The expression that shows the number of baseball cards is 12n
How make an expression that shows how many baseball cards?An algebraic expression in mathematics is an expression that is made up of letters and numbers, along with algebraic operations (addition, subtraction, multiplication, etc). Expressions are made up of terms
Given that: Carter bought p packs of baseball cards and there are 12 cards in each pack
To know the number of baseball cards, we have to multiply the number of packs by the number of cards in each pack:
Since the number of packs = n and the number of cards in each pack = 12.
Thus, total number of baseball cards = 12 x n = 12n
Therefore, the expression that shows how many baseball cards Carter bought is 12n
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Brad had a small gathering at a local steakhouse. The steakhouse offers three dinner platters which vary by size and price. They ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters.
Steak Platter Prices
• 6-ounce $9.95
• 8-ounce $12.95
• 11-ounce $15.95
If a gratuity of 18% was added to the bill, which of the following is closest to the total of the steak platters and gratuity, ignoring sales tax?
Hello!
If Brad had a small gathering at a local steakhouse where they ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters. After adding an 18% gratuity their total before sales tax should have been $130.45
Step-by-step explanation:
[tex]4[/tex] x [tex]9.95=39.80[/tex]
[tex]3[/tex] x [tex]12.95=38.85[/tex]
[tex]2[/tex] x [tex]15.95=31.90[/tex]
[tex]31.90+[/tex][tex]38.85+[/tex][tex]39.80=[/tex][tex]110.55[/tex]
[tex]110.55[/tex] x [tex]0.18[/tex] [tex]=19.899[/tex]
[tex]110.55+19.90[/tex][tex]=130.45[/tex]
Solve for an angle in right triangles
I just need the answer :)
Answer:
19.47
Step-by-step explanation:
Answer:
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio sine.
[tex]\sin(m\angle A) = \dfrac{2}{6}[/tex]
[tex]\sin(m\angle A) = \dfrac{1}{3}[/tex]
[tex]m\angle A = \sin^{-1}\left( \dfrac{1}{3} \right)[/tex]
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Evalúa \dfrac{2}{5}g+3h-6
5
2
g+3h−6start fraction, 2, divided by, 5, end fraction, g, plus, 3, h, minus, 6 cuando g=10g=10g, equals, 10 y h=6h=6h, equals, 6
The value of the algebraic expression 2/5g + 3h - 6 if evaluated when g = 10 and h = 6 is 16.
How to evaluate algebraic expression?2/5g + 3h - 6
When g = 10 and h = 6
Substitute the value of g and g into the expression2/5g + 3h - 6
2/5(10) + 3(6) - 6
open parenthesis20/5 + 18 - 6
4 + 18 - 6
16
In conclusion, the value of the expression 2/5g + 3h - 6 when evaluated is given by 16
Complete question:
Evaluate 2/5g + 2h - 6 start fraction, 2, divided by, 5, end fraction, g, plus, 3, h, minus, 6 when g=10 g, equals, 10 and h=6 h, equals, 6
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A police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets. Should he be on a perpendicular bisector, a median, an angle bisector, or an altitude?
ALSO… Draw a picture to show solution to this problem and label all parts of your picture and the name of the segment the police officer should use.
A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.
Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.
What is a perpendicular bisector?A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.
Perpendicular bisector: A line that bisects a line segment in two equal parts.
Median: The middle number; found by ordering all data points and picking out the one in the middle.
Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.
Therefore, a police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.
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50 POINTS
Your parents have heard about your business and would like to invest in it to help you earn as much money this summer as possible. They decide to give you $100 towards your business. However, there's a catch. They want 10% of the money you make.
1. if you mowed 10 lawns while charging $15 a lawn, how much would you have to pay your parents?
2. if you needed to make $300 to buy a switch, how many lawns would you have to mow?(Hint: don't forget about how much you would have to pay your parents.)
3. With all cost taken into account, your start up money, the money your parents gave you and what you paid your parents, how much profit did you make after 20 lawns?
The profit made from the business that receives an initial $100 investment are as follows;
1. The amount received from the investment is $15
2. The number of lawns that should be mowed to buy the switch is 23 lawns
3. The profit made from the business considering the cost and the initial investment of the parents is $170
What is an investment?An investment is the money directed towards an asset purchase to increase the valuation of the business and products within a time period.
