In this Matrix A= [-2 -3
3 12]
the matrix of A - 1 is
[-4/5 -1/5
1/5 2/15]
According to the question, given that
[-2 -3
3 12 ] ^ -1
First, we find the determinant
-2 * 12 - (-3 *3) = -24 - (-9) = -24 +9 = -15
Multiply 1 over the determinant by The matrix with the -2 and 12 switched and negate the -3 and the 3
1/-15 [12 3
-3 -2 ]
after multiply by 1/ - 15, we get
[-4/5 -1/5
1/5 2/15]
Therefore, In given Matrix A, after solving we get the value A- 1 is
[-4/5 -1/5
1/5 2/15]
Matrix
If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,
Matrix. [ 5 6 3
-2 3 2 ]
is a 2 × 3 matrix. A square matrix of order n have n rows and n columns. Ordinary numbers can be thought of as 1 1 matrices, making the number 3 the matrix [3]A row vector is a matrix with one row and n columns, and a column vector is a matrix with one column and n rows.
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In 2012, the U.S. population was about
314 million. How many people over the
age of 64 were in the U.S.?
There are 38,936,000 people over the age of 64 were in the U.S.
Option 2 is true.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
In 2012, the U.S. population was about 314 million.
Now,
Total population = 314,000,000
In the pie chart, The percent of people over the age of 64 were in the U.S will be 12.4%
Hence, Solve as;
Number of people over the age of 64 = 314,000,000 × 12.4%
= 314,000,000 × 12.4 / 100
= 31,400,00 × 12.4
= 38,936,000
Thus,
There are 38,936,000 people over the age of 64 were in the U.S.
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please solve the inequality in the picture shown below i will give brainliest
[tex]\frac{3}{4} -\frac{1}{2} p > \frac{5}{4} \\\frac{3}{4}(4)-\frac{1}{2} p(4) > \frac{5}{4} (4)\\3-2p > 5\\-2p > 5-3\\-2p > 2\\\frac{-2p}{-2} > \frac{2}{-2} \\p < -1[/tex]
when you divide or multiply by a negative number the signs <> change directions.
A right rectangular prism is packed with cubes of side length 1/8 inch. if the prism is packed with 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height, what is the volume of the prism?A. 1 1/2 cubic inchesB. 1 3/4 cubic inchesC. 2 1/2 cubic inchesD. 2 3/4 cubic inches
Answer:
A. 1 1/2 cubic inches
Explanation:
We are told that the side length of the cube is 1/8 of an inch. Furthermore, we are also told that the rectangular prism fits 16 cubes along the length, 8 cubes along the width, and 6 cubes along the height. This means the measures of the dimensions of the prism are
[tex]\begin{gathered} \frac{1}{8}\times16\: in=2\: in \\ \end{gathered}[/tex][tex]\frac{1}{8}\times6\: in=0.75\: in[/tex][tex]\frac{1}{8}\times8\: in=1\: in[/tex]Therefore, the volume of the prism is
[tex]2\: in\times0.75\: in\times1\: in=1\frac{1}{2}\: in^3[/tex]Hence, the volume of the prism is 1 1/2 cubic inches
You get paid an annual salary of $67,100/year. You get paid bi-
weekly. Calculate the gross pay.
A garden table and a bench cost $830 combined. The garden table costs $80 more than the bench. What is the cost of the bench?
The most appropriate choice for linear equation will be given by-
The cost of bench is $375
What is linear equation?
A one degree equation is called a linear equation.
Here,
Let the cost of the bench be $x
cost of garden table = $(x + 80)
Total cost of bench and garden table= $(x + x + 80)
= $(2x + 80)
By the problem,
2x + 80 = 830
2x = 830 - 80
2x = 750
x = [tex]\frac{750}{2}[/tex]
x = $375
So,
The cost of bench is $375
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Blake was assigned the problem below. Analyze his work and determine if it is correct.If it is wrong, describe all mistakes.Problem:53x-5 = ( 625 )#*?53x-s5 "(x+2)3x-5 = 4 (x+7)3x-5= 4x+7-3x-3xS = x +7-7-7x= -12
1) Let's solve that exponential equation
Converting the bases:
2) Since we are on the same base let's just calculate the exponents.
3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.
When He started operating the exponents.
Mr. Burke wants to invest part of his lottery winnings in a safe fund that earns 2.5% annual interest and the rest in a
risky fund that expects to yield 8% annual interest. The amount of money invested in the safe fund, x, is to be exactly
four times the amount invested in the risky fund, y. Use the system of equations to determine the amount to be
invested in each fund if a total of $1080 is to be earned at the end of one year.
Answer:
eywgw6 the car is in the car is in the car is in
Step-by-step explanation:
Wu and I will be in the car is in the car is in the car is in the car is here and we can 4
Answer:
Safe fund = $24,000
Risky fund = $6,000
Step-by-step explanation:
Definition of variables:
Let x = the amount of money invested in the safe fund.Let y = the amount of money invested in the risky fund.Given information:
Safe fund = 2.5% annual interest.Risky fund = 8% annual interest. Total interest earned at the end of one year = $1080.The amount of money invested in the safe fund, x, is to be exactly four times the amount invested in the risky fund, y.Convert the percentages into decimal form:
[tex]\implies 2.5\%=\dfrac{2.5}{100}=0.025[/tex]
[tex]\implies 8\%=\dfrac{8}{100}=0.08[/tex]
Create a system of equations from the given information and defined variables:
[tex]\begin{cases}0.025x+0.08y=1080\\x=4y\end{cases}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 0.025(4y)+0.08y=1080[/tex]
[tex]\implies 0.1y+0.08y=1080[/tex]
[tex]\implies 0.18y=1080[/tex]
[tex]\implies \dfrac{0.18y}{0.18}=\dfrac{1080}{0.18}[/tex]
[tex]\implies y=6000[/tex]
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x=4(6000)[/tex]
[tex]\implies x=24000[/tex]
Therefore, the amount invested in each fund was:
Safe fund = $24,000Risky fund = $6,000Is it right?????????
Check the picture below.
let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.
given a number line C=11 and D=13 CD=?can u help me solve this problem?
The diagram of the number line is shown below
Thus, the distance CD which is the distance between point D and point C is
13 - 11 = 2
CD = 2
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.
Therefore, it should be noted that the depth in July is -18.
Therefore, the difference between the depths in February and July will be:
= -5 - (-18)
= -5 + 18
= 13
Therefore, the difference is 13 feet.
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On a given planet the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 80 KG weighs 80 n calculate the mass of another object that weighs 70 n
We are told that the weight of an object varies directly with the mass of the object. This basically means that if w is the weight and M is the mass then these two magnitudes are related by the following expression:
[tex]w=k\cdot M[/tex]Where k is a constant.
We know that an object with a mass of 80kg weights 80 newtons. Then for this object we have w=80kg and M=80n so we get:
[tex]80n=k\cdot80kg[/tex]We divide both sides of this equation by 80:
[tex]\begin{gathered} \frac{80n}{80}=\frac{k\cdot80kg}{80} \\ 1n=k\cdot1kg \end{gathered}[/tex]Here it's important to remember that 1 newton (i.e. 1n) is equal to:
[tex]n=\frac{kg\cdot m}{s^2}[/tex]Then we get:
[tex]1\frac{kg\cdot m}{s^2}=k\cdot1kg[/tex]We divide both sides by 1 kg:
[tex]\begin{gathered} \frac{1\frac{kg\cdot m}{s^2}}{1kg}=\frac{k\cdot1kg}{1kg} \\ 1\frac{kg\cdot m}{kg\cdot s^2}=k\cdot\frac{1kg}{1kg} \\ k=1\frac{m}{s^2} \end{gathered}[/tex]So now that we found k we have the following expression for the weight of an object as a function of its mass:
[tex]w=M\cdot1\frac{m}{s^2}[/tex]For an object that weights 70n we get:
[tex]\begin{gathered} 70n=M\cdot1\frac{m}{s^2} \\ 70\frac{kg\cdot m}{s^2}=M\cdot\frac{m}{s^2} \end{gathered}[/tex]We divide both sides by 1 m/s²:
[tex]\begin{gathered} \frac{70\frac{kg\cdot m}{s^2}}{1\frac{m}{s^2}}=\frac{M\cdot\frac{m}{s^2}}{1\frac{m}{s^2}} \\ 70\frac{kg\cdot m\cdot s^2}{m\cdot s^2}=M\cdot\frac{m\cdot s^2}{s^2\cdot m} \\ 70kg=M \end{gathered}[/tex]AnswerSo the mass of an object that weights 70n is 70kg.
