Answer:
6 units
Step-by-step explanation:
Given: Triangle L N P has centroid S.
[tex]NS=7x-3, SR=5x-3[/tex]
To find: NS
Solution:
Centroid is the point of intersection of the medians of the triangle such that it divides each of the median in ratio [tex]2:1[/tex]
So,
[tex]NS:SR=2:1\\\frac{NS}{SR}=\frac{2}{1} \\[/tex]
Put [tex]NS=7x-3, SR=5x-3[/tex]
[tex]\frac{7x-3}{5x-3}=\frac{2}{1}\\ 7x-3=10x-6\\10x-7x=-3+6\\3x=3\\x=1[/tex]
Therefore,
[tex]NS=7x-3=7(1)-3=4\,\,units\\SR=5x-3=5(1)-3=2\,units[/tex]
So,
[tex]NS=NS+SR=4+2=6\,\,units[/tex]
Answer:
The answer is 4
Step-by-step explanation:
It asks for the length of NS not the length of NR
Evaluate the sine of angle X for the right triangle below.
Answer: C
Step-by-step explanation:
Sine is opposite/hypotenuse. Unfortunately, the hypotenuse is blank. Therefore, we need to solve for hypotenuse. We use Pythagorean Theorem to find hypotenuse.
Pythagorean Theorem: a²+b²=c²
7²+24²=c²
49+576=c²
625=c²
c=√625
c=25
Now that we have found the hypotenuse, we can find sine of x. Opposite of x is 7. Hypotenuse is 25. Therefore, sinx=7/25.
Answer:
7/25
Step-by-step explanation:
Just finished the lesson and checked the answer key :D
Ursula tosses two six-sided number cubes and ADDS the numbers rolled. Which of these is a list of the outcomes of the two row? A) 3, 4, 5, 6, 7, 8 B) 2,4,6,8, 10, 12 C) 5, 8, 11, 14, 17, 20 D) 0/25, 1/25, 3/25, 5/25, 6/25, 25/2
Answer:
A) 3, 4, 5, 6, 7, 8
Step-by-step explanation:
2+1, 2+2, 2+3, 2+4, 2+5, 2+6= 3, 4, 5, 6, 7, 8
Use Cramers Rule to solve the system
-x-3y=-8
2x+4y=12
Answer:
x = 2 y = 2
Step-by-step explanation:
just do equation form
Answer:
[tex]x=2[/tex] and [tex]y=2[/tex]
Step-by-step explanation:
To use Cramer's Rule, we first need to turn this system of equations into a matrix
[tex]A=\left[\begin{array}{cc}-1&-3\\2&4\\\end{array}\right][/tex] , [tex]b=\left[\begin{array}{c}-8\\12\\\end{array}\right][/tex]
The first step to use Cramer's Rule is to find the determinant of the original matrix
[tex]detA=(4)(-1)-(2)(-3)\\\\detA=-4+6\\\\detA=2[/tex]
Next, we need to replace column 1 of matrix A with b and then find the determinant of that matrix
[tex]A_1=\left[\begin{array}{cc}-8&-3\\12&4\\\end{array}\right][/tex]
[tex]detA_1=(-8)(4)-(12)(-3)\\\\detA_1=-32-(-36)\\\\detA_1=4[/tex]
And now we need to replace column 2 of matrix A with b and then find the determinant of that matrix
[tex]A_2=\left[\begin{array}{cc}-1&-8\\2&12\\\end{array}\right][/tex]
[tex]detA_2=(-1)(12)-(2)(-8)\\\\detA_2=-12-(-16)\\\\detA_2=4[/tex]
Now that all of this is done, we can find the values for our x matrix.
Recall that Cramer's Rule states that
[tex]x=\left[\begin{array}{c}\frac{detA_1}{detA} \\\frac{detA_2}{detA} \\\end{array}\right][/tex]
Now that we know all of the required determinants, we can find x
[tex]x=\left[\begin{array}{c}\frac{4}{2} &\frac{4}{2} \end{array}\right] \\\\x=\left[\begin{array}{c}2\\2\\\end{array}\right][/tex]
This means that the solutions to this system are [tex]x=2[/tex] and [tex]y=2[/tex]
Kate gets a paycheck twice a month. Every month, a total of $345.67 is deducted from her paychecks for taxes. If she has received 7 paychecks so far this year, which best represents the total effect the taxes have had on the amount she has earned??
Answer:
The correct answer is -$1,209.85-verified by Edg. Thank you.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What is the slope? 50 points + brainly
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
1/2
Step-by-step explanation:
Hi there, let me show you how to answer this question.
If you notice, the line goes over (-1,-10) and (1,-9). But overall, the rise/run is 1/2 as the rise is 1 and the run is 2.
