The values of x are (4+k)/2 and 10. The value of the variable x in terms of y is x = y -4
System of equationsThese are equations that contains several equations and unknowns.
Given the following system of equation
x+y=4
x-y=k
Add both equation
x + x = 4 + k
2x = 4+k
x = (4+k)/2
For the equation
x+y-z=8
x-y+z=12
Add both equations
2x = 8 + 12
2x = 20
x = 10
The value of x from the equation is 10
Given the equations
x=3b
y = 2/6b+4,
______________
b = x/3
Substitute
y = 2/6(x/3)+4
y = x + 4
x = y - 4
Hence the value of the variable x in terms of y is x = y -4
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Mark's Digital Place has a compact digital camera at a price of $425, a 8 inch tablet for $540 and a
game console for $610. If you want to get an additional three years warranty, then you need to pay
15% extra on the original price and $50.
Daphne wants to buy a digital camera and a tablet to start a photography course. When she went into
the store, she found that the store id offering a discount of 5% on the camera and 80 on the tablet.
Daphne also want the additional three years warranty. How müch money does Daphne need to pay to
buy both the items with a three years additional warranty on each item?
Answer:
jjxfzhfxjgjhzjjjtxjxjxktxjtxjtxtxh
A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.
Each rectangle contains a shaded rhombus. The left angle is 50 degrees and the top angle is (2 x + 20) degrees.
What is the value of x?
50
55
125
145
According to the computations, this rhombus's value of x is equal to 55°.
How can we calculate x's value?The total of all the angles in a rhombus should be 360 ° because the opposing angles in a rhombus are always identical.
We may infer the preceding information from the rhombus's picture:
Neighboring angles= 2x+ 20 & 50°
Opposite angles=2x+ 20 & 50°
Combining the angles results in:
2x+20+50+2x+20+50=360
⇒4x+140= 360
⇒4x=360-140
⇒4x=220
⇒x=220/4
⇒x=55°
Hence, it is concluded that the value of x is (b) 55°.
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The height of a cone is twice the radius of its base. a cone has a height of 2 x and a radius of x. what expression represents the volume of the cone, in cubic units?
Answer:
Step-by-step explanation:
The volume of a cone is V = 1/3 [tex]\pi[/tex] * h * r^2
The height of the cone = the diameter of its circle.
Here is the expression:
Volume = 1/3 π * 2x * x^2
[tex]\frac{\pi *x^{2} *2x}{3}[/tex]
Hope I helped!
evaluate the following expression when x=-4 and y=4
x³-x /4y[tex]\frac{x}{y}[/tex]
Answer: - 60
Step-by-step explanation:
[tex]\frac{(-4)^3 - (-4)}{4(4)^-4/4} \\\\= -60[/tex]
help asap!!!!
Select the correct answer.
Which equation could represent the data in the table?
Answer:
A. y = 3x + 1
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Take two points: (0, 1), (1, 4)
[tex]\sf \rightarrow slope \ (m) : \dfrac{4-1}{1- 0 } = 3[/tex]
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 1 = 3(x - 0)[/tex]
[tex]\sf y = 3x + 1[/tex]
What is the equation of the line that passes through the point (8,4) and has an undefined slope?
Answer:
x = 8
Step-by-step explanation:
An undefined slope indicates that the line is vertical and parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (8, 4 ) with x- coordinate 8 , then
x = 8 ← equation of line
4
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cotpheta•sin2pheta=
1+cos2pheta
1+cospheta
1+sin2pheta
Answer:
Step-by-step explanation:
Did you mean.
[tex] = \cot( \theta) . \sin(2 \theta) [/tex]
[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]
[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]
[tex] = 2 \cos {}^{2} ( \theta) [/tex]
[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]
[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]
No option Solution.
GEOMETRY! 50 POINTS
Please explain as best as you can for the second part of the question, I dont understand how to do it.
The geometry is that the number of sides for a 15- gon is 15 sides and the angles are 156° each.
How to calculate the angle?The total angles in a 15 gon will be calculated as:
= (n - 2) × 180
= (15 - 2) × 180
= 2340
The value of each angle will be:
= 2340/15
= 156°
The total angles in a 16 gon will be calculated as:
= (n - 2) × 180
= (16 - 2) × 180
= 2520
The value of each angle will be:
= 2520/16
= 157.5°
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Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.
Answer:
1.2x = 22x = 55/3 ≈ 18.3322 AUD = 18.33 USDStep-by-step explanation:
1 USD - 1.2 AUD
x USD - 22 AUD
cross multiply
1.2 · x = 1 · 22
1.2x = 22multiply both sides by 10
12x = 220
divide both sides by 12
x=55/3 ≈ 18.33USD - United States dollar
AUD - Australian dollar
What is the difference between normal definition of set and contors definition of set
Step-by-step explanation:
The collection of well defined object is called set
express 80 as a product of its prime factors, write the prime numbers in accending order
Answer:
80 as a product of prime numbers can be expressed as 2×2×2×2×5
How do u solve 3/8+1/8-2/7+1/4
Answer:
13/28
Step-by-step explanation:
using pemdas we can determine that the equation is directly solves from left to right
so
first
we have
3/8 + 1/8
which is 4/8
you can simplify this to 1/2
then you have 1/2 - 2/7
you must make them have the same numerator
you can multiple 1/2 by 7/7 and 2/7 by 2/2
7/14 - 4/14 = 3/14
now you must add 3/14 and 1/4
but you to make them have the same numerator
so you multiply 3/14 by 2/2 and 1/4 by 7/7
6/28 + 7/28 = 13/28
that is your final answer
Which triangles in the diagram are congruent?
70°
triangle 1
70°
triangle 3
OA triangle 1 and triangle 2
OB. triangle 1, triangle 2, and triangle 3
OC. triangle 1 and triangle 3
OD. triangle 1, triangle 3, and triangle 4
70°
triangle 2
#
triangle 4
Submit Test
Rea
Answer:
its e
Step-by-step explanation:
because e is is referring to savvy
How to determine whether square root equation is always, sometimes , never, or true?
Answer:
While identity is true for all values of x, an equation may be true only for some values of x, or for no values of x. Examples: 2x + 6 = 4 is true when x = -1, but not when x = 0. The equation x + 5 = x is never true because a number is never equal to five more than itself.
Step-by-step explanation:
I hope this helps
A rectangular prism has a base that is 4 m by 6 m and a height of 10 m. If all dimensions are doubled, what happens to the volume? Explain why he steps that you take to arrive your answer.
If we double the dimension the volume will be increased by 8 times, and the volume will be 1920 cubic m.
What is the Volume of a rectangular prism?The Volume of rectangular prism = l×b×h
The volume of a prism,
V = L x B x H
V = 4 x 6 x 10
V = 240
When all the dimensions are doubled, the new volume will become
V1 =2L x 2B x 2H
V1 = 8(4 x 6 x 10)
V1 = 8(240)
V1 = 1920 cubic m
If we double the dimension the volume will be increased by 8 times, and the volume will be 1920 cubic m.
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In the diagram Below
Answer:
∠UTC = 55°∠UCD = 70°∠BCT = 55°Step-by-step explanation:
In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.
__
UTC∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair
∠UTC = 180° -125° = 55°
__
UCD∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair
∠UCD = 180° -110° = 70°
__
BCT∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles
7. Miguel draws a square on a coordinate plane. One vertex is located at (5, 4). The
length of each side is 3 units. Circle the letter by all the ordered pairs that could be
another vertex.
A. (5, 1)
B. (5, 7)
C. (7, 8)
D. (2, 6)
E. (2, 1)
Answer:
A, B and E
Step-by-step explanation:
Answer: A,B and E i did the test
Step-by-step explanation:
PLEASE HELP. FUNCTIONS AND RELATIONS. PROVIDE ANSWER OPTION A,B,C OR D? THANKS!!
Step-by-step explanation:
please mark me as brainlest
Graph g(x)=|x−4|+3.\
I insert an image graphing the function.
Function:[tex] \boxed{ \boxed{g(x) \: = \: |x \: - \: 4| \: + \: 3}}[/tex]
MissSpanishExit A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and event B is defined as drawing a white ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 2/7
B. 3/14
C. 4/15
D. 4/11
please hurry
P(B|A) expressed in simplest form is 4/15. Option C is correct answer.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of event A = 4/15
probability of event B = 4/15
P(B|A) = P(A ∩ B)/P(B)
P(A ∩ B) = P(A) X P(B)
= (4/15)(4/15)
= 16/225
Now, conditional probability;
P(B|A) = (16/225) / (4/15)
= (16/225)(15/4)
= (16 X 15) / (225 X 4)
= 4/15
Thus, P(B|A) expressed in simplest form is 4/15. Option C is correct answer.
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Suppose we want to choose 6 letters without replacement from 10 distnict letters. how many ways can this be done if the order of the choices is relavant
The number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Suppose we want to choose 6 letters without replacement from 10 distinct letters.
Number of letters = 10
Number of letters need to select = 6
Order is important.
A number of ways:
C(10, 6) = 10!/(10-6)!
= 10!/(4)!
= 151200
Thus, the number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.
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In which funtion is x=2 mapped to 32?
The function g(x)=4(x+3)² - 68 is mapped to 32.
What is equation?An equation is a mathematical expression in terms of one or more unknown variable.
Given are the following functions:
f(x)= - 3x² - 4
g(x)= 4(x+3)²-68
f(x)= 3x
f(x)= 2x-62
To get the mapped function, we substitute the value of x in all function,
a) f(x)=-3x²- 4
Put x=2,
f(2)= -3 (2)² - 4
f(2)= -16
It is not mapped.
b) g(x)=4(x+3)² - 68
Put x=2,
g(2) = 4(2+3)² - 68
g(x) =32
It is mapped to 32.
c) f(x)=3x
Put x=2,
f(2) = 3 x 2 =6
It is not mapped.
d) f(x)=2x - 62
Put x=2,
f(2) =2x2 -62
f(2) = -58
It is not mapped.
Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.
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NEED HELP ON THIS ASAP!!!!!!
Answer: Choice B (If you need to do questions like this in the future i recommend using the desmos graphing calculator online, inputting the equations and comparing them)
Find the y-intercept of the rational function.
A (0, -10)
B (-10, 0)
C (0 , -2)
D (-2, 0)
Answer:
C
Step-by-step explanation:
The y intercept is when the graph passes the y axis. This occurs at (0,-2)
Preform the indicated operation.
(2x+y)(3 x² + y)
Answer:
[tex]6x^3+3x^2y+2xy+y^2[/tex]
Step-by-step explanations:
[tex](2x+y)(3x^2+y)\\2x*3x^2+2xy+3x^2y+y*y - Distribute\\6x^3+3x^2y+2xy+y^2 - Simplify[/tex]
Answer:
6x^3 + 2xy + 3x^ 2y + y^2
Step-by-step explanation:
Apply the distributive property of multiplication. First multiply (3x^2 + y) by 2, obtaining 6x^3 + 2xy, and then multiply (3x^2 + y) by y, obtaining
3x^2y + y^2. Finally, combine like terms (if any) in these two results:
6x^3 + 2xy + 3x^ 2y + y^2
Reece and Sarah share some money in the ratio 9 : 16.
Reece says that Sarah gets more than 60% of this money. Show that Reece is correct.
Answer:
64% > 60%
Step-by-step explanation:
Total Units = 9 + 16 = 25 units.
Sarah Receives 16 units out of 25.
Percentage = 16/25 * 100
= 64%
Therefore Sarah received more than 60% of this money and therefore Reece is correct.
A biologist is studying the effects of using a type of bacteria to clear drain pipes. She creates a simulation of a typical kitchen drain system and
uses it regularly for three days before introducing the bacteria. She then carries out her simulation for another 15 days.
The population of bacteria can be approximated using function b, where dis the number of days since she started the experiment and (d) is the
bacteria population in hundreds.
b(d) = √5.2d-15.6 +2
Use this information to complete the statement.
The domain over which the bacteria population Increases is
The domain over which the bacteria population Increases is [tex]d \ge 3[/tex]
How to determine the domain?The function is given as;
[tex]d = \sqrt{5.2d - 15.6} + 2[/tex]
Set the radicand greater than or equal to 0
[tex]5.2d - 15.6 \ge 0[/tex]
Add 15.6 to both sides
[tex]5.2d \ge 15.6[/tex]
Divide both sides by 5.2
[tex]d \ge 3[/tex]
Hence, the domain over which the bacteria population Increases is [tex]d \ge 3[/tex]
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Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.
B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.
D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.
Answer:
The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.
40 points, please help lol
The simplified expression of [tex]x^{-2/3} . x^{6/7}[/tex] is [tex]x^{4/21}[/tex]
How to simplify an expression?The expression [tex]x^{-2/3} . x^{6/7}[/tex] can be simplified as follows:
using law of indices,
xⁿ . xᵇ = xⁿ⁺ᵇ
Therefore,
[tex]x^{-2/3} . x^{6/7}[/tex] = [tex]x^{-2/3 + 6/7}[/tex]
[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21}[/tex]
[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21} = x^{4/21}[/tex]
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There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
Answer:
11:12
Step-by-step explanation:
You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio
