[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[5-(-3)]^2+[-6-2]^2}\implies d=\sqrt{(5+3)^2+(-8)^2} \\\\\\ d=\sqrt{8^2+8^2}\implies d=\sqrt{2(8^2)}\implies d=8\sqrt{2}[/tex]
The distance between (-3, 2) and (5, -6) is [tex]\(8\sqrt{2}\)[/tex] units.
The distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in a two-dimensional Cartesian plane can be found using the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
In this case, the points are (-3, 2) and (5, -6). Let's plug in these values into the formula:
[tex]\[ d = \sqrt{(5 - (-3))^2 + ((-6) - 2)^2} \][/tex]
Simplify the expression inside the square root:
[tex]\begin{aligned}& d=\sqrt{(5+3)^2+(-8)^2} \\& d=\sqrt{8^2+64} \\& d=\sqrt{64+64} \\& d=\sqrt{128} \\& d=8 \sqrt{2}\end{aligned}[/tex]
Which property of inequality should you use to solve 3x ≤ 27?
division property would help you solve this inequality
Which of the following could be a function with zeros of -3 and two?
Answer:
x^2+x-6
Step-by-step explanation:
We just find the factored form of the equation which would be (x+3)(x-2).
Then we multiply it out to get x^2+x-6
What is the length of segment AB
A. 5
B. 6
C. 8
D. 10
Answer:
D. 10Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the graph we have the points A(6, 2) and B(0, 10). Substitute:
[tex]AB=\sqrt{(0-6)^2+(10-2)^2}=\sqrt{(-6)^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]
The length is D. 10
√ (x2 - x1)^2 + (y2 - y1)^2
√ (0-6)^2 + (10 - 2)^2
√ (-6)^2 + (8)^2
√ 36 + 64
√ 100 = 10
What is the solution to the system of equations? 3x-6 = -12
x-2y = -8
(a) Use the substitution method to justify that the given system of equations has no solution.
(b) What do you know about the two lines in this system of equations?
Answer:
Part a) In the procedure
Part b) Line A and Line B are different parallel lines
Step-by-step explanation:
Part a) we have
[tex]3x-6y=-12[/tex] ----> equation A
[tex]x-2y=-8[/tex] ----> equation B
Isolate the variable x in the equation B
[tex]x=2y-8[/tex]
Substitute the value of x in the equation A
[tex]3(2y-8)-6y=-12[/tex]
[tex]6y-24-6y=-12[/tex]
[tex]-24=-12[/tex] ------> is not true
therefore
The system of equations has no solutions
Part b) What do you know about the two lines in this system of equations?
[tex]3x-6y=-12[/tex] ------> equation A
isolate the variable y
[tex]6y=3x+12[/tex]
[tex]y=(1/2)x+2[/tex]
[tex]x-2y=-8[/tex] -------> equation B
isolate the variable y
[tex]2y=x+8[/tex]
[tex]y=(1/2)x+4[/tex]
Line A and Line B are parallel lines, because their slopes are the same
Line A and Line B are different lines because their y-intercept is not the same
URGENT !!!!!!!!!!!!!!!!!
no, the angles in triangles have to add up to 180 deg. but this adds up to 190
Solve the equation
7v=1+8v
Answer:
v = -1
Step-by-step explanation:
Solve for v:
7 v = 8 v + 1
Subtract 8 v from both sides:
7 v - 8 v = (8 v - 8 v) + 1
7 v - 8 v = -v:
-v = (8 v - 8 v) + 1
8 v - 8 v = 0:
-v = 1
Divide both sides by -1:
Answer: v = -1
which of the following will always determine exactly one triangle
Answer:
Which of what following? There's no options.
Step-by-step explanation:
A basketball team will play 12 home games during the season. it has played 6 home games so far. of the season's remaining games,1/3 will be played at home. The equation 1/3g+6=12 can be used to find the the total number of games,g,remaining this season. How many games,g,remain in the season
Answer:
18
Step-by-step explanation:
⅓g + 6 = 12
⅓g = 6 Subtracted 6 from each side
g = 18 Multiplied each side by 3
18 games remain in the season.
Check:
⅓ × 18 + 6 = 12
6 + 6 = 12
12 = 12
a soccer team played 47 games and won 33.Rounding to the nearest whole number,what percent of its games did the team win?
Answer:
70%
Step-by-step explanation:
1. divide the number of games won (33) by the total number of games (47)
33/47 = 0.702
2. Move the decimal two places to the right = 70.2%
3. round down to 70%
Final answer:
The soccer team won 70% of its games after calculating the fraction of games won, converting it to a decimal, then to a percent, and finally rounding to the nearest whole number.
Explanation:
To calculate the percent of games won by the soccer team, we divide the number of games won by the total number of games played and then multiply by 100 to convert the fraction to a percentage.
Step 1: Find the fraction of games won: 33 (games won) ÷ 47 (total games).
Step 2: Convert the fraction to a decimal: 33 ÷ 47 = 0.7021.
Step 3: Convert the decimal to a percent: 0.7021 × 100 = 70.21%.
Step 4: Round to the nearest whole number: 70.21% rounded to the nearest whole number is 70%.
Therefore, the soccer team won 70% of its games.
Factor 35x+10x-5 please explain your work
[tex]\bold{Hey\ there!} \\ \\ \bold{Combine\ like\ terms\downarrow} \\ \bullet\bold{35x\ \&\ 10x} \\ \bold{35x+10x=45x} \\ \\ \bold{Since,\ -5\ doesn't\ have\ any\ like\ terms\ it\ stays\ the\ same!} \\ \\ \\ \boxed{\boxed{\bold{Answer:45x-5}}}\checkmark[/tex]
[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ day!} \\ \\ \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
four less than the quotient of a number x and 4.
Answer:
(x/4) -4
Step-by-step explanation:
quotient means divide
quotient of a number x and 4.
x/4
four less than
x/4 -4
Answer:
This can be written as x/4 - 4
Step-by-step explanation:
To find this, note that quotient denotes a division problem. Then we subtract 4, since it starts with four less than,
solve the simultaneous equations y =x+2 and x + y = 3
Answer: [tex]\bold{\bigg(\dfrac{1}{2},2\dfrac{1}{2}\bigg)}\qquad \implies \qquad \bold{\bigg(\dfrac{1}{2},\dfrac{5}{2}\bigg)}[/tex]
Step-by-step explanation:
y = x + 2 x + y = 3
Solve using Substitution Method by replacing y with x + 2:
x + (x + 2) = 3
2x + 2 = 3
2x = 1
x = [tex]\dfrac{1}{2}[/tex]
Next, replace x with 1/2 in one of the original equations and solve for y:
y = x + 2
= [tex]\dfrac{1}{2}[/tex] + 2
= [tex]2\dfrac{1}{2}[/tex]
Answer:
x = 1/2
y = 5/2
Step-by-step explanation:
So we're gonna use the elimination method, by eliminating one of x or y to find the value of the other one.
y = x + 2 --------------(1)
x + y = 3 --------------(2)
In (1), x is in LHS and y is in RHS. To make things simpler, we take both x and y to the same side.
y = x + 2
y - x = x + 2 - x ( take x to the other side)
y - x = 2-------------------------(3)
Note that in (2), x is positive and in (3), x is negative. So by adding these two, we can single out y because +x and -x cancels out. So we can eliminate x.
(3) + (1) : (x+y) + (y- x) = 3 + 2
2y = 5
y = 5/2
Substituting y = 5/2 for (1),
5/2 - x = 2
5/2 = 2 + x
5/2 - 4/2 = x
x = 1/2
∴ x = 1/2
y = 5/2
Hope i helped you :)
Which of these are greater than 1.27 CHOOSE ALL ANSWERS THAT APPLY
Answer:
Choices A and C
Step-by-step explanation:
Answer:
A, C
Step-by-step explanation:
We can see in the graph that it is done by ticks of 1/10s
Therefore we can determine that point A is on 1.6.
Since 1.6 > 1.27, this is true.
1 one and 7 hundreths is 1.07
And since 1.07 < 1.27, this is not true.
Finally 27 tenths is the equivalent of 2.7
2.7 > 1.27 so this is true.
PLZ HELP QUICK
President Monroe's decision to appoint John Quincy Adams as Secretary of State was partially intended to
A. End the institution of slavery.
B.end the War of 1812.
C.end the "Virginia Dynasty."
D.end the "Massachusetts Dynasty."
Answer:
B
Step-by-step explanation:
Adams headed the Commission that negotiated the Treaty of Ghent in 1814, which ended the War of 1812 with Great Britain.
plzzzzz help worth 15 points
Which expression is equivalent to one over threep + 15? one over three(p + 45) one over three(p + 5) 3(p + 45) 3(p + 5)
Answer:
[tex]\large\boxed{\dfrac{1}{3p+15}=\dfrac{1}{3(p+5)}}[/tex]
Step-by-step explanation:
"one over threep + 15":
[tex]\dfrac{1}{3p+15}=\dfrac{1}{(3)(p)+(3)(5)}=\dfrac{1}{(3)(p+5)}=\dfrac{1}{3(p+5)}[/tex]
the size of an iPod would be what aspect of the product
A. quality
B. benefit
C. feature
D. asset
Answer:
C: feature
that is the correct answer
Please help me with this. 20 points.
Answer:A,C
Step-by-step explanation:
Answer:
A, C
Step-by-step explanation:
The domain is the set of all possible x-values that will make the function work.
Here, m is the x-value (the independent variable).
The month number m is an integer, so the appropriate number type for the domain of r is integer.
The month numbers run from 1 to 12, inclusive, so the appropriate domain is 1 ≤ m ≤ 12.
Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu,
to maximize profits. The taco truck's owner decides to adjust the price per taco and record data on the
number of tacos sold each day with each new price. When the taco truck charges $4 for a taco, it sells
an average of 60 tacos in one day. With every $1 increase in the price of a taco, the number of tacos
sold per day decreases by 7. The owner can calculate the daily revenue using the polynomial
expression -7x2 + 32x + 240, where x is the number of $1 increases in the taco price. In this activity.
you'll interpret and manipulate this expression and the scenario it represents.
Part A
What is the constant term in the polynomial expression -7x2 + 32x + 240, and what does it
represent?
The constant term is "240." The number represents the daily revenue when the price of a taco is 0 dollars.
Answer:
The constant term is 240. It represents the initial daily revenue.
Step-by-step explanation:
It is given that Tico's Taco Truck is trying to determine the best price at which to sell tacos, the only item on the menu, to maximize profits.
The owner can calculate the daily revenue using the polynomial expression
[tex]-7x^2+32x+240[/tex]
where x is the number of $1 increases in the taco price.
Constant term does not contain any variable.
In the given expression 240 is free from variable x. So, the constant term is 240.
The value of expression is 240 for x=0. Since x is the number of $1 increases in the taco price, therefore 240 is the daily revenue when the taco price is not increased or the taco price increased by 0.
Therefore the constant term is 240 and it represents the initial daily revenue.
there are 495 coins in a bottle.
1/3 of the coins are £1 coins.
124 of the coins are 50p coins.
the rest of the coins are 20p.
work out the total value of the 495 coins.
Answer:
The total value is £268.20.
Step-by-step explanation:
Given : There are 495 coins in a bottle.
1/3 of the coins are £1 coins.
124 of the coins are 50p coins.
The rest of the coins are 20p.
To find : Work out the total value of the 495 coins?
Solution :
According to question,
Total coins = 495
[tex]\frac{1}{3}[/tex] of the coins are £1 coins.
i.e. The number £1 coins are
[tex]\frac{1}{3}\times 495 =165[/tex]
So, We have £165
124 of the coins are 50p coins.
50p=£0.50
Number of coins were
[tex]124\times0.50 =62[/tex]
So, We have £62 .
Remaining coins were,
[tex]495-(124+165)=206[/tex]
i.e. remaining coins are 206 are of 20p.
20p=£0.20
Number of coins were
[tex]206\times0.20 =41.20[/tex]
So, We have £41.20 .
Now, Adding all of them together,
i.e. £165+£62+£41.20=£268.20
So, The total value is £268.20.
Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. What fraction of the tomatoes did mrs Jenkins use to make the salad?
Answer:
Final answer is 1/3.
Step-by-step explanation:
Question says that Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. After that she used 3/4 of the remainder to make a salad. Now we need to find about what fraction of the tomatoes did Mrs Jenkins use to make the salad.
As she used 5/9 of the tomatoes to make pasta sauce.
Now remaining amount of tomatoes = 1- 5/9 = 9/9 -5/9 = 4/9
Then she used 3/4 of the remainder to make a salad. So fraction of the tomatoes did Mrs Jenkins use to make the salad = (4/9)(3/4)=12/36=1/3
Hence final answer is 1/3.
If g(x) is the inverse of f(x) and f(x)=4x+12, what is g(x)?
g(x)=12x+4
g(x)=1/4x-12
g(x)=x-3
g(x)=1/4x-3
Answer: Last option.
Step-by-step explanation:
To find the inverse of the function f(x), you must follow the proccedure shown below:
- Rewrite the function,as following:
[tex]y=4x+12[/tex]
- Solve for x. Then:
[tex]y-12=4x\\x=\frac{1}{4}y-\frac{12}{4}\\\\x=\frac{1}{4}y-3[/tex]
- Now, substitute y with x.
Therefore, you obtain that the inverse function g(x) is the following:
[tex]g(x)=\frac{1}{4}x-3[/tex]
Then, the answer is the last option.
Answer:
Last choice is the answer.
Step-by-step explanation:
We have given a function.
f(x) = 4x+12
We have to find the inverse of given function.
Let y = f(x)
y = 4x+12
Solving for x, we have
x = 1/4y-3
Since, x = f⁻¹(y)
f⁻¹(y) = 1/4y-3
Replacing y with x , we have
f⁻¹(x) = 1/4x-3
Given that g(x) = f⁻¹(x)
g(x) = 1/4x-3 which is the answer.
Which of the following inequalities match the statement “nine is more than a number”? 9 < n 9 ≥ n 9 ≤ n 9 > n
The correct answer is 9>n since it doesn't say greater than or equal to, we can cross out the 2 and that leaves us with 9<n and 9>n but it actually says 9 is more than a number so that leaves us with 9>n
a motorboat maintains a constant speed of 38 miles per hour. it takes 30 minutes to travel upstream and 27 minutes back. what is the speed of current?
Answer:
r = 2 [stream's speed is 2 mph downstream
Step-by-step explanation:
Remark
The distances traveled [upstream and downstream] are the same.
If it takes longer to go upstream, it means the speed of the current is going against him. So the rate is 38 - r where r is the speed of the current.
The rate of the downstream is 38 + r because it takes him less time to go downstream and the current is helping him go.
The times are given
Givens
Time Upstream = 30 minutesTime Downstream = 27 minutesDistance upstream = d1Distance downstream = d2rate upstream: 38 - rrate downstream: 38 + rd1 = d2Formula
d1 = d2
d1 = (38 - r) * 30
d2 = (38 + r) *27
(38 - r) * 30 = (38+r)*27
Solution
Remove the brackets on both sides.
38*30 - 30*r = 38*27 + 27r Add 30r to both sides
38*30 - 30r + 30r =38*27 + 27r + 30r Combine the numbers
1140 = 1026 + 57r Subtract 1026 from both sides.
114 = 57r Divide by 57
114/57 = 57r/57
r = 2
If a wheel has a diameter of 15 centimeters what is the area of the wheel nearest centimeter
Answer:
A = 177 cm²Step-by-step explanation:
A diameter is two times longer than a radius. Therefore, if the diameter
d = 15cm, then the radius r = (15cm) : 2 = 7.5cm.
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
Substitute:
[tex]A=\pi(7.5)^2=56.25\pi\ cm^2[/tex]
[tex]\pi\approx3.14[/tex]
Then
[tex]A\approx(56.25)(3.14)\approx177\ cm^2[/tex]
Maria ate 1/4 of a pizza. If there were 20 slices of pizza, how many slices did Maria eat?
Answer:
Step-by-step explanation:
1/4x20=5 so Maria ate 5 slices of pizza.
Cube A has a side length of 3 meters and cube B has a side length of 6 meters. Calculate the volume of the two cubes. Which statement accurately represents the relationship between the two volumes? A) The volume of cube A is half the volume of cube B. Eliminate B) The volume of cube B is 4 times the volume of cube A. C) The volume of cube B is 6 times the volume of cube A. D) The volume of cube B is 8 times the volume of cube A.
Answer: The correct answer is choice D.
Step-by-step explanation: In order to answer this question you need to calculate the volume of each of the cubes.
Cube A has a side which is 3 meters, so the volume = 3 x 3 x 3 = 27
Cub B has a side which is 6 meters, so the volume = 6 x 6 x 6 = 216
216/27 = 8. Therefore, the volume of cube B is 8 times the volume of cube a.
The volume of cube A is 27 cubic meters and the volume of cube B is 216 cubic meters. Cube B's volume is 8 times greater than cube A's. The correct answer is option D)
Explanation:The volume of a cube is calculated by cubing the length of its side. So, the volume of cube A is 3 meters x 3 meters x 3 meters = 27 cubic meters. The volume of cube B is 6 meters x 6 meters x 6 meters = 216 cubic meters. Comparing the volumes, cube B's volume is 216/27 = 8 times greater than the volume of cube A. Therefore, the statement that accurately represents the relationship between the two volumes is option D) The volume of cube B is 8 times the volume of cube A.
Learn more about Volume of Cubes here:https://brainly.com/question/31600527
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Need step by step ASAP please
Answer:
C. 8x+80.
Step-by-step explanation:
To make this a simple expression, we need to distribute the 8 into x+10. We do this by multiplication. 8*x=8x. 8*10=80. Our new equation is 8x+80.
Which of the following is a polynomial function in factored form with zeros at -8,-1 and 3
Answer:
[tex]\large\boxed{y=a(x+8)(x+1)(x-3)}[/tex]
Step-by-step explanation:
[tex]\text{Factored form:}\\\\y=a(x-x_1)(x-x_2)(x-x_3)\\\\x_1,\ x_2,\ x_3-zeros\\\\\text{We have}\ x_1=-8,\ x_2=-1\ \text{and}\ x_3=3.\ \text{Substitute:}\\\\y=a(x-(-8))(x-(-1))(x-3)\\\\y=a(x+8)(x+1)(x-3)\\\\\text{Where}\ a\neq0\ (\text{any real number except 0})[/tex]
What is the exact value of tan (-x/3)
Final Answer:
The exact value of [tex]\(\tan\left(\frac{-x}{3}\right)\)[/tex] is [tex]\(-\tan\left(\frac{x}{3}\right)\).[/tex]
Explanation:
To find the exact value of [tex]\(\tan\left(\frac{-x}{3}\right)\),[/tex] we can use the periodicity property of the tangent function. The tangent function has a period of [tex]\(\pi\),[/tex] which means that [tex]\(\tan(\theta) = \tan(\theta + \pi)\)[/tex].
Therefore, [tex]\(\tan\left(\frac{-x}{3}\right)\)[/tex] is equivalent to [tex]\(\tan\left(\frac{-x}{3} + \pi\)\).[/tex] Additionally, the tangent function is an odd function, so [tex]\(\tan(-\theta) = -\tan(\theta)\). Combining these properties, we get \(\tan\left(\frac{-x}{3}\right) = -\tan\left(\frac{x}{3}\right)\).[/tex]
In summary, the exact value of [tex]\(\tan\left(\frac{-x}{3}\right)\) is \(-\tan\left(\frac{x}{3}\right)\)[/tex] due to the periodicity and odd function properties of the tangent function.
HELP BRAINLIEST!
Which of the following is a statistical question?
A.
How many students attend Natasha's school?
B.
How many players are on Greg's football team?
C.
What are the checking account balances of the shoppers in a grocery store?
D.
What volume of milk is used to make cupcakes according to Paula's cookbook?
Answer:
The answer is C for sure
Step-by-step explanation:
I would say the answer is C. What are the checking account balances of the shoppers in a grocery store?
Hope this helps!