Which equation is parallel to the line LaTeX: y=\frac{1}{2}x+3y = 1 2 x + 3and passes through the point (10, -5)?
Group of answer choices
Plz help asap thank you!!
Answers
Answer:
[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]
Step-by-step explanation:
[tex]Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c[/tex]
[tex]-5=-5+c\\\\c=-10[/tex]
[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]
Related Questions
GL Stats: lviixea conrldence Intervals Practice
On each problem, verify that the conditions for a confidence interval are met!
(1) Suppose the height of senior girls at Anytown High School is known to be normally distributed. A sample of
leights in inches of 23 randomly selected senior girls were: 63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60,
66, 67, 68, 66, 70, 79, 76, 75, 65. Construct and interpret a 99% confidence interval for the true mean height
Answers
Answer:
99% Confidence interval: (63.65,69.65
Step-by-step explanation:
We are given the following data:
63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60, 66, 67, 68, 66, 70, 79, 76, 75, 65
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{1533}{23} = 66.65[/tex]
Sum of squares of differences = 575.217
[tex]S.D = \sqrt{\dfrac{575.217}{22}} = 5.11[/tex]
99% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 22 and}~\alpha_{0.01} = \pm 2.818[/tex]
[tex]66.65 \pm 2.818(\dfrac{5.11}{\sqrt{23}} ) = 66.65 \pm 3.002 = (63.65,69.65)[/tex]
What is 2/15+8/15 in simplest form
Answers
Answer:2/3
Step-by-step explanation:
So you add 8 plus 2 And keep the denominator the same and then simplify with 5
how do you add and subtract
Answers
Passing through (-6, -1) and PARALLEL 2x + 3y = 3
Answers
Answer:5
Step-by-step explanation:
I have 60 coins both quarters and dimes. The combined total is 9.45. What are two equations I can use to solve this problem?
Answers
Answer:
q+d = 60.25q +.10d = 9.45Step-by-step explanation:
Assuming the problem you want to solve is finding the number of each coin, you can let variables represent those numbers. I like to use mnemonic variables, such as q for the number of quarters, and d for the number of dimes.
The two equations you can write are based on the given information:
q + d = 60 . . . . . . you have 60 coins
.25q +.10d = 9.45 . . . . . their value is 9.45
_____
You have 23 quarters and 37 dimes.
_____
I like to solve these by substitution, using an expression to replace the variable representing the lowest-value coin.
d = 60 -q . . . . . . . expression for the number of dimes
.25q +.10(60 -q) = 9.45
.15q +6.00 = 9.45 . . . . . eliminate parentheses, collect terms
.15q = 3.45 . . . . . . . . . . .subtract 6.00
q = 23 . . . . . . . . . . . . . . . divide by 0.15
d = 60 -q = 37
What is the slope of (0,1) and (5,4)
Answers
Answer:
3/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-1)/(5-0)
m=3/5
Choose one of the theorems about chords of a circle and state it using your own words.
Create a problem about chords that uses the theorem that you explained.
Answers
See the explanation
Explanation:Theorem:
A perpendicular dropped from the center of the circle to a chord bisects it. It means that both the halves of the chords are equal in length.
In my own words, I'd explain this by drawing a circle and the diameter of the circle drawn in red. Also, we have a chord of the circle drawn in blue. The theorem says that the diameter bisects the chord in a right angle, so we will have two halves that measure the same so that's why we drew two hash marks on each half of the chord.
A problem about this is indicated in figure 2. Suppose you have a perpendicular dropped from the center of the circle to a chord and you know that the left half measures 2 cm, so we want to know the x-value of the right half. Since the diameter bisects the chord, then it is true that [tex]x=2cm[/tex] as well.
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Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles, Find the probability of selecting one green marble from bag A and one black marble from bag B.
Answers
Answer:
3/20
Step-by-step explanation:
Prob. (For green (Bag A)) = 3/12
Prob. (For Black (Bag B)) = 9/15
3/12 x 9/15 = 3/20
The probability of selecting one green marble from bag A and one black marble from bag B is 0.15
There are 3 green marbles in bag A out of a total of 12 marbles (i.e. 3 green and 9 red).
So, the probability of selecting a green marble from bag A is:
[tex]Pr = \frac 3{12}[/tex]
There are 9 black marbles in bag B out of a total of 15 marbles (i.e. 9 black and 6 orange).
