After simplification, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.
In the given question we have to solve the given expression.
The given expression is (-7 + i)(-3 + 6i).
Using the distributive property to solve the given expression.
a(b+c)=ab+ac
Now simplifying the expression.
(-7 + i)(-3 + 6i) = -7(-3 + 6i) + i(-3 + 6i)
(-7 + i)(-3 + 6i) = (-7)*(-3) + (-7)*(6i) + (-3)i + (6i)i
(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6i^2
As we know that i^2 = -1. So
(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6(-1)
(-7 + i)(-3 + 6i) = 21 - 42i - 3i - 6
Simplifying
(-7 + i)(-3 + 6i) = 15 - 45i
Hence, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.
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I need help I am very confused on this Thank you for your guys help!!
The measure of the side MK of the triangle is 109.6.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.
For the triangles, the scale factor will be calculated as,
Scale factor = 57 /13
The measure of the side MK will be calculated as,
57 / 13 = MK / 25
MK = ( 57 x 25 ) / 13
MK = 1425 / 13
MK = 109.61
Therefore, the measure of the side MK of the triangle is 109.6.
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Mrs. sisneros ran 3 miles in 27 minutes on monday. she ran 5 miles in 50 minutes on wednesday. on which day did mrs. sisneros run at a faster rate? what was that rate?
Friday hope that this helps
Given Two Points: Write the equation of the line with the two given point
5. (1, 3) and (-3, -5)
6. (1, 4) and (6, -1)
7. (-12, 14) and (6, -1)
8. (-4,-2) and (4, 0)
Writing Parallel & Perpendicular Equations
9. Write an equation parallel to y = 3x + 6 that passes through the point (4, 7).
M3L3
As Long, As Wide
David's kitchen has an area of 60 square feet. The kitchen is 6 times as many square feet as
David's pantry. If the pantry is 2 feet wide, what is the length of the pantry? ")
First find the area of the pantry.
Solve on paper and check you answer on Zearn. -->
The area of the pantry is square ft.
8
9
Enter ✓
The area of the David's pantry = 10 square feet.
The length of the pantry = 5 feet.
Define the term area of the rectangle?The territory inhabited by a rectangle inside its 4 sides or limits is known as its area. The area of such a rectangle is determined by its sides. Essentially, the formula calculating area is equivalent to the product of the rectangle's length and breadth.For the given question.
David's kitchen is 60 square feet in size. The kitchen is six times the size of the living room.Thus,
Area of kitchen = 6 x area of the pantry
60 = 6 x area of the pantry
area of the pantry = 60 / 6 = 10 square feet.
Area of the pantry = length x breadth
10 = length x 2
length = 10/2 = 5 feet.
Thus, the length of the pantry is found as the 5 feet.
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One type of plant root splits 4 times while growing in the ground. The number of new roots after each split can be modeled by the function f(x)=3x, where x is the number of times the root splits. What is the domain of f(x)? CLEAR CHECK All positive integers All positive integers less than or equal to 4 All integers All positive integers greater than or equal to 4
The domain of the function f(x) = 3x is (b) All positive integers less than or equal to 4
How to determine the domain of the function?From the question, we have the following equation of the function that can be used in our computation:
f(x) = 3x
In this case, the notations are given as
x = Number of splits
f(x) = number of new roots in each split
From the question, we have
Splits = 4
This means that the maximum value of x is 4
The other values of x would be
x = 1, 2, 3, 4
This can be represented as
0 ≤ x ≤ 4
The interpretation of the above notation is all positive values less than or equal to 4
Hence, the domain value is option (b)
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The function h is defined by h (x) = 2(x − 7).
What is the value of h (8) ?
2
23
30
9
Answer:
h(8) = 2
Step-by-step explanation:
substitute x = 8 into h(x) , that is
h(8) = 2(8 - 7) = 2(1) = 2
Another thing you will need to know before you can perform a rotation is
direction of rotation
corresponding angles
corresponding sides
the angle measures
Solve for x.
9x3x36
0-6
O-4
O
4
6
Answer:
[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]
hopefully this will u...^_^
Find the area of a regular hexagon
with a side length of 5 cm. Round to
the nearest tenth.
5 cm
[? ]cm²
Answer: 64.95
Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95
,
Admission to the art museum is $3 per person. When the museum opened this
there was $150 on hand in the ticket booth. At closing time, there was $1254. How many
people paid admission today?
Had:
Tickets:
Total:
Step-by-step explanation:
so the ticket booth had $150 so $1254 -$150=$1104
so $1104 ÷ by $3 each person = to 368 people paid the admission
Had: $150
Tickets :368
Total :$1254
You and your friend went out to lunch and your total bill (before
taxes) was $36.50. You enjoyed your
service and want to leave a tip of $20%. What is your tip amount?
$7.30
$0.73
$20.00
$36.70
Answer: Your answer is $7.30
Step-by-step explanation:
Finding the amount for a tip is simple!
all that's required is multiplying the bill (36.50) by the amount you want to tip (.20, because 20% is equal to .20)
36.50×.2= $7.30
A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce.
a. Find an exponential equation that gives the height h the ball will attain during the nth bounce.
h =
b. If the ball is dropped from 13 feet above the ground onto hard a surface, how high will it bounce on the 5th
bounce?
On the 5th bounce, the ball will reach a height of ____feet.
The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
A golf ball is fabricated so that assuming it is dropped from A feet over the ground onto a hard surface, the most extreme level of each skip will be one portion of the level of the past bob.
Then the equation is given as,
h = a (1/2)ˣ
Where 'a' is the initial height.
The exponential equation that gives the height h the ball will attain during the nth bounce will be given as,
h = a (1/2)ⁿ
If the ball is dropped from 13 feet above the ground onto hard a surface. Then the height on the 5th bounce will be given as,
h = 13 (1/2)⁵
h = 13 x 1 / 32
h = 0.40625 feet
The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.
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How do you use distributive property to express the expression as the multiple of a sum of two whole numbers with no common factor? 27 + 99, 99+36, 3+33, 33+27, 10+50
I need help please!!!!
=========================================================
Explanation:
x = number of weeks
y = height of the plant (inches)
The first sentence of "plant is 4 inches tall on week 8" gives us the point (x,y) = (8,4)
The second sentence gives us the point (32,16)
To find the growth rate, compute the slope.
[tex](x_1,y_1) = (8,4) \text{ and } (x_2,y_2) = (32,16)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{16 - 4}{32 - 8}\\\\m = \frac{12}{24}\\\\m = \frac{1}{2}\\\\m = 0.5\\\\[/tex]
The slope of 0.5 means the plant grows 0.5 inches per week.
Put another way, the plant grows 1 inch per every 2 weeks.
-----------------
Another approach:
The plant goes from 4 inches to 16 inches. It has grown 16-4 = 12 inches over the timespan of 24 weeks (since 32-8 = 24).
So its growth rate is 12/24 = 0.5 inches per week.
Notice how these values and calculations were mentioned in the previous section.
2015
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many
students are boys?
I need help like asap !!!
only numbers and decimal points
The value of c is 20.35 (approx).
What is Pythagorean Theorem?The Pythagorean Theorem states that the hypotenuse, or side opposite the right angle, of a right triangle, which is represented by the square, is equal to the sum of the squares on the legs of the triangle (or, in popular algebraic notation, a2 + b2 = c2).
Where is the Pythagorean theorem used?The following are some significant applications of the Pythagorean theorem in daily life: used in architecture and building, used to determine the shortest distance in two-dimensional navigation. used to measure how steep a mountain's or hill's slope is.
Let the other 2 sides of the triangle be named a and b
Given:- a = 15.5ft
b = 13.2ft
According to the Pythagorean Theorem, We know that
[tex]a^{2}+b^{2}=c^{2}[/tex]
By substituting the values of a and b we get
[tex]15.5^{2}+13.2^{2}=c^{2}[/tex]
[tex]c^{2}= 414.5\\c=\sqrt{414.5}\\ c=20.35[/tex]
c is the hypotenuse of the triangle.
Hence the value of c is 20.35
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Shakira went bowling with her friends. She paid $3 to rent shoes and then $4.75 for each game of bowling. If she spent a total of $22, then how many games did Shakira bowl?
Help!! Can someone state all the statements and reasons to prove that triangle WXY is congruent to triangle WZY!! It’s geometry proofs.
Whoever gives me the answer I’ll give them 20!
It is true that WXY ≅ WZY.
What is a congruent?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Properties of Congruence
Reflexive Property: An angle is congruent to itself.
Symmetric Property: The order of congruence does not matter.
Transitive Property: If two angles are both congruent to a third angle, then the first two angles are also congruent.
Here, It is given that
Angle ZWY is congruent to angle XWY
Segment WZ is congruent to Segment WX
Segment WY is congruent to Segment WY - Reflexive Property of Congruence (which states that one thing is congruent to itself.
Hence, Triangle WXY is congruent to Triangle WZY because of Side Angle Side (SAS) postulate.
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Can I get some help with this
The final velocity of a vehicle with a mass of 800kg is 20000 m/s.
What is velocity?The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.The speed at which an object goes in one direction is known as its velocity. Speed may be used to calculate both the speed of the car traveling north on the major highway and the speed of the rocket bursting into space.So, calculate the final velocity as:
Formula: v = √u² + 2asWhere u is initial velocity, a is acceleration and s is displacement.Now, we know that:
u = 108 km/ha = 4 km/s²s = 50 kmInsert values in the formula and calculate as follows:
v = √u² + 2asv = √108² + 2(4)(50)v = √11,664 + 400v = √12,064v = 20000.022499991 m/sRounding off: v = 20000 m/s
Therefore, the final velocity of a vehicle with a mass of 800kg is 20000 m/s.
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a circular curve is to be constructed with a 225 ft radius and an interior angle of 55 degrees. the separation between the stakes along the arc is 50 ft. assuming the curve is laid out from point to point, what is the last deflection angle?
The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°
In the given question we have,
Radius of circular curve (R) = 225 ft
intersection or central angle in circular curve (I or delta) = 55°
separtion between stakes alaong arc = 50 ft
Angle of deflection is measured from tangent at PC or PT to any point .
deflection angle formula
deflection angle = (Lc /L)(I/2)
where, Lc is long chord and L is lenth of arc , I is central angle
first we find out the value of Lc and L
using formula , R = Lc / 2sin(I/2)
Lc = 225× 2 sin(55°/2) = 208 ft
L = R × I ×π/180°
L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft
put all the vales in deflection angle formula we get ,
deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°
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solve the equation. justify each step
2(-x - 5) = 12
2(-x - 5) = 12
Step 1 : Expand the bracket.
=> -2x - 10 = 12
Step 2 :Add both side by 10.
=> -2x - 10 + 10 = 12 + 10
=> -2x = 22
Step 3 : Divide both side by -2.
=> -2x : (-2) = 22 : (-2)
=> x = -11
Therefore, x = -11.
Answer:
x = - 11
Step-by-step explanation:
2(- x - 5) = 12 ( divide both sides by 2 )
- x - 5 = 6 ( add 5 to both sides )
- x = 11 ( multiply both sides by - 1 )
x = - 11
Some doctors recommend that men drink 3 liters of water every day. there are approximately 29.6 milliliters in 1 fluid ounce. which measurement is closest to the number of fluid ounces in 3 liters? responses 89 fl oz 89 fl oz 10 fl oz 10 fl oz 101 fl oz 101 fl oz 33 fl oz 33 fl oz
The measurement closest to the number of fluid ounces there are in 3 liters is 101 fl oz.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
If there are approximately 29.6 milliliters in 1 fluid ounce, then divide 3 liters by 29.6 milliliters to get the amount of fluid ounces it has.
29.6 milliliters = 1 fluid ounce
3 liters = 3000 milliliters
3000 milliliters / 29.6 milliliters = 101 fluid ounce
Hence, 3 liters ≈ 101 fluid ounces.
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4. Use the rules of measurement to add:
12.32 L +251 L +4225 L
Point O is the center of this circle. What is mzBCA?
A. 56
B. 62
C. 72
D.76
Answer:
B
Step-by-step explanation:
∠ ADB and ∠ AOB sum to 180° , that is
56° + ∠ AOB = 180° ( subtract 56° from both sides )
∠ AOB = 124°
An angle on the circle is half the central angle subtended on the same arc , so
∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°
help help help help help help
When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
What are graph equations?Equations with graphs as unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory.Different graph equations may be used to express the aforementioned graphs.So, the equations are graphs are:
Given equation: f(x) = 3x + 4Which is transform to equation: h(x) = f(x + 3)Now, graph both equations as follows:
Both equations are parallel to each other.(Refer to the graph attached below)Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
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a survey of a congressional race finds 52 percent of voters supporting candidate a and 48 percent supporting candidate b, with a 5 percent margin of error. given this information, we can say that:
Answer:
When you round the number to 5
Step-by-step explanation:
5a-2-3a+7 Simplify this expression.
Answer: 2a+5
5a-2-3a+7
First gather together the like terms
5a-3a and -2+7
then solve
5-3=2 and -2+7=5
answer = 2a+5
An angle is bisected. Each resulting angle is 78 degree. how is the original angle
Write and solve and equation for each scenario. Use x for the variable in your equation. Show your work by first writing an equation and then solving it. Put the solution of your equation in the answer box. If you multiply a number (x) by 5, the product is equal to the sum of 20 and 15.
Based on the calculations, the unknown number (x) is equal to 7.
How to determine the unknown number?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the unknown number. Therefore, translating the word problem into an algebraic equation, we have the following;
Multiply a number (x) by 5 = 5x
The product is equal to the sum of 20 and 15 = 20 + 15 = 35.
Combining the above information, we have:
5x = 20 + 15
5x = 35
Dividing both sides by 5, we have:
x = 35/5
x = 7.
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What are the roots of this polynomial? f(x) = (x+9)(x-9)(x+10)?
The solution for the given polynomial are x = -9, 9 and -10.
What is polynomial?
Polynomials are algebraic expressions that contain coefficients and variables. Variables are sometimes known as indeterminates. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations but division by variables cannot.
Given polynomial:
(x+9)(x-9)(x+10)
Equating it wit zero,
we get solutions as:
x = -9, 9, -10
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