Answers
-16 + 37i
Explanation:
Note that i^2 = -1
(4+7i)(3+4i) = 4*3 + 4*4i + 7i*3 + 7i*4i
= 12 + 16i + 21i + 28i^2
= 12 + 37i + 28(-1)
= 12 + 37i - 28
= -16 + 37i
Hope this helps :)
Related Questions
PLEASE HELP ME!!
BRAIINLIEST WILL BE GIVEN
Answers
Hope this helps,
♥A.W.E.S.W.A.N.♥
1. SCHOOL PLAY Marika and her three friends attended the school play. Tickets cost $5.75 each, and Marika paid for everyone. Find the totał cost of the tickets. Justify your answer by using the Distributive Property
Answers
The 8 foot diameter circular table has a 4 foot wide extension. What is the total area with the extension? How does the area compare to the area of the 10 foot diameter table? Show your work.
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A tiger in captivity is fed 13.5 pounds of food an elephant in captivity eats per day. Compare the function by comparing their rates of change.
Answers
SEE ATTACHED IMAGE.
The first thing that we are going to do in this case is to find the slope of the line for the function that simulates the amount of food of the elephant.
We have then:
m = (y2-y1) / (x2-x1)
Substituting any two points:
m = (625-125) / (5-1)
m = 125 pounds / day
125> 13.5
Answer:
The elephant eats more than the tiger daily.
Multiply and simplify if possible.
√5x(√x - 5 √5)
Answers
x√5 - 25√x
Hannah is saving money for a car. She earns $160 each week working part time after school and on the weekends at Papa's Pizza. Hannah currently has $1,280 in savings. Her parents put $50 in her savings account each week and she saves one-half of her paycheck each week. Which expression represents the situation? (n represents the number of weeks)
Answers
Since we know that Hanna currently has $1,280 in her saving's account and each week she and her parents deposit $130 to the account, with [tex]n[/tex] representing the number of weeks, we can model the situation as follows:
[tex]f(n)=1280+130n[/tex]
Answer:
The answer is A because
Step-by-step explanation:
1,280 in savings
160n
2
Hannah saves each week
50n parents put in savings each week
thus,
1,280 + 160n/2+ 50n
1,280 + 80n + 50n
1280 + 130n
You really have to think this one through all the way. All the other answer choices are steps in finding the answer
Write the expression as a product of polynomials:
a(p–q)+q–p
p^2q+r^2–pqr–pr
PLZ ANSWER ASAP
Answers
1. a(p–q)+q–p
We take out common factor
To change q - p as p - q we pull out -1
So q - p becomes -1(p - q)
a(p–q)+q–p
a(p–q) -1(p - q)
p -q is in common so we factor out p-q
(p - q) (a - 1)
2. p^2q+r^2–pqr–pr
WE change the order of terms
[tex] p^2q-pqr+r^2-pr [/tex]
We group first two terms and last two terms
[tex] (p^2q-pqr)+(r^2-pr) [/tex]
Now we factor out pq from first group and -r from second group
[tex] pq(p-r) - r(p - r) [/tex]
[tex] (p - r) (pq - r) [/tex]
To write the answer as a product of polynomials we try to factor the polynomial
a(p–q)+q–p
we can write this expression as
a(p-q)+(q-p)
from second parenthesis we can factor out -1 , so we get
a(p-q) -1(p-q)
Now it has two terms a(p-q) and -1(p-q) , from these two terms we can factor out (p-q)
So we get it
(p-q)(a-1)
So we get the polynomial as a product of two polynomials.
Second
[tex] p^2q+r^2- pqr-pr [/tex]
we can rewrite the expression as
[tex] (p^2q- pqr)+(r^2-pr) [/tex]
Now try to factor the groups
factor out "pq" as GCF from first group and "-r" as GCF from second group
[tex] pq(p- r)-r(p-r) [/tex]
Now we can factor it out for final step
[tex] (p- r)(pq-r) [/tex]
Suppose you travel at 60 mph for 222 miles. How many hours will it take you to reach your destination?
A.) 4.3 hours
B.) 4.5 hours
C.) 3.7 hours
D.) 1.05 hours
Answers
Divide 60 by 222 for the number of hours you will need to travel to get to your destination.
222/60= 3.7
"C" 3.7 hours <== the answer
I hope this helps!
~kaikers
Which is more 3 liters or 2997 millilliters
Answers
Which set of points correctly demonstrates a pre-image that has been is reflected over x = -1? A(0,-1) and A'(4,-1) A(0,-5) and A'(0,3) A(-5,0) and A'(3,0) A(0,-4) and A'(0,4)
Answers
A(0, -1) and A'(4, -1)
See if the x-values are the same distance from -1.
|0 - (-1)| = 1
|4 - (-1)| = 5
The distances are different so let's try the other one:
A(-5, 0) and A'(3, 0)
See if the x-values are the same distance from -1.
|-5 - (-1)| = 4
|3 - (-1)| = 4
The distances are the same, so these points correctly demonstrate a pre-image that has been reflected over x = -1.
The correct set of points that demonstrate a pre-image that has been reflected over x = -1 is A(0,-1) and A'(−2,−1).
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
To reflect a point over the line x = -1, we simply need to flip the x-coordinate of the point across the line. In other words, if a point has coordinates (x,y), its image after reflection over x = -1 will have coordinates (-x,y).
Using this rule, we can check each of the given options:
A(0,-1) and A'(4,-1): The reflection of A(0,-1) over x = -1 should have an x-coordinate of -0, which means it should be the same as the original point. A'(4,-1) does not fit this requirement, so this is not the correct set of points.A(0,-5) and A'(0,3): The reflection of A(0,-5) over x = -1 should have an x-coordinate of -0, which means it should be the same as the original point. A'(0,3) does not fit this requirement, so this is not the correct set of points.A(-5,0) and A'(3,0): The reflection of A(-5,0) over x = -1 should have an x-coordinate of 5, which means it should be (-5,0). A'(3,0) does not fit this requirement, so this is not the correct set of points.A(0,-4) and A'(0,4): The reflection of A(0,-4) over x = -1 should have an x-coordinate of -0, which means it should be the same as the original point. A'(0,4) does not fit this requirement, so this is not the correct set of points.Therefore, the correct set of points is A(0,-1) and A'(−2,−1).
Learn more about coordinates here:
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If two figures have the same perimeter, they are congruent. True or false?
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Two figures may be different shape and have the same perimeter (a square and a circle, for example). If they are different shape, they will not be congruent.
This figure is made up of a quadrilateral and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round your final answer to the nearest tenth.
15.7 units²
17.9 units²
25.7 units²
31.4 units²
Answers
Answer:
Option B. 17.9 units²
Step-by-step explanation:
This figure consist of two figures
1). One quadrilateral
2). One semicircle
Now to get the area of total figure
= Area of triangle + area of semicircle
1). Area of quadrilateral = length × width
= √(3-1)²+(1-2)² × √(3-1)²+(1+3)² = √(4 + 1) ×√(4 + 16) = √5×2√5 = 10
2) Area of semicircle = (1/2)πr²
Radius of the circle = (1/2)√(3-1)²+(1+3)² = (1/2)√(4 + 16) = (1/2)(√20)
r = √5
Area of semicircle = (1/2).(π).(√5)² = (1/2).(3.14)(5) = 7.85
Area of the total figure = 10 + 7.85 = 17.85 ≈ 17.9 units²
Option B is the correct answer.
The non-congruent angle in an isosceles triangle is called the
Answers
Hope this helps =)
The non-congruent angle in an isosceles triangle is called the vertex angle.
What is an isosceles triangle?
An isosceles triangle is a triangle that has at least two sides of equal length.
Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
The two angles opposite to the equal sides are congruent with each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.
The angle which is not congruent to the two congruent base angles is called an apex angle.
To know more about the isosceles triangle
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Please if some one can help help ! Thank you !!
Answers
As compared to the equations in the 1st step the equations in the 4th step have this description.
The first equation in the first step has been multiplied by 2.
The second equation in the first step has been multiplied by 3.
Selection C is appropriate.
What are the asymptotes of the graph of f(x) ?
Answers
The 3rd and 4th choices are appropriate.
_____
This is what is known as a "logistic function." It is used to model population growth when there is a resource limit. It starts out exponential, but then slows as it reaches the "carrying capacity" of the environment. The lower asymptote is zero; the upper one is the carrying capacity of the resource--here 15/1 = 15.
Choose the correct simplification of the expression a to the 7th power times b to the 8th power all over a to the 4th power times b to the 4th power
Answers
[tex] \frac{ a^{7} b^{8} }{ a^{4} b^{4} } [/tex]
When you will simplify this fraction, you can divide the expressions. Based on the law of exponents when you divide like terms with different exponents, you can subtract the exponents of the denominator from the numerator.
So if you will simplify the equation:
[tex] \frac{ a^{7} b^{8} }{ a^{4} b^{4} } [/tex]
Subtract the following:
Exponents of a 7-4 and;
Exponents of b 8-4
Your answer should be
[tex] a^{3} b^{4} [/tex]
The vertices of triangle jkl are j(-2,1), k(2,-3), and l(2 2). The triangle is reflected over the line y=x. Graph triangle jkl and triangle j’k’l’.
Answers
find the lateral area of the given prism
Answers
26 is the height
6 is the width
15 is the length
2(26)(6+15) 2(26) means you multiply them
52 (21)
1092m² is you answer
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $12.50 per hour at her job, and Jack is paid $10 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $750 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
Answers
The inequality representing their combined pay would be
[tex]12.50x+10.00y \geq 750[/tex]. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
[tex]x+y \leq 65[/tex], since they do not want their combined hours to be over 65. In both of these inequalities, x represents the number of hours Jane works and y represent the number of hours Jack works.
To graph these, we solve both of them for y:
[tex]x+y \leq 65 \\ x+y-x \leq 65-x \\ y \leq 65-x[/tex]
[tex]12.50x+10.00y \geq750 \\12.50x+10.00y-12.50x \geq 750-12.50x \\10.00y \geq 750-12.50x \\ \frac{10.00y}{10.00} \geq \frac{750}{10.00} - \frac{12.50x}{10.00} \\y \geq 75-1.25x[/tex]
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Answer:
20
Step-by-step explanation:
just did it on study island
One liter is approximately 1.06 quarts. Write a direct variation equation that relates x liters to y quarts. what is an equation
Answers
y = k * x
Where,
k: proportionality constant.
We have then that the equation for this case is:
y = 1.06 * x
That is to say:
k = 1.06
Answer:
an equation is:
y = 1.06 * x
Divide 9x^2-21x-20 by x-1
Answers
1) quotient: 9x - 12
2) remainder: - 32
Explanation:
I will use short division, which consists in using just the coefficients.
This is the full operation:
literal x^2 x 0
coefficient | 9 - 21 - 20
|
1 | 9 - 12
-------------------------------------
9 -12 - 32
Result:
1) quotient: 9x - 12
2) remainder: - 32
You can prove the result by multiplyin (9x - 12) times (x - 1) and then adding the remainder (-32).
=> (9x - 12) (x - 1) - 32 = 9x^2 - 9x - 12x + 12 - 32 = 9x^2 - 21x - 20 which proves the answer.
What is the greatest common factor of 14c^3, 70c^4, and 28c^2
Answers
[tex]14 {c}^{2} [/tex]
Answer:
14c^2
Step-by-step explanation:
The greatest common factor is the factor between the 3 expressions that once divided by each expression, 1 becomes the only number common to all 3. Considering all the expressions as follows (broken into all the factors that make up each expression)
14c^3 = 2 × 7 × c × c
70c^4 = 2 × 5 × 7 × c × c × c × c
28c^2 = 2 × 7 × c × c
From the above, the common factors are 2, 7, c and c,the product of these
= 2 × 7 × c × c
= 14c^2
Find the slope of (2,3) and (6,7)
Answers
Slope = Change in Y / Change in X = (Y1 - Y2) / (X1 - X2)
Since our coordinates are given as (X, Y), we must pick a coordinate to be #1, and the other coordinate will be #2.
I'll use the first coordinate as our #1.
(3 - 6) / (2 - 7) = (-3) / (-5) = 3/5 which is our answer
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
cm²
Answers
Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²
if 2π radians (full circumference) has an area of -----------------> 352.81 cm²
3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²
the answer is 105.84 cm²
Factor –7x3 + 21x2 + 3x – 9 by grouping. What is the resulting expression? (3 – 7x)(x2 – 3) (7x – 3)(3 + x2) (3 – 7x2)(x – 3) (7x2 – 3)(3 + x)
Answers
If you apply the distributive property in (3–7x²)(x–3), you obtain:
3x-9-7x²(x)+21x²
3x-9-7x³+21x²
When you order the expression, you have:
-7x³+21x²+3x-9
Then, the answer is (3–7x²)(x–3)
Explanation:
1) Given: -7x^3 + 21x^2 + 3x - 9
2) Group the first two terms and the second two terms:
[-7x^3 + 21x^2] + [3x - 9]
3) Extract common factor -7x^2 from the first group and common factor 3 from the second group:
-7x^2 [x - 3] + 3[x - 3]
4) Take common factor x - 3
(x - 3) (3 - 7x^2)
By commutative property that is equal to (3 - 7x^2) (x - 3)
Choose as many answers as apply. Which of the following are sources of income? salary deductions part-time work odd jobs wishful thinking
Answers
Answer:
salary . part time work . odd jobs.
Step-by-step explanation:
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A telephone pole that is 14 ft. tall has fallen against a house. If the top of the telephone pole touches the house 8 ft. above the ground, what is the angle that the telephone pole makes with the ground?
29.7 degrees
55.2 degrees
60.3 degrees
34.8 degrees
Answers
From the given information , we can make a rough figure as shown in attachment.
Now in the given triangle we can use following formula of sin to get the angle,
[tex] sin x = \frac{Perpendicular}{opposite} [/tex]
We can see from the figure that:
perpendicular = 8 and opposite =14.
Plugging the given values in the formula for sin x,
[tex] sin x = \frac{8}{14} [/tex]
sin x = 0.5714
to find x we have to find sin inverse of 0.5714 ,
x = sin⁻¹(0.5714)
x=34.8 degrees.
Answer : the angle that the telephone pole makes with the ground is 34.8 degrees. option D
Match the statements
1. m<2 = 122° and m<3 = 58°
If corresponding angles are equal, then lines are parallel.
2. 3 and 5 are supplementary angles
Exterior Sides in Opposite Rays
3. m<3 + m<5 = 180°
Given
4. 58° + m<5 = 180°
Second Substitution
5. m<5 = 122°
Definition of Supplementary Angles
6. m<2 = m5
First Substitution
7. l || m
Subtraction Property of Equality
Answers
1. m<2 = 122° and m<3 = 58° - C. Given
2. 3 and 5 are supplementary angles - E. Definition of Supplementary Angles
3. m<3 + m<5 = 180° - D. Second Substitution
4. 58° + m<5 = 180° - F. First Substitution
5. m<5 = 122° - G. Subtraction Property of Equality
6. m<2 = m5 - A. If corresponding angles are equal, then lines are parallel
7. l || m - B. Exterior Sides in Opposite Rays
The given geometry statements are matched with appropriate geometric principles, such as the definition of supplementary angles, substitution properties, and theorems related to parallel lines and angles.
To match the statements given with the correct reasons, we need to analyze the relationships between angles and understand the geometric principles involved.
Here are the matches:
1. m<2 = 122° and m<3 = 58° - C. Given
2. 3 and 5 are supplementary angles - E. Definition of Supplementary Angles
3. m<3 + m<5 = 180° - D. Second Substitution
4. 58° + m<5 = 180° - F. First Substitution
5. m<5 = 122° - G. Subtraction Property of Equality
6. m<2 = m5 - A. If corresponding angles are equal, then lines are parallel
7. l || m - B. Exterior Sides in Opposite Rays
The probable question may be:
Match the statements
1. m<2 = 122° and m<3 = 58°
2. 3 and 5 are supplementary angles
3. m<3 + m<5 = 180°
4. 58° + m<5 = 180°
5. m<5 = 122°
6. m<2 = m5
7. l || m
A. If corresponding angles are equal, then lines are parallel.
B. Exterior Sides in Opposite Rays
C. Given
D. Second Substitution
E. Definition of Supplementary Angles
F. First Substitution
G. Subtraction Property of Equality
Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Ishaan now?
Answers
C= Christopher's age
35 years ago means we have to subtract 35 from their current age. Ishaan minus 35 equals 7 times Christopher minus 35 years.
CHRISTOPHER'S AGE:
I - 35= 7(C-35)
substitute I=2C in for I
multiply 7 by all in parenthesis
2C - 35= 7C - 245
add 35 to both sides
2C= 7C - 210
subtract 7C from both sides
-5C = -210
divide both sides by -5
C= 42 Christopher's age
ISHAAN'S AGE:
I= 2C
substitute C=42 to find Ishaan's age
I= 2(42)
I= 84 Ishaan's age
CHECK:
Substitute answers in original equation
I - 35= 7(C-35)
84 - 35= 7(42-35)
49= (7*42)+(7*-35)
49= 294-245
49=49
Hope this helps! :)
explain how a table cn be used to find the rate of change?