The of interest earned by Cedric's account after 1 year and 9 months is $34.83.
What is the amount of interest in Cedric's account after 1 year and 9 months?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $796Interest rate r = 2.5%Elapsed time t = 12months + 9months = 21 monthsInterest I = ?Plug the given values into the above formula and solve for interest.
I = P × r × t
I = $796 × 2.5% × 21/12
I = $796 × 0.025 × 1.75
I = $796 × 0.025 × 1.75
I = $34.83
Therefore, the interest earned in the account is $34.83.
Option B is the correct answer.
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A movie theater has a seating capacity of 317. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2298, and the theater was filled to capacity, how many children, students, and adults attended?
The total ticket sales was $ 2298, and the theater was filled to capacity
Children: 158
Students: 158
Adults: 79
What exactly is a math area?The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper. Now picture that your square is composed of smaller unit squares.
Where is the usage of area?According to Study.com, area is a mathematical concept that is defined as the two-dimensional space occupied by an item. Area is used in many real-world contexts, including building, farming, architecture, science, and even determining how much carpet you'll need to cover your home's rooms.
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what is 50% of 950? Hint: We can think of 50% as a common fraction.
Answer:
Step-by-step explanation:
To find 50% of 950, you can multiply 950 by 0.50. 50% is the same as 0.50.
The calculation is: 50% * 950 = 0.50 * 950 = <<50*.01*950=475>>475
So, 50% of 950 is 475.
Fill in the blanks to complete the equation that describes the diagram.
Answer:
-9
Step-by-step explanation:
-3+-6=-9
ents
Select all of the triangles that are congruent to triangle A by the SSS postulate.
A
B
HHH
A A
G
O Triangle H
O Triangle D
O Triangle I
O Triangle C
O Triangle F
O Triangle B
O Triangle E
O Triangle G
À l
H
HE
Answer:
Triangle B
Step-by-step explanation:
The triangles have three pairs of congruent sides.
Solve the system: x + 2y = 30 -2x - 2y = -38 ordered pair
Answer:
(8, 11)
x=8
y=11
Step-by-step explanation:
I solved using elimination.
I set the equations over one another getting x+2y=30 over -2x-2y=-38.
I chose elimination because the y values were already the opposite so it can easily cancel each other out. After it get's canceled out I get x=30 over -2x=-38. When using elimination we always add so you'd add x+ -2x and 30+ -38. When you add x + -2x you'd get -1x. When you add 30 + -30 you'd get -8. Now you have 1x=-8 divide both sides by -1 and you get x=8. Now you plug in 8 to one of the equations. I chose to plug it into the 1st equation which is x+ 2y=30. But because I plugged in the 8 the equation is now 8+2y=30. I subtracted 8 on both sides canceling the 8 out. So now I have 2y=22. divide both sides by 2 and x=11. So your order pair is (8, 11)
(Hopefully you were able to understand it..)
Use cylindrical coordinates. Evaluate E(x+y+z)dV where E is the solid in the first octant that lies under the paraboloid z=4x2y2.
Evaluation of E(x+y+z)dV where E is the solid in the first octant that lies under the paraboloid z = 4 - x² - y² is [tex]\frac{128}{15} + \frac{8\pi}{3}[/tex]
Cylindrical coordinates are a set of three coordinates used to locate a point in the cylindrical coordinate system.
When the polar coordinates are extended to a three-dimensional plane, an additional z coordinate is added.
These three measurements combine to form cylindrical coordinates. The coordinates describe two distances and one angle.
According to the question,
We have to find the area under paraboloid
Given : E is a region that lies under paraboloid z = 4 - x² - y² and in the first octant.
The intersection of this paraboloid with the xy plane will give z = 0,
z = 4 - x² - y² , z = 0, that is a circle x² +y² = 4 with radius 2
Therefore , 0 ≤ z ≤ 4 - r²
Therefore, the region E in cylindrical coordinates is
[tex]E = ( r , \theta , z ) | 0 \leq \theta \geq \frac{\pi}{2} , 0 \leq 4 \geq , 0 \leq z \geq 4 - r^2[/tex]
f(x , y ,z ) = x + y + z
=> f(x , y ,z ) = rcosθ + rsinθ + z
=> f(x , y ,z ) = r(cosθ + sinθ) + z
Integration ,
[tex]{\int \int \int }\limits_E {z} \,dv[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r ( cos \theta + sin \theta) + z] r \, dzdrd\theta[/tex]
simlifying,
[tex]= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 \int\limits^{4 - r^2}_0 {[r^2 ( cos \theta + sin \theta) + rz] \, dzdrd\theta\\= \int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [r^2 ( cos \theta + sin \theta)z + r\frac{z^2}{2}] \, drd\theta[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 \int\limits^{2}_0 [(4r^{2} - r^{4})( cos \theta + sin \theta) + \frac{r(4 - r^2)^2}{2}] \, drd\theta[/tex]
=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(\frac{4}{3} r^{3} - \frac{r^{5}}{5})( cos \theta + sin \theta) + \frac{(4 - r^2)^3}{12}]^{2}_{0} \, d\theta[/tex]
Putting the limit and solving,
=> [tex]\int\limits^{\frac{\pi}{2}}_0 [(cos \theta + sin\theta )\frac{64}{15} + \frac{16}{3} \theta ]\, d\theta[/tex]
=> [tex][(sin\theta - cos\theta )\frac{64}{15} + \frac{16}{3} \theta ]^\frac{\pi}{2} _0[/tex]
Evaluating the limits,
[tex]\int\int\int\limits_E {x + y +z } \,dV = \frac{128}{15} + \frac{8\pi}{3}[/tex]
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Please answer correctly It's pre-calculus
Initial size of bacteria is 313, population of bacteria after 5 hours is 3.346 ×10¹¹.
What is bacterial growth?here growth means increases in the number of bacterial populations with respect to time. Generally, the rate of growth of bacteria is occurred exponentially. We use the following exponential equation to calculate the number of bacteria.
N= N° e∧(kt)
How to calculate the initial sizes of bacteria and the population after certain time period?In the above equation, N and N° denotes the number of populations after t minutes and initial time respectively.
k is a constant of proportion
t is the time in minutes
as per given data, the number is doubled after 10 min
N=2N°, t=10
2N°=N° e∧(k10)
2= e∧(k10)
㏑2 = k10 [we took ㏑ in both side]
k= 0.0693
after t= 80 min, the population N= 80000
now using the equation, 80000=N° e∧(k80)
as k=0.0693, N°= 313
the initial number is 313'
after t=5 hours =300 min, the population will be
N= 313 e∧ (0.0693x300)
N = 3.346×10¹¹
hence, initial population is 313 and the number increase to 3.346×10¹¹ after 5 hours.
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Each year caronline deposited a certain amount of money in an account which pays an annual interest rate of r so that at the end of each year, the balance in the account is multiplied by a growth factor of x=1+r. $600 is deposited at the start of the first year, and $200 at the start of the following year. Write an expression for a value of the account at the end of three years in terms of growth factors x. Find the value at the end of 3 years if the interest rate is 4%.
For the following, find the length of AB:
(Use \large \pi=3.14 when necessary and round your final answer to the hundredths.)
Arc AB =
A circle is a two-dimensional figure with a radius and circumference of
2πr.
The arc length of AB is 10.05.
What is a circle?
A circle is a two-dimensional figure with a radius and circumference of
2πr.
We have,
The radius of the circle = 12
The circumference of the given circle.
= 2πr
This means,
The whole circle is 360°.
= 360/360 x 2πr
= 2πr
Now,
We need to find 48°
So,
The arc length of AB.
= 48/360 x 2πr
= 48/360 x 2 x 3.14 x 12
= 48/30 x 2 x 3.14
= 10.048
Rounding to the nearest hundredths.
= 10.05
Thus,
The arc length of AB is 10.05.
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Answer: 10.05
Step-by-step explanation:
The arc length of AB.
= 48/360 x 2πr
= 48/360 x 2 x 3.14 x 12
= 48/30 x 2 x 3.14
= 10.048
Rounding to the nearest hundredths.
= 10.05
The arc length of AB is 10.05.
PLEASE HELP ME ASAP!!!! PLEASE I WILL GIVE YOU BRAINLIST!!!
LM is translated 5 units right and 2 units up to LM' as the graph shows the move in positive direction.
What is graph?In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Here,
As the graph indicates a move in the right direction, LM is translated 5 units right and 2 units up to LM'.
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If log102=0.3010, then log210 is equal to:
If log₁₀2=0.3010, the value of log₂10 will be 3.3×10⁻⁴.Logarithm identity is used to find the value of the log₂10.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
It is given that, log₁₀2=0.3010
We have to find the log₂10
The following logarithm identity is used as,
logₐn=logₙa
log₂10 =1/ log₁₀2
log₂10 =1/ 0.3010
log₂10 =3.3×10⁻⁴
Thus, if log₁₀2=0.3010, the value of log₂10 will be 3.3×10⁻⁴. Logarithm identity is used to find the value of the log₂10.
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Mr. Hansen has three sticks that measure 5 inches, 10 inches and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
The three sticks will not form a triangle.
What is the triangle inequality theorem?
The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.
Given, Mr Hansen has three sticks that measure 5 inches, 10 inches and 17 inches
From the above definition of the Triangle inequality theorem,
Sum of two sides = 5 + 10 = 15 which is less than
the length of the third side = 17
So, the three sticks will not form a triangle.
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How far can an object be pushed if 22 J is used with 17.5 N of force? *
A 1.25 meters,
B 0.80 meters
C 4.5 meters
D 385 meters
Answer:
[tex]\huge\boxed{\sf d = 1.25\ m}[/tex]
Step-by-step explanation:
Given Data:Work = W = 22 J
Force = F = 17.5 N
Required:Distance = d = ?
Formula:W = Fd
Solution:Put the given data in the above formula.
22 = 17.5 (d)
Divide 17.5 to both sides
22/17.5 = d
1.25 m = d
d = 1.25 m[tex]\rule[225]{225}{2}[/tex]
Of the 400 students in the 8th grade, four-fifths have purchased tickets for the end of year trip. If there needs to be two chaperones for every 75 students, how many chaperones are needed?
The number of chaperones that are needed is 128/15.
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that the number of students in 8th grade is 400.
Four fifth of total number of students go for trip.
The number of student who goes for the trip is 400 × 4/5
= 320.
To carry 75 students, we need 2 chaperones.
Apply unitary method:
To carry 1 student, we need 2/75 chaperones.
To carry 320 students, we need (2 ×320)/75 chaperones.
= (2 × 64)/15
= 128/15
= 8.533
= 9
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Match the amplitude, midline, period, and frequency for the cosine equation.
Amplitude is 5, midline is 3, period is π and the frequency is 2
We can describe the cosine function as y = Acos(B(x + C )+ D
where,
amplitude is A
Frequency is B
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
Step 1:
Identify
5 cos(2x) + 3 → Acos(B(x + C )+ D
Hence
A = 5 = Amplitude
B = 2.C = 0. So,
Period = 2π / B
= 2π / 2 = π
Period = π
Frequency = B = 2
Vertical shift = D = 3
Step 2:
Midline
The equation of the midline of periodic function is the average of the maximum and minimum values of the function.
a) we have a maximum when
cos(2x) = 1
x =0, because (cos 0) = 1 Now, replace
y = 5 cos(2x) + 3
y = 5cos(2. 0 ) +3
= 5.1 + 3
= 8
So, the maximum is 8
b) we have a minimum when
cos(2x) = -1
x = π/2 , because
cos(2.π/2) = cos(π) = -1
Now, replace
y = 5cos(2.π/2) + 3
= 5. (-1) + 3
= -5+3
= -2
So, the midline is the average of 8 and -2
Midline = y = [8 + (-2)] / 2
= 6/2
y = 3
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Let's compare
5/8 and 7/10
Answer:
5/8=25/40 7/10=28/40
Step-by-step explanation:
5/8<7/10
A football player throws a ball down the side line. The ball's height above the
ground is modeled by the equation h=-8t^2+24t+4, where h is the height
in feet and t is the time in seconds.
At what two times will the ball be at a height of 16 feet?
Answer: t₁=1.5-0.5√3 c ≈0.634 c t₂=1.5+0.5√3 c ≈2.366 c
Step-by-step explanation:
h=-8t²+24t+4 h=16 feet t₂=?
[tex]16=-8t^2+24t+4\\\\16-16=-8t^2+24t+4-16\\\\0=-8t^2+24t-12\\[/tex]
Divide both parts of the equation by -4:
[tex]0=2t^2-6t+3[/tex]
Thus,
[tex]2t^2-6t+3=0[/tex]
a=2 b=-6 c=3
D=b²-4ac
D=(-6)²-4(2)(3)
D=36-24
D=12
√D=√12
√D=√(4*3)
√D=2√3
[tex]t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-(-6)б2\sqrt{3} }{2(2)} \\\\t=\frac{6б2\sqrt{3} }{4} \\\\t_1=1.5-0.5\sqrt{3}\ c \\\\t_2=1.5+0.5\sqrt{3}\ c[/tex]
A loan used for buying a home is called a mortgage. The Fortunato family is buying a $430,000 home. They are taking out a 30-year
mortgage at a rate of 8%.
a. Compute the monthly payment.
b. Find the total of all of the monthly payments for the 30 years.
c. What is the finance charge?
d. Which is greater, the interest or the original cost of the home?
Answer:
a. $3155.19
b. $1,135,868.40
c. $705,868.40
d. interest
Step-by-step explanation:
You want to find the monthly payment, total repaid, and finance charge on a 30-year mortgage for $430,000 at the rate of 8%.
a. PaymentYou can use a spreadsheet, financial calculator, app, or the amortization formula to find the payment amount.
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where P is the principal amount of the loan, r is the annual interest rate, and t is the number of years.
A = 430,000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 3155.19
The monthly payment is $3,155.19.
b. Total repaidThe total of the 12·30 = 360 payments is ...
360 · $3155.19 = $1,135,868.40
It will take about $1,135,868.40 to pay off the loan.
c. Finance chargeThe finance charge is the difference between the amount repaid and the original loan amount:
$1135868.40 -430000 = $705,868.40
The finance charge is $705,868.40.
d. ComparisonThe finance charge at $706k is considerably greater than the original cost of the home, $430k.
The finance charge is greater.
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The table represents a quadratic function C(t).
t C(t)
2 4
3 1
4 0
5 1
6 4
What is the equation of C(t)?
C(t) = −(x − 4)2
C(t) = (x − 4)2
C(t) = −x2 + 4
C(t) = x2 + 4
The quadratic equation of the function C(t) is; C(t)= (x - 4)²
How to find the quadratic function?
We are given the coordinates as;
When t = 2, C(t) = 4
When t = 3, C(t) = 1
When t = 4, C(t) = 0
When t = 5, C(t) = 1
When t = 6, C(t) = 4
The general formula formula for quadratic equation is;
y = ax² + bx + c
where c is y-intercept
We are given that x = 4, when y = 0. Thus, x = 4 is a root of the equation.
Put x = 2and y = 4 into the equation to get;
4a + 2b + c = 4 -----(1)
Put x = 3 and y = 1 into the equation to get;
9a + 3b + c = 1 -----(2)
Put x = 4 and y = 0 into the equation to get;
16a + 4b + c = 0 -----(3)
Using simultaneous equation solver gives;
a = 1, b = -8 and c = 16. Thus, our equation is;
y = x² - 8x + 16
By factorization;
y = x² - 4x - 4x + 16
y = x(x - 4) - 4(x - 4)
y = (x - 4)²
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What is m/1?
68°
49°
The points (d, 7) and (0, 10) fall on a line with a slope of 1/3. What is the value of d?
The value of missing coordinate d of the point (d, 7) in the line such that its slope is 1 / 3 is - 9.
What are the missing coordinates that satisfies a given slope?
In this problem we must determine the value of the missing coordinates of a point in a line such that its slope is 1 / 3. The slope of the line can be determined by means of the secant line formula:
m = Δy / Δx
Where:
Δx - Change in the x-coordinates.Δy - Change in the y-coordinates.If we know that (x₁, y₁) = (d, 7), (x₂, y₂) = (0, 10) and m = 1 / 3, then the missing coordinate is:
1 / 3 = (10 - 7) / (0 - d)
1 / 3 = - 3 / d
d = - 9
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leo has 2 less than twice the toys gen, z has. if Leo has 6 toys how many does zen have?
Answer:10
Step-by-step explanation:10 times two is twelve and minus 2 is ten.
I Need help on this problem! please!
The pairs of triangles that are congruent are;
A. Δ1 and Δ5
B. Δ1 and Δ2
C. Δ2 and Δ3
D. Δ3 and Δ5
E. Δ1 and Δ3
F. Δ3 and Δ4
G. Δ1 and Δ4
H. Δ4 and Δ5
What are congruent triangles?Congruent triangles are triangles that have all three sides and all three angles on each triangle having the same length and the same measure.
The congruent angles are indicated by the number of markings
The angles in the figures are;
Angle with one arc
Angles with two arcs marks
Angles with three arc marks
The congruent sides are indicated by one dash, and two dashes
Therefore;
Δ2 s congruent to Δ1 is congruent to Δ3 by Angle-Side-Angle rule of congruency
Similarly, we have;
Δ3 is congruent to Δ4 by Angle-Side-Angle congruency postulate
Therefore;
Triangle Δ2 is congruent to Δ3 by Angle-Side-Angle congruency postulate
From the diagram, the one arc, two arcs, and three arc angles form a linear pair, therefore;
Therefore, Δ4 is congruent to Δ5
Δ1 is congruent to Δ4
Δ2 is congruent to Δ5, therefore; Δ3 is congruent to Δ5
Similarly;
Δ1 is congruent to Δ3
Δ1 is congruent to Δ2, therefore , therefore, Δ1 is congruent to Δ5
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The graph displaying the prices of laptops at two different stores is shown. You are helping your friend Marcus decide how much money to spend on a laptop. Which of the following statements are true? Pls help
b,d and e option are correct
What is statement?
A statement, like "Pizza is tasty," is a declaration that something is true. In the fields of law, finance, and government, there are more types of statements. Every statement makes a claim or a point.
These statements are true:
The least Marcus would pay for a laptop from electro's is $500
Marcus can accept to pay about $700 for a laptop from electro's and $1500 for a laptop from bits and bytes.
The middle 50% of laptops from electro's are priced between $500 and $900.
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g(t)=3t+4 Find g(-3)
Simplify the following equation:
17/6 = -1 2/3 + x
Answer: x=27/6
Step-by-step explanation:
-1 2/3 = -5/3
17/6 = -5/3 + x
x = 17/6 + 5/3
x = 17/6 + 10/6
x = 27/6
Kelly recorded the following data while observing the temperature, in degrees Fahrenheit, of a chemical liquid cooling in her science class.
What is the rate of change for the temperature of this liquid?
The rate of change of temp w.r.t time is -1.875°F
What is rate of change?
The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time. When discussing momentum, the term "rate of change" (ROC) is frequently used. It is typically defined as the ratio of a change in one variable to a matching change in another; visually, the rate of change is represented by the slope of a line. The Greek letter delta () is frequently used to represent the ROC.
The term "rate of change" (ROC) describes the rate at which something changes over time.
Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace).
Time Temperature Difference
4 89.5 -
10 78.25 78.25 - 89.5 = -11.25
16 67.00 67 - 78.25 = -11.25
There is a common difference of -11.25 in each successive term.
Therefore, cooling of a chemical represents a linear function.
Rate of change of temp from 4 min to 10 min
=78.25 - 89.5 = -11.25
= -11.25/6
=-1.875
So, the rate of change of temp w.r.t time is -1.875°F
which means temperature is decreasing continuously when the time is increasing
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David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos
cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of
$78,50 and sold a total of 87 nachos and sodas combined. Which system of equations
represents this situation?
Answer:
x + y = 87
1.5x + 0.5y = 78.50
Step-by-step explanation:
Let x be the number of nachos sold and y be the number of sodas sold
x nachos will cost 1.50x dollars
y sodas will cost 0.50y dollars
So total sales = 1.5x + 0.5y and we know he made $78.50
so one equation is
1.5x + 0.5y = 78.50
Total sold = x + y and we know that this number is 87
So the second equation is
x + y = 87
Match the graph to the slope of that function
Choices:
-3/2
-1/2
2
-1/5
Also pls answer my other questions
For the first graph, slope = 1/5.
For the second graph, slope = -1/2.
For the third graph, slope = 2.
For the fourth graph, slope = 1.42.
What is the slope of the line?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the first graph, the coordinates will be (-15, 0) and (0, 3)
Slope = 3 - 0/0-(-15)
= 3/15
Slope = 1/5
For the second graph, the coordinates will be (0, 5) and (10, 0)
Slope = 0 - 5/10- 0
= -5/10
Slope = -1/2
For the third graph, the coordinates will be (2.5, 0) and (0, -5)
Slope = -5-0/0 - 2.5
= -5/-2.5
Slope = 2
For the fourth graph, the coordinates will be (-2.8, 0) and (0, 4)
Slope = 4 - 0/0 - (-2.8)
= 4/2.8
Slope = 1.42
Hence,
For the first graph, slope = 1/5.
For the second graph, slope = -1/2.
For the third graph, slope = 2.
For the fourth graph, slope = 1.42.
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how do i get an equation perpendicular to 5/4x + 2 that passes through the point (-6,2)
Answer: -4/5x - 22/5
Step-by-step explanation:
To find an equation of a line that is perpendicular to a given line and passes through a given point, we need to first find the slope of the given line. The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate of any two points on the line. For example, the slope of the line 5/4x + 2 is 5/4.
To find the equation of a line that is perpendicular to a line with slope m, we need to use the equation:
y - y1 = -1/m(x - x1)
where (x1, y1) is the given point that the line passes through. In this case, the given line has slope 5/4 and the given point is (-6,2), so the equation of the line perpendicular to 5/4x + 2 that passes through (-6,2) is:
y - 2 = -1/((5/4))(x + 6)
y - 2 = -4/5(x + 6)
y - 2 = -4/5x - 24/5
y = -4/5x - 22/5
Therefore, the equation of the line perpendicular to 5/4x + 2 that passes through (-6,2) is -4/5x - 22/5 (option "-4/5x - 22/5").
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