Hi there!
Given an equation in point-slope form, explain how to determine the coordinates of its y-intercept.
The y-intercept of a line occurs when x=0. Replace x with 0 in the equation and solve for y to find the y-intercept.Given an equation or graph of a line, describe how to write an equation of a parallel line that goes through a given point.
Determine the slope of the line. In slope-intercept form [tex]y=mx+b[/tex], the slope would be [tex]m[/tex], and in point-slope form [tex]y-y_1=m(x-x_1)[/tex], the slope would be [tex]m[/tex] as well. Given a graph, it would be necessary to solve for the slope. Find two points and plug them into the equation [tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}}[/tex] as [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] to solve for the slope.Parallel lines always have the same slope. Now that we've just solved for the slope, plug it into [tex]y=mx+b[/tex].Now, all that's left to solve in the equation is [tex]b[/tex]. Plug the given point into [tex]y=mx+b[/tex] along with the slope and solve for [tex]b[/tex].Plug both the slope and y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation.Given an equation or graph of a line, describe how to write an equation of a perpendicular line that goes through a given point.
Determine the slope of the line.Perpendicular lines always have slopes that are negative reciprocals. To determine the slope of a perpendicular line, take the slope from step 1 and find its negative reciprocal. For example, the negative reciprocal of 2 is -1/2. Plug this slope into [tex]y=mx+b[/tex].Now, all that's left to solve in the equation is [tex]b[/tex]. Plug the given point into [tex]y=mx+b[/tex] along with the slope and solve for [tex]b[/tex].Plug both the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation.I hope this helps!
Simplify[tex]\frac{9x^{16} }{6(x^{2} )^{3}x^{2} } }[/tex]
Answer:
[tex]\displaystyle \frac{3x^8}{2}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex] Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex] Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{9x^{16}}{6(x^2)^3x^2}[/tex]
Step 2: Simplify
Exponential Rule [Powering]: [tex]\displaystyle \frac{9x^{16}}{6x^6x^2}[/tex]Exponential Rule [Multiplying]: [tex]\displaystyle \frac{9x^{16}}{6x^8}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{9x^8}{6}[/tex]Simplify: [tex]\displaystyle \frac{3x^8}{2}[/tex]With the help of scientists, farmers in the United Kingdom have been able to produce more and more grain per hectare each year. Here are the crop yields for several years:
Assuming that this trend continues, what crop yield is predicted for the year 2020 by the model? Round your answer to the nearest whole number. You must find the linear regression equation first.
A. 8,603 kg/ha
B. 8,232 kg/ha
C. 9,447 kg/ha
D. 7,382 kg/ha
Crop yield prediction in year 2020 is 9,447 kg/ha
What is linear regression ?Linear regression is an analytic statistical approach for predicting the relationships between an independent variable that determines the values of of or more dependent variables.
From the data given in the question
Equation of a straight line is y = a + bx
∑y = an + b∑x
∑xy = a∑x +b∑x²
The values are calculated in the table given below
X y x=X-1985 x² xy
1961 3090 -24 576 -74160
1968 4040 -17 289 -68680
1987 5830 2 4 11660
1992 5680 7 49 39760
2001 7630 16 256 122080
2004 8020 19 361 152380
_ _ _ _ _
∑x =11913 ∑y=34290 ∑x=3 ∑x²=1535 ∑xy=183040
Substituting the values
6a + 3b = 34290
3a + 1535b = 183040
solving the two by suitable elimination
6a + 3b = 34290
3(2a+b) = 3×11430
2a + b = 11430....(i)
and 3a + 1535b=183040....(ii)
a=173620/3067 = 5660.91
Putting a=5660.91 in (i)
2(5660.91) + b = 11430
b = 108.81
∴ a = 5660.91 and b = 108.81
Now substituting the values in the equation y=a+bx
y = 5660.91 + 108.81x
y = 5660.91 + 108.81(X-1985)
∴In 2020
y =5660.91 +108.81(2020 - 1985)
y = 9447.245
Learn more about Statistics here :
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A 42 gallon hot water tank hose 350 pounds of water what weight of water at 53 gallon tank hold
Answer:
441.66667 pounds
Step-by-step explanation:
divide 350/42 then multiply the quotient by 53
in order to apply the law of cosines to find the length of the side of a triangle, is it enough to know which of the following?
