The value of p is 1 unit.
The distance between two points A( x₁, y₁) and B(x₂, y₂) is given by:
d= [tex]\sqrt{((y_{2}-y_{1})^{2}+({x_{2}-x_{1})^{2}) }[/tex]
Given that the distance between the origin and point P(-2, p-1) is 2p units.
i.e. 2p = [tex]\sqrt{(p-1-0)^2+(-2-0)^2}[/tex]
⇒ 2p = [tex]\sqrt{(p-1)^{2} +(-2)^2}[/tex]
⇒ 2p = [tex]\sqrt{p^2 + 1- 2p +4}[/tex]
⇒ 2p = [tex]\sqrt{p^2 - 2p +5}[/tex]
Squaring both sides, we get:
4p² = p² - 2p + 5
⇒ 3p² + 2p - 5 = 0
⇒ 3p² + 5p - 3p - 5 = 0
⇒ p (3p + 5) - 1 (3p + 5) = 0
⇒ (3p + 5) (p-1) = 0
p = 1 unit
Note: p ≠ -5/3 since distance cannot be negative.
Hence p = 1 unit.
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Integrate e^(1-3x) dx with upper limit 1 and lower limit-1
After getting the integration [tex]e^{(1-3x)} dx[/tex] with upper-limit 1 and lower-limit -1, we get [tex]\frac{-1}{3}[e^{-2}-e^{4}][/tex]
We know,
[tex]\int\limits^a_{b} {f(x)} \, dx[/tex] = [tex][F(x)]\limits^a_b[/tex]=F(a)- F(b).
Where,
a⇒Upper limit.
b⇒Lower limit,
f(x)⇒Any function of x.
F(x)⇒ [tex]\int {f(x)}[/tex] gives its antiderivative F(x).
Now here,
a is given as +1, and b is given as -1.
f(x)= [tex]e^{(1-3x)}[/tex].
Suppose, 1-3x =t.
∴ -3dx =dt.[By applying derivative rule]
Now,[tex]\int\limits e^{(1-3x)} dx[/tex]
=[tex]\int e^t.(\frac{-1}{3} ) dt[/tex]
=[tex]-\frac{1}{3} \int {e^t} dt[/tex].
=[tex]-\frac{e^t}{3}dt[/tex]
=[tex]\frac{1}{3}e^{(1-3x)}[/tex]
∴,[tex]\int\limits e^{(1-3x)} dx[/tex] =[tex]\frac{1}{3}e^{(1-3x)}[/tex].
So,[tex]\int\limits^1_{-1} e^{(1-3x)} \, dx[/tex]
=- [tex][\frac{1}{3}e^{(1-3x)}]^1_{-1}[/tex]
=[tex]\frac{-1}{3}[e^{(1-3)}-e^{(1+3)}][/tex]
=[tex]\frac{-1}{3}[e^{-2}-e^{4}][/tex]
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2. Amanda is having a party. She invited
36 people. She has tables that seat 5
people each. How many tables will
Amanda need for her guests?
Answer box:
8
6
5
7
Answer:
7................
Step-by-step explanation:
36 ÷ 5 = 7 So Yea
Answer:
8
Step-by-step explanation:
after seating 35 guests in 7 tables (5 guests per table), she will have 1 guest left
so she will require 8 tables in total to allow every guest a seat.
any number of tables below 8 is likely to result in guests unable to have a seat
note: if this is NOT a trick question, this answer might be sufficient
hope it helps
if tan theta =(√2)/3, what is the value of cos theta?
Answer: cos∅ = (3√11)/11
Step-by-step explanation:
See image
Answer:
cos∅ = 3/√11
Step-by-step explanation:
If tan ∅ = √(2)/3
We know the relationship:
1 + tan²∅ = sec²∅As given, putting the value to this equation we get:
1 + (√(2)/3)² = sec²∅1 + 2/9 = sec²∅11/9 = sec²∅sec∅ = √(11)/3(Taking square root on both sides)We know that sec∅ = 1/cos∅
Hence cos ∅ = 1/ sec∅
Putting the value of sec∅, we get:
cos∅ = 1/(√11)/3cos∅ = 3/√11This is an interesting method by using square relationship!
Find the area of a circle with a radius of 11 inches. Use pi 3.14 . The area of the circle is
____ approximately blanksquare inches. Enter only the number.
Answer: 381 square inches
Step-by-step explanation: The area of a circle with radius r is given by the formula:
A = πr^2
Substituting r = 11 and π = 3.14, we get:
A = 3.14(11)^2
A = 3.14(121)
A = 380.94 (rounded to two decimal places)
Therefore, the area of the circle is approximately 381 square inches.
If A is a matrix consisting of 4 rows and 5 columns, what must be the number of columns in the matrix B so that the product BA is defined?
Answer:
Step-by-step explanation:
For the product BA to be defined, the number of columns in matrix A must equal the number of rows in matrix B. Since matrix A has 5 columns, matrix B must have 4 rows. Therefore, the number of columns in matrix B must be 4.
Answer:
Matrix B must also be 5 columns
Step-by-step explanation:
For easy multiplication both matrix should have same number of columns
The ratio of Mary's saving to Janet's savings in January was 7:4. When Mary's saving was decreased by 40% in February and Janet's savings increased by half as much, their total savings in February became $2040. How much was Janet's savings in January?
Janet's savings in January is $800
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
Represent Mary's savings by x and Janet's savings by y
7/4 = x/y
40/100 × x = 40x/100 = 2x/5
New savings for Mary =
x -2x/5 = 5x - 2x)/5 = 3x/5
50/100 × y = y/2
New savings for Janet =
y + y/2 = 3y/2
3y/2 + 3x/5 = 2040
15y + 6x = 20400
7y = 4x
y = 4/7x
Substitute (4/7)x for y
15( 4/7) x + 6x = 20400
(60/7 )x + 6x = 20400
60x + 42x = 142800
102x = 142800
x = 142800/102
x = $ 1400
y = 4/7 × 1400
y = $800
Therefore, the savings for Janet in January is $800.
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Please help me:
4x+8=20
Solve for x
We can isolate the x term by subtracting 8 from both sides of the equation, giving us 4x=12. dividing by 4 on each side gives us x=3.
So, our answer is x=3.
Step-by-step explanation:
[tex]4x + 8 = 20 \\ 4x = 20 - 8 \\ 4x = 12 \\ x = \frac{12}{4 \\ } \\ x = 3ans [/tex]
hope that it helps
What is the range of the function shown on the graph
Answer:
-2<=y<=-7
Step-by-step explanation:
12
10-
8
6
4
2
5-4-3 42
-4
&+
-0-
-10-
R
160
23456
964
Which statement is true regarding the functions on the
graph?
Of(-3) = g(-4)
Of(-4)= g(-3)
Of(-3) = g(-3)
Of(-4)= g(-4)
The division by zero is not possible and f/g division is undefined, {20, 6, -4, 39} f /g is undefined (because of division by zero)
The scope and image of a given function and its operations.
f = {(2,4), (5,6), (8,-1), (10,3)}
g = {(2,5), (7,1) , ( 8,4), (10,13), (11,5)}
a) f - g (subtraction):
To find the domain of f - g, find the common element in the domain of f must be considered.
In this case the domains of both f and g are {2, 5, 8, 10}.
Therefore, the domain of f - g is {2, 5, 8, 10}.
Now let's compute the image of f - g using the subtraction operation:
f - g = {(2, 4-5), (5, 6-1), (8, -1-4 ), (10 , 3 -13)}
= {(2, -1), (5, 5), (8, -5), (10, -10)}
Images from f to g are {- 1, 5, -5, -10}.
b) f + g (addition):
As in the previous case, the domain of f + g is {2, 5, 8, 10}.
Now let's compute the image of f + g using the addition operation:
f + g = {(2, 4+5), (5, 6+1), (8, -1+4 ), (10 , 3 +13)}
= {(2, 9), (5, 7), (8, 3), (10, 16)}
f + g image is {9, 7, 3, 16 } .
c) f * g (multiplication):
Again, the domain of f * g is {2, 5, 8, 10}.
