Answers
Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.
10x - 2y = 3
-2y = -10x + 3
-2y/-2 = -10x / -2 + 3/-2
y = 5x - 3/2
The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.
point slope form = y – y1 = m(x – x1)
Remember m = slope = 5. Now plugin our x and y cord from the point (0,1) and our slope of 5
y - y1 = m(x - x1)
y - 1 = 5(x - 0)
y - 1 = 5x - 0
y - 1+1 = 5x + 1
y= 5x + 1
So the point (0,1) passes through y = 5x + 1
Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.
8)
Point = (5,8)
Slope = 7
y - y1 = m(x - x1)
y - 8 = 7(x - 5)
y = 7x - 27
So for number 8 the point (5,8) passes through y = 7x - 27
(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.
Point = (-4, 6)
Slope = 2/5
perpendicular slope = 5/2
y - 6 = 5/2(x - (-4))
y = 5/2 x + 16
So point (-4, 6) passes through y = 5/2 x + 16
(10) Point (4,1) passes through y = 7/5 x - 23/5
7)
so is parallel to 10x-2y=3... now, let's solve that for "y", to put it in slope-intercept form
[tex]\bf 10x-2y=3\implies 10x-3=2y\implies \cfrac{10x-3}{2}=y \\\\\\ \stackrel{\textit{slope-intercept~form}}{\cfrac{5}{2}x-\cfrac{3}{2}}=y\impliedby \textit{slope is }\frac{5}{2}[/tex]
so then, we're looking for a line whose slope is 5/2 and passes (0,1)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 0}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=\cfrac{5}{2}(x-0)\implies y-1=\cfrac{5}{2}x \\\\\\ \boxed{y=\cfrac{5}{2}x+1}[/tex]
8)
now, is parallel to [tex]\bf y=\stackrel{slope}{7}x-6[/tex] , now, that's already in slope-intercept form, so the slope we can see is just 7, so then.
we are looking for a line whose slope is 7 passes (5,8)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 8}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 7 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-8=7(x-5)\implies y-8=7x-35 \\\\\\ y=7x-35+8\implies \boxed{y=7x-27}[/tex]
9)
well, this function is also already in slope-intercept form, so we can tell the slope is 2/5.
now, the line we're looking for, is perpendicular to it, so it has a negative reciprocal slope, let's check
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{5}\\\\ slope=\cfrac{2}{{{ 5}}}\qquad negative\implies -\cfrac{2}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{2}[/tex]
so, we're looking for a line whose slope is -5/2 and passes (-4,6)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -4}}\quad ,&{{ 6}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-6=-\cfrac{5}{2}[x-(-4)] \\\\\\ y-6=-\cfrac{5}{2}(x+4)\implies y-6=-\cfrac{5}{2}x-10\implies \boxed{y=-\cfrac{5}{2}-4}[/tex]
10)
let's solve for "y" first
[tex]\bf 5x-7y=44\implies 5x-44=7y\implies \cfrac{5x-44}{7}=y \\\\\\ \stackrel{slope}{\cfrac{5}{7}}x-\cfrac{44}{7}=y[/tex]
now, let's find the negative reciprocal of that
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{5}{7}\\\\ slope=\cfrac{5}{{{ 7}}}\qquad negative\implies -\cfrac{5}{{{ 7}}}\qquad reciprocal\implies - \cfrac{{{ 7}}}{5}[/tex]
so, we're looking for a line whose slope is -7/5 and passes (4,1)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 4}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{7}{5} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=-\cfrac{7}{5}(x-4)\implies y-1=-\cfrac{7}{5}x+\cfrac{28}{5} \\\\\\ y=-\cfrac{7}{5}x+\cfrac{28}{5}+1\implies \boxed{y=-\cfrac{7}{5}x+\cfrac{33}{5}}[/tex]
Related Questions
Express 9 - y2 as the product of two binomial factors
Answers
(3-y)(3+y)
[tex]3^2-y^2[/tex]
[tex](3+y)(3-y) [/tex]
The sum of three consecutive even integers is 72. Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.
Which equation can be used to find the first integer?
3x + 72 = 2x + 6
2x + 64 = 72
3x = 2x + 6
3x + 6 = 72
Answers
The equation 3 x + 6 = 72 be used to find the first integer.
Option 4 is true.
Here,
The sum of three consecutive even integers is 72.
Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.
We have to find equation which can be used to find the first integer.
What is Integers?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Now,
The sum of three consecutive even integers is 72.
So,
x + ( x + 2 ) + ( x+ 4 ) = 72
x + x + 2 + x+ 4 = 72
3x + 6 = 72
Hence, The equation 3 x + 6 = 72 be used to find the first integer.
Learn more about the Integers visit:
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A diver swims 5.875 feet up to the surface of the water. Which number represents the diver’s position in relation to the surface before swimming to the top?
Answers
In relation to the surface, before swimming up, the diver was -5.875 feet under the water. The negative sign implies that the diver was beneath the surface of the water.
Explanation:The diver's position in relation to the surface before swimming to the top is represented by a negative number because swimming upwards implies moving in a positive direction. In this case, the diver was -5.875 feet from the surface before they started swimming up. This negative sign indicates that the diver was beneath the surface of the water.
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Bill can mow his mother's lawn in 45 minutes. his brother jim can mow it in 65 minutes. how long will it take them to do it together, if each has his own lawnmower? (record your answer in minutes rounded to one decimal place.
Answers
1 hour and 50 minutes
P(n) models the fundraiser's profit (in dollars) if n tickets are sold. A negative profit means the expenses exceeded the income from tickets.
P(n) = 70n-1500
what is the price of a single ticket
Answers
profit = revenue - expenses
so the revenue, what is made from selling tickets.....70n....where n represents the number of tickets....the 70 represents the cost of each ticket.
the 1500 is the expenses. So for them to make a profit, they would have to sell more then $ 1500 worth of tickets.
the price of a single ticket is $ 70 <==
The price of a single ticket is given by the expression [tex]\( \frac{70n - 1500}{n} \),[/tex] where n represents the number of tickets sold.
To find the price of a single ticket, we need to understand that the profit P(n) represents the income from ticket sales.
In the given equation [tex]\( P(n) = 70n - 1500 \)[/tex], n represents the number of tickets sold, and P(n) represents the profit from selling n tickets.
If we divide the total profit P(n) by the number of tickets n, we can find the price of a single ticket.
So, the price of a single ticket is given by:
[tex]\[ \text{Price of a single ticket} = \frac{P(n)}{n} \][/tex]
Substituting [tex]\( P(n) = 70n - 1500 \)[/tex], we get:
[tex]\[ \text{Price of a single ticket} = \frac{70n - 1500}{n} \][/tex]
Now, the price of a single ticket is dependent on the number of tickets sold, so we cannot determine a specific price without knowing the value of n. However, we can say that as the number of tickets sold increases, the price per ticket decreases due to the fixed costs (expressed by the constant term -1500) being spread out over a larger number of tickets.
Simplify r^4st^7 / 5r^5st^3
Simplify 7x^3y^9z^4 /28x^8y^2
Simplify 3a^3b * 2a^2b^4 / a^10b^3c^2
Explain if you can thankyou!!
Answers
1) r^4st^7 / 5r^5st^3 = st^4 / 5r
2) 7x^3y^9z^4 /28x^8y^2 = y^7z^4 /4x^5
The last one you need to multiply the factors first (add exponents of common factors)
3) 3a^3b * 2a^2b^4 / a^10b^3c^2 = 6a^6b^5/a^10b^3c^2 = 6b^2/a^4c^2
Hope this helps, let me know if you need more explanation!
After working 80 hours at his job, Tyler earned a total of $1100. How much does Tyler earn per hour?
Answers
1100/80=13.75
there ya have it Tyler makes $13.75 per hour
What is the algebraic expression for the following word phrase: the quotient of j and 8
A.j-8
B.j+8
C.j
-
8
D.8j
Answers
[tex] \frac{j}{8} [/tex]
This is the correct algebraic expression for the quotient of j and 8. Quotient is just a fancy term for the answer to a division problem.
Answer:
[tex]\frac{j}{8}[/tex]
Step-by-step explanation:
the quotient of j and 8
We need to write the given word phrase in algebraic expression
Algebraic expression contains terms with numbers and variables with operators in between.
In the given word phrase , 'j' is the variable
quotient occurs only on division . so we divide 'j' and 8
The expression for word phrase the quotient of j and 8 is
[tex]\frac{j}{8}[/tex]
Leslie needs to roll an 8 with 2 dice to win a game. how many possible outcomes are there for her to win?
Answers
2+6
3+5
3 if im not mistaken
Answer: 5
Step-by-step explanation:
Given : Leslie needs to roll an 8 with 2 dice to win a game.
Number of outcomes , when we roll a die {1 ,2,3,4,5,6} =6
When we roll two dice the total number of outcomes are:
[tex]6\times6=36[/tex]
The possible outcomes when we roll two dice :-
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The favorable outcomes to get sum as 8 :-
{(2,6), (6,2), (3,5), (5,3), (4,4)}
Hence, the number of possible outcomes are there for her to win = 5
when ms. morley was three times as old as jennie, they were seven years younger than they are now. now Ms morkie is twice as old as jennie. how old are they?
Show your work
Answers
__________ will produce an irrational answer when added to , because __________.
Answers
Through 3,1 slope -1
Answers
y-1=-x+3
y=-x+4
The endpoints of line segment RS are R(-2,-1), and S (2,3). Find the coordinates of the midpoint of line segment RS.
Answers
= (0,1) Answer
A fair coin is tossed 10 times. what is the probability of (a) five heads; (b) at least five heads?
Answers
Answer:
Are these all of the options to pick from for this question? If so, then your answer would be A.) five heads.
Explanation:
PLATO
Leon correctly found the slope and y-intercept of the line that passes through the points (9, –8) and (3, 4) as follows.
m = -8, -4 = -12
9-3 -6 =-2
y = -2x+b
-8=-2(9)+b
-8= -18+b
10=b
a)y=-2x+10
B) y=-2x+10
C) y= 10x-2
D)y=10x +2
Answers
Answer:
[tex]\displaystyle y = -2x + 10[/tex]
Step-by-step explanation:
The work is already done. This is EXACTLY how you find the parallel line, however, two answer choices are an EXACT REPLICA of each other. Perhaps there was a typographical error?
I am joyous to assist you anytime.
the correct answer is option
a)y=-2x+10.
How do you locate the slope?pick factors on the line and decide their coordinates. determine the difference in y-coordinates of these two factors (upward thrust). determine the difference in x-coordinates for those two factors (run). Divide the difference in y-coordinates by means of the difference in x-coordinates (upward thrust/run or slope).
How do u find slope-intercept shape?resolve for the slope (m). recollect, the slope is equal to the alternate in y divided with the aid of the change in x (upward push overrun).remedy for the y-fee of the y-intercept (b). replace m and b with their values inside the y=mx+b system.Learn more about slope-intercept shape here: https://brainly.com/question/1884491
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the sum of 18 and the number of x in algebriac expression
Answers
Simplify -|-5 + 2|.
a)-7
b)-3
c)3
d)7
Answers
if it would have been | - (-5 + 2) | ur answer would have been 3 because the negative sign fell in ur absolute value bars.
[tex]-|-3|[/tex]
Step 2. Simplify [tex]|-3|[/tex] to [tex]3[/tex]
[tex]-3[/tex]
Done! :)
A ball is launched into the sky at 19.6 feet per second from a 58.8 meter tall building. The equation for the ball’s height, h, at time t seconds is h = -4.9t2 + 19.6t + 58.8 . When will the ball strike the ground?
Answers
Is that a typo, or a real mixture of units?
The equation is only good if the launch speed is actually 19.6 m/s, so I'll assume that.
It will strike the ground when the ball's height = 0 m !!!
-4.9t² +19.6t + 58.8 = 0
You can always use the "quadratic formula" if you want to, but ...
This set of numbers is beloved by physics teachers everywhere. Everything divides by -4.9
t² - 4t -12 = 0
...and factorizes easily:
(t + 2)(t - 6)
So t = 6 or t = -2 Disregard the negative solution.
The ball will strike the ground at t = 6 seconds
What is the period of the function y=5/2 cos x/4?
Answers
...............................
During a storm, why do you see the flash of lightning before you hear the roar of thunder? What would it mean if you saw the flash of lightning and heard the roar of thunder at the same time? What would it mean if there were many seconds in between the flash of lightning and the roar of thunder?
Answers
T/5=miles away when T is time from the strike of lightning to hearing thunder
Final answer:
You see lightning before hearing thunder due to the faster speed of light compared to sound. A simultaneous occurrence suggests the lightning is very close, while a delay indicates distance, with every five seconds equaling approximately one mile.
Explanation:
During a storm, you see the flash of lightning before you hear the roar of thunder because light travels much faster than sound. Lightning, a massive discharge of electricity, heats and expands the air rapidly, creating the sound of thunder. The difference in the travel speeds of light (3 × 10⁸ meters per second) and sound means that we perceive these events at different times.
If you saw the flash of lightning and heard the roar of thunder at the same time, it would mean that the lightning strike occurred very close to your location, practically overhead. Conversely, a noticeable delay between the flash of lightning and the sound of thunder indicates that the lightning strike is farther away. Each 5-second gap between seeing lightning and hearing thunder equates to approximately one mile distance from the lightning strike.
To estimate the distance of a storm, you only need to know the speed of sound, as the speed of light is so fast that the time it takes for light to reach you is negligible for this calculation. This method of estimating distance helps understanding the physical phenomena and ensuring safety during storms.
whatt are some inportant rules to dividing and multipling positives and negitives.
Answers
3 × 2 = 6
m × n = mn
Positive × Negative = Negative
8 × -4 = -32
m × -n = -mn
Negative × Negative = Positive
-5 × -4 = 20
-m × -n = mn
(-x) × (-x) = x²
The same rules apply for division as multiplication.
A baseball team has home games on thursdaythursday and saturdaysaturday. the two games together earn $4285.004285.00 for the team. thursdaythursday's game generates $295.00295.00 less than saturdaysaturday's game. how much money was taken in at each game?
Answers
1,995+1,995=3,990
3,990+295=4,285.00
Evaluate the expression. Drag the answer into the box to match the expression. 27⋅((33)−1) 27 3 1 1/9
27
3
1
1/9
Answers
3^3 = 27
27^-1 = 1/27
1/27 x 27 = 1
I took this test and got this question right.
Answer:
Step-by-step explanation:
answer is 1
What makes an irrational number irrational?
Answers
Answer:
Step-by-step explanation:
Is an equation with an integer coefficient will always have an integer solution true or false?
Answers
4 x = 5 ( 4 is an integer coefficient )
x = 5 : 4 = 1.25 ( not an integer )
Answer:
This is false.
A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a _____ conjecture. transformation. tessellation. composition.
Answers
Answer:A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.
Step-by-step explanation:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes are called tiles, without overlaps or gaps.They can be generalized to higher dimensions and a variety of geometries.Therefore, A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.
The gcf of 25 and 12 is 1.number with 1 as the gcf are called relatively prime.find another pair of numbers whose gcf is 1
Answers
The GCF of 25 and 12 is 1, which means they are relatively prime. Another example of a pair of relatively prime numbers is 8 and 15, as their only common divisor is 1.
The greatest common factor (GCF) of 25 and 12 is 1. Numbers that have a GCF of 1 are called relatively prime. Another pair of numbers whose GCF is 1 could be 8 and 15. To verify, we look for any common divisors. The divisors of 8 are 1, 2, 4, and 8 while the divisors of 15 are 1, 3, 5, and 15. The only common divisor is 1, which confirms they are relatively prime.
I REALLY NEED THIS ONE IT'S MY LAST ONE.
Verify the identity. Justify each step.
please help and show your work.
Answers
[tex]\bf \cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}-\frac{cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}+\frac{cos(\theta )}{sin(\theta )}}\implies \cfrac{\frac{1}{cos(\theta )}}{\frac{1-cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1+cos(\theta )}{sin(\theta )}} \\\\\\ \cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1-cos(\theta )}-\cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1+cos(\theta )}[/tex]
[tex]\bf \cfrac{sin(\theta )}{cos(\theta )[1-cos(\theta )]}-\cfrac{sin(\theta )}{cos(\theta )[1+cos(\theta )]} \\\\\\ \cfrac{sin(\theta )[1+cos(\theta )]~-~sin(\theta )[1-cos(\theta )]}{cos(\theta )[1+cos(\theta )][1-cos(\theta )]} \\\\\\ \textit{notice that }[1+cos(\theta )][1-cos(\theta )]\textit{ is a difference of squares}[/tex]
[tex]\bf \cfrac{\underline{sin(\theta )}+sin(\theta )cos(\theta )\underline{-sin(\theta )}+sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]} \\\\\\ \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]}\\\\ -------------------------------\\\\ \textit{recall that }sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\qquad thus\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[sin^2(\theta )]}\implies \cfrac{2\underline{sin(\theta )cos(\theta )}}{\underline{cos(\theta )sin(\theta )} sin(\theta )}\implies \cfrac{2}{sin(\theta )} \\\\\\ 2\cdot \cfrac{1}{sin(\theta )}\implies 2\cdot csc(\theta )\implies 2csc(\theta )[/tex]
How to get the B by itself
Answers
(a + b + c)/3 x 3 = A x 3
a + b + c = A(3)
a- a + b + c - c = A(3) - a - c
b = A(3) - a - c
hope this helps
( i dont know if the A is suppose to be there or not sorry)
Martin is logging the number of strikes he bowls per hour. He has determined the function to be f(x) = 2x + 5, where x represents hours and f(x) represents the number of strikes he has bowled. Which of the following options describes the restrictions to the domain and range correctly?
Domain, nonnegative values; range, values greater than −2.5
Domain, nonnegative values; range, values greater than or equal to 5
Domain, nonnegative values; range, values less than −2.5
Domain, nonnegative values; range, values less than or equal to 5
Answers
range (f(x) values are : values greater then or equal to 5
Answer:
B. Domain, nonnegative values; range, values greater than or equal to 5
Step-by-step explanation:
Basically, domain is the set of values that x can take and range is the set of values that the result of f(x) can be.
Since x is the time Martin spends bowling, it cannot be negative. The least he can bowl is zero hours, so x cannot be a negative number.
For the lowest x can be (zero), f(x) is calculated as:
f(x) = 2(0)+5 = 0+5 = 5
For higher values of x, the equation can only yield higher results because the 2 that is multiplying it is positive. Multiplying a two positive numbers (2 and x, which cannot be negative) will always give a positive number. In other words, f(x) is directly proportional to x because its coefficient 2 is positive, which means that when x grows, f(x) grows.
This means that f(x) can never be lower than 5.
The best description is, then, nonnegative values for the domain and values greater or equal to 5 for the range.