find the value of k given both points lie on a line passing through the orgin (-12,-2) and (k,8)
The value of k given that both points lie on a line passing through the origin is 48.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Since both points lie on a line which passes through the origin, we can logically deduce the following points:
Point (x, y) = (0, 0)
Substituting the given points into the formula, we have;
Slope, m = Δy/Δx
Slope, m = (-2 - 0)/(-12 - 0)
Slope, m = -2/-12
Slope, m = 1/6
At point (-12, -2) and (k, 8), we have:
1/6 = (8 - (-2))/(k - (-12))
1/6 = (8 + 2)/(k + 12)
1/6 = 10/(k + 12)
k + 12 = 10(6)
k + 12 = 60
k = 60 - 12
k = 48
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Starting at the origin (0,0), what is the ordered pair of a value that is 4 units to the left and 5 units up?
(-4,5)
4 to the left on the axis is neg. 5 units up on the y axis makes it positive.
circle C has centre D and equation
x^2+y^2+2x-8y+8=0
A line is drawn through the point P (4,6),so that it touches the circle C at the point T
Show that PT=square root 20
find the equation of the circle centre P which passes through the point T
The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Here, we are given a circle with center D and equation as-
[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]
Comparing this to the general form of equation of a circle which is [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-
g = 1, f = -4 and c = 8
thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3
Now, since PT is a tangent to the circle, DP will e perpendicular to PT.
We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)
= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]
= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]
= [tex]\sqrt{25 +4 }[/tex]
=[tex]\sqrt{29}[/tex]
Thus, in triangle, PDT by using Pythagoras theorem, we will have-
[tex]PT^{2} + DT^{2} = PD^{2}[/tex]
since DT is the radius of the circle, DT = 3
⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]
[tex]PT^{2} + 9 = 29[/tex]
[tex]PT^{2} = 29 - 9[/tex]
[tex]PT^{2} = 20[/tex]
[tex]PT = \sqrt{20}[/tex]
Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.
Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]
so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)
Thus, the equation of the circle will be-
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
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P
TU =
UV =
32°
-
5.5 cm
3.1 cm
VW-
Tech Support
151°
S
cm
cm
Q
Look carefully at quadrilateral PQRS.
Consider the transformation Rz (PQRS) that produces its image, quadrilateral
TUVW.
Find all the following:
cm
147°
3.8 cm
6.0 cm
30°
R
N
Answer:
Step-by-step explanation:
Which conversion factors can be used to multiply to 4 km/min to get meters per hour?Select each correct answer. 1 km1000 m1 h60min60min1 h1000 m1 km
Step 1: Concept
To convert km to meters you will multiply with 1000.
To convert minute to hour you will divide by 60
Step 2: Convert
[tex]\begin{gathered} 4\operatorname{km}\text{ to meters = 4 }\times\text{ }\frac{1000m}{1\operatorname{km}}\text{ } \\ 1\text{ min to hour = 1}\min \times\frac{1\text{hour}}{60\text{ min}} \end{gathered}[/tex]Step 3: Final answer
[tex]\frac{1000m}{1\operatorname{km}}\text{ and }\frac{1hour}{60\min }[/tex]Option B and D
3.4-2.8d+2.8d-1.3Combine like terms to create an equivalent expression.
The given expression is
3.4 - 2.8d + 2.8d - 1.3
By collecting like terms, we have
- 2.8d + 2.8d + 3.4 - 1.3
= 0 + 2.1
= 2.1
If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
A. 3-2x
B. 4x+1
C. 2x-3
D. 2x-1
Steve has a new credit card with an APR of 11.99% and a credit limit of $1800. The minimum monthly payment is 6.5 % of the new balance. If Steve buys $550 dollars in school supplies at the beginning of the month, what will Steve’s new balance be at the end of the month? Explain your answer rounded to the nearest cent
Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.
What is a credit card balance?A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.
The credit card balance consists of purchases, finance charges, and repayments.
Credit card's APR = 11.99%
Credit limit = $1,800
Minimum monthly payment = 6.5%
Purchase at the beginning of the month = $550
Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)
New balance = $555.50
Minimum payment = $36.11 ($555.50 x 6.5%)
Balance after the minimum payment = $519.39 ($555.50 - $36.11)
Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.
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The product of 3 and the difference of a number and 1
Where”a number” is the letter x
HELP ASP YOULL GET 20 POINTS AND BRAINLIEST!!!
Answer:
7 Games
Step-by-step explanation:
1. take the information and put it into a equation (being y=3.25x+3 or f(x)=3.25+3)
2. replace the x with a whole number because you can't bowl half a game.
Ex: f(3)=12.75 or f(6)=22.50
3. The highest you can go without going over your money is 7 games ($25.75) leaving you with a total of 2.25.
Use the diagram find the image of c under the translation described by the translation rule
(X,y) (x+11,y-8)
○ B
○ A
○ D
○ E
Three consecutive integers have a sum of 81. Find the integers
Answer:
26, 27, 28
Step-by-step explanation:
Let the 3 integers be: x, x+1, x+2
x+x+1+x+2 = 81
3x+3 = 81
3x = 78
x = 26
x+1 = 27
x+2 = 28
Write the given transformation in vector notation (please help its due in 20 mins)
Answer:
-1, 1
Step-by-step explanation:
The translation is 1 unit left and 1 unit up.
Given the following Information, find the length of the missing side. Leave your answer as a simplified radical.
Hypotenuse = 10
Long = ?
A. 5
B. 5/3
C. 10
D. 10/3
Answer: B. (5√3)
Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.
30% of 3000
I know how to do it but I just need to be sure
Answer:900
Step-by-step explanation: 1. set up an equation
x= (p * n)/100 when x= the answer p= the percentage and n= the total number
2. plug in the numbers
x= (30 * 3000)/100
3.solve
x= (30*3000)/100
x= (90000)/100
x= 900
Help me answer this please!!!
Answer:2 choice
Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2
list 3 points that are on the line 2x=6y+4
The three Points that lie on the given line 2x=6y+4 are (5,1) , (8,2) and (11,3).
The given equation of line is given below,
2x=6y+4 equation 1
We need to find the points that lie on the given line.
Point 1 :
Put x = 5 in equation 1
2(5) = 6y + 4
6y = 6
y=1
So, Point (5,1) lie on the given line.
Point2:
Put x = 8 in equation 1
2(8) = 6y + 4
6y = 12
y=2
So, Point (8,2) lie on the given line.
Point 3 :
Put x = 11 in equation 1
2(11) = 6y + 4
6y = 18
y=3
So, Point (11,3) lie on the given line.
Thus, Points (5,1) , (8,2) and (11,3) lie on the line 2x=6y+4 .
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uppose that the rela
S={(-1, -9), (-9, 1), (3, 1)}
ve the domain and range of S.
rite your answers using set notation.
domain =
range =
Help me please
Answer:
Domain = {-9, -1, 3}Range = {-9, 1}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
write a quadratic function in standard form containing the point (5,-6) and x-intercepts -7 and 3
WILL GIVE BRAINLIEST
Answer:
[tex]y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Given:
x-intercepts: -7 and 3Point on the curve: (5, -6)Substitute the given values into the formula and solve for a:
[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies-6&=a(5-(-7))(5-3)\\-6&=a(12)(2)\\-6&=24a\\a&=\dfrac{-6}{24}\\\implies a&=-\dfrac{1}{4}\end{aligned}[/tex]
Substitute the given x-intercepts and the found value of a into the formula:
[tex]\implies y=-\dfrac{1}{4}(x+7)(x-3)[/tex]
Expand to standard form:
[tex]\implies y=-\dfrac{1}{4}(x^2-3x+7x-21)[/tex]
[tex]\implies y=-\dfrac{1}{4}(x^2+4x-21)[/tex]
[tex]\implies y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]