-2 3/4 + (-1 1/3) I need this for a test pls help
Answer:
-77/12, -6 5/12, or -6.416
Step-by-step explanation:
convert
calculate
done
Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
~Thanks in advance !
Answer:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Step-by-step explanation:
We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.
First, we will need the distance formula, given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let the point on the locus be P(x, y).
So, the distance from P to (0, 2) will be:
[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]
And, the distance from P to (0, -2) will be:
[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]
So sum of the two distances must be 6. Therefore:
[tex]d_1+d_2=6[/tex]
Now, by substitution:
[tex](\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6[/tex]
Simplify. We can subtract the second term from the left:
[tex]\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}[/tex]
Square both sides:
[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]
We can cancel the x² terms and continue squaring:
[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]
We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:
[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]
We can divide both sides by -4:
[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]
Adding 9 to both sides yields:
[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]
And, we will square both sides one final time.
[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]
Distribute:
[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]
The 36y will cancel. So:
[tex]4y^2+81=9x^2+9y^2+36[/tex]
Subtracting 4y² and 36 from both sides yields:
[tex]9x^2+5y^2=45[/tex]
And dividing both sides by 45 produces:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.
Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number.
Answer:
Please check the explanation.
Step-by-step explanation:
Given the statement:
''Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number''.
Let us break down the statement into an algebraic expression.
First Portion:
Let the number be: n
The difference of a number n and 2: n -2
Twice the difference of a number n and 2: 2(n-2)
Twice the difference of a number and 2 is added to 6 = 2(n-2) + 6
Second Portion:
3 times the number n: 3n
4 more than 3 times the number: 3n + 4
Combine the First portion and Second Portion:
Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number:
2(n - 2) + 6 = 3n + 4
Therefore, the required algebraic expression is:
2(n - 2) + 6 = 3n + 4BONUS SOLUTION to determine the number n
Let us solve the expression
2(n - 2) + 6 = 3n + 4
2n - 4 + 6 = 3n + 4
flip the equation
3n + 4 = 2n - 4 + 6
3n + 4 = 2n + 2
3n - 2n = 2 - 4
n = -2
Thus, the value of n = -2
Use the fact that 15⋅324=4,860.What is the exact product of 1.5⋅3.24?
Answer:
Step-by-step explanation:
From the question, we are informed that 15⋅324=4,860. Thee exact product of 1.5⋅3.24 will be:
= 1 × 5 × 3 × 24
= 360
The answer will therefore be 360
need help with this question! due tomorow so pls help. Brainiest to first correct answer
Answer:
8x-8
Step-by-step explanation:
if 2x-2 is mutiplied by 4 is 8x-8
Please i don’t understand this i don’t understand the least common denominator and how can i write an equivalent fraction.please help me my exam is tomorrow
Answer:
Least common denominator is the lowest number in similarity that a fraction can share and be divided into
Step-by-step explanation:
For example, in this example 1/5, and 1/2 the least common denominator would be 10 because when putting these fractions together you might want to find the total of what they equal. For example, think of this example as a pizza, to make one whole pizza in the first one would be 5 pieces but instead of all five pieces, all you have left is 1 piece of the five. so you only have 1/5. now just imagine you had another pizza the same size of the first one but instead of five pieces you it's only two pieces however, from this two piece pizza all you have left is 1/2. You want to find the in terms of what fraction would make them both equal each other in which you would eventually be able to find out how much pizza you would have left. The denominator is the lower number under the fraction where that is the one most needed for a fraction to change. The least common denominator is a number that goes into both fractions that in reverse can be divided by against each other. our denominators are 5 and 2. Numbers that are divisible are 10, 20, 40 and so on since 5x2=10, 2x5=10; 5x4=20, 2x10=20; 5x8=40, 2x20=40. The least common denominator would be the lowest number which in this case would be 10.
If f(x)=2x−2 and g(x)=x2−8x+19, then f(x)=g(x) for what values of x?
x=−1 and x=−4
x=−3 and x=−7
x=1 and x=4
x=3 and x=7
Answer:
D) x =3 and x =7
Step-by-step explanation:
Step(i):-
Given function f(x) = 2x -2
g(x) = x² - 8x +19
Given that f(x) = g(x)
⇒ 2x -2 = x² - 8x +19
⇒ x² - 8x +19 -2x +2 =0
⇒ x² -10x +21 =0
Step(ii):-
The factors are x² -10x +21 =0
⇒ x² - 7x - 3x +21 =0
⇒ x( x-7) -3( x-7) =0
⇒ (x-3)(x-7) =0
x =3 and x =7
Answer:
d: x=3 and x=7
Step-by-step explanation:
solve the inequality 31< 3x+4
Answer:
31-4<3x
27<3x
9<x
Step-by-step explanation:
Pls help its math it was due yesterday my teacher said i could still get 3/4 credit if i turn it in now
i need what is 5(7 - m) and also 2(3 + f) im really bad at my math class for distibutive property this was due yesterday
and im still sad trying to pay attention to my english class but i just got told off by someone who my best friend talk to on here and- and they said that i dont know her or what she needs a- and that im clueless to what shes going through,and that i- i never listened to her. i thought she was doing better now...... i feel like ive done nothing before, and now shes struggling......... again uhm, please answer my math questions i need the answers it was due yesterday*_*and also dont listen to my story just wanted to express my feelings
Answer:
•35 - 5m
•6 + 2f
Step-by-step explanation:
•5(7-m):
[5×7] - [5×m]=
35 - 5m
•2(3+f):
[2×3] + [2×f]=
6 + 2f
4|m-n|
If m=-7 and n=2
Kelly worked and earned $17 per hour working at the bakery. She got a holiday bonus of $150. Write an algebraic expression to represent the amount of money Kelly earned. Define the variable.
Answer:
150 + 17x = y
x = hours worked
y = her overall profit
Angle A and Angle B are complementary. If angle A is 48°, what is the measure of angle B?
Answer:
B = 42°
Step-by-step explanation:
hope it help
plz fo"ow me
The measure of the angle B when angle A and angle b is complementary angle should be 42 degrees.
Calculation of the measure of angle B:Since
Angle A and Angle B are complementary. And, angle A is 48°.
We know that
The sum of complementary angles is 90 degrees
So it can be like
A + B = 90
48 + B = 90
B = 90 - 48
= 42 degrees
hence, The measure of the angle B when angle A and angle b is complementary angle should be 42 degrees.
Learn more about an angle here: https://brainly.com/question/23854119
Deb's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 2 single-shot espressos and 6 double-shot espressos. What percentage of the espressos sold were single-shot?
Answer:
오늘하루도 트친해요수고하셨습니다 ㅊ풔ㅓㅎ나지금너무배고파죽겠는데난지금바로응모하세요!
divide both sides of 15=5x by 5 what is the result
A farmhouse shelters 14 animals. Some are
pigs, and some are chickens. Altogether there
are 44 legs between the animals. Let p
represent the number of pigs and c represent
the number of chickens.
9514 1404 393
Answer:
8 pigs6 chickensStep-by-step explanation:
Maybe you want to know the number of each kind of animal.
__
We can write two equations in the two unknowns.
p + c = 14 . . . . . . number of animals
4p +2c = 44 . . . number of legs
Dividing the second equation by 2, it becomes ...
2p +c = 22
Then subtracting the first equation gives ...
(2p +c) -(p +c) = (22) -(14)
p = 8
8 +c = 14
c = 6
The farmhouse shelters 8 pigs and 6 chickens.
Ian and his family went out for lunch. The bill was $34.98. If they left a 15%
tip, how much did they pay in total?
Answer:
40.22
Step-by-step explanation:
What is the slope and what does the slope represent in this context? *
dollars in savings account
400
360
320
280
240
200
160
120
80
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14
weeks of saving
What is the slope
Answer:
plssss
Step-by-step explanation:
i need your help to answer my module plsss :(
A train leaves at 1314 and arrives at 1508. It travelled at an average speed of 105 km/h.
How far did it travel? Give your answer in km to 1DP
Answer: The train traveled 199.5 km
Step-by-step explanation:
We know the relationship:
Distance = Time*Speed
We know that the speed of the train was 105km/h
And we know that it leaves at 13:14, and arrives at 15:08.
Then the total amount of time that the train was traveling is:
T = (15 hours and 8 mins) - (13 hours and 14 mins)
= (15 - 13) hours and (8 - 14) mins
= 2 hours and (-6) mins.
We know that one hour has 60 minutes, then this is equal to:
T = 1 hour and 54 minutes.
But because the speed is kilometers per hour, we need to rewrite the 54 minutes in hours.
This can be done as follows:
1 hour = 60 minutes.
Then: 54 minutes = (54/60) hours = 0.9 hours.
Then:
1 hour and 54 minutes = 1.9 hours.
Now we know the speed and the time, then the distance can be calculated as:
Distance = speed*time = 105km/h*(1.9 h) = 199.5 km
The train traveled 199.5 km
Answer:
The train traveled 199.5 km
Step-by-step explanation:
We know the relationship:
Distance = Time*Speed
We know that the speed of the train was 105km/h
And we know that it leaves at 13:14, and arrives at 15:08.
Then the total amount of time that the train was traveling is:
T = (15 hours and 8 mins) - (13 hours and 14 mins)
= (15 - 13) hours and (8 - 14) mins
= 2 hours and (-6) mins.
We know that one hour has 60 minutes, then this is equal to:
T = 1 hour and 54 minutes.
But because the speed is kilometers per hour, we need to rewrite the 54 minutes in hours.
This can be done as follows:
1 hour = 60 minutes.
Then: 54 minutes = (54/60) hours = 0.9 hours.
Then:
1 hour and 54 minutes = 1.9 hours.
Now we know the speed and the time, then the distance can be calculated as:
Distance = speed*time = 105km/h*(1.9 h) = 199.5 km
The train traveled 199.5 km
X - 2y = 10
X + 2y = 5
Answer:
x = 2y +10
x = -2y + 5
Step-by-step explanation:
Help me please...........
Answer: No
Step-by-step explanation:
2/4 would 1/2 and 14/16 would be 7/8 so no I think
Which row of the table reveals the x-intercept of function f?
Answer:
Row two (-4, 0)
Step-by-step explanation:
Because of the zero in the y the point does not move from the x-axis.
Abby and Cruz are playing a game. Abby's score is 586 points. Cruz's score is 754. About how many more points does Abby need to reach Cruz's score? Estimate the amount.
Answer:
168
Step-by-step explanation:
754-586=168
Answer:
168 points
Step-by-step explanation:
subtract cruz's points by abby's so
754-586=
168 points
PLS HELP!!! WILL GIVE BRAINLIEST!!!!!!
You are getting a car wash for $45.50. You have to pay 5% sales tax and you want to tip the person who washed your car 20%. How much will you spend in total? Please show work.
Answer:
$56.88
Step-by-step explanation:
amount paying for sales tax---> $2.28
amount paying for tip---> $9.1
amount paying for car wash---> $45.50
$2.28 + $9.1 + $45.50= $56.88
hope this helps please give brainliest <3
Which of the following statements is true?
n = m
n = 4m
- (0,0) is a solution to n=m and to n=4m
- No point on the line n=m is also on the line n=4m
-The graph of the solution is parallel lines
-Every solution to n=m is also a solution to n=4m
Answer:
(0,0) is a solution to n=m and n=4m
Step-by-step explanation:
For the first equation, If u insert 0 as m into n=m
n=(0) then n will equal 0.
For the second equation, if u insert 0 as m in n=4m
n=4(0) then n will also equal 0.
So the answer is (0,0) is a solution to n=m and to n=4m
Hope this helps :)
The populations and land areas of four cities in Texas are shown. Which statements are true? Check all that apply. The population density for City B can be found using the ratio 48,592 : 26. The population density for City D can be found using the ratio 258 : 196,429. City A has the greatest population density of the four cities. The population density of City B is greater than that of City C. City D has the lowest population density of the four cities.
Answer:
The population density for city b would be 48,592 ÷ 26
The population density for city b is more than the city c
And, the city d contains the lowest population density
Step-by-step explanation:
The computation is given below:
As we know that
Population density = Population ÷ Area
So
For city A = 2,195,914 ÷ 1,553 = 1413.98
For city B = 48,592 ÷ 26 = 1868.15
For city C = 1,257,676 ÷ 999 = 1258.93.
For city D = 196,429 ÷ 258 = 761.35.
The following are the true statements:
The population density for city b would be 48,592 ÷ 26
The population density for city b is more than the city c
And, the city d contains the lowest population density
Answer:
A, D, E
Step-by-step explanation:
Just did it on edge!
how can i teach an entire year of alg 2 before next school year? i learned nothing this year and i want to take an advanced physics class next year but i’m scared it will affect me if i don’t learn it on my own ://
Answer:
use khan academy, its a website or an app which a lot of kids which are homeschooled learn education on.
What is the solution to this inequality? -9x - 15 2
A. x > 2
B. x > -2
C. x < -2
D. x < 2
Answer:
Step-by-step explanation:
x>-2
Becuase multiply it and divide
find the
volume or air
4m
by
5m which is only 3m
high
Answer:
volume of cuboid=l×w×h
volume of cuboid=4×5×3=60cm³
Given the equation y = -3x + 1/2 , what is the y-intercept? -3 3 1/2 -1/2
============================================
Explanation:
The given equation y = -3x+1/2 is in slope intercept form y = mx+b
We match the terms to find that m = -3 is the slope and b = 1/2 is the y intercept.
The y intercept is where the graph crosses the vertical y axis.
Please help
Write an equation of the line that passes through (2, −1) and is parallel to the line y=−3x+8.
An equation of the parallel line is y=
Answer:
Step-by-step explanation:
The slope of the line in question is the same as the slope of the line parallel to it. Using y = mx + b, where m is the slope, we find the slope of our line is -3.
Using the pt-slope form, y - y1 = m( x - x1), we get y - (-1) = -3( x - 2) or y + 1 = -3x + 6. Which leads us to y = -3x + 5. QED