Answer:
x=10
Step-by-step explanation:
x-3(+3)=7+3
We need to add 3 to both sides to isolate x.
x=10
Answer:
x = 10Step-by-step explanation:
x - 3 = 7
x = 7 + 3
x = 10
2. If P = √2+1 √2-1 and Q = √2-1 √2+1 Find P2 + Q2 + PQ 1
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
How to find the value of a expression including elimination of radical in denominators
Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:
P = (√2 + 1) / (√2 - 1)
P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]
P = (√2 + 1)² / (2 - 1)
P = (√2 + 1)²
P = 2 + 2√2 + 1
P = 3 + 2√2
Q = (√2 - 1) / (√2 + 1)
Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]
Q = (√2 - 1)²
Q = 2 - 2√2 + 1
Q = 3 - 2√2
Then, the value of P² + Q² + P · Q is:
M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)
M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8
M = 9 + 8 + 9 - 8 + 3 - 8
M = 21 - 8
M = 13
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
RemarkThe statement is poorly formatted and reports typing mistakes, correct form is presented below:
If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.
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The rate of inflation in the fictional land of sardonia is such that the price of a car costing 24000 dollars in u.s. currency will double in eleven years. what is the annual rate of inflation? what will be the price of this car in five years?
The annual rate of inflation is 35560.86%.
What is inflation?Inflation is defined as an increase in the overall price of goods and services in an economy.When the general price level rises, each unit of currency purchases fewer products and services; hence, inflation equates to a loss of money's purchasing power. Deflation, or a sustained reduction in the general price level of goods and services, is the inverse of inflation. The inflation rate, which is the annualized percentage change in a general price index, is the most commonly used metric of inflation.To find the annual rate of inflation:
48,000=24,000e^k(7)24,000 24,0002=e^k(7)ln2=lne^k7ln2=k77 7k=0.099 --> k=9.9%Now, sub in 4 and 0.099
=24,000e^(0.099)(4)=35560.86Therefore, the annual rate of inflation is 35560.86%.
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The correct question is given below:
The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?
How does the mean absolute deviation (mad) of the data in set 1 compare to the mean absolute deviation of the data in set 2? set 1: 12, 8, 10, 50 set 2: 13, 9, 8 the mad of set 1 is 13 less than the mad of set 2. the mad of set 1 is 13 more than the mad of set 2. the mad of set 1 is 2 more than the mad of set 2. the mad of set 1 is 2 less than the mad of set 2.
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
How to estimate the Mean Absolute Deviation from the given data?Set 1: 12, 8, 10, 50
Set 2: 13, 9,8
To determine the mean for each set
Mean = totality of elements/number of elements
Mean of Set 1:
[tex]$=\frac{12+8+10+50}{4}[/tex]
[tex]$=\frac{80}{4}=20$[/tex]
Mean of Set 2:
[tex]$=\frac{13+9+8}{3}[/tex]
[tex]$=\frac{30}{3}=10$[/tex]
To determine the mean absolute deviation (MAD) of the data in each set.
M.A.D of Set 1:
[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]
[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]
M.A.D of Set 2:
[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]
[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
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what is the range of this graph
An ellipse has a vertex at (4, 0), a co-vertex at (0, 2), and a center at the origin. Which is the equation of the ellipse in standard form?
Answer:
x^2/ 16 + y^2/4 = 1
Step-by-step explanation:
The major axis is 4 and that goes with the x variable. It is the major axis because 4 is a larger value than 2.
4 x 4 = 16
2 x 2 = 4
The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.
How to derive the standard form of the equation of the ellipse
In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Center of the ellipsea - Major semiaxis lengthb - Minor semiaxis lengthThe major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:
x² / 16 + y² / 4 = 1
The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.
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Which of the following are possible measures of the interior angles of a regular polygon? If possible, how many sides does the polygon have: 90°, 100°, 110° 125°,
150°, 175°.
Step-by-step explanation:
180(n-2)/n=90 ( this is the solution for the 90)
cross multiplying
180n-360=90n
180n-90n=360
90n=360
90n/90=360/90
n=4, the number of sides for the polygon with 90° is 4 sides
Solution for 100°
180(n-2)/n=100
180n-360=100n
180n-100n=360
80n=360
80n/80=360/80
n=4.5
Same applies to the rest 110°,125° ,150°,175°
M angle JKL=
Help me please thank u so much
Answer:
22°
Step-by-step explanation:
Since IJ is a diameter, arc LJ measures 68 degrees.
Therefore, the measure of angle JKL is (112-68)/2=22°
having trouble with this
Answer:
Step-by-step explanation:
13
PLS HELP PLS
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
The scale factor from Figure A to Figure B is 4
How to determine the scale factor from Figure A to Figure B?From the question, we have the following statement:
Figure B is a scaled copy of Figure A.
The corresponding side lengths of figure A and figure B are:
Figure A = 10
Figure B = 40
The scale factor from Figure A to Figure B is then calculated as:
Scale factor = Figure B/Figure A
Substitute the known values in the above equation
Scale factor = 40/10
Evaluate the quotient
Scale factor = 4
Hence, the scale factor from Figure A to Figure B is 4
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The marked price of an article is rs 10000 . If he discounted rate and VAT rate are equal and the price with VAT is 9900 find the vat rate .
The rate of VAT is 10%.
In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.
We assume the rate of discount and the rate of VAT to be r%.
Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.
Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)
Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).
Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).
The price after VAT is given to be Rs. 9900.
Thus, (100 + r)(100 - r) = 9900,
or, 100² - r² = 9900,
or, r² = 100² - 9900,
or, r² = 10000 - 9900 = 100,
or, r = ±√100 = ±10.
Since r is the rate of VAT, it cannot be negative, making r = 10.
Thus, the rate of VAT is 10%.
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Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?
688,747,536 ways in which the people can take the seats.
How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.
When the whistle blows, each person needs to change to an orthogonally adjacent seat.
(This means that the person can go to the seat in front, or the seats in the sides).
This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.
Now, if we take the options that each seat has, and we take the product, we will get:
P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.
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What is the volume of this rectangular prism? 1cm,6cm,2cm
Step-by-step explanation:
The result is 12 cm³ because to get the volume of a figure you have to multiply all the characters
Simplify 7 + (−3)
A: -10
B: -4
C: 4
D: 10
Answer: 4
Step-by-step explanation:
[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]
JUST NEEDDD A BIT OF HELPPP PLSS
Answer:
They are all true except for D
Step-by-step explanation:
What they are asking you to do, is take your rectangle and flip it over the top. QR would stay right where it is and line ST would now be on top and line QR would be the bottom. If you can picture that, you can see that all the statements would be true but D.
Find the area of the region r bounded by y = 4 1 − x2 , y = 4e−x, x = 0, and x = 1 2
The area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.
For given question,
We need to find the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2]
The region bounded by given curves is as shown below.
The area of this region would be,
[tex]\Rightarrow A=\int\limits^\frac{1}{2} _0 {y-\frac{4}{\sqrt{1-x^{2}}}} \, dx \\\\\Rightarrow A=\int\limits^\frac{1}{2} _0 {4e^{-x}-\frac{4}{\sqrt{1-x^{2}}}} \, dx[/tex]
Now we evaluate above integral.
[tex]\Rightarrow A=4\int\limits^\frac{1}{2} _0 {e^{-x}-\frac{1}{\sqrt{1-x^{2}}}} \, dx\\\\\Rightarrow A=4[\int\limits^\frac{1}{2} _0 {e^{-x}}\,dx -\int\limits^\frac{1}{2} _0{\frac{1}{\sqrt{1-x^{2}}}} \, dx]\\\\\Rightarrow A=4([e^{-x}]_0^{\frac{1}{2} } -[sin^{-1}(x)]_0^{\frac{1}{2} })\\[/tex]
[tex]\Rightarrow A=4([1-\frac{1}{\sqrt{e} } ] -[\frac{\pi}{6} ])\\\\\Rightarrow A=4(1-\frac{1}{\sqrt{e} } -\frac{\pi}{6} )\\\\\Rightarrow A=|4~\times (-0.13013)|\\\\\Rightarrow A=0.521[/tex]
Therefore, the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.
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Find the equation of a line in slope-intercept form with a slope of 5 that contains the point (3,8).
Group of answer choices
y=5x−15
y=5x+8
y=5x−7
y=3x+8
Answer:
y = 5x - 7
Step-by-step explanation:
y = mx + c
y = 5x + c
to find c, input given coordinates
8 = 5 x 3 + c
8 = 15 + c
-c = 15 - 8
-c = 7
c = -7
put that all together and you get:
y = 5x - 7
The equation of the line with a slope of 5 that contains the point (3,8) is
y = 5x - 7.How to find the equation of the lineThe equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the slope is 5 and the line contains the point (3,8), we can substitute these values into the equation and solve for the y-intercept (b).
Using the point-slope form of the equation:
y - y₁ = m(x - x₁)
We have:
y - 8 = 5(x - 3)
Expanding and simplifying:
y - 8 = 5x - 15
Now, let's isolate y:
y = 5x - 15 + 8
y = 5x - 7
Therefore, the equation of the line with a slope of 5 that contains the point (3,8) is y = 5x - 7.
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Select the correct answer.
Consider this expression.
x-4
2(x+4)
For which product or quotient is this expression the simplest form?
O A.
B.
O C.
O D.
2x+8
x²16
x²16
2x+8
2x+8
x²16
x²16
2x+8
÷
÷
.
.
x² + 8x + 16
x +4
x +4
x² + 8x + 16
x² + 8x + 16
x + 4
x+4
x² + 8x + 16
The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Multiplying rational expressionsRational expressions are written in the form a/b where a and b are integers.
According to the question, we need to determine the expression that is equal to x-4/2(x+4)
From the fourth option;
x²-16/2x+8 * x+4/x²+8x+16
Factorize the quadratic part to have;
x²-16/2x+8 * x²+8x+16/x+4
(x+4)(x-4)/2(x+4) * x+4/(x+4)^2
Cancel out the common expression to have;
x-4 * 1/2(x+4)
x-4/2(x+4)
Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
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Using addition rules, show how to add the two real numbers. 7 + (-14)
Answer:
- 7
Step-by-step explanation:
note that
+ (- ) = - ( adding a negative is equivalent to subtraction )
- (- ) = + ( subtracting a negative is equivalent to addition )
then
7 + (- 14) = 7 - 14 = - 7
How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members?
Answer:
3024
Step-by-step explanation:
Each chosen member (out of 9 members) will occupy a different position
out of these four (president , vice-president , secretary , treasurer).
So, here we have to calculate the Number of Permutations of 9 members Taken 4 at a Time :
= 9P4
= 9 × 8 × 7 × 6
= 3024
Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?
Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
What was the relationship between the lines with equations 4x − 8y = 9 and 8x − 7y = 9?Given: 4x - 8y = 9 ............(1)
8x - 7y = 9 ............(2)
To be the same line, the equations have to be multiples of each other.
Multiplying (1) by 2, we get
2(4x - 8y = 9) = 8x - 16y = 18
From (1) solve the value of y, we get
4x - 8y = 9 ............(1)
-8y = -4x + 9
The value of y = (1/2)x - 9/8
From (2),
8x - 7y = 9
solve the value of y, we get
-7y = -8x + 9
The value of y = (8/7)x - 9/7
To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
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g+ 3 = 17
(one step equation)
Answer:
14
Step-by-step explanation:
Subtract 3 from both sides to isolate g / make g the subject :
g + 3( -3 ) = 17 (-3)
g = 17-3
g = 14
Substituting this into the equation gives us :
14 + 3 = 17
17 = 17
So our final answer is 14
Hope this helped and have a good day
The area of the regular octagon is approximately 54 cm2.
A regular octagon has an apothem with length 4 centimeters and an area of 54 centimeters squared. Line segment A B is a side of the octagon.
What is the length of line segment AB, rounded to the nearest tenth?
3.4 cm
4.8 cm
24 cm
27 cm
The length of the line segment of octagon which is AB equal to 3.4 cm.
Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.
We are required to find the length of the line segment AB.
A regular octagon has eight equal sides.
Area of regular octagon=Perimeter*apothem/2-----------1
We have to put the value of area and apothem in equation 1.
54=perimeter*4/2
Perimeter=(54*2)/4
=27 cm
Perimeter=27 cm.
Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,
Perimeter=8*side
27=8*AB
AB=27/8
=3.375 cm
After rounding off it will be equal to 3.4 cm.
Hence the length of line segment is equal to 3.4 cm.
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Answer:
A
Step-by-step explanation:
Three lorries each making five trips per day transport 2500 crates from a factory to a distributor in two days .how many lorries each making 6 trips a day are needed to transport 10000 such crates in a day
Step-by-step explanation:
3×5×2 = 30 lorry trips to deliver 2,500 crates.
3 lorries, 5 trips per day, 2 days
that means that one lorry trip transports
2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.
now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.
that looks like
x × 6 × 83.33333... = 10,000
x × 6 × 83 1/3 = 10,000
x × (6×83 + 6 × 1/3) = 10,000
x × (498 + 2) = 10,000
500x = 10,000
x = 20
so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.
these are altogether 20×6 = 120 lorry trips.
that is 4 times the number of the original scenario (30 trips).
and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).
What number is represented by the question mark?
111= 0, 3213=0, 7756= 1,7662= 2, 6855= 3, 8096= 5,6666=4 . 8193= 3,9313= 1,8639= 4,1234=0, 2581 = 2,7186= 3, 2679=?
Based on the sequence of numbers given, the number that is represented by the question mark is 2679 = 2.
What is the sequence given?The sequence requires that you count the number of circles that a group of number has. For instance 9 has one circle and 8 has two circles because of the way they are drawn.
The numbers 111, 3213, and 1234 will therefore be equal to 0 because there is no number that has a circle in it.
The number 8096 however, will be equal to 5 because there are 5 circles. Two in 8. 1 in 0. 1 in 9. 1 in 6.
This means that the last number of 2679 will therefore be equal to 2 because there are two circles. One circle is in 6, and the other circle is in 9.
In conclusion, the number represented by the question mark is 2.
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A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.
A solid right pyramid has a square base. The base edge length is 2 centimeters longer than the height of the pyramid. The height of the pyramid is 6 centimeters.
If the height is 6 cm, what is the volume of the pyramid?
24 cm3
48 cm3
128 cm3
144 cm3
Answer: it’s 128 (also what you did on my question was not cool, do better)
Step-by-step explanation:
We know the height is 6 and the length is 2 more than the height then the length is 8 (6+2=8) and then you solve for volume and get 128
The correct answer for the volume of the pyramid is [tex]128[/tex] cm³.
Given:
Square base edge lenght 2 cm than the height of the pyramid.
Height of the pyramid is 6 cm.
Square base edge length = Height of pyramid + 2cm
= 8 cm.
Base area:
Area of the square is calculated as side².
Area of square = 8*8
= 64 cm²
Volume of pyramid is calculated as [tex]\dfrac{1}{3} *basearea*height[/tex]
[tex]\dfrac{1}{3}*64*6\\\\ =128[/tex]
The volume of the pyramid is [tex]128[/tex] cm³.
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The table shows the temperature of a cooling cup of coffee.
Minutes 1 2 3 4
Temperature (degrees C) 97 95.1 93.2 91.3
What is the common ratio of the sequence? Express your answer as a decimal rounded to the nearest hundredth.
Write an explicit formula for the nth term of the sequence where n represents the number of minutes and T(n) represents the temperature of the coffee.
If the pattern continues, what will be the temperature of the coffee after 15 minutes? Express your answer as a decimal rounded to the nearest tenth.
Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C
Geometric sequenceCommon ratio, r = second minutes / first minutes
= 95.1 / 97
= 0.98041237113402
Approximately,
r = 0.98
nth term of the sequence, Tn = ar^n -1
Tn = 97 × 0.98^(n-1)
Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)
= 97 × 0.98^(15-1)
= 97 × 0.98^14
= 97 × 0.7536419414749019520643907584
= 73.1032683230654893502459035648
Approximately,
T15 = 73.1°C
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A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. what is the name of the polygon?octagonhexagonheptagonquadrilateral
The name of the polygon is (B) hexagon.
What is a hexagon?A hexagon is a six-sided polygon or 6-gon in geometry. The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.To find the name of the polygon:
Let the number of sides in a polygon be n.Triangles are formed by drawing diagonals from one vertex to each of the others.Because there is no overlapping of the triangles, no diagonal will be drawn back to itself, and the diagonals to each adjacent vertex will lie on top of the adjacent sides, so the number of diagonals from a single vertex is three less than the number of sides or n - 3, and the number of triangles is one more, or n - 2. Number of triangles = number of sides in polygon - 2 Number of triangles = n - 2 n = 4 + 2 n = 6The polygon containing 6 sides is called a hexagon.Therefore, the name of the polygon is (B) hexagon.
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The complete question is given below:
A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?
A) Octagon
B) Hexagon
C) Heptagon
D) Quadrilateral
Find the slope when y2=9, y1=13, x2=4, and x1=0.
Answer:
Formula=√(x2-x1)²+(y2-y1)² =√(4-0)²+(9-13)2 =√16+16 =√32
Answer: slope=-1
Step-by-step explanation:
9-13 -4
------ --------- -4/4=-1
4-0 4
Solve the following question
Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.
When is a fraction not defined?A fraction is not defined when the denominator is zero.
In this problem, the expression is given by:
cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.
The denominators are zero in two cases:
1 - sin(θ) = 0 -> sin(θ) = 1 -> θ = 90º.1 + sin(θ) = 0 -> sin(θ) = -1 -> θ = 270º.Hence the equation is not defined for an angle of 90º.
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Rearrange the formula to highlight the radius
[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{3V}{\pi h} } .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\V=\frac{1}{3} \pi r^2h.\\[/tex]
Multiply both sides of the equation by 3:
[tex]3V=\pi r^2h.[/tex]
Divide both sides of the equation by πh:
[tex]\displaystyle\\\frac{3V}{\pi h} =\frac{\pi r^2h}{\pi h} \\\frac{3V}{\pi h}=r^2\\ r^2=\frac{3V}{\pi h} .\\r*r=\sqrt\frac{3V}{\pi h} *\sqrt{\frac{3V}{\pi h} } \\r=\sqrt{\frac{3V}{\pi h} } .\\[/tex]