The amount invested = $100
The amount desired as return = 10% of the amount made from the business
1. The amount charged per lawn = $15
The number of lawn mowed = 10
The revenue of the business = 10 × $15 = $150
The amount paid as return on investment = 10% × $150 = $15
2. The amount required to buy the switch = $300
The number of lawns to be mowed, n, is therefore;
300 = 15 × n - 10% × 15 × n = 15·n - 1.5·n = 13.5·n
300 = 13.5·n
n = 300/13.5 ≈ 23 ( rounding up to the nearest whole number)
The number of lawns to be mowed is 23 lawns
3. The revenue from mowing 20 lawns is 20 × $15 = $300
The amount received by the investing parents = 10% × $300 = $30
The amount received from the parents investment = $100
The profit made after 20 lawns = $300 - $30 - $100 = $170
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80% into a decimal from
Answer: 0.8
Step-by-step explanation:
Please help me solve this
The value of a=2 and b= 4.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
a + 1 / b-1 = 5/1 and a-1/ b+ 1 = 1/1
So, a + 1 / b-1 = 5/1
now, cross multiplying
a+ 1 = 5b - 5
a- 5b = -6............(1)
Also, a-1/ b+ 1 = 1/1
a-1 = b + 1
a - b = 2 ..............(2)
solving Equation (1) and (2) , we get
2+ b - 5b= -6
-4b = -8
b= 2
and, a = 2 + 2 = 4
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estion 11 of 42
What is the equation of a line with a slope of 6 and a y-intercept of -2
O A. y = -2x + 6
OB. y = 6x + 2
OC. y = 6x-2
OD. y = 2x+6
Find the probability P(0.21 distribution.
The probability of the value of (0.21) distribution using the normal distribution table is: 0.3166
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
In the question, we have
Probability of (0.21 < z <1.28)
= P(z < 1.28) - P(z < 0.21)
Probability of value for z
= 1.28 using z table is 0.8997
=> P(z < 1.28)
= 0.8997
probability of value for z = 0.21
Now, find the value of the probability using the normal distribution table:
using the z table of 0.21; we get:
The value of z is: 0.5832
=> P(z < 0.21) = 0.5832;
The value of Probability of (0.21 < z <1.28)
= Probability of (z < 1.28) - Probability of (z < 0.21)
= 0.8997 - 0.5832
= 0.3165
~ 0.3166
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Please help. Will mark brainliest. Please choose one answer
Which of the following is the most reasonable estimate of the correlation coefficient? Image is provided
0.5
0.7
0.9
1.0
The most reasonable estimate of the correlation coefficient is 0.9
What is the correlation coefficient?The correlation coefficient gives an estimate of how strong is the linear relationship between two variables.
The correlation coefficient, r, is given by the formula;
[tex]r = \dfrac{\sum(x_i-\overline x)\cdot (y_i-\overline y)}{\sqrt{\sum (x_i-\overline x)^2\sum(y_i-\overline y)^2} }[/tex]
Where;
[tex]x_i[/tex] = The ith x-value
[tex]\overline x[/tex] = The mean (average of the x-values)
[tex]y_i[/tex] = The ith y-value
[tex]\overline y[/tex] = The mean (average of the y-values)
The give points on the scatter plot graph are;
(8, 9), (6, 9), (6, 6), (5, 5), (4, 5), (3, 4), (3, 3), (2, 4), (1, 2), (1, 3)
Plotting the above points on MS Excel gives;
The equation of the regression line is; y = 0.9407·x + 1.3313
The square of the correlation coefficient, R² = 0.8322
Therefore, R = √(0.8322) ≈ 0.9122
The option that is the most reasonable estimate of the correlation coefficient is therefore; 0.9
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if you conduct a hypothesis test (for example, a z test), and find a p-value of .30, what is the meaning of the p-value?
The value for p is 30.
Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 700) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.learn more about hypothesis click here:
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Where do i start?
This is only a grade 11 math problem thanks
The smallest positive integer is 267 that should be multiply with given series.
What is meaning of series?
A series in mathematics is the total of a given set of terms. Real or complex numbers are typically used in these terms, but considerably more generality is conceivable.
Given series is 3, 6, 9, .... , 2400.
Assume that n should be multiply with the given series.
The series becomes 3n, 6n, 9n, .... , 2400n.
