M = 5 - 4i
J = 3 + 2i
J* = -3 + 2i (Conjugate)
Therefore M + J*
= (5 + -3) + (-4i + 2i)
= 2 - 2i
△KIX can be mapped onto \triangle REM△REM by a rotation. If \text{m}\angle X = 117^{\circ}m∠X=117
∘
and \text{m}\angle I = 2^{\circ}m∠I=2
∘
, find \text{m}\angle Rm∠R.
\text{m}\angle Rm∠R
can
be determined. \text{m}\angle R =m∠R=
The measure of angle R, found through the angle sum property of a triangle and corresponding angles in ΔKIX and ΔREM is m∠R = 61°
What are corresponding angles?Corresponding angles are angles in two congruent or similar triangles, located between a pair of segments in one triangle that are congruent to a pair of segment in the other triangle
The details of the question are;
The transformation that maps triangle ΔKIX unto triangle ΔREM is a rotation.
Please see attached the example drawing of ΔKIX and ΔREM created with MS Excel.
A rotation transformation is a rigid transformation, therefore, the side lengths and shape of triangle ΔKIX is preserved in the image of the triangle, ΔREM
The measure of angle ∠X in triangle ΔKIX is ∠X = 117°
The measure of angle ∠I in ΔKIX is ∠I = 2°
∠K + ∠I + ∠X = 180° (angle sum property of a triangle)
The measure of angle ∠K = 180° - (∠X + ∠I)
Therefore;
m∠K = 180° - (117° + 2°) = 61°
m∠K = 61°
Based on the naming of the triangles ΔKIX and ΔREM, we have;
∠K corresponds to ∠R, ∠I corresponds to ∠E, and ∠X corresponds to angle ∠R, therefore;
∠K ≅ ∠R, ∠I ≅ ∠E, ∠X ≅ ∠R, which by the definition of congruency indicates;
∠K = ∠R, ∠I = ∠E, ∠X = ∠R
m∠R = m∠K = 61°
m∠R = 61°
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Tanya walked for 17 minutes from her home to a friend that lives 1.5 kilometers away.
d(t) models Tanya's remaining distance to walk (in kilometers), t minutes since she left home.
What's the appropriate domain?
I need help with this problem asap
Answer:
bro that question is absolute whack
Line SD is a line of symmetry for figure ASMHZDPX. Tyler says that ASDPX is congruent to SMHZD because side
Tyler's statement is incorrect , SMHZD and SAXPD are correct congruence for the given pentagons.
a.
Tyler's congruence is incorrect because line SD is a line of symmetry for ASMHZDPX so ASDPX and SMHZD are about SD symmetry therefore the figure division must be start from S or D.
b.
SMHZD And SAXPD are correct congruence for the given pentagons because they both start with the letter S which is in the line of symmetry SD.
Therefore Tyler's statement is incorrect , SMHZD and SAXPD are correct congruence for the given pentagons.
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2b - 15 = 33
What is the answer?
Answer:
Step-by-step explanation:
2b - 15 = 33
+15 +15
2b = 48
b = 24
HELLPPPPPP I DONT UNDER
Answer:
y=16
Step-by-step explanation:
Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation
Identify the slope and y-intercept of the function y = -2x + 3.
OA. The slope is 2.
The y-intercept is (0, 3).
OB. The slope is 3.
The y-intercept is (0, -2).
OC. The slope is 3.
The y-intercept is (0, 2).
OD. The slope is -2.
The y-intercept is (0, 3).
The slope and the y-intercept of the function y = -2x+3 is -2 and (0,3).
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. The slope is constant (the same) anywhere on the line.
Slope is calculated as (change in y divided by change in x). i.e.
slope=dy/dx
What is y-intercept?The y- intercept of a graph is the point where the graph intersects the y-axis.
The x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.
So the y-intercept of the function y = -2x+3 is y= 3 i.e. (0,3).
slope = dy/dx = d/dx(-2x) + d/dx(3) = -2
⇒slope = -2.
Therefore slope of y = -2x+3 is -2 and y-intercept is (0,3).
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Alec buys a frying pan priced at $13. If the sales tax is 10%,how much tax will Alec pay?
Rebecca is x years old.
Mary is 8 years older than Rebecca. Jill is three times older than Mary. The sum of their ages is 67.
(a) Form an equation in terms of x
(b) Solve the equation and work out Rebecca’s, Mary’s and Jill’s ages.
Given that Rebecca is x years old and Mary is 8 yrs older than her , so the age of Mary will be;
[tex]\longrightarrow Age_{Mary}= x+8 [/tex]
Again Jim is 3 times older than Mary, so the age of Jim will be,
[tex]\longrightarrow Age_{Jim}= 3(x+8) [/tex]
Now we are given that the sum of their ages is 67. So that ;
Equation in terms of x :-
[tex]\longrightarrow x + (x+8) +3(x+8)=67 [/tex]
Solving the equation,
[tex]\longrightarrow x + x +8+3x+24=67\\ [/tex]
[tex]\longrightarrow 5x + 32 =67\\ [/tex]
[tex]\longrightarrow 5x = 67-32 \\ [/tex]
[tex]\longrightarrow 5x = 35\\ [/tex]
[tex]\longrightarrow x = 7 [/tex]
So ,
Age of Rebecca= x = 7 yrs Age of Mary = x+8 = 15yrsAge of Jim =3(x+8) = 45 yrs .And we are done!
Hair alon increaed it price for a hair cut from $25 to $50, what might happen to demand for that ervice? What hould happen if the oppoite occurred - if the price wa reduced from $50 to $25? What other factor could influence conumer demand in thee ituation? EXPLAIN
If the price is increased from $25 to $50 the demand will fall whereas when the price is decreased from $50 to $25 the demand for haircut will increase.
The price has the greatest influence on a product's demand. The cost of a thing and the demand for it generally go hand in hand. Demand of a product is inversely proportional to its price.
Lower prices increase demand, while higher prices decrease it. This is a result of consumer satisfaction levels.
The other factors influencing consumer demand are:-
Tastes and preferences.Consumer's income.Availability of substitutes.Number of consumers in the market.Consumer's expectations.Elasticity vs. inelasticityTo study the demand in detail visit;
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Evaluate 23x-1 for x = 1.
A: 4
B: 1
C: 7
D: 8
Answer:
23-1=22
Step-by-step explanation:
What is the sum of three consecutive numbers as an expression?
(*Consecutive means in a row. Example: 1, 2, 3)
The sum of three consecutive numbers as an expression is 3x + 3.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Let the consecutive numbers be x, x + 1 and x + 2.
The sum of three consecutive numbers as an expression will be:
= x + x + 1 + x + 2
= 3x + 3.
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Why is the area of a triangle 1/2 Bxh?.
By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).
Some properties of rectangle are ?The opposite sides are parallel and equally spaced apart, and each internal angle is 90 degrees.360 degrees are equal to the total of all internal angles.Both of the diagonals are identical in length and parallel to one another.A rectangle's perimeter is equal to 2a+2b units if its sides are of lengths a and b.A rectangle with sides that are a and b long has an area that is equal to ab sin 90 square units.Diagonally is the diameter of the circumference of a rectangle.To Prove:- Area of a triangle= 1/2 (base×height)
Diagonals of the rectangle divide it into two parts of equal areas.
Let ABCD be a rectangle.
In ΔABC and ΔADC,
AC=AC
By Alternate Interior Angles:
∠BAC=∠CAD
∠BCA=∠CDA
Hence, ΔABC≅ΔACD
∴ar(ΔABC) =ar(ΔACD)
Let ΔABC,
We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.
In rectangle ADBE,
we get,
ar(ΔABE)=ar(ΔADB)
Similarly, in rectangle ADCF,
ar(ΔADC)=ar(ΔACF)
Now, area of rectangle BCFE, from axiom,
=(length)⋅(breadth)
=AB⋅BC
=AD⋅BC
Also,
ar(BCFE)
=ar(ADBE) + ar(ADCF)
=2⋅ar(ΔADC) + 2⋅ar(ΔADB)
=2(ar(ΔADC) + ar(ΔADC)
=2(ar(ΔABC))
From (1) and (2),
2(ar(ΔABC)) = AD⋅BC
ar(ΔABC) = 1/2AD⋅BC
ar(ΔABC) = 1/2(base)⋅(height)
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Celine i etimating the number of tile in a moaic. There are 7 different color, and 472 tile of each color. There are alo 96 blank tile. What hould Celine’ etimate be?
Celine should estimate 3400 tiles in a mosaic.
The total number of tiles in mosaic will be sum of coloured tiles and blank tiles. So, there is a variety in coloured tiles. To calculate this we will perform multiplication.
Number of coloured tiles = Number of different coloured tiles × Number of each different coloured tile
Number of coloured tiles = 7 × 472
Performing multiplication on Right Hand Side of the equation
Number of coloured tiles = 3304
Total number of tiles = 3304 + 96
Performing addition on Right Hand Side of the equation
Total number of tiles = 3400 tiles
The estimate will be 3400 tiles.
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math pls help!!!!! rewarding points
Answer:
x=90. 3x=270
Step-by-step explanation:
120•6=45•2+135•2+4x
X=90
3X=270
Work out an estimate for
√4.98 +2.16×7.35
The estimated value of √4.98 +2.16×7.35 = 18.1075
Mathematical Operations:Operators are Mathematical methods that emphasize particular actions like adding, dividing, and adding multiple times are known as Mathematical Operations. The basic mathematical operations are 4 types they are Addition, Subtraction, Multiplication, and Division.
While we use mathematical operations to solve a problem we will use the BODMAS rule as given below
B - Brackets (Calculating numerical parts in brackets comes first )
O - Orders (Simplify powers and square roots)
D - Division (Complete division parts )
M - Multiplication (complete multiplication)
A - Addition (complete additions part )
S - Subtraction ( End with subtractions )
Here we have
√4.98 +2.16×7.35
Here the value of √4.98 = 2.2315 (approximately)
From above value
=> √4.98 +2.16×7.35
=> 2.23 + 2.16 × 7.35
By using the BODMAS rule
=> 2.23 + 15.876 [ Do multiplication ]
=> 18.106 [ Do adding ]
Therefore,
The estimated value of √4.98 +2.16×7.35 = 18.106 (approx)
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The average class size at Lexington Middle School is 21 students, which is 5% larger than it was a decade ago. What was the average class size then?
Proportionately, the average class size at Lexington Middle School a decade ago was 20.
What is the proportion?Proportion is the ratio or relative numerical relationship of two or more values equated to one another.
Proportions are fractional values, showing how much of a number is contained in another or the whole.
Proportions are depicted as decimals, fractions, or percentages.
The current average class size at Lexington Middle School = 21 students
The percentage increase in class size = 5%
Let the current average class size = 105% (100 + 5)
The previous decade's average class size = 21/105% = 20
Thus, a decade ago, the average class size was 20, proportionately increasing by 5%.
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3/7 of a number is 69. What is the number?
The number is 161.
Given,
In the question:
3/7 of a number is 69.
To find the what is the number?
Now, According to the question:
Based on the given condition :
Formulate:
3/7 of a number is 69.
=> 3/7 = 69
=> 3 = 69 x 7
Calculate the product or quotient.
=> 3 = 483
Divide by 3 on both sides:
=> 483/3
= 161
Hence, The number is 161.
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select all that apply. in a population of 250 students, 60% are whites, 20% are latinos, 15% are blacks, and 5% others. in a proportionate stratified random sample of 120, group of answer choices the number of whites selected is 72. the number of blacks selected is 50. the number of latinos selected is 37. the number of other racial and ethnicity background selected is 6.
In proportionate stratified random sample of 120, 72 are Whites, 24 are latinos, 18 are blacks, and 6 are others.
From the question, we have
In a population of 250 students, 60% are whites, 20% are latinos, 15% are blacks, and 5% others.
sample = 120
Number of whites = 60% of 120
= 0.6 × 120
=72
Number of latinos = 20% of 120
= 0.2 × 120
=24
Number of blacks = 15 % of 120
= 0.15 × 120
= 18
Number of others = 5% of 120
= 0.05 × 120
= 6
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. We frequently do one of the fundamental mathematical procedures. Using multiplication tables is the most obvious application. To represent the repetitive addition of one number to another, mathematicians multiply two numbers. Natural numbers, fractions, integers, whole numbers, and other types of numbers can be included. When M is multiplied by n, M is either added to itself 'n' times or subtracted from itself.
Complete question:
select all that apply. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a proportionate stratified random sample of 120, ______.
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3.
How many times the value of the 7 in 107 is the value of the 7 in 170?
Answer:
14
Step-by-step explanation:
For the function, the vertex of the function's graph is given. Find the unknown coefficients.
y=[tex]x^{2}[/tex]+bx+c; (3,-5)
The unknown coefficients will be b = -2/3 and c = -12
Vertex of a graph is a point where two lines meet in a parabola.
It is represented as ( h , k ) = ( -2a / b , f( -2a / b) )
Vertex is given to us in the question as (3 , -5)
Also coefficient of [tex]x^{2}[/tex] is given to us as 1
Now by putting values of 'a' and vertex in the vertex formula we get
3 = -2a / b
b = -2/3
Now put value of b in y = [tex]x^{2}[/tex] + bx + c
b = -2/3
As we know that vertex (3 , -5) are points on parabola for the given function we will replace it with x and y respectively
x = 3
y = -5
-5 = [tex]3^{2}[/tex] + ( -2/3 ) * 3 + c
-5 = 9 - 2 + c
c = -12
Therefore b = -2/3 and c = -12.
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Graph the equation y+4=x
Answer:
here you go..
Step-by-step explanation:
please mark brainliest...
Daiy i given a cale drawing with the route to her campite. The route to the campite i 28 cm on the drawing. The cale on the drawing i 1 : 300. What i the actual length of the route?
metre
According to scale drawing, the actual length of route is 84 metres.
The calculations will be based on the concept of ratio and proportion -
Ratio in real :: Ratio of scale drawing
Let us assume the actual length of route be x.
28 : x :: 1 : 300
Writing the ratio as fraction
28/x = 1/300
Cross multiplying the fraction
x = 28 × 300
Performing multiplication on Right Hand Side of the equation
x = 8400 cm
Converting centimetres to meters. As per the known fact, 100 cm = 1 metre
8400 cm = 84 meters
Thus, the actual length is 84 meters.
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Write the Parabola in standard form
Y=-x² + 4x-1
What fraction can we use to rename 5 2 as tenths?
25/10 is used as tenths.
From the question, we have
5/2 = 5*5/2*5 = 25/10
25/10 is used as tenths.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Write the following expression in simplest form. the expression quantity negative three fifths times x minus 7 end quantity minus quantity negative 12 plus three tenths times x end quantity
Answer:
[tex]-\frac{9}{10} x+5[/tex]
Step-by-step explanation:
[tex](-\frac{3}{5} x-7)-(-12+\frac{3}{10} x)\\\\-\frac{3}{5} x-7+12-\frac{3}{10} x\\\\-\frac{3}{5} x+5-\frac{3}{10} x\\\\-\frac{6}{10} -\frac{3}{10}x+5\\\\-\frac{9}{10} x+5[/tex]
w/5=3
can someone please help me on this asap
Reason:
Multiply both sides by 5 to undo the division.
w/5 = 3
5*(w/5) = 5*3
w = 15
As a way to check, plug in w = 15
w/5 = 3
15/5 = 3
3 = 3
We get a true statement at the end to confirm w = 15 is indeed the answer.
What is the sum
of the solutions to
x² - 7 = 6x?
Step-by-step explanation:
x² - 7 = 6x
x² - 6x - 7 = 0
the generation solution to such a quadratic ratatouille
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (6 ± sqrt((-6)² - 4×1×-7))/(2×1) =
= (6 ± sqrt(36 + 28))/2 = (6 ± sqrt(64))/2 =
= (6 ± 8)/2 = (3 ± 4)
x1 = 3 + 4 = 7
x2 = 3 - 4 = -1
the sum of both solutions is : 7 + -1 = 7 - 1 = 6
Manny and Ada pool their money from a fundraiser. Manny raised 7 dollars less than twice what Ada raised.
Manny made $45 more than Ada. If the amount that Ada raised is represented by a then which of the following equations correctly models the information given?
(1) 2a-7-a=45
(2) 7-2a + a = 45
(3) 2a -7+ a = 45
(4) 2a-7+45=a
PLEASE HELP ME!!
Amelia needs to buy some cat food. At the nearest store, 2 bags of cat food cost $9.50 . How much would amelia spend on 3 bags of cat food?
Answer:
$14.25
Step-by-step explanation:
2 bags of cat food costs $9.50. To calculate the price of one, divide $9.50 in half.
$9.50/2 = $4.75
Now, to calculate how much she'd have to spend on 3 bags, you need to multiply $4.75 by 3
$4.75 x 3 = $14.25
by using division, we can find what 1 bag of cat food is worth. Then, we can use multiplication to find what 3 bags of cat food are worth
Process:Worth of One Bag
where w is the worth of one bag
Set up equation w = 9.50/2
Solve w = $4.75
Worth of Three Bags
where w is the worth of 3 bags
Set up equation w = 4.75(3)
Solve w = $14.25
Answer: $14.25