Answer:
<-4,4>
Step-by-step explanation:
-4 * <1,-1> = <-4 * 1, -4 * -1> = <-4, 4>
Please help
Find the angles:
Arc QR =
Arc RS =
QPS =
PSR =
SRQ =
The angles of the cyclic quadrilateral and the arc angle is as follows:
arc QR = 48°arc RS = 96°∠QPS = 72°∠PSR = 87°∠SRQ = 108°How to find the angles in a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral drawn inside a circle. In other words, a cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.
A cyclic Quadrilateral's opposite angles add to 180°.
Therefore,
∠PSR = 180 - 93 = 87 degrees.
An inscribed angle is one-half of the measure of the arc that it intercepts.
Therefore,
87 = 1 / 2 arc PQR
cross multiply
arc PQR = 87 × 2
arc PQR = 174 degrees
Hence,
arc QR = 174 - 126
arc QR = 48 degrees
arc RS = 360 - 90 - 174
arc RS = 96 degrees.
∠QPS = 1 / 2 (96 + 48)
∠QPS = 1 / 2 (144)
∠QPS = 144 / 2
∠QPS = 72 degrees
∠SRQ = 180 - 72
∠SRQ = 108 degrees
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Answer:
48°
96°
72°
87°
108°
Step-by-step explanation:
arc QR = 48°
arc RS = 96°
∠QPS = 72°
∠PSR = 87°
∠SRQ = 108°
A group spends $277.50 to rent 15 tubes for a float down the Ichetucknee River. One person tubes cost $12.50 and two person tubes cost $20. How many of each type of tube does the group rent?
The number of One-person tubes and two-person tubes is 3 and 12 respectively.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
A group spends $277.50 to rent 15 tubes for a float down the Lchetucknee River. One-person tubes cost $12.50 and two-person tubes cost $20.
The equation can be written as,
12.5x + 20y = 277.5
Here, x is the number of One-person tubes and y is two-person tubes.
Also, x + y = 15
Solve the above equation by elimination method,
x = 3 and y = 15 - 3 = 12
Therefore, the number of One-person tubes and two-person tubes is 3 and 12 respectively.
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A sample of 200g of an isotope decays to another isotope according to the function A(t)=200 e⁰.⁰⁵⁴⁺
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
The amount of sample after 25 years and the half life are given as 51.8 g and 12.83 years respectively.
How to find the decay rate of an exponential function?An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.
The given function for the decay of an isotope is given as A(t) = 200[tex]e^-0.054t[/tex].
Now, the given problem can be solved as follows,
(a) The amount of sample after 25 years is given as,
A(25) = 200[tex]e^{-0.054 \times 25}[/tex]
= 200[tex]e^{-1.35}[/tex]
= 200 × 0.259
= 51.8
(b) The half life can be calculated as,
100 = 200[tex]e^{-0.054t}[/tex]
=> [tex]e^{-0.054t}[/tex] = 1/2
=> t = 12.83
Hence, the sample left after 25 years will be 51.8 g and it will take 12.83 years for the sample to decay to half of its amount.
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I need alot of help with this question???
Answer:
no clue bro just help yourself
Step-by-step explanation:
add them
or multiply or divide or subtract and you'll get it
Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the
area under the graph using first two and then four rectangles.
f(x) = x³ between x = 2 and x = 4
The area under the graph using first two and then four rectangles f(x) = x³ between x = 2 and x = 4 is 0.2421875.
Here a=0, b=1 and n=2( two rectangles), so
Δx = (1 - 0)/2
Δx = 1/2
Δx = 0.5
M2 = (0.5) * ( f((0+0.5)/2)) + f((0.5+1)/2)) )
= (0.5) * ( f(0.25) + f(0.75) )
Using f(x) = x^3
=(0.5) * ( 0.015625 + 0.421875 )
=0.21875
Here a=0, b=1 and n=4( four rectangles), so
Δx = (1 - 0)/4
Δx = 1/4
Δx = 0.25
M4 = (0.25) * ( f((0+0.25)/2)) + f((0.25+0.5)/2)) + f((0.5+0.75)/2)) + f((0.75+1)/2)) )
=(0.25) * ( f(0.125) + f(0.375) + f(0.625) + f(0.875) )
Using f(x) = x^3
= (0.25) * ( 0.001953125 + 0.052734375 + 0.244140625 + 0.669921875 )
= 0.2421875
Hence, the area under the graph using first two and then four rectangles f(x) = x³ between x = 2 and x = 4 is 0.2421875.
