Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))
For example:
Slope = 2 or [tex]\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]-\frac{1}{2}[/tex] (flip the sign from + to -, and flip the fraction)
Slope = [tex]-\frac{3}{4}[/tex]
Perpendicular line's slope = [tex]\frac{4}{3}[/tex] (flip the sign from - to +, and flip the fraction)
y = 1/3x + 4 The slope is 1/3, so the perpendicular line's slope is [tex]-\frac{3}{1}[/tex] or -3.
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
y = -3x + b To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself
2= -3(1) + b Add 3 on both sides to get "b" by itself
2 + 3 = -3 + 3 + b
5 = b
y = -3x + 5
The equation of the line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4) is (y = -3x + 5) and this can be determined by using the given data.
Given :
The line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4).
The following steps can be used in order to determine the equation of the line:
Step 1 - When two lines are perpendicular to each other then their slopes are:
mm' = 1
where m and m' are the slopes of the lines.
Step 2 - So, the slope of the line which is perpendicular to the line (y = 1/3x + 4) is:
[tex]\rm \dfrac{1}{3}\times m' = -1[/tex]
m' = -3
Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:
[tex]\rm (y -2) = -3(x-1)[/tex]
Step 4 - Simplify the above equation.
y = -3x + 5
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If mAngle3 = 29°, what is mAngle4?
mAngle4 =
°
Answer:
M angle=151
Step-by-step explanation:
180-29=151
Answer:
Angle M 4 = 151 degrees
Step-by-step explanation:
i just did the practice on edge :) its funny how since we're all in quarantine doing edge everyone is helping each other out on sites and apps like this yanno.. it makes me kinda happy that we can all come together like we are ahaha
A rectangle is always a square? True or false?
Answer:
False
Step-by-step explanation:
A square is defined as a quadrilateral with 4 congruent sides, but a rectangle is defined as a quadrilateral with 2 pairs of congruent sides, so unless the 2 pairs in a rectangle are the same length, no the rectangle is not a square. However all squares are rectangles.
"A rectangle is always a square" is false statement.
Rectangle:A rectangle is quadrilateral, in which opposite sides are equal in length and all four angles are equal to 90 degree.
A square is quadrilateral, in which all four sides are equal in length and all four angles are equal to 90 degree.
A square is always a rectangle, but a rectangle is not always a square.
Therefore, given statements is false.
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Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately how long does it take until the soccer ball hits the ground again? (1 point)
Group of answer choices
0.6 sec
0.8 sec
1.6 secs
2.8 secs
Answer:
the answer is 1.6 seconds
Step-by-step explanation:
Which two lines are parallel?
Which two lines are perpendicular?
Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines = - 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
All the equations given are in slope- intercept form
y = 2x + 1 → with m = 2
y = [tex]\frac{1}{2}[/tex] x - 4 → with m = [tex]\frac{1}{2}[/tex]
y = x + 1 → with m = 1
y = - [tex]\frac{1}{x}[/tex] x - 3 → with m = - [tex]\frac{1}{2}[/tex]
y = 10 + x → y = x + 10 → with m = 1
Thus
y = x + 1 and y = 10 + x are Parallel since both have m = 1
y = 2x + 1 and y = - [tex]\frac{1}{2}[/tex] x - 3 are Perpendicular since 2 × - [tex]\frac{1}{2}[/tex] = - 1
What positive integer is closest to the value of √230 ?
Answer:
15
Step-by-step explanation:
sqrt230=15.165...
Answer:
I believe that it is 15
Describe a Positive Correlation on a Scatter Plot.
Answer:
A positive correlation on a scatter plot would show the points closer tog.ether heading in an upward direction
Step-by-step explanation:
Katie wants to measure the length from the pitcher mound to home plate on the softball field. Should she use inches or feet to to measure it?
Answer: Feet
Step-by-step explanation:
Well, Katie can use whatever unit of measure she prefers. However, in this case she must take into account the measuring instrument that she is going to use and the unit of measurement that is generally used or according to the established rules.
On the other hand, a softball field has an average area of [tex]225 ft^{2}[/tex], which is quite a lot. Therefore Katie needs to use a convenient unit of measure (let's assume she uses a measuring tape, which gives her the option to measure in feet or inches) to quickly measure the distance between the pitcher mound and home plate.