Now let's use the multiplication operation to compute the f * g image:
f * g = {(2, 45), (5, 61), (8, -14), (10, 313 )}
= { ( 2, 20), (5, 6), (8, -4), (10, 39)}
The f * g image is {20, 6, -4, 39}.
Division operations must ensure that the denominator is not zero. Looking at the function g, we can see that the x value of 7 has no corresponding y value in g.
Therefore, division by zero is not possible and f/g division is undefined.
region of f - g, f + g, f * g = {2, 5, 8, 10}
region of f / g is undefined (because of division by zero) of f Images - g = {-1, 5, -5, -10} f + g
images in {9, 7, 3, 16} f * g
images in {20, 6, -4, 39} f /g is undefined (because of division by zero).
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PLS HELP WILL MAKE U BRAINLIEST
The equation of the line given the table values, we need to identify the slope and y-intercept. However, with only two y-values provided (13 and 18),
For example, if the two points on the line were (x1, 13) and (x2, 18), we could calculate the slope using the formula m = (y2 - y1) / (x2 - x1). With the slope and one point, we could determine the equation of the line in slope-intercept form.
But without the x-values or any additional information, we cannot determine the equation of the line accurately. We would need more data points or some other form of information to find the equation of the line.
To determine the equation of the line given the table values, we need to identify the slope and y-intercept. However, with only two y-values provided (13 and 18), it is not possible to accurately determine the equation of the line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. In this case, we cannot determine the slope or the y-intercept with the given information.
To find the equation of a line, we typically require at least two points or additional information such as the slope. With only two y-values provided, it is insufficient to determine the equation of the line accurately.
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PLEASE ANSWER AND FILL IN THE BOX if needed
The true statement is that (d) the system has no solution
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix
In the augmented matrix, we have
Rows = 2
Columns = 4
This means that
There are 2 equations in the system and there are 3 variables
The general rule is that
The number of variables must be equal to or less than the number of equations
Hence, there is no solution in the system
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Carl works at a veterinarian office. The first dog he sees is a Chihuahua who weighs 3 kilograms. The second dog he sees is a Great Dane who weighs 27 times as much as the Chihuahua. How much does the Great Dane weigh?
Carl works at a veterinarian office. The first dog he sees is a Chihuahua who weighs 3 kilograms. The second dog he sees is a Great Dane who weighs 27 times as much as the Chihuahua. The Great Dane weighs 81 kilograms.
Let's denote the weight of the Chihuahua as "x" kilograms. We know that the Great Dane weighs 27 times as much as the Chihuahua. Therefore, the weight of the Great Dane can be expressed as 27x.
Given that the weight of the Chihuahua is 3 kilograms, we can substitute this value into the equation:
27x = 3
To find the weight of the Great Dane, we need to solve for x:
x = 3 / 27
x = 1 / 9
Therefore, the weight of the Chihuahua is 1/9 kilograms.
Now, we can calculate the weight of the Great Dane by multiplying the weight of the Chihuahua by 27:
Weight of the Great Dane = 27 * (1/9) = 27/9 = 3 kilograms
So, the Great Dane weighs 81 kilograms, which is 27 times the weight of the Chihuahua.
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Two wires are attached to a pole and create similar triangles with the ground. The longer wire is attached to the ground 32 feet from
the base of the pole and the shorter wire is attached to the ground 16 feet from the base of the pole.
If the cosine of the angle formed by the shorter wire and the ground is 8/41, what is the length of the longer wire?
Please help im so confused!
The length of the longer wire is 82 feet.
Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.
We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.
In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:
cos(θ) = adjacent/hypotenuse = 16/L
Given that cos(θ) = 8/41, we can substitute this value into the equation:
8/41 = 16/L
To solve for L, we can cross-multiply and solve for L:
8L = 41 * 16
L = (41 * 16)/8
L = 82
Therefore, the length of the longer wire is 82 feet.
