Answer:
1. CA is defined
2. B^T * C^T defined
3. AC is NOT defined
4. A - B is defined
5. B - C is NOT defined
6. B^T is defined
Hence, 1,2,4, and 6 are defined
Step-by-step explanation:
Order of the matrices:
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
To determine which are defined
1. CA
CA means product of Matrix C and Matrix A
To determine the product of two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. For example, given that matrix X is a (m × n) matrix, matrix Y is a (n × k) matrix and matrix Z is (k × n) matrix. From the definition above,
XY can be determined because number of columns in X equals number of rows in Y
XZ cannot be determine because number of columns in X is not equal to the number of rows in Z.
YZ can be determined because number of columns in Y equals number of rows in Z
(NOTE: A matrix of order (m × n) means the matrix has m rows and n columns)
Hence, for CA
Matrix C is a (7 × 4) matrix
Matrix A is a (4 × 6) matrix
Number of columns in C equals number of rows in A, hence CA is defined
2. B^T * C^T
B^T means transpose of matrix B
Transpose of a matrix is defined as a new matrix whose rows are the same as the columns of the original matrix and whose columns are the rows of the original matrix. Hence, for a matrix of order (m × k), the transpose of the matrix will have an order (k × m).
Hence,
Matrix B is a (4 × 6) matrix
∴B^T gives a matrix of order (6 × 4)
Matrix C is a (7 × 4) matrix
∴ C^T gives a matrix of order (4 × 7)
Since the number of columns in B^T equals the number of rows in C^T, then B^T * C^T defined
3. AC
Matrix A is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
The number of columns in A is NOT equal to the number of rows in C, hence AC is NOT defined
4. A - B
To find the difference between two matrices, the matrices must have the same order.
Matrix A is a (4 × 6) matrix
Matrix B is a (4 × 6) matrix
Since matrices A and B have the same order [(4 × 6)], hence A - B is defined
5. B - C
Matrix B is a (4 × 6) matrix
Matrix C is a (7 × 4) matrix
Since matrices B and C are of different orders [(4 × 6) and (7 × 4) respectively], then B - C is NOT defined
6. B^T
B^T means the transpose of matrix B
Matrix B is a (4 × 6) matrix
From the above definition
B^T gives a (6 × 4) matrix
Hence, B^T is defined
Justin’s lemonade stands didn't do well this year. He.spent $14.28 on supplies (lemons and paper cups). He paid his friend $13 to help him build his lemonade stand. He sold forty-one cents each. What was his profit?
Answer:
16 + (–7) + 22 + (–12)
Hope this helped!!!
Solve the formula 2x+3y=12 for y.
Answer:
y=4 - [tex]\frac{2x}{3}[/tex]
Step-by-step explanation:
The value of y for 2x + 3y = 12 is (12 - 2x) / 3.
Given,
2x + 3y = 12
We will solve for y.
How to solve an equation for a variable?We will keep the like terms on one side of the equation and solve for the required variable.
Example: x + 2x + y = 3 + 2y
Solve for y:
x + 2x + y = 3 + 2y
3x = 3 + 2y - y
3x - 3 = y
3(x - 1) = y
y = 3(x - 1) is our answer.
Solve 2x + 3y = 12 for y.
We have,
2x + 3y = 12
Keep y on one side of the equation.
3y = 12 - 2x
Divide both sides by 3.
y = (12 - 2x) / 3
Thus the value of y for 2x + 3y = 12 is (12 - 2x) / 3.
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The sale price of a new refrigerator is $648 and sales tax is figured at 0.10 times the price. What is the total amount paid for the refrigerator?
Answer:
$712.80
Step-by-step explanation:
648×0.10=64.8
648+64.8=712.8
The total amount paid for the refrigerator is $712.8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Sale price = $648
Sales tax = 0.10 times the price
The total amount paid.
= 648 + 0.10 x 648
= 648 + 64.8
= 712.8
Thus,
The total amount paid is $712.8.