So, the probability of selecting a black marble from bag B is:
[tex]Pr = \frac 9{15}[/tex]
The required probability is then calculated as:
[tex]P = \frac 3{12} * \frac 9{15}[/tex]
Multiply
[tex]P = 0.15[/tex]
Hence, the probability of selecting one green marble from bag A and one black marble from bag B is 0.15
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What is the value of X: X^2=9/144
Answers
Answer:
3/12
Step-by-step explanation:
To solve this problem, we can use square roots. Due to x being squared, we can square root both the top and the bottom. The square root of 9 is 3 with 144 being 12. In the end, x equals 3/12
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{What\ is\ the\ value\ of\ x: x^2=\dfrac{9}{144}\ ?}[/tex]
[tex]\mathsf{First,\ you\ have\ to\ simplify\ both\ sides\ of\ your\ equation!}[/tex]
[tex]\mathsf{\dfrac{9}{144}= \dfrac{9\div9}{144\div9} = \boxed{\dfrac{1}{16}}}[/tex]
[tex]\mathsf{New\ equation\ (for\ now): x^2=\dfrac{1}{16}}[/tex]
[tex]\mathsf{Take\ your\ square\ root!}[/tex]
[tex]\mathsf{x=\pm\sqrt{\dfrac{1}{16}}}[/tex]
[tex]\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: x =0.25\ or\ x = -0.25}}}[/tex][tex]\boxed{\boxed{\checkmark}}[/tex]
[tex]\boxed{\boxed{\boxed{\mathsf{You\ could\ also\ say\ x= \dfrac{3}{12}\ or\ x=-\dfrac{3}{12}}}}}[/tex][tex]\boxed{\boxed{\boxed{\checkmark}}}[/tex]
[tex]\mathsf{Side\ note: that's\ when\ the\ plus\ or\ minus\ sign\ (\pm)\ came\ in\ handy!}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
What is the area of a triangle with A = 15°, B= 113', and b = 7?
a. 3.8 units
c. 5.4 units
b. 4.2 units
d. 4.4 units
Answers
Answer:
The answer is C, 5.4 units
Step-by-step explanation:
What’s the slope for Y=8x+2
Answers
Rewrite the following as a mix numbers 17/3
Answers
answer is 5 2/3.............
Answer:
5 2/3
Step-by-step explanation:
answer key for middle school math with pizzazz! book d d-47
Answers
Answer:
hola
Step-by-step explanation:
The sum of two numbers is 18. Three times the greater number exceeds four times the smaller number by 5. Find the numbers
Answers
Answer:
6 1/8 and 11 7/8
Step-by-step explanation:
Just use algebra. x+y is equal to 18. 3x=4y+5. Then you substitute the value x for y by dividing by three. From there it is just computation
Answer:
The numbers are 11 and 7
Step-by-step explanation:
Let the numbers be P and V
Let P be the greater number and V be the smaller number.
From the question, the sum of the numbers equals 18 i.e
P + V = 18
Also from the question,
We were told that three times the greater number exceeds four times the smaller number by 5 i.e
3P = 4V + 5
P = (4V + 5) / 3
Substituting the value of P into equation (1), we obtain:
P + V = 18.
(4V + 5) / 3 + V = 18
Multiply through by 3 to express in linear form, we have:
4V + 5 + 3V = 54
Collect like terms
4V + 3V = 54 - 5
7V = 49
Divide both side by the coefficient of V i.e 7
V = 49/7
V = 7
P + V = 18
P = 18 - V
P = 18 - 7
P = 11
The numbers are 11 and 7
100 increased by 3.1%
Answers
Answer:
103,1
Step-by-step explanation:
Use this formula: 100*(1+3.1%)
17. WEATHER Heavy rain in Brieanne's town caused the river to rise. The river rose three
inches the first day, and each day after rose twice as much as the previous day. How
much did the river rise in five days?
Answers
Answer:
30
Step-by-step explanation:
It states that it rained twice as much in 5 days all you do is multiply the 2 times 3 which is 6 so then u multiply 6 times 5 which is 30.
The river rose a total of 93 inches over five days.
The question asks how much a river rises in five days given a certain pattern of increase. To find the solution, we use a geometric sequence because the river rises by a constant multiple each day. On the first day, the river rises three inches. Since on each subsequent day the river rises by twice the amount it did the previous day, the sequence of increases over five days is: 3 inches, 6 inches, 12 inches, 24 inches, and 48 inches.
The total rise of the river is the sum of these increases:
3 + 6 + 12 + 24 + 48 = 93 inches.
Therefore, the river rose a total of 93 inches over the span of five days.
An Investment of $2,000 is earning interest at the rate of 6.2% compounded quarterly over 5 years. Approximately how much
interest is earned on the investment?
Answers
Answer: $720.37
Step-by-step explanation:
interest = 2000(1.0155)^20 - 2000
= 720.37
Hope this helps!!! Good luck!!! :)
what is 6(5−8v)+12=−54
Answers
Answer:
v = 2
Step-by-step explanation:
After traveling 345 miles, the
Johnston family stopped at a
rest stop for lunch. Looking at
the map, they realized they had
completed of the trip. If d
represents the total distance in
miles, which equation can be
used to find d ?
Answers
Answer:
3/5 x d = 345
Step-by-step explanation:
got the question right on the quiz
The expression 210,000\left(1.02\right)^x210,000(1.02)
x
models the estimated home value after x years. Which statement is the correct representation of the 1.02 in the expression?
The house has a starting value of 1.02.
The house is decreasing in value by 2% each year.
The house is increasing in value by 2% each year.
The value of the house is changing by 0.02% each year.
Answers
Answer:
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
Step-by-step explanation:
For this case if we have this expression
[tex] 210000(1.02)^x[/tex]
We have the same functional forma like the exponential model given by:
[tex] y = a b^x[/tex]
Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.
So let's analyze the possible options:
The house has a starting value of 1.02.
False the starting value for this case is 210000 since if x=0 then we see that the value is 210000
The house is decreasing in value by 2% each year.
False the increase is 1.02 each year so then in % we have
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
We have an increase of 2% each year
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
The value of the house is changing by 0.02% each year.
False the increase is 2% per year
: Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck was in the amount of $6,500, including her salary of $1,000. Her sales for the week totaled $25,000. Express her rate of commission as a percent. Round to the nearest whole number.
Answers
Answer:
[tex]Rate\ of\ commission=22\%[/tex]
Step-by-step explanation:
Let her rate of commission[tex]=x\%[/tex]
Salary[tex]=\$ 1000[/tex]
Weekly Amount[tex]=\$ 6500[/tex]
So earning from commission=Weekly Amount-Salary
Earning from the commission[tex]=6500-1000[/tex]
Earning from the commission[tex]=\$ 5500[/tex]
Total Sales[tex]=\$ 25000[/tex]
Commission is[tex]=x\%\ of\ 25000[/tex]
[tex]x\%\ of\ 25000=5500\\\\\frac{x}{100}\times 25000=5500\\\\x\times 250=5500\\\\x=\frac{5500}{250}\\\\x=22\%[/tex]
[tex]Rate\ of\ commission=22\%[/tex]
You volunteer at an animal shelter on the weekends and today is adoption day! At the beginning of the event, you start with 44
44
cats/kittens.
x
number of cats/kittens get adopted. But then, at the end of the day, someone drops off twice as many new cats/kittens as were adopted. You now have 50
50
cats/kittens.
How many
cats/kittens were adopted.
Answers
6 cats/kittens were adopted.
Step-by-step explanation:
Given,
Number of cats/kittens at the event = 44
Number of cats/kittens adopted = x
Number of cats/kittens returned = Twice returned as adopted = 2x
New total = 50
We will subtract the adopted and add the returned cats/kittens.
Total cats/kittens at event - adopted + returned = New total
[tex]44-x+2x=50\\44+x=50\\x=50-44\\x=6[/tex]
6 cats/kittens were adopted.
Keywords: expression, variables
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4. Which of the following points are solutions to the system of inequalities 2x - 3y > 9 and -x -
4y > 8?
• (-1,-3)
(1,3)
(-1,3)
(1,-3)
Answers
Answer:
(1, -3)
Step-by-step explanation:
30 divided by 18 into improper fraction
Answers
Answer:
5/3
Step-by-step explanation:
30/18
you can easily simplify a large improper fraction by finding a common number.
in this case the number is 6.
6x5=30 & 6x3=18
therefore, if you divide each number by 6 you get 5/3
decimal: 1.66667 or 1.67 or 1.7
improper fraction: 5/3
proper fraction 1 2/3
Final answer:
30 divided by 18 as an improper fraction is ⅓, or 5/3, obtained by converting the division result into a mixed number and then back into an improper fraction.
Explanation:
To convert 30 divided by 18 into an improper fraction, you first divide 30 by 18 to get the decimal form, which is approximately 1.666. To express this as an improper fraction, we recognize that 1.666 is 1 and 2/3 in mixed number form.
Since 2/3 is already a fraction, we can convert the mixed number back into an improper fraction by multiplying the whole number 1 by the denominator 3 and then adding the numerator 2. This gives us 3 + 2 = 5, so the improper fraction is 5/3.
Solve for y. y + 1.05 = 7.26 y = -6.21 y = -8.31 y = 6.21 y = 8.31
Answers
To solve for 'y' in the equation 'y + 1.05 = 7.26', subtract 1.05 from both sides of the equation, the answer is 'y = 6.21'.
Explanation:In mathematics, solving for 'y' involves rearranging the equation to isolate the 'y' variable. In this case, the equation is 'y + 1.05 = 7.26'.
To solve for y, begin by performing the inverse operation of addition on both sides of the equation. This means subtracting 1.05 from both sides.
After doing so, the equation would look like this:
So the solution for y in this equation is 6.21.
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Which expression is equivalent to (x3 · x2)5? x10
Answers
Step-by-step explanation:
The given expression is
[tex]x^3.x^2[/tex]
To write the given expression is equivalent = ?
The given expression is
[tex]x^3.x^2[/tex]
We know that,
The exponential identity,
[tex]a^{m}.a^{n}=a^{m+n}[/tex]
= [tex]x^{3+2}[/tex]
= [tex]x^{5}[/tex]
∴ The given expression is equivalent = [tex]x^{5}[/tex]
Thus, the given expression is equivalent to [tex]x^{5}[/tex].
You can also see:
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Answer:
The answer to (x3*x2)5 is x25
Step-by-step explanation:
Give each trig ratio as a fraction in simplest form.
1 point
Sin A=
Sin A=
Your answer
Answers
[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]
Explanation:The trigonometric functions are very important in math and physics. Sound, light and electricity all involve oscillations and are modeled by sine and cosine functions. So, we can provide a trig ratio for the sine and cosine function by taking a right triangle as shown in the figure below. So the relationships are as follows:
[tex]sinA=\frac{Opposite \ side}{Hypotenuse} \\ \\ cosA=\frac{Adjacent \ side}{Hypotenuse} \\ \\ \\ For \ the \ figure: \\ \\ a:Opposite \ side \\ \\ b:Adjacent \ side \\ \\ c:Hypotenuse[/tex]
So we can write:
[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]
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write an equation in slope - intercept form, and then find the slope and y- intercept 3x-y=14
Answers
Answer:
slope-intercept form: y = 3x - 14
slope: 3
y-intercept: -14
Step-by-step explanation:
To find the equation in slope-intercept form, isolate the "y" variable by moving everything to the other side. Slope-intercept form looks like y = mx + b.
"x" and "y" mean points that are on the line.
"m" is the slope.
"b" is the y-intercept.
Rearrange the equation to isolate "y"
3x - y = 14
3x - 3x - y = 14 - 3x Subtract 3x from both sides
-y = 14 - 3x Multiply both sides by -1.
y = -14 + 3x Put "3x" in front of "-14" because it has the 'x'
y = 3x - 14 Looks like y = mx + b
State the "m" and "b".
m = 3 (Slope of the line)
b = -14 (y-intercept of the line)
Therefore the equation of the line in slope-intercept form is y = 3x - 14. The slope is 3 and the y-intercept is -14.
A family ordered some candy bars and bags of chips for snacking. The number of candy bars was twice as much as the number of bags of chips. If the family spent a total of $5.50, how many bags of chips did the family buy?
Answers
Answer:
The family bought approximately 2 bags of chips.
Step-by-step explanation:
Given:
Total spent by family = $5.50
We need to find bags of chips did the family buy.
Solution:
Let number of bags of chips bought be 'x'.
Also Given:
The number of candy bars was twice as much as the number of bags of chips.
number of candy bars = [tex]2x[/tex]
Now we can say that;
Total spent by family is equal to sum of the number of bags of chips bought and number of candy bars.
framing in equation form we get;
[tex]x+2x=5.5\\\\3x=5.5[/tex]
Dividing both side by 3 we get;
[tex]\frac{3x}{3}=\frac{5.5}{3}\\\\x=1.83\approx2[/tex]
Hence the family bought approximately 2 bags of chips.
The student council is planning the school carnival. Each ticket costs $2.50. Explain how to write an equation that represents this scenario. Let x represent the number of tickets sold, and y represent the total amount of money raised.
Answers
Answer:
Step-by-step explanation:
Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.
Answer:
y=2.5x
The total amount of money raised(y) = how many tickets are sold(x) x the price per ticket(2.5)
Hypothetically, if 24 tickets were sold, we could substitute 24 into x...
y=2.5(24)
y=60
Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.
The x variable represents the number of tickets sold.
The y variable represents the total amount of money raised from ticket sales.
The equation for the scenario is y = 2.50x.