In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.
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which expression is equivalent to the given expression assume the denominatior does not equal zero 14x4y5/7xry2
The expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.
This expression can be simplified as follows: Simplifying the expression 14x^4y^5/7xr^y^2First, we can write the given expression as shown below:14 x 4 * y^5 / (7 * x * r * y^2) = 2 * 7 * x^3 * y^3 / 7 * r * x * y^2 = 2x^2y/rr.
Now, the numerator and the denominator have x, y, and r, and we can cancel them out as shown below:2x^2y/rr = 2xy * x * x / rr * y * y / y * y = 2x^3y^3/r.
Therefore, the expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.
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find the inverse of each equation
The inverse of the equation is determined as [tex]y = \log_{6}(-3x)[/tex].
option D is the correct answer.
What is the inverse of the equation?The inverse of the equation is calculated by applying the following method;
The given equation;
y = - 6ˣ/3
The inverse of the equation is calculated as;
multiply through by 3
[tex]-3x = 6^y[/tex]
Take the logarithm of both sides of the equation with base -6:
[tex]\log_{6}(-3x) = y[/tex]
Finally, replace y with x to obtain the inverse equation as follows;
[tex]y = \log_{6}(-3x)[/tex]
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Una pelota es lanzada horizontalmente desde la ventana de un edificio con una velocidad inicial de 10 m/s y cae al suelo después de 5 s. Determinar:
The window is 125 meters high and the distance that the ball lands from the base of the building is 50 meters.
How to find the height of the window?The height of the window can be found by using the formula for the distance travelled under constant acceleration, which in this case is due to gravity.
The formula is: d = ut + 0.5at ²
Since the ball was thrown horizontally, the initial vertical velocity (u) is 0. Substituting these values into the equation gives:
d = 05 + 0.510 * (5 ² )
= 0 + 0.51025
= 125 meters
The horizontal distance the ball travels can be found by multiplying the horizontal speed by the time.
So, the horizontal distance is:
d = vt = 10 x 5
= 50 meters
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The full question is:
Una pelota es lanzada horizontalmente desde una ventana con una velocidad inicial que tiene una magnitud de 10 m/s y cae al suelo después de 5 segundos
¿a que altura se encuentra la ventana?
¿a que distancia cae la pelota de la base del edificio?
Which translates to:
A ball is thrown horizontally from a window with an initial velocity that has a magnitude of 10 m/s and falls to the ground after 5 seconds.
How high is the window?
How far does the ball land from the base of the building?
the volume of a spherical ball is 5000 cm3.What is the radius of the ball correct to one decimal place?
The radius of the spherical ball, correct to one decimal place, is approximately 8.5 cm.
To find the radius of a spherical ball when the volume is given, we can use the formula for the volume of a sphere:
[tex]Volume = (4/3) * π * r^3[/tex]
Given that the volume of the ball is 5000 cm^3, we can set up the equation as follows:
[tex]5000 = (4/3) * π * r^3[/tex]
To find the radius, we need to isolate it in the equation. Let's solve for r step by step:
1. Divide both sides of the equation by (4/3) * π to isolate r^3:
[tex]r^3 = 5000 / [(4/3) * π][/tex]
2. Simplify the right side of the equation:
r^3 = 3750 / π
3. Take the cube root of both sides to solve for r:
r = (3750 / π)^(1/3)
Using a calculator, we can approximate the value of r:
r ≈ 8.532
Therefore, the radius of the spherical ball, correct to one decimal place, is approximately 8.5 cm.
It's important to note that the value of π used in the calculation should be accurate to the required level of precision. In this case, we have used the standard value of π (approximately 3.14159).
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A car that averages 22 miles per gallon emits 4.3 metric tons of carbon dioxide per year. A passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. How much less carbon dioxide does a commuter who takes a bus emit in a year compared to a commuter who drives everyday?
13.5 metric tons
2.1 metric tons
5.1 metric tons
3.99 metric tons
The answer is 3.99 metric tons.
To calculate the difference in carbon dioxide emissions between a commuter who takes a bus and one who drives a car every day, we need to compare the emissions of each mode of transportation per person.
The car averages 22 miles per gallon, which means it emits 4.3 metric tons of carbon dioxide per year. However, we don't know the number of passengers in the car.
The passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. To find the emissions per person, we divide the total emissions by the number of passengers. In this case, each person on the bus emits 9.2 / 30 = 0.3067 metric tons of carbon dioxide per year.
To determine the difference in emissions, we subtract the emissions per person for the bus from the emissions per person for the car. Therefore, the difference is 4.3 - 0.3067 = 3.9933 metric tons of carbon dioxide per year.
Rounding this value to two decimal places, we get 3.99 metric tons.
Therefore, the answer is 3.99 metric tons.
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How many times smaller is 1.2 x 10^6 than 1.47 x 10^7?
Answer:
Step-by-step explanation:
To determine how many times smaller 1.2 x 10^6 is than 1.47 x 10^7, we need to divide the larger number by the smaller number:
1.47 x 10^7 / 1.2 x 10^6 = 12.25
Therefore, 1.2 x 10^6 is approximately 12.25 times smaller than 1.47 x 10^7.
To confirm this result, we can also calculate the difference between the two numbers:
1.47 x 10^7 - 1.2 x 10^6 = 1.35 x 10^7
So 1.2 x 10^6 is approximately 1/12.25 = 0.0816 times as large as 1.47 x 10^7.
I NEED HELP ASAP PLSSS
The areas under the curve of the z-scores are 0.5098, 0.4357 and 0.1254
Calculating the areas under the curve of the z-scoresFrom the question, we have the following parameters that can be used in our computation:
(a) z = -0.69 to 0.69
This is represented as
Area = P(-069 < z < 069)
Using a graphing calculator, we have
Area = 0.5098
(b) z = -1.52 to 0
This is represented as
Area = P(-1.52 < z < 0)
Using a graphing calculator, we have
Area = 0.4357
(c) z = -0.75 to -0.38
This is represented as
Area = P(-1.52 < z < -0.38)
Using a graphing calculator, we have
Area = 0.1254
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Ordered: 1 L hyperalimentation solution for 1 hour
Drop factor: 15 gtt/mL
Flow rate:
gtt/min
The flow rate for the ordered 1 L hyperalimentation solution for 1 hour, with a drop factor of 15 gtt/mL, is approximately 250 gtt/min.
To calculate the flow rate in gtt/min, we need to use the information provided about the ordered volume, drop factor, and time. Here are the steps to determine the flow rate:
Step 1: Convert the ordered volume to mL if necessary. In this case, 1 liter (L) is equivalent to 1000 mL.
Step 2: Determine the total number of drops needed for the ordered volume by multiplying the volume in mL by the drop factor.
Total drops = Volume (mL) x Drop factor (gtt/mL)
Total drops = 1000 mL x 15 gtt/mL
Total drops = 15000 gtt
Step 3: Divide the total number of drops by the time in minutes to calculate the flow rate in gtt/min.
Flow rate (gtt/min) = Total drops / Time (min)
Flow rate (gtt/min) = 15000 gtt / 60 min
Flow rate (gtt/min) ≈ 250 gtt/min
Therefore, the flow rate for the ordered 1 L hyperalimentation solution for 1 hour, with a drop factor of 15 gtt/mL, is approximately 250 gtt/min.
It's important to note that this calculation assumes a constant flow rate and does not take into account any adjustments or interruptions that may occur during the infusion. The flow rate may vary based on factors such as the specific administration set used, the viscosity of the solution, and any specific instructions or guidelines provided by medical professionals.
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How do I solve this question
pls help me with math i’ll give uu brainlist
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(10') For the following probability function,
x = 2, y = 3
= 3, y = 2
x = -3, y = -2
x = -2, y = -3
= 17, y = 19
otherwise.
