Answers
We are asked to find the total surface area of the right triangular prism.
Recall that the total surface area of a right triangular prism is given by
[tex]TSA=P\cdot h+2B[/tex]Where P is the perimeter of the base, h is the height of the prism, and B is the area of the base.
From the figure, we see that
height = 11
side 1 = 9
side 2 = 12
We can apply the Pythagorean theorem to find the length of the third side. (hypotenuse)
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=9^2+12^2 \\ c^2=81^{}+144 \\ c^2=225 \\ c=\sqrt[]{225} \\ c=15 \end{gathered}[/tex]Now we can find the perimeter of the base,
[tex]\begin{gathered} P=s_1+s_2+s_3 \\ P=9+12+15 \\ P=36 \end{gathered}[/tex]The area of the base is given by
[tex]\begin{gathered} B=\frac{1}{2}\cdot b\cdot h \\ B=\frac{1}{2}\cdot12\cdot11 \\ B=66 \end{gathered}[/tex]So, the total surface area of the right triangular prism is
[tex]\begin{gathered} TSA=P\cdot h+2B \\ TSA=36\cdot11+2(66) \\ TSA=396+132 \\ TSA=528\: \text{unit}^2 \end{gathered}[/tex]Therefore, the total surface area of the right triangular prism is 528 square units.
Related Questions
Given the following function, which table shows correct values for f(x)Where f(x)=-9x-5
Answers
Since the given function is
[tex]f(x)=-9x-5[/tex]Substitute x by 0, 1, 2, 3, 4 to find f(x), then you can find the correct table
[tex]\begin{gathered} x=0 \\ f(x)=-9(0)-5 \\ f(x)=0-5 \\ f(x)=-5 \end{gathered}[/tex][tex]\begin{gathered} x=1 \\ f(x)=-9(1)-5 \\ f(x)=-9-5 \\ f(x)=-14 \end{gathered}[/tex][tex]\begin{gathered} x=2 \\ f(x)=-9(2)-5 \\ f(x)=-18-5 \\ f(x)=-23 \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ f(3)=-9(3)-5 \\ f(3)=-27-5 \\ f(x)=-32 \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ f(x)=-9(4)-5 \\ f(x)=-36-5 \\ f(x)=-41 \end{gathered}[/tex]The correct table is the 4th answer
Find the area of the figure.3 in.3 in.2 in.9 in.
Answers
To find the aread of such construct, the first thing to do is to split the shape into 2 parts.
The area of the Shape A = 3 x 3 = 9 inch squared
The area of the Shape B = 9 x 2 = 18 inch squared
The total area = 18 + 9 = 27 inch squared
The equation for (5,-4)
Answers
If you are asking for an equation for a line that passes through 5,-4:
y + 4 = x - 5
y = x - 9
HELPP ASAP PLEASE, WILL GIVE BRAINLIEST !!!!!Sarah would like to hire a clown for her daughter’s birthday party. Clown A is offering his services for an initial fee of $100 in addition to $11 per hour. Clown B is offering her services for an initial $150 fee in addition to $8 per hour. When will the two clowns charge the same amount of money? Use a table to estimate the amount of money?As illustrated in the table above, the solution must be between ___________ and __________hours.
Answers
I need help with this
Answers
SOLUTION
In this question, we are going to solve each expression one after the other, and after we arrive at the solution, we will compare it to A, B, and C to see which matches. That will be the correct option to choose.