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Evaluate the polynomial when a.x=0 and b.x=-1
x2 – 3x - 7
Answer:
a) -7 & b) -6
Step-by-step explanation:
Here,
a) x = 0
Solution ↦
[tex]x2 - 3x - 7 \\ = 0 \times 2 - 3 \times 0 - 7 \\ = - 7[/tex]
b) x = -1
Solution ↦
[tex]x2 - 3x - 7 \\ = - 1 \times 2 - 3 \times ( - 1) - 7 \\ = - 2 + 3 - 7 \\ = - 9 + 3 \\ = - 6[/tex]
Write an equation with a slope of -7 and a y-intercept of (0,4)
Answer:
Step-by-step explanation:
y - 4 = -7(x - 0)
y = -7x + 4
Name the coordinate of P(-5, 8) under a translation along the
(x+2, y -1)
What is 31 1/2 divided by 3 1/2
Answer:
9
Step-by-step explanation:
used a calculator
what is the difference between 585 and -8
Answer:
593
Step-by-step explanation:
when you are subtracting a negative it is the same as adding
Write a numerical expression for the verbal phrase. The quotient of 81 and 3.
A. 3÷81
B. 27
C. 81÷3
D.81×3
Answer:
C. 81÷3
Step-by-step explanation:
We want to write a numerical expression for the phrase: "the quotient of 81 and 3"
Quotient indicates division, so we must divide 81 by 3.
81÷3
This can be further simplified, but the questions asks for a numerical expression. This is defined as an expression with numbers and at least one operation. So, B is correct, because 81 divided by 3 is 27, but it is not a numerical expression.
Therefore, the best answer choice is C. 81÷3
how do i do linear functions?
Answer:
1. Substitute the value of f(x) into the problem. 8=3x-1.
2. Isolate the variable. Add 1 to both sides to isolate the variable term by using the opposite operation to move the constant term across the equal sign. ...
3. Continue to isolate the variable. ...
4. Simplify.
Step-by-step explanation:
A local pizza shop has a membership program for frequent buyers the membership cost $25 per month the members get a discount price of 150 per pizza slice Aaliyah purchased a membership to this pizza shop how much would a Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month what would be the monthly cost for a slice of pizza
This question was not written properly
Complete Question
A local pizza shop has a membership program for frequent buyers the membership cost $25 per month the members get a discount price of $1.50 per pizza slice. Aaliyah purchased a membership to this pizza shop , how much would Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month ?
What would be the monthly cost for a slice of pizza?
Answer:
a) $34
b) $26.50
Step-by-step explanation:
From the question:
Membership for frequent buyers in a month = $25
Discount price = $1.50 per pizza slice
a) How much would Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month ?
This is calculated as:
Membership cost in a month + Discount price × Number of pizzas bought
= $25 +( $1.50 × 6 slices of pizza)
= $25 + $9
= $34
b) What would be the monthly cost for a slice of pizza?
This is calculated as:
Membership cost + Discount price × Number of slices
= $25 + $1.50 × 1
= $26.50
Please assist me with these problems and show the work. Part 1 4. From a horizontal distance of 80.0 m, the angle of elevation to the top of a fragpole is 18°. Calculate the height of the flagpole to the nearest tenth of a metre. 5. A 9.0 m ladder rests against the side of a wall. The bottom of the ladder is 1.5 m from the base of the wall. Determine the measure of the angle between the ladder and the ground, to the nearest degree.
Answer:
4) About 26.0 feet
5) About 80 degrees.
Step-by-step explanation:
Please refer to the (badly drawn, sorry) drawings.
4)
So for a horizontal distance of 80 meters, the angle of elevation is 18 degrees. And we want to find the height.
The horizontal distance is adjacent to the angle, and the height is opposite to the angle. Thus, we can use the trigonometric ratio tangent.
Recall that tangent is:
[tex]\tan(x)=opp/adj[/tex]
Substitute 18 for x, h for opposite, and 80 for adjacent. Thus:
[tex]\tan(18)=\frac{h}{80}[/tex]
To solve for h, multiply both sides by 80:
[tex]h=80\tan(18)[/tex]
Use a calculator:
[tex]h\approx25.9938[/tex]
So, the height is approximately 26.0 feet.
5)
So, this time, we need to find the angle. We know the hypotenuse and the side adjacent to the angle. So, we can use cosine. Recall that:
[tex]\cos(x)=adj/hyp[/tex]
Substitute 1.5 for adjacent and 9 for the hypotenuse. Thus:
[tex]\cos(x)=\frac{1.5}{9}[/tex]
Take the inverse cosine of both sides:
[tex]x=\cos^{-1}(\frac{1.5}{9})[/tex]
Use a calculator:
[tex]x\approx80.4059\textdegree\approx80\textdegree[/tex]
So, the angle is about 80 degrees.
And we're done!
Answer:
4) About 26.0 feet
5) About 80 degrees.
Step-by-step explanation:
Write the equation of the line in slope-intercept form.
what is 8.546 rounded to the nearest tens?
Answer:
10
Step-by-step explanation:
In this problem we need to round off 8.546 to the nearest tens. 8 is in ones place, 5 is in tenths place, 4 is in hundredths place and 6 is in thousandth place.
8 falls between 5 and 10 on the number line. It is less than 5 and more than 10. When it is rounded off to nearest tens it can be given by 10.
There are two numbers which add up to 20. If one number is five more than four times the other, find the numbers.
Answer:
3 and 17
Step-by-step explanation:
Let x and y represent the numbers.
x + y = 20 . . . . . . . . the numbers add up to 20
x = 5 + 4y . . . . . . . . one number is 5 more than 4 times the other
Substituting the second equation into the first:
(5 +4y) +y = 20
5y = 15 . . . . . . . . . . subtract 5
y = 3 . . . . . . . . . . . . divide by 5
x = 20 -3 = 17
The numbers are 17 and 3.
Which fractions are equivalent to 6/8 ? Check all that apply.
1/4
2/8
4/16
3/4
12/16
Answer:
3/4
Step-by-step explanation:
you got to find the half of the number
Is the answer (-1,1)???
Answer:
yes
Step-by-step explanation:
Answer:
(1 , -1)
Step-by-step explanation:
7( 1 ) - 3( -1 ) = 10
7 - - 3 = 10
7 + 3 = 10
10 = 10
true
Evaluate and simplify the following complex fraction.
Answer:
The answer is
[tex] - \frac{10}{7} \: \: \: or \: \: - 1 \frac{3}{7} [/tex]Step-by-step explanation:
[tex] \frac{ - \frac{5}{7} }{ \frac{2}{4} } [/tex]First of all we can write the fraction as
[tex] - \frac{5}{7} \div \frac{2}{4} [/tex]Simplify the second fraction
That's
[tex] \frac{2}{4} = \frac{1}{2} [/tex]So we have
[tex] - \frac{5}{7} \div \frac{1}{2} [/tex]Next change the division sign to multiplication sign and reverse the second fraction
That's
[tex] -\frac{5}{7} \times \frac{2}{1} [/tex]Multiply the terms
We have the final answer as
[tex] - \frac{10}{7} \: \: \: or \: \: - 1 \frac{3}{7} [/tex]Hope this helps you
A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose 3 tiles from the bag without looking. What is the probability that you chose tiles with the letters A,B,C?
Ps: don’t text me only if u know the answer that’s it
Answer:
for each letter 1 /26 is the probability
Step-by-step explanation:
probability = no. of events / no. of outcome
probability for tile A
= no. of events / no. of outcome
= 1 / 26
probability for tile B
= no. of events / no. of outcome
= 1 / 26
probability for tile C
= no. of events / no. of outcome
= 1 / 26
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if 5a + 2b + 6c 32, what is the value of c?
Answer:
c= (-5a-2b+32)/6
Step-by-step explanation:
this is the answer, but you will b=have to a little more work to figure out each variable so you can get a number
Why is the answer for letter b 9?
Answer:
Take a look at the 'proof' below
Step-by-step explanation:
The graph of the function g(x) is similar to that of the function f(t). The local minimum, local maximum, absolute minimum, maximum etc... of 'x' is always the closest x-intercept of the graph of f(t).
Let's check if this statement is right. The two local minimum(s) of the function f(t) occurs at x = 2, and x = 6. The two local maximum(s) occur at 1/4 and 4. As you can see the maximum / minimum of the function g(x) is always an x-intercept, x = 3, x = 7.
For part (b) the absolute maximum value of the function f(t), is 8. The closest x-intercept is 9, which is our solution.
Step-by-step explanation:
From x=0 to x=1, the function is above the x-axis, so the area is positive.
From x=1 to x=5, the area above the x-axis is greater than the area below the x-axis, so the net area is positive.
