inches is equal to 1.75 yards and when converted to inches, equals 63 inches.
Answer:
63 inches
Step-by-step explanation:
2 yards - 9 inches = 1.75 yards and when converted is 63 inches
How many solutions does this system of equations have?
exactly two
none
infinitely many
exactly one
Graph of a system of linear equations. Equation 1 is 3x plus 2y equals 6. Equation 2 is negative 4x plus 5y equals 15. The graphs intersect at a point.
Answer:
exactly oneStep-by-step explanation:
The system of linear equations have:
one solution, infinitely many solutions or no solution.
One solution if the lines intersect.
Infinitely many solutions if the lines are the same (overlap)
There is no solution if the lines are parallel (they do not have a common point).
In the graph, two lines intersect. Therefore, the system of equations has one solution (0, 3).
What is the equation of the line that is parallel to the line 2x+3y=-8 and passes through the point (2,-2)?
Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Solution:Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)
Generic slope intercept form of a line is given by y = mx + c
where "m" = slope of the line and "c" is the y - intercept
Let’s first find slope intercept form of 2x+3y=-8 to get slope of line
[tex]\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}[/tex]
On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,
[tex]\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}[/tex]
We know that slopes of parallel lines are always equal
So the slope of line passing through (2, -2) is also [tex]m=-\frac{2}{3}[/tex]
Equation of line passing through [tex](x_1 , y_1)[/tex] and having slope of m is given by
[tex]\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)[/tex]
[tex]\text { In our case } x_{1}=2 \text { and } y_{1}=-2[/tex]
Substituting the values in equation of line we get
[tex](y-(-2))=-\frac{2}{3}(x-2)[/tex]
[tex]\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}[/tex]
[tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
What additional information is required for the 2 triangles to be congruent by SAS?
solve this pls!!! I need to turn it into
-3
_____
(x+2)(x-5)
Step-by-step explanation:
[tex]\dfrac{-3}{(x+2)(x-5)}\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{-3}{(x)(x)+(x)(-5)+(2)(x)+(2)(-5)}\\\\=\dfrac{-3}{x^2-5x+2x-10}\qquad\text{combine like terms}\\\\=\dfrac{-3}{x^2-3x-10}[/tex]
[tex]\dfrac{64x-8x^2}{10x-80}=\dfrac{-8x(x-8)}{10(x-8)}\qquad\text{cancel}\ (x-18)\\\\=\dfrac{-8x}{10}=-\dfrac{8x:2}{10:2}=-\dfrac{4}{5}x[/tex]
A book sold 34,100 copies in the first month the release suppose this represents 7.9% of the number of copies sold to date how many copies have you sold to date? Round to the nearest whole number
Answer:
431,646
Step-by-step explanation:
[tex]\frac{7.9}{100} = \frac{34,100}{x} \\[/tex]
Simply multiply 100x34,100 (3,410,000) and divide by 7.9 to get your answer= 431,645.57. Round to the nearest whole number and you get your finl outcome which is 431,646.
Answer:
Step-by-step explanation: Let the no. of copies sold to date be y
A.T.Q
7.9/100 * y = 34100
y = 34100*100/7.9
= 3410000/7.9
= 431645.56
Rounding it off to nearest no. it will be
Total 431646 copies have been sold to date.
Hope this helps u :)
Rewrite the equation correctly.
Answer:
y = 2x - 5Step-by-step explanation:
2x - y = 5 subtract 2x from both sides
2x - 2x - y = -2x + 5
-y = -2x + 5 change the signs
y = 2x - 5
what is 60 times one fourth as a whole number
Answer:
150
Step-by-step explanation:
60 x 1/4 = 150
Answer:
15
Step-by-step explanation:
" 60 times one fourth" can be written as 60/4, which in turn is 15.
What is 8% of 525 answer
Answer: 8% of 525 is 42
Step-by-step explanation:
Answer:
Step-by-step explanation:
a good way to find 8% is find 1% and multiply it by 8 (5.25 * 8 = 42)
another way would be to simply multiply 525 by 0.08 (525 * 0.08 = 42)
either way, the answer is 42
The sum of two numbers is 53 and the difference is 27. What are the numbers?
Final answer:
The two numbers are 40 and 13.
Explanation:
We are given that the sum of two numbers is 53, and their difference is 27. Let's denote the two unknown numbers as x and y, where x is the larger number.
The system of equations based on the given information is:
x + y = 53x - y = 27By adding the two equations, the y's cancel out:
(x + y) + (x - y) = 53 + 272x = 80x = 40Now, we can find the value of y by substituting x into the first equation:
40 + y = 53y = 53 - 40y = 13The two numbers are 40 and 13.
A triangle has sides with lengths of 12 miles, 12 miles, and 15 miles. Is it a right triangle?
Answer: not a right triangle
Step-by-step explanation:
if it is a right triangle the pyth. theorem must stand
12^2+12^2 does not equal 15^2
so it is not a right triangle
I need help with 25 and 26 plzz
Answer:
Step-by-step explanation:
25.
Combine like terms.
4t+7=-33
subtract 7 from both sides
4t=-40
divide both sides by 4
t=-10
26.
Subtract 2a from both sides
5=7a-16
add 16 to both sides
21=7a
divideby 7 on both sides
a = 3
I'd suggest getting the app photomath or using cymath to help you with these problems. they give you the answer and how to get it step by step
Your company takes orders over the phone. The company’s average time is 4.6 minutes.The graph below shows 4 calls and the difference between the call time and the company’s average call time.
Answer:
0.4
Step-by-step explanation:
The mean difference between the call will be 0.4. Then the correct option is C.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Your company takes orders over the phone. The company’s average time is 4.6 minutes. The graph below shows 4 calls and the difference between the call time and the company’s average call time.