A. The area of a triangle
B. The lengths of two of the triangle's sides and the measure of the angle between them
C. At least two of the angles of the triangle and the length of one of its sides
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Answer:
B. The lengths of two of the triangle's sides and the measure of the angle between them
Step-by-step explanation:
The usual formulation of the law of cosines is something like this:
c² = a² +b² -2ab·cos(C)
where 'c' is the side opposite angle C, and 'a' and 'b' are the other two sides. That is, to use this formula directly, one needs two side lengths and the measure of the included angle.
_____
Additional comment
One can use the law of cosines to solve a triangle when any two sides and one angle are known. The use of the formula will give a quadratic in the unknown side length, if it is not the side opposite the known angle. As with the law of sines, if the angle is opposite the shorter of the two given sides, there may be two solutions for the length of the third side.
Answer:
The answer is B.)
Step-by-step explanation:
Find the ratio of A : B: C when
(a) A : B = 3 : 5 A : C = 6 : 7
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Answer:
A : B : C = 6 : 10 : 7
Step-by-step explanation:
The A value is common to both ratios. In order to form the ratio A:B:C we must have the number of ratio units representing A be the same in both A:B and A:C. That number must be the least common multiple of 3 and 6, which is 6.
Multiplying the first ratio by 2, we have ...
A : B = 6 : 10
A : C = 6 : 7
So, we can write the triple ratio as ...
A : B : C = 6 : 10 : 7
Convert the following fraction to a decimal.
1/3
A. 0.3
B. 0.03
C. 0.303
D. 3.9
Answer:
Option A, 0.3
Step-by-step explanation:
Step 1: Convert the fraction into a decimal
Technically, 1/3 is an irrational number meaning that it never ends. However, if we round it, it would round to 0.3 since 1/3 = 0.3333333.....
Answer: Option A, 0.3
the table shows linear relashonsips between x and y write an equation in slope intercept form for this relashonsip!!!!!!!!!!!!!!!!!!!!!!!
QUICK PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]y=-2x+6[/tex]
Step-by-step explanation:
Slope-intercept form is given as [tex]y=mx+b[/tex], where [tex]m[/tex] is slope and [tex]b[/tex] is the y-intercept.
To find the slope of a line that passes through two points [tex](x_1, x_2)[/tex] and [tex](y_1, y_2)[/tex], use the slope formula:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1, y_1)\implies (1, 4)\\(x_2, y_2)\implies (0, 6)[/tex]
The slope of the line that passes through these two points is:
[tex]m=\frac{6-4}{0-1}=\frac{2}{-1}=-2[/tex]
Now substitute [tex]m=-2[/tex] and any point to solve for [tex]b[/tex]:
[tex]y=mx+b,\\6=-2(0)+b,\\6=0+b,\\b=6[/tex]
Therefore, the slope-intercept form of a line that is represented by the table is [tex]\boxed{y=-2x+6}[/tex]
A man invested N80 at a certain rate of simple interest. If at the end of 5 years the money amounted to N88, what was the rate of simple interest paid?
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Answer:
2%
Step-by-step explanation:
The amount of interest is the difference between the total amount and the principal amount:
N88 -N80 = N8 . . . . the amount of interest
The interest amount is given by the formula ...
I = Prt
Solving for r, we find ...
r = I/(Pt) = 8/(80×5) = 1/50 = 2%
The rate of simple interest paid was 2%.
What is the length of PO
These are similar triangles, therefore their sides are proportional.
36 / 24 = PO / 36
24PO = 1296
PO = 54
Hope this helps!
Problem
Combine the like terms to create an equivalent expression:
y−(−3y)
please someone explain to me how to do this?
Find the measure of the missing angles.
WILL GIVE BRAINLIEST
Answer:
h= 60
g= 120
m= 147
k= 33
Step-by-step explanation:
We know that all three lines are straight an continuous, so, at any given point the angles should add up to 180 degrees.
