[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]
Hello, can someone help me with the working out to this problem
[tex]\text{If}~ \alpha ~\text{and}~ \beta~ \text{are the roots,}\\ \\x^2 -(\alpha + \beta)x +\alpha\beta = 0\\\\\text{For}~ x^2+3x-2=0\\\\\alpha +\beta=-\dfrac ba=-3\\ \\\alpha \beta = \dfrac ca = -2\\\\[/tex]
[tex]\text{So,~} \alpha^3+\beta^3 = (\alpha + \beta)(\alpha^2 + \beta^2 -\alpha \beta)\\ \\~~~~~~~~~~~~~~~~=(\alpha+\beta)\left[(\alpha +\beta)^2 -2\alpha \beta - \alpha \beta\right]\\\\~~~~~~~~~~~~~~~~=(\alpha+\beta)\left[(\alpha +\beta)^2 -3\alpha \beta \right]\\\\~~~~~~~~~~~~~~~~=-3\left[(-3)^2-3(-2)\right]\\\\~~~~~~~~~~~~~~~~=-3(15)\\\\~~~~~~~~~~~~~~~~=-45\\\\\text{And}~~~\alpha^3 \beta^3= (\alpha \beta )^3 = (-2)^3 = -8\\\\[/tex]
[tex]\text{Hence the equation whose roots are}~ \alpha^3 ~\text{and}~ \beta^3~ \text{is:}\\ \\ x^2-(\alpha^3 + \beta^3)x +\alpha^3 \beta^3 =0\\\\\implies x^2 -(-45)x+(-8)=0\\\\\implies x^2 +45x -8=0[/tex]
Solve for n:
n
---- = 1
20
A. n = 23
B. n = 15
C. n = 20
D. n = 32
Answer:
The answer is C
Step-by-step explanation:
[tex]\frac{n}{20}*20 = 1 * 20[/tex]
1 x 20 = 20
Answer:
C) n = 20
Step-by-step explanation:
hope it helps!
need help with geometry question
Find the slope of the line passing through the points(-9,-6) and (-4,5)
Hey there!
We're given 2 points that the line intersects, so we can easily determine the line's slope.
This is the formula:
[tex]\bold{\displaystyle\frac{y2-y1}{x2-x1} }[/tex]
[tex]\bold{\displaystyle\frac{5-(-6)}{-4-(-9)}}[/tex]
[tex]\bold{\displaystyle\frac{5+6}{-4+9}}[/tex]
[tex]\bold{\displaystyle\frac{11}{5}}[/tex]
Hence, the answer is
[tex]\boxed{\boxed{\bold{\frac{11}{5} }}}[/tex]
Hope everything is clear.
Let me know if you have any other questions!
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:-)
[tex]\rule{200}{2}[/tex]
9
These lists show the ages of attendees in a yoga class and a dance dass
Yoga: 18, 31, 17, 14, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Select from the drop-down menus to correctly complete each statement about the attendees in the two cases
The median age of the attendees in the yoga class is
the median age of the attendees in the dance
The range of ages of the attendees in the yoga class is
the range of ages of the attendees in the conce
Answer:
median is 20
Step-by-step explanation:
due to both of them having it in there 1 time
Answer:
The Median Age: Yoga Class (31) Dance Class (30)
The Range: Yoga Class (17-44) Dance Class (20-47)
Step-by-step explanation:
For a class activity, a teacher put students into teams of 5. The teams were made up of 2 students randomly chosen from group A and 3 students randomly chosen from group B.
If group A has 4 students and group B has 6 students, how many different team combinations were possible?
Enter your answer as a number, like this: 42
Answer:
120
Step-by-step explanation:
6p3 = 120
The number of the different combinations of the teams will be 26.
What are permutation and combination?A permutation is an act of arranging objects or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.
Given that for a class activity, a teacher put students into teams of 5. The teams were made up of 2 students randomly chosen from group A and 3 students randomly chosen from group B. If group A has 4 students and group B has 6 students,
The number of possible combinations will be calculated as,
C = ⁶C₃ + ⁴C₂
C = ( 4 x 3 ) / 2 + ( 6x 5 x 4 ) /( 3x 2 )
C = 6 + 20
C = 26
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The giraffes at the Liberia zoo eat 75 pounds of food per day, and 52.5 pounds per day comes from acacia leaves. How much of their diet comes from other types of leaves?
Julia, the zookeeper, used the equation 52.5 + x = 75 to find the answer. Which equation is an equivalent equation that can be used to solve the problem?
Answer:
Step-by-step explanation:
75-52.5=x
I need lateral surface
Answer:
un rhgdb tennis felicidades ID remix estoy do do ID do ID Rockband do ID do TX
Which is the best definition for adjacent angles?
Answer:
Adjacent Angles are 2 angles with common sides and a common vertex that don't overlap in any way.
Step-by-step explanation:
Leave a comment if you need any more help. Give Brainiest, please.
What expression is equivalent to 12x^4/4x^16 helpppp
Answer: 48x/64
Work (assuming ^ is multiplication):
12x^4/4x^16
12x ^ 4x = 48x
4 ^ 16 = 64
WILL MARK BRAINLIEST
Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y-6= -5(x-3)
y - 6 = - 5 * x - 5 * (-3)
y - 6 = -5x + 15
y + 5x = 15 + 6
5x + y = 21
Answer:
5x + y = 21.
Step-by-step explanation:
y - 6 = -5(x - 3)
y - 6 = -5x + 15
5x + y - 6 = 15
5x + y = 15 + 6
5x + y = 21.
The regular price of a color TV is $539.22. During a sale, Hill TV is selling the TV for $456.56. Determine the percent decrease in the price of the TV
Hey there!
Answer: = 15.3296% decrease
How to Calculate Percentage Decrease
Subtract starting value minus final value=> 539.22 - 456.56
=> 79.66
Divide that amount by the absolute value of the starting value=> 79.66 ÷ 539.22
=> 0.153296
Multiply by 100 to get percent decrease=> 0.153296 × 100
=> 15.3296%
If the percentage is negative, it means there was an increase and not an decrease.
Therefore, percentage decrease is 15.3%
Evan owns a small business selling ice-cream. He knows that in the last week 83
customers paid cash, 8 customers used a debit card, and 2 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
debit card or a credit card as a percent to the nearest whole number.
The probability that the next customer will pay with a debit card or a credit card is 12%.
What is the probability that the next customer would pay with a debit card or a credit card?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the next customer would pay with a debit card or a credit card = (number of customers that paid with a debit card + number of customers that paid with a credit card) / total number of customers
(8 + 2)/ 83 = 0.12 = 12%
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See the picture below and answer for 50 points and brainliest
Answer:
Non-linear equations:
[tex]y=x^2 +2x-3[/tex]
[tex]3y=2^x[/tex]
Step-by-step explanation:
Linear equation: y = mx + b
Therefore, a linear equation has 2 variables that have no exponents.
So the non-linear equations are:
[tex]y=x^2 +2x-3[/tex] (this is a quadratic equation - polynomial with degree 2)
[tex]3y=2^x[/tex] (this is an exponential equation)
zeros.
Find a polynomial of the specified degree that has the given
Degree 5; zeros -4, -3, 0, 4,3
Answer:
f(x)=x(x+4)(x+3)(x-4)(x-3)
Step-by-step explanation:
hello :
an polynomial is : f(x)=(x+4)(x+3)(x-0)(x-4)(x-3)
means : f(x)=x(x+4)(x+3)(x-4)(x-3)
At the store grapes are on sale. You can buy 3 pounds for
$2 dollars. At that rate, how many pounds can you buy
for $8? Show how you know.
Answer:
If you buy 3 pounds for $2, and have 8 dollars to spend, then multiply 2x4 to get $8. Since we multiplied by 4 for the money, we do the same thing for the pounds of grapes. So, we multiply 3x4 to get 12 pounds. So, you can buy 12 pounds of grapes for $8.
Step-by-step explanation:
Hope this helps! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP.
The table below shows a proportional relationship. True or False?
True
False
Answer:
False
Step-by-step explanation:
2/10 is not equal to 4/16.
Pam kicked a soccer ball down the field. Part of the ball's path, including its highest
point, is described by the function below, where f(x) is the height of the ball in feet.
According to the function, what is the ball's maximum height, in feet? (Use only the
digits 0-9 to enter the height.)
f(x) =
12x2+2x
Answer:
maximum height is 45/4 in feet
The maximum height of the ball is 45/4 in feet
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given tha Pam kicked a soccer ball down the field. Part of the ball's path, including its highest point, is described by the function below, where f(x) is the height of the ball in feet.
F(x)= 12x^2+2x
Thus for this quadratic , the max value will occur at x= -b/2a
= - 2 / (2 x 1/12) = -12
Plug in -12 to find the max height
= (-12)^2 + 2 x-12
= 45/4 in feet
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[tex] \\ { \rm{If \: }{\tt{A = \left [ \: \begin{array}{ c c c} \: \: \: \: 2 & -3 & - 5 \\ - 1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1& - 3 & - 4\end{array} \: \: \: \right] \: and \: B = \left[\begin{array}{c c c} \: \: \: \: 2 & - 2 & - 4 \\ - 1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & - 2 & - 3\end{array} \right]}}}, { \rm{shown \: that \: AB = A \: and \: BA = B}}[/tex]
[tex] \: [/tex]
Don't Spam
Explain well
Answer:
Given:
[tex] \\ {\tt{A = \left [ \: \begin{array}{ c c c} \: \: \: \: 2 & -3 & - 5 \\ - 1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1& - 3 & - 4\end{array} \: \: \: \right] \: and \: B = \left[\begin{array}{c c c} \: \: \: \: 2 & - 2 & - 4 \\ - 1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & - 2 & - 3\end{array} \right]}}[/tex]
Matrix A is of order 3 × 3 and Matrix B is of order 3 × 3
To Show:
Matrix AB = A , BA = BFormula Used:
[tex]\\ { \rm{ \left[ \begin{array}{c c c} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array} \right] \times \left[ \begin{array}{c c c} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{array} \right] = \: \left[ \begin{array}{c c c} \: \: a_{11}b_{11} + a_{12}b_{21} + a_{13}b_{31} & a_{11}b_{12} + a_{12}b_{22} + a_{13}b_{32} & a_{11}b_{13} + a_{12}b_{23} + a_{13}b_{33} \\ \: \: a_{21}b_{11} + a_{22}b_{21} + a_{23}b_{31} & a_{21}b_{12} + a_{22}b_{22} + a_{23}b_{32}&a_{21}b_{13} + a_{22}b_{23} + a_{23}b_{33} \\ \: \: a_{31}b_{11} + a_{32}b_{21} + a_{33}b_{31}&a_{31}b_{12} + a_{32}b_{22} + a_{33}b_{32} & a_{31}b_{13} + a_{32}b_{23} + a_{33}b_{33}\end{array} \right]}}[/tex]
If A is a matrix of order a×b and B is a matrix of order c×d , then matrix AB exits and is of order a×d , if and only if b = c.
[tex] \: \: [/tex]
If A is a matrix of order a×b and B is a matrix of order c×d , then matrix BA exits and is of order c×b , if and only if d = a.
[tex] \: \: [/tex]
____________________________________________________________________For Matrix AB, a = 3, b = c = 3, d = 3 , thus Matrix AB is of order 3×3
[tex]\\ { \rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right] \times \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] = \left[\begin{array}{c c c} \: \: \: \: 2(2)-3(-1)-5(1) & \: \: \: \: 2(-2)-3(3)-5(-2) & \: \: \: \: 2(-4)-3(4)-5(-3) \\ -1(2)+4(-1)+5(1) & -1(-2)+4(3)+5(-2) & -1(-4)+4(4)+5(-3)\\ \: \: \: \: 1(2)-3(-1)-4(1) & \: \: \: \: 1(-2)-3(3)-4(-2) & \: \: \: \: 1(-4)-3(4)-4(-3) \end{array} \right]}}[/tex]
[tex]\\ {\rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 4 + 3 - 5 & \: \: \: -4 -9 + 10 & \: \: -8 - 12 + 15 \\ -2 - 4 + 5 & \: \: \: \: \: \: + 2 + 12 - 10 & \: \: \: \: \: 4 + 16 - 15 \\ \: \: \: \: \: 2 + 3 - 4 & \: \: -2 - 9 + 8 & -4 - 12 + 12 \end{array} \right] = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right]}}[/tex]
[tex]\\ {\rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right] = Matrix \: A}}[/tex]
Matrix AB = Matrix A____________________________________________________________________For Matrix BA, a = 3, b = c = 3, d = 3 , thus Matrix BA is of order 3 × 3
[tex]\\ {\rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] \times \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: \: 1 & -3 & -4 \end{array} \right]}}= \left[ \begin{array}{c c c} \: \: \: \: \: 2(2) -2(-1) -4(1) & \: \: \: \: 2(-3) -2(4) -4(-3) & \: \: \: \: 2(-5) -2(5) -4(-4) \\ \: -1(2) + 3(-1) + 4(1) & -1(-3) + 3(4) +4(-3) & -1(-5) + 3(5) + 4(-4) \\ \: \: \: \: \: 1(2) -2(-1) -3(1) & \: \: \: \: 1(-3) -2(4) -3(-3) & \: \: \: \: 1(-5) -2(5) -3(-4) \end{array} \right][/tex]
[tex]\\{ \rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 4 + 2 - 4 & \: \: \: -6 -8 + 12 & \: \: -10 - 10 + 16 \\ -2 - 3 + 4 & \: \: \: \: \: \: +3 + 12 - 12 & \: \: \: \: \: + 5 + 15 - 16 \\ \: \: \: \: \: 2 + 2 - 3 & \: -3 -8 +9 & \: \: \: \: \: -5 -10 + 12 \end{array} \right] = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right]}}[/tex]
[tex]\\{ \rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] = Matrix \: B}}[/tex]
Matrix BA = Matrix B____________________________________________________________________Find the value of x. 1222° 0 111 O 55 O 42 O 138
Based on the outside angles theorem, the value of x is: 42°
What is the Outrside Angles Theorem?The outside angles theorem states that the measure of the angle that is formed outside a circle when two tangents or secants intersect is half the measure of the diffrence of the intercepted arcs.
Given the following:
One arc measure = 222°The second arc measure = 360 - 222 = 138°Therefore, based on the outside angles theorem, we would have the following:
x = 1/2(222 - 138)
x = 42°
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please help me it's ,due, by 30 minutes please help me.
Step-by-step explanation:
I hope its helped ! studied well.
Answer:
a: The tape diagram represents the story because there’s 5 boxes representing the 5 weeks and x-2 in each box since x represents the amount Andre’s neighbor will pay him weekly to mow the lawn. This all equals 40 because that’s how much money he has to save.
B: Andre’s neighbor pays him 10 dollars each week to mow the lawn.
Step-by-step explanation:
b: For this part you have to make an equation combining all the five weeks which would be 5x-10. Then you would make it equal 40 because that’s how much he needs to save 5x-10=40. The you solve to find x by adding 10 to both sides of the equation and get 5x = 50. Then if you divide 5 on both sides you get 10!
You can check you work by plugging in 10 as x into the diagram.
What is the value of x?
13 m
15 m
Answer:
which one?
Step-by-step explanation:
CAN SOMEBODY HELP ME SOLVE THIS EQUATION
Lori puts up a sign for her business 500 meters from the main entrance. She once read that it takes the average adult 6 minutes to walk 500 meters. She decides to test this by having 200 adults walk the 500 meters from her sign to her store. Which of the following is the sample in Lori's experiment?
Step-by-step explanation:
She decided to test this by 200 adults, so. Divide 6 by 500 = 0.012 (200)=2.4mins.
Answer: The 200 adults
Step-by-step explanation:
What is the product of the two binomials below?
(3A + 4B)(3A - 4B)
A. 9A^2 - 16B^2
B. 2A^2 - 4B^2
C. 3A^2 + 4B^2
D. 9A^2 + 16B^2
Answer:
A. 9A² - 16B²
Step-by-step explanation:
(3A + 4B)(3A - 4B)
Distribute:
3A(3A - 4B)
4B(3A - 4B)
Multiply:
3A(3A - 4B)
3A(3A) + 3A(-4B)
9A² - 12AB
4B(3A - 4B)
4B(3A) + 4B(-4B)
12AB - 16B²
Combine like terms:
9A² - 12AB + 12AB - 16B² <== -12AB + 12AB cancels out
9A² - 16B²
Therefore, our final answer is 9A² - 16B²
Hope this helps!
the length of a rectagle is 6 ft longer than its width. if the perimeter of the rectangle is 64 ft, find its length and width
Answer:
19 and 13
Step-by-step explanation:
width = x
length = x + 6
2x + 2(x + 6) = 64
2x + 2x + 12 = 64
4x = 64 - 12
4x = 52
x = 13
x + 6 = 19
Answer:
19 and 13
Step-by-step explanation:
what is the angle measure of an arc bounding sector with an area of 5pie square miles?
if the diameter is 20, the its radius must be half that or 10.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}[/tex]
At the beginning of the summer,
Shay had $27 in her savings
account. Shay worked as a
lifeguard and by the end of the
summer had a total of $575 in
her savings account. How much
did Shay save over the summer?
Maya sells candles to her 5 neighbors. Each neighbor buys 2 boxes of candles. There are 6 candles in each box. What is the total number of candles that all of her neighbors will get?
A.
16 candles
B.
30 candles
C.
40 candles
D.
60 candles
Answer:
D. 60 Mark brainliest<3
Step-by-step explanation:
Each neighbor buys 2 boxes which contains 6 candles meaning they in total contain 12.
5x12 = 60
Betsy, a recent retiree, requires $5,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $5,000 in interest per year?
A. The amount of money invested at 13% = ___
B. The amount of money invested at 5% = ___
A. The amount of money that Betsy should invest n B-rated bonds at 13% is $20,000.
B. The amount of money that Betsy should invest in a certificate of deposit (CD) at 5% is $50,000.
How are CDs different from Bonds?Certificates of deposit (CDs) are short-term investments in financial institutions (money market) while Bonds are long-term investments in the stock exchange (capital market).
CDs pay reduced interest rates when compared to bonds'.
Data and Calculations:The amount required per year in interest = $5,000
Total investible funds = $70,000
Interest rate of B-rated bonds = 13%
Interest rate in CD = 5%
Since Betsy is not interested in realizing more than $5,000 in interest per year, she should invest $50,000 in the CD and $20,000 in the B-rated bonds.
The interest in CD = $2,500 ($50,000 x 5%)
The interest in bonds = $2,600 ($20,000 x 13%)
Total interest in CD and bonds = $5,100 ($2,500 + $2,600)
Thus, Betsy should invest $50,000 in the CD and $20,000 in the B-rated bonds.
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