Then the mean difference between the call will be
Mean = (Sum of the observation) / (Number of the observation)
Mean = (-2.32 - 1.55 + 4.79 + 0.68) / 4
Mean = 1.6 / 4
Mean = 0.4
The mean difference between the call will be 0.4. Then the correct option is C.
Your question was incomplete, but the complete question is attached below.
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IM GIVING THE REST OF MY POINTS FOR THIS 45 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!
ANSWER QUICK THANK YOU
THERE ARE 5 QUESTIONS!!!!!!!!!!!
Answer:
1b 2d 3c 4d 5a
Step-by-step explanation:
The length of a rectangle is 6 units less than the width. The area of the rectangle is 27 units. What is the width, in units, of the rectangle?
The width of rectangle is 9 units.
Step-by-step explanation:
Given,
Width of rectangle = w
Length of rectangle = l = w - 6
Area of rectangle = A = 27 units
[tex]Area\ of\ rectangle=\l*w\\27=(w-6)(w)\\27=w^2-6w\\0=w^2-6w-27\\w^2-6w-27=0\\w^2+3w-9w-27=0\\w(w+3)-9(w+3)=0\\(w+3)(w-9)=0\\[/tex]
Either,
w+3=0 =>w= -3
Or,
w-9=0 =>w=9
As width cannot be negative, therefore,
Width = 9 units
The width of rectangle is 9 units.
Keywords: rectangle, area
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. The diameter of a circle is 5.7 cm. What is the circumference? (Express your answer in pi form)
Step-by-step explanation:
radius =diameter÷2
r=5.7÷2=2.85
let pi=x (since there is no symbol for pi on the phone )
Circumference =2xr
Circumference =2x×2.85=5.7x (5.7pi)
The circumference of the circle whose diameter is 5.7 cm is 5.7π cm.
The circumference is the distance around the boundary of a closed curve or geometric figure.
In the context of a circle, the circumference is the length of the boundary that encloses the circular shape.
It is calculated using the formula:
Circumference = 2 π r = 2d
Given: diameter of the circle is 5.7 cm
Substitute d= 5.7 cm into the formula:
C = π * 5.7 cm
Thus, the circumference is 5.7π cm.
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Is -2/-5 equivalent to 2/5?
Answer:
yes
Step-by-step explanation:
Note that a [tex]\frac{-}{-}[/tex] results in a +, thus
[tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
Ắner:-2:-1=2
-5:-1=5
-2/-5=2/5
Step-by-step explanation:
4 MATH QUESTIONS AND YOU WILL GET 20 POINTS PLEASE PLEASE HELP I NEED THIS
Answer:
1. x=160 (here given as ques no. 5)
2. x=81 (here given as ques no.5)
4. No (here given as ques no. 8)
Step-by-step explanation:
1. Given ∠STR=∠SRT=20°
we know ∠STR+∠STU=180
x+20=180
x=160
2. By external angle property
x+24=105
x=81
3. By Angle Sum Property
∠ 1=∠2=∠3=∠4=90
and
∠5=∠6=∠7=∠8=90
Hence all angles are equal to 90
and we know only parallel lines have
∠4=∠5
∠3=∠6
hence line 'r' and line 't' are parallel.
4. For being parallel side pieces must not form a triangle(i.e. sum two interior angle must be equal to 180)
But here sum of interior angle 174
Hence a triangle is possible.
So , lines are not possible .
Jim’s soccer team is making fruit baskets for a fundraiser. They have 88 peaches, 60 bananas, and 54 kiwis to use. If each baskets have the same numbers of each type, what is the greatest number of fruit baskets they can make?
Answer:
2 baskets
Step-by-step explanation:
so basically find LCM(least common multiple) of 88, 60 and 54. prime factor 88 to get 2^3, and 11, 60 for 2^2, 3, 5 and 54 for 3^3, 2. we then find the numbers that are in all of them which is only two, once
12. You have $150 to spend on video games. The inequality 7x + 32y = 150 represents the number x
of used video games and the number y of new video games that you can purchase. Can you
purchase 10 used video games and 3 new video games? Explain.
Answer:
NO
To purchase 10 used video games and 3 new video games you need $166.With $150 is not enough
Step-by-step explanation:
7(10) + 32(3) =
70+96= 166
You can purchase 12 used and 2 new And you will have $2 left
7(12) +2(32) = 148
84+62=148
You cannot purchase 10 used video games and 3 new video games because their total cost of $166 exceeds your budget of $150.
Given inequality: 7x + 32y = 150
Substitute x = 10 and y = 3 into the inequality:
=7(10) + 32(3)
=70 + 96 = 166
Compare with the budget:
166 > 150
Hence, 7(10) + 32(3) = 166
Thus, 66 > 150
4*f(6) - 6*g(5) = can u help me
Answer:
45
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
8 * 4 = (A * 7) – (A * 3)
Answer:
A=32
Step-by-step explanation:
If 60% of the students prefer waffles to pancakes. If there are 5 students in the class how many students prefer waffles
n is a positive integer.Explain why n(n-1) must be an even number.
Please can someone explain this algebraically.
Answer:
n and (n - 1) are consecutive integers.
Step-by-step explanation:
We are given 'n', a positive integer.
This 'n' can either be odd or even.
Case I:
When 'n' is odd
The n - 1 is even.
Note that the product of odd and even is always even. That is the product of n and (n - 1) is even.
Case II:
when 'n' is even
Then n - 1 is odd.
Again, using the similar logic we can say that the product of n and n - 1 should be even because here, 'n - 1' is even and 'n' is odd.