A) W is a sub space of V
given that V =R^4 and W= [(x1, x2, x3, 0)|x1 ,x2, x3 E..R]
W is a subspace of V because of the following.
let (x1, x2, x3, 0), (y1, y2, y3, 0) ∈ W and a, b ∈ V
now
a(x1, x2, x3, 0)+b (y1, y2, y3, 0)= (a x1, a x2, a x3, 0)+(b y1, b y2,b y3, 0)
= (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)=
(a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)
LHS =RHS
∈W
since (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ) are all elements of R
W is closed under vector addition and scalar multiplication.
Hence W is a sub space of V.
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Evaluate,f(-4) for f(x)=-x^2-4x+42
Please explain by step by step please!
The output value of f( -4 ) in the function f(x) = -x² - 4x + 42 is 42
What is the output value of f( -4 ) in the given function?A function is simply a relationship that maps one input to one output. Every x-value can only have one y-value to qualify as a function.
Given the data in the question;
f( x ) = -x² - 4x + 42f( -4 ) = ?To find the output value of f( -4 ), replace all the occurrence of x with -4 in the function and simplify.
f( x ) = -x² - 4x + 42
f( -4 ) = -(-4)² - 4(-4) + 42
f( -4 ) = -( 16 ) + 16 + 42
f( -4 ) = -16 + 16 + 42
f( -4 ) = 42
Therefore, the output value of f( -4 ) is 42, this forms an ordered pair of (-4, 42).
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How to make x the subject if m=n+x/p
Variable x as the subject of the equation given is expressed as: x = p(m - n).
How to Make a Variable the Subject of the Formula?To make a variable the subject of a formula implies that we express the equation in terms of the variable. Thus, to make a variable the subject of the formula, we have to make the variable stand alone on one side of the equation.
Given the equation, m = n + x/p, make x the subject as explained below:
m = n + x/p [given]
Subtract n from both sides
m - n= n + x/p - n (subtraction property of equality)
m - n = x/p
Multiply both sides by p
p(m - n) = x/p(p) (multiplication property)
p(m - n) = x
x = p(m - n)
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A cylindrical drum is 20m tall and has the inner diameter of 30m. How many liters of water can be stored in it ?
Answer:
14137167 liters approximately
Step-by-step explanation:
Total Volume of a cylinder
V = π R² H
where R - base radius
H = height
Given diameter of base = 30m, base radius R = 30/2 = 15
H = 20m
Volume = π x 15² x 20 = 4500π m³ = 14,137.16694 m³
Since 1 m³ = 1000 liters
this works out to 14137.16694 x 1000 ≈ 14137167 liters
A car uses 3 1/8 gallons of gasoline per hour when driving on the highway, how many gallons will it use after three hours?
Answer:
The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway
Step-by-step explanation:
if a car uses 3 1/8 gollon per one hour
Multiply the gallon usage of the car by the hours the car will travel on the road
3 1/8(gallons) x 3(hours on the road)
9 3/8 or if you change it to simple form it will be equal to 9.375
What would 6 + -4 3/4 + -2 1/8 be?
Answer: -0.875
Step-by-step explanation:
Answer: -1 1/8
Step-by-step explanation:
6 - 4 3/4 = 1 1/4
1 1/4 - 2 1/8 = -1 1/8
How many tiles measuring 20cm by 50cm are needed to completely cover a wall 4m by 8m?
The number of tiles measuring 20cm by 50cm that are needed to completely cover a wall 4m by 8m is :320.
Number of tiles neededFirst step is to convert the Meters to Centimeters
4m = 400cm
8m = 800 cm
Hence,
4m by 8m = 400 cm × 800 cm
4m by 8m = 320,000 cm²
Second step is to determine the how many tiles are needed
Number of needed tiles = 320,000 cm² / ( 20 cm × 50 cm)
Number of needed tiles = 320,000 cm² /1,000 cm²
Number of needed tiles = 320
Therefore 320 tiles are needed.
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Write the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
The quadratic equation will be; 3x² + 6x + 9
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.
The factors are; (x + 3) and (x + 1)
f(x) = a(x + 3)(x + 1)
As, a = 3.
Then we get;
f(x) = 3(x + 3)(x + 1)
= 3(x² + 2x + 3)
= 3x² + 6x + 9
The quadratic equation will be; 3x² + 6x + 9
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Need help simple stuff that I forgot in algebra. How do u get 5x/2-x???
Answer: 7/12 =x
Step-by-step explanation:
Find the approximate side length of a square game board with an area of 160
in2.
The approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.
As given in the question,
Area of the square game board is equal to 160in².
Let 'x' inches be the side length of the square game board.
Area of the square game board = (side length)²
⇒ 160 = ( x )²
Take square root both the sides we get,
x = √160
⇒ x = 12.649 inches
⇒ x = 12.6 inches( approximately)
Therefore, the approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.
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Calculate the force created from an object with a mass of 1250 grams and an acceleration of 3 m/s^2
Please help!! I will mark as brainliest
The force created by the object is 3.75 Newton.
Given
Mass of the object (m) = 1250 grams
Convert 1250 grams to kilograms by dividing it by 1000.
Mass (m) = 1.25 kg
Acceleration of the body (a) = 3 [tex]m/s^{2}[/tex]
From Newton's second law we know [tex]F= m *a[/tex]
By Substituting in the above equation we get
Force = 1.25 x 3
Force = 3.75 [tex]kg/m /s^{2}[/tex]
It can also be written as force = 3.75 N
Hence Force created by the body is 3.75 Newton.
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10. The sales tax rate in a certain state
Find the total price paid for a pair of shoes
that cost $35.
the total price paid for a pair of shoes after tax is included is $37.1.
A sales tax is a tax paid to the government for sales of certain types of goods and services.
According to the question,
Cost of the shoes = $35. (given)
Total amount/price paid = cost + tax
As the tax percentage is not given in the question, we will assume it to be 6% for example. Then,
Tax amount = 6% of $35
= 6/100*35
= $2.1
Now, total price = cost + tax
= $35+$2.1
= $37.1
Therefore, we conclude that the total price paid for a pair of shoes after tax is included is $37.1.
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Each handmade pin needs inch 1/4 of wood. How much wood would you need to make 120 pins?
We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.
What do we mean by mathematical operations?A mathematical "operation" is the process of calculating a value using operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The arithmetic operators perform the operations of addition, subtraction, multiplication, division, exponentiation, and modulus.So, the wood we need to make 120 pins:
The wood used to make 1 pin is ¼.Then, 120 pins:120 × ¼ = 30Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.
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The slope of the line that passes through the point (2, 4) and (3, 8) is
[tex]m=\frac{y_{2-y_{1} } }{x_{2} -x_{1} } \\m=\frac{8-4}{3-2} \\m=\frac{4}{1} \\m=4[/tex]
I also provided the formula on how to calculate the slope between the points
 I REALLY NEED HELP WITH THIS!!
Determine the angles of a rotation
A) 90º clockwise
B) 90º counterclockwise
C) 180º
D) 270º clockwise
E) 270º counterclockwise
is 2 correct answers ❗️
Answer: B) 90º counterclockwise
Step-by-step explanation:
First, let us look at clockwise vs counterclockwise. Clockwise is in the direction of a clock, spinning around to the right. Counterclockwise is the opposite, spinning to the left.
A) 90º clockwise
➜ This is 90 degrees to the right.
B) 90º counterclockwise
➜ This is 90 degrees to the left
C) 180º
➜ This is directly flipped.
D) 270º clockwise
➜ This is 270 degrees to the right.
E) 270º counterclockwise
➜ This is 270 degrees to the left.
We will look at the answer options and decide which makes the most sense. This looks to be option B, 90º counterclockwise as shown in the image attached.
Find the nth term of this quadratic sequence
-1, 2, 7, 14, 23, . . .
Answer:
The pattern the sequence follows is a perfect square, minus 2
Step-by-step explanation:
esentially use ( n^2 - 2 ) to find the nth number in the sequence.
the 5th number ( n = 5 ), would look like ( 5^2 - 2 ), simplfiying to ( 25 - 2 ), then being 23.
The same applies to all numbers listed in the sequence.
Determine the total number of roots of each polynomial function.
g(x) = 5x - 12x²+3
The number of bald eagles in the state in the winter of 2000 is
(Round to the nearest whole number.)
Save
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function
f(x) = -3.334x4 +35.607x3-97.645x² +41.268x + 177.537
where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 2000.
Answer:
206
Step-by-step explanation:
Let x=4.
[tex]f(4)=-3.334(4)^4+35.607(3)^3-97.645(4)^2+41.268(4)+177.537 \approx 206[/tex]
Solve the proportion.
I WILL USE CROSS MULTIPLICATION
[tex]t(1.3) = 6.5(1.2) \\ 1.3t = 7.8 \\ \frac{1.3t}{1.3} = \frac{7.8}{1.3} \\ t = 6 [/tex]
ATTACHED IS THE SOLUTION
Ang has x dollars in his savings account, and Julia has y dollars in her savings account. Ang gives Julia 1/3 of the money in his savings account, which Julia deposits into her savings account. Julia then spends 1/4 of the total in her savings account. Express the amount of money Julia spent non terms of x and y.
Answer choices
1. y/4 + x/12
2. y/4 + x/3
3. y/4 + x/7
4. 3y/4 + x/4
In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.
What does algebraic expression mean?An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.
What is an illustration of an algebraic expression?Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an example of an algebraic expression.Both Ang and Julia have savings balances of x and y dollars, respectively.
Ang = x dollars
Julia = y dollars
Ang offers Julia a third of his savings, which she then transfers to her own savings account.
Amount in Julia's account = (1/3)x + y
Julia then spends a quarter of the total into her savings account.
Amount of money Julia spent = 1/4 × [(1/3)x + y]
= (1/12)x + (1/4)y
= y/4 + x/12
Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.
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Denver,Colorado often experiences snowstorms resulting in multiple inches of accumulated snow. During the last snow storm, the snow accumulated at 4/5 inch/hour. If the snow continues at this rate for 10 hours, how much snow will accumulate?
Answer:8
Step-by-step explanation:if it is 4/5 per hour then you mulitply 4/5 x 10
and 4/5=.8
.8 x 10=8
Suppose a jar contains 11 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
22.44% probability that the marbles are red, 77.55% probability that they are blue
Find a and b*
9√√3
2
a
60°
b
The value of a is 9 and b is 4.5
What is trigonometric function ?The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that can be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.
[tex]sin(60)=\frac{opposite}{hypotenuse} \\\frac{\sqrt{3} }{2}=\frac{\frac{9\sqrt{3} }{2} }{a}\\ a =9\\ tan(60)=\frac{opposite}{adjacent}\\ \sqrt{3}=\frac{\frac{9\sqrt{3} }{2} }{b} \\b=4.5[/tex]
The value of a is 9 and b is 4.5
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Kai received a $40 Amazon gift card that she wanted to use to rent movies. After she rented 5 movies at $x each, she had $25 left. What was the cost x of each movie Kai rented?
Answer: x=3
Step-by-step explanation:
40-25=15
15 divided by the 5 movies is 3
so $3 per movie
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A car dealership wants to try out a new leasing arrangment, which will allow a buyer to trade a car back to the dealership for a certain amount of credit at any time throughout the first three years of ownership. For a car in good condition, the arrangement will value the car at 1/3 the original price at the end of three years, and will depreciate the value of the car linearly over the course of the three years. What is the value of a car with initial purchase price P at the end of the second year? Write your answer as an expression in terms of P. Write the exact answer. Do not round.
The expression in term numerator and denomerator of P the write answer would be
25.
Sol-
we have a deal an arrangement where, at the end of 5 years, the value of the car is going to be a fifth, the original price. So that's what i have written here after 5 years, the value of the car will be the price, the original price divided by 5 point. What we also know is that at 0 years, our initial value, the output here- should be the price of the car. So what we're going to do is when we use these 2 values to find the slope of this line, so we're going to do y 2, minus 1 y 1 over x, 2 minus x 1. It doesn't matter which 1 is y 2 and which 1 is y 1 as long as you're consistent here, i'm going to do p minus p over 5, and since i started here in the numerator, i need to start there in the denominator.
So we know here that x equals 4 we're doing that in the problem. So i'm goin t go ahead and replace this right here. We'Re gonna have y equals 16 p over negative 25 plus p, and if we get a common denominator here to add this, we have y equals 16 p plus 25 over 25. With this p right here, because it's gonna be 25 p over 25 here and then i recognize that are y value here, that was that was v or value here. All right and, let's see 25 p minus 16 p is going to give us 9 p. All right, so 9 p over 25 is going to be the value of the car, giving the original price p after 4 years.
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4x-6(3x+4)
please help, i cannot find an answer :( (Ill give crown or wtv)
Answer:
Is this correct??
if yes then reply
Answer/Step-by-step explanation:
I don't know whether to distribute -6 or multiply 4x - 6 by 3x + 4. So I'll do both.
1. Multiply
(4x - 6)(3x + 4)
4x (3x + 4) - 6 (3x + 4)
12x² + 16x - 18x - 24
12x² - 2x - 24
2. Distribution
4x - 6(3x + 4)
4x - 18x - 24
-14x - 24
I hope either of my answers helps!
Jordan needs to order some new supplies for the restaurant where he works. The restaurant needs at least 730 knives. There are currently 204 knives. If each set on sale contains 10 knives, write and solve an inequality which can be used to determine xx, the number of sets of knives Jordan could buy for the restaurant to have enough knives
Answer:
53 sets
Step-by-step explanation:
730 - 204 = 526
526 / 10 = 52 r 6
therefore he'd have to buy 53 sets to have enough knives.
There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The restaurant needs at least 730 knives.
There are currently 204 knives.
And, each set on sale contains 10 knives.
Now,
By the given condition, we formulate;
⇒ 730 ≤ 204 + 10x
Solve for x as;
⇒ 730 ≤ 204 + 10x
⇒ 730 - 204 ≤ 204 + 10x - 204
⇒ 529 ≤ 10x
Divide by 10 as;
⇒ 52.9 ≤ x
After rounding, we get;
⇒ 53 ≤ x
Thus, There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.
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Need help on probability. Please explain how you did it so I can know how to do it.
Answer:
I believe it should be 5/6
Step-by-step explanation:
Here's why, the probability of getting a B, or an even number is 3/6 since there are 3 even numbers on a dice. The probability of getting a multiple of 3 is 2/6 since the only multiples of 3 are 1 and 3. Add the 2 together to get 5/6. Hope this helps.
Answer:
[tex]\text{P}(B \text{ or }C)=\dfrac{5}{6}[/tex]
Step-by-step explanation:
Mutually Exclusive Events
For two events, A and B, where A and B are mutually exclusive:
[tex]\boxed{\text{P}(A \text{ or }B)=\text{P}(A)+\text{P}(B)}[/tex]
Probability distribution table:
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6 \\\cline{1-7} \text{P}(X=x)\phantom{\dfrac11}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}\\\cline{1-7}\end{array}[/tex]
where X is the score on a fair, six-sided dice.
P(B or C) means "the probability of rolling an even number or a multiple of 3".
As an even number of a fair, six-sided dice can never be a multiple of 3, the two events B and C are mutually exclusive.
Calculate the probabilities for events B and C.
Event B
Rolling an even number.
[tex]\begin{aligned}\implies \text{P}(X \text{ is even})&=\text{P}(2 \text{ or }4\text{ or }6)\\\\&=\text{P}(X=2)+\text{P}(X=4)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{3}{6}\end{aligned}[/tex]
Event C
Rolling a multiple of 3.
[tex]\begin{aligned}\implies \text{P}(X \text{ is multiple of 3})&=\text{P}(3 \text{ or }6)\\\\&=\text{P}(X=3)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{2}{6}\end{aligned}[/tex]
Solution
[tex]\begin{aligned}\implies \text{P}(B \text{ or }C)&=\text{P}(B)+\text{P}(C)\\\\& = \dfrac{3}{6}+\dfrac{2}{6}\\\\& = \dfrac{5}{6}\end{aligned}[/tex]
Chrystal helps her grandmother plant seeds in the garden.they plant squash, corn, sunflower, and tomatoe seeds. they plant 6 rows of each type of seed and they plant 20 seeds in each row. how many seeds do they plant?
They plant a total number of 480 seeds.
In the given question, Chrystal and her grandmother plant seeds in the garden. They plant a total of 4 types of seeds: Squash, Corn, Sunflower, and Tomato. They plant 6 rows of each type of seed. Also, each row has 20 seeds. We have to calculate the total number of seeds that they plant.
Given that,
=> Total number of types of seeds, T = 4
=> Number of rows, R = 6
=> Number of seeds in each row, S = 20
To calculate the Total Number of seeds planted we use the formula:
=> Total = T * R * S, Putting values we get:
=> Total = 4 * 6 * 20
=> Total = 480
Hence, the Total number of seeds planted is 480.
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Suppose 84% of students chose to study German their sophomore year, and that meant that there were 525 such students. How many students chose not to take German their sophomore year?
Answer: 100
Step-by-step explanation:
525/84 x 100= 625 total students
625 - 525 = 100
A printer prints 75 pages in 5 minutes.
At the same rate, how many pages does the printer print in 7 minutes?\
Answer:
105
Step-by-step explanation:
5 minutes=75 pages
1 minute=15 pages
7 minutes=15*7
7 minutes=105pages
Answer: 105
Step-by-step explanation:
75pg —-> 5mins
X ——> 7 mins
•
•
x= (75 x 7)/5 = 105pages