Answer:
The x-axis is closer to B.
Step-by-step explanation:
Since the ratio PB:AB = 2/7 is positive, the line divides internally. So, we use the equation for the coordinates of a point that internally divide a line.
So, x = (mx₂ + nx₁)/(m + n) and y = (my₂ + ny₁)/(m + n)
where PB/AB = 2/7 = n/m. So, n = 2 and m = 7
Also, Point A = (0,0) = (x₁, y₁) and point P = (10, -5) = (x₂, y₂).
Substituting these values into x and y, we have
x = (mx₂ + nx₁)/(m + n)
x = (7(10) + 2(0)₁)/(7 + 2)
x = (70 + 0)/9
x = 70/9
x = 7⁷/₉
y = (my₂ + ny₁)/(m + n)
y = (7(-5) + 2(0)₁)/(7 + 2)
y = (-35 + 0)/9
y = -35/9
y = -3⁸/₉
So, the x and y coordinates of B are 7⁷/₉ and -3⁸/₉ respectively. So, point B is -3⁸/₉ units away from the x-axis and 7⁷/₉ units away from the y-axis. So the x-axis is closer to B.
Three times a number is equal to the sum of half the number and 30. What is the number?
Answer:
12.
Step-by-step explanation:
3x = 0.5x + 30
2.5x = 30
x = 30 / 2.5
x = 12
A test has five questions. To pass the test, at least three of the questions must be answered correctly. question ----> Find the probability that Mark guesses 4 questions correctly.
Answer:
1/5
Step-by-step explanation:
Total Question no. 5
Three must be answer correctly so 3/5 to pass
and 2/5 to fail
So 1/5 because to pass the test he can answer it correctly only one time
Mary's bank account was overdrawn by
$21. If she deposits $60, find the new
balance.
Answer:
39
Step-by-step explanation:
If her bank account is overdrawn, that means that it has a negative balance. This means that without the $60, she has -$21 and once she deposits the $60, twenty one of the 60 will be subtracted
Answer: The answer is 39
Step-by-step explanation: -21+60=49
hope you like it :)
A recipe for 2 loaves of banana bread calls for 3 bananas and 2 cups of flour. How many
bananas are needed to make 10 loaves of bread?
Answer:
15 bananas
Step-by-step explanation:
If two loaves of bread uses 3 bananas then multiply that by 5 because 10 divided by 2 is 5 and get 15 bananas.
Multiply.
(9√3+√5)(9√3+√5)
Simplify your answer as much as possible.
Answer:
[tex]248 + 18\sqrt{15}[/tex]
Step-by-step explanation:
[tex](9\sqrt{3}+\sqrt{5} )(9\sqrt{3}+\sqrt{5} )=(9\sqrt{3}+\sqrt{5} )^2[/tex]
[tex]81 \cdot 3 + 2\cdot 9\sqrt{3} \cdot \sqrt{5} + 5[/tex]
[tex]243 + 18\sqrt{15} + 5[/tex]
[tex]248 + 18\sqrt{15}[/tex]
Please prove this!!!!