This immediately helps with angle h:
120 + h = 180
h = 60
As well as m:
33 + m = 180
m = 147
There are two ways to solve the next part:
First and most familiar way:
h + g = 180
60 + g = 180
g = 120
and:
m + k = 180
147 + k = 180
k = 33
The other way that I prefer is that the angles opposite of each other when two lines intersect are equal. I don't know if that makes sense, it's hard to explain in this format.
Surface roughness of pipe. Refer to the Anti-corrosion Methods and Materials (Vol. 50, 2003) study of the sur- face roughness of coated interior pipe used in oil fields, Exercise 7.26 (p. 311). The data (in micrometers) for 20 sampled pipe sections are reproduced in the table on p. 391.
a. Give the null and alternative hypotheses for testing whether the mean surface roughness of coated interior pipe, H, differs from 2 micrometers.
b. The results of the test, part a, are shown in the MINITAB printout at the bottom of the page. Locate the test statistic and p-value on the printout.
The minitab report isn't given.
Answer:
H0 : μ = 2 um
H1 : μ ≠ 2 um
Step-by-step explanation:
The mean surface roughness of coated interior pipe is given as 2um.
This refers to the population mean, μ = 2 um
Therefore, the null hypothesis which usually aligns with the population mean value will be stated as :
H0 : μ = 2 um
The alternative hypothesis is used to test the claim that the mean surface roughness is different from 2 ; hence no direction is given, this is thus a 2 - tailed test
H1 : μ ≠ 2 um
Which of the following is another way of expressing 2 out of 8.
2.5%
25%
25
2.5
Pls help me
Answer:
it will be 25 percent
Step-by-step explanation:
divide 2 by 8
Answer: 25 %
Step-by-step explanation:
2/8
on simplifing we got 1/4 in fraction that is equal to 0.25 that is equal tp 25 % in percentage form.
Hope this will help you
Determine the big-O of the function: 1^k + 2^k +⋯+ n^k
While hovering near the top of Ribbon Falls in Yosemite National park at 1600 feet, a helicopter pilot accidentally drops his sunglasses. The height h(t) of the sunglasses after t second is given by the polynomial function h(t)=-16t^2+1600. When will the sunglasses hit the ground? (Hint: Let the height,h(t), be 0 and solve for t.)
Answer:
10 seconds
Step-by-step explanation:
Plug in 0 as h(t) and solve for t:
h(t) = -16t² + 1600
0 = -16t² + 1600
-1600 = -16t²
100 = t²
10 = t
So, the sunglasses will hit the ground after 10 seconds
2 2/3 +2 2/3 + 2 2/3 +2 2/3
Answer:
10.6666666667 is your answer
just round this to the nearest tenth
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Answer:
10 2/3
Step-by-step explanation:
Multiplication works nicely on problems involving repeated addition:
2 2/3 +2 2/3 + 2 2/3 +2 2/3 = 4 × (2 2/3) = 4×2 +4×2/3 = 8 +8/3
= 8 + 2 2/3 = 10 2/3
fill in each blank with a true statement
Answer:
See below.
Step-by-step explanation:
7.)
Supplementary angles add up to 180°. ∠B's supplement is 22°. This means ∠B is 158°. Since ∠A ≅ ∠B, the m∠A = 158°.
8.)
Again, supplementary angles add up to 180°. ∠P is a right angle meaning it is 90°. Therefore, the m∠Q is 90° as well.
9.)
Complementary angles add up to 90°. In order for ∠S and ∠T to be complementary, they both need to angle measurements less than 90° meaning they both need to be acute angles.
Now that we know that ∠T is acute, the only way ∠U can be its supplement is if it has an angle measure greater than 90°. Therefore, ∠U is an obtuse angle.
10.)
Similar to question 9, if an angle is obtuse, its supplement must be an acute angle.
Once again another one
Answer:
S = 23.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin S = opp / hyp
sin S = 4/10
sin S = 2/5
Taking the inverse sin of each side
sin^-1 ( sin S) = sin ^-1 (2/5)
S=23.57817
Rounding to the nearest tenth
S = 23.6
Can someone be my math teacher ? pls message
Answer:
which grade do you want to get helped by ?
Consider the function f(x)=10^x and function g. G(x)=f(x+4)
how will the graph of function g differ from the graph of function f?
A. The graph of function g is the graph of function f shifted 4 units down
B. Shifted 4 units to the left
C, shifted 4 units up
D. Shifted 4 units to the right
the top answer correct :)
Catriona spotted a major problem having to do with patient billing. A number of people may have received the wrong bills. When should she have told her boss? O a) When she was evaluating how to alert the patients O b) After she sent patient notices out c) When she first noticed the problem O d) After she decided on a communication plan
Answer:
C
Step-by-step explanation:
When she first noticed the problem
Graph the line. y = -5x + 1
What is a40
a
40
of the arithmetic sequence for which a8=60
a
8
=
60
and a12=48
a
12
=
48
?
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Answer:
-36
Step-by-step explanation:
Using the expression for the general term, you can fill in the known values and solve for the parameters of the sequence.
an = a1 +d(n -1)
a8 = a1 + d(8 -1) = 60
a12 = a1 + d(12 -1) = 48
The difference of these equations is ...
(a1 +7d) -(a1 +11d) = (60) -(48)
-4d = 12
d = -3
Substituting into the first equation, we have ...
a1 +7(-3) = 60
a1 = 81 . . . . . . . . . add 21
Then the 40th term is ...
a40 = 81 -3(40 -1) = 81 -117
a40 = -36
What does he call "Squaring"?
When someone has a funny head
When you double a number
When you multiply a number by itself
Answer:
when you multiply a number by itself
Step-by-step explanation:
Each day a cashier counts the number of pennies left in the "take a penny, leave a penny" dish. Estimate the probability that there are fewer than 4 pennies on any given day
1 3 5 17 4 9 1 9 2 8 20
A.11/7 B.4/11 C.7/11 D.3/11
Answer:
B.4/11
Step-by-step explanation:
hope it helps
consider making my answer as BRAINLIST
Part C of Jim and his dad are building a rectangular flower bed.
If Jim and his dad decide to decrease the width of the flower bed from 15 feet, what happens to its length?
The probability of someone ordering the daily special is 52%. If the restaurant expected 65 people for lunch, how many would you expect to order the daily special? Group of answer choices
Answer:32.5% fo people will buy
Step-by-step explanation:
mostly half of the people with order
Identify the first 4 terms in the arithmetic sequence given by the explicit formula ƒ(n) = 8 + 3(n – 1).
A) 8, 11, 14, 17
B) 3, 11, 19, 27
C) 8, 5, 2, –1
D) 3, –5, –13, –21
Answer:
A
Step-by-step explanation:
an arithmetic sequence adds a constant from every previous term to create the next term.
it starts with a first term, a1, meaning that n >=1
a1 = 8 + 3×(1-1) = 8 + 3×0 = 8
so, B and D are out.
the next term is a2.
a2 = 8 + 3×(2-1) = 8 + 3×1 = 11
and so, only A can be correct.
just to verify
a3 = 8 + 3×(3-1) = 14
a4 = 8 + 3×(4-1) = 17
and it also fits overall,
starting with 8, every new term is the previous term + 3.
Convert 0.181818 … to a fraction by writing the repeating decimal as an infinite geometric series. Show all of your work (please)
0.181818… = 18 (0.010101…)
… = 18 (0.01 + 0.0001 + 0.000001 + …)
… = 18 (1/100 + 1/100² + 1/100³ + …)
… = 18 (1 + 1/100 + 1/100² + 1/100³ + …) - 18
Then you have
[tex]0.181818\ldots = \displaystyle18\sum_{k=0}^\infty\frac1{100^k} - 18 = \frac{18}{1-\frac1{100}} - 18 = \boxed{\frac2{11}}[/tex]
FIND THE LENGTH OF MP
Answer:
D.21
Step-by-step explanation:
MP=MV - PV= 67 -46 = 21
