The original price of a laptop that is 65% of the sales price is R3 1076923.07692
How to find the original price when given the percentage?The sale price of a laptop is R3 700,00,which is only 65% of the original price.
Therefore,
let
x = original price
Hence,
700, 000 = 65% of x
700,000 = 65 / 100 of x
cross multiply
70000000 = 65x
divide both sides by 65
x = 70000000 / 65
x = 1076923.07692
Therefore, the original price of the laptop is R3 1076923.07692
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When using three letters to name an angle, the middle letter represents the ____.
Answer:
Vertex
Step-by-step explanation:
Vertex is the 'point' of an angle
Find the value of b.
Answer: [tex]230^{\circ[/tex]
Step-by-step explanation:
For convenience, I labeled some points as shown in the attached picture.
Also, I assume [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex] are tangents to the circle.
[tex]\overline{BO} \cong \overline{BO}[/tex] (reflexive property)[tex]\overline{AB} \cong \overline{BC}[/tex] (tangents drawn from a common external point are congruent)[tex]\angle BAO \cong \angle BCO[/tex] (right angles are congruent)Therefore, we know [tex]\triangle ABO \cong \triangle CBO[/tex] by HL.
Thus, by CPCTC,
[tex]\angle AOB \cong \angle BOC \implies m\angle BOC=65^{\circ}\\\\\implies m\angle AOC=130^{\circ}[/tex]
This means the measure of minor arc AC is [tex]130^{\circ}[/tex], and thus [tex]b=360^{\circ}-130^{\circ}=\boxed{230^{\circ}}[/tex]
Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
What does point T represent in this context?
Answer:
A number of books and their costs where the subscription with the annual fee costs less
The first subscription option is given by T = 92 while the second subscription option is given as T = 3x. Where T represent the cost of borrowing x number of books.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let T represent the cost of borrowing x number of books.
For the first subscription option:
T = 92
For the second subscription option:
T = 3x
The first subscription option is given by T = 92 while the second subscription option is given as T = 3x. Where T represent the cost of borrowing x number of books.
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Which relation below represents a one-to-one function?
A 2-column table has 5 rows. The first column is labeled x with entries 5, 14, 7, 13, 12. The second column is labeled f (x) with entries 26, 197, 50, 170, 197.
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 5, 2, 1, 2, 5.
A 2-column table has 5 rows. The first column is labeled x with entries 7.25, 7.5, 7.75, 8, 8.5. The second column is labeled f (x) with entries 11, 13, 15, 13, 11.
The relation that represents a one-to-one function is
A. x with entries 5, 14, 7, 13, 12.
f(x) with entries 26, 197, 50, 170, 197.
Option A is the correct answer.
We have,
A one-to-one function is a function that has one output for one input.
Now,
A.
x with entries 5, 14, 7, 13, 12.
f x) with entries 26, 197, 50, 170, 197.
This is a one-to-one function.
B.
x with entries -2, -1, 0, 1, 2.
f(x) with entries 5, 2, 1, 2, 5.
This is not a one-to-one function.
The x values -1 and 1 have the same f(x) value 2.
C.
x with entries 7.25, 7.5, 7.75, 8, 8.5.
f(x) with entries 11, 13, 15, 13, 11.
This is not a one-to-one function.
The x values 7.25 and 8.5 have the same f(x) value 11.
Thus,
The relation that represents a one-to-one function is
A. x with entries 5, 14, 7, 13, 12.
f(x) with entries 26, 197, 50, 170, 197.
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Cost of a computer game: $32.00
Markup: 20%
Answer:
38.4
Step-by-step explanation:
32×%20=6.4
32+6.4=38.4 new price
Write the equation of the line with a slope of 2/3 and y-intercept of 1. Write your answer in slope-intercept form
B = y - mx = 1 - (2/3)(0) = 1
y = (2/3)x + 1
What is the inverse of function f?
F(x) =3-x/7
Answer:
the answer is (D) F-1 (X) = 7x - 3
Step-by-step explanation:
You enter a room. 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.
How many legs are on the ground?
Answer:
28
Step-by-step explanation:
1 dog = 4 legs, 2 dogs = 8 legs
1 horse = 4 legs, 4 horses = 16 legs
1 giraffe = 4 legs.
So we need to add "2 dogs = 8 legs", "4 horses = 16 legs", and 1 giraffe = 4 legs.
(8 + 16 + 4)
We get the final answer: 28
John currently pays $500 monthly towards his minimum payments on his credit cards. , John now pays $350 towards the same credit cards through his debt relief program. How much does John save off his minimums after 3 months
The amount John saves off his minimums after 3 months is $450
Calculating amount savedFrom the question, we are to determine the amount John saves off his minimums after 3 months
The amount John saves off his minimums after 3 months =
($500 - $350) × 3
$150 × 3
= $450
Hence, the amount John saves off his minimums after 3 months is $450
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A system of inequalities is shown.
The graph shows a dashed upward opening parabola with a vertex at negative 2 comma negative 6, with shading inside the parabola. It also shows a dashed line passing through the points negative 3 comma negative 5 and 0 comma 4, with shading below the line.
Which system is represented in the graph?
The required system hence becomes
3x-y+4>0,
y + 6 > (x + 2)²
When the symbols “>”, “<”, “≥”, “≤”, are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.
The Graph is given below of the given problem statement.
Observe that the parabola y=x² has vertex at (0,0) we can shift the vertex to (-2,-6) to get the parabola
y + 6 = (x + 2)²
And the inequality is
y + 6 > (x + 2)²
Hence, this parabola is as required by the problem.
And the line passing through (-3,-5) and (0,4) is
[tex]\frac{\left(y-4\right)}{\left(-5-4\right)}=\frac{\left(x\right)}{-3}[/tex]
The required inequality hence becomes
3x-y+4>0
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Solve each inequality Exercises 65-70 and graph the solution set on a real number line.
Answer:
Where are the exercizes.
Which point corresponds to the real zero of the graph of y = log2 (x + 2) - 1?
Answer:
(0, 0)
Step-by-step explanation:
Ok so you have the equation: [tex]y = log_2{(x+2)}-1[/tex]. To find the zero you simply set the y equal to zero and then solve for x
[tex]0 = log_2{(x+2)}-1[/tex]
Add 1 to both sides
[tex]1 = log_2{x+2}[/tex]
Rewrite the equation in exponential form:
[tex]2^1=x+2[/tex]
Subtract 2 from both sides
[tex]0 = x[/tex]
So the zero of the function is at the origin (0, 0)
Find the lengh of AB
Joe piad $5 for a burger. He has more than $25 left. How much money did he have before buying the burger?
Answer:
More than 30 dollars
Step-by-step explanation:
This situation can be described with the inequality:
x - 5 > 25
1. Add 5 to both sides
2. X > 30
Simplify the expression 3-8 × 34.
Answer:
3-8x 34= -5x 34 = -170
Step-by-step explanation:
What is the value of h(2)?
-2
-1
0
3
Answer:
0
Step-by-step explanation:
all the question is asking is
if x is 2 then what is y
the line on the left is downward facing line which ends at
(2,0) <- where is x is 2 and y is 0
the upward facing line on the right does start at (2,3)
but the dot there is a
hollow dot
hollow dot represents excluded value
You are buying a used car which costs $10,200. You plan to sell the car after keeping it for 5 years. Research shows that this car will lose value at a rate of 8% per year. How much will the car be worth after 5 years?
Answer:
$6,722.63
Step-by-step explanation:
Now: $10,200
In 1 year: 0.92 × $10,200 = $9,384
In 2 years: 0.92 × $9,384 = $8,633.28
In 3 years: 0.92 × $8,633.28 = $7,942.6176
In 4 years: 0.92 × $7,942.6176 = $7,307.208192
In 5 years: 0.92 × $7,307.208192 = $6,722.63
Answer: $6,722.63
Answer:
$6,722.63
Step-by-step explanation:
Using this formula A=P(1-d/100)^n where
A = Amount
P = Principal
d = percent
n = number of year
A=P(1-d/100)^n
A = 10,200(1-8/100)⁵
A = 10,200(1-0.08)⁵
A = 10,200(0.92)⁵
A = 10,200(0.6591)
A= $6,722.63
what is the answer to
√a³-7 + -4
Answer:
√a^3−7-4
Step-by-step explanation:
Replace all occurrences of + − with a single −. A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because 1⋅ −1= −1
11. Name a pair of complementary angles in this figure.
angles DEF and DEH
angles DEH and HEJ
angles DEH and DEK
angles DEH and DEJ
Answer:
DEH & DEJ
Step-by-step explanation:
It a acute and angle so it equal complementary
Item cost $430 sales tax was $8.60 what is the percentage of the sales tax rate
Answer:
2%
Step-by-step explanation:
You can write it out as equation first.
430*x%=8.60, leave x% alone, so the equation will change into
x%=8.60/430
8.60/430=0.02=2%
therefore, x%=2%
11
24
1
4
I’m very lost with this one can anyone answer this for me please
Answer:
So let start with 1/4 simplest form of that would be 9/4 and for 11/24 simplest would be just that so now we got 11/24 - 9/4 = 1/72
Step-by-step explanation:
11/24
4/9
now we do 11 x 9 equals 99 so now 4 x 24 = 96
now we take the two new denominators2 24 and 9
and we do 24 x 9 = 216 so now we got
99/216
96/216
now 99 - 96 is 3 so we got a new fraction
3/216 now we just simplify that so we get 1/72
Write the logarithmic expression as a single logarithm.
Answer:
[tex]\log_48[/tex]
Step-by-step explanation:
[tex]\log_432-\log_4(4) = \log_4(\frac{32}{4} )=\log_48[/tex]
Please solve this question
Using the Poisson distribution, the probabilities are given as follows:
[tex]P(X = 0) = e^{-10.6}[/tex][tex]P(X \geq 1) = 1 - e^{-10.6}[/tex][tex]P(X \leq 2) = 67.78e^{-10.6}[/tex]What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The mean is given as follows:
[tex]\mu = 10.6[/tex]
Hence the probability of no dandelions in an area of 1 m² is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-10.6}(10.6)^{0}}{(0)!} = e^{-10.6}[/tex]
The probability of at least one dandelion is:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - e^{-10.6}[/tex]
The probability of at most two dandelions is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-10.6}(10.6)^{0}}{(0)!} = e^{-10.6}[/tex]
[tex]P(X = 1) = \frac{e^{-10.6}(10.6)^{1}}{(1)!} = 10.6e^{-10.6}[/tex]
[tex]P(X = 2) = \frac{e^{-10.6}(10.6)^{2}}{(2)!} = 56.18e^{-10.6}[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = e^{-10.6} + 10.6e^{-10.6} + 56.18e^{-10.6} = 67.78e^{-10.6}[/tex]
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what is the value of the expression below when x= 2? for y²-2y+10
Answer:
I think its y = 2.
Then, your answer will be 10.
Step-by-step explanation:
y²- 2y + 10
=2² - 2.2 + 10
=4 - 4 + 10
=10 ans.
Hope its helpful!
Answer:
If y = 2.
Your answer is 10.
Step-by-step explanation:
y²- 2y + 10
=2² - 2.2 + 10
=4 - 4 + 10
=10 ans.
Hope its helpful!
Geometry
Pls list steps so I can learn :)
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
Factorize this equation:
6=x^2-x
The factored form of the given expression is (x+2)(x-3)
Factorizing equationQuadratic equation are equation that has a leading degree of 2. Given the equation below
6=x^2-x
Equate to zero
x^2-x - 6 = 0
Factorize
x^2 - 3x + 2x - 6 = 0
x(x-3)+2(x-3) = 0
x = 3 and -2
Hence the factored form of the given expression is (x+2)(x-3)
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Eight more than seven times a number is equal to four more than five times the number. What is the number?
Answer: -2
Step-by-step explanation:
convert it to a equation:
7x+8=5x+4
move x's to a side and numbers to the other
2x=-4
divide by 2
x=-2
Let us consider the number to be 'n'.
Given condition :
7n + 8 = 5n + 4Subtract '5n' from each side :
7n + 8 - 5n = 5n + 4 - 5n2n + 8 = 4Subtract '8' from each side :
2n + 8 - 8 = 4 - 82n = -4Divide '2' from each side :
2n/2 = -4/2[tex]\fbox {n = -2}[/tex]∴ The number is -2.
Which steps would prove the circles similar?
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4.
Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4.
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.
The steps needed is :Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
What is dilation?Dilation is a transformation, which is used to resize the object.
As the radius of big circle is 6 then the dilation should be scale factor 3.
As well as they should share the same center.
The radius of circle y being 2, has to increase by 3 times the value to equal the radius of circle x, and hence has to dilate by a scale factor of 3 as to match circle x,
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Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Round your answers to three decimal places.)
f(x) = (2x+3)²(x-2)^5/x³(x-5)²
The local minima of [tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex] are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)
How to determine the local minima?The function is given as:
[tex]f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}[/tex]
See attachment for the graph of the function f(x)
From the attached graph, we have the following minima:
Minimum = (-1.5, 0)
Minimum = (7.980, 609.174)
The above means that, the local minima are
(x, f(x)) = (-1.5, 0) and (7.980, 609.174)
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evaluate the expression when a= -7 and b=4 for 3b-a
Step-by-step explanation:
By putting value of a and b in 3b-a
The value of the expression 3b - a is 19 when a= -7 and b=4 the answer is 19.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
= 3b - a
Plug a = -7 and b = 4
= 3(4) - (-7)
= 12+7
= 19
Thus, the value of the expression 3b - a is 19 when a= -7 and b=4 the answer is 19.
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