Both of these are ways to express linear equations.
[tex]y - y_1 = m(x - x_1)[/tex] is the equation for a line with slope m which contains the point [tex](x_1,y_1)[/tex]. This is called point-slope form.
[tex]y = mx + b[/tex] is the equation for a line with slope m and y-intercept b. That is, it contains the point (0, b). This is called slope-intercept form.
Both of these are perfectly valid ways of writing lines, though sometimes one will be easier to use than the other.
Answer:
Hey there!
Both of these can be used to write the equation of the line. However, for the Y-Y1=M(X-X1) equation, we must know one point on the line (X1, Y1) and the slope of the line, while in the Y=MX+B equation, we need to know the slope and the x or y intercept.
For example, we can convert from Y-Y1=M(X-X1) to Y=MX+B
For example, say the point is (2, 3) and the slope is 1
Then, we have Y-3=1(x-2)
This simplifies to Y-3=1x-2
And to Y=X+1
So it is very possible to change from one form to another.
Let me know if you need more help.
Find the mean of the data in the dot plot below.
Answer:
1.6
Step-by-step explanation:
So, first, write down the number of jokers in each deck of cards.
That would be: 0, 1, 2, 2, 3
Then, add up all those numbers.
0+1+2+2+3=8
Now, divide that sum by the number of decks or cards shown in the data set, which would be 5.
8/5=1.6
So, the mean of the data in the dot plot shown is 1.6.
The mean of the data in the dot plot below is 1.6.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
Jokers in each of Marcie's decks of card would be 0, 1, 2, 2 and 3.
The mean,
= 0 + 1 + 2 + 2 + 3/5
= 8/5
= 1.6
Therefore, the mean is 1.6.
To learn more about the mean;
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What is the answer of 4(b+3) when b is 6?
Answer:
36
Step-by-step explanation:
Well first if b is 6 we plug that into the following.
4(b+3)
To,
4(6+3)
6+3 is 9 and 9*4 is 36.
Answer:
36
Step-by-step explanation:
4(6+3)
4(9)
36
What is the x xx-intercept of the line?
Answer:
(3,0)
Step-by-step explanation:
The graph is a line so it will have an equation with this form:
y = mx+b
m is the slope and b is the y-intercept.
Let's calculate m:
● m = (-32-(-64))/(-9-(-21)) = 8/3
Now replace m with its value and x,y with coordinates of a point.
● -32 = (8/3)*(-9) +b
● -32 = -24 +b
● -32+24 = b
● -8 =b
Solve y = 0
●(8/3)*x+b = 0
● (8/3) *x = 8
● x = 3
The coordinates of the x-intercept are (3,0)
Hi, guys whoever can help me with this question and give me the right answer, I will award brainliest. Please give answer fast. Find the value of X
Answer:
X= 65
Step-by-step explanation:
180°-50°=130 (Angles on a straight line)
2x=130 ( Corrresponding Angle)
X= 130÷ 2
= 65
Hope this helps.
Answer:
x = 65Step-by-step explanation:
In the bottom corner to find 2x you have to make an equation. So 180 - 50 = 130. 130 has the equal angle as 2x.
180 - 50 = 130
2x = 130
Simplify by dividing
2x = 130
/2 /2
x = 65Which sign makes this number sentence true? |-101| __ -85 A. > B. < C. = D. x
Answer:
|-101| > -85
Step-by-step explanation:
|-101| __ -85
The absolute value is taking the positive value
101 __ -85
101 is greater than -85
|-101| > -85
Answer:
>
Step-by-step explanation:
Which represents the polynomial written in standard form?
Answer:
Step-by-step explanation:
b
Answer:
I think it's 4x4 - 7xy3- 3x3v/2 +8x2y2
Step-by-step explanation:
Help me ASAP for this question? Estimate 48% of $33.95. $18 $20 $16
$17
Answer:
$16
Step-by-step explanation:
0.48 x 33.95 = 16.296
Answer:
Hey there!
48% of 33.95, is about half of 33.95. Thus, the answer is roughly equal to 16.
Hope this helps :)
Question 4(Multiple Choice Worth 5 points)
(05.05 LC)
The base length of a triangle is 12 feet and the height is 6 feet. What is the area of the triangle?
10 square feet
12 square feet
18 square feet
36 square feet
Answer:
A = 36 ft^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 1/2 ( 12) * 6
A = 36 ft^2
Answer:
36 square ft
Step-by-step explanation:
Select the arithmatic sequence from the following:
Select one:
a.-2, 3, 5, 10, 18
b.- 2.0, 8, 13, 17
C. - 2, 3, 8, 15, 20
d. - 2, 3, 8, 13, 18
Answer:
d) -2, 3, 8, 13, 18
Step-by-step explanation:
d) is the only one that has the same change each time (+5)
Answer:
[tex]\huge\boxed{d.\ where\ a_1=-2;\ d=5}[/tex]
Step-by-step explanation:
[tex]\text{If}\ a_1,\ a_2,\ a_3,\ ...,\ a_n\ \text{is an arithmetic sequesnce, then}\\\\a_2-a_1=a_3-a_2=a_4-a_1=...=a_{n}-a_{n-1}=d=constant\\\\d-\text{common difference}\\\\\text{We have:}\\\\a.\ -2;\ 3;\ 5;\ 10;\ 18\\18-10\neq10-5\\\\b.\ -2,\ 0;\ 8;\ 13;\ 17\\17-13\neq13-8\\\\c.\ -2;\ 3;\ 8;\ 15;\ 20\\20-15\neq15-8\\\\d.\ -2;\ 3;\ 8;\ 13;\ 18\\18-13=13-8=8-3=3-(-2)=5[/tex]
At the grocery store, you can purchase lemons at 2 for $0.99. you can also buy a bag of 6 lemons for $2.50. Which is the better buy?
Answer:
The 6 lemons for 2.50 is the better deal.
Step-by-step explanation:
2*3=6
3*0.99=2.97
2.97>2.50
please hurry write a vector equation of a line that passes through p(-4,12) and is parallel to q=(14,-8)
The line containing the vector q can be obtained by scaling q by an arbitrary scalar t. To make this line pass through the point p, translate this line by a vector p pointing from the origin to p.
So the line we want has equation
r(t) = qt + p = (14, -8)t + (-4, 12) = (14t - 4, 12-8t)
where t is any real number.
The Vector Equation which passes through point p(-4, 12) and parallel to q(14, -8) is r(t) = (14t-4, 12-8t).
What is a vector equation?A vector equation is an equation involving a linear combination of vectors with possibly unknown coefficients.
Here, the line containing the vector q can be obtained by scaling q by an arbitrary scalar t. To make this line pass through the point p, translate this line by a vector p pointing from the origin to p.
r(t) = q*t + p
r(t) = (14, -8)t + (-4, 12)
r(t) = (14t - 4, 12-8t)
where t is any real number
Thus, the Vector Equation which passes through point p(-4, 12) and parallel to q(14, -8) is r(t) = (14t-4, 12-8t).
Learn more about vector equations on:
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Write the function f(x) = x^2 + 8x + 12 in vertex form. Enter all work. Please help me.
Hello!
Answer:
f(x) = (x + 4)² - 4
Step-by-step explanation:
Write the equation f(x) = x² + 8x + 12 in vertex form by completing the square:
f(x) = (x² + 8x + (8/2)²) + 12 - (8/2)²
Simplify:
f(x) = (x² + 8x + 16) + 12 - 16
Subtract to find the 'k' value:
f(x) = (x + 4)² - 4. This is the equation in vertex form.
5. A biologist is measuring the lengths of frogs in a certain location. The lengths
of the frogs have a mean of 7.4 centimeters and a standard deviation of 0.8
centimeters. What is the probability that a randomly selected frog will measure
between 5.8 cm and 8.2 cm?
Your answer
6. Using the data from question #5, what is the probability that a randomly
selected frog will measure less than 6.6 cm?
Your answer
7. Using the data from #5, if 100 frogs are measured, how many of them would
you predict to measure longer than 8.2 cm?
Your answer
Answer:
Question
5) 0.81859
6) P(x<6.6) = 0.15866
7) 15.866 frogs would be longer than 8.2cm
Step-by-step explanation:
5. A biologist is measuring the lengths of frogs in a certain location. The lengths
of the frogs have a mean of 7.4 centimeters and a standard deviation of 0.8
centimeters. What is the probability that a randomly selected frog will measure
between 5.8 cm and 8.2 cm?
Using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
z1 = (x-μ)/σ
x is the raw score = 5.8cm
μ is the population mean = 7.4cm
σ is the population standard deviation. = 0.8cm
= 5.8 - 7.4/0.8
= -2
Using a z score table to find the probability of -2
P(z = -2) = 0.02275
z2 = (x-μ)/σ,
x is the raw score = 8.2cm
μ is the population mean = 7.4cm
σ is the population standard deviation. = 0.8cm
z = 8.2 - 7.4/0.8
z = 1
Using the Z-Table to find the probability
P(z = 1) = 0.84134
Hence, the probability that a randomly selected frog will measure between 5.8 cm and 8.2 cm is calculated as:
0.84134 - 0.02275 = 0.81859
6. Using the data from question #5, what is the probability that a randomly
selected frog will measure less than 6.6 cm?
Your answer
Using z score formula
z = (x-μ)/σ, where
x is the raw score = 6.6cm
μ is the population mean = 7.4cm
σ is the population standard deviation. = 0.8cm
z1 = (x-μ)/σ
= 6.6 - 7.4/0.8
= -1
Using the Z-Table to find the probability a randomly selected frog will measure less than 6.6 cm
P(x<6.6) = 0.15866
7. Using the data from #5, if 100 frogs are measured, how many of them would you predict to measure longer than 8.2 cm?
z = (x-μ)/σ,
x is the raw score = 8.2cm
μ is the population mean = 7.4cm
σ is the population standard deviation. = 0.8cm
z = 8.2 - 7.4/0.8
z = 1
Using the Z-Table to find the probability
P(x<8.2) = 0.84134
To find the probability of frogs that would be longer than 8.2cm
P(x>8.2) = 1 - P(x<8.2) = 0.15866
To calculate the number would be predicted to measure longer than 8.2 cm is :
0.15866 × 100 = 15.866% is longer than 8.2cm
Therefore,
15.866% × 100 frogs = 15.866 frogs.
Find the path of the numbers from the upper left corner to the bottom right corner. The sum of the numbers must be equal to the number at the exit arrow. You are allowed to move either down or to the right only.
Answer:
8, 11, 19, 1, 6, 18, 3
Step-by-step explanation:
8+11+19+1+6+18+3=66
A very simple question for trigonometry! So lets say I want to use a formula for example csc = 1/sin a. Would that still apply if instead of sin a it is - sin a? If not, can I still use this formula is sin a is negative? Thanks!
Answer:
Step-by-step explanation:
csc = 1/sin a would be OK if you'd insert the argument 'a:'
csc a = 1/sin a is an identity (a relationship that is always true).
If you write csc a = 1 / (-sin a) you are creating a conditional equation which may be true for some values of a but not for all.
The taxi fare in Gotham City is $2.40 for the first ½ mile, and each additional mile costs $0.20. You plan to give the driver a $2.00 tip. How many miles can you ride for $10.00?
Answer:
He can ride for 28 miles
Step-by-step explanation:
Total cost of the ride = $ 10
Tips = $ 2
Cost of ride excluding tips = 10 - 2 = $ 8
Taxi fare for first 500 miles = $ 2.40
Taxi fare excluding first 500 miles = 8 - 2.40 = $ 5.60
distance traveled by him excluding first 500 miles = 5.60 ÷ cost of additional mile
= 5.60 ÷ 0.20
=28 miles
Let P(A)=35 and P(B|A)=89. What is the probability of events A and B occurring?
I'm assuming you meant to say P(A) = 3/5 and P(B|A) = 8/9.
If so, then we multiply the probabilities to get P(A and B)
P(A and B) = P(A)*P(B|A)
P(A and B) = (3/5)*(8/9)
P(A and B) = (3*8)/(5*9)
P(A and B) = 8/(5*3)
P(A and B) = 8/15
Answer: 8/15Reflect the given preimage over y=−1 followed by y=−7. Find the new coordinates. What one transformation is this double reflection the same as? (Note: when you are reflecting over a y= line, the x-values of the preimage will remain the same and you will be changing the y-values)
Answer:
Reflecting over y = -1 line:
A'(8, -10)
B'(10, -8)
C'(2, -4)
Reflecting over y = -7 line:
A''(8, -4)
B'(10, -6)
C''(2, -10)
Step-by-step explanation:
Reflect the given preimage over y=−1 followed
by y=−7. Find the new coordinates. What one transformation is this double reflection the same as? (Note: when you are reflecting over a y= line, the x-values of the preimage will remain the same and you will be changing the y-values)
The coordinates of the preimage are:
A(8,8)
B(10,6)
C(2,2)
Answer: Reflecting over y = -1:
If a point is reflected over a y line, the x values remain the same while the y values change.
For point A(8, 8): The y distance between the y = - 1 line and point A is 9 units. (8- (-1)). If point A is reflected, the y value would be 9 units below the y = -1 line, i.e the new y coordinate would be at -10 (-1-9)
The new coordinate is at A'(8, -10)
For point B(10, 6): The y distance between the y = - 1 line and point B is 7 units. (6- (-1)). If point B is reflected, the y value would be 7 units below the y = -1 line, i.e the new y coordinate would be at -8 (-1-7)
The new coordinate is at B'(10, -8)
For point C(2, 2): The y distance between the y = - 1 line and point C is 3 units. (2- (-1)). If point C is reflected, the y value would be 3 units below the y = -1 line, i.e the new y coordinate would be at -4 (-1-3)
The new coordinate is at C'(2, -4)
Reflecting over y = -7 line:
For point A'(8, -10): The y distance between the y = - 7 line and point A' is 3 units. (-7- (-10)). If point A' is reflected, the y value would be 3 units above the y = -7 line, i.e the new y coordinate would be at -4 (-7+3)
The new coordinate is at A''(8, -4)
For point B'(10, -8): The y distance between the y = - 7 line and point B' is 1 units. (-7- (-8)). If point B' is reflected, the y value would be 1 units above the y = -7 line, i.e the new y coordinate would be at -6 (-7 + 1)
The new coordinate is at B'(10, -6)
For point C'(2, -4): The y distance between the y = - 7 line and point C' is 3 units. (-4- (-7)). If point C' is reflected, the y value would be 3 units below the y = -7 line, i.e the new y coordinate would be at -10 (-7-3)
The new coordinate is at C''(2, -10)
We can also see that h= −7−(−1)=−6. We know that two reflections is the same as a translation of 2h units down. So 2(−6) is a translation of −12 units down.
Find the the perimeter of the shape with verticales (2,3) (5,3) and (5,7)
Answer:
12 units
Step-by-step explanation:
from (2, 3) to (5, 3) = 3
from (5, 3) to (5, 7) = 4
from (2, 3) to (5, 7) = √3²+4² = 5
3 + 4 + 5 = 12
HELPPP HURRYYYYYY Each group of students receives a bag that has 8 red cubes, 2 green cubes, and 10 blue cubes. If each group makes 100 pulls and replaces the cube after each pull, how many times would you expect them to draw a green cube?
Answer:
10
Step-by-step explanation:
There are 20 cubes total.
2 of the twenty are green.
2/20=10%
10% of 100 is 10
Answer:
Step-by-step explanation:
So, In all there are 20 cubes, And If they are making 100 pulls then it could be put into a percent. So 10 would be 50%, 2 would be 5%, and 8 would be 45%, so it would be pulled 5 times. Hope This Helps Dreamer!
simplify the expression
[tex]10.8 + - 7.6 + 10.2h + 9.2[/tex]
Write the following expressions without using absolute value. |7m–56|, if m<8
Answer:
I think you want this answer below:
Step-by-step explanation:
7m - 56 < 0 if m < 8.
Answer:
56-7m
Step-by-step explanation:
Find the value of the expression 3m2 + 2p2 − 15 when m = 3 and p = 10.
Answer:
212
Step-by-step explanation:
3m² + 2p² - 15
Plug in the values.
3(3)² + 2(10)² - 15
Evaluate.
