The Solution:
Given that the vertices of a quadrilateral are:
[tex]I(5,2),J(9,5),K(5,-2)\text{ and L(2,-3)}[/tex]We are required to find the coordinate of J' when J(9,5) is reflected in the line x=1.
The new x-coordinate will become:
[tex]x=1-9=-8[/tex]So, the required coordinate of J' is:
[tex](-8,5)[/tex]Therefore, the correct answer is J'(-8,5)
50 POINT HELP FAST LOOK AT THE SCREENSHOT
Answer:
6(3+7)
Step-by-step explanation:
The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.
The greatest common factor is six.
To put it in distributive form, divide both by 6:
6(3+7)
I need help with this pls
nswer:
cvents A and B are independent because P(A|B) = P(A)
pxplanation:
f aA and B are independent, then:
[tex]P(A\text{ }and\text{ }B)=P(A)\cdot P(B)[/tex]In this case,
P(A) = 0.4, P(B) = 0.2
If we multiply:
[tex]P(A)\cdot P(B)=0.4\cdot0.2=0.08[/tex]Which verify what the problem tell us.
Next, the definition of two independent events is P(A|B) = P(A)
Pat has 3 times as many dimes as nickels. In all she has $1.40. How many coins of each does she have?
Answer:
Step-by-step explanation:
d=3n
0.10d+0.05n=1.40
0.10(3n)+0.05=1.40
0.3n+0.05n=1.40
0.35n=1.40
n=4
d=3(4)
d=12
12(0.10)+.05(4)=1.40
1.40=1.40
What is the total amount to be paid on a 9 year, $60,500 loan at 7.3% p.a.?
The total amount to be paid on a 9 year, $60,500 loan at 7.3% p.a. is $100248.50.
How to calculate the amount?It should be noted that simple interest is calculated as:
Interest = Principal × Rate × Time / 100
Interest = 60500 × 7.3 × 9 / 100
Interest = $39748.50
It should be noted that the amount will be the addition of the principal and the interest. This will. be:
= Principal + Interest
= $60500 + $39748.50
= $100248.50
The amount is $100248.50.
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A recent report at a particular college said that 5476 students are taking math this semester, which represents 79% of the student population.
How many students attend this college?
Round answers to the nearest whole number as needed.
Answer: 6931
Step-by-step explanation:
79% of all students are taking math this semesters. So there is an additional 21% of students not taking math.
5476/x = 79/100
cross multiply and divide to get the total number of students.
5476 x 100 = 547600
547600 divided by 79 = 6931
check 5476 divided by 6931 = 79%
Further proof of correct answer:
21% of 6931 = 1455
1455 + 5476 equals 6931, so the answer calculated is correct.
16. Fill in the left side of the two-column proof (4 points).
Given:
32 = 2x + 4y; x = 2
y = 7
Prove:
32 = 2x + 4y; x = 2
Given
Substitution Property
Subtraction Property of Equality
Division Property of Equality
Symmetric Property of Equality
The left side of the two-column proof should be filled as follows:
Statements Reasons_______________
32 = 2x + 4y; x = 2 ⇒ Given
32 = 2(2) + 4y ⇒ Substitution Property
32 - 4 = 4 + 4y - 4 ⇒ Subtraction Property of Equality
28/4 = 4y/4 ⇒ Division Property of Equality
7 = y, y = 7 ⇒ Symmetric Property of Equality
What is the division property of equality?The division property of equality states that when both sides (left and right) of an algebraic expression or equation are divided by the same (common) real number that isn't equal to zero (0), the quotients would always remain equal.
What is the subtraction property of equality?The subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
In conclusion, it has been proven that y is equal to 7 by using the two-column proof.
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4. ALGEBRA Jim Russo deposited into his savings account
a check for $536.75, a check for $347.50, and a third check.
His total deposit was for $1,253.25 after he received $75.00
in cash. What was the amount of the third check deposited?
