Answer:
[tex]\huge\boxed{a = 10 \ , \ b = 0}[/tex]
Step-by-step explanation:
Conjugate of -1 + 3i = -1 - 3i
Their Product:
[tex]=(-1+3i)(-1-3i)\\Using \ Formula : (a+b)(a-b) = a^2-b^2\\=(-1)^2 - (3i)^2\\=1 - 9i^2\\We \ know \ that \ i^2 = -1\\=1 - 9(-1)\\=1 + 9\\=10[/tex]
Since the answer is 10, It seems like:
a + bi = 10
So, This means that:
a = 10
b = 0
What is the area of this figure? 15 yd 4 yd 7 yd 25 yd 21 yd 22 yd square yards Submit
3. Represent each addend with number disks in the place value chart. Show the composition of larger units
from 10 smaller units. Write the sum in standard form.
a.
4 thousands + 11 hundreds =
:51 100
tens
ones
hundred
thousands
thousands
hundreds
ten
thousands
millions
O
b. 24 ten thousands + 11 thousands=_ 25 11000
hundreds
tens
ones
millions
hundred
thousands
thousands
ten
thousands
25
o
O
Answer:
4(1000) +11(100) + 24(10,000) +11(1000) = 256,100
Step-by-step explanation:
Maybe you want to add 4000 +1100 to 24(10,000) +11,000.
1 thousand = 10 hundreds, so 4000 = 40 hundreds
4000 +1100 = (40 +11) hundreds = 51 hundreds
__
1 ten-thousand = 10 thousands, so 24(10,000) = 240 thousands
24(10,000) +11,000 = (240 +11) thousands = 251 thousands
__
So, we want to add 251,000 and 51 hundreds. The latter can be considered to be 5000 +100, so we have ...
251,000 +5100 = 251,000 +5,100 = (251 +5) thousands + 1 hundred
= 256,100
3 Question
Simplify this expression:
4(1 - 25) + 70 - 10.
Type the correct answer in the box
Answer:
-36
Step-by-step explanation:
4(1 - 25) + 70 - 10
PEMDAS
Parentheses first
4( -24) + 70 -10
Then multiply and divide
-96 + 70-10
Then add and subtract
-36
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60?
Hey There!! ☄️ The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
and a indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis
The graph is made narrower.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
The graph of f(x) = x2 is made narrower
The graph of f(x) = x2 is made narrower.
It is given that f(x) = x2 and g(x) = –3x2 – 36x – 60.
To find the transformations applied to the graph.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
Indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
So, the graph of f(x) = x2 is made narrower.
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The sum of a number and three is six less than twice that number
Answer:
Algebraic expression = x+3=2x-6
Step-by-step explanation:
Let the unknown number be x ;
[tex]x+3 =2x-6[/tex]
Further explanation
[tex]x+3=2x-6\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}x+3-3=2x-6-3\\\\Simplify\\x=2x-9\\\\Collect\:like\:terms\\x-2x =-9\\\\Simplify\\-x =-9\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{-9}{-1}\\\\x =9[/tex]
The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,
Answer:
7th measurement = -26
Step-by-step explanation:
The sequence is 16, 9, 2, –5, ...,
First term( a)= 16
Second term=9
Common difference (d) = 9-16
Common difference= -7
The sequence is a arithmetic progression
For AP's ,the terms formula is
Term(n) = a + (n-1)d
Where n represent the term to be found
In this case,we Are looking for the 7th term , so n= 7
Term(7) = 16+ (7-1)-7
Term(7)= 16 +6(-7).
Term (7) = 16-42
Term(7) = -26
7th term =-26
Solve each equation. Check your solutions.
15. 27 - 31 = 29
Answer:
y=16, -13
Step-by-step explanation:
The absolute value operator makes all negative numbers positive. So y has two values in this equation: one where (2y-3)=29 and one where it =-29.
Work is in the attachment.
please halp with this step by step to further understand thank you!
. . . . . . plssssss
The value, V(m), of a comic book m must be months after publication has an average rate of change of -0.04 between m=36 and m=60. Which statement must be true?
A) The value of the comic book decreased by a total of $0.04 between m=36 and m=60
B) The value of the comic book increased by a total of $0.04 between m=36 and m=60
C) The value of the comic book decreased by an average of $0.04 each month between m=36 and m=60
D) The value of the comic book increased by an average of $0.04 each month between m=36 and m=60
Answer:
A
Step-by-step explanation:
The average is over the months not added each month
A formula to find the frequency, f, of a cyclic phenomena based on the period, T, is
f = . Solve the formula for T' in terms of f.
Step-by-step explanation:
The frequency and the time period is related by the formula as follows :
[tex]f=\dfrac{1}{T}[/tex]
Here, f is frequency and T is time period
Now, we need to solve T in terms of f.
Firstly, cross multiplying the above equation,
[tex]f\times T=1[/tex]
Now dividing both sides by T.
[tex]\dfrac{f\times T}{T}=\dfrac{1}{T}\\\\f=\dfrac{1}{T}[/tex]
Hence, this is the required solution.
Answer:
T= 1/f
Step-by-step explanation:
T= one OVER f
www.g Suppose that 59% of people own dogs. If you pick two people at random, what is the probability that they both own a dog
Answer:
The value is [tex]P(O) = 0.3481[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of people that own a dog is [tex]p = 0.59[/tex]
Generally the probability of the two selected people owning a dog is mathematically evaluated as
[tex]P(O) = p^2[/tex]
[tex]P(O) = (0.59 )^2[/tex]
[tex]P(O) = 0.3481[/tex]
If P is between L and A, PL = x+4, PA = 2x - 1, and LA = 5x - 3, then x = ____ and LA = ____. PLEASE HURRY
Answer:12
Step-by-step explanation:
La= LP + PA
5x-3=x+4+2x-1 Combine like terms.
5x-3=3x+3 Combine like terms
2x-3=3 Combine 3 and 3 ( Add)
2x=6 Divide by 2
X=3
LA=5x-3
5(3)-3 Multiply 5 and 3
15-3
LA=12
PLEASE SOMEONE HELP
I WILL GIVE 25 POINTS JUST PLEASE HELP
Answer:
50) 8, 16, 24, 32, 40, 48 (count by 8’s)
12, 24, 36, 48, 60, 72 (Count by 12’s)
Common Multiples: 24, 48
Least Common Multiple: 24
51) 7: 7, 14, 21, 28, 35, 42
11: 11, 22, 33, 44, 55, 66
Common Multiples: none
Least Common Multiple: none
52) 25: 25, 50, 75, 100, 125, 150
10: 10, 20, 30, 40, 50, 60
Common Multiples: 50
Least Common Multiple: 50
53) 24: 24, 48, 72, 96, 120, 144
36: 36, 72, 108, 144, 180, 216
Common Multiples: 72, 144
Least Common Multiple: 72
Step-by-step explanation:
50) 8, 16, 24, 32, 40, 48 (count by 8’s)
12, 24, 36, 48, 60, 72 (Count by 12’s)
Common Multiples: 24, 48
Least Common Multiple: 24
51) 7: 7, 14, 21, 28, 35, 42
11: 11, 22, 33, 44, 55, 66
Common Multiples: none
Least Common Multiple: none
52) 25: 25, 50, 75, 100, 125, 150
10: 10, 20, 30, 40, 50, 60
Common Multiples: 50
Least Common Multiple: 50
53) 24: 24, 48, 72, 96, 120, 144
36: 36, 72, 108, 144, 180, 216
Common Multiples: 72, 144
Least Common Multiple: 72
Which property is illustrated by the equation –8 + 8 = 0?
additive inverse
additive identity
commutative property
distributive property
Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased
Answer:
The answer is B: $29.35x + $17.45y
A number close to an exact form is called?
Answer:
estimate or approximate number
Step-by-step explanation:
trust
The first significant digit in any number must be 1, 2, 3, 4,5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. Forexample, the following distribution represents the first digits in 187 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.
a.) Using the level of significance alpha 0.10, test whether the first digits in the allegedly fraudulent checks obeyBenford's Law. What is the null hypothesis?
b.) What is the alternative hypothesis?
c.) What is the test statistic?
d.) What is the p-value?
e.) Using the P-value approach, compare the P-value with the given alpha = 0.10, level of significance. Based on theresults, do the first digits obey the Benford's Law?
f.) (b) Based on the results of part (a),could one think that the employee is guilty of embezzlement?
Digit Probability Frequency
1 0.301 36
2 0.176 25
3 0.125 28
4 0.097 26
5 0.079 23
6 0.067 17
7 0.058 9
8 0.051 16
9 0.046 7
Answer:
We fail to reject the null hypothesis
Step-by-step explanation:
See the attachment for detailed calculations
-170=5(8n+6)
Help please !!
Answer:
Step-by-step explanation:
40n + 30 = -170
40n + 30 = -170
40n = -200
n = -5
the number of real solutions to the quadratic equ
5a² + 30a + 45 = 0
The answer is 1.
There is one unique real solution, which is x = -3.
Hello, please consider the following.
[tex]5a^2+30a+45 = 0\\\\<=> 5(a^2+6a+9)=0\\\\<=> a^2+6a+9=0\\\\<=> a^2+2*3*a+3^2=(a+3)^2=0\\\\<=>\boxed{a=-3}[/tex]
Thank you
Answer:
two equal, real solutions
Step-by-step explanation:
The quickest way to determine this is to find the discriminant b^2 - 4ac. If this determinant (D) is > 0, the quadratic has two different real roots; if + 0, the quadratic has two equal real roots, and if < 0, the quadratic has two imaginary or complex roots.
Here a = 5, b = 30 and c = 45. The discriminant is
30^2 - 4(5)(45) = 900 - 900 = 0
and so this quadratic has two equal, real solutions.
what is the probability of spinning a multiple of 3 The Spinner is 1-8 numbered
Answer:
1/4
Step-by-step explanation:
There are 8 possible outcomes
Multiples of 3 are
3,6 = 2 outcomes
P ( multiple of 3) = number of multiples of 3/ total
= 2/8
= 1/4
The probability of spinning a multiple of 3 The Spinner is 1-8 numbered will be [tex]P= \dfrac{1}{4}[/tex]
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
There are 8 possible outcomes
Multiples of 3 are
3,6 = 2 outcomes
[tex]\rm P ( multiple \ of\ 3) =\dfrac{ number\ of\ \ multiples\ of\ 3 }{ total }[/tex] [tex]= \dfrac{2}{8}[/tex] [tex]= \dfrac{1}{4}[/tex]
Hence the probability of spinning a multiple of 3 The Spinner is 1-8 numbered will be [tex]P= \dfrac{1}{4}[/tex]
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Could anyone help me with this?
Answer:
x = 17
KNM = 131
Step-by-step explanation:
(8x - 5) + (4x - 19) = 180
12x - 24 = 180
12x = 204
x = 17
Answer:
x = 17
Step-by-step explanation:
Opposite Angles must be the Same Value so In other words, 2(8x - 5) + 2(4x - 19) = 360.
2(8x - 5) + 2(4x - 19) = 360
24x - 48 = 360
24x = 408
x = 17
1 kilometre is how much miles
Answer:
1 kilometre is 0.621 mile
Answer:
1 Kilometer = 0.621 mile
Step-by-step explanation:
The distance d in miles (mi) is equal to the distance d in kilometers (km) divided by 1.609344
Chester, the dog, loves to eat treats. He has eaten twice as many today as yesterday. He has eaten a total of 15 dog treats in both days.
-write the equation-
Answer:
The equations are:
[tex]T = 2Y[/tex] and [tex]T + 2Y = 15[/tex]
Step-by-step explanation:
Given
Represent bones eaten Today with T and yesterday with Y
Required
Write the equation
In the first statement, we have that:
[tex]T = 2Y[/tex]
Reading further; In the second statement
[tex]T + 2Y = 15[/tex]
Hence, the equations are:
[tex]T = 2Y[/tex] and [tex]T + 2Y = 15[/tex]
Solving further:
Substitute 2Y for T in the second equation
[tex]2Y + 2Y = 15[/tex]
[tex]4Y = 15[/tex]
Divide both sides by 4
[tex]Y = \frac{15}{4}[/tex]
[tex]Y = 3.75[/tex]
Recall that
[tex]T = 2Y[/tex]
[tex]T= 2 * 3.75[/tex]
[tex]T= 7.5[/tex]
Laura purchased two puppies from a
litter. One of the puppies weighs 4 5/6 pounds.
.
and the other puppy weighs 5 1/2 pounds.
How much more does the second puppy
weigh than the first?
Logan wants to have $130,000 to pay for a surgery on his retractable forearm claws in 30 months. If he can invest money in an account right now that will give him 7.5% interest compounded monthly, how much would he have to
invest now to end up with the amount needed for the surgery later on?
Answer: $107,836.69 or about $107,837 (to the nearest dollar)
Step-by-step explanation:
Formula to the accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :
[tex]A=P(1+\dfrac{r}{12})^{t}[/tex]
As per given , A = $130,000
r= 7.5% = 0.075
t= 30 months
Now,
[tex]130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69[/tex]
Hence he need to invest $107,836.69 .
How can you prove that a conjecture is false?
Answer:
In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers avoid going down blind alleys and learn how to modify conjectures to produce provable theorems.
Step-by-step explanation:
The angled lines used to indicate the surfaces which are cut by the imaginary cutting-plane are called:
Answer:
Section lines
Step-by-step explanation:
Sectioning is the process of cutting a surface by an imaginary plane, the view of the surface that is cut is shown in the section view.
Section lines are used to indicate where an imaginary cutting plane cuts a material. The imaginary cut is then represented using section lines which are usually thin, crosshatched.
Section lines shows the surface that have been cut by the cutting plane. There are different ways of sectioning such as full section, half section, off set section and so on
Estimate the mean of the age of the people in group A
Answer:
48
Step-by-step explanation:
The ages are 18,28,38,48,58,68,78 I don't use 88 bacause the graph don't show any data so there is 88 years old
now lets find the mean
18+28+38+48+58+68+78= 336= 48
7 7
so the mean of the age is 48
i hope u like it
Which of the following graphs represent a function?
Graph A
Graph B
Graph
Graph
a. Graph A and Graph C
b. Graph A
C. Graph D
D. graph b and d
The graphs that represent functions are given as follows:
a. Graph A and Graph C.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we have that:
Graph B has one vertically aligned point, hence it is not a function.Graph D has multiple vertically aligned points, hence it is also not a function.Hence the graphs that represent functions are given as follows:
a. Graph A and Graph C.
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Answer: The only graphs that classify as function are Graph A and Graph C, so the answer is C. It's not possible for B and D to be functions.
Round the following number to the nearest hundred
123,456
Answer:
Hey!
Your answer is 123,500!
Step-by-step explanation:
TO ROUND TO THE NEAREST HUNDRED we need to look at the TENS column...
IN THIS CASE WE LOOK AT '5'...
If its bigger than 4 INCREASE THE DIGIT IN THE HUNDREDS PLACE BY ONE
If its smaller than 5 DECREASE THE DIGIT IN THE HUNDREDS PLACE BY ONE!
So as 5 is a digit that makes us ROUND UP...we change 4 to a 5 to have 123,500 as our answer!
HOPE THIS HELPS!