[tex]\vec A = \left[\begin{array}{cccc}- 3&- 14&7 &18\\-13&-2&-5 & -6\end{array}\right][/tex]
How to determine the value of a matrix
In this problem we find a matrix as result of the addition of two matrices. According to linear algebra, matrix addition is performed between matrices with same number of rows and columns. There, matrix A must have two rows and two columns to make addition operation possible, that is:
[tex]\vec A + \left[\begin{array}{cccc}3&9&-1 &-8\\16&- 2&3 & 13\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]
[tex]\left[\begin{array}{cccc}3 + a_{11}&9+a_{12}&-1+a_{13} &-8+a_{14}\\16+a_{21}&- 2+a_{22}&3+a_{23} & 13+a_{24}\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]
And we shall solve the following equations:
First row
3 + a₁₁ = 0
9 + a₁₂ = - 5
- 1 + a₁₃ = 6
- 8 + a₁₄ = 10
Second row
16 + a₂₁ = 3
2 + a₂₂ = 0
3 + a₂₃ = - 2
13 + a₂₄ = 7
The solutions to the equations are: a₁₁ = - 3, a₁₂ = - 14, a₁₃ = 7, a₁₄ = 18, a₂₁ = - 13, a₂₂ = - 2, a₂₃ = - 5, a₂₄ = - 6.
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hey can anuyone please help with this question
answer is 25
use the formula to get the rest of the a's
a cylinder container 12 inches tall with a radius of 6 inches is completely filled with vanilla, chocolate, and strawberry ice cream in the ratio 3:2:1. Which statement(s) are correct?
A.) The volume of vanilla ice cream is V = 216π in^3
B.) The total volume of ice cream is V = 1728π in^3
C.) The total volume of ice cream is V = 432π in^3
D.) The volume of strawberry ice cream is V = 288π in^3
E.) The volume of chocolate ice cream is V = 576π in^3
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2 (12)\implies \stackrel{\textit{total volume of ice-cream}}{V=432\pi ~in^3}[/tex]
the quotient of 18 and a number a as an experision
The expression is 18/a
What is an algebraic expression?An algebraic expression can be described as mathematical expressions consisting of variables, coefficients, terms, factors and constants.
They are also made up of arithmetic operations, such as;
BracketParenthesesDivisionAdditionSubtractionMultiplication, etcWhat is quotient?A quotient can be defined as a quantity determined by the division of two numbers.
From the information given, we have that;
the quotient of 18 and a number a
This is represented as;
18/a
Hence, the representation is 18/a
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An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 6° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft
Answer:
28.1 ft
Step-by-step explanation:
d = 350 * ( tan 10.5 - tan 6) = 28.1 ft
Janice drives to the grocery store and
back every Tuesday. The drive home
takes twice as long because of traffic.
If her total travel time is forty-eight
minutes, how long does it take Janice
to drive to the grocery store?
PLEASE HELP ILL GIVE YOU 25 POINTS
The length of side x for the triangle is 5√3.
What is an equilateral triangle?An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. It is also known as an equiangular triangle since each angle is 60 degrees.
Given an equilateral triangle,
length of the side is 10 units,
and a perpendicular is drawn with length x,
so a perpendicular drawn from one of the vertices to the opposite side of an equilateral triangle bisects that side.
we know the angle of the equilateral triangle is 60°,
by the sine function, we can calculate the value of x
sinФ = p/h
p = perpendicular = x
h = hypotenuse = 10
Ф = 60°
sin60 = x/10
x = 10*sin60
x = 10(√3/2)
x = 5√3
Hence the value of x is 5√3.
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Sum up the series 2/3+5/9+8/27+11/81+..... to n terms
Hope it helps.
If you have any query, feel free to ask.
Find an equation for the line with the given properties . Express your answer using either the general form or the slope- intercept form of the equation of a line. Slope = - 5; y - intercept = 4
Answer:
y = -5x + 4
Step-by-step explanation:
The general form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.
Given that the slope of the line is -5 and the y-intercept is 4, we can substitute these values into the general form of the equation of a line to get:
y = -5x + 4
This equation represents a line with a slope of -5 and a y-intercept of 4.
how to round 456.173 to the nearest hundredth?
Answer:
456.17
Step-by-step explanation:
Rounding to the nearest hundredths' is asking is the number given 456.173 closer to 146.170 or 146.171. You can see that the number is closer to 146.170 which is the same number as 146.17
Rule
Look at the digit in the thousandths' place. In this case 3. If this number is 5 or greater round up, if this number is 4 or smaller round down. We will round down.
456.17
Answer:456.17
Step-by-step explanation:
If the thousandth place is 5-9, for example 456.178, the answer rounded to hundredth place will be 456.18.
But if the thousandth place is 1-4, the answer rounded to hundredth will be 456.17.
So the answer is 456.17.
(Look at picture) thanks! <3
Answer:
Here are the true statements:
Initially, the gas tank has 10 gallons of gasoline. (This is the y-intercept of the equation G(t) = 10 - 2t)It takes 10 hours for the vehicle to run out of gas. (This is the x-intercept of the equation G(t) = 10 - 2t)The rate of gas consumption of the vehicle is 2 gallons per hour. The slope of G(t) represents the rate of fuel consumption of the vehicle.The false statement is:
The G-intercept of G(t) represents the total distance the vehicle traveled. The t-intercept of G(t) represents the time it takes the vehicle to run out of gas. (This is not the case, the y-intercept represents the initial amount of gas and the x-intercept represents the time it takes the vehicle to run out of gas)
The Empty Number Line
Consider the list of six variable expressions:
1. With your partner, think about where you would place each
expression and sketch your conjecture.
2. Compare your number line with another group's number line.
What is the same? What is different?
An empty number line is a visual tool used to represent numbers and their relative positions. It can be used to compare, order, and perform operations on numbers.
How to learn and understand comparison of numbers?A number with more digits is always greater than a number with fewer digits, according to Rule I.
Rule II states that when two numbers have the same number of digits, we compare the digits starting from the leftmost position until we find an unequal number of digits. Greater numbers are those with more digits.
As far as we are aware, a number with more digits is always greater than one with fewer digits.
The sum of the first two digits is bigger than the sum of the first one.The number with three digits is larger than the number with two or one.A four-digit number has more digits than a three-, two-, or one-digit number.A five-digit number over a four-digit number. Three-digit number, etc.Six digits > Five digits > Four-digit number, etc..To learn more about number line visit:
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If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week?
Answer:
Step-by-step explanation:
a) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 3 days is 3/1, or 3/1 of a tank.
b) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 1 week is 7/1, or 7/1 of a tank.
It's worth noting that tanks of gas come in different sizes, so the amount of gas consumed in a day, week, or any other period of time will depend on the size of the tank, and the consumption of the car, so this answer is based on the assumption that a full tank is used every day.
When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1. A small ice cream freezer requires cups of crushed ice. How much rock salt should be mixed with the ice to create the necessary brine solution?
If the ratio of crushed ice to rock salt is 5 to 1, for every 5 cups of crushed ice, 1 cup of rock salt is needed.
To find out how much rock salt is needed for the small ice cream freezer, you can use this formula:
Rock Salt = (Crushed Ice / 5) * 1
If the small ice cream freezer requires cups of crushed ice, then:
Rock Salt = (5 cups / 5) * 1 cup
Rock Salt = 1 cup
So, you will need 1 cup of rock salt to mix with the 5 cups of crushed ice to create the necessary brine solution.
Which choice correctly expresses the number below in scientific notation? 0.000611
D. 6.11 * 10 ^ - 5
C. 6.11 * 10 ^ - 3
OE. 6.11 * 10 ^ - 4
OF. 611 * 10 ^ - 6
B. 611 * 10 ^ - 4
A. 61.1 * 10 ^ - 5
0.000611
The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
The given decimal number is 0.000611.
0.000611 in scientific notation, we get
6.11×10⁻⁴
Therefore, option E is the correct answer.
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construct a right-angled isosceles triangle whose equal side measure 2 cm
A construction of a right-angled isosceles triangle whose equal side measure 2 cm is shown in the image attached below.
What is an isosceles right triangle?In Mathematics, an isosceles right triangle can be defined as a type of right-angled triangle in which two (2) of its side lengths are equal and one of its angle is a right angle.
What are the steps for the construction of a right-angled isosceles triangle?Generally speaking, the steps that are required for the construction of a right-angled isosceles triangle include the following:
You should draw a line segment, with line AB equal to 2 cm (AB = 2cm).At point A, draw an angle with a measure of 90 degrees (90°).You should draw an arc of radius from point A in order to intersect the perpendicular drawn at point A at the point C.You should join point A and point B.In conclusion, triangle ABC (ΔABC) is the required right-angled isosceles triangle as shown in the image attached below.
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In the binomial expression of (1+x)
n
the first three terms are 1+3+4+---. Calculate
the numerical values of n and x, and the values of the fourth term of the expression.
Answer:
x = 1/3n = 9fourth term = 28/9Step-by-step explanation:
Given the first three terms of the expansion of (1 +x)^n are 1 +3 +4, you want the values of x and n, and the next term.
Binomial expansionThe first few terms of the binomial expansion of (1 +x)^n are ...
[tex](1+x)^n=1^n+n\cdot1^{n-1}x+\dfrac{n(n-1)}{2}1^{n-2}x^2+\dfrac{n(n-1)(n-2)}{2\cdot3}1^{n-2}x^3+\dots[/tex]
Comparing termsComparing the terms to those given, we have ...
[tex]nx=3\\\\(nx)((n-1)x)/2=4[/tex]
Expanding the second of these equations, and substituting the first, we get ...
[tex](nx)(nx -x)=8\qquad\text{multiply by 2}\\\\3(3-x)=8\qquad\text{substitute $nx=3$}\\\\9-8=3x\qquad\text{add $3x-8$}\\\\\boxed{x=\dfrac{1}{3}}\qquad\text{divide by 3}\\\\\dfrac{1}{3}n=3\qquad\text{substitute for $x$ in $nx=3$}\\\\\boxed{n=9}\qquad\text{multiply by 3}[/tex]
Fourth termThen the fourth term is ...
[tex]\dfrac{n(n-1)(n-2)}{6}x^3=\dfrac{9\cdot8\cdot7}{6}\cdot\left(\dfrac{1}{3}\right)^3=\boxed{\dfrac{28}{9}}[/tex]
__
Additional comment
Then the expansion is ...
(1 +1/3)^9 = 1 + 3 + 4 + 28/9 + 14/9 + 14/27 + ...
The n-th term is (11-n)/(3(n-1)) times the term before.
It's raining, and Vince and his friends are stuck inside. They decide to play a marble game called Revenge. To start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
The total number of marbles are 30.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, to start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
Here, m/3 =10
m=30
Therefore, the total number of marbles are 30.
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Each survey respondent is asked to rate a specified supermarket based on a variety of factors such
as quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the
rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all factors. Sample data
representative of independent samples of Publix and Trader Joe's customers are shown below.
Publix
N₁= 250
X bar 1= 86
Trader Joe's
N₂ = 300
X bar ₂ = 85
p-value= (to 3 decimals)
There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.
what is random sample ?chosen at random (purely random, unpredictable). Every person in the demographic being surveyed should have an equal chance of being chosen. She gave an example of a simple representative sample, choosing 25 names at random from a group of 250 employees. The sampling in this case is random since there are 250 of her coworkers in total, and every one has an equal chance of being picked. Researchers select people at random from a population using simple random sampling, which is a type of probability sampling. Every member of the population is given an equal chance at selection.
Given that,
mean(x)=86
standard deviation , σ1 =12
number(n1)=250
y(mean)=85
standard deviation, σ2 =12
number(n2)=300
null, u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
we got |zo | =0.973 & | z alpha | =1.96
(b) test statistic: 0.97
There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.
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Use elimination to solve
-3x+12y = 9
x-4y=-3
Answer:
Step-by-step explanation:
Elimination is a method of solving a system of equations by adding or subtracting the equations from each other to eliminate one of the variables.
In this case, we will be using elimination to solve the system of equations:
-3x + 12y = 9
x - 4y = -3
Step 1: Multiply the first equation by -1.
(Multiplying by -1 switches the sign of every number in the equation)
3x - 12y = -9
Step 2: Add the two equations together.
3x - 12y = -9
+x - 4y = -3
______________
4x - 16y = -12
Step 3: Isolate the y-variable by adding 16y to both sides of the equation.
4x - 16y = -12
+16y +16y
______________
4x = -12 + 16y
Step 4: Divide both sides of the equation by 4 to isolate the y-variable.
4x = -12 + 16y
4/4 4/4
______________
x = -3 + 4y
Therefore, the solution to the system of equations is x = -3 + 4y.
The rectangle below has the dimensions:
5.3 × 5.7
Create another rectangle that is scaled to 4
times the size of the current rectangle.
Answer:
A rectangle of 10.6 x 11.4 dimensions.
Step-by-step explanation:
(5.3*2)*(5.7*2)=5.3*4*5.7=10.6x11.4.
Obtain an estimate for the following computation by rounding the numbers so that the resulting arithmetic can easily
be performed by hand or in your head. Then, use a calculator to perform the computation. How reasonable is your
estimate when compared to the actual answer?
348 +598
is O
Round the two numbers to the nearest ten. An estimate of the sum is
More
x 946 is not answer also I need help this homework math please
Answer: it should be 946, maybe you worded Wong
Step-by-step explanation:
o obtain an estimate for the computation 348 + 598, we can round the two numbers to the nearest ten.
348 rounded to the nearest ten is 350
598 rounded to the nearest ten is 600
So, our estimate for the sum of 348 + 598 is 350 + 600 = 950
Using a calculator, the actual computation is 348 + 598 = 946
Our estimate of 950 is 4 more than the actual answer of 946. This means that our estimate is slightly higher than the actual answer. This is not a big difference and it is reasonable as the numbers are rounded to nearest 10.
Please look at the picture and answer the question thank you
Answer:
[ 5, ∞ )
Step-by-step explanation:
brackets on the ends of the interval indicate x can equal the value inside the bracket
parenthesis on the ends of the interval indicate x cannot equal the value inside the parenthesis.
x ≥ 5
expressed in interval notation as
[ 5, ∞ )
What is the value of y that makes T Parallel to U
The required value of y for the angle is 18.
What is corresponding angles?The angles created when a transversal intersects two parallel lines are known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.
According to question:By Corresponding angles
7x = 3x + 36
4x = 36
x = 9
And
Angle in straight line
(6y + 9)+(3x+36) = 180
(6y + 9)+(27+36)
6y + 72 = 180
6y = 108
y = 18
Thus, required value of y is 18.
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Method 1 Table of Values
Please help, I’ll mark brainlest
The graph of the quadratic function g(x) = - (x - 2)² + 4 on Cartesian plane is shown in the image attached below.
How to analyze and graph a quadratic equation
In this question we find the case of a quadratic equation in vertex form, whose definition is shown below:
y - k = a · (x - h)²
Where:
(h, k) - Coordinates of the vertex.a - Vertex constantThe equation of the axis of symmetry is shown below:
x = h
We can graph by using the coordinates of the vertex and two other points and understanding the vertex constant. Please notice that the parabola has an absolute minimum when vertex constant is positive, otherwise it is an absolute maximum.
First, find the coordinates of the vertex of the parabola:
(h, k) = (2, 4)
Second, determine the nature of the absolute extreme by interpretating the sign of vertex constant:
a = - 1 (The vertex is an absolute maximum)
Third, evaluate the function at two distinct points:
x = 0
g(0) = - (0 - 2)² + 4
g(0) = - (- 2)² + 4
g(0) = 0
x = 4
g(4) = - (4 - 2)² + 4
g(4) = - 2² + 4
g(4) = - 4 + 4
g(4) = 0
Fourth, graph the parabola on Cartesian plane. (Image is done with the help of a graphing tool)
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Suppose f(x) = x² − 2x³ + ax²+x+3, where a is a constant. If f(3) = 2, then
what is a?
Answer:
a = [tex]\frac{41}{9}[/tex]
Step-by-step explanation:
Evaluate f(3):
f(3) = (3)² -2(3)³ + a(3)² +3 +3
9a - 39 = 2
9a = 41
a = [tex]\frac{41}{9}[/tex]
6. Using any method(s), solve △KHP when h=16.1, p=24.9 and k=12.8
The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.
How to determine the measures of missing angles in a triangle
In this question we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below:
p² = h² + k² - 2 · h · k · cos P
h² = p² + k² - 2 · p · k · cos H
k² = h² + p² - 2 · h · p · cos K
Where:
h, k, p - SidesH, K, P - AnglesIf we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are:
cos P = (p² - h² - k²) / (- 2 · h · k)
cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)
cos P = - 0.478
P ≈ 118.555°
cos H = (h² - p² - k²) / (- 2 · p · k)
cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)
cos H = 0.823
H ≈ 34.614°
cos K = (k² - h² - p²) / (- 2 · h · p)
cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)
cos K = 0.892
K ≈ 26.844°
Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°.
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A free bus service operates throughout the day around Brelney City Centre. The bus starts from the Railway Station, then stops successively at the Castle, the Shopping Centre, the Park and the Stadium, before returning to the Railway Station. The journey time for each section of the circuit is 5 minutes.
The first departure of the day from the Railway Station is at 09:15. Each time the bus arrives back at the Railway Station it waits for 10 minutes before setting off again.Bart will be the driver for the first 4 circuits tomorrow.At what time will Bart arrive back at the Railway Station for the final time tomorrow?
A 11:25
B 11:35
C 11:45
D 11:55
Answer:
The bus journey takes 25 minutes (5 minutes per stop x 5 stops). The bus leaves the Railway Station every 10 minutes (the wait time between circuits).
The first departure is at 09:15, so the bus will arrive back at the Railway Station at:
09:15 + 25 minutes = 09:40
Bart will drive the bus for 4 circuits, so the bus will arrive back at the Railway Station for the final time at:
09:40 + (4 x 25 minutes + 4 x 10 minutes) = 09:40 + 130 minutes =
11:50.
So the final arrival time will be D 11:55.
Answer:
Step-by-step explanation:
Each circuit takes 25 minutes (5 destinations times 5 minutes) plus the 10 minute wait at the Railway Station. So the entire circuit is 35 minutes with the wait. Bart drives 4 circuits - 4 times 35 minutes is 140 minutes.
140 minutes equals 2 hours and 20 minutes.
Add 2 hrs and 20 minutes to 9:15 and the sum = 11:35
The answer is B - 11:35
Write an equation for a line perpendicular to y= -5x-1 and passing through the point (10,3)
Answer: A line is perpendicular to another line if the slope of the first line is the negative reciprocal of the second line. The equation of the line y = -5x-1 has a slope of -5. The negative reciprocal of -5 is 1/5.
A line passing through a point (x1, y1) has an equation in slope-intercept form of y = m(x-x1) + y1, where m is the slope of the line.
So, we can use the point (10,3) and the slope of the line which is 1/5 to write the equation of the line:
y = 1/5(x-10) + 3
Therefore, the equation of the line perpendicular to y = -5x-1 and passing through the point (10,3) is y = 1/5x + 1/5
Step-by-step explanation:
if the hour hand of a clock is turned anticlockwise from 2 pm to 9 am, through how many degrees will it have turned?
Answer: The hour hand of a clock makes one complete rotation, 360 degrees, in 12 hours or 720 minutes.
The hour hand of a clock turns 30 degrees in one hour or 0.5 degrees in one minute.
In this case, the hour hand is turned anticlockwise from 2 pm to 9 am, which is 21 hours.
So, it will have turned 21 * 30 = 630 degrees.
It is important to note that this answer only accounts for the rotation of the hour hand and does not take into account the rotation of the minute hand.
Step-by-step explanation:
3.
Mrs. Slana pays a babysitter $10.00 an
hour plus an extra $3 for every hour over
five hours. If Santos babysits for eight
hours, how much money will he make?
Answer: $89
Step-by-step explanation: The equation would be P = 10(x) + 3(x-5) assuming P is profit and x is greater than 5. By pluggin in x, the number of hours, we can find that it is 89.
Answer: Santos will make $89
Step-by-step explanation:
Hour 1 - $10
Hour 2 - $10
Hour 3 - $10
Hour 4 - $10
Hour 5 - $10
Hour 6 - $13
Hour 7 - $13
Hour 8 - $13