3(9) + 2(100) - 15
27 + 200 - 15
200 + 12
= 212
Answer: 212
Step-by-step explanation:
substitute the given values into the expression
3 ( 3 ) ^ 2 + 2 (10)^ 2 − 15 =
(3 ×9 ) + (2 × 100 ) - 15
= 27 + 200 - 15 =212
Hope this helped
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6), B(-3,-6), C(-3, -4), and D(-8, -4). Given these coordinates, what is the length of side AB of this rectangle?
Answer:
Step-by-step explanation:
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
A(-8,-6) ; B(-3,-6)
[tex]AB= \sqrt{(-3-[-8])^{2}+(-6-[-6])^{2}}\\\\=\sqrt{(-3+8)^{2}+(-6+6)^{2}}\\\\=\sqrt{(5)^{2}+ 0}\\\\= 5 units[/tex]
1. Find the value of x in the figure below.
Answer:
see details and attached figure below.
Step-by-step explanation:
Going row by row
1. 12 (isosceles triangles have equal legs from the vertex)
2. 55 deg. (isosceles triangles have equal base angles)
3. 90 = 180-45-45 (isosceles triangles have equal base angles)
4. 2x-8 = 10
=> x = 18/2 = 9 (isosceles triangles have equal legs from the vertex)
5. sum of angles of triangle = 180
3x+3x+2x+4 = 180 => 8x = 176, x = 22, angle A = 3x = 66 deg.
6. sum of angles of triangle = 180
(isosceles triangles have equal base angles)
25+25+angle Z = 180 => angle Z = 180-25-25 = 130
Which expression is equivalent to ...
Answer:
[tex] \sqrt{6} [/tex]Step-by-step explanation:
[tex]3 \sqrt{54} - 4 \sqrt{24} [/tex]
Simplify the radical expression
[tex]3 \sqrt{2 \times 3 \times 3 \times 3} - 4 \sqrt{2 \times 2 \times 2 \times 3} [/tex]
[tex]3 \times 3 \sqrt{2 \times 3} - 4 \times 2 \sqrt{2 \times 3} [/tex]
[tex]9 \sqrt{6} - 8 \sqrt{6} [/tex]
collect the like terms
[tex]9 - 8 \sqrt{6} [/tex]
[tex]1 \sqrt{6} [/tex]
[tex] \sqrt{6} [/tex]
Hope this helps...
good luck on your assignment..
How do I figure of the 7/3 I'm not sure how to add a fraction with a different denomination
Step-by-step explanation:
Hi there!!
Here, the thing is we should add them first yaa.
so, let's add them
[tex] = - 2 \frac{1}{6} + \frac{7}{3} [/tex]
by taking lcm we get their lcm is 6 and let's do it according to that,
[tex] = \frac{ - 12 \times 1}{6} + \frac{7 \times 2}{6} [/tex]
now, let's simplify them ok..
[tex] = \frac{ - 12 + 14}{6} [/tex]
so, we get 2/6 (i.e 1/3)
now, the number line must be greator than 1 and less than 1.
Hope it helps...
Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?
Answer:
12
trust me it works i just took the test.
Find the value of x needed to make the equation below true.
Answer:
x= -3
Step-by-step explanation:
distribute and get -6x+20+4x=26
then simplify and get -2x=6
simplify again and get x=-3
Answer:
x= -3
Step-by-step explanation:
-4(1.5x-5)+4x=26
Simplify the problem:
-2x+20=26
Subtract 20 from both sides:
(-2x+20)-20=(26)-20
Simplify:
-2x=6
Divide both sides by -2
(-2x)/-2=(6)/-2
Simplify:
x=-3
I hope that was helpful! (Brainliest???) :P
Jessa bought her home for $125,000 in 2010. Property values have increased 15% every year since she has owned the home. Which of the following equations can be used to represent the price of the home x years after 2010?
Answer:
y= 125,000 (1.15x)
Step-by-step explanation:
Answer: y = 125000(1.15)^x
Step-by-step explanation:
The formula we use is y = p(1 + r)^x p is price and r is rate
the initial price is $125000 and the rate is 15%, or 0.15.
y = 125000(1 + 0.15)^x
y = 125000(1.15)^x