Yesterday, Pete had 14 shirts. Today, he donated n shirts. Using n, write
an expression for the number of shirts Pete has left.
Answer:
14 - n.
Step-by-step explanation:
If he donated 'n' shirts, we can simply subtract 'n' from his initial amount of shirts, which is stated as '14'. Therefore:
'14 - n' is an expression that can represent how many shirts are remaining after he donated them.
Mr. Mudd gives each of his children $2000 to invest as part of a friendly family competition. The competition will last 10 years. The rules of the competition are simple. Each child can split up his or her $2000 into as many separate investments as they please. The children are encouraged to do their research on types of investments. The initial investments made may not be changed at any point during the 10 years; no money may be added and no money may be moved. Whichever child has made the most money after 10 years will be awarded an additional $10,000. Child Performance of investments over the course of the competition Albert $1000 earned 1.2% annual interest compounded monthly $500 lost 2% over the course of the 10 years $500 grew compounded continuously at rate of 0.8% annually Marie $1500 earned 1.4% annual interest compounded quarterly $500 gained 4% over the course of 10 years Hans $2000 grew compounded continuously at rate of 0.9% annually Max $1000 decreased in value exponentially at a rate of 0.5% annually $1000 earned 1.8% annual interest compounded biannually (twice a year) 1. What is the balance of Albert’s $2000 after 10 years? 2. What is the balance of Marie’s $2000 after 10 years? 3. What is the balance of Hans’ $2000 after 10 years? 4. What is the balance of Max’s $2000 after 10 years? 5. Who is $10,000 richer at the end of the competition?
Answer:
Step-by-step explanation:
Albert:
$1000 earned 1.2% annual interest compounded monthly
= 1000 (1+.001)120
(periodic interest = .012/12 ,n is periods = 10yr x 12 mos)
$500 lost 2% over the course of the 10 years
= 500 (.98)
$500 grew compounded continuously at rate of 0.8% annually
= 500 e^008(10) 10 years interest .008 (in decimal form)
Add these three to see how Albert did with his investments
The balance of Albert is $2159.07; the balance of Marie is $2244.99, the balance of Hans is $2188.35, and the balance of Max is $2147.40. Marie is $10,000 richer at the end of the competition.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To determine the balance of Albert’s $2000 after 10 years :
If the amount of $1000 at 1.2 % compounded monthly,
A = P(1 +r/n)ⁿ n = 10 years
here P = $1000 and r = 1.2
A = 1000(1 + 0.001)¹²⁰
A = $1127.43
If Albert $500 losing 2%
So 0.98 × 500 = $490
If $500 compounded continuously at 0.8%
So A = P[tex]e^{rt}[/tex]
A = 500[tex]e^{0.008\times 10}[/tex]
A = 541.6
So the balance of Albert’s $2000 after 10 years :
Total balance = 1127.43 + 490.00+ 541.64 = $2159.07
To determine the balance of Marie’s $2000 after 10 years:
If 1500 at 1.4 % compounded quarterly,
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
If $500 Marie’s gaining 4 %
So 1.04 × 500 = $520.00
So the balance of Marie’s $2000 after 10 years
Total balance = 1724.99 + 520.00 = $2244.99
To determine the balance of Hans’ $2000 after 10 years:
If $2000 compounded continuously at 0.9%
So A = 2000[tex]e^{0.009\times 10}[/tex]
A = $2188.3
To determine the balance of Max’s $2000 after 10 years :
If $1000 decreasing exponentially at 0.5 % annually
So A = 1000(1 - 0.005)¹⁰= $951.11
If $1000 at 1.8 % compounded bi-annually
So A = 1000(1 + 0.009)²⁰ = $1196.29
So the balance of Max’s $2000 after 10 years
Total balance = 951.11 + 1196.29 = $2147.40
Therefore, Marie is $10,000 richer at the end of the competition.
Learn more about Compound interest here :
brainly.com/question/25857212
#SPJ2
Subtract the equations 5x+4y= 25 -(5x+2y=3)
The given equation has been solved in the table. Step Statement 1.) 3x - 10 = -16 2.) 3x - 10 + 10 = -16 +10 3.) 3x = - 6 4.) 3x/3 = -6/3 5.) x = -2 Use the table to complete each statement. In step 2, the _____ property of equality was applied. In step 4, the_____ property of equality was applied.
The answer is
In step 2, the addition property of equality was applied.
In step 4, the division property of equality was applied.
Proof that the answer is correct.
Answer:
addition
division
Step-by-step explanation:
The total amount of water a tank can hold is 14 and one-half gallons. Raul wants to find out how many 1 and one-fourth-gallon buckets of water can be used to fill the tank. Which expressions could be used to represent this scenario? Select two options..