From x=5 to x=9, the area above the x-axis is greater than the area below the x-axis, so the net area is positive.
Since the area increases in each interval, the area is a maximum at x=9.
Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 90 ÷ [ 10 + ( 3 2 − 4 ) ]
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression when simplified is equal to 2.3684.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
As per the PEMDAS, we will first solve the parenthesis. Since the round parenthesis is solved first, therefore, we can write,
90 ÷ [10 + ( 32 − 4 )]
= 90 ÷ [10 + (28)]
= 90 ÷ [10 + 28]
Solving the next parenthesis, therefore, the square brackets,
= 90 ÷ [10 + 28]
= 90 ÷ 38
At last, we will solve the division, therefore, we can write,
= 90 ÷ 38
= 2.3684
Hence, the value of the expression when simplified is equal to 2.3684.
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Mrs. Yakubov needs to distribute 4 colored pencils and 3 glue sticks to the 6 tables in her classroom. Which expression represents the number of materials being distributed this situation? 6(4 + 3) 4(3 + 6) 3(4 + 6)
Answer:
[tex]6(4 + 3)[/tex]
Step-by-step explanation:
Given
Pencils = 4
Glue = 3
Required
Distribute these to 6 tables
Represent the pencils with P and Glue with G
The distribution to 6 tables will be:
[tex]6P + 6G[/tex]
Apply distributive property
[tex]6(P + G)[/tex]
Substitute values for P and G
[tex]6(4 + 3)[/tex]
Hence, the first option answers the question
In a volcano, erupting lava flows continuously through a tube system about 13 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hour and calculate how long it takes to reach the sea.
Answer:
26 hours
Step-by-step explanation:
speed = distance/time
s = d/t
st = d
t = d/s
t = (13 km)/(0.5 km/h)
t = 26 h
Answer: 26 hours
Solve for the variable!
1. 2x + 21 = 40
2. 4x - 12 = 3x + 9
3. 3(x -1) + 2 = 7x
Step-by-step explanation:
1. 2x + 21 = 40
2x = 40 - 21
2x = 19
x = 19/2 = 9.5
2. 4x - 12 = 3x + 9
4x - 3x = 9 + 12
x = 21
3. 3x - 3 + 2 = 7x
3x - 1 = 7x
-1 = 7x - 3x
-1 = 4x
4x = -1
x = -1/4
= - 0.25
What is the midpoint of AB?
point F
point G
point H
point I
Answer:
g
Step-by-step explanation:
Answer:
point g is the answer
Step-by-step explanation:
A faucet leaks water at a constant rate of 58 quart every 15 minutes.How many quarts does the faucet leak per hour?
Answer:
232 quarts
Step-by-step explanation:
58 quarts per 15 minutes, so 15 minutes x4 is an hour, so you would also do 58x4 which gets your answer of 232 quarts
Hope this helped :)
7 - 5 + 14 / 2 + 6. workings pls
Answer:
15
Step-by-step explanation:
PEMDAS
7-5+14/2+6
14/2=7
7-5=2
6=6
7+2+6=15
[tex]\text {Hello! To answer this question you must...}[/tex]
[tex]\text {Subtract:}[/tex]
[tex]\text {7-5=2}[/tex]
[tex]\text {Divide:}[/tex]
[tex]\text {14/2=7}[/tex]
[tex]\text { Your new equation should be 2+7+6}[/tex]
[tex]\text {Now for the final step you add}[/tex]
[tex]\text {2+7+6=}[/tex]
[tex]\fbox {15}[/tex]
[tex]\text {Bext of Luck!}[/tex]
[tex]\text {-LimitedX}[/tex]
If h(x)= 4(x + 6), what is the value of h(4)? a 16 b -5 c 32 d 40
Answer:
40
Step-by-step explanation:
h(x)= 4(x + 6)
Let x=4
h(4)= 4(4 + 6)
= 4(10)
= 40
Answer:
D
Step-by-step explanation:
So we have the function:
[tex]h(x)=4(x+6)[/tex]
To find h(4), substitute 4 for x. Thus:
[tex]h(4)=4(4+6)[/tex]
Add within the parentheses:
[tex]h(4)=4(10)[/tex]
Multiply:
[tex]h(4)=40[/tex]
The answer is D.
And we're done!