So, if we have to choose between feet and inches, we must consider the following:
[tex]1 ft=12 in[/tex]
This means [tex]ft[/tex] as a unit of distance is greater than [tex]in[/tex]. Hence, Katie should use feet instead of inches.
In addition, according to the Softball rules, generally the dimensions are given in feet. So, it is better for Katie to use feet to measure the distance from Pitchers Mound to Home Plate.
What is the surface area of the prism in square inches? A prism is made up of 3 rectangles and 2 triangles. A rectangle has base of 12 and height of 10. A rectangle has base of 10 and height of 13. A rectangle has base of 10 and height of 5. 2 triangles have a base of 12 inches and height of 5 inches. 300 square inches 360 square inches 390 square inches 460 square inches
Correct option B) 360 square inches .
Step-by-step explanation:
Here we have , A prism is made up of 3 rectangles and 2 triangles. A rectangle has base of 12 and height of 10. A rectangle has base of 10 and height of 13. A rectangle has base of 10 and height of 5. 2 triangles have a base of 12 inches and height of 5 inches. We need to find What is the surface area of the prism in square inches . Let's find out:
3 rectangles and 2 triangles
A rectangle has base of 12 and height of 10 :
⇒ [tex]Area = length(width)[/tex]
⇒ [tex]Area =12(10)[/tex]
⇒ [tex]Area =120[/tex]
A rectangle has base of 10 and height of 13
⇒ [tex]Area = length(width)[/tex]
⇒ [tex]Area =13(10)[/tex]
⇒ [tex]Area =130[/tex]
A rectangle has base of 10 and height of 5
⇒ [tex]Area = length(width)[/tex]
⇒ [tex]Area =5(10)[/tex]
⇒ [tex]Area =50[/tex]
2 triangles have a base of 12 inches and height of 5 inches.
⇒ [tex]Area = \frac{1}{2}base(height)(2)[/tex]
⇒ [tex]Area =12(5)[/tex]
⇒ [tex]Area =60[/tex]
Hence , Total Area :
⇒ [tex]120+130+50+60[/tex]
⇒ [tex]360in^2[/tex]
Correct option B) 360 square inches .
10 POINTS!!
What is the length of side PQ in this figure?
Answer:
C
Step-by-step explanation:
o find the side PQ ; we need to first find the length of the given line segment which is perpendicular to side PR; let name it as QS.
Now as ΔQSR is an right angled triangle.
and the length of the side QR and SR is given , so using Pythagorean theorem we have
QR^{2}=SR^{2}+QS^{2}
5^{2}=3^{2}+QS^{2}\\ \\QS^{2}=5^{2}-3^{2}\\\\QS^{2}=25-3=16=4^2
⇒ QS=4
Now again ΔQSP is an right angled triangle; so using Pythagorean theorem in ΔQSP we have
PQ^{2}=QS^{2}+PS^{2}\\ \\PQ^{2}=4^{2}+6^{2}=16+36=52
This means QS=\sqrt{52}=2\sqrt{13}
Hence, the length of side PQ is \sqrt{52}=2\sqrt{13}.
Hence, option C is correct.
plz mark brainliest
Answer:
C
Step-by-step explanation:
I just got it right
Find the sale price of a $90 item after a 30% discount.
The sale price is $
Answer:
$63
Step-by-step explanation:
100%-30% = 70% of original price.
Thus .7 *90 = $63
Elena said, “I think this line is a good fit because half of the points are on one side of the line and half of the points are on the other side.” Do you agree?
Final answer:
While Elena's method of dividing the points equally on either side of a line might be a rough starting point for finding a 'line of best fit,' accurate data analysis requires more sophisticated methods, like least squares regression, to determine how well a line truly fits a set of data points.
Explanation:
Elena's consideration that a line is a good fit because half of the points are on one side and half are on the other may indicate an attempt at balancing data around a potential 'line of best fit' when visually estimating in scatter plots. However, a good fit in the context of data analysis typically relates to how closely the line follows the trend of the points, which is better determined by methods such as least squares regression, rather than just the number of points on either side of the line.
Statistical measurements, such as the correlation coefficient, are used to quantify how well a line fits the data in question. Therefore, while Elena's observation might be useful as an initial, rough estimation, more rigorous statistical methods would provide a more accurate assessment of a good fit for the data.
Trina uses One-half cup of sugar and Three-fourths cup of flour in a recipe. How many cups of sugar would she need if she uses 3 cups of flour?
Answer:
2 cups
Step-by-step explanation:
Answer: 4 1/2 cups of sugar
Step-by-step explanation: Math
solve 5=625e^{0.02x}
Answer:
x=-150ln(5)
this should be the answer
Please answer this!
Tony opens a savings account. The graph represents the amount of money in dollars that Tony expects to deposit in his account in terms of the number of years since opening the account.
We have been given that a graph that represents the amount of money in dollars that Tony expects to deposit in his account in terms of the number of years since opening the account.
We are asked to find the rate of change and initial value from our given graph.
We know that initial value is the point, where, graph intersects y-axis that is when x is equal to 0.
We can see that graph starts at 5000 on y-axis, therefore, initial value is $5000.
The rate of change will be equal to slope of line. Let us find slope of line using points (0,5000) and (1,7500).
[tex]m=\frac{7500-5000}{1-0}[/tex]
[tex]m=\frac{2500}{1}[/tex]
[tex]m=2500[/tex]
Therefore, the rate of change is $2500 per year.
The equation [tex]y=2500x+5000[/tex] represents the amount of money in dollars that Tony expects to deposit in his account.
The equation [tex]\rm y = 2500x+5000[/tex] represents the amount of money in dollars that Tony expects to deposit in his account.
The rate of change is $2500 per year.
Given that,
Tony opens a savings account.
The graph represents the amount of money in dollars.
Tony expects to deposit in his account in terms of the number of years since opening the account.
We have to determine,
The equation represents the amount of money in dollars that Tony expects to deposit in his account and rate of change per year.
According to the question,
The graph that represents the amount of money in dollars that Tony expects to deposit in his account in terms of the number of years since opening the account.
The rate of change and initial value from our given graph.
The initial value is the point, where, graph intersects y-axis that is when x is equal to 0.
The equation represents the amount of money in dollars that Tony expects to deposit in his account is,
[tex]\rm y = 2500x+5000[/tex]
The graph starts at 5000 on y-axis, therefore, initial value is $5000.
The rate of change will be equal to slope of line.
Let us find slope of line using points (0,5000) and (1,7500).
Therefore,
The slope of line is,
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{7500-2500}{1-0}\\\\m = 2500[/tex]
Hence, the rate of change is $2500 per year.
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is 62784 divisible by 4
Answer:
yes it is the answer is 15696
What is the area of this figure
Given:
Image of the figure.
To find:
The area of the figure.
Solution:
Length of larger rectangle = 9
Width of larger rectangle = 8
Area of larger rectangle = length × width
= 9 × 8
Area of larger rectangle = 72 square units
Length of smaller rectangle = 4
Width of smaller rectangle = 2
Area of smaller rectangle = length × width
= 4 × 2
Area of smaller rectangle= 8 square units
Area of the figure = Area of larger rectangle - Area of smaller rectangle
= 72 - 8
= 64 square units
The area of the figure is 64 square units.
A circle has a center at (4,-1) and a radius of 6. Which of the following that are
points on the circle.
a(-2,-1)
b(4,-9)
c(0, -5)
d(8,-5)
Answer:
c
Step-by-step explanation:
reflection across the x-axis
K(1, −1), N(4, 0), Q(4, −4)
The reflection across the x-axis changes the y-coordinate to its opposite. Thus, K(1, −1) becomes K(1, 1), N(4, 0) doesn't change, and Q(4, −4) becomes Q(4, 4).
The question's task is a reflection across the x-axis. This change involves flipping the coordinates in the plane over the x-axis. For a given point with coordinates (x, y), its reflection will have coordinates (x, -y). Let's apply this rule to the points given:
K(1, −1) will become K(1, 1)
N(4, 0) will remain N(4, 0) because it lies on the x-axis
Q(4, −4) will become Q(4, 4)
So, the reflected coordinates are K(1, 1), N(4, 0), Q(4, 4).
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#SPJ2
HELP PLZZZZ I DONT KNOW
Answer:
41.5 cm^2
Step-by-step explanation:
The area of the right triangle is
A =1/2 bh where b = (2+7) and h=(4+7)
=1/2(9)(11)
49.5
The area of the rectangle is
A = l*w where l is 2 and w is 4
A = 2*4 = 8
The shaded region is the area of the triangle minus the area of the rectangle
A shaded = 49.5 - 8 = 41.5
A right triangle has a hypotenuse of square root of 50. What are possible lengths of the two legs of this triangle?
For 45-45-90 degree triangle
The length of other two legs: 5
For 30-60-90 degree triangle
The shorter leg= 3.53
The larger leg = 6.11
Step-by-step explanation:
length of Hypotenuse = [tex]\sqrt{50}[/tex]
We need to find possible lengths of the two legs of this triangle.
If the triangle is 45-45-90 degree triangle the length of other two sides would be same and can be found by:
[tex]Length\,\,of\,\,leg:\frac{\sqrt{50} }{\sqrt{2} } \\Length\,\,of\,\,leg:5[/tex]
Since both legs are of same size so, length of other leg = 5
If the triangle is 30-60-90 degree triangle then:
To find shorter length: Divide hypotenuse by 2.
To find other side length: Multiply shorter length by [tex]\sqrt{3}[/tex]
The shorter leg = [tex]\frac{\sqrt{50} }{2}= 3.53[/tex]
The other leg (larger) = [tex]3.53\times \sqrt{3} =6.11[/tex]
The probability of drawing a silver ball out of a certain bag is
1 third. What is the probability of not drawing a silver ball?
The probability of not drawing a silver ball, when the probability of drawing a silver ball is 1/3, is 2/3.
Explanation:The probability of not drawing a silver ball can be found by subtracting the probability of drawing a silver ball from 1, since the sum of the probabilities of all possible outcomes must equal 1. If the probability of drawing a silver ball is 1/3, then the probability of not drawing a silver ball is 1 - 1/3 = 2/3.
(HURRY PLEASE) What is the rate of change of the function represented by the table?
Answer:2.5
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
y values are getting less negative so ROC has to be positive. numbers are not going up by 1. They are going up by 2.5
Help please ^^ I am confused
Answer:
180
Step-by-step explanation:
4 x 28 + 64 = 176 round up to 180
Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
Answer:
3
Step-by-step explanation:
Ann has some dimes and quarters. If she has 13 coins worth a total of $2.50, how many of each type of
coin does she have?
Answer:
2 quarters and 5 dimes
Step-by-step explanation:
2 quarters equal to $2
5 dimes = 50 cents
add them and get $2.50
please help me find the answer to this problem
Answer:
13.5
Step-by-step explanation:
6 + 3 = 9
9 × 3 = 27
27 ÷ 2 = 13.5
brainliest?
In this line of circles
OOOO
the ratio of red circles to blue circles is 1:3
How many more red circles would
need to be added to make the ratio of red to blue 3: 1?
Answer:
3 red circles
Step-by-step explanation:
You require three red circles and blue circles reduced by two.
Which statements are true? Check all that apply
mCB = 120°
MCB = 60°
mZCOB = 2(m_CAB)
m_COB = 120
mzCOB = 1 (m_CAB)
600
Answer:
A,C,D
Step-by-step explanation:
Snap
Jona_Fl16
The correct statements are mCB = 120°, m∠COB = 2(m∠CAB), m∠COB = 120°
What is a circle?A circle is the locus of a point such that its distance from a fixed point known as the center is always constant.
From the diagram:
mCB = 2 * m∠CAB (angle at center is twice angle at circumference)
mBC = m∠COB = 2(60) = 120°
The correct statements are mCB = 120°, m∠COB = 2(m∠CAB), m∠COB = 120°
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What is the MAD for tamika: (10, 9, 5, 20, 12, 4) points in tmr basketball game
Answer:
4
Step-by-step explanation:
Choose the best description for the real number 4 point 6 repeating
Answer:
irrationanal
Step-by-step explanation: