Answer:
D
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate of the denominator.
Note that i² = - 1
The conjugate of 10 + 3i is 10 - 3i , then
[tex]\frac{(3+5i)(10-3i)}{(10+3i)(10-3i)}[/tex] ← Expand numerator/denominator using FOIL
= [tex]\frac{30-9i+50i-15i^2}{100-30i+30i-9i^2}[/tex] ← simplify
= [tex]\frac{30+41i+15}{100+9}[/tex]
= [tex]\frac{45+41i}{109}[/tex] → D
A sailboat travels a distance of miles in of an hour. Which complex fraction represents the unit rate in miles per hour?
Answer: I think its D and A
Step-by-step explanation:
Answer:
im pretty sure its D and also A
Step-by-step explanation:
If PQ = 6x - 1 and PR = 15x - 29,
then QR = ?
what is a number in exponential notation that decreases in value as the exponent increases in value
Answer:
Any fraction
Step-by-step explanation:
Example:
(2/3)² = 4/9
2/3 > 4/9
Answer:
Any Fraction
Step-by-step explanation:
Example:
(1/3)² = 1/9
1/3 > 1/9
factorize the following questions
1. a^8-b^8
2. 32y^4 - 162
Answer:
1. [tex]2(16 {y}^{4} - 81)[/tex]
2. [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex]
Step-by-step explanation:
1. [tex] a^{8} - {b}^{8} [/tex]
➡️ [tex]( {a}^{4} - {b}^{4} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex]( {a}^{2} - {b}^{2} ) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex](a - b) \times (a + b) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex]2(16 {y}^{4} - 81)[/tex] ✅
---------------------------------------------------
2. [tex] 32 {y}^{4} - 162[/tex]
➡️ [tex] 2(16y^{4} - 81)[/tex]
➡️ [tex]2(4 {y}^{2} - 9) \times (4 {y}^{2} + 9)[/tex]
➡️ [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex] ✅
IF A= { a, b, c d and B={a,b,c,d}
how can I solve this
Answer:
what we have to prove or equation ?
3 3/4÷3/4
pls I need this for my tuition in 5 min
Step-by-step explanation:
15/4÷3/4
15/4×4/3 (2 reciprocal of 3 upon 4)
5/1
or 4 1/1 Answer
4,4 will be cancelled 15 will be cancelled by 3
Amaya wants to jog 8 Miles this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday how many miles does amaya still need to jog to meet her goal
Answer:
2 1/10 miles.
Step-by-step explanation:
She has already jogged 2 1/2 + 3 2/5 miles. This is 2 5/10 + 3 4/10 or 5 9/10. 8 miles is also equal to 7 10/10 miles. So, to find the remaining amount of miles, we can do 7 10/10 - 5 9/10 = 2 1/10.
Amaya still needs 2.1 miles to jog to meet her goal.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Operators who let do basic mathematical calculations.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday
She has already jogged 2 1/2 + 3 2/5 miles.
⇒ [tex]2\dfrac{1}{2} + 3\dfrac{2}{5} = \dfrac{5}{2} + \dfrac{17}{5}[/tex]
Convert fractions into decimals,
⇒ 2.5+3.4
Apply the arithmetic operation,
⇒ 5.9
So, to find the remaining amount of miles,
⇒ 8 -5.9 = 2.1
Hence, Amaya still needs 2.1 miles to jog to meet her goal.
Learn more about Arithmetic operations here:
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Amy owes her mother $76. She pays her mother $14 on Sunday and $24 on Monday. Use an expression to describe the situation. How much does Amy still owe her mother?
Answer:
Amy still owes her mother $38.
Step-by-step explanation:
76 - 14 - 24
76 - 14 = 62
62 - 24 = 38
A(-2,3)
Triangle ABC has vertices at A(-2,3), B(-3,6), and
C(2,-1) Is triangle ABC a night triangle? If so, which
angle is the night angle?
O No, the triangle has no right angles.
O Yes, the right angle is angle A
O Yes, the right angle is angle B
O Yes, the right angle is angle C
VA
C (2-1)
B (-3,-6)
second choice i’m prolly wrong
Cuanto da √(1 ÷ 6^2 - 1 ÷ 10^2)
Answer:
It is 2/15
Step-by-step explanation:
[tex] = \sqrt{ \frac{1}{ {6}^{2} } - \frac{1}{ {10}^{2} } } \\ \\ = \sqrt{ \frac{4}{225} } \\ \\ = \frac{ \sqrt{4} }{ \sqrt{225} } \\ \\ = \frac{2}{15} [/tex]
Please help me it's the lateral area of a cone along with the surface area
Answer:
the lateral area of cone is L=A﹣πr2
the surface area of cone is
[tex]a = \pi \: r \sqrt{h^{2} + r {}^{2} }[/tex]
Show work please
[tex] \sqrt{ \frac{45}{5} } [/tex]
Answer: 3
Step-by-step explanation:
[tex]\sqrt{ \dfrac{45}{5}} =\sqrt{9}=\bold3[/tex]
Answer:
3
Step-by-step explanation:
We don't really need to simplify this, but if you do:
45/5 is the same as 45 ÷ 5 so
45/5 = 9
Now we have to find the square root of 45/5(or 9). The square root of a number(x for example) is the number(y) that multiplied by itself once will equal x or y · y = x.
For this you can use a calculator:
[tex]\sqrt{\frac{45}{5} }[/tex] = 3
or
[tex]\sqrt{9}[/tex] = 3
How would I prove the congruency of these triangles?
Answer:
SAS
Step-by-step explanation:
line AB = line CD S = SIDE
AB = CD because the shape is a parallelogram and opposite sides of a parallelogram are equal.
Hence, proved AB = CD
Answer:
Step-by-step explanation:
In ΔADC & ΔABC,
Statement Reason
AD = BC Given
∠DAC ≅ ∠ACB {AB // BC , AC is transversal, ⇒ alternate interior angles are equal}
AC = CA Reflexive property
ΔADC ≅ ΔABC SAS congruent
AB = CD CPCT -> Corresponding Part of Congruent Triangles
How many significant figures does 4857.169 have?
Answer:
Significant Figures
7
4857.169
Decimals
3
4857.169
Scientific Notation
4.857169 × 103
E-Notation
4.857169e+3
Words
four thousand eight hundred fifty-seven point one six nine
Explanation: Mark Brainliest plz
Answer:
plz mark me as a brainliest i really need it
Step-by-step explanation:
4857.169
Sig Figs
7
4857.169
Decimals
3
4857.169
Scientific Notation
4.857169 × 103
E-Notation
4.857169e+3
Words
four thousand eight hundred fifty-seven point one six nine
Refer to the number line. Find the coordinate of point H that is 1/5 of the distance from C to F.
A B C
DEF
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
Number lines are used to represent numbers on a line at regular intervals. The coordinate of point H is -2.2
From the number line, we have:
[tex]C = -4[/tex]
[tex]F = 5[/tex]
First, we calculate the distance between C and F using absolute functions
[tex]CF = |C - F|[/tex]
[tex]CF = |-4- 5|[/tex]
[tex]CF = |-9|[/tex]
Remove absolute bracket
[tex]CF = 9[/tex]
Point H is [tex]\frac 15[/tex] of the distance so, we have:
[tex]H = \frac 15 CF[/tex]
[tex]H = \frac 15 \times 9[/tex]
[tex]H = 1.8[/tex]
This means that point H is 1.8 from the right of C.
So, the coordinate of H is:
[tex]H = C + 1.8[/tex]
[tex]H = -4 + 1.8[/tex]
[tex]H = -2.2[/tex]
Hence, the coordinate of point H is -2.2
Read more about number lines at:
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hi please help i’ll give brain
Answer:
The GCF is going to be 7
Step-by-step explanation:
This Is how I find the GCF of 2 numbers. I find the prime factorization first, then I find the common factors and multiply them. Here
The prime factorization of 21, 3 × 7 = 21
The prime factorization of 28, 2 × 2 × 7 = 28
The one and THE only common factor is 7, which is going to be the GCF
A rectangle has perimeter 56 cm and length 21 cm. What is its width?
hhhhhhhhhhh
Answer:
width=7 cm
Step-by-step explanation:
perimeter=2(lengths+width)
56 =2(21+x)
56 =42+2x
56-42 =2x
2x = 14
x =7
therefore the width=7 cm
5x + 2) mize
2.
P has coordinates (2, 4). Q has coordinates (-10, 12). Find the midpoint of PQ.
122
Is -√15 irrational or rational
what is the awnser y= 4x-9
Answer:
x = y+9/4
Step-by-step explanation:
if you were trying to rearrange to make x the subject. Take minus 9 to another side which will be plus 9, then divide y+9 by 4
Change 3224in^2 to cm^3
Answer:
98
Step-by-step explanation:
show work
Solve 3x − x + 2 = 12.
2x=12_2 2x=10 x=5 that answer
find the value of x and y
<1=(10x)
<2=(10y+20)
<3 =100
Answer:
1008010080x = 10
y = 6
Step-by-step explanation:
We can use the vertical angle theorem to solve for most of this problem. We know that 1/3 will have the same measure and so will 4/2. We can create an equation to solve for 1 and 3.
10x = 100
x = 10
We aren't given angle 4 so we are going to have to solve that ourselves. We can create an equation knowing that 4 and 3 will create a supplementary angle.
100 + z = 180
z = 80
Now, that we have angle 4, we know that angle 2 will have the same measure because they are vertical angles. Now to find the value of y, we can take the angle measure and solve for it.
10y + 20 = 80
10y = 60
y = 6
Best of Luck!
Which of the following describes a correct process for solving the equation 3(x + 6) = 21 and arrives at the correct solution?
A. Divide both sides of the equation by 3, and then subtract 6 from both sides of the equation. The solution is x = 1.
B. Subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 5.
C. Distribute the 3, subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 5.
D. Add 6 to both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 9.
Answer:
A. Divide both sides of the equation by 3, and then subtract 6 from both sides of the equation. The solution is x = 1.
Step-by-step explanation:
3(x + 6) = 21
Divide both sides by 3
(x + 6) = 7
Subtract 6 from each side
x = 7-6
x=1
Answer:
x=1
Step-by-step explanation:
multiply 3 with (x+6) resulting into 3x+18=21
cross-multiply and divide through by 3.
There u go
The size of a population of fish in a pond is modeled by the function P, where P(t) gives the number of fish and t gives the number of years after the first year of introduction of the fish to the pond for 0≤t≤10. The graph of the function P and the line tangent to P at t=4 are shown above. Which of the following gives the best estimate for the instantaneous rate of change of P at t=4 ?
The slope (m) will be "279.33". A further solution to the question is provided below.
At one moment this same instantaneous modification rate would be the same with the functionality derivative assessed somewhere at the time. In certain other terms, the pitch of such tangent line towards the curvature is somewhere at a level equivalent to that as well.
According to the question,
(x₁, y₁) = (3, 0)(x₂, y₂) = (6, 838)As we know,
⇒ [tex]Slope (m) = \frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the values, we get
⇒ [tex]=\frac{838-0}{6-3}[/tex]
⇒ [tex]=\frac{838}{3}[/tex]
⇒ [tex]=279.33[/tex]
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The instantaneous rate of change is the rate of change at a particular point or instant in the graph. The instantaneous rate of change of P at [tex]t=4[/tex] is 250
I've added as an attachment, the graph that represents the population of the fish.
To determine the instantaneous rate of change at [tex]t=4[/tex], we simply calculate the slope (m) of the tangent line using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Because of the scale of the graph, I will use the following estimated points from the tangent line
[tex](x_1,y_1) = (3,0)[/tex]
[tex](x_2,y_2) = (4,250)[/tex]
So, the slope is:
[tex]m = \frac{250 - 0}{4 - 3}[/tex]
[tex]m = \frac{250}{1}[/tex]
[tex]m = 250[/tex]
Hence, the instantaneous rate of change of P at [tex]t=4[/tex] is 250
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PLEASE HELP WILL MARK BRAINLIEST
Simplify the expression.
12÷2⋅33(3)
3
2
23
29
Answer:
I can't understand what you wrote but I think it's 594
Step-by-step explanation:
You divide 12 by 2, it is igual to 6.
6 x 33 = 189
189 x 3 = 594
I try to help if it not work :(
answer choices:
A. 98
B. 72
C. 44
D. 42
Answer:
B
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Bh ( B is the area of the triangular base and h the height )
B = [tex]\frac{1}{2}[/tex] bh
Here b = 8 and h = 6 ( perpendicular legs )
B = [tex]\frac{1}{2}[/tex] × 8 × 6 = 4 × 6 = 24 ft² , then
V = 24 × 3 = 72 ft³ → B
How do write 5,248,663,711 in words
Answer:
Five billion, two hundred forty-eight million, six hundred sixty-three thousand, seven hundred eleven.
need some help with 8th grade math
Answer:
D = (3,3)
E = (-5,0)
F = (-2,2)
Step-by-step explanation:
the y axis is the vertical line of the graph so an example of flipping would be (-3,5) turns to (3,5) changing only the x value same the other way around (5,-9) turns to (-5,9) only the x value changes symbol
Answer:
D1 = (3, 3) E1 = (-5, 0) F = (-2, -2)
Step-by-step explanation:
D1 = (3, 3)
E1 = (-5, 0)
F = (-2, -2)
order of operations. please help!