The equation of the line, in slope-intercept form, is written as
[tex]y=mx+b[/tex]wherein m is the slope of the line and b is the y-intercept.
The first step to solve the equation of the line that passes through two points is to find the slope of the line given two points. The slope of the line can be computed using the equation
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For points (5, -4) and (-1, 8), the slope of the line is
[tex]m=\frac{8-(-4)}{-1-5}=\frac{12}{-6}=-2[/tex]Now, we have the initial equation of the line written as
[tex]y=-2x+b[/tex]To solve for the value of b, we use one of the points and substitute it on the initial equation above. In my case, I will be using points (5,-4), we have
[tex]\begin{gathered} -4=-2(5)+b \\ -4=-10+b_{} \\ b=10-4 \\ b=6 \end{gathered}[/tex]Hence, the equation of the line that passes through (5,-4) and (-1,8) is
[tex]y=-2x+6[/tex]Finds the measures of angle b and d given that m ll n. Explain.
Answer:
b = 60.7
d = 43.1
Explanation:
The angles of measure 60.7 and b are alternate interior angles because they are on opposite sides of the transversal and in the inside of the parallel lines m and n. These angles have the same measure, so
b = 60.7
Angle d and the angle of measure 136.9 form a straight line, so they sum to 180 degrees. Therefore, the measure of angle d is
d = 180 - 136.9 = 43.1
Therefore, the answers are
b = 60.7
d = 43.1
what is the linear equation of (0,10) (-10,-7)
Consider that the general form of a linear equation can be writen as follow:
y = mx + b
where m is the slope of the line and b the y-intercept
use the following formula for the calculation of m:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) = (-10,-7) and (x2,y2) = (0,10). Replace these values of the coordinates into the formula for m:
m = (10 - (-7))/(0-(-10))
m = (17)/(10)
m = 1.7
The y-intercept of the line is the value of the y coordinate when x=0, from the point (0,10) you can notice that y=10 when x=0. Then, the y-interceot is b =10
FInally, replace the values of m and b into the general expression for y:
y = mx + b
y = 1.7x + 10
Melissa is choosing between two exercise routines,In Routine #1, she burns 42 calories walking. She then runs at a rate that burns 14.25 calories per minute.In Routine #2, she burns 25 calories walking. She then runs at a rate that burns 18.5 calories per minute.For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #27Use t for the number of minutes spent running, and solve your inequality for t.
Suppose in routine 1 and 2, Melissa rune for t minutes.
She burns 42 calories walking and then she runs at a rate that burns 14.25 calories per minute in rouitne 1.
So, total calories she burns in routine 1 is
[tex]42+14.25t[/tex]Again, in routine 2, she burns 25 calories walking and she runs at a rate that burns 18.5 calories per minute in rouitne 2.
So, total calories she burns in routine 2 is
[tex]25+18.5t[/tex]Accordingly,
[tex]\begin{gathered} 42+14.25t\leq25+18.5t \\ 18.5t-14.25t\ge42-25 \\ 4.25t\ge17 \\ t\ge4 \end{gathered}[/tex]So, Melissa should run for minimum 4 minutes
Tom buys some shirts for $15 each. He has a coupon for $9 dollars off the total price. If he pays $36, how many shirts, s , did he buy
We have to find how many shirts (s) he has bought.
We know that each shirt costs $15, so the total cost of the shirts should be 15*s.
If we substract the discount, we have the total final cost C as:
[tex]C=15\cdot s-9[/tex]If we know that this total cost was $36, we can find the number of shirts as:
[tex]\begin{gathered} C=36 \\ 15s-9=36 \\ 15s=36+9 \\ 15s=45 \\ s=\frac{45}{15} \\ s=3 \end{gathered}[/tex]Answer: He bought 3 shirts (s = 3).
If you translate the triangle below 5 units down and 5 units to the left, what quadrant(s) would it be in?
The traslated triangle would be:
We can conclude that it would be in the 3rd quadrant.
Answer: Option 3
Kayla is learning to sew a quilt. The first step is to use a pattern to cut squares from pieces of fabric. Onthe pattern, one side of the square starts at point (5,-4) and ends at point (5,2). If each unit on thepattern is one inch, how many inches long is the side of the square?
Answer:
6 inches
Explanation:
On the square pattern, one side of the square starts at point (5,-4) and ends at point (5,2).
To determine the length of a side of the square, find the distance between the endpoints.
From the endpoints: (5, -4) and (5,2)
The x-coordinates are the same, therefore, the distance between the endpoints is:
[tex]|2-(-4)|=|2+4|=6\text{ units}[/tex]If each unit on the pattern is one inch, the length of a side of the square is 6 inches.
5) Kendall is making a cone shaped party hats for his birthday. Then, each hatwill be filled with candy. The height on each cone is 7.5 inches and theradius is 1.5 inches. If she has 12 friends coming, how many cubic incheswill he need to fill all 12 hats with candy?
Explanation
In the question, we are given that,
[tex]\begin{gathered} height\text{ of cone = 7.5 inches} \\ radius\text{ of cone = 1.5 inches} \end{gathered}[/tex]We will need to find the volume of the cone.
[tex]volume\text{ of a cone =}\pi r^2h[/tex]Therefore, we will have;
[tex]V=\pi\times1.5^2\times7.5=53.0144[/tex]So for 12 hats with candy, we will have;
[tex]12\times V=12\times53.0144=636.1728[/tex]Answer: 636.1728 cubic inches
AHow many degrees mustFigure A be rotatedcounterclockwise aroundthe origin in order toline up with Figure B?BA. 90B. 180C. 270D. 360
The figure A when rotated through 180 degrees counterclockwis, figure B will be obtained
correct answer is OPTION B
Please assist me in knowing how to figure these out.
we have the equation
[tex]H(t)=180-a(108)^{-t}[/tex]A) since H is an exponential function 180 represents the maximum posible value of H or the maximum temperature that the center of the cake can reach
b)
we have
H(t)= 22° C
when placed in the oven or t=0
[tex]22=180-a(108)^0[/tex][tex]22=180-a(1)[/tex][tex]a=180-22=158[/tex]the value of a is 158
C)
H(t)=150°C
we already know a=158
let's solve for t
[tex]150=180-(158)(1.08)^{-t}[/tex][tex]-30=-(158)(1.08)^{-t}[/tex][tex]\frac{30}{158}=1.08^{-t}[/tex][tex]ln(\frac{30}{158})=ln(1.08^{-t)}[/tex][tex]ln(\frac{30}{158})=-t*ln(1.08)[/tex][tex]-t=\frac{ln(\frac{30}{158})}{ln(1.08)}[/tex][tex]t=-\frac{ln(\frac{30}{158})}{ln(1.08)}=21.587[/tex]now this is the time 29 minutes before taking the cake out of the oven
so the total time is 29+21.587
then the total time the baking thin was in the oven
is 50.587 minutes
What is the least common multiple of 12, 48 and 72
SOLUTIONS
What is the least common multiple of 12, 48 and 72
[tex]\begin{gathered} L.C.M=2\times2\times2\times2\times3\times3 \\ L.C.M=144 \end{gathered}[/tex]Therefore the least common multiple of 12, 48 and 72 = 144
Question 11 of 44In ADEF, sin D = 36. What is cos E?
We will have the following:
[tex]\cos (E)=\frac{\sqrt[]{39^2-15^2}}{39}\Rightarrow\cos (E)=\frac{36}{39}[/tex]We remember that:
[tex]\cos (\alpha)=\frac{\text{adjacent side}}{hypotenuse}[/tex]I need help with this question please. This is non-graded.
The standard form of a quadratic equation is the following:
[tex]y=ax^2+bx+c[/tex]Where a, b and c are numbers. In this case we are given a quadratic equation in vertex form:
[tex]y=(x-4)^2-16[/tex]We can expand the squared binomial:
[tex]\begin{gathered} y=x^2-2\cdot4\cdot x+(-4)^2-16 \\ y=x^2-8x+16-16 \\ y=x^2-8x \end{gathered}[/tex]AnswerThen the answer is the second option.
If angle YWV is 48 degrees, what is the measure of angle Y?Required to answer. Single choice. 52429048
According to the image given there is a right triangle formed in which we are missing one of the angles, for that we know that the sum of thr interior angles of every triangle has to be equal to 180°.
Using this information
[tex]90+48+Y=180[/tex]we clear the equation for Y
[tex]\begin{gathered} Y=180-90-48 \\ Y=42 \end{gathered}[/tex]The measure of angle Y is 42°.
about 3.9×10 people live in California about 1.3×10 people live in Maine about how many more people live in California than in Maine
so the answer is
[tex]3.77\times10^7[/tex]QUESTION Bgraph the line with the given slope and point 2 stepsthere are two steps with in 1 question
By definition, the slope of a line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]You can observe that it is the change in "y" divided by the change in "x".
In this case, you have the following slope:
[tex]m=\frac{2}{3}[/tex]Then the change in "y" in 2 and the change is "x" is 3.
Given the point (-4,1), you can follow these steps to graph the line:
1. Plot the given point on the coordinate plane.
2. Knowing that the slope is
[tex]m=\frac{2}{3}[/tex]You must move 3 units to the right and then 2 units up. This will give you a new point.
3. Graph the line. It must pass through those points.
The graph is:
which of the following number lines represents the inequality x> 1.5?
Answer:
The answer would be D
Step-by-step explanation:
The inequality x>1.5, or x is greater than 1.5, has to have a line going to the right because x has to be greater than 1.5, so answers B and C can't be it. Because the symbol is greater than instead of greater than or equal to, the circle will be open, and the circle for option A is closed, so the answer is D
I know that the equation is 5/9 (x-1) squared -3 What is the y-coordinate for the point where the parabola intersects the x-axis?
Answer:
-22/9
Explanation:
If the equation of the parabola is
y = 5/9 (x - 1)² - 3
The y-coordinate for the point where the parabola intersects the x-axis can be calculated by replacing x = 0, so
y = 5/9 (0 - 1)² - 3
y = 5/9 (-1)² - 3
y = 5/9 (1) - 3
y = 5/9 - 3
y = -22/9
Therefore, the y-coordinate is -22/9
I’m not sure on how to do it right as I keep getting this wrong. Please help!
Given the function:
[tex]A(t)=40(0.83)^t[/tex]Where A(t) shows the amount of drug in a body after t hours.
Let's solve for the following:
• (a). Initial dosage:
Apply the exponential functions:
[tex]f(x)=a(b)^x[/tex]Where:
a is the initial value
b is the change factor.
Thus, we have the following:
a = 40
b = 0.83
Therefore, the initial dose is 40 mg.
• (b). What percent leaves the body each hour?
Apply the function:
[tex]f(x)=a(1-r)^x[/tex]Where:
r is the decay rate.
Thus, we have:
b = 1 - r
r = 1 - b
r = 1 - 0.83
r = 0.17
The percent that leaves the body each hour will be:
0.17 x 100 = 17%
Therefore, 17 percent of the drug leaves the body each hour.
• (c). What amount of drug is left after 12 hours?
Substitute 12 for t and solve for A(12):
[tex]\begin{gathered} A(12)=40(0.83)^{12} \\ \\ A(12)=40(0.1068900077) \\ \\ A(12)=4.28 \end{gathered}[/tex]The amount left after 12 hours is 4.28 mg.
• (d). The first whole number of hours at which there is less than 6 mg left.
Plug in 5.9 for A(t) and solve for t.