First expression calculation:
[tex]\begin{gathered} (3x^2-6x+11)-(10x^2-4x+6) \\ 3x^2-6x+11-10x^2+4x-6 \\ \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 3x^2-10x^2-6x+4x+11-6 \\ -7x^2-2x+5 \end{gathered}[/tex]The first expression is equivalent to the expression A
Second expression calculation:
[tex]\begin{gathered} (-3x^2-5x-3)-(-10x^2-7x+2) \\ -3x^2-5x-3+10x^2+7x-2 \\ C\text{ollect like terms} \end{gathered}[/tex][tex]\begin{gathered} -3x^2+10x^2-5x+7x-3-2 \\ 7x^2+2x-5 \end{gathered}[/tex]The second expression is equivalent to the expression C
Third expression calculation:
[tex]\begin{gathered} (12x^2+6x-5)-(5x^2+8x-12)_{} \\ 12x^2-5x^2+6x-8x-5+12 \\ 7x^2-2x+7 \end{gathered}[/tex]The third expression is equivalent to the expression B
Jermey paid 20.40 for a box of 15 pens.How much does each pen cost?
Answers
Jeremy paid $20.40 for a box of 15 pens.
The cost of one pen can be calculated by dividing the total cost by 15. This is shown below:
[tex]\Rightarrow\frac{20.40}{15}=1.36[/tex]Hence, each pen costs $1.36.
The cost of each pen is $1.36.
We will use the formula:
Cost of one pen = total amount/number of pens
Given in the question,
Total amount = $20.40
Number of pens = 15
Now, we will put the values in the above formula,
Cost of one pen = 20.40 / 15
= $1.36
Therefore, the cost of each pen is $1.36.
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Segment JB= angle K= triangle MLC= angle M= triangle KBJ=
Answers
Given that triangle LMC and BJK are conrguent, i.e LMC≅BJK
The triangles are shown below
From the diagram above, the following congruence statements are true,
i) Segment JB≅ML
ii) ∠K≅∠C
iii) ΔMLC≅ΔJBK
iv) ∠M≅J
v) ΔKBJ≅ΔCLM
Solve the problem as fast as you can it’s not a timed assessment or test
Answers
Answer:
[tex]\text{B }[/tex]Explanation:
Here, we want to solve the given quadratic equation
We start by dividing through by 4
We have that as:
[tex]x^2\text{ + 6 = 0}[/tex]Then we proceed to evaluate the above, solving for x
[tex]\begin{gathered} x^2=\text{ -6} \\ x\text{ = }\sqrt{-6} \\ x=\text{ }\sqrt{6\text{ }\times(-1)} \\ x\text{ = }\sqrt{6}\text{ }\times\text{ }\sqrt{(-1)} \\ \sqrt{(-1)}\text{ = i} \\ x=\text{ i}\pm\sqrt{6} \\ x\text{ = +i}\sqrt{6}\text{ or -i}\sqrt[]{6} \end{gathered}[/tex]restaurant Distributing offers a commercial pasta maker for $980 with a trade discount of 25% what is the additional discount needed to match a competitor's price of a $661.50
Answers
Restaurant Distributing offers a commercial pasta maker for 980 with a trade discount of 25%. This means the company is offering to sell the product at the price calculated below;
[tex]\begin{gathered} \text{Discount}=0.25 \\ \text{Discounted price=980-(980 x 0.25)} \\ \text{Discounted price=980-245} \\ \text{Discounted price=735} \end{gathered}[/tex]However, a competitor is offering to sell at $661.50. This means the discount to be offered should be equal to 980 - 661.50. Hence the new discount amount shoud be $318.50. Therefore the additional discount would be calculated as follows;
[tex]\begin{gathered} \text{Discount}=\frac{318.5}{980}\times100 \\ \text{Discount}=\frac{3185}{98} \\ \text{Discount}=32.5 \end{gathered}[/tex]This means, rather than offering a discount of 25%, Restaurant distributing should offer an additional discount of 32.5 - 25 which gives you 7.5%
what digit is in the
Answers
71 x 98
to make an estimation, we round as follows:
70 x 100
and that's equal to 7000
If A and B are events with P(A) = 0.6, P(A OR B)0.98, PCA AND B)0.02, find P(B)
Answers
We are given the following:
[tex]\begin{gathered} P\mleft(A\mright)=0.6 \\ P\mleft(A,orB\mright)=0.98 \\ P(A,\text{and }B)=0.02 \\ \\ \text{For Mutually }Exclusive,\text{ we have:} \\ P\mleft(A,orB\mright)=P\mleft(A\mright)+P\mleft(B\mright)=0.98 \\ \Rightarrow0.6+P(B)=0.98 \\ P\mleft(B\mright)=0.98-0.6=0.38 \\ P\mleft(B\mright)=0.38 \\ \\ \text{For Mutually }Inclusive,\text{ we have:} \\ P(A,orB)=P(A)+P(B)-P(A,\text{and }B) \\ 0.98=0.6+P(B)-0.02 \\ P(B)=0.98+0.02-0.6 \\ P(B)=1-0.6 \\ P(B)=0.4 \\ \\ For\text{ Independent Events, we have:} \\ P(A,\text{and }B)=P(A)\times P(B) \\ 0.02=0.6\times P(B) \\ P(B)=\frac{0.02}{0.6} \\ P(B)=0.033 \end{gathered}[/tex]The answer for P(B) would therefore be determined by the type of events that A & B are
If y is proportional to x, find the missing number.1. 2.82. 9.63. 12.64. 14.2
Answers
Given
y is proportional to x.
And,
To find: The missing value.
Explanation:
It is given that,
y is propertional to x.
And,
That implies,
Since y is proportional to x.
Then,
[tex]\begin{gathered} y\propto x \\ \Rightarrow y=kx \\ \Rightarrow k=\frac{y}{x} \end{gathered}[/tex]Then, for x=5, and y=6.
[tex]\begin{gathered} k=\frac{6}{5} \\ k=1.2 \end{gathered}[/tex]Therefore, for x=8,
[tex]\begin{gathered} y=1.2\times8 \\ =9.6 \end{gathered}[/tex]Hence, the missing value is 9.6.
Rewrite the following expression using the distribute property:4.5(3m + 7n)
Answers
Answer: 13.5m + 31.5n
Given that
4.5(3m + 7n)
Firstly, we need to open the parenthesis by multiplying through by 4.5
4.5 x 3m + 4.5 x 7n
13.5m + 31.5n
The answer is 13.5m + 31.5n
5. Which transformation could have been applied to A WXY to obtain AW'X'Y'?wA reflection across the v-axisBreflection across the lineC clockwise rotation of 90° about the originD. counterclockwise rotation of 90° about the origin
Answers
The transofrmation applied was a Clockwise rotation of 90°about the origin.
Answer: Option C
If a1 =5 and an = 2a n-1 + 5 then find the value of a4
Answers
According to the arithmetic progression, the value of a4 is 75
Arithmetic progression:
An arithmetic progression (A.P.) is the sequence of numbers that has a fixed common difference between any two consecutive numbers.
Given,
Here we have the value of a1 = 5 And the function for arithmetic progression which is an = 2(an-1) +5
Now we need to find the value of a4.
To find the value of a4, we have to find the value of a2 and a3.
For that, we have to apply the given value into the function,
So, the value of a2 is calculated as,
a2 = 2 (a2 - 1) + 5
WE know that the value of a1 = 5, then the value of a2 is
a2 = 2 (a1) + 5
a2 = 2(5) + 5
a2 = 15
So, the value of s3 is
a3 = 2 (a3 - 1) + 5
a3 = 2(a2) + 5
a3 = 2(15) + 5
a3 = 35
Finally, the value of a4 is calculated as,
a4 = 2 (a4 - 1) + 5
a4 = 2(a3) + 5
a4 = 2(35) + 5
a4 = 75.
Therefore, the value of a4 is 75.
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Statistics show that the fractional part of a battery 8that is still good after hours of use is given by B 4-0 What fractional part of the battery is still operatingafter 300 hours of use)AnswerHow to answer nens in new window)Keypad
Answers
Given,
[tex]B=4^{-0.01t}[/tex]t = 300
Replace,
[tex]B=4^{-0.01\cdot\:300}[/tex]Multiply -0.01*300 = 3
[tex]B=4^{-3}[/tex]Apply exponent rule,
[tex]a^{-b}=\frac{1}{a^b}[/tex][tex]B=\frac{1}{4^3}[/tex]Simplify, 4^3=64
[tex]B=\frac{1}{64}[/tex]Answer: B = 1 / 64
Olivia wants to record her favorite songs to one CD. The function t = 40 - 5n represents the recording time t available after n songs are recorded. Find the zero of this function. Describe what this value means in this context.
Answers
The zero of the function is 8. Because songs are countable, there will be no more room for recording after the first eight. Furthermore, there will not be enough space to finish recording the ninth song.
What is the value?The value refers to the worth of each digit in relation to its position in the number. We compute it by multiplying the digit's place and face values. Place Value + Face Value = Value.
The absolute value of 9 is represented by the symbol |9| and is equal to 9. As a result, the absolute value of 9 = |9| = 9. 5 has a place value of 500 and is in the hundreds. 4 is a tens number with a place value of 40. 8 is in the first position and has a place value of 8.
The monetary value of something in the market.A reasonable payment in the form of products, services, or cash for the item exchanged. The value of base stealing in baseball communicates nothing of value.Relative value, utility, or significanceGiven:
c = 40 - 5n
Where
c = recording time available
n = number of songs recorded
When c = 0, the
40 - 5n = 0
n = 40/5 = 8
The zero of the function is 8
Because songs are countable, it means that after 8 songs are recorded, there will be no room to record additional songs. Furthermore, there will not be enough room to finish recording the 9-th song.
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cual es la ecuacion perpendicular de la recta y=-2x+1 que pasa por el punto (-1,4)
Answers
y = 1/2 (x) + 4 1/2
Explanation:
ecuación de la recta: y = mx + c
la ecuación dada: y = -2x + 1
comparando ambas ecuaciones:
m = -2
c = 1
Para que la ecuación de una recta sea perpendicular a otra, la pendiente de una será el recíproco de la pendiente de otra
m = -2
recíproco de -2 = 1 / -2 = -1/2
recíproco negativo = - (- 1/2)
recíproco negativo = 1/2
El punto de la nueva línea: (-1, 4) = (x, y)
insertamos el punto y la pendiente en la fórmula de la ecuación de la línea para obtener la intersección:
y = mx + c
4 = 1/2 (-1) + c
4 = -1/2 + c
4 + 1/2 = c
4 1/2 = c
y = 1/2 (x) + 4 1/2
La ecuación de la recta perpendicular ay = -2x + 1 es y = 1/2 (x) + 4 1/2
a punch recipe calls for 5 lb of grape juice for every 2 L of cranberry juice how many liters of grape juice is needed in 5 L of cranberry juice for used
Answers
Answer:
12.5 L of grape juice is needed in 5L of cranberry juice.
Step by step explanation:
We can solve this situation by using proportional relationships:
[tex]\begin{gathered} \frac{5}{2}=\frac{x}{5} \\ \end{gathered}[/tex]Now, solve for x:
[tex]\begin{gathered} 25=2x \\ x=\frac{25}{2} \\ x=12.5\text{ L} \end{gathered}[/tex]A car is purchased for $45,000. Each year it loses 20% of its value. After how many years will the car be worth $14,500 or less?
Answers
Answer:
6 years
Step-by-step explanation:
D(t) = 45,000/(1.2)^t
D(t) <= 14,500
45,000/(1.2)^t = 14,500
cross multiply
(1.2)^t = 45,000/14,500
(1.2)^t = 3.1034
natural log of both sides
LN(1.2^t) = LN(3.1034)
t * LN(1.2) = 1.1325
t * 0.1823 = 1.1325
t = 6.2123
round up whole number = t = 6
My brain hurts
d+f+e=180
d=4x+2
f=7x-8
e=4x+6
Answers
⇒You are given the values of the variables d,f,e
⇒d=4x+2
⇒e=4x+6
⇒f=7x-8
In the place of of the variable plug in the values:
[tex](4x+2)+(4x+6)+(7x-8)=180\\4x+4x+7x+2+6-8=180\\15x+8-8=180\\15x=180\\\frac{15x}{15} =\frac{180}{15} \\x=12[/tex]
To find the values of the variable d,e and f plug in the the value of x and and simplify.
