Consequently, y-1 = 2 is the point-slope form linear equation for the line passing through (1, 3) and having a slope of 2. (x-3).
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Y = mx + c in this instance.
(y- y₁) = m(x - x₁)
where,
The coordinate for the x-axis is x and x1,
The coordinate for the y-axis is y and y1.
The slope of the line is m, and
The y-intercept can be represented by the letter c.
Replace the value of the slope and the point in the general equation to obtain the equation for the line passing through (1, 3) and having a slope of 2.
y-1 = 2(x-3) (x-3)
Consequently, y-1 = 2 is the point-slope form equation for the line passing through (1, 3) and having a slope of 2. (x-3).
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The diagram shows an isosceles triangle. All the measurements are in cm, work out the perimeter of the triangle.
Ben Nevis has a height of approximately 1300 metres above sea level.
Assuming that temperature decreases by 1°C for every 100 metres above
sea level, work out the temperature at the summit of Ben Nevis when the
sea level temperature is 5°C.
The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.
To work out the temperature at the summit of Ben Nevis, we can use the formula:
Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres
We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.
So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C
Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C
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EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.
QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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Solve the inequality 3 x+2 y≥−6 graphically.
Answer:
Step-by-step explanation:
Answer: y ≥ −3/2x − 3
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
Hope this helps!
PLEASE HELP Water flowed out of a tank at a steady rate. A total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. Which expression determines the quantity of water leaving the tank per hour?
The expression determines the quantity of water leaving the tank per hour is (18 1/2 gallons)/(4 1/4 hours)
How to find which expression determines the quantity of water leaving the tank per hour?
Rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, rate is one quantity divided by the other quantity.
If a total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. We can write that the rate as follows:
rate = (18 1/2 gallons)/(4 1/4 hours)
rate = 4 6/17 gallons per hour
Thus, the expression determines the quantity of water leaving the tank is (18 1/2 gallons)/(4 1/4 hours)
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what number is in the same ratio to 64 as 5 is to 8
Answer: 102.4
Given ratio 5:8
Let's assume the answer to be x
5÷8 should be equal to 64÷x
∴ x= (64×8) ÷ 5
=102.4
The number that has the same ratio to 64 as 5:8 is gotten as; 40
How to Calculate Ratio?
We have the ratio 5:8.
Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;
x/64 = 5/8
Cross multiply to get;
x = 64 * 5/8
x = 40
Can someone please help me? :(
HELP
i been trying for a while and cant get it
The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the function:
y = -(x/3) + 2
At x = -3:
y = -((-3)/3) + 2 = 3
At x = 0:
y = -(0/3) + 2 = 2
At x = 3:
y = -(3/3) + 2 = 1
At x = 6:
y = -(6/3) + 2 = 0
The value of y when x = -3 is 3
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What is the inverse of 7 5?
The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.
let's try to learn what is multiplicative inverse.
1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.
One is obtained when a number is multiplied by its own multiplicative inverse.
When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.
Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.
Given question is incomplete complete question here:
What is the multiplicative inverse of 7/5?
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please help: find m∠BCF
Step-by-step explanation:
so, clearly, the triangles BCF and DCF are congruent.
that makes the line CF a bisector of the kite figure.
and so, both angles are identical halves of the total angle at C.
therefore,
3x + 13 = 13x - 7
13 = 10x - 7
20 = 10x
x = 20/10 = 2
Find $(-1)^{-10} (-1)^{-9} (-1)^{-8} \cdots (-1)^9 (-1)^{10}$. (The dots $\cdots$ mean that there are 21 numbers being added, one for each integer from $-10$ to 10.)
The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1
Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]
here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.
We need to find the sum.
We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1
We know that the formula of the sum of n-terms of a geometric sequence is:
[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]
For n = 21, r = -1 and a1 = 1
[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]
Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1
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What is Y + 4 = 3x + (-5) as a y = mx + b equation??
Suppoe that the tatitical power of a tudy deign i 80% to detect a treatment effect of 0. 5 tandard deviation, and that take-up of the program i 100%. Other thing equal, do we have more, le, or the ame amount of power to detect an effect ize of 0. 4 SD?
The correct option is option C which states that , less than 80% power to detect the standard deviation is 0.4.