Now add the series:
(3n + 6n + 9n + ....+ 2400n)
Taking common 3n:
= 3n( 1 + 2 + 3 + ...+ 800)
Apply the formula the sum of the first n positive integers is n(n+1)/2
= 3n ×{800(800+1)}/2
=3n × 400 × 801
= 3n × 4 × 100 × 3 × 3 × 89
= (4 × 100 × 3 × 3) × (3 × 89) × n
The product of (4 × 100 × 3 × 3) is a perfect square. But 3 × 89 is not a perfect square. Thus n = 3 × 89 = 267.
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3. Tina needs to build a fence. The fence
is 30 feet long and 20 feet wide. She
realizes she needs more so she increases
the length and width by x feet. Create an
expression that represents the perimeter
for the fence.
Q1 Write a quadratic polynomial
, sum of whose zeroes is 3 and product is -40
The quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.
Define the term quadratic polynomial?When a variable term as in polynomial expression has a highest power of 2, the polynomial is said to be quadratic. A second-order polynomial is another name for a quadratic polynomial. A quadratic equation or quadratic function is created if a quadratic polynomial becomes equal to 0. The roots or zeros of both the quadratic equation are the name given to the solutions of this equation.For the stated values,
Sum of zeroes is 3 and product is -40
Use formula,
x² - x (sum of zeros) + (product of zeros) = 0.
Put the values.
x² - x (3) + (-40) = 0.
x² - 3x + -40 = 0.
Thus, the quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.
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Could someone help quick
The constant of proportionality is 1/7
What is constant of proportionality?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.Direct Variation: The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace. Example: y x represents the cost per item(y), which is directly proportional to the number of items(x) purchased.Inverse Variation: The indirect proportionality equation, y = k/x, demonstrates that when y rises, x falls, and vice versa. As shown by the formula y 1/x, the speed of a moving object (y) inversely varies with the amount of time (x) needed to travel a distance.K is constant in both circumstances. The coefficient of proportionality is the name given to this constant's value. The unit rate is another name for the proportionality constant.To learn more about constant of proportionality, refer to https://brainly.com/question/26171814
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I need a quick answer please !!!
——————————————————
The diagram (below) shows a game in which you use the pieces at the top to form solid rows at the bottom. Using only translations and rotations, describe the transformations of the pieces at
the top that will form two solid rows at the bottom.
meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow
In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia.
If Amelia scores 5 points, how many points did Bryce score?
Group of answer choices
A. 6
B. 10
C. 18
D. 5
Answer:
b
Step-by-step explanation:
b
Answer: Amelia 5, Keturah 10, Jordan 6, Bryce 18
Step-by-step explanation:
If Amelia scored 5 and Keturah scored 2 times of Amelia's score, then 5 x 2 is 10, so Keturah scored 10. If Keturah scored 10 and Jordan scored 4 points fewer than Jordan's score, then 10 - 4 is 6, so Jordan scored 6. If Jordan scored 6 and Bryce scored 3 times of Jordan's score, then 6 x 3 is 18, so Bryce scored 18. So C is the correct answer.
[tex]\sf -31 - 4x = -5 - 5(1 + 5x)[/tex]
Answer:
x = 1
Step-by-step explanation:
Given equation,
→ -31 - 4x = -5 - 5(1 + 5x)
Now the value of x will be,
→ -31 - 4x = -5 - 5(1 + 5x)
→ -31 - 4x = -5 - 5 - 25x
→ -4x + 25x = -10 + 31
→ 21x = 21
→ x = 21/21
→ [ x = 1 ]
Hence, the value of x is 1.
The value of the variable x in the equation -31 -4x = -5- 5(1+ 5x) will be 1.
The given algebraic expression with the variable x is,
-31 - 4x = -5 -5(1+ 5x)
By further solving it, we get,
- 31 - 4x = -5 -5 -25x
To simplify the equation, we have to first separate the constants and variables,
=> 25x - 4x = -5 -5 + 31
=> 21x = 31 - 5 -5
=> 21x = 31- 10
=> 21x = 21
=> x = 21/21
=> x= 1.
Hence, the value of the variable x in the algebraic expression, -31 - 4x = -5 -5(1+ 5x), is found to be 1.
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assume the average number of times that a typical american says a word that is considered to be profane is 4 times per day with a standard deviation of 5.6. a sample of 15 students from your university is found to vocalize 3.4 profane words per day. assume that we expect the students at your university to vocalize fewer profane words. conduct directional (left-tailed) hypothesis test to determine if there is a difference between you university's population and the general population. what is the z-observed value for the test?
The z-observed value for the test of average number of times that a typical american says a word that is considered to be profane is -0.41.
Define the term z-score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from mean are used to measure Z-score.The formula for calculating the z-score is-
z = (x - μ)/s
in which,
n = sample size (= 15)
μ = mean (= 4)
σ = standard deviation (= 5.6)
s = σ/√n
s = 5.6/√15
s = 1.44
Put the value in z score;
z = (3.4 - 4)/1.44
z = -0.41
Because of how near to zero this test statistic is, we will not be able to rule out the null hypothesis. Seven.
There isn't enough proof to claim that there is a mean difference or that it exists in your circumstance.
Thus, they're basically arguing that we can't rule out the null hypothesis.
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In the first round of math contest, each students had to answer 2 questions. Miriam averaged 76 seconds per question. Jake and Rafael averaged 84 seconds per question, and Sam averaged 80 seconds per question. At the end of the first round, what was the total time for all 4 students?
a) 324 seconds
b) 400 seconds
c) 480 seconds
d) 568 seconds
e) 648 seconds
At the end of the first round, the total time is 648 seconds ( option E )
What is average ?An average is the result that you get when you add two or more numbers together and divide the total by the number of numbers you added together.
For example, if there are 10 students in a class with ages 10, 11, 12, 10, 10,12,12,10,11,12 their average age will be( 10+ 11+12+10+10+12+12+10+11+12)/10
for Mariam her average time is 76 which means her total time is 76× 2= 152
for Jake and Rafael their average time is 84 which means their total time is 84×4= 336
for Sam,his average time is 80 which means is total time is 80×2= 160
therefore the total time spent by the 4 students is 152+336+160=648seconds
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Factor the polynomial by factoring out the Greatest Common Factor
The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
We are given an algebraic expression:
18y^4 + 24y^3 + 6y^2
We need to factorize by factoring out the Greatest Common Factor.
In the given algebraic expression, we can see that;
6 is the Greatest Common Factor of 18, 24, and 6.
y^2 is the Greatest Common Factor of y^4, y^3 and y^2.
So, we will take the common 6y^2 from the given expression;
18y^4 + 24y^3 + 6y^2
= 6y^2 (3y^2 + 4y + 1)
So, option A is correct.
Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
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Find a1 if d = -2 and a21 = 18.
The answer is either 58 or 60
For the given values of the arithmetic sequence d = -2 , a₂₁ = 18,then the value of a₁ = 58.
As given in the question,
Given values of the arithmetic sequence :
Common difference 'd' = -2
Twenty first term a₂₁ = 18
Formula for the nth term of arithmetic sequence with common difference 'd' and first term a₁ is given by:
aₙ = a₁ + (n -1) d
Substitute the value n =21 , a₂₁ =18 and d = -2 in the above equation we get,
⇒a₂₁ = a₁ + (21 -1)(-2)
⇒18 = a₁ + 20(-2)
⇒ a₁ = 18 +40
⇒a₁ = 58
Therefore, for the given values of the arithmetic sequence d = -2 ,
a₂₁ = 18,then the value of a₁ = 58.
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if you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your:
If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your working memory.
Define working memory.A cognitive apparatus known as working memory has a finite capacity and can only temporarily store information. It is crucial for reasoning, decision-making, and behaviour direction. When working on a long-division problem, kids use their working memory abilities to retain the long-division steps. Other instances include keeping track of complicated instructions, taking notes in class, recalling an argument while someone else is speaking, or performing mental calculations. In contrast to long-term memory, which stores a large amount of knowledge over a lifetime, working memory is the little amount of information that may be kept in mind and used to carry out cognitive tasks. One of the most often used concepts in psychology is working memory.
Given,
If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your:
d) Working memory
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f(x)=-1²-3x+ 20
Find f(5)
Answer:
6
Step-by-step explanation:
-1^2-3(5)+20
1-15+20
1+5
6
hopes this helps
Compare the governments of Germany and Russia. Make three lists pointing out similarities and differences. In the first list, point out the unique traits of the German government. In the second list, point out the unique traits of the Russian government. In the third list, point out the traits both governments have in common.
DON'T write an entire essay i just need a paragraph
Answer: During the Russian war, The Russians and Germans were at war with each other, Beating them brutally.
Step-by-step explanation:
According to flightstats com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 20 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 12 flights are on time. (d) Find and interpret the probability that fewer than 12 flights are on time. (e) Find and interpret the probability that at least 12 flights are on time. (f) Find and interpret the probability that between 10 and 12 flights, inclusive, are on time.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
The value of p=0.8 and n=20
The probability that exactly 12 flights are on time = 0.1772
The probability that exactly fewer than 12 flights are on time = 0.1049
The probability that at least 12 flights are on time = 0.8951
The probability that between 10 and 12 flights, are on time = 0.1795
(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,
p = 80% = 0.8
As, we made 20 trials and n is the total number of trials then,
the value of n be,
n = 20
(c) Now, if the probability of success on an individual trial is p ,
Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)
The probability that exactly 12 flights are on time, be
P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)
P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)
P(X=12) = 10,07,760×0.0687×0.00000256
P(X=12) = 0.1772
(d) Now, the probability that exactly fewer than 12 flights are on time, be
P(X<12) = 1 - P(X>12)
So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)
So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115
P(X>12) = 0.8951
P(X<12) = 1 - 0.8951
P(X<12) = 0.1049
(e) Now, the probability that at least 12 flights are on time, be
P(X>12)=0.8951
(f) The probability that between 10 and 12 flights, are on time, be
P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772
P(X=10)+P(X=11)+P(X=12) = 0.1795
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Please help, the blue dot is random
The equation would be 5(x + 3) = 45
To solve:
1) Distribute 5 to x and then 5 to 3
2) That gives you this equation: 5x + 15 = 45
3) Then subtract 15 from both sides
4) You should get this: 5x = 30
5) Then divide 5/5 and 30/5 to isolate the x
6) The answer should be: x = 6
Have a good day/night :)
Evaluate the expression when g = 0.6.
400g2−0.9÷g
what are the coordinates of the circumcenter of ABC A(-5,-4) B(3,-4) C(-1,6)
P(-4,-1) are the coordinates of circumcentre of the triangle
How to find the coordinates of the circumcenter of a triangle?The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.
Let A(-5,-4), B(3,-4), C(-1,6) be the vertices of the given △ABC.
Let P(x,y) be the circumcentre of △ABC. Then,
PA = PB = PC
Also, PA² = PB² = PC²
PA² = PB²
(x-(-5))² + (y-(-4))² = (x-3)² + (y-(-4))²
(x+5)² + (y+4)² = (x-3)² + (y+4)²
x²+10x+25 + y²+8y+16 = x²-6x+9 + y²+8y+16
10x-6x = 9-25
4x = -16
x = -16/4 = -4
Also, PB² = PC²
(x-3)² + (y+4)² = (x+1)² + (y-6)²
x²-6x+9 + y²+8y+16 = x²+2x+1 + y²-12y+36
-6x-2x+8y+12y = 37-9-16
-8y+20y = 12
-2x+5y = 3 .......(1)
put x= -4 into (1):
-2(-4)+5y = 3
8+5y = 3
5y = 3-8
5y = -5
y = -1
Therefore, the coordinates of circumcentre of △ABC are P(-4,-1)
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5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas
cost me $1.41.
a) Represent this information as a matrix equation.
b) Find the cost of a banana and an orange.
A) The matrix equation that represents the given information is;
[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]
B) The cost of a banana is; $0.05
The cost of an orange is; $0.12
How to create and solve a matrix equation?A matrix equation is defined as an equation where a variable stands for a matrix .
Let x represent cost of oranges
Let y represent cost of bananas
5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas
cost me $1.41. Thus, the equations are;
5x + 14y = 1.30 ----(1)
8x + 9y = 1.41 -----(2)
A) Now, the matrix form of the simultaneous equation above will be;
[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]
B) Multiply the first equation by 8 and the second one by 5 to get;
40x + 112y = 10.4
40x + 45y = 7.05 Subtract to get;
67y = 3.35
Divide both sides by 67 to get;
y = $0.05 per banana
Plug in 0.05 for y into eq 1 to get;
5x + 14(0.05) = 1.30
5x + 0.7 = 1.3
5x = 1.3 - 0.7
5x = 0.6
x = 0.6/5
x = $0.12
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