[tex]d=4(12)+2\\d=48+2\\d=50[/tex]
[tex]e=4(12)+6\\e=48+6\\e=54\\[/tex]
[tex]f=7(12)-8\\f=84-8\\f=76[/tex]
GOODLUCK!!!!
Solve the following using substitution: 3X = 6Y -94X + 3Y = -1
Answers
So we need to solve the following system of equations:
[tex]\begin{gathered} 3x=6y-9 \\ 4x+3y=-1 \end{gathered}[/tex]We must use the method of substitution. This means that the first step is to choose one of the equations and clear one of the variables, either x or y. So let's pick the first one and clear x:
[tex]\begin{gathered} 3x=6y-9 \\ x=\frac{6y-9}{3} \\ x=2y-3 \end{gathered}[/tex]Now we have an expression for x where x is a function of y. The next step is to take the right side of this expression and substitute the x on the second equation with it:
[tex]\begin{gathered} 4x+3y=-1 \\ 4\cdot(2y-3)+3y=-1 \\ 8y-12+3y=-1 \end{gathered}[/tex]Now we find y:
[tex]\begin{gathered} 8y-12+3y=-1 \\ 11y-12=-1 \\ 11y=-1+12=11 \\ y=\frac{11}{11}=1 \end{gathered}[/tex]Now we take the expression we find for x and substitute y=1 on it:
[tex]\begin{gathered} x=2y-3=2\cdot1-3=2-3 \\ x=-1 \end{gathered}[/tex]So the answer is:
[tex]\begin{gathered} x=-1 \\ y=1 \end{gathered}[/tex]Which is the point (-1,1) in the cartesian grid.
Between what two integers does log 2 1000 lie
Answers
Solution:
Given;
[tex]\log_21000[/tex]From law of logarithm;
[tex]\log_ba=\frac{\log_{10}a}{\log_{10}b}[/tex]Thus;
[tex]\begin{gathered} \log_21000=\frac{\log_{10}1000}{\log_{10}2} \\ \operatorname{\log}_21000=\frac{\operatorname{\log}_{10}10^3}{\operatorname{\log}_{10}2} \\ \end{gathered}[/tex]Another law of logarithm;
[tex]\log_ba^c=c\log_ba[/tex]Thus;
[tex]\begin{gathered} \log_21000=\frac{3\log_{10}10}{\log_{10}2} \\ \log_aa=1 \\ \log_21000=\frac{3\left(1\right)}{\log_{10}2} \\ From\text{ a table of common logarithm;} \\ \log_{10}2=0.3010 \\ \log_21000=\frac{3}{0.301} \\ \log_21000=\frac{3000}{301} \\ \log_21000=9\text{ remainder 291} \\ \end{gathered}[/tex]FINAL ANSWER
[tex]\log_21000\text{ lies between }9\text{ and }10[/tex]
In a certain region the average movie theater ticket price in 2009 was $7.80 in 2008 it was $7.37 find the increase in average movie theater ticket price from 2008 to 2009. The increase in average movie theater ticket price from 2008 to 2009 was? (simplify your answer. type a whole number or a decimal.)
Answers
In order to find the average increase in the price, we need to divide the difference in the price by the difference of time.
The price changed from $7.37 to 7.80, and the time changed from 2008 to 2009, so we have:
[tex]\text{average increase}=\frac{7.80-7.37}{2009-2008}=\frac{0.43}{1}=0.43[/tex]So the average increase in the price was $0.43.
4. Use the hyperbola equationand y-values in the table.(2 - 21) (y - yı)a262= 1 to find the y-values to the nearest integer from the gis(2-2)²9( 1)4y6210100 - 40-6-202
Answers
Isolate y from the equation:
[tex]\frac{(x-2)^2}{9}-\frac{(y-1)^2}{4}=1[/tex][tex]\Rightarrow-\frac{(y-1)^2}{4}=1-\frac{(x-2)^2}{9}[/tex][tex]\begin{gathered} \Rightarrow(y-1)^2=(1-\frac{(x-2)^2}{9})(-4) \\ =\frac{4}{9}(x-2)^2-4 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow y-1=\pm\sqrt[]{\frac{4}{9}(x-2)^2-4} \\ \Rightarrow y=1\pm\sqrt[]{\frac{4}{9}(x-2)^2-4} \end{gathered}[/tex]Substitute x=10 to find the two possible values for y:
[tex]\begin{gathered} y=1\pm\sqrt[]{\frac{4}{9}(10-2)^2-4} \\ =1\pm\sqrt[]{\frac{4}{9}(8)^2-4} \\ =1\pm\sqrt[]{\frac{4}{9}(64)^{}-4} \\ =1\pm\sqrt[]{\frac{256}{9}-4} \\ =1\pm\sqrt[]{\frac{256-36}{9}} \\ =1\pm\sqrt[]{\frac{220}{9}} \\ =1\pm\frac{2\sqrt[]{55}}{3} \end{gathered}[/tex]The aproximate values of y are:
[tex]\begin{gathered} y_1\approx5.944\ldots \\ y_2\approx-3.944\ldots \end{gathered}[/tex]To the nearest whole number, we can see that the second value of y is approximately -4.
A ball is thrown from a height of 217 feet with an initial downward velocity of 17 ft/s. The ball's height h (infeet) after t seconds is given by the following.h=217-177-161How long after the ball is thrown does it hit the ground?Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)secondsorХ5?ground
Answers
The equation representing the ball's movement is given as follows;
[tex]h=217-17t-16t^2[/tex]To determine the value of t (that is, time), we shall now make the equation become;
[tex]217-17t-16t^2=0[/tex]This is because when the height is zero, then the ball has actually touched the ground. So making h equal to zero, we now have a quadratic equation and we shall solve it using the quadratic equation formula as follows;
[tex]t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The variables are,
[tex]\begin{gathered} -16t^2-17t+217=0 \\ a=-16,b=-17,c=217 \end{gathered}[/tex]We now have;
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-(-17)\pm\sqrt[]{(-17)^2-4\lbrack-16\rbrack\lbrack217\rbrack}}{2(-16)} \\ t=\frac{17\pm\sqrt[]{289+13888}}{-32} \\ t=\frac{17\pm\sqrt[]{14177}}{-32} \\ t=\frac{17\pm119.0672}{-32} \\ t=\frac{17+119.0672}{-32},t=\frac{17-119.0672}{-32} \\ t=-4.2521,t=3.1896 \end{gathered}[/tex]The quadratic equation now has two solutions.
Note however, that the question requires us to determine the time taken and we know this cannot be a negative value.
Therefore, we shall take t = 3.1896, and rounded to the nearest hundredth this becomes;
[tex]t\approx3.19\text{ (rounded to the nearest hundredth)}[/tex]Consider the following word problem:A pizzeria sells three sizes of pizza: small, medium, and large. The pizzas sell for S7, S10, and SII.respectively. One evening they sold 47 pizzas and received $469. If they sold 17 more large than smallpizzas, how many of each size did they sell?Use the Gaussian elimination method with back substitution to solve the given word problem.AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutssmall=medium=large=
Answers
System of Equations
Let:
x = number of small pizzas
y = number of medium pizzas
z = number of large pizzas
They sold 47 pizzas, thus:
x + y + z = 47
They received 7x for the small pizzas, 10y for the medium pizzas, and 11z for the large pizzas, thus:
7x + 10y + 11z = 469
The last condition states they sold 17 more large than small pizzas, thus:
z = 17 + x
Rearranging the system of equations:
x + y + z = 47
7x + 10y + 11z = 469
x + 0y - z = -17
Now we write the expanded matrix of the system:
[tex]\begin{bmatrix}1{} & {1} & {1} & {47} \\ {7} & {10} & {11} & {469} \\ {1} & {0} & {-1} & {-17} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Apply Gauss-Jordan Elimination Method.
Multiply row 1 by -7 and add it to row 2:
[tex]\begin{bmatrix}1{} & {1} & {1} & {47} \\ 0 & 3 & 4 & 140 \\ {1} & {0} & {-1} & {-17} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Divide row 2 by 3:
[tex]\begin{bmatrix}1{} & {1} & {1} & {47} \\ 0 & 1 & \frac{4}{3} & \frac{140}{3} \\ {1} & {0} & {-1} & {-17} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Multiply row 2 by -1 and add it to row 1:
[tex]\begin{bmatrix}1{} & 0 & -\frac{1}{3} & \frac{1}{3} \\ 0 & 1 & \frac{4}{3} & \frac{140}{3} \\ {1} & {0} & {-1} & {-17} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Multiply row 1 by -1 and add it to row 3:
[tex]\begin{bmatrix}1{} & 0 & -\frac{1}{3} & \frac{1}{3} \\ 0 & 1 & \frac{4}{3} & \frac{140}{3} \\ 0 & {0} & -\frac{2}{3} & {-\frac{52}{3}} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Multiply row 3 by -3/2:
[tex]\begin{bmatrix}1{} & 0 & -\frac{1}{3} & \frac{1}{3} \\ 0 & 1 & \frac{4}{3} & \frac{140}{3} \\ 0 & {0} & 1 & 26 \\ {} & {} & {} & {}\end{bmatrix}[/tex]Multiply row 3 by 1/3 and add it to row 1:
[tex]\begin{bmatrix}1{} & 0 & 0 & 9 \\ 0 & 1 & \frac{4}{3} & \frac{140}{3} \\ 0 & {0} & 1 & 26 \\ {} & {} & {} & {}\end{bmatrix}[/tex]Multiply row 3 by -4/3 and add it to row 2:
[tex]\begin{bmatrix}1{} & 0 & 0 & 9 \\ 0 & 1 & 0 & 12 \\ 0 & {0} & 1 & 26 \\ {} & {} & {} & {}\end{bmatrix}[/tex]Now we have the identity matrix 3x3 to the left and the column of solutions to the right:
x = 9, y = 12, z = 26
They sold 9 small pizzas, 12 medium pizzas, and 26 large pizzas
If 3 1/3 lb of turkey costs $10.50, how much is one pound of turkey?
Answers
Answer:
$3.15
Step-by-step explanation:
Cost of 3 1/2 lb of turkey = $10.50
Cost of 1 lb of turkey = $ (10.50 ÷ 3 1/3) = $(10.50 ÷ 10/3) (∵ 3 1/3 = [tex]\frac{3*3+1}{3}[/tex] = 10/3)
=> $ (10.50 x 3/10) = $(1.05 * 3) = $ 3.15
Hence the cost for 1 lb of turkey is $3.15.
Hope you understood!!
Tanisha and her friends were playing a card game where the smallest number wins. Below is their scorecard.Tanisha −15Tyrell −18Carlos −12Samantha −9Who won the game?TanishaSamanthaCarlosTyrell
Answers
It is known that the smallest number wins the game.
As per the given data, Samantha has a score of 9 which is lowest.
Hence Samantha won the game.
A parallelogram has height 9cm and area 45cm? What
is the length of its base?
Answers
Answer: Firstly the area of parallelogram is. = b×h. so value of base is 9cm and height is 45cm . So area is equal to. base×height. = 9×45= 405² cm.
405cm²