We know that the power is less and the effect size is small therefore we can say that all other things given as equal, it's harder to detect than the larger effect. As a result power is reduced.
Statistical power is a measure of research efficiency that is estimated before the study begins . This is done so as to predict the likelihood of discovering an actual effect rather than receiving a false negative result or, in the worst case scenario, overestimating the effect by identifying noise in the data.
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Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. What will his monthly payments be? Round to the nearest cent.
If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.
What is monthly payment?Monthly payment can be defined as the amount a person received on a monthly basis.
Now let find the monthly payment
Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷ ( 1+ 0.0429/12)^12×10 -1
Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷ ( 1+ 0.003575)^120 -1
Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷ ( 1.003575)^120 -1
Monthly payment = $87.31
Therefore the monthly payment is $87.31.
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The complete question is:
Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?
Radicals help please
√6/3 is the value after rationalization of √2/√3
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is √2/√3
Square root two divided by square root three.
We need to rationalize the denominator
To rationalize multiply numerator and denominator by √3
√2/√3×√3/√3
√2×3/3
√6/3
Hence, √6/3 is the value after rationalization of √2/√3
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please help: solve for x
Answer:
x=3
Step-by-step explanation:
Since the altitude of this triangle is at the midpoint of the base,
It is a isosceles triangle making MJ=MK
9x-18=3x
6x-18=0
6x=18
x=3
We have a drawer with 30 pairs of different socks. How many (individual) socks do we need to pull from the drawer before getting one pair for certain
Answer:
60 because their a 2 induivedinal in 1 sock.
Step-by-step explanation:
30 x 2 = 60
Is (3,6) a solution to this system of equations?
y=2x+1
y=4x+6
Step-by-step explanation:
y = 2x + 1 -------- (I)
y = 4x + 6 --------(ii)
from eqn (I)
y = 2x + 1
sub y = 2x + 1 in eqn (ii)
2x + 1 = 4x + 6
2x - 4x = 6 - 1
-2x = 5
x = -5/2
sub x = -5/2 in eqn (I)
y = 2(-5/2) + 1
y = -5 + 1
y = -4
Therefore, (x, y) = (-5/2, -4)
PLEASE HELP!! And explain :) THANKS
Because two triangles are said to be congruent when all three of their corresponding sides and all three of their corresponding angles have the same measure, the right answer is SSS.
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found.
In the order below, beginning with triangles DAB and BCD, write the names of the vertices.
AB = CD
DA = BC
Since both triangles' BD sides are the same, BD = BD.
The SSS feature of a congruent triangle allows us to conclude that the triangles DAB and BCD are congruent since they share the same three sides.
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What is the distance of 2/3 from the horizontal axis in Cartesian plane?
Distance of 2/3 from the horizontal axis is 2 for a cartesian plane.
What is cartesian coordinate system?
The coordinate system in where the location of a point is identified by a pair of numerical terms and that has two reference axis is termed as cartesian coordinate system.
In cartesian plane the reference axis are named as X - axis and Y -axis.
In this system, location of a point p is identified by p (x, y) that means x is the x coordinate of point p and y is the y coordinate of point p. Generally, X-axis is horizontal, and Y-axis is vertical. Both axes are intersected at the origin.
What is the distance of 2/3 from the horizontal axis in cartesian plane?The point coordinate 2/3 denotes the location of a point with respect to a reference direction in the polar coordinate system. In the polar coordinate system, the angle between horizontal axis and a reference point is called polar angle. we know tan angle = vertical coordinate / horizontal coordinate.
hence, tan angle = 2/3
for this reason, if we imagine a cartesian coordinate system 2 is the y coordinate and 3 is the x coordinate.
Finally, the distance of 2/3 from the horizontal axis is 2.
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Jonathan and Oscar began saving money the same week. The table shows the models for the amount of money Jonathan and Ove saved after x weeks.
Jonathan's Savings
F (x)=18x+5
Oscar's Savings
G(x)=8x + 25
Jonathan and Oscar will have the same amount of money saved after
Jonathan and Oscar will have the same amount of money saved after 2 weeks.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.
For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.