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Evan added -2 1/2+4 and got 6 1/2 draw arrows on the number line to represent the problem and explains Evans error
Evan's error was that he subtracted -2 1/2 from 4, and thus he got 6 1/2. On adding he would be getting 1 1/2
What is number line?A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.
It is given that Evan added -2 1/2 and 4 but got 6 1/2
The mistake that Evan did was instead of adding, he substracted -2 1/2 from 4, and thus he got 6 1/2. This is because
4 - (-2 1/2)
= 4 + 2 1/2
= 6 1/2
This is wrong as he was asked to add -2 1/2 and 4 not to subtract.
Therefore, on adding -2 1/2 and 4, we get,
= 4 - 2 1/2
= 1 1/2
Evan's error was that he subtracted -2 1/2 from 4, and thus he got 6 1/2 . On Evan's error was that he subtracted from 4, and thus he got . On adding he would be getting 1 1/2
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is -0.25 a rational number
Answer:
Yes
Step-by-step explanation:
Solve 8x - 2y = 0 and -6x + 14y = 50 using elimination. Show steps. Put your answer in coordinate form (x,y)
The required solution (1, 4) of a linear system of the equation is determined by the elimination method.
Given the linear system of equations:
8x - 2y = 0 or 4x - y = 0 …(i)
-6x + 14y = 50 or -3x + 7y = 25 …(ii)
Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.
So, we have to find out the value of 'x’ and 'y’.
By multiplying 7 by equation (i) and adding both equations
28x - 7y -3x + 7y = 25
25x = 25
x = 25/25
x = 1
Substitute the value of x = 1 in the equation (i), and solve for y
4(1) - y = 0
y = 4
Hence, the required solutions are x = 1 and y = 4.
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Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.
The equivalent expressions are 16a + b, 17b + 11a, and 17b.
What are Equivalent expressions:A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.
In general, if anything is considered equal then the two of them are said to be equivalent. Similarly to this, if any two or more algebraic equations have identical solutions or roots then the equations are Equivalent expressions even they look different.
Here we have
Expressions
3a +b +13a
20b +11a -3b
20b -5b +2b
To simplify given expressions add or subtract like terms as given below
3a +b +13a => (3a+13a) +b = 16a + b
Therefore,
The equivalent expression of 3a +b +13a is 16a + b
20b +11a -3b => (20b-3b) + 11a = 17b + 11a
Therefore
The equivalent expression of 20b +11a -3b is 17b + 11a
20b-5b+2b => 20b+2b - 5b = 22b -5b = 17b
Therefore,
The equivalent expression of 20b-5b+2b is 17b
Therefore,
The equivalent expressions are 16a + b, 17b + 11a, and 17b.
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help meeeeeeeeeee pleaseee
The time taken for the population to reach 26.6 million is 2 years while the population in year 2000 is 18.5 million.
What is the population growth?We can be able to define population growth as the process by which the population of an area is increasing. We know that the increase or the decrease of population would have to be an exponential function.
Given that we have the function A =18.5e^0.1708t where A is the population after a given time from year 2000 and t is the number of years after year 2000. It then follows that 18.5 million refers to the population of the united states as at year 2000.
We now have;
26.6 =18.5e^0.1708t
26.6/18.5 = e^0.1708t
1.44 = e^0.1708t
ln(1.44) = 0.1708t
t = ln(1.44)/ 0.1708
t = 2 years
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As Jupiter and Earth travel along their respective orbits, what happens to the one-way communication time of radio waves carrying information between the two planets?
The one-way communication time between the Jupiter and Earth increases.
What are radio waves?Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 Ghz and below.
Given is that Jupiter and Earth travel along their respective orbits.
As the Jupiter and Earth travel along their respective orbits, they start to get apart from each other. This leads to an increase in one-way communication time.
Therefore, the one-way communication time increases as the Jupiter and Earth travel along their respective orbits.
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5. How long will it take Debbie to save $4,000 for the down payment if she continues to add $75 every month?
Explain how you arrived at your answer.
Answer: 4.5 years or 54 months
Step-by-step explanation: Divide $4,000 by $75 a month to get 53.33 then round to 54. 54 months = 4.5 years.
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=√t, y=t^2−2t; t=4
The equation of the tangent to the given curve x = t⁴ + 3 , y = t³ + t at the corresponding point is y = x - 2 .
