[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \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-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-6)}) \implies y -1= \cfrac{1}{2} (x +6) \\\\\\ y-1=\cfrac{1}{2}x+3\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+4 \end{array}}[/tex]
find the volume of this prism
The volume of the prism with area 41 cm^2 and height 11 cm is 451 cm^3
How to solve for the volume of the prismVolume refers to three dimensional solid. The three dimensions include some elements which are
heightlength widthWhile area is 2 dimensional which is solved by length * width
In the figure the area is already solved to be 41 cm^2 and height is given to be 11 cm
The volume of the solid is given
= length * width * height
= area * height
= 41 * 11
= 451 cm^3
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1. Griffin wants to go hiking, but the weather is not cooperating. Right now, there are 2 inches of snow on the ground and snow is falling at a rate of 0.25 in/hr.
(a) Write the linear equation that represents the total amount of snow, y, after x number of hours.
(b) How much snow will be on the ground after 4 hours? You must use your equation above to solve, and you must show all of your work.
(c) If Griffin does not want to be hiking when there are 6 inches of snow on the ground, how long does he have to complete his hike? Do you think he will finish his hike in time? You must use your equation above to solve, and you must show all of your work.
a) The linear equation that represents the total amount of snow, y, after x number of hours is: y = 2 + 0.25x.
b) 3 inches is the amount of snow that is on the ground after four hours.
c) The time until the snow reaches 6 inches is of 16 hours, which is enough to finish the hike, as they usually take at most five hours.
What is a linear function?The slope-intercept representation of a linear function is shown by the equation as follows:
y = mx + b
In which the parameters m and b of the linear equation are explained as follows:
m is the slope, representing the rate of change of the output relative to the input, in the context of this problem how much snow falls by hour.b is the y-intercept, which is the initial value of the function, that is, how much snow was there initially.Thus the values of these parameters are given as follows:
m = 0.25, b = 2.
The equation that represents the total amount of snow, y, after x number of hours is:
y = 0.25x + 2.
The numeric value of function after four hours is found replacing the lone instance of x on the function by 4, hence:
y = 0.25(4) + 2 = 3 inches.
To find when the amount will be of six inches, we have to solve for x when y = 6, hence:
2 + 0.25x = 6
0.25x = 4
x/4 = 4
x = 16 hours.
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The cost of two cell phones and three headphone sets is $286.00. The cost of two cell phones and six headphone sets is $392.50. What is the cost of one cell phone?
Answer: 89.75
Step-by-step explanation:
So 392.50 is the cost of 2 phones and 6 headphones and 286.00 is the cost of 2 cell phones and three headphones. so 392.50-286.00 is the cost of 3 headphones since you added three headphones to the price. so the price of 3 headphones is 106.50. Then you subtract 106.50 from 286.00 to get the cost of the two cell phones. And you get 179.50. Then, you divide 179.50 in order to get the price of one cell phone and you get 89.75. So the cost of one cell phone is $89.75.
The dimensions of a rectangular garden
were 5 m by 12 m. Each dimension
was increased by the same amount.
The garden then had an area of 120 m².
Find the dimensions of the new garden.
A softball is larger than a baseball. Its circumference is about 12 inches. The circumference of a baseball is about 9 inches. What is the approximate difference in the diameters of the balls?
Answer:
0.96 inches
Step-by-step explanation:
The first step is to find the diameter given the circumference. This is the formula for circumference:
[tex]C=\pi d[/tex]
In terms of d, the formula looks like this:
[tex]d=\frac{C}{\pi}[/tex]
For the softball, the diameter is approximately:
[tex]d=\frac{12}{\pi} =3.82[/tex]
For the baseball:
[tex]d=\frac{9}{\pi } =2.86[/tex]
Find the difference:
[tex]3.82-2.86=0.96[/tex]
The approximate difference in diameters is 0.96 inches!
Answer: 0.96 inches
Step-by-step explanation:
S. Which equation represents the line that passes through the points (6, -12) and (16,-10)?
(A) y=-x-13
[B] y=x+13
[C] y=x-13
[D] y=-x+13²
The equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2
The first point = (6, -12)
The second point = (16, -10)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (-10 -(-12) / (16 - 6)
= (-10 +12) / 10
= 2/10
= 1/5
The slope intercept form is
y = mx + b
Consider the point (6, -12)
-12 = (1/5)6 + b
-12 = 6/5 + b
b = -12 - 6/5
b = -13.2
The equation will be
y = 1/5x - 13.2
Hence, the equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2
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A total of 25 trials of the simulation were performed. The number of makes in each set of 10 simulated shots was recorded on the dotplot. What is the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts?.
The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25
Given,
Number of trials of the simulation were performed = 25
Number of set of simulated shots = 10
We have to find the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts;
The dots in the 5 shot mark is 9, 6 shot mark is 2, and 7 shot mark is 1.
Now the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated below:
P(x5) = (dots in 5 short mark + dots in 6 shot mark + dots in 7 short mark) / 25
= (9 + 2 + 1) / 25
= 12 / 25
Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25
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genetically modified foods: according to a 2016 pew research survey, a majority of the american general public (56%) says that genetically modified (gm) foods are generally unsafe to eat. this month, in a survey of 500 randomly selected american adults, 60% says that gm foods are generally unsafe to eat. we test the hypothesis that the percentage who says that gm foods are generally unsafe to eat is greater than 56% this year. the p -value is 0.084. which of the following interpretations of this p -value is valid?
"If we assume that 57% of Americans says that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60%or more who says that GM foods are generally unsafe to eat" is valid interpretations of this p-valid.
Given info;
Genetically modified foods: A 2016 Pew Research survey found that 56% of Americans believe that eating genetically modified (GM) food is generally harmful. This month, a survey of 500 randomly chosen American citizens found that 60% believe gm foods are typically dangerous to consume. We examine the possibility that more people than 56% believe that eating GM food is generally unsafe this year. 0.084 is the p-value.
If we assume that 57% of Americans say that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60% or more who say that GM foods are generally unsafe to eat” is a good interpretation of the P-value. The P-value is the probability that results will be as or more extreme than those from the latest survey if opinions have not changed since 2014.
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Write an equation of the line passing through point P(-1, 3) that is perpendicular to y = 4x - 7
The equation of line is y = -1/4x + 11/12.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
line passing through P(-1, 3) that is perpendicular to y = 4x - 7.
Now, the slope of perpendicular line is
slope= -1/ 4
and, the lines passes through (-1, 3)
Thus, using slope- intercept form
y- 3 = m( x + 1)
y- 3 = -1/4 ( x+ 1)
y- 3 = -1/4x - 1/4
y = -1/4x + 11/12
Hence, the equation of line is y = -1/4x + 11/12
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PLEASE HELP! It would be greatly appreciated
Mrs.Galicia bakes and then sells cookies and brownies from her bakery. Her revenue for each baked good (in dollars) is modeled by the equations, where x is the number of days since the bake goods started to sell.
Brownies: () = 2^2 + 8 − 4
Cookies: () = 2 + 4
(a) Solve the system algebraically. After how many days is the revenue for each item the same? Show
your work and explain your answer.
(b) Graph this system to show both solutions. Label each axis appropriately.
a) The revenues for both items will be the same after 1 day.
b) The graph with the solution is given by the image at the end of the answer.
How to obtain the number of days for which the revenues will be the same?The functions defining the revenues for the selling of x brownies and of x cookies are presented as follows:
Brownies: B(x) = 2x² + 8x - 4.Cookies: C(x) = 2x + 4.The revenues will be the same after x days, for which:
B(x) = C(x).
Hence:
2x² + 8x - 4 = 2x + 4
2x² + 6x - 8 = 0.
x² + 3x - 4 = 0.
The quadratic function can be factored as follows:
(x + 4)(x - 1) = 0.
Applying the Factor Theorem, the solutions are given as follows:
x + 4 = 0 -> x = -4, which is an extraneous solution, as the number of days cannot be negative.x - 1 = 0 -> x = 1, which is the number of days when the revenues are the same.The graph shows the intersection of the two curves, B(x) and C(x).
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The father is 37 years old and his son's age is 5 years.After how many years,the father's age will be five times that of his son?
Answer:Let the age of son be x.
Thus, age of father is 4x.
After 5 years, their ages will be x+5 and 4x+5 years respectively.
As per the question, we have
4x+5=3(x+5)
⇒4x+5=3x+15
⇒x=10
Age of father will be 4x=4×10=40 years.
Thus when son is 10 years old, father is 40 years.
Step-by-step explanation:
After 3 years father's age will be five times that of his son. Father age will be 40 years and son age will be 8 years .
Given,
Present age of father = 37 years.
Present age of son = 5 years.
Now,
Let the number of years be x after which the fathers age will be 5 times the age of his son.
So,
Ages after 3 years ,
Age of father = 40 years
Age of son = 8 years.
Thus age of father is 5 times the age of son.
Therefore after 3 years father's age will be five times that of his son.
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please help
triangle 1:10 and 8
2: 6
3: 13 and 6
4: 8
x=?
Answer:
lo siento soy muy malo para las matemáticas y además soy nuevo en este aplicación
Suppose x has a distribution with = 64 and = 8.
For the given condition the x distribution is normal. Option B is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
n=64
√n=8
μ=8
σ=16
The sample size (n > 30) is enough. Using the Central Limit Theorem
¯X∼N(8,16²/64)
The formulas below give the mean and standard deviation of the mean value of x:
The sampling distribution of x has a mean value of 8.
The following equation gives the sampling distribution's standard deviation:
=σ/√n
=16/√64
=16/8
=2
The sample distribution's standard deviation is 2.
Yes, this distribution can be regarded as normal as it roughly follows the normal distribution (By using CLT)
Thus, for the given condition the x distribution is normal. Option B is correct.
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Peter collected a total of 1,170 stamps. He collected 4 times as many US stamps as foreign
stamps. How many US stamps did he collect?
He collected 936 US stamps.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Total number of stamps - 1170
US stamps - 4 times as many as foreign stamps
Let x be the number of foreign stamps.
4x as the number of US stamps.
To find the number of US and foreign stamps Peter collected, we are going to represent the given data as:
x + 4x = 1170.
x + 4x = 1170
5x = 1170
5x/5 = 1170/5
x = 234
Peter collected 234 foreign stamps.
US stamps = 4x
= 4(234)
= 936
Peter collected 936 US stamps.
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a mason builds two patios with the same area. one is a square and the other is a rectangle 10 m longer than the square but 8 m less wide than the square. what is the area of each patio?
The area of each of the patios is 1600 m².
The mason builds two patios with the same area. One of the patios is square, and the other is rectangular. The rectangular patio is 10 m longer but 8 m less wide than the square patio. We need to find the area of each patio.
Let the side length of the square patio be denoted by the variable "x". The area of the square can be calculated as follows.
A1 = x²
The length and breadth of the rectangular patio is "x + 10" and "x - 8", respectively. The area of the rectangular patio is calculated below.
A2 = (x + 10)*(x - 8)
A2 = x² + 2x - 80
We know that the areas of both patios are equal.
A1 = A2
x² = x² + 2x - 80
2x = 80
x = 40
Hence, the area of each patio is A = x² = 40² = 1600 m².
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Seventy-five percent of the players in the basketball program are 5th graders. There are 80 players in the class. How many players are NOT 5th graders?
There are 20 players are not in 5th grades.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Total players in the class = 80
And, 75% of the players in the basketball program are 5th graders.
Now.
Number of players in the basketball program are 5th graders = 75% of 80
= 75/100 x 80
= 60
Thus, Number of players are not in 5th graders = 80 - 60
= 20
Therefore, There are 20 players are not in 5th grades.
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Graph the linear equation that passes through (-2, 5) and whose slope is 2/3.
r-3s + t=4
3r-6s+9t=5
4r-9s +10t=9
Find solution using substitution/ elimination
For the given equation the solution would be
[tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]
What is the system of linear equations in three variables?
Three-variable equation systems are only slightly more difficult to solve than two-variable equation systems. Substitution and the use of 3x3 matrices are the two most straightforward methods for solving these types of equations.
The given equations are
r - 3s + t = 4 ------------(I)
3r - 6s +9t = 5 ---------(II)
4r - 9s + 10t = 9--------(III)
from equation (I), we get
r = 4 + 3s - t ------------(IV)
Now put the value of 'r' in equations (II) and (III), and we get
3(4 + 3s - t) - 6s + 9t = 5
4(4 + 3s - t) - 9s + 10t = 9
Solving the above equations, we get
3s + 6t + 12 = 5 --------(V)
3s + 6t + 16 = 9 --------(VI)
Now isolate the value of 's' from equation (IV), we get
3s = - 6t + 5 -12
[tex]s=\frac{-6t-7}{3}[/tex]
Now put the value of 's' in equation (IV), and we get
[tex]r=4 +3s -t\\r=4+3\cdot(\frac{-6t-7}{3}) -t\\ r=4-6t-7-t\\r=-7t-3[/tex]
Hence, For the given equation the solution would be
[tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]
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Solve the system of equation by the substitution method 3x-2y=-4 y=2x
Answer: ( 4 , 8 )
Step-by-step explanation:
3x - 2y = -4
y = 2x
Substitute the second equation into the first
3x - 2(2x) = -4
3x - 4x = -4
-1x = -4
x = 4
y = 2(4)
y=8
( 4 , 8 )
K
Solve the matrix equation AX = B for X.
1 1
[42]
X =
A =
ہلے
B=
23
78
Answer:
Step-by-step explanation:
I'm impressed that they make you do this in H.S. Linear Algebra. it's good for more complex math . so that's why i'm impressed. Is this an AP class?
Ax=B is our formula. we need to know something about x, it's size
so we look at rows and columns of A, 2x2 , also we need to know about B as well it's also 2x2
so now we know, that a matrix A, of size 2x2, *x = B of size 2x2
2x2*x=2x2 .... 2x2|2x2 since the two inside number match, we can do this multiplication, and the two ouside numbers tell us the size of x... it's also a 2x2. I know, a lot of explaining to just get 2x2. Maybe that is obvious, and i'm mansplaining, :DD , but I don't know what you know.
I'll put big subscripts on my matrix variable so you can see it well. You understand the subscript is the element location in the matrix , right? 1,1 is just the top left corner element of the matrix. ect , ect.
so now we need, a1,1 * x1,1 + a1,2 * x2,1 = 2 in b1,1
then we need a2,1 * x1,1 + a2,2 * x2,1 = 7 in b2,1
next we need a1,1 * x1,2 + a1,2 * x2,2 = 3 in b1,2
finally we need a2,1 * x2,1 + a2,2 * x2,2 = 8 in b2,2
X = [tex]\left[\begin{array}{ccc}\frac{3}{2} &1\\\frac{1}{2} &2\end{array}\right][/tex] I did that by observation. have you learned any RREF methods yet?
The perimeter of a triangle is 6p + 2q - 5 units. One side length is p - 3 units. The second side length is 2p + 3q units. Which expression represents the length, in units, of the third side of the triangle?
Answer: 3p-q-2
Step-by-step explanation:
Perimeter is the sum of all the sides.
Add the known sides together:
(p-3) + (2p+3q) = 3p + 3q - 3
To find the unknown side, subtract the sum of the 2 known sides from the perimeter (combine like terms):
(6p+2q-5) - (3p+3q-3) = 3p-q-2
Add all 3 sides together as a check of your answer!
Brian pays £465. 98 a year on his car insurance. The insurance company reduces the price by 3. 6%. How much does the insurance cost now? give your answer rounded to 2 dp.
The insurance cost now is £449.204.
Given:
Brian pays £465. 98 a year on his car insurance. The insurance company reduces the price by 3. 6%.
Insurance = 465.98*3.6%
= 465.98*3.6/100
= 465.98*36/10*100
= 46598/100 * 36/1000
= 46598*36 / 100000
= 1677528/100000
= 16.77528
Insurance cost now = 465.98 - 16.77528
= £449.20472
Therefore the insurance cost now is £449.204.
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You start with $200 in bank account
and deposit $50 per week. Write an
equation for scenario.
Answer:
y= 50x + 200
Step-by-step explanation:
pool empties at a rate of 12 quarts every 2 minutes. how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons? (1 gallon
After the conversion, 133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.
In the given question we have to find how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons.
As given that pool empties at a rate of 12 quarts every 2 minutes.
In 12 quarts = empties in 2 minutes
As we know that 1 gallon = 4 quarts
So 1 quarts = 1/4 gallon
In 12 quarts = 12/4 gallon
12 quarts = 3 gallon
So 3 gallon = empties in 2 minutes
So 1 gallon = empties in 2/3 minutes
12,000 gallon = empties in 2/3 ×12,000 minutes
Simplifying
12,000 gallon = empties in 2×4,000 minutes
12,000 gallon = empties in 8,000 minutes
Now converting minutes in hours.
As we know that 1 minute = 1/60 hours
So 8000 minute = 8000/60 hours
8000 minutes = 133 hours 33 minutes
133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.
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PLEASE HELP!!! QUESTION ON PICTURE
Answer:
120[tex]ft^{2}[/tex]
Step-by-step explanation:
4 yards is 12 feet
10(12) = 120
Answer:
120 square feet
1 ) We first need to convert the 4 yards into feet...
1 yard = 3 feet
so 4 yards = 12 feet
2 ) To find area we do length x width...
length = 10
width = 12
10 x 12 = 120
( 120 square feet )
Hope this helps! :)
Type an equation of a line that is parallel to the equation y = 5.
The equation is y = -3
Since, the line parallel to the line y=5, its slope is zero.
so, the equation has the form
y = constant
it passes through (-2,-3), the equation is
y = -3
Slope of a Line :
In mathematics, a line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
The net change in the y-coordinate and the net change in the x-coordinate are denoted by the letters Y and X, respectively.
Since the slope of a line is denoted by "m," the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.
The slope, intercept, and y-intercept values on the graph of the equation y = mx + c are all equal to m. M and C are real integer values in the slope-intercept version of the linear equation.
Complete question:
find an equation of the line parallel to the line y=5 and passing through -2,-3
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rerrange 3g=d with the subject g
Step-by-step explanation:
[tex]3g = d[/tex]
[tex] \frac{3g}{3} = \frac{d}{3} \\ [/tex]
[tex]g = \frac{d}{3} \\ [/tex]
[tex]{ \purple{ \bold{g = \frac{d}{3}}}} [/tex]
Step-by-step explanation:
The given formula is [tex]{ \orange{ \sf{3g = d}}}[/tex]
In order to get formula for g, let us divide 3 on both the sides.
[tex]{ \orange{ \sf{ \frac{ \cancel3}{ \cancel3}g}}} = { \orange{ \sf{ \frac{d}{3}}}} [/tex]
Therefore, [tex]{ \boxed{ { \tt{g = \frac{d}{3}}}}} [/tex]
Find X Find Y PLEASE HELP ME
Issac earns money tutoring kids on how to solve a Rubik’s cubes. He always saves 30% of his earnings and spends the rest. If he spent $80 last week, how much money did he earn in total
-7+2i/3-6i It’s operations with complex numbers is how to solve it. The answer is not -11-4/15 ok I need another answer
..........................................
[tex]\displaystyle\\Answer: \frac{-11-12i}{15}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\\frac{-7+2i}{3-6i}=\\\\\frac{(-7+2i)(3+6i)}{(3-6i)(3+6i)}=\\\\ \frac{-21-42i+6i+12i^2}{3^2-(6i)^2} =\\\\\frac{-21-36i-12}{9+36}=\\\\\frac{-33-36i}{45} =\\\\\frac{3(-11-12i)}{3(15)} =\\\\\frac{-11-12i}{15}[/tex]