Write the sentence as an inequality. The temperature is not more than 82F.
1) Let's call Temperature by T
Since the temperature is not more than 82 F, then we exclude any value above 82º F, and we include 82.
T≤82
Please help I’ll mark you as brainliest if correct!!
As a result of the sequences, the numbers for the first equation are 31,37,43, 64,128,256, and 37,42,47 for the second and third equations, respectively.
What is Arithemetic Progression?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
What is Geometric Progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
so for the first equation:
we see the common difference is constant :
second term/third term - first term/second term =7-1 or 13-7
=6
the next three terms in this series would be calculated by adding the common difference to consecutive last terms =31,37,43
for the third equation
the common difference is a constant:
second term-first term=5
the next three terms in this series would be calculated by adding the common difference to consecutive last terms =37,42,47
for the second equation we don't see a constant value as a common difference ,then we conclude that it is a Geometric progression
difference in series = second term/first term
=4/2
=2
so for the three consecutive terms we will multiply the last consecutive terms by 2=64,128,256
Therefore the numbers for First equation are 31,37,43 for the second equation are 64,128,256 and third equation are 37,42,47
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shape J is reflected in the line y=x and then translated. The result is shape K. a) what is the vector that describes the translation? b) if shape J was first translated and then reflected in the line y=x to give shape K, what would the vector be that describes that translation?
Using transformations, the vector that describes the translation that J underwent is:
(x,y) -> (x - 1, y + 2).
Which rules model these transformations?The vertices of the transformed figure K are given as follows:
(4,0), (6,0), (6,-1), (5,-1), (5,-2), (4,-2).
The rule for a reflection about the line y = x is given by:
(x,y) -> (y,x).
Hence, taking the vertices of figure K, the vertices of the translated figure were given by:
(0,4), (0,6), (-1,6), (-1,5), (-2,5), (-2,4).
The vertices of the original figure J are given as follows:
(1,2), (1,4), (0,4), (0,3), (-1,3), (-1,3).
Hence the vector rule from J to the translated figure is given as follows:
(x,y) -> (x - 1, y + 2).
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Find an exponential equation that passes through the points (2,1.8) and (5,14.4) .
An exponential equation that passes through the points (2,1.8) and (5,14.4) is y = (0.6708)2ˣ
Exponential equation:
If you have two points, (x1, y1) and (x2, y2), you can define the exponential function that passes through these points by substituting them in the equation
y = abˣ
and solving for a and b.
In general, you have to solve this pair of equations:
y1 = abˣ¹ and y2 = abˣ²
Given,
The points (2,1.8) and (5,14.4).
Here we need to find the exponential equation that passes through the points.
This yields the following pair of equations:
1.8 = ab²
14.4 = ab⁵
If you divide the second equation by the first, you get
b³ = 14.4/1.8
b³ = 8
b = ∛8
b = 2
so b = 2. It's possible for b to also be equal to -2, but in this case, assume it's positive.
Now, we can substitute this value for b in either equation to get a. It's easier to use the first equation, so:
1.8 = a² x (2)²
1.8 = a² x 4
a² = 1.8/4
a² = 0.45
a = √0.45
a = 0.6708
Therefore, the exponential form of the equation is,
y = (0.6708)2ˣ
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You deposit $400 each month into an account earning 4% interest compounded monthly. a) How much will you have in the account in 30 years?
Answer:
$14540
Step-by-step explanation:
you are earning 4 dollars per 400 dollars per month. there are 12 months in a year. 400 * 12*30 = 144000. 144000 divided by 400 is 360.
360 times 4 is 1440.
my dog has a 30%chance of tearing up the trash on a given day and there's a 10% chance of rain tomorrow. What is the chance that my dog tears up the trash and it rains tomorrow
The probability that that my dog tears up the trash and it rains tomorrow is 0.03.
How to illustrate the information?From the information, the dog has a 30% chance of tearing up the trash on a given day and there's a 10% chance of rain tomorrow.
Therefore, the that my dog tears up the trash and it rains will be:
= Probability of tearing up × Probability of rain
= 30% × 10%
= 0.3 × 0.1
= 0.03
The probability is 0.03.
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The decimal 105.7 becomes 1,057 when multiplied by 10. The same number becomes 10.57 when multiplied by 0.10. Explain why.
-Multiplying by 10 makes the number
(Type whole numbers or decimals.)
by a factor of Multiplying by 0.10 makes the number
by a factor of
The length of the batter's box on a softball field is 1 ft more than twice the width. The area of the batter's box is 78 ft2. Find the length and width of the rectangular batter's box.
The length and width of the rectangular box are 13 ft and 6 ft respectively.
How to find the length and width of a rectangle?The length of the batter's box on a softball field is 1 ft more than twice the width.
The area of the batter's box is 78 ft².
The length and width of the rectangular batter's box can be found as follows:
Therefore,
area of a rectangle = lw
where
l = lengthw = widthTherefore,
area of the rectangular box = 78 ft²
l = 1 + 2w
Hence,
78 = (1 + 2w)w
78 = w + 2w²
2w² + w - 78 = 0
Hence,
w = 6 and w = -13 /2
we can only use positive values.
Therefore,
width = 6 ft
length = 2(6) + 1 = 13 ft
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the inverse of conditional w > ~v
The inverse of the conditional statement w > ~v is ~v < w
What is an inverse statement?An inverse statement is seen as a type of conditional sentence having an immediate change that is made from original statement.
It is known to carry the negation of both the hypothesis and conclusion from the given original statement.
It is known to carry the opposite of the original statement that is given.
An inverse statement is formed by negating the hypothesis and conclusion of a statement.
It is expressed as;
Original statement: If a, then b
Inverse statement: If not b, not a
Given the expression;
w > ~v
The inverse is represented as;
~v < w
Hence, the inverse is ~v < w
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i need help please.......................................................
Answer:
252558855555335555422358236
Answer:
[tex]y=\frac{-1}{4}x+2[/tex]
Step-by-step explanation:
The function can be written in point-slope form following this equation:
[tex]y=m(x-x_{0} )+y_{0}[/tex]
where y and x are variables, and [tex]x_{0}[/tex] and [tex]y_{0}[/tex] are x and y values of any chosen point on the curve (line)
m (slope) can be calculated by the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] where you need to find 2 chosen points on the line where [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the x and y values of the first set, and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the x and y values of the second set.
solve for m and we get [tex]-\frac{1}{4}[/tex]
Plug it into the equation with any set of x and y values on the line into the point-slope form equation, then you get the answer
The depth of water in a tank thats in the shape of a rectangular prism is inversely proportional to the area of its base if the tanks volume is kept constant. if the area of the tanks base is 200 square feet, the depth of the water in the tank is 12 feet. which pair of statements best describe this situation
The relationship between the depth(d), the base area (b) and volume (V) is d = 2400/b
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let d represent the depth of the tank, b represent the area of the base and V represent the volume.
The depth of water is inversely proportional to the area of its base at constant volume. Hence
d = V/b
When b = 200 ft² and d = 12:
12 = V/200
V = 2400
d = 2400/b
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57 POINTS 2 QUESTIONS HELP ASAP
Given p(x)=−3(x−4)^2+14, what is the value of p(2)?
What is the value of f(3) for the function described in the table?
Answer:
p(2) = 2
f(3) = 7
Step-by-step explanation:
Given p(x) = -3(x - 4)² + 14 find p(2)
Simply substitute x with the value 4 in the above expression
p(2) = -3(2-4)² + 14
= -3(-2)² + 14
= -3(4) -+ 14
= -12 + 14
= 2
f(3) can directly read from the table
for x = 3, f(x) = 7
so f(3) = 7
Wat is 3 times 4? cause i don’t know what it could be
Answer:
13
Step-by-step explanation:
3X4=12
Twelve skateboards have 48 wheels what is the value of the ratio of skateboards wheel in simplest form
The value of the ratio of skateboards wheel in its simplest form is 1:4.
What is the ratio?The ratio refers to the numerical relationship between two variables.
Ratios show the quantity of one variable contained in another.
Ratios are expressed in fractions, decimals, or percentages. They can also be written using the ratio symbol (:).
The total number of skateboards = 12
The total number of wheels = 48
The ratio value of skateboards wheels = 48:12
= 4:1 or 1:4
Thus, we can conclude that for every skateboard, there must be 4 wheels, given their ratio values.
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Stocks and bonds both have costs, risk, and (interest or returns) associated with them. Bonds offer an interest payment through a ( coupon date or maturity date), while stocks may offer(dividends or interest) that will grow until it is sold.
Select the correct answer for the blanks
Stocks and bonds both have costs, risks, and returns associated with them. Bonds offer an interest payment through a maturity date while stocks may offer dividends that will grow until it is sold.
How to illustrate the information?Over the long term, stocks have the highest potential for growth for investors. Investors who have chosen to hold onto stocks for an extended length of time have typically been rewarded with robust, profitable returns. However, stock prices fluctuate both up and down.
An IOU-like debt security called a bond. Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.
A dividend is a payment made by a corporation to its shareholders that is decided by the board of directors. Dividend payments are frequently made quarterly and might take the form of cash payments or stock reinvestments.
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Would you classify 121 as a perfect square, perfect cube, both, or neither?Choose the correct answer below.O A. The number is a perfect square because = 121.OB. The number is a perfect cube because= 121OC. The number is both a perfect square and a perfect cube because= 121 and= 121OD. The number is neither a perfect square nor a perfect cube because there is no integer thatcan be squared to get 121 and no integer that can be cubed to get 121.
To know if a number is a perfect sqare of a perfect cube you:
perfect sqare
determine if its sqaure root is an integer. If is not an interger, then the number is not a perfect sqare
[tex]\sqrt[]{121}=11[/tex]perfect cube
determine if its Cube root is an interger. If is not an interger then the number is not a perfect cube
[tex]\sqrt[3]{121}=4.94[/tex]Then so, 121 is a perfect cube, because is the result of (11*11)
121 is not a perfect cube
if the gradient of a line is 3, what is the gradient of the line which is perpendicular to A
Question 2 (1 point)
g(x) = x + 1
What is g(-16)?
g(−16) =
Previous Page
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Page 2
Answer:
[tex]g( - 16) = - 3[/tex]
Step-by-step explanation:
substitute
[tex]x = - 16 \: by \: g(x) = \frac{1}{4} x + 1 \\ g( - 16) = \frac{1}{4} x( - 16) + 1 \\ g( - 16) = - \frac{1}{4} x16 + 1 \\ g( - 16) = - 4 +1 \\ g( - 16) = - 3[/tex]
A car consumes 110 litres of fuel withira a distance of 250km What is the rate of fuel consumption in km/L?
If a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter
The distance travelled by the car with 110 liters of fuel = 250km
To find the rate of fuel consumption we have to apply the unitary method
The distance travelled by the car with 1 liters of fuel = The distance travelled by the car with 110 liters of fuel /110
Substitute the values in the equation
The distance travelled by the car with 1 liters of fuel = 250/110
= 2.5 km
So a car consumes 1 liters of fuel to cover 2.5 km
The rate of fuel consumption = 2.5 km/liter
Hence, if a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter
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HELP!
lines G and H are parallel.
find the measures of angles 1,2 and 3.
The measure of angle:-
angle 1 = 78 degree
angle 2 = 40 degree
angle 3 = 140 degree
what is triangle ?A triangle is a type of polygon which have only three vertices and no parallel sides.