In the question ,
it is given that ,
the parametric equation is x = t⁴ + 3 , y = t³ + t ,
differentiating with respect to t ,
we get ,
dx/dt = 4t³ and dy/dt = 3t² + 1
On dividing dx/dt by dy/dt to get the slope ,
we get
dy/dx = (3t² + 1)/ (4t³)
Substituting in t=1
dy/dx = (3 + 1)/4 = 1
Slope (m) = 1 ;
Substituting t = 1 , in the parametric equation ,
we have , x = 4 and y = 2 .
So , (y - 2) = 1(x - 4)
y - 2 = x - 4
y = x - 2
Therefore , the equation of the tangent is y = x - 2 .
The given question is incomplete , the complete question is
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t⁴ + 3 , y = t³ + 3 ; t = 4 ?
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The area of the triangle formed by the x and y intercepts of the parabola y=0.5(x-3)(x+k) is 1.5 find all possible values of k
Answer:
The possible values of k are -0.56, -3.56, -2 and -1.
Step-by-step explanation:
We have the equation of the parabola, .
Substituting x=0, we get that i.e. y = -1.5k
So, the y-intercept is (0,-1.5k).
Thus, the height of the triangle becomes |-1.5k| = 1.5k
Again, substituting y=0, i.e. i.e. x=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.
We see that 'k' cannot be 0 or -3 as if k=0, then height = 0, which is not possible. If k= -3, then the base = 0, which is also not possible.
As, area of a triangle = .
Substituting the values, we get,
1.5=
i.e.
i.e. k = -0.56 and k = -3.56
or
1.5=
i.e.
i.e. k = -2 and k = -1.
Thus, the possible values of k are -0.56, -3.56, -2 and -1.
How do I find the inverse of the relation
Answer:
5, -11. -3, 8. 10, 17. -15, 13.
Step-by-step explanation:
All you have to do is switch x and y
18. Find the total length of segment A E.
Using Pythagorean Theorrem the length of AE = 46 units
What is a Right Angle Triangle?
A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Solution:
In Triangle ABC using Pythagorean Theorem
AC = √(21*21 + 20*20)
AC = √841
AC = 29
In Triangle CDE using Pythagorean Theorem
CE = √(8*8 + 15*15)
CE = √289
CE = 17
From the figure we can say that AE = AC + CE
AE = 29 + 17
AE = 46 units
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Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5. Use Table 2. a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "Sample mean" to 3 decimal places and "Sample standard deviation" to 2 decimal places.) Sample mean 17.000Sample standard deviation 79.42 b. Construct the 95% confidence interval for the population mean (Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval 83.41 to -49.418 c. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)Confidence interval 70.21 to -36.218 d, what happens to the margin of error as the confidence level increases from 95% to 90%?as the confidence level increases, the margin of error becomes smaller
For the given data
(a) sample mean is 17 and sample standard deviation = 8.91 .
(b) the 95% confidence interval is (9.551 , 24.449) .
(c) the 90% confidence interval is (11.032 , 22.968) . .
In the question ,
the data is given as 25, 11, 12, 27,26, 22, 8,5.
So , the number of terms (n) = 8
Part(a)
the sample mean(μ) is = (25+11+12+27+26+22+8+5)/8 = 17
the standard deviation is calculated as :
= √[(25 - 17)² + (11 - 17)² + (12 - 17)² + (27 - 17)² + (26 - 17)² + (22 - 17)² + (8 - 17)² + (5 - 17)²)]/7
Simplifying the above data further ,
we get
= 8.91
Part(b)
we know that at 95% confidence interval , the critical value is t₀.₀₂₅,₇ = 2.3646
So , the 95% confidence interval is :
= μ ± t₀.₀₂₅,₇*s/√n
= 17 ± 2.3646*8.91/√8
= 17 ± 7.449
So , the interval is ⇒ (9.551 , 24.449) .
Part(c)
we know that at 90% confidence interval , the critical value is t₀.₀₅,₇=1.8946
So , the 90% confidence interval is :
= μ ± t₀.₂₅,₇*s/√n
= 17 ± 1.8946*8.91/√8
= 17 ± 5.968
So , the interval is ⇒ (11.032 , 22.968) .
Therefore ,(a) the sample mean and standard deviation are 17 and 8.91
(b) the 95% interval is (9.551 , 24.449) .
(c) the 90% interval is (11.032 , 22.968) .
The given question is incomplete , the complete question is
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5.
