Answer:
b=(cd-ax)/y
Step-by-step explanation:
b=(cd-ax)/y
1. Which expression has a whole-number product?
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
C (-6+ i)(3- i)
D(-4+3i)(4-3i)
Option (B) (3 + 2i) (3 - 2i) is the expression that has the whole number product.
Whole number:
Whole number refers the numbers without fractions and it is a collection of positive integers and zero and represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.
Given,
Here we have the following expression:
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
(C) (-6+ i)(3- i)
(D) (-4+3i)(4-3i)
Now, we need to find the whole number product.
In order to find the solution we have to perform the multiplication on the given expression,
First expression will gives the following,
(A) (4 - 2i) (4 - 2i)
When we apply the (a-b)² formula in it then we get,
=> 4²+ (2i)² - (2 x 4 x 2i)
=> 16 - 4 - 16i
=> 12 - 16i
Which is not a whole number product.
Second expression,
(B) (3 + 2i) (3 - 2i)
Apply the (a + b)(a - b) formula in it,
Then we get,
=> 3² - (2i)²
=> 9 + 4
=> 13
Therefore, this one is the whole number product.
Third expression,
(C) (-6 + i) (3 - i)
When we perform the multiplication on it, then we get,
=> -18 + 6i +3i -i²
=> -18 + 9i + 1
=> -17 + 9i
his one is not a whole number product.
Final expression,
(D) (-4 + 3i) (4 - 3i)
When we perform the multiplication on it, then we get,
=> -16 + 12i + 12i - (3i)²
=> -16 + 24i + 9
=> -7 + 24i
This one is also no the whole number product.
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Estimate 6769 x 925 by first rounding each number so that it has only 1 nonzero digit.
The resulting value of the the expression 6769 x 925 by first rounding each number so that it has only 1 nonzero digit is 63,000
Round off
Round off refers a number is made simpler by keeping its value intact but closer to the next number. And it is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
Given,
Here we need to estimate 6769 x 925 by first rounding each number so that it has only 1 nonzero digit.
Here we have to take individual terms to round off then we get,
By rounding 6799 so that it has only one non-zero digit is rounding it to nearest thousand.
6769 rounds to nearest thousand as 7000 as hundreds digit 7 > 5.
Similarly, by rounding 925 so that it has only one non-zero digit is rounding it to nearest hundred.
925 rounds to nearest hundred as 900 as tens digit 2 < 5.
Now, the estimated value after rounding each number so that it has only one non-zero digit is
=> 7000 x 900
=> 63000.
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Find the volume of the prism. Round to the nearest tenth if necessary.
options: 504.0 cm3 204.7 cm3 252.0 cm3 291.7 cm3
The volume is the amount of space thus the volume of the given prism will be 204.7 cm³ thus option (B) is correct.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Volume has units of cube example meter³,cm³, etc.
The volume of the given prism will be the area of the front triangle with a length of 12 cm.
The form triangle has been attached below,
The length x will be,
x = √(6² - 3.5²) = 4.87 cm.
The area of from triangle = (1/2) × 7 × 4.87
A = 17.06 cm²
The volume of the prism = A × length (12 cm)
Volume = 17.06 × 12 = 204.68 cm².
Hence "The volume is the amount of space thus the volume of the given prism will be 204.7 cm³".
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The complete question has been attached below ;
Use the formula F = mg-3t²
m = 4, g = 6 and t = 2
Evaluate the Laplace transform of L[(sin 2t-cos 2t)^2]
The Laplace transform of the given integral function is 1/s +4 / (s²+16) .
The integral transform, commonly known as the Laplace transform in mathematics, converts a function of either a real variable t in the time domain into a function of something like a complex variable s.
The Laplace transform is equal to the integral for the suitable functions
[tex]{\displaystyle {\mathcal {L}}\{f(t)\}(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt.}[/tex]
Now we will use this to find the suitable Laplace transform of the trigonometric function:
(sin 2t-cos 2t)²
= sin² 2t + cos² 2t - 2sin 2tcos 2t
= 1 - sin 4t
Now we will use the Laplace transform of the function.
L [1 - sin 4t] = L[1] - L[sin 4t]
Now L[1] = 1/s
L[sin 4t] = 4/ (s²+4²) = 4 / (s²+16)
Hence the Laplace transform will be
L [1 - sin 4t] = 1/s +4 / (s²+16)
Pierre-Simon Laplace invented the complex frequency domain, often known as the s-domain or the s-plane. There are numerous uses for the transform, a method for solving differential equations, in both science and engineering.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y2−5y=750
750 -y(y-5)=0750−y(y−5)=0 and (y+25)(y-30)=0
Pahelpppp po pang grade 6 po yan na math
Question 3(Multiple Choice Worth 1 points)
(02.04 MC)
In triangle DEF, if mZD = (2x)°, mZE = (2x - 4)º, and mZF = (x + 9)°, what is the value of x?
A)35
B)37
C)44
D)71
By using property of triangle and trapezium, it is obtained that
a) value of x is 35°
b) Third option is correct
What is a triangle and trapezium?
Triangle is a three sided two dimensional figure.
Trapezium is a quadrilateral whose one pair of opposite side is parallel and another pair of opposite side is non parallel
Here property of triangle is used
[tex]m \angle D = (2x)^{\circ}, \ m\angle E = (2x - 4)^{\circ}, m \angle F = (x +9)^{\circ}[/tex]
[tex]m \angle D + m\angle E + m \angle F = 180\\2x + 2x - 4 + x + 9 = 180\\5x + 5 = 180\\5x = 180 - 5\\5x = 175\\x = \frac{175}{5}\\x = 35^{\circ}[/tex]
In the second question, if the trapezoid is rotated 90° clockwise, then (x, y ) will change to (y, -x) and new coordinate of A is (1, 5)
Third option is correct
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Pedro has $18 to spend at the grocery store. His mother wants him to use the money to buy fruit. Apples cost $2 a pound and pears cost $3 a pound
Answer:
Pedro can buy 4 pounds of pears and 3 pounds of apples.
Step-by-step explanation:
Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.
$2×3lb + $3×4lb=$18
Luna uses graphic design software to resize a photo. For all sizes
of the photo, length and width are in a proportional relationship.
Which equation represents the proportional relationship shown?
Oy=0.8x
y = 1.2x
Width (n)
543N-
x
0 123456
Length (in)
Oy=x+1.2
O y = 2x + 1
Length (n)
X
1
2
3
Submit Answer
Process
1.2 11.2
1.2.2 = 2.4
1.2 3 = 3.6
Width (n)
Y
1.2
2.4
3.6
Answer:
y = 1.2·x
x = 1; y = 1.2·1 = 1.2
x = 2; y = 1.2·2 = 2.4
x = 3; y = 1.2·3 = 3.6
You have a budget of $300 to order shirts for a math club. The equation 10x + 12y = 300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
a. Interpret the terms and coefficients in the equation.
b. Graph the equation. Interpret the intercepts.
c. Find three possible solutions in the context of the problem.
a) The coefficients are the costs of the respective shirts.
b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)
c) 3 solutions are:
(0, 25), (30, 0), (25, 4)
What does each coefficient means?
Here we know that:
x = number of short-sleeved shirtsy = number of long-sleeved shirts.And we have the linear equation:
10x + 12y = 300
The first coefficient is the one in the term "10x"
The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.
The second coefficient is on the term "12y"
And 12 means the cost in dollars of each long-sleeved shirt.
b) The graph of the linear equation can be seen on the image at the end.
The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.
The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.
c) 3 possible solutions can be seen on the graph, some examples are:
(0, 25), (30, 0), (25, 4)
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5k+(2k)-(-1)……………..
……………………
Pete's appliance received a bill dated July 15 for $26,000 with terms of 2/10, 1/15, n/60. On July 27 Pete sent in a partial payment of $6,000. What is the amount credited as well as the balance due?
The amount that would be credited, given the partial payments and the terms, would be $6, 060.61. The balance due would be $19, 939.39.
How to find the balance due?The terms 2/10 and 1/15 mean that if the buyer pays their bill in 10 days, they get a 2% discount. If they pay in 15 days, they get a 1% discount.
Pete paid on the:
= 27 - 15
= 12 days
This means that the 1 % discount would apply on the $6, 000. The credited amount would be:
= 6, 000 / (1 - 1%)
= $6, 060.61
The balance due would be:
= 26, 000 - 6, 060.61.
= $19,939.39
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Alicia deposited $400 in the bank. The bank paid her simple interest at the rate of 5 percent
she have in her account at the end of 6 months?
O $10
O $20
O $410
O $420
At the end of 6 months she will have $410 when calculated using simple interest.
What is simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Main Body:
Principle =$400
Rate = 5%
Time = 6 months = 1/2 years
Simple interest = P*R*T/100
S.I. = 400*5*(1/2)/100
S.I. = 10
Hence total amount is 400+ 10= $410.
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DUE IN A FEW MINS!!!!Do only number 25 pls I’m confused!! Also, please explain how u got it !!
Answer:
value of x are 2 and 3 which make the inequality true
A speed limit in Europe is 80 km per hour. What is the speed in miles per hour? There are about 1.6 kilometers in 1 mile. (1 point)
Responses
50 miles per hour
50 miles per hour
75 miles per hour
75 miles per hour
128 miles per hour
128 miles per hour
50 miles
ned asap
pls answer rightly not spam
Answer:
50 miles per hour
Step-by-step explanation:
80 km 1 mi
---------- x ------------ = 50 mi/hr
1 hr 1.6 km
what is the nearest hundreth in 1.2983 if you round it
Answer:
1.3000
Step-by-step explanation:
To Round Numbers...
1 ) Decide which is the last digit to keep ( In this case it would be the hundredths )
2 ) Leave it the same if the next digit is less than 5 (this is called rounding down)
3 ) But increase it by 1 if the next digit is 5 or more (this is called rounding up)
Hope this helps! :)
Given (0.25 x 12.3) x 8, which two numbers are compatible, and which
property would you use to calculate this mentally?
4a) Two numbers
4b) Property
The two numbers that are compatible are 0.25 and 8. The property which helps to calculate it is commutative property.
What is the commutative property?
This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution.
Given numerical expression is (0.25 x 12.3) x 8.
First remove the parenthesis from the numerical expression:
(0.25 x 12.3) x 8 = 0.25 x 12.3 x 8
Now apply commutative property:
(0.25 x 12.3) x 8 = (0.25 x 8) x 12.3
(0.25 x 12.3) x 8 = 2.00 x 12.3
(0.25 x 12.3) x 8 = 24.6
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What’s the the anwser?
The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.
What is inequality?The relation between two unequal expressions is defined as inequality.
The given inequalities are 3x + 6 < 15 and 2x - 5 >7.
Solve the first inequality:
3x + 6 <15
3x < 15 -6
3x < 9
x < 3
Solve the second inequality:
2x - 5 > 7
2x > 7 + 5
2x > 12
x > 6
Hence, the solution to the compound inequality is x < 3 and x >6.
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Kenneth is making a cake for the first time. His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try. He uses a small spoon to remove the extra suger. If he needs to remove 12 spoonfuls, how many milligrams of sugar does his spoon hold?
The spoon holds 1250 milligrams of sugar if Kenneth needs to remove 12 spoonfuls.
We are given;
Kenneth is making a cake for the first time.
His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try.
He uses a small spoon to remove the extra sugar.
He needs to remove 12 spoonfuls.
We need to find the quantity of sugar his spoon hold.
First, let us find the extra amount of sugar;
Extra sugar = 295 - 280 = 15 grams.
We will find each spoon by using the unitary method;
Since 12 spoonfuls hold 15 grams.
So, 1 spoonful holds 15 / 12 grams = 1.25 grams = 1250 milligrams.
So, 1 spoonful holds 1250 milligrams of sugar.
Thus, the spoon holds 1250 milligrams of sugar if Kenneth needs to remove 12 spoonfuls.
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what the area and pelase explain give brainly points
Answer: 10 squares
Step-by-step explanation:
The answer for the area is 10 squares but I’m not sure that’s what they’re asking for.
Finding slope for (-1,1) and (5,4)
Answer:
Slope = 0.75
Step-by-step explanation:
Slope Formula: y2-y1/x2-x1
4-1/5-1=3/4=0.75
Question 8 of 10
What is the complete factorization of the polynomial below?
x3+3x²+ 9x+27
OA. (x+3)(x+3/)(x-3)
OB. (x-3)(x+3)(x+3)
OC. (x-3)(x+3)(x-3/)
D. (x+3)(x+3)(x+3/)
The factorization of the expression [tex]x^3+3x^2+9x+27[/tex] is [tex](x+3)(x^2+9)[/tex].
What is factorization?
The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. A factorization is just the procedure by which an algebraic expression gets expanded in the opposite direction. The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. Factorization is the reverse process of expansion of an algebraic statement. If an algebraic expression is a product of prime factors, it has undergone complete factorization.
Here the given polynomial expression is ,
=> [tex]x^3+3x^2+9x+27[/tex]
=> [tex]x^2(x+3)+9(x+3)[/tex]
=> [tex](x+3)(x^2+9)[/tex]
Hence the complete factorization of the given expression is [tex](x+3)(x^2+9)[/tex].
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Find the unit rate for this relationship
2/3 is the unit rate of the relationship
How to determine the unit rate of the relationship?
A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e. $5 for one orange.
On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:
Slope = y2-y1 / x2-x1
Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:
Slope = y2-y1 / x2-x1
Slope = 6-2 / 9-3 = 4/6 = 2/3
Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer
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Translate the equation into a verbal sentence 8-x=2
Answer:
See below
Step-by-step explanation:
Eight minus unknown quantity 'x' equals two.
How can i find the domain
Complete steps to find domain of function is describe below.
What is domain ?Domain is defined as the all input values which satisfy the function or can say all inputs any function have.
Steps to find the domain of function:suppose we have a function f(x) = 6x^2 + 5x - 4
For domain solve it for x
⇒ 6x^2 + 5x - 4
⇒ 6x^2+ 8x - 3x - 4
⇒ 2x(3x + 4)· -1(3x + 4)
⇒ (3x + 4) (2x - 1)
values of x are positive for quadratic equation,
⇒ (3x + 4) (2x - 1)≥0
⇒ x ≥ 1/2 or x ≥ -4/3
These are the domain of function.
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Find the ordered pair (s,t) that satisfies the system
s/2 + 5t = 3 + 5t
3t - 6s = 9 + 3t
Answer:
There isn't one. There is no solution.
Step-by-step explanation:
There are multiple ways to solve this system, but here's what I did:
Solve the both equations for s:
s/2 + 5t = 3 + 5t ⇒ s = 6
3t - 6s = 9 + 3t ⇒ s = -3/2
Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.
Hello, please answer this correctly and you will get 5 stars and 20 points.
Answer:
Step-by-step explanation:
90
When Max was a puppy, he weighted 5 1/2 pounds. At his 1-year check-up with the vet, Max weighted 15.8 pounds. How much weight did Max gain between the time he was a puppy and his 1-year check-up?
Max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
When Max was a puppy, he weighted [tex]5\frac{1}{2}[/tex] pounds
At his 1-year check-up with the vet, Max weighted 15.8 pounds
We need to find the weight did Max gain between the time he was a puppy and his 1-year check-up.
To find this we need to find the difference when Max was a puppy and after one year check up.
Difference is nothing but subtracting one value from another value.
Let us convert mixed fraction [tex]5\frac{1}{2}[/tex] pounds to improper.
[tex]5\frac{1}{2}[/tex] =11/2=5.5
Now subtract 15.8-5.5
10.3 pounds.
Hence, max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.
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step by step solution
x+1≥ 3or4/3x<-8
Answer:
Step-by-step explanation:
The answer for this can be an inequality or an interval notation or a graph
* Subtraction of (1) in both sides of the inequality
* Let's call part A: [tex]X+1\geq 3[/tex]
* Let's call part B: [tex]\frac{4}{3} X < -8[/tex]
* Solve part A first:
Do the subtraction of (1) on both sides of the inequality.
X ≥ 3 −1
X ≥ 2
Subtract
* Solve part B now:
Multiply for 3/4 both sides of the inequality to eliminate the [tex]\frac{4}{3}[/tex]
[tex]\frac{4}{3} X (\frac{3}{4} < -8 (\frac{3}{4})[/tex])
X < -24/4
X < -6
Answer
Inequality Form:
x < −6 or x ≥ 2
Interval Notation:
( − ∞,−6)∪[2,∞)
In Graph:
See the attach