Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix
[tex]A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}[/tex]
Let's compute the determinant by taking the cofactor expansion along the first column:
[tex]\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}[/tex]
[tex]\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))[/tex]
[tex]\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)[/tex]
[tex]\det A = \boxed{74}[/tex]
(write in algebraic expression) Ice cream shop is open within the month of june,july and august
The shop served 100 fewer customers than they did in july
They served twice as many customers in august as they did in june
In total they served 400 customers over these three months
The algebraic expression of the situation above is 4x - 100 = 400
How to form an algebraic expression?Let
the amount of ice cream they serve in July = x + 100
the amount of ice cream they serve in June = x
They served twice as many customers in august as they did in June.
Therefore,
the amount of ice cream they serve in August = 2(x)
the amount of ice cream they serve in August = 2x
Therefore,
2x + x + x + 100 = 400
4x - 100 = 400
4x = 500
x = 500 / 4
x = 125
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E
6m
10m
8m
F
1.1
Calculate the length of the following
a)
DG
b)
EF
1.2 Determine the value of x
1.3
Given 17sinA-15-0 and 0° SA≤90°
Determine the values of the following with the aid of a diagram
a)
tan A
b)
1-cosA
c)
cos¹ A-cosecA
1.4 Simplify the following fraction WITHOUT USING A CALCULATOR
tan 45°.sin 30°-cot45°
sec 60⁰
මමමමම
(1)
(4)
(2)
(5)
(23)
The value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length which is 8 units.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
Here the diagram and some data are missing.
But using Pythagoras or trigonometric ratio we can find the length.
We have:
17sinA-15-0
sinA = 15/17
Using Pythagoras theorem:
Base length = √(17² - 15²) = 8 units
= tanA = 15/8
= 1 - cosA = 1 - 8/17 = 9/17
We can find the rest of the trigonometric ratio.
Thus, the value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length, which is 8 units.
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Calculate the volume of each diagrams.
The volume of the solid objects are 612π in³ and 1566πcm³
Volume of solid objectThe given objects are composite figures consisting of two shapes.
The volume of the blue figure is expressed as;
Volume = Volume of cylinder + volume of hemisphere
Volume = πr²h + 2/3πr³
Volume = πr²(h + 2/3r)
Volume = π(6)²(13+2/3(6))
Volume = 36π(13 + 4)
Volume = 612π in³
For the other object
Volume = Volume of cylinder + volume of cone
Volume = πr²h + 1/3πr²h
Volume = π(9)²(15) + 1/3π(9)²(13)
Volume= 81π (15+13/3)
Volume= 1566πcm³
Hence the volume of the solid objects are 612π in³ and 1566πcm³
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(A+1)/a = y make a the subject of this equation
The functions f(x) and g(x) are shown on the graph.
Using f(x), what is the equation that represents g(x)?
g(x) = log3(x) – 4
g(x) = log3(x) + 4
g(x) = log3(x – 4)
g(x) = log3(x + 4)
We can see that g(x) is a translation of 4 units to the left of f(x), then:
g(x) = log₃(x + 4).
How to get the equation that represents g(x)?
Here we can see that g(x) is a shift of f(x). Is clear that the asymptote of g(x) is 4 units to the left of the asymptote of f(x), so we can say that g(x) is a shift of 4 units to the left of f(x).
Remember that for a given function f(x), an horizontal shift of N units is given by:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is positive, the shift is to the right.Then a shift of 4 units to the left is written as:
g(x) = log₃(x + 4).
Then the correct option is the last one.
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Which expression is equivalent to (1/^y)-1/5
Answer:
5-y/5y
Sorry Im not to sure but maybe this will help?
Step-by-step explanation:
In a parallelogram PQRS, if angle P = (2x+25) degrees and angle Q = (3x-5) degrees, then write the measures of angle S and angle R.