In this question we use property of triangle that :-
1:- Sum of interior angle is 180 degree
2:-Exterior angle of a triangle is equal to the sum of angle of opposite sides
A.T.Q:-
lets vertices of triangle be A,B, and C
so,
angle A + angle B +angle C = 180
62 +78+ angle C = 180
140 + angle C = 180
angle C =40 degree
we know that , angle C and angle 3 makes 180 degree
angle C + angle3 =180 , 40+ angle 3= 180
angle 3 = 140 degree And , angle 2 = angle C
:- angle 2=40 finally;
angle 1 = angle B
angle 1 = 78 degree
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please help im struggling
Label the points, lines, and planes to show Line AB and line m perpendicular to each other in plane S at point B, plane S intersecting plane R in line p, and Line AB both perpendicular to line p and intersecting line n at point A.
The labelled points on the intersected planes shown in the attachment are;
1) Lines AB and m are both coplanar on plane S and are perpendicular to each other intersecting at point B
2) Plane R and plane S intersect on line p
3) Line AB and line p are perpendicular to each other and both intersect with line n at point A
How to label intersecting planes?We want to label the points, lines, and planes showing the following;
Line AB and line m perpendicular to each other in plane S at point B.
Plane S intersecting plane R in line p.
Line AB both perpendicular to line p and intersecting line n at point A.
Therefore, the given parameters are;
1) Lines AB and m are both coplanar on plane S and are perpendicular to each other intersecting at point B
2) Plane R and plane S intersect on line p
3) Line AB and line p are perpendicular to each other and both intersect with line n at point A
The diagram showing the labelled points is as attached.
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Solve the differential equation
[tex] \frac{dx}{dy} = \frac{1}{y( {x}^{2} + 1)} \\ [/tex]
Answer:
[tex]{ \sf{ \frac{dy}{dx} = y( {x}^{2} + 1)}} \\ \\ { \sf{ \frac{dy}{y} = ( {x}^{2} + 1)dx}} \\ \\ { \sf{ \int \frac{1}{y} dy = \int ( {x}^{2} + 1) \: dx}} \\ \\ { \sf{ ln(y) = \frac{ {x}^{3} }{3} + x + c }}[/tex]
Answer:
[tex]\large\text{$y& = e^{\frac{1}{3}x^3+x+\text{C}}$}[/tex]
Step-by-step explanation:
Given differential equation:
[tex]\dfrac{\text{d}x}{\text{d}y}=\dfrac{1}{y(x^2+1)}[/tex]
Rearrange the equation so that all the terms containing y are on the left side, and all the terms containing x are on the right side:
[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}y}&=\dfrac{1}{y(x^2+1)}\\\\(x^2+1)\;\dfrac{\text{d}x}{\text{d}y}&=\dfrac{1}{y}\\\\(x^2+1)\;\text{d}x}&=\dfrac{1}{y}\;\text{d}y\\\\\dfrac{1}{y}\;\text{d}y&=(x^2+1)\;\text{d}x}\end{aligned}[/tex]
Integrate both sides:
[tex]\begin{aligned}\implies \displaystyle \int \dfrac{1}{y}\;\text{d}y &= \int (x^2+1)\;\text{d}x}\\\\\int \dfrac{1}{y}\;\text{d}y &= \int x^2\;\text{d}x}+\int 1\;\text{d}x}\\\\\ln y & = \dfrac{1}{3}x^3+x+\text{C}\\\\e^{\ln y} & = e^{\frac{1}{3}x^3+x+\text{C}}\\\\y& = e^{\frac{1}{3}x^3+x+\text{C}}\\\\\end{aligned}[/tex]
Therefore, the solution to the given differential equation is:
[tex]\large\text{$y& = e^{\frac{1}{3}x^3+x+\text{C}}$}[/tex]
Integration rules used:
[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
Which of the ten basic functions in
our toolkit are decreasing on the
interval (-∞, 0)?
15,0
Step-by-step explanation: