Answers
Answer:
B.80
Step-by-step explanation:
use of pythagoras theorem.
a^2 + b^2 = c^2
where c is hypotenuse
Answer:
D
Step-by-step explanation:
first we can see from question is finding perimeter which means first step we need is
24+24=48
second , we can know it from picture
ABD=[tex]\frac{1}{2}[/tex] times 60= 30, which means it is 1/2 marks
P=DB/BA
which we see DB=BE
so 2 time DB( or BE)=18 which is 18
so we just need use 24+24+18=66
Related Questions
Question
Add.
7 2/6 + 3 2/6
Enter your answer in the box as a mixed number in simplest form.
Answers
Answer:
10 4/6 = 10 2/3
Step-by-step explanation:
dude this is easy and not for college but thanks anyway
∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15). ∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15). ∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7). ∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2). can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.
Answers
Triangle congruence is proved by a sequence of reflections and translations.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Given that, ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17).
By using distance formula, distance =√(x₂-x₁)²+(y₂-y₁)²
AB = 6 units BC = 11 units AC = 12.53 units
∆XYZ X(-10, 5), Y(-12, -2), and Z(-4, 15)
XY = 7.14 units YZ = 18.79 units XZ = 11.66 units
∆MNO M(-9, -4), N(-3, -4), and O(-3, -15).
MN = 6 units NO = 11 units MO = 12.53 units
∆JKL J(17, -2), K(12, -2), and L(12, 7).
JK = 5 units KL = 9 units JL = 10.30 units
∆PQR P(12, 3), Q(12, -2), and R(3, -2)
PQ = 5 units QR = 9 units PR = 10.30 units
So, we have the ∆ABC and the ∆MNO
With all three sides equal are congruent
We have the ∆JKL and the ∆PQR
with all three sides equal are congruent
Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).
1) If ∆MNO by a sequence of reflections and translation, it can be obtained ∆ABC, then ∆MNO ≅ ∆ABC
a) Reflection (On x-axis)
The coordinate notation for the Reflection is (x,y)→(x,-y)
∆MNO M(-9, -4), N(-3, -4), and O(-3, -15).
M(-9, -4)→ M1(-9,4)
N(-3, -4)→ N1(-3,4)
O(-3,-15)→ O1(-3,15)
B) Reflection (y-axis)
The coordinate notation for the Reflection is (x,y)→(-x,y)
In ∆M'N'O', M'(-9, 4), N'(-3, 4), and O'(-3, 15).
M'(-9, -4)→M"(9,4)
N'(-3, -4)→N"(3,4)
O'(-3,-15)→O"(3,15)
C) Translation
The coordinate notation for the Translation is (x,y)→(x+2,y+2)
∆M"N"O", M"(9,4), N"(3,4), and O"(3, 15).
M"(9, 4) → A(11,6)
N"(3,4)→B(5,6)
O"(3,15)→C(5,17)
So, we have ∆ABC, A(11, 6), B(5, 6) and C(5, 17)
From ∆MNO to ∆M'N'O' reflection, from ∆M'N'O' to ∆M"N"O" reflection, and from ∆M"N"O" to ∆ABC its translation.
2)If ∆JKL, by a sequence of rotation and translation
We obtained ∆PQR
So, ∆JKL ≅ ∆PQR
D) Rotation 90 degree anticlockwise
The coordinate notation for the Rotation is (x,y)→(-y, x)
In ∆JKL, J(17, -2), K(12, -2), and L(12, 7).
J(17, -2)→J'(2,17)
K(12, -2)→K'(2,12)
L(12,7)→L'(-7,12)
E) Translation:
The coordinate notation for the translation is (x, y)→ (x+10, y-14)
Then, ∆J'K'L' has vertices J'(2, 17), K'(2, 12), and L'(-7, 12).
J'(2, 17)→P(12,3)
K'(2, 12)→Q(12,-2)
L'(-7, 12)→R(3,-2)
So, ∆PQR has P(12, 3), Q(12, -2) and R(3, -2)
From ∆JKL to ∆J'K'L' its rotation and from ∆J'K'L' to ∆PQR its translation.
Therefore, ∆JKL ≅ ∆PQR
Hence, triangle congruence is proved by a sequence of reflections and translations.
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During a camp event basketball, football, and volleyball competitions were organized. The ratio of the football players to volleyball players to basketball players was 5 : 3: 4. If the 36 players were participating in the volleyball competition, how many players participated in the event?
HELP ASAP!
Answers
Answer:
To find the total number of players participating in the event, we need to find the total number of players for each sport, then add those values together.
Step 1: Find the number of players for each sport based on the ratio:
Football players: 5 : 3 : 4 = 5 * 36 players / (5 + 3 + 4) = 60 players
Volleyball players: 36 players
Basketball players: 4 : 3 : 5 = 4 * 36 players / (5 + 3 + 4) = 48 players
Step 2: Find the total number of players:
60 players + 36 players + 48 players = 144 players
Answer:
144 players participated in the event.
if x^x=4^(x+16), find x
Answers
The value of x in the equation x^x = 4^(x + 16) is 16
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
x^x = 4^(x + 16)
Take the logarithm of both sides
So, we have
xlog(x) = (x + 16)log(4)
At this point, we make use of a graphing calculator
From the calculator, we have
x = 16
Hence, the solution is x = 16
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Please help me with this question.
Answers
The domain of function U(x) = x √(1-x²/a²) is x = a or x = 0. The function of U(x) is an odd function. When a = 1, the plot function is as the attached graph below. The optimum point of the function is x = 1/2 a.
The domain of function U(x) can be find by making U(x) equals to 0:
U(x) = x √(1 - x²/a²) = 0
U(x) = √x² - x⁴/a² = 0
U(x) = x - x²/a = 0
x - x²/a = 0
ax - x² = 0
x² - ax = 0
x (x - a) = 0
x = 0 or x = a
The function of U(x) is an odd function because its biggest order is 2.
If a = 1, then the value of U(x) would be:
U(x) = x √(1 - x²/a²)
U(x) = x √(1 - x²/1)
U(x) = x - x²
x = a = 1
U(x) = 1 - 1
U(x) = 0
The graph is as attached below
The critical point of U(x) function can be determined by differentiate the function equals to 0.
U(x) = x - x²/a
U'(x) = 1 - [(2ax - 0)/a²] = 0
U'(x) = 1 - 2x/a = 0
2x/a = 1
x = 1/2 a --> optimum point
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The domain of the function is x < a
The function is oddThe critical points are x = ±1 and x = ±1/√2The domain of the functionGiven that
U(x) = x√(1 - x²/a²) where a > 0
Set the radicand greater than or equal to 0
1 - x²/a² > 0
So, we have
1 > x²/a²
Rewrite as
x²/a² < 1
This gives
x² < a²
Take the square roots
x < a
This represents the domain
The function typeWe have
U(x) = x√(1 - x²/a²) where a > 0
For even function;
U(x) = U(-x)
For odd function
U(-x) = -U(x)
So, we have
U(-x) = -x√(1 - (-x)²/a²)
U(-x) = -x√(1 - x²/a²) ---- not an even function because U(x) ≠ -U(x)
U(x) = x√(1 - x²/a²) ---- an odd function because U(-x) = -U(x)
Hence, it is neither
The graph of the function when a = 1See attachment
The critical pointsThe critical points are points where the function is defined and its derivative is zero or undefined
We have
U(x) = x√(1 - x²/a²)
a = 1
U(x) = x√(1 - x²)
Using a graphing tool, we have the critical points to be
x = ±1 and x = ±1/√2
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Can someone please answer this question?
Answers
Answer:
40 dollars per hour
A seven-character database password is formed from 10 digits and 26 upper-case letters. What is the probability that a randomly selected password has no digits? SHOW ALL YOUR WORK and Round your answer to four decimal places.
Answers
The probability that a randomly selected password has no digits is 10.24%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, a seven-character database password is formed from 10 digits and 26 upper-case letters.
Number of characters in passwords: 7
The possible number of ways to formed the first value of passwords is sum of 26 (upper letters) and 10 (0 to 9 numbers).
The required number of possible passwords is 36⁷
= 78364164096
Favorable out comes is 26⁷
= 8031810176
Now, probability of an event = 8031810176/78364164096
= 0.1024
= 10.24%
Therefore, the probability that a randomly selected password has no digits is 10.24%.
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You work at a restaurant/bar. -Your boss comes to you, knowing you are studying
economics, and asks for your opinion on the following question:
Which of the following would increase the demand for drinks the most? Explain in
detail why.
A. a reduction in the price of a complementary good such as an appetizer
B. a reduction in the price of drinks
Answers
The equation x+53=15
can be solved by performing two operations on both sides. State the operations in order of use. There may be more than one correct answer.
A. Subtract 5
from both sides first, then multiply both sides by 3
B. Divide both sides by 3
first, then subtract 5
from both sides
C. Multiply both sides by 3
first, then subtract 5
from both sides
D. Subtract 5
from both sides first, then divide both sides by 3
E. Multiply both sides by 3
first, then divide both sides by 5
F. None of the above
(b) Give the solution of the equation x+53=15
.
x=
help (numbers)
Answers
Which fraction is closest to 1/2
?
Answers
The fraction which is closest to 1/2 is, 3/8. So option B is correct
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
A fraction number 1/2
In decimal form = 0.5
Closest fraction number = ?
Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,
Lets take, A fraction 1/6
In decimal form it can written as, 0.167
Difference 1 = 0.5 - 0.167
= 0.333
Similarly, For numbers 3/8, 3/4, -1/2
Difference 2 = 0.5 - 0.375 = 0.125
Difference 3 = 0.5 - 0.75 = -0.25
Difference 4 = 0.5 - (-0.5) = 1.0
It can be seen that,
Magnitude of difference in case of 3/8 is very less
Hence, the closest number is 3/8
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Modeling with Composite Functions
A store offers a 20% discount on all items and you also have a $3 coupon. Suppose you want to buy an item that originally costs $30.
Let the price of the item you want to purchase be x dollars. Use composition of functions to write two functions: one function for applying 20% discount first, and another function for applying the $3 coupon first.
Answers
The composite function c(x) = 0.8x - 3, and the cost of a $30 item would be $21.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.
In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Let, 'x' be the original cost of the item.
A store offers a 20% discount on all items,
So, f(x) = [(100 - 20)/100]×x.
f(x) = (80/100)×x.
f(x) = 0.8x.
Again, you also have a $3 coupon.
Let, g(x) = x - 3.
Now, The composition of the functions f(x) and g(x) is f(x) + g(x) = C(x).
C(x) = 0.8x - 3.
Now, The cost of an item is $30.
Therefore, C(30) = 0.8×30 - 3.
C(30) = 24 - 3.
C(30) = 21.
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In the 2018 winter Olympics there were 240 athletes from the USA and 7 /20 of them were skiers. How many Olympic skiers were there?
Answers
Answer:
84
Step-by-step explanation:
Number of skiers = Number of athletes * Fraction of skiers
= 240 * 7/20
= 84 skiers
Answer:
84
Step-by-step explanation:
240/20=12
12*7=84
what fraction of clockwise revolution does the hour hand of clock turn through when it goes from 3 to 9
Answers
Answer:
1/2
Step-by-step explanation:
On the clock from 3 to 9, the hour hand turns clockwise 1/2 of the revolution. On the clock from 4 to 7, the hour hand turns clockwise 1/4 of the revolution
The table below shows Bashir's earnings on the job. Time (hours) Time (hours) Earnings (dollars) Earnings (dollars) 15 $ 228 $228 23 23 $ 349.60 $349.60 33 33 $ 501.60 $501.60 How much does he make in 15.5 15.5 hours?
Answers
Bashir earns $235.6 in 15.5 hours.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Slope= 501.60-349.60/33-23
=152/10
=15.2
Now let us find the y intercept
228=15.2(15)+b
228=228+b
b=0
Now let us find how much he earns in 15.5 hours.
y=15.2(15.5)
y=235.6
Hence, Bashir earns $235.6 in 15.5 hours.
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Ratio for 63 inches to 4 yards
Answers
Answer:
The ratio for 63 inches to 4 yards is 1:16. To calculate this, divide 63 inches by 4 yards, which is equal to 48 inches per yard. Therefore, the ratio for 63 inches to 4 yards is 1:16.
An inequality is modeled below.
What is the solution for the inequality?
A.x<−2
B.x<−1
C.x<2
D.x<1
Answers
Answer:
D. x < 1
is correct answer
ANSWER FAST!!! U WILL GET BRAINLEST WHEN U ANSWER!!
Answers
Answer: 31
Step-by-step explanation:
You need to find the perimeter of something, you just add the numbers of the sides.
6 + 9 = 15
15 + 5 = 20
20 + 3 = 23
23 + 5 = 28
28 + 3 = 31
Perimeter = 31 in.
Step-by-step explanation:1. Remember the concept of perimeter.A perimeter of any shape is just the total length of all its sides. In other words, is the distance around the edge of the shape.
2. Add up all the measures.Perimeter = 5 in + 3 in + 5 in + 9 in + 6 in + 3 in = 31 in.
3. Conclude.Perimeter = 31 in.
What's the area of this?
Answers
Answer:
5 units^2
Step-by-step explanation:
a rectangle is drawn so the width is 2 inches longer than the height. if the rectangle's diagonal measurement is 24 inches, find the height.
Answers
Answer:
15.94
Step-by-step explanation:
(2+h)² + h² =24²
4+4h+h²+ h² =24²
2+2h+h²= 576/2
h²+2h-286=0
solve h=15.94
Pls solve fast .. . . . . . . . .
Answers
The value of the angle ∠I = 13
What is an isosceles triangle?An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.
in this figure, it is an isosceles triangle as two sides of the triangle are equal.
given in the ΔGHI is an isosceles triangle.
So the other two angles will be 13
Hence The value of the angle ∠I =13°
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6 The figure shows the dimensions of a compost bin. Can the expression
below be used to find the surface area of the compost bin? Explain.
Include a net in your explanation.
6.5 +4.5 +3.5+5.5+ 2[3.4+ (3•4)]
Answers
The surface area of the composite bin can be found using the expression 6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]
Please find attached the drawing of the net of the composite bin, created with MS Word
What is the surface area of a composite figure?The surface area of a composite figure can be found finding the sum of the individual exposed surface area of the composite figure.
Please find attached the possible drawing of the diagram in the question, created with MS Word
The possible complete expression in the question, obtained from a similar, online question, is presented as follows;
6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]
The surface area of the figure consists as follows;
Two trapezoidal faces (in front and on the rear
Four rectangular faces, orthogonal to the trapezoidal faces
Please find attached the net of the composite bin created with MS Word
The area of the trapezoidal faces = (3 + 6)×4/2 = ((1/2)·(3·4) + ((1/2)·(6·4))
((1/2)·(3·4) + ((1/2)·(6·4)) = ((1/2)·(3·4) + (3·4)
((1/2)·(3·4) + ((3·4)) = 3·4 + (1/2)·(3·4)
Therefore, the area of the two trapezoidal faces = 2 × (3·4 + (1/2)·(3·4))
The area of the four rectangular faces are;
Face [tex]{}[/tex] Area
Orthogonal rear face = 6 × 5
Orthogonal front face = 3 × 5
Face at the bottom of the figure = 4 × 5
The slant face at the top = 5 × 5
The area is therefore;
The surface area of the composite bin, A, is therefore;
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For this example, use the function 1 () 1 2 fx x = + and an initial value of 4. Note that
with each successive iteration, you can use the previous output as your new input
to the function.
• 1 (4) 4 1 3 2 f = ⋅+=
• 2 1 (4) (3) 3 1 2.5 2 f f = = ⋅+=
• 3 1 (4) (2.5) 2.5 1 2.25 2 f f = = ⋅ +=
Questions
3. What happens to the value of the function as the number of iterations
increases?
4. Choose an initial value that is less than zero. What happens to the value of
the function as the number of iterations increases?
5. Come up with a new linear function that has a slope that falls in the range
−< < 1 0 m . Choose two different initial values. For this new linear function,
what happens to the function’s values after many iterations? Are the
function’s values getting close to a particular number in each case?
6. Use the function gx x () 2 =− + with initial values of 4, 2, and 1. What happens
after many iterations with all three initial values? How do the results of all
three iterations relate to each other?
Answers
a) for initial value 4 function oscillate between 4 and -2
b) for a initial value of 2 function oscillate between 2 and 0
c) for a initial value of 1 function value is constant = 1
What is a function?A function is a relationship between a set of inputs that each have one output. A function, in simple terms, is a relationship between inputs, with each input corresponding to exactly one output. Each function has a domain as well as a co-domain or range. The general notation for a function is f(x), where x is the input. A function is generally represented as y = f. (x).
In math, there are various types of functions. Among the most important types are:
Injective function: When there is a mapping for a range for each domain between two sets.Surjective functions, also known as Onto functions, are used when there are multiple elements mapped from domain to range.A polynomial function is a function made up of polynomials.Inverse Functions: A function that has the ability to invert another function.f(x) = 1/2.x + 1
f(4) = 1/2*4+1=3
f(4) = 1/2*3+1=2.5
f(4) = 1/2*2.5+1=2.25
f(4) = 1/2*2.25 + 1 = 2.125
f(4) = 1/2*2.125+1 = 2.0625
f(4) = 1/2*2.0625 + 1 = 2.0123
As the iteration increases function value converges to 2
You can write a simple MATLAB program to check it
matlab code:
clc;
clear all;
close all;
syms x;
f=-x+2;
y(1)=4;
g(1)=2;
h(1)=1;
for n=1:20
y(n+1)=subs(f,x,y(n));
g(n+1)=subs(f,x,g(n));
h(n+1)=subs(f,x,h(n));
end
t=[y',g',h'];
output :
t =
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
a) for initial value 4 function oscillate between 4 and -2
b) for a initial value of 2 function oscillate between 2 and 0
c) for a initial value of 1 function value is constant = 1
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Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
√a³ - 7+ |b|
When a = 2 and b = -4, the value of the expression is
Answers
The given expression √(a³-7)+ | b |, when a = 2 and b = -4, the value of the expression is, 5
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression,
√(a³-7) + | b |
where, a = 2
b = -4
Now, by putting values of a and b in the given equation,
⇒ √(a³-7) + | b |
⇒ √(2³-7) + | -4 |
For whatever value of x, |x| will give always positive value
So, now it can be further written as,
⇒ 1 + 4
⇒ 5
Hence, the value is 5
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Convert the following equations from standard form to slope-intercept form. 1-x-2y=-6
Answers
Answer:
Step-by-step explanation:
Slope intercept form is
[tex]y=mx+b[/tex]
Start with your equation and move y terms to one side and all other terms to the other side:
[tex]1-x-2y=-6[/tex]
[tex]1-x+6=2y[/tex]
Combine numbers:
[tex]7-x=2y[/tex]
Divide both sides by 2
[tex]\frac{7}{2} - \frac{x}{2} =y[/tex]
Write y on the left hand side and put the rest of the equation in standard slope intercept form:
[tex]y=-\frac{1}{2}x+\frac{7}{2}[/tex]
This is slope intercept form with m = -1/2 and b =7/2
Can someone show me the steps to solve these subtraction problems using base five notation
Answers
Answer:
a)
[tex]\boxed{22}\\\\\boxed{19} - \boxed{7} = \boxed{12}[/tex]
b)
[tex]\boxed{ 243}\\\\\boxed{117} - \boxed{44} = \boxed{73}[/tex]
Step-by-step explanation:
The easiest way is to convert each base 5 number in each expression to base 10, perform the calculations and then convert from base 10 back to base 5.
a) 34₅ - 12₅
34₅ = (3 x 5¹ + 4 x 5⁰) = (3 x 5) + (4 x 1) = 15 + 4 = 19₁₀
12₅ = (1 x 5¹ + 2 x 5⁰) = (1 x 5) + (2 x 1) = 5 + 2 = 7₁₀
There are online calculators to do this job so no one really goes through this exercise by hand
Conversion from base 10 to base 5 is rather more complex process of repeatedly dividing by 5 noting the quotients and remainders of each division and working backward through the remainders
Again online calculators are available to ease your pain of doing this
Let's illustrate with a number like 123₁₀
123÷ 5 : Quotient: 24; Remainder: 3
24 ÷ 5: Quotient 4 ; Remainder: 4
4 ÷ 5 : Quotient 0 ; Remainder: 4
Since quotient is 0, we stop
Going from bottom to top the remainders are 4, 4, 3 so 443 is the equivalent in base 5
We can check
443₅ = (4 x 5² + 4 x 5¹ + 3 x 5⁰) = 100 + 20 + 3 = 123₁₀
I am simply going to use a calculator to convert from base 10 to base 5
Final result
34₅ - 12₅ = 19₁₀ - 7₁₀ = 12₁₀
12₁₀ = 22₅
Answer
34₅ - 12₅ = 22₅
19₁₀ - 7₁₀ = 12₁₀
b)
432₅ - 134₅
432₅ = (4 x 5²) + (3 x 5¹) + (2 x 5⁰)
= 4 x 25 + 3 x 15 + 2 x 1
= 117₁₀
134₅ = (1 x 5²) + (3 x 5¹) + (4 x 5⁰)
= 25 + 15 + 4
= 44₁₀
So the equivalent computation in base 10 is
117₁₀ - 44₁₀ = 73₁₀
73₁₀ = 243₅
Answer:
432₅ - 134₅ = 243₅
117₁₀ - 44₁₀ = 73₁₀
Note I have been using 5 not five for the subscript. The final answer asks you only to enter the numbers in the boxes so it does not matter
The conversions of the number bases gives;
a) 12 ten
b) 73 ten
What is the number base?We have to note that the number base is the ground work upon which we can be able to perform mathematical operations. We know that in this case, we would have to change the numbers from base five to base 10.
For the first problem, we have;
34 five = 19 ten
12 five = 7 ten
We then have;
19 - 7 = 12 ten
For the second problem;
432 five = 117 ten
134 five = 44 ten
Then;
117 - 44 = 73 ten
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Solve this equation
|z+7|=|z-4|
Answers
The solutions for the equation |z+7|=|z-4| general is z = -7/2 and z = 11/2.
What are the two cases that has to be considered to solve the equation?To solve the equation |z + 7| = |z - 4|, we consider two cases:
z + 7 = z - 4
z + 7 = -(z - 4)
In the first case, solving for z we get:
z + 7 = z - 4
11 = -4
z = -7/2
In the second case, solving for z we get:
z + 7 = -(z - 4)
z + 7 = -z + 4
2z = 11
z = 11/2
So, the solutions are z = -7/2 and z = 11/2.
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Rachel's bedroom window is rectangular with an area of 81.9 square feet. If the panel is 26 feet long, how wide is it? a 0.315 feet b 2.15 feet c 3.15 feet d 31.5
Answers
The panel of the window is 3.15 ft width.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.
Given that, Rachel's bedroom window is rectangular with an area of 81.9 square feet, and the panel is 26 feet long
We need to find the width of the window,
Let the width be w
Area of a rectangle = width × length
81.9 = w × 26
w = 81.9 / 26
w = 3.15
Hence, the panel of the window is 3.15 ft width.
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IREADY MATH AREA pls help ty!
Answers
The area of the shaded region is πr² - (2 × 13.5π).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a shaded region inside a circle.
The area of each section is -
A{S} = 13.5π
We can write the area of the shaded region as -
πr² - (2 × 13.5π)
Therefore, the area of the shaded region is πr² - (2 × 13.5π).
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Given:
\(\text{m}\angle BAC=46°\)
\(\text{m}\angle CBA=54°\)
Part I: Use the given information to determine \(\text{m}\angle DEC\). Show all of your work.
Part II: Use complete sentences to explain the steps necessary in solving for \(\text{m}\angle DEC\). Justify your explanation by including all theorems, postulates, or definitions used.
Answers
The value of angle ∠DEC = 60 degree.
In the given the figure , m∠BAC = 64° and m∠CBA = 56°.
What is a Triangle ?A triangle is a polygon with three sides and three vertices and three angles.
WE are given that AB || CD
Let BC be the transversal , then ∠CBA = ∠DCB (by alternate opposite angles)
∠DCB = 56 degree
As we know the sum of opposite interior angle sis equal to exterior angle therefore, ∠ ECB = 120 degree
∠DCE = 120-56 = 64 degree
BC || DE
∠EDC = ∠DCB = 56 degree (By alternate opposite angles)
The Sum of all the interior angles of a triangle is equal to 180 degree.
56 +64+∠DEC = 180
∠DEC = 60 degree.
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Independent and Dependent Variable examples.
Answers
Answer:
Independent variable: The variable that is changed or manipulated in an experiment to observe its effect on the dependent variable. Example: The number of hours of studying (Independent variable) and the test score (Dependent variable)
Dependent variable: The variable that is being measured or observed in an experiment. Its value is dependent on the independent variable. Example: The temperature of water (Independent variable) and the volume of the water (Dependent variable)
Answer:
y=5x
Here y is dependent variable because it's depend on x but x is not depend on any other variable. So, it's independent variable.