Consecutive angles of a parallelogram are supplementary, so:
[tex]2x+25+3x-5=180\\5x+20=180\\5x=160\\x=32[/tex]
This means [tex]m\angle P=2(32)+25=89^{\circ}[/tex] and that [tex]m\angle Q=3(32)-5=91^{\circ}[/tex].
Since opposite angles of a parallelogram are congruent,
[tex]\boxed{m\angle S=91^{\circ}, m \angle R=89^{\circ}}[/tex]
A card is drawn from a standard deck of cards without jokers
What is the probability that the card is either black or a heart
Answer:
Step-by-step explanation:
Remark
The two black suites are
Clubs
Spades
Each of them has 13 cards so the total number of black cards is 2*13 = 26
Add to that the hearts which also has 13 cards
The total number of possible good cards is 13 + 26 = 39
Answer
P(hearts or Black) = 39/52
P(hearts or Black) = 3/4
P(hearts or Black) = 0.75
Are these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 1. Rational 2. Irrational please answer quickly I need to get this test done
Answer:
-7, rational
sqrt 10, irrational
sqrt 16 = 4, rational
52% = 0.52, rational
1.235, rational
[tex]\text{A rational number is a real number that is in the form of}~ \dfrac pq,\\\\\text{where p and q are integers and}~ q \neq 0\\\\\text{The real numbers that cannot be expressed as the ratio of two integers}~ \\\text{ are called Irrational numbers.}\\\\-7 = \dfrac{-7}1 \\\\\text{So}~ -7 ~ \textbf{is rational.}\\\\\\\sqrt{10} ~ \text{is irrational because 10 is not a perfect square.}\\\\\text{So}~ \sqrt{10}~ \textbf{is irrational.}\\\\\\[/tex]
[tex]\sqrt{16} = \sqrt{4^2} = \left(4^2 \right)^{\tfrac 12} = 4 = \dfrac 41\\\\\text{So,}~ \sqrt{16}~ \textbf{is rational.}\\\\\\52\% = \dfrac{52}{100}\\\\\text{So,}~ 52\%~ \textbf{is rational.}\\\\\\1.235 =\dfrac{1235}{1000}\\\\\text{So,}~1.235~ \textbf{is rational.}[/tex]
Properties of Light Lab Report
Instructions: In the Properties of Light—Bending Light Lab you will explore how light rays interact as they pass from one material, or medium, to another. Record your observations in the lab report below. You will submit your completed report.
Name and Title:
Include your name, instructor's name, date, and name of lab.
Objective(s):
In your own words, what was the purpose of this lab?
Hypothesis:
In this section, please include the if/then statement you developed during your lab activity. This statement reflects your predicted outcome for the experiment.
If I project light rays through (choose one: air, water, glass), then they will refract, or bend, the most.
Procedure:
Please be sure to identify the test variable (independent variable) and the outcome variable (dependent variable) for this investigation. Remember, the test variable is what is changing in this investigation. The outcome variable is what you are measuring in this investigation.
Test variable (independent variable):
Outcome variable (dependent variable):
Select Intro to begin.
Once the simulation loads, you will drag the protractor onto the screen so that the 0 lines up with the dotted line in the center of the screen. Select the More Tools icon at the bottom of the lab interactive and be sure to select the Normal and Angles boxes. Do Not move the laser light.
You will test all three materials in the bottom, blue half of the screen: air, water, and glass. Remember, do not move the laser light.
Record your observations of how the light rays interact as they pass from air, on the top of the screen, through the three materials on the bottom of the screen
Data:
Record the data from each trial in the data chart below. Be sure to fill in the chart completely.
Material Interactions
List any observations you made as the light rays passed from the air on the top of the screen to the selected material on the bottom of the screen. Evidence
Using the protractor, measure the angle as the light passes from the top material to the bottom material on the screen. Also, note the index of refraction for each as indicated on the screen.
Trial One Air on top
Bottom angle:
Bottom index of refraction:
Air on bottom
Trial Two Air on top
Bottom angle:
Bottom index of refraction:
Water on bottom
Trial Three Air on top
Bottom angle:
Bottom index of refraction:
Glass on bottom
Conclusion:
Your conclusion will include a summary of the lab results and an interpretation of the results. Please write in complete sentences.
Did your data support your hypothesis? Use evidence to explain.
Which material refracted the light rays the most: air, water, or glass?
Which material refracted the light rays the least: air, water, or glass?
How does density affect refraction?
Diamonds are a very dense material. Predict what would happen to the light ray if you projected it from air through a diamond.
Explain where you observe reflection, refraction, and absorption of light in your everyday activities.
Answer:
Can You Give Me Some More Information
Step-by-step explanation:
6. Use the following matrices to answer the questions. (2 points each)
5 -8
2 -6
-8
-2 3
A
외
B =
[4
18] c- [5 5] -
C=
9 1
03
9
1
a. Is the operation E + C possible? Circle YES or NO
If yes, state the dimensions of the answer:
b. Is the operation B + C possible? Circle YES or NO
If yes, state the dimensions of the answer:
c. Is the operation E. D possible? Circle YES or NO
If yes, state the dimensions of the answer:
d. Is the operation D E possible? Circle YES or NO
If yes, state the dimensions of the answer:
e. Is the operation A D possible? Circle YES or NO
If yes, state the dimensions of the answer:
1
-1 10
E
11
7 -1 0
Answer:
its a such a hard questions i think you should ask to you're teacher ?
Can anyone answer this?
HELP WHAT DOES THIS EVEN MEAN
Answer:
59.5
Step-by-step explanation:
He is asking for angle A
cosA = adjacent/hypotenuse
= 33/65
we'll do shift cos(33/65) = 59.48 to bring A
Please Answer Fast
3.4 × 107 is the scientific notation for:
3.40000000
34 000 000
340 000 000
Answer:
34000000
Step-by-step explanation:
hope it helps you and give me a brainliest
Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
What is the sum of the 3rd and 5th square number??
Answer:
34
Step-by-step explanation:
3rd and 5th square numbers means 3² and
5² .
so we know 3² is another word of saying 3×3
3×3=9
5×5=25
9+25=34
Triangle DEF is a right triangle with point F at the origin. Segment DE has endpoints located at D(8, 0) and E(0, −2). What is the area of triangle DEF?
Answer: 8
Step-by-step explanation:
Using the formula [tex]A=\frac{1}{2}bh[/tex],
[tex]A=\frac{1}{2}(8)(2)=\boxed{8}[/tex]
help me solve this please help I will gave u brilliant answer
Answer: 1.) 3 2/3 2.) 2 9/10 3.) 9 11/15 4.) 7 11/12
B. Question 2,
My answer is reasonable, because if we round 1 7/10 to 2 and 1 1/5 to 1
2+1=3 and my answer is 2 9/10. This estimate makes sense because 2 9/10 can be rouned to 3, meaning it is reasonable.
Step-by-step explanation:
1 1/6 + 2 3/6= 3 4/6
Simplifyed=3 2/3
1 7/10 + 1 2/10 = 2 9/10
7 5/15 + 2 6/15= 9 11/15
4 8/12 + 3 3/12= 7 11/12
The following scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.
Hint: A line of best fit follows the pattern of the data and is in the middle of the points.
Answer:
whats the question
Step-by-step explanation:
Determine if the triangle with the given sides is acute, obtuse, or right.
7, 12, 16
HELP URGENT WILL GIVE
BRAINLIEST!!!
Elsa is putting money into a
savings account. She starts
with $550 in the savings
account, and each week she
adds $70.
Let S represent the total
amount of money in the
savings account (in dollars),
and let W represent the
number of weeks Elsa has
been adding money. Write
an equation relating S to W
Then use this equation to
find the total amount of
money in the savings
account after 11 weeks.
Equation:__
Total amount of money after
11 weeks:
$__
Answer:
S x W + 550 = answer
Step-by-step explanation:
eh u dont need to know, yw
Answer:
Step-by-step explanation:
S= total amount in savings acc.
W= # of weeks
You have 550 in your acc and your adding 70 every week?
S= 550+70w
Then for 11 weeks: Equation- S=550+70*11
70*11=770
S= 550+770 - S= 1320
Total after 11 weeks is 1320
A. Using the spinner above, what is the probability that a player will draw 3 cards?
B. What is the probability that a player will draw 1 card on the first spin and 2 cards on a second spin?
C. Harold wants the probability that a player draws 3 cards and moves 2 spaces to be 3/8. How can he change the spinners to result in this probability?
Answer:
A-1/3
B-1/8
C-?
Step-by-step explanation:
order the numbers from least to greatest
Answer:-3, -2, -1/10, -0.8, 0.8, 7
Step-by-step explanation:
Noah borrowed $5000 from the credit union for 180 days. The interest rate is 11.4% per year. How much must Noah pay to the credit union after 180 days?
The amount that Noah pays to the credit union after 180 days will be $5143.85.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
We have
P = $5,000
r = 0.114 / 12 = 0.0095
n = 3
A = 5000(1 + 0.114)³
A = $5143.85
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Bob wants to take his wife, Jessica, to Europe in three years to commemorate their 40th wedding anniversary. He recently received a $23,000 inheritance from an uncle, which he plans to put towards the trip. The trip is expected to cost $32,200, according to Bill. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, F (From the tables provided, select the appropriate factor(s).)
What annual compounded interest rate must Bill earn to save enough money to pay for the trip? (Round to the nearest whole percentage your interest rate.)
Answer:
10%
Explanation:
Use future value formula
Future Value = Present Value ((1+r)^n)
26,600 = 20,000 ((1+r)^3
26,600/20,000 = (1+r)^3
1.33 = (1+r)^3
1.33^1/3 = 1+r
1.0997 = 1+r
1.0997 - 1 = r
r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)
(pls give brainliest)
The perimeter of a rectangle is 78 cm. If the length is 24 cm, how wide is the rectangle?
Write an equation you can use to answer this question. Use w as your variable in the equation.
Answer:
15(cm)
Step-by-step explanation:
48 + 2w = 78
2w = 30
w = 15(cm).
EASY POINTS
What is the slope-intercept equation of this line?
Answer:
B
Step-by-step explanation:
The y-intercept is 8
The slope is -2x
Therefore the slope-intercept is y = -2x + 8
Put these numbers in order from least to greatest 1/8, -0.333, -1/7
Answer:
-0.333, -1/7, 1/8
Step-by-step explanation:
1/8 is the greatest because it is a positive number while the other two numbers are negative.
-0.333 or -1/3 is smaller than -1/7.
k5500 is invested for a period of 4 years in a savings account. for the first year , the investment grows at a simple interest rate of 11% per annum and then at a rate of 12.5% per annum compound and quarterly for the rest of the period. Determine the value of the investment at the end of the 4 years
manyy is really short time samma basyo is really an amazing
What is the vertex of the quadratic function f(x) =(x-6)(x+2)
Answer:
(2, -16)
Step-by-step explanation: set both (x +2) and (x-6) = 0.
You get the two x-intercepts -2 and 6. Find the midpoint of the two intercepts by -2 + 6 / 2 which gives you x=2. Then plug 2 in for x and solve the original equation. ( 2 - 6)(2+2) = -16. Therefore the vertex is at (2,-16).
Answer:
Step-by-step explanation:
f(x) = x^2 - 4x - 12
x = -(-4)/2 = 4/2 = 2
(2)^2 - 4(2) - 12 = 4 - 8 - 12 = -4 - 12 = -16
vertex: (2, -16)