Answer:
11 3/5 (12) buckets
Step-by-step explanation:
I can't see any options but this is how you'd work it out:
You divide 14 1/2 by 1 1/4
= 29/2 / 5/4
= 29/2 * 4/5
= 29*2 / 5
= 58/5
= 11 3/5 buckets
Answer:
the answer is A C
Step-by-step explanation:
Write your question here (Keep it simple and clear to get the best answer)if use the spinner 200 times how many pink colour would you get if it has 0.2
Answer: 40 times.
Step-by-step explanation:
If the probability in a sigle spin of getting the colour pink is p = 0.2
This means that in 0.2*100% = 20% of the spins we should see the colour pink.
Then, out of 200 spins, the 20% of 200 is
(20%/100%)*200 = 0.2*200 = 40
This means that out of 200 spins, in around 40 of them we will se the colour pink.
Mrs. Olga’s credit card charges an interest rate of 19% compounded annually. If her current balance is $250, what will her balance be after 3 years?
Answer:
$421.30
Yearly Componded Interest
$250 * 19% = $47.50 = $297.50 <-- Year One Balance
$297.50 * 19% = $56.53 = $354.03 <-- Year Two Balance
$354.03 * 19% = $67.27 = $421.30 <-- Year Three Balance
Answer:
$421.29
Step-by-step explanation:
$250
19%
3 years
----------
$250*1.19³= $421.29Find the x-intercept for the line represented by this equation 7x=2y-3 A. (-3/7,0) B.(0,-3/7) C.(3/2,0) D.(0,3/2)
Answer:
(-3/7, 0)
Step-by-step explanation:
7x=2y-3
To find the x intercept, set y = 0 and solve for x
7x = 0-3
7x = -3
Divide each side by 7
7x/7 = -3/7
x = -3/7
The x intercept is
(-3/7, 0)
Answer: A
Step-by-step explanation:
For the x-intercept, we know y=0. We can eliminate B and D.
We know either A or C is the correct answer. This line is linear so there should be only one x-intercept. We can solve this equation to see which is correct. Let's plug in A and C into the equation to see which is right.
A. Correct
[tex]7(-\frac{3}{7} )=2(0)-3[/tex]
[tex]-3=-3[/tex]
C. Incorrect
[tex]7(\frac{3}{2} )=2(0)-3[/tex]
[tex]\frac{21}{2}\neq -3[/tex]
Look in pic to help!!
Answer:
Step-by-step explanation:
140-105 gives you the angle of X, X is then 35
Answer:
x = 65°
Step-by-step explanation:
The 2 base interior angles are adjacent to the external angles and are supplementary.
180° - 105° = 75°
180° - 140° = 40°
The sum of the 3 interior angles of a triangle = 180°
Subtract the sum of the 2 known interior angles from 180 for x
x = 180° = (75 + 40)° = 180° - 115° = 65°
Find the radius of a circle that has a circumference of 16 .
O r=4
O r=8
O r= 12
O r=16
Answer:
2.55
Step-by-step explanation:
To find the radius, the formula is:
R = C/2 x pi
pi = 3.14
16/(2 x 3.14) = 2.54648
= 2.55
Describe how to use the formula C = StartFraction 5 Over 9 EndFraction (F minus 32) to find
Answer:
Answer is below
Step-by-step explanation:
C = 5/9(F - 32) This equation is used to convert from Fahrenheit to Celsius on the temperature scale.
An example is listed below
C = 5/9(32 - 32) Subtract in the parentheses
C = 5/9(0) Multiply
C = 0 When it is 32 degrees Fahrenheit, it is 0 degrees Celsius
Answer:
you answer the question
Step-by-step explanation:
hope this help
Please help me with my question!!
Answer:
56 tiles
Step-by-step explanation:
[tex]\dfrac{252}{4\frac{1}{2}}= \\\\\\\dfrac{252}{\frac{9}{2}}= \\\\\\252\times \dfrac{2}{9}= \\\\\\\boxed{56}[/tex]
Hope this helps!
Same with the other question we did, we are given the area of each tile which is 4 1/2in^2.
All we need to do it divide.
252 / 4.5 = 56
So, she would need 56 tiles in total.
Best of Luck!
Ken built a 20 foot square fence in his back yard and planted a tree every 5 feet along the fence. How many trees did Ken plant?
Answer: 41
Step-by-step explanation:
Answer:
c:16
Step-by-step explanation:
How many solutions exist for the given equation?
CO
3(x - 2) = 22-X
name
zero
one
two
infinitely many
can someone help me pls
Answer:
one
Step-by-step explanation:
3(x - 2) = 22 - x
3x - 6 = 22 - x
3x + x = 22 + 6
4x = 28
4x/4 = 28/4
x = 7
Two points on a line are (3, 6) and (4, 9). What is the slope of the line?
Answer:
slope of line= 3
Step-by-step explanation:
slope of line= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
(X₁, Y₁)= (4, 9)
(X₂, Y₂)= (3, 6)
* The order of which one is the first coordinate or second does not matter. Just ensure that if you let the x-coordinate of 1 point to be X₁, the y-coordinate of the same point has to be Y₁.
Thus, slope of line
[tex] = \frac{9 - 6}{4 - 3} \\ = \frac{3}{1} \\ = 3[/tex]
PLEASE HELP FOR A BRAINLIEST!!!! Create your own example and explain how to solve Quadratic Equation using Quadratic Formula. What part in the Quadratic Formula is the discriminant and how do you know the number of solutions based on the value of the discriminant?
Answer:I'm gonna be doing a quadratic equation explaining step by step and using the formula so the example i'm gonna be using for today is
3[tex]x^{2}[/tex] +5[tex]x^{}[/tex]=7 I'm gonna answer the question then explain how i got the answer the i will explain to you about the discriminant section
Step-by-step explanation:
So here is the explanation for the equation given above
One thing you need to know about quadratic equation is that there has to be a 0 on the other side of the equation given to you
3[tex]x^{2}[/tex]+5[tex]x^[/tex]-7=0
Therefore you have to group the numbers into a,b and c
a=3
b=5
c=7
Your'e gonna use a plus or minus sign like the one below
x=-(5)+[tex]\sqrt{}[/tex]5
sorry i cannot understand it very well i tried though
-
Please help me! Anyone know this answer :(
Answer:
A
Step-by-step explanation:
2x-3=5(x+6)
2x-3=5x+30
2x-33=5x
3x=-33
x=-11
Hope this helps!
Help me please this is due today help me
Answer:
Below
Step-by-step explanation:
1. -4, -|2|, -1, |-3|, 4
2. -7.5, -7.2, 9.5, 10.5
3. 7
5. 13
6. -9
7. [tex]\frac{5}{12}[/tex]
8. -1.36
9. [tex]\frac{13}{5}*[/tex][tex]\frac{-4}{3}[/tex][tex]=\frac{-52}{15}[/tex]
10. -27.2
11. 22 * 2 + 7 * 0 - 5 * 1 = 39
What is the volume of this rectangular prism?
Please help I need the answer fast
Answer:
24.5 cubic centimeters
Step-by-step explanation:
The volume of a rectangular prism is the width multiplied by the length and then height. In this case, this means that the volume is:
[tex]\dfrac{7}{2}\cdot 5 \cdot \dfrac{7}{5}=24.5[/tex]
Hope this helps!
Answer:
Step-by-step explanation:
V=7/5*5*7/2=49/2=24.5 cm^3
WILL GIVE BRAINIEST!!! Find the sum of the first 200 positive even numbers.
Answer:
2+4+6+8+10+12+14+16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50+52+54+56+58+60+62+64+66+68+70+72+74+76+78+80+82+84+86...+400=40200
Step-by-step explanation:
Colin spends 1/3 of his wages on rent and 1/4 on food. If he makes £636 per week, how much money does he have left?
Answer:
£265
Step-by-step explanation:
Total fraction of money spent= [tex]\frac{1}{3} +\frac{1}{4}[/tex]
= [tex]\frac{7}{12}[/tex]
Actual money spent = [tex]\frac{7}{12}[/tex] * £636
= £371
Money he has left = £(636 - 371)
= £265
Answer:
$265
Step-by-step explanation:
Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?
The slope is One-half.
The slope is Negative 2.
The y-intercept is 7.
The y-intercept is 13.
Answer:
The y-intercept is 13.
1. What is the surface area of the pyramid below
6 , 5.2 ,8.2
The library is 3 miles east of the city hall. The mall is 10 miles west of the library. How far and in what direction is the mall from the city hall?
A. 7 miles west
B. 7 miles east
C. 13 miles west
D. 13 miles east
Answer:
A
Step-by-step explanation:
If the library is 3 miles east of the hall, and the mall is 10 miles west of the library, then do 10 - 3 to find the distance between the mall and hall, which is 7 miles.
The mall is also west of the city hall.
Answer:
a 7 miles west
Step-by-step explanation:
i took the test plz mark brainliest
In RST, the measure of
Answer:
27.5 degrees
Step-by-step explanation:
First, choose which method would work in this problem, SOH, CAH, or TOA.
We have opposite, O and adjacent, A. So we have an O and an A.
Thus, we should use TOA.
Tangent x = 44/84
Tangent x= 0.52
x= Tangent^-1 (0.52)
x=27.5 degrees
Answer:27.6
Step-by-step explanation: