[tex]\bf J(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})\qquad K(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-5)}{-6-(-4)}\implies \cfrac{3+5}{-6+4}\implies \cfrac{8}{-2}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-4[x-(-4)]\implies y+5=-4(x+4)[/tex]
[tex]\bf y+5=-4x-16\implies y=-4x\stackrel{b}{\boxed{-21}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Can someone please help me out with this question?
Answer:
[tex]\frac{300}{t}[/tex] chairs at each table
Step-by-step explanation:
Total number of chairs : 300
Total number of tables : t
If we divide 300 chairs equally among t tables, then each table must have 300 chairs ÷ t tables = [tex]\frac{300}{t}[/tex] chairs at each table.
What is the solution to the system of equations below? y = 3/4 x - 12 and y = 4x - 31
(–4, –15)
(–4, –12)
(4, –9)
(4, –47)
Answer:
(4,-47) is the solution
Step-by-step explanation:
4 is x
-47 is y
Just substitute these numbers into the equations and your solution must equal y which is - 47. This solution did equal -47 so its the one
Answer:
X= -4 Y= -15
Step-by-step explanation:
Got Correct On Mypath.
Find the standard deviation of 21, 31, 26, 24, 28, 26
Given the dataset
[tex]x = \{21,\ 31,\ 26,\ 24,\ 28,\ 26\}[/tex]
We start by computing the average:
[tex]\overline{x} = \dfrac{21+31+26+24+28+26}{6}=\dfrac{156}{6}=26[/tex]
We compute the difference bewteen each element and the average:
[tex]x-\overline{x} = \{-6,\ 5,\ 0,\ -2,\ 2,\ 0\}[/tex]
We square those differences:
[tex](x-\overline{x})^2 = \{36,\ 25,\ 0,\ 4,\ 4,\ 0\}[/tex]
And take the average of those squared differences: we sum them
[tex]\displaystyle \sum_{i=1}^n (x-\overline{x})^2=36+25+4+4+0+0=69[/tex]
And we divide by the number of elements:
[tex]\displaystyle \sigma^2=\dfrac{\sum_{i=1}^n (x-\overline{x})^2}{n} = \dfrac{69}{6} = 11.5[/tex]
Finally, we take the square root of this quantity and we have the standard deviation:
[tex]\displaystyle\sigma = \sqrt{\dfrac{\sum_{i=1}^n (x-\overline{x})^2}{n}} = \sqrt{11.5}\approx 3.39[/tex]
To find the standard deviation of the set 21, 31, 26, 24, 28, 26, first calculate the mean, then the squared deviations from the mean, followed by the variance, and finally take the square root of the variance. The standard deviation is approximately 2.52.
The question asks how to find the standard deviation of the numbers 21, 31, 26, 24, 28, 26. To calculate the standard deviation, follow these steps:
Find the mean (average) of the data set. Subtract the mean from each number to get the deviations from the mean, then square each result. Find the average of these squared deviations, which is the variance. Take the square root of the variance to get the standard deviation.
Let's calculate it together:
Mean = (21 + 31 + 26 + 24 + 28 + 26) / 6 = 26 Squared deviations: (5^2) + (5^2) + (0^2) + (2^2) + (2^2) + (0^2) = 38 Variance = 38 / 6 = 6.33 (rounded to two decimal places) Standard Deviation = √6.33 = 2.52 (rounded to two decimal places)
Therefore, the standard deviation of the data set is approximately 2.52.
Durind the summer, Ms. Stevenson likes to swim. Her goal next summer is to swim1,456 laps. If she swims 28 laps a day, how many days will it take Ms. Stevenson to reach her goal?
Answer:
52
Step-by-step explanation:
1456/ 28 = 52 days
Answer:
52 days
Step-by-step explanation:
If she swims 28 laps a day, it will take her 52 days to reach her goal.
1,456/28 = 52
determine the slope of each pair with fractions
Answer:
Step-by-step explanation:
The slope here is -3.
This answer is found by using the formula I clipped below.
Hope that Helps!
If 100 mL of a solution contains 20 g, how many milligrams will 20 mL contain?
Answer:
There are 4,000 milligrams
Step-by-step explanation:
We know that in 1 gram there are 1000 milligrams
To calculate how many milligrams equals 20 grams we perform the following operation
[tex]20\ g*\frac{1000\ mg}{1\ g}=20,000\ mg[/tex]
Then 100 mL of a solution contains 20,000 mg
To calculate how many milligrams there are in 20mL of the solution we perform the following operation
[tex]20\ mL*\frac{20,000\ mg}{100\ mL}=4,000\ mg[/tex]
What is the area of the kite? Height of 6ft base of 14ft. 21 square feet 40 square feet 42 square feet 84 square feet
Answer:area is 84
Step-by-step explanation:
6*14
Answer:
its c 42 square feet
Step-by-step explanation:
About 60% of the normal human
being's body weight is composed of
water. How much of a 125 pound
person is water weight?
F 72 pounds H 76 pounds
G 75 pounds I 80 pounds
The water weight of a 125lb person is 75lbs.
The diagram shows a sector of a circle with radius 15 cm.
Calculate the perimeter of this sector.
Answer:
≈ 36.81 cm ( to 2 dec. places )
Step-by-step explanation:
The perimeter (P) of the sector is calculated as
P = circumference of circle × fraction of circle + radii
= 2π × 15 × [tex]\frac{26}{360}[/tex] + 30
= 30π × [tex]\frac{26}{360}[/tex] + 30
= [tex]\frac{26\pi }{12}[/tex] + 30 ≈ 36.81 cm
Answer:
36.81 cm to the nearest hundredth (or 30 + 13 π / 6).
Step-by-step explanation:
The perimeter of the circle of which this sector is a part = 2 π 15
= 30 π cms
So the length of the curved part of the sector = 26 * 30 π / 360
= 2.167π
The perimeter = 2(15) + 2.167 π
= 36.81 cm.
Find the indicated side of the triangle.
Please Help!!!
Answer:
Step-by-step explanation:
So you can use the special formula for 30-60-90 triangle or you can use the whole Soh Cah Toa thing.
I honestly prefer trig. so a is the opposite side of the 30 deg and 12 is the hyp. This should scream sine to you since sine goes with opposite/hypotenuse.
sin(30 deg)=a/12
Multiply both sides by 12
giving a=12 sin(30)
Type into calculator unless you know your unit circle well.
a=6
Answer:
a = 6
Step-by-step explanation:
Since the triangle is right use the sine ratio to find a
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{12}[/tex]
Multiply both sides by 12
12 × sin30° = a, hence
a = 6
what is the answer for this math problem
7/8 is tricky to do on a computer, but I will say that it is 87.5 percent or 0.875.
Do you know how to do normal long division? This is like that. Just after the decimal point, drop a 0 down.
I hope this helps!
Answer:
7/8 = .875 7/8=87.5%
Step-by-step explanation:
Divide 1/4(.25) by 2 and you get 1/8(.125)
Multiply .125 by 7 which gives you .875.
For the percent just multiply .875 by 100
Hope this helps.
The graphs of f(x) =2/3x and g(x) =2/3x-2 are shown below.
Y1=2/3x , Y2=2/3x-2
those are the graph of the functions
what values complete this function
Answer:
f(x) = - (x - 3) (x + 4)
Step-by-step explanation:
* Lets explain the graph
- The graph is a parabola, which is the graph of the quadratic function
- The general form of the quadratic function is f(x) = ax² + bx + c
- a is the coefficient of x², if a > 0 the parabola is oped upward, if a < 0
the parabola is opened down ward
- c is the y-intercept of the parabola means the curve intersect the
y-axis at point (0 , c)
- The roots (zeroes) of the quadratic function are the x-intercept of the
parabola means values of x when f(x) = 0
* Now lets solve the problem
- The parabola is downward
∴ The coefficient of x² is negative
- The y-intercept is 12
∴ c = 12
- The x-intercepts are 3 , -4
∴ The zeroes of the function are 3 , -4
∴ x = 3 ⇒ subtract 3 from both sides
∴ x - 3 = 0
∴ x = -4 ⇒ add 4 for both sides
∴ x + 4 = 0
- The factors of f(x) are (x - 3) and (x + 4)
∴ f(x) = -(x - 3)(x + 4)
- Lets find the general form of the function to be sure from the answer
- Multiply the two brackets
∵ f(x) = - [(x)(x) + (x)(4) + (-3)(x) + (-3)(4)] = - [x² + 4x + -3x + -12]
∴ f(x) = - [x² + x - 12] ⇒ multiply the bract by the (-)
∴ f(x) = -x² - x + 12
- Lets check the value of the y-intercept
∵ a = -1 , c = 12
∴ The coefficient of x² is -ve ⇒ the parabola is downward
∴ The y-intercept is 12
∴ f(x) = - (x - 3) (x + 4) is the answer
On Thursday the high temperature was 0 °C. If it was three degrees colder on Friday, what was the temperature?
Answer:
-3 degrees C
Step-by-step explanation:
We need to subtract 3 degrees from Thursdays temperature
0 - 3
-3 degrees C
What is the axis of symmetry of f(x) = -2x2 + 8x - 7
bearing in mind that the squared variable is the "x", and thus this is a vertical parabola, therefore its axis of symmetry will come from the x-coordinate of its vertex.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{8}{2(-2)}~,~-7-\cfrac{8^2}{4(-2)} \right)\implies \left( \cfrac{8}{4}~,~-7+8 \right)\implies (2,1) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=2}~\hfill[/tex]
Which of the following is the general term for the sequence a, -a, a, -a, . . . ?
Answer:
a(-1)^(n-1).
Step-by-step explanation:
This is a Geometric Sequence with common ratio r = -1.
The general term is a(-1)^(n-1).
The general term for the sequence a, -a, a, -a, ... is given by the mathematical formula (-1)^(n+1) * a, where n is the term's position in the sequence, starting at n=1 for the first term.
Explanation:The general term for the sequence a, -a, a, -a, ... can be described using a formula that alternates between a and -a as the sequence progresses. This pattern is a common example of a simple mathematical sequence where the terms alternate in sign.
To express this sequence as a general term, we can use the concept of the n-th term in a sequence. If we let n represent the position of the term in the sequence (starting with n=1 for the first term), we could describe the n-th term using the formula (-1)^(n+1) * a. This formula takes advantage of the fact that raising -1 to an even power results in 1, and raising it to an odd power results in -1, thus alternating the sign of a as n increases.
For example, if n=1, the formula gives (-1)^(1+1) * a = 1 * a = a. If n=2, the formula gives (-1)^(2+1) * a = -1 * a = -a, and so on.
Use the graph to complete the statements.
Answer:
the slope of jk is -6/5
the slope of pq is 4/5
the lines are (I don't know what options are given)
Step-by-step explanation:
you can use the x1 y1 formula
[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{-7-5}{10-0}[/tex]=[tex]\frac{-12}{10}[/tex]=[tex]\frac{-6}{5}[/tex]
therefore, the slope is -6/5
using the same formula;
tex]\frac{y2-y1}{x2-x1}[/tex]= [tex]\frac{4-(-8)}{0-(-5)}[/tex]=[tex]\frac{12}{15}[/tex]=[tex]\frac{4}{5}[/tex]
therefore, the slope is 4/5
and I would glady re-edit this answer if you can comment what the options for the last one are :)
Answer:
The slope of Jk is -6/5
The slope of PQ is 4/5
The lines are neither parallel or perpendicular
Step-by-step explanation:
Need help plz and thank you
Answer:
y = 3x + 1
Step-by-step explanation:
The equation is in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, 4) ← 2 ordered pairs from table
m = [tex]\frac{4-1}{1-0}[/tex] = 3
Note the line crosses the y- axis at (0, 1) ⇒ c = 1
y = 3x + 1
Julian spent $15.00 to purchase some notebooks that cost $3.50 each and some pens that cost $4.50 each. Assuming he bought at least one notebook, what is the greatest number of pens Julian could have purchased?
Answer:
If Julian bought 1 notebook, he would only have enough money for 2 pens
Step-by-step explanation:
Pen = $4.50
Notebook = $3.50
2 pens = $9.
9 + 3.50 = 12.50.
15 - 12.50 = 2.50.
$2.50 is not enough money for another notebook or pen.
Answer:
2 notebooks.
Step-by-step explanation:
To evaluate this you just have to create an equation to solve this problem, it says that Julian has $15 in total, and he has to buy at least one notebook, so you´d have to withdraw the money of a notebook from the total, and the pens cost 4.50 each, we will be expressing the number of pens by "X" and the number of notebooks by "y" so your equation would be like this:
[tex]4.5x+3.5y=15[/tex]
The number of notebooks is one, so you can put it into the equation:
[tex]4.5x+3.5y=15[/tex]
[tex]4.5x+3.5(1)=15[/tex]
Now you clear "x"
[tex]4.5x=15-3.5[/tex]
[tex]4.5x=11.5[/tex]
[tex]x=\frac{11.5}{4.5}[/tex]
[tex]x=2.55[/tex]
Since he can not buy .55 of a pen, he will only be able to buy 2 pens.
Consider the function g(x)=10/x
Answer:
The correct answers are:
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
Step-by-step explanation:
(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) =
Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) =
We can write it as:
g(x) =
If power of x in numerator is less than the power of x in denominator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denominator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denominator).
If power of x in numerator is greater than the power of x in denominator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y =
The data set represents the total number of tuba players in each of 11 different school band
0,1,3,3, 4, 4, 4, 5, 6, 6, 8
What is the lower quartile of the data?
O
1
ooo
Answer:
3
Step-by-step explanation:
To find the lower quartile first locate the median.
The median is the middle value of the data set arranged in ascending order.
The data given is in ascending order
0, 1, 3, 3, 4, 4, 4, 5, 6, 6, 8
↑ ← The median is 4
The lower quartile is then the middle value of the data to the left of the median.
0, 1, 3, 3, 4
↑ ← the lower quartile is 3
The lower quartile of the data is given as 3
What is lower quartile of the data?Lower quartile of the data is the median of all the observations till the median of the given observations.
What is median?Median is the middle observations of the set of observations.
How to find the what is the lower quartile of the data?First we should find the median of given observations.The median is the mid value which is 4
So, the values till 4 are 0, 1 , 3, 3, 4,
Now we have to find the median of these observations.∴ The median is the mid value which are 3
∴ The lower quartile of the data is given as 3
Find more about "Lower quartile" here: https://brainly.com/question/10005803
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Michael and Tom are brothers. Their combined age is 20, and Tom is 4 years older than Michael. What are Michael and Tom’s ages?
Answer:
Micheal is 8, and Tom is 12 years old.
Step-by-step explanation:
To solve this, we can set each of their ages as a variable. Let's say Michael's age is x.
We know Tom is 4 years older than Michael, so Tom's age is x+4.
We also know that their combined age is 20, so if we add both of their ages, we should get 20.
Solving;
[tex]x + (x+4) = 20\\2x+4 = 20\\2x=16\\x=8.[/tex]
So Michael's age is 8, and Tom is 12.
Answer:
Tom is 12 and Michael is 8
Step-by-step explanation:
which sentence explains why the slope of AB is equal to the slope of BC?
Answer:
Since AB = BE and DB =CE
Step-by-step explanation:
The ratio and of these two give the concept of slope
The last sentence explains why the slope of AB is equal to slope of BC.
What is a slope?It is the measure of steepness of a line.
In the given figure, AD = BE and DB = EC
So, the ratio AD to BE is equal to the ratio BE to EC.
The slope of a line is given by,
slope = rise / run
Which is same as the above mentioned ratio.
Since AD = BE and DB = EC, their proportions are also equal. Therefore the slope of AB is equal to the slope of BC.
To learn more about slope, use the link given below:
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One x-intercept of a parabola is at the point (-3,0). Use the factor method to find the other x-intercept for the parabola defined by this equation:
y= -x^2-5x-6
Separate values with a comma
Answer:
The other x-intercept is (-2,0)
Step-by-step explanation:
-x^2-5x-6
-(x^2+5x+6)
We know x=-3 is a x-intercept so x+3 is a factor
-(x+3)( )
The other factor has to be x+2 since 3(2)=6 and 2+3=5
So -x^2-5x-6 is the same as -(x+3)(x+2)
Which means the other x-intercept is (-2,0)
Y=2x
x+y=9
Solve using substitution
Answer:
x = 3; y = 6
Step-by-step explanation:
x + 2x = 9
3x = 9
x = 3
what is the area of the polygon given below?
Answer:
C 340 square units
Step-by-step explanation:
Divide it into smallest pieces.
I see two rectangles that I'm going to do.
The long rectangle reading the paper from bottom to top is a 4 by (4+11+4) rectangle.
The wide rectangle reading the paper from left to right is a 24 by 11 rectangle.
We need to find the area of both of these rectangles and then just add them together to get the total area.
So first rectangle has area 4(19)=76 and the second rectangle has area 264. The sum of these two numbers are 340 square units.
Hello There!
The answer would be 340 square units
First, let's find the area of our small rectangle located to the left. The formula for a rectangle is width*height so we would multiply19 because we know that on our right rectangle the height is 11 and we would add 4 to that and add another 4 to that to get our length of our rectangle on the left.
Next, we multiply 24 by 11 because we are using our same formula for the rectangle on the right and once we multiply, we get a product of 264.
Finally, we add 264 and our area of the rectangle on the right together and get a sum of 340 square units.
Have A Great Day!
Please help me now please
Answer:
The model represents the expression:
A. 7/8 ÷ 1/8
Step-by-step explanation:
In the question, the number line model represents 7/8 divided into 7 equal units. Each arrow represents a unit and there are a total of seven arrows.
The size of each unit is 1/8 as shown.
Showing that 1/8 divides 7/8 into 7 divisions:
7/8 ÷ 1/8
= 7/8 x 8/1
= 7/1 x 8/8
= 7 x 1
= 7
Hence, the number line represents seven divisions given by 7/8 ÷ 1/8.
Solve system of equations 2x + 2y + 5z = 7 6x + 8y + 5z = 9 2x + 3y + 5z = 6
Answer:
the values of x, y and z are x= 2, y =-1 and z=1
Step-by-step explanation:
We need to solve the following system of equations.
We will use elimination method to solve these equations and find the values of x, y and z.
2x + 2y + 5z = 7 eq(1)
6x + 8y + 5z = 9 eq(2)
2x + 3y + 5z = 6 eq(3)
Subtracting eq(1) and eq(3)
2x + 2y + 5z = 7
2x + 3y + 5z = 6
- - - -
_____________
0 -y + 0 = 1
-y = 1
=> y = -1
Subtracting eq(2) and eq(3)
6x + 8y + 5z = 9
2x + 3y + 5z = 6
- - - -
______________
4x + 5y +0z = 3
4x + 5y = 3 eq(4)
Putting value of y = -1 in equation 4
4x + 5y = 3
4x + 5(-1) = 3
4x -5 = 3
4x = 3+5
4x = 8
x= 8/4
x = 2
Putting value of x=2 and y=-1 in eq(1)
2x + 2y + 5z = 7
2(2) + 2(-1) + 5z = 7
4 -2 + 5z = 7
2 + 5z = 7
5z = 7 -2
5z = 5
z = 5/5
z = 1
So, the values of x, y and z are x= 2, y =-1 and z=1
What is the solution to the inequality? 17 < 9 + x
Answer:
x > 8
Step-by-step explanation:
Given
17 < 9 + x ( subtract 9 from both sides )
8 < x , hence
x > 8
Express 45 = x as a logarithmic equation.
Answer:
[tex]5 = log_{4}x[/tex]
Step-by-step explanation:
You know that [tex]45=4^{5}[/tex]
Then: [tex]4^{5}=x[/tex]
Taking log with base 4 in both sides, we have:
[tex]log_{4} 4^{5}=log_{4}x[/tex]
Applying the logarithmic rules, we have:
[tex]log_{4}4^{5}=log_{4}x[/tex] → [tex]5log_{4}4=log_{4}x[/tex]
→ [tex]5 = log_{4}x[/tex]
In conclusion, 45 = x expressed as a logarithmic equation equals: [tex]5 = log_{4}x[/tex]
Answer:
[tex]4^5=x[/tex] as a logarithmic equation [tex]\log_4 (x)=5[/tex]
Step-by-step explanation:
Given : Expression [tex]4^5=x[/tex]
To find : Express the expression as a logarithmic equation?
Solution :
Expression [tex]4^5=x[/tex]
Taking log with base 4 both side,
[tex]\log_4(4^5)=\log_4 (x)[/tex]
Using logarithmic property, [tex]\log_a a^b=b[/tex]
[tex]5=\log_4 (x)[/tex]
Therefore, [tex]4^5=x[/tex] as a logarithmic equation [tex]\log_4 (x)=5[/tex]