[tex]5.9=40(0.83)^t[/tex]Divide both sides by 40:
[tex]\begin{gathered} \frac{5.9}{40}=\frac{40(0.83)^t}{40} \\ \\ 0.1475=(0.83)^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} ln(0.1475)=tln(0.83) \\ \\ t=\frac{ln(0.1475)}{ln(0.83)} \\ \\ t=10.2 \end{gathered}[/tex]Therefore, the first whole number of hours where there is less than 6 mg left is 10 hours.
ANSWER:
• (a) 40 mg
,• (b) 17%
,• (c). 4.28 mg
,• (d). 10 hours
Peanuts are sold in 8 ounce and 12 ounce packages. what is the fewest number of ounces you can buy of each package to have equal amounts of each package size
The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.
Given that the Peanuts are sold in 8-ounce and 12-ounce packages
We have to determine the number of ounces you can buy from each package to have equal amounts of each package size
8 = 2 × 2 × 2
12 = 2 × 2 × 3
The LCDs 8 and 12 are 24
Thus, three 8 oz packets and two 12 oz packets.
Therefore, you can buy from each package to have equal amounts of each package size the number o ounces as 3 packets of 8 ounces and 2 packets of 12 ounces.
Use the fact that the sum of the angles in a triangle is 180° for this question.Two angles of a triangle have the same measure and the third one is 9º greater than the measure ofeach of the other two. Find the measure of the angles in the triangle.The 2 SMALLER angles each have a measure ofThe LARGER angle has a measure of0Question Help: Message instructorSubmit QuestionJump to Answer
Let
x ------> measure of the two angles that have the same measure
y -----> teh larger angle
we have that
2x+y=180 --------> equation A
y=x+9 -------> equation B
substitute equation B in equation A
2x+(x+9)=180
solve for x
3x=180-9
3x=171
x=57 degrees
Find the value of y
y=x+9
y=57+9
y=66 degrees
therefore
The 2 SMALLER angles each have a measure of 57 degrees
The LARGER angle has a measure of 66 degrees
simplify the expression 5x + 6 (x-2) -8 (x-3)A. 19x + 36 B. 19x + 12 C. 3x - 36 D. 3x + 12
Given the expression:
5x + 6 (x-2) -8 (x-3)
Let's simplify the exression using the following steps:
Step 1.
Apply distributive property:
5x + 6x + 6(-2) - 8x - 8(-3)
5x + 6x - 12 - 8x + 24
Step 2.
Combine like terms:
5x + 6x - 8x - 12 + 24
3x + 12
Therefore, the simplified expression is:
3x + 12
ANSWER:
D. 3x + 12
Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times
that the coin shows heads. You have previously shown that all conditions have been met and that this scenario
describes a binomial setting.
Determine the value of n and p and calculate the mean and standard deviation of X. Round the standard deviation to
three decimal places.
■ n=
■
■
p=
Hx=
0x =
h
Done
Using the normal distribution, it is found that, the standard deviation is 0.86
What does "normal" describe in statistics?Normal usually refers to the word "normal" in a normal distribution.
The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.
In a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is;
σ = √np(1- p)
After finding the z-score, we need the p-value associated with this z-score, which is the percentile of X.
The given parameters are:
n = 3 ---- the number of flips
p = 0.5 --- the probability
The standard deviation is calculated as:
σ = √np(1- p)
σ = √3 (0.5) (0.5)
σ = 0.86
Hence, the standard deviation is 0.86
Learn more about normal distribution here:
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Ruth has a piece of wood that measures 2 2/9 feet. She cut off 1 1/3 feet of
wood for a project. How much wood does she have remaining?
After finding the difference between total measure of wood and cut off wood, she have remaining 8/9 wood.
In the given we have to find the remaining wood.
Ruth has a piece of wood that measures 2 2/9 feet.
Now converting the mixed fraction in improper fraction by multiplying the 2 and 9 then add 2 in the multiplication of 2 and 9.
So the improper fraction is 20/9.
So The measure of wood = 20/9 feet
She cut off 1 1/3 feet of wood for a project.
Now converting the mixed fraction in improper fraction by multiplying the 1 and 3 then add 1 in the multiplication of 1 and 3.
So the improper fraction is 4/3.
So, she cut the wood = 4/3 feet
Now the remaining wood = Total measure of wood−cut the wood
Remaining wood =20/9−4/3
Now equal the denominator of both values.
Remaining wood =20/9 −4/3 ×3/3
Remaining wood =20/9 −12/9
Remaining wood =(20−12)/9
Remaining wood =8/9
To learn more about difference of fraction link is here
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A sine function has an amplitude of 3, a period of π, and a phase shift of pi over 2 period What is the y-intercept of the function?
The sine fuction we have is
[tex]f(x)=3\sin \mleft(2x+\frac{\pi}{2}\mright)[/tex]If we want the y-intercept, we must put x = 0, then
[tex]\begin{gathered} f(x)=3\sin (2x+\frac{\pi}{2}) \\ \\ f(0)=3\sin (\frac{\pi}{2}) \\ \\ f(0)=3\cdot1 \\ \\ f(0)=3 \end{gathered}[/tex]Therefore the y-intercept is 3.
Answer: 0
Step-by-step explanation: trust me
it's already graded and I got it wrong can you tell me the answer
The slope is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \text{let:} \\ (x1,y1)=(1,-17) \\ (x2,y2)=(5,-1) \\ m=\frac{-1-(-17)}{5-1}=\frac{-1+17}{4}=\frac{16}{4}=4 \end{gathered}[/tex]Identify the values of a, b, and c. b =
We have the following:
[tex]undefined[/tex]Drag the red and blue dots along the x-axis and y-axis to graph 7x+3y=127x+3y=12
Answer:
Explanation:
A linear equation can be graphed in a simple manner. We just have to find two points that lie on the line of the equation and then connect them to produce a line.
Now what two points lie on 7x + 3y = 12?
Well, let us pick a point where x = 0. What is the y-coordinate? Putting x = 0 into our equation gives
[tex]\begin{gathered} 7(0)+3y=12 \\ 3y=12 \end{gathered}[/tex]diving both sides by 3 gives
[tex]\begin{gathered} y=12/3 \\ y=4 \end{gathered}[/tex]Hence a point with x = 0, y= 4 lies on the line. In other words, (0, 4) lies on the line.
We now need to find a second point that lies on the line. How about
A 40 kilogram bag of seeds are spread out throughout the entire yard, how much in kilograms of seeds will not be watered? Percentage of my previous question is 96.1%In the last question 96.1% of grass was covered in water Their were 123 squares that got water except 5 of them so I divided 123 by 128 to find the percentage of grass covered by waterIf their were 5 squares that didn’t get water out of 128 then can’t we work from that? To find the 40 kilograms that wouldn’t get water from those 5 squares
5 squares of 128 didn't get water.
If 40kg are spread out throughout the entire yard, how much in kilograms of seeds will not be watered?
Use a rule of three to solve the question:
[tex]\begin{gathered} x=\frac{40\cdot5}{128} \\ \\ x=\frac{200}{128} \\ \\ x=1.56 \end{gathered}[/tex]Then, 1.56 kilograms of seeds will not be watered
Find the distance between the pair of parallel lines with the given equations.y = -5xy = -5x + 26A) 5 unitsOB) 10V2 or about 14.14 unitsOC)/26 or about 5.10 unitsO D) 6 units
For two lines of the form:
[tex]\begin{gathered} y_1=a_1x+c_1 \\ \text{And} \\ y_2=a_2x+c_2 \end{gathered}[/tex]The distance between the two lines is:
A random sample of 150 people are asked if they own dogs and 57 of them say yes what would you estimate the percentage of dog owners to be in this population
Answer:
38%
Step-by-step explanation:
Dog owners=57
Total population=157
Percentage of owners=(dog owners/total population) ×100=(57/157)×100=0.38×100=38%