If they have same amount of money then,
f(x) = g(x)
18x+5 = 8x+25
10x = 20
x = 2 weeks
Therefore, Jonathan and Oscar will have the same amount of money saved after 2 weeks.
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What is the simplified value of the expression below?
1/3 divided by 2/3
0
1/3
1/2
1
Answer: 1/2
Step-by-step explanation:
( see image ) ( Keep Change Flip )
a) Complete the prime factor trees for 24 and 40:
24
2
2
6
2
40
2
2
3
b) What is the Lowest Common Multiple of 24 and 40?
2
2
1
5
Submit Answer
Answer:
a)
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 120
Step-by-step explanation:
a)
24 40
/ \ / \
2 12 2 20
/ \ / \
2 6 2 10
/ \ / \
2 3 2 5
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 2³ × 3 × 5
LCM = 120
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.
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What literary devices are used in The Importance of Being Earnest?
Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.
What is The Importance of Being Earnest?
Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.
It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.
The characters maintain false personae to avoid onerous social duties.
The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.
In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.
Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.
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√2x-1- x = 0
How do I solve this equation?
Answer:
x = 1
Step-by-step explanation:
Immediately, we will simplify like terms on the left side of the equation. This will give us:
[tex]\sqrt{2x-x-1}[/tex] = 0
Simplifying gives us:
[tex]\sqrt{x-1}[/tex] = 0
Now, an important thing to note, is that for the square root of a number to be 0, the number has to be 0. Therefore, x - 1 must equal 0. So, x = 1. Checking our work gives us:
[tex]\sqrt{2x - x - 1}[/tex] = 0
[tex]\\\sqrt{2 - 1 - 1}[/tex] = 0
[tex]\sqrt{0}[/tex] = 0
It all checks out.
Hope this helped!
A cleaning company charges a fixed amount for a house call and a second amount for each room it cleans the total cost to clean six rooms is $250 and the total cost to clean eight rooms is $320 how much would this company charge to clean two rooms
The cleaning company would charge $150 for cleaning two rooms according to the fixed charges.
What is fixed amount?A fixed amount is a fixed amount or amount established by agreement or contract. This amount is usually a specified amount, does not change over time, and is usually paid on demand or by a certain date. Fixed amounts are commonly used in loans, insurance, and other financial contracts.
This cost is calculated by dividing the difference between the total cost of 6 and 8 rooms by the number of rooms cleaned (6 - 2 or 4).
= ($250 - $320)/4
= $40
This will give you a price of for each additional room.
To calculate the cost of two rooms, simply add the fixed amount of the home visit and double the cost ($40) for each additional room. That's a total of $150 for two rooms.
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The depth of water in a tank oscillates sinusoidally once every
8 hours. If the smallest depth is 6. 6 feet and the largest
depth is 9. 4 feet, find a possible formula for the depth in terms
of time t in hours. Assume that at t=0 the water level is at
the average of the depth and is rising.
.
The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
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What is the relationship between the ratios of sin x° and cos y°?
The ratios are both identical (three fifths and three fifths).
b
The ratios are opposites (negative three fifths and three fifths).
c
The ratios are reciprocals (three fifths and five thirds).
d
The ratios are both negative (negative five thirds and negative three fifths).
Answer:
A. The ratios are both identical (three fifths and three fifths).
Step-by-step explanation:
ratio means fraction
ratio also means division
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"SOHCAHTOA"
sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent
mathworldwolframcom
sine equals opposite over hypotenuse
sine X equals 3 over 5
cosine equals adjacent over hypotenuse
cosine Y equals adjacent over hypotenuse
cosine Y equals 3 over 5
side thats 3 is adjacent for y but
side thats 3 is also opposite for x
both identical, aka C on their question is right
its the 1st option for flvs
Which tatement correctly compare the meaure of center of the data in the dot plot
A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.
The correct answer is an option (A)
Consider plot A.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 6, 6, 7, 7, 10
Using the formula of mean, the mean of Plot A would be:
mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10
mean = 57/10
mean = 5.7
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 6)/2
= 11/2
= 5.5
Consider plot B.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 5, 6, 6, 6, 7
mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10
mean = 51/10
mean = 5.1
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 5)/2
= 5
Hence, both the mean and median are greater for Plot A than for Plot B.
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The complete question is:
Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.