Answer: see proof below
Step-by-step explanation:
Use the following Sum/Difference Identities:
sin(A + B) = sin A · cos B + sin B · cos A
sin(A - B) = sin A · cos B - sin B · cos A
Use the following Half-Angle Identities:
[tex]\sin\bigg(\dfrac{\theta}{2}\bigg)=\dfrac{\sqrt{1-\cos \theta}}{\sqrt2}\\\\\\\cos\bigg(\dfrac{\theta}{2}\bigg)=\dfrac{\sqrt{1+\cos \theta}}{\sqrt2}[/tex]
[tex]\text{Use the Unit circle to evaluate:}\ \cos\dfrac{\pi}{4} = \sin\dfrac{\pi}{4} = \dfrac{\sqrt2}{2}[/tex]
Use the following side work:
[tex]\sin\bigg(\dfrac{\pi}{8}\bigg)=\sin\bigg(\dfrac{\frac{\pi}{4}}{2}\bigg)=\dfrac{\sqrt{1-\cos \frac{\pi}{4}}}{\sqrt2}=\dfrac{\sqrt{2-\sqrt2}}{2}\\\\\\\cos\bigg(\dfrac{\pi}{8}\bigg)=\cos\bigg(\dfrac{\frac{\pi}{4}}{2}\bigg)=\dfrac{\sqrt{1+\cos \frac{\pi}{4}}}{\sqrt2}=\dfrac{\sqrt{2+\sqrt2}}{2}[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \qquad \qquad \sin^2\bigg(\dfrac{\pi}{8}+\dfrac{A}{2}\bigg)-\sin^2\bigg(\dfrac{\pi}{8}-\dfrac{A}{2}\bigg)\\\\\text{Sum/Difference Identity:}\qquad \bigg(\sin\dfrac{\pi}{8}\cdot \cos \dfrac{A}{2}+\sin \dfrac{A}{2}\cdot \cos \dfrac{\pi}{8}\bigg)^2\\\\.\qquad \qquad \qquad\qquad \qquad \quad -\bigg(\sin\dfrac{\pi}{8}\cdot \cos \dfrac{A}{2}-\sin \dfrac{A}{2}\cdot \cos \dfrac{\pi}{8}\bigg)^2[/tex]
[tex]\text{Expand and Simplify:}\qquad \quad 4\sin \dfrac{\pi}{8}\cdot \cos\dfrac{A}{2}\cdot \sin \dfrac{A}{2}\cdot \cos \dfrac{A}{2}\\\\\\\text{Substitute:}\qquad \qquad \qquad 4\bigg(\dfrac{\sqrt{2-\sqrt2}}{2}\bigg)\cdot \cos \dfrac{A}{2}\cdot \sin \dfrac{A}{2}\bigg(\dfrac{\sqrt{2+\sqrt2}}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \sqrt2\cos \bigg(\dfrac{A}{2}\bigg)\cdot \sin \bigg(\dfrac{A}{2}\bigg)[/tex]
[tex]\text{Half-Angle Identity:} \quad \sqrt2\bigg(\dfrac{\sqrt{1+\cos A}}{\sqrt2}\bigg)\bigg(\dfrac{\sqrt{1-\cos A}}{\sqrt2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \dfrac{\sqrt{1-\cos^2 A}}{\sqrt2}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{\sqrt{\sin^2 A}}{\sqrt2}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{\sin A}{\sqrt2}[/tex]
[tex]\text{LHS = RHS:}\quad \dfrac{\sin A}{\sqrt2} = \dfrac{\sin A}{\sqrt2}\quad \checkmark[/tex]
$9.40 per hour times 22 hours round to the nearest cent
Answer:
The answer is 206.8. But you want me to round to the nearest cent so the real answer is $207.00
Step-by-step explanation:
The sum of a number and 4 equals the same number times 3. What is the Number?
Answer:
2
Step-by-step explanation:
let the number be n, then sum of number and 4 is n + 4 and 3 times the number is 3n, thus
n + 4 = 3n ( subtract n from both sides )
4 = 2n ( divide both sides by 2 )
2 = n
That is the number is 2
Answer:
2
Step-by-step explanation:
1.form an equation
call the number x
x+4=3x
2.solve using inverse operations
x=2
Melissa and Rachel like to make funny hats. Melissa has made 202020 zebra-printed hats, and Rachel has made hhh striped hats. Together they have made a total of 424242 hats. Write an equation to describe this situation.
Answer:
42= 20 +hStep-by-step explanation:
Given from the problem statement
Melissa has made 20 zebra-printed hats
and Rachel has made h amount of striped hats
and also the total amounts of hats made by both of them is 42 hats
We can write a simple equation for the scenario as
[tex]42= 20 +h[/tex]
We can solve the equation to know the amount of hats made by Rachel
[tex]42= 20+h\\\\h= 42-20\\\\h= 22[/tex]
Hence Rachel has made 22 hats
Micha washed a car in 20 minutes. At this rate, how many hours would it take to wash 9 cars?
Answer:
3 hours
Step-by-step explanation:
he washed one car in 20 minutes so 9 cars will be 20 x 9=180minutes which is 3 hours
A cart starting from rest travels a distance of 12.7 meters in 3.6 seconds. The average speed of the cart is
Select one:
a. 3.5 m/s
b. 0.3 m/s
C. 45.7 m/s
d. 16.3 m/s
Answer:
A
Step-by-step explanation:
12.7 meters divided by 3.6 seconds is 3.527 round it up and it stays 3.5 m/s
The average speed of the cart is: 3.5 m/s
The correct option is (A).
What is Average speed?The average speed is the total distance traveled by the object in a particular time interval.
Given:
distance = 12.7m, time= 3.6 seconds
Average speed will be,
= Distance/time
=12.7/3.6
=3.522 m/s
Hence, the average speed is 3.522 m/s.
Learn more about average speed here:
https://brainly.com/question/12322912
#SPJ2
Find any 5 rational numbers between; a) -1 and 2 b) −3 8 −5 14
Answer:
Step-by-step explanation:
Hello,
You can list the following ones which are correct for a), b) and c)
[tex]\boxed{\sf \bf \ \ 1, \dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5} \ \ }[/tex]
Thanks
1
Is the value of -6 -6 POSITIVE, NEGATIVE, or ZERO?
Answer:
Negetive
Step-by-step explanation:
It helps to re-write.
-6 + -6 is the same as -6 -6
-6 + -6 = - 12
It would be different if these were multiplied together, but AS WRITTEN, they are subtracted. If it was (-6)(-6) or -6(-6) that would indicate multiplication as well.
The answer is negative.
ALG II NEED HELP QUICK! Will mark the brainliest answer
Yesterday morning, the temperature was -11°F. The temperature increased 7°F by noon and then decreased 4°F by nightfall. What was the temperature at nightfall last night?
Answer:
1
Step-by-step explanation:
1
A bag contains 6 red marbles, 2 green, and 4 blue marbles. You randomly pick a marble and then pick a second marble, returning the marbles to.the bag each time. What is the probability of pulling a blue marble first and then a red marble.second?
Answer:
Probability of pulling a blue marble is 1/3 about 33% chance
Probability of pulling a red marble is 1/2 = 50% chance
Step-by-step explanation:
Total marbles = 6+2+4 = 12
4 of those 12 are blue
4/12=1/3 when reduced
________________________
Total marbles are still = 12
6 of the 12 are red
6/12=1/2 when reduced
Hope this helps! :)
Factoring the expression 20a^3b^3 – 24a^5b^2 + 4a^3b^2 gives a new expression of the form
Ua^xb^y (Wa^2 + Vb+ z), where U > 0.
What is the value of U?
What is the value of W?
What is the value of V?
What is the value of Z?
What is the value of x?
What is the value of y?
Answer:
[tex]U = 4\\W = -6\\V = 5\\Z = 1\\x = 3\\y = 2[/tex]
Step-by-step explanation:
Then given expression is:
[tex]20a^3b^3-24a^5b^2+4a^3b^2[/tex]
To express the given expression in the form:
[tex]Ua^xb^y(Wa^2+Vb+Z)[/tex]
and to find the values of [tex]U, W, V, Z, x, y[/tex].
First of all, let us check the maximum common powers of [tex]a, b[/tex] in each term from the given expression.
The maximum common power of [tex]a[/tex] is 3 and
The maximum common power of [tex]b[/tex] is 2.
So, we can take [tex]a^3b^2[/tex] common out of each term.
And maximum common coefficient that can be taken out common is 4.
Taking 4[tex]a^3b^2[/tex] common from each term of given expression, we get:
[tex]4a^3b^2(-6a^2+5b+1)[/tex]
Now, let us compare the given term with:
[tex]4a^3b^2(-6a^2+5b+1)[/tex] = [tex]Ua^xb^y(Wa^2+Vb+Z)[/tex]
Now, the values that we get the following values:
[tex]U = 4\\W = -6\\V = 5\\Z = 1\\x = 3\\y = 2[/tex]
which is our answer.
What is an algebraic expression for 58 less than a number n?
Answer:
n-58
Step-by-step explanation:
Answer: n - 58
Step-by-step explanation:
The n goes first. You are subtracting 58 to find the missing value once n is determined.
Another way to write g(h(x))
Answer:
(gOh)(x) on edg 2020
Step-by-step explanation:
how would one go about solving this graph?
Density = Mass / Volume, so you could use that information to solve for each value in the graph.
2. Mass = Density * Volume = 8.07 * 1.04 = 8.59 g
3. Volume = Mass / Density = 8.26 / 8.10 = 1.02 mL
4. Density = Mass / Volume = 7.91 / 0.99 = 7.99 g/mL
5. Mass = Density * Volume = 8.05 * 0.98 = 7.89 g
6. Volume = Mass / Density = 8.53 / 8.05 = 1.06 mL
The diagonal of a square is 4 cm. Find its ar
ea.
Answer:
Area of square= d²/2
= 4²/2
= 16/2
= 8cm²
Step-by-step explanation:
A=
[tex]a {?}^{2} [/tex]
d=
[tex] \sqrt{2a} [/tex]
we can find A.USE THIS FORMULA
A =1/2 d squared
so 1/2×4 squared=8
8 is the answer
Mrs. Zhang's bee farm has a population that is about 1 tenth as large as Mr. Doyle's bee farm. If Mrs. Zhang's bee population is about 46,000, about how many bees does Mr. Doyle have?
Answer:
Mr. Doyle has 460000 bees
Step-by-step explanation:
We are told that Mrs. Zhang's bee farm has a population that is about 1 tenth as large as Mr. Doyle's bee farm.
Thus;
Population size of Mrs. Zhang's bee farm = 1/10 × population size of Mr. Doyle's bee farm
Now, we are given that Mrs. Zhang's bee population is about 46,000.
Thus, from the earlier equation, we have;
46000 = 1/10 × population size of Mr. Doyle's bee farm
Thus, when we multiply both sides by 10,we get;
population size of Mr. Doyle's bee farm = 46000 × 10 = 460000 bees
write this as a simplified expression. if you want to write the rules so that i could later figure out this problem later :)
Answer:
4x - 2
Step-by-step explanation:
Perimeter of triangle
[tex] =( 2x - 5) + (3x - 2) +( 5 - x) \\ = 2x + 3x - x - 5 - 2 + 5 \\ = 5x - x - 2 \\ = 4x - 2[/tex]
solve for x 4(2x+9)=-44+8
Please help me if you can..
It costs twelve dollars to get in to the fair. Tickets for rides cost extra and are d dollars each. If Tyra buys 20 tickets, how much would it cost her for the fair?
Answer:
12 + 20d
Step-by-step explanation:
OG fare = 12
Ticket price =d
20 Tickets =20d
Pete earns $8.50 per hour plus tips. On Tuesday, he received $16 in tips. How many hours did Pete work if he earned a total of $50 on
Tuesday?
Answer:
4 hours .
Step-by-step explanation:
4x8.50=34
34 + 16=50
Answer:
He worked 4 hours i think
Step-by-step explanation:
Take 50 and subtract his tips ($16)
then divide your answer by how much he makes an hour ($8.50)
Suppose the average yearly salary of an individual whose final degree is master's is $40 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $110 thousand. Find the average yearly salary of an individual with each of these final degrees.
Answer:
x=50000 dollars ( the average salary of bachelor degree)the average salary of Masters degree = 2x-400002(50000)-40000=60000 dollarsstep by step explanation :let x be the salary of individual with bachelor degree
Then the average salary of individual with Masters degree is:
(2x-40000)
the combined of two salaries is 110000:
x+(2x-40000)=110000
3x-40000=110000
3x=110000+40000
x=150000/3
x=50000 dollars ( the average salary of bachelor degree)the average salary of Masters degree = 2x-400002(50000)-40000=60000 dollarsAt a sale, coats were sold for $10 each. If the coats originally cost $20 each, what percentage of its original price was a coat sold for?
Answer: 50%
Step-by-step explanation:
10/20×100=50%
Answer:
50
Step-by-step explanation:
See your levels
Brenna went on vacation and sent postcards to all of her family and friends. She needed 45
postcards, but the store only sold them in packs of 12. She bought 4 packs. How many
postcards did she have left over?