(a) Calculate the sample mean and the sample standard deviation.
(b) Construct the 95% confidence interval for the population mean.
(c) Construct the 90% confidence interval for the population mean.
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6z+2y=10 solve for y
Answer:
[tex]y = 5 - 3z[/tex]
Step-by-step explanation:
[tex]6z+2y=10[/tex]
divide by 2
[tex]3z + y = 5[/tex]
move the terms
[tex]y = 5 - 3z[/tex]
In a busy airport, aeroplanes from EZPlanes Airways depart every 264 minutes
whilst aeroplanes from Bryanair Airlines depart every 198 minutes. If both airlines
have aeroplanes departing at 06:20 when is the next time they will depart from
the airport together again?
The next time they will meet again is 08:44 (next day)
How to determine the next time they will meet againFrom the question, we have the following parameters that can be used in our computation:
EZPlanes Airways depart = every 264 minutes
Bryanair Airlines depart = every 198 minutes
Both airlines depart = at 06:20
Using the above as a guide, we have the following departure times
EZPlanes Airways depart = 264, 528, 792, 1056, 1320, 1584, 1848, 2112, 2376 and 2640 minutes,
Bryanair Airlines depart = 198, 396, 594, 792, 990, 1188, 1386, 1584, 1782 and 1980 minutes
The common departure time in the above is
Time = 1584 minute
So, we have
Common departure time = 06:20 + 1584 minutes
Evaluate the sum
Common departure time = 06:20 + 26 hours + 24 minutes
Evaluate the sum
Common departure time = 08:44 (next day)
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solve the inequality n minus four sevenths is greater than or equal to negative two thirds for n.
n is greater than or equal to negative 2 over twenty one
n is less than or equal to two over twenty one
n is greater than or equal to negative twenty six over twenty one
n is less than or equal to twenty six over twenty one
The solution to the inequality n - 4/7 ≥ -2/3 is (a) n ≥ -2/21
How to solve the inequality expression?From the question, we have the following parameters that can be used in our computation:
n minus four sevenths is greater than or equal to negative two thirds
By definition, inequalities are used to relate unequal values
Express the inequality properly
So, we have
n - 4/7 ≥ -2/3
Add 4/7 to both sides
So, we have
n ≥ -2/3 + 4/7
Evaluate the sum of the fractions
This gives
n ≥ -2/21
Hence, the solution is (a) n ≥ -2/21
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i need someone to solve this absolute value inequaility -3{x + 2} _< -9
Answer:
x > 1
Step-by-step explanation:
I am solving this equation, not including the "_" in the equation.
-3(x+2)<-9
Multiply both sides by -1 to reverse the inequality.
3(x+2)>9
Divide by 3
x+2>3
Subtract
x>1
find the point at which the given lines intersect find a n equation of the plamn tjat cpontains these lines
The point at which the given lines intersect is (6,0,2) and an equation of the plane that contains these lines is x+y=6.
(a) In the given question we have to find the point at which the given lines intersect.
r = [3,3,0] + t[3,-3,2]
r = [6,0,2] + s[-3,3,0]
The equations of the lines can be written as :
The points for first line is
L(1)⟹x=3+3t, y=3-3t, z=0+2t and
The points for second line is
L(2)⟹x=6-3s , y=0+3s , z=2+0s .
Set the z coordinates equal from the line one and two, and we get :
2t = 2
Divide by 2 we get
t=1 .
Substitute the value of t into the point of x of first line :
x=3+3(1)
x=3+3
x=6
Equating the value of x equal to the coordinate of x of line two
6=6-3s
Subtract 6 on both side, we get
-3s=0
s=0
Now substitute the value of t into the point of y of first line:
y=3-3(1)
y=3-3
y=0
Equating the value of y equal to the coordinate of y of line two
0=0+3s
s=0
Now substitute the value of t into the point of z of first line:
z=0+2(1)
z=2
Equating the value of z equal to the coordinate of z of line two
2=2+0(s=0)=2 .
We thus have the point of intersection is :
P=(x,y,z)
P=(6,0,2)
Hence, the point at which the given lines intersect is (6,0,2)
(b) The direction vector for the first line is
[tex]\vec{v_{1}}=3\hat{i}-3\hat{j}+2\hat{k}[/tex]
and the direction vector for the second line is
[tex]\vec{v_{2}}=-3\hat{i}+3\hat{j}+0\hat{k}[/tex]
We can find a normal vector to the line as :
[tex]\vec{N_{1}}=\vec{v_{1}}\times\vec{v_{2}}[/tex]
[tex]\vec{N_{1}}=\begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\-3 &3 &-2 \\ -3 &3 & 0 \end{vmatrix}[/tex]
[tex]\vec{N_{1}}=\hat{i}(0-(-6))-\hat{j}(0-6)+\hat{k}(-9-(-9))[/tex]
[tex]\vec{N_{1}}=6\hat{i}+6\hat{j}[/tex]
is a normal vector
But , we can also use
[tex]\vec{N}=\frac{\vec{N_{1}}}{6}[/tex]
[tex]\vec{N}=\hat i+\hat j[/tex]
as the normal vector to the plane .
We can thus use the point P=(6,0,2) and the normal vector [tex]\vec{N}=\hat i+\hat j[/tex] to write the equation of the plane :
1(x-6)+1(y-0)+0(z-2)=0
x-6+y+0=0
x+y=6
Hence, an equation of the plane that contains these lines is x+y=6.
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The right question is
(a) Find the point at which the given lines intersect.
r = [3,3,0] + t[3,-3,2] r = [6,0,2] + s[-3,3,0]
(x,y,z) = ( )
(b) Find an equation of the plane that contains these lines.
PLS HELPPPPPPPPPPPPPPP
Answer:
1: 50
2: 1
3: 2
4: 36
5: 0
6: -12
7: -2
8: 3
Step-by-step explanation: Use PEMDAS
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
I need understanding this
Answer:
x > 65/7
Step-by-step explanation:
First, we make the equation positive.
-7/5x < -13
We have to switch the sign when multiplying or dividing a negative number.
7/5x > 13
Now, we multiply by 5 and divide by 7.
7x > 65
x> 65/7
The same digits are used for the expressions 7² and 2⁷ . Explain how to compare the value of each expression.
Choose the correct answer below.
A. Write each power as repeated multiplication. These compare the bases of the exponents.
B. Write each power as repeated multiplication. Then compare the number of factors.
C. Write each power as repeated multiplication. Then evaluate and compare their values.
Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.
What is the relation between power and base?
In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.Compare 7² and 2⁷.
7 ≠ 2
So, write the power as repeated multiplication of the given expression:
7² = 7 * 7
2⁷ = 2*2*2*2*2*2*2
Evaluate:
7² = 49
2⁷ = 128
Compare the values:
128 > 49
2⁷ > 7²
Hence, Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.
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Use the distance formula to find the distance between the points (−1,6) and (−1,7).
The required distance between the points (−1,6) and (−1,7). is 1 unit.
Given that,
using the distance formula to evaluate the distance between the points (−1,6) and (−1,7).
Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1
Thus, the required distance between the points (−1,6) and (−1,7). is 1 unit.
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{y: y is an integer and y ≥ 2}
Answer:
Step-by-step explanation:
i believe the total would be 4
Answer: The set of integers greater than or equal to 2 is {2, 3, 4, 5, ...}. This set can be represented using set notation as:
{y: y is an integer and y ≥ 2}
This set includes all the integers that are greater than or equal to 2, including 2 itself. It does not include negative integers or fractions.
For example, the following are all elements of this set:
2, 3, 4, 5, 6, 7, 8, ...
The following are not elements of this set:
-1, 0, 1, 1.5, -3.14, ...
This set is infinite, because there are an infinite number of integers greater than or equal to 2.
a number squared divided by 15
Answer:
Step-by-step explanation:
If a number is squared and then divided by 15, the resulting expression can be written as (x^2)/15, where x is the number. For example, if the number is 5, then the expression can be written as (5^2)/15 = 25/15. In general, the value of the expression (x^2)/15 will be the square of the number x divided by 15.
austin wants to pour 71.26 grams of salt into a container so far he has poured 23.1 How much more salt should Austin pour?
Answer:
Your answer is 48.16 grams.
Austin needs to pour 48.16 grams of salt.
Here the total amount of salt is 71.26 grams.
But he pours 23.1 grams.
So when we minus 71.26-23.1, it is equal to 48.16 grams.
Therefore, Austin needs to pour 48.16 grams of salt.
To know more about How much salt should Austin pour:
e(x) = 10(4-x)
Find e(-3).
Answer:
70
Step-by-step explanation:
Substitute the value -3 into the expression and simplify:
10(4 - -3)
10(4 + 3)
10(7)
70