PX,Y (x, y) =
1/5
1/5
1/5
1/5
1/5
0
Calculate the following probabilities, 1. px; 2. py:
3. P(Y>X); 4. P(Y=X); 5. P(XY<0).
P(x) = 1
P(y) = 1
P(Y > X) = 2/5
P(Y = X) = 1/5
P(XY < 0) = 4/5
To calculate the requested probabilities based on the given probability function PX,Y (x, y), let's evaluate each one:
P(x): To calculate P(x), we need to sum up the probabilities for all y-values associated with each x-value:
P(x = 2) = 1/5
P(x = 3) = 1/5
P(x = -3) = 1/5
P(x = -2) = 1/5
P(x = 17) = 1/5
Therefore, P(x) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.
P(y): Similarly, to calculate P(y), we need to sum up the probabilities for all x-values associated with each y-value:
P(y = 3) = 1/5
P(y = 2) = 1/5
P(y = -2) = 1/5
P(y = -3) = 1/5
P(y = 19) = 1/5
Thus, P(y) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1.
P(Y > X): We need to calculate the probabilities where Y is greater than X. Looking at the given probability function, we can see that there are two cases where Y is greater than X: (x = -3, y = -2) and (x = -2, y = -3), both with a probability of 1/5. Therefore, P(Y > X) = 2/5.
P(Y = X): We need to calculate the probability where Y is equal to X. From the given probability function, there is only one case where Y is equal to X: (x = 17, y = 19) with a probability of 1/5. Therefore, P(Y = X) = 1/5.
P(XY < 0): We need to calculate the probability where the product of X and Y is less than 0. Looking at the given probability function, we can see that there are four cases where the product of X and Y is less than 0: (x = 2, y = -3), (x = 3, y = -2), (x = -3, y = 2), and (x = -2, y = 3), each with a probability of 1/5. Therefore, P(XY < 0) = 4/5.
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your club awards one student a $2000 scholarship, and each member contributes an equal amount. Your contribution y depends on the number of members x. Write an inverse variation equation that represents this situation
Answer:
The inverse variation equation that represents this situation is:
xy = k
where x is the number of members, y is the contribution made by each member, and k is a constant of proportionality.
Since each member contributes an equal amount, we can let y be the contribution made by each member. If there are x members, then the total amount contributed is 2000 + xy. Since this total amount is divided equally among the x members, we can set y equal to the total amount divided by x, which gives:
y = (2000 + xy) / x
Multiplying both sides by x, we get:
xy = 2000 + xy
Subtracting xy from both sides, we get:
0 = 2000
This is a contradiction, which means that our assumption that y depends on x is incorrect. Therefore, we cannot write an inverse variation equation that represents this situation.
hope it helps you
Parallelograms and Proofs
Question 7 of 10
Which of the following are necessary when proving that the opposite angles
of a parallelogram are congruent? Check all that apply.
A. Opposite sides are perpendicular.
B. Opposite sides are congruent.
C. Corresponding parts of similar triangles are similar.
D. Corresponding parts of congruent triangles are congruent.
SUBMIT
When proving that the opposite angles of a parallelogram are congruent, the proofs are;
B. Opposite sides are congruent.
D. Corresponding parts of congruent triangles are congruent.
How to determine the statementsThe properties of a parallelogram are;
Opposite sides are parallelOpposite sides are congruentOpposite angles are congruentSame-Side interior angles (consecutive angles) are supplementaryEach diagonal of a parallelogram separates it into two congruent trianglesThe diagonals of a parallelogram bisect each other.Learn more about parallelograms at: https://brainly.com/question/10744696
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3. In ∆ JAM, which of the following statement is always TRUE?
The option that shows the missing angles in the triangle is:
Option C: m∠1 < m∠4
How to identify the missing angle?We know that the sum of angles in a triangle is 180 degrees.
Therefore looking at the given triangle, we can say that:
m∠1 + m∠2 + m∠3 = 180°
We also know that the sum of angles on a straight line is 180 degrees and as such we can say that:
m∠3 + m∠4 = 180°
By substitution we can say that:
m∠4 = m∠1 + m∠2
Thus:
m∠1 < m∠4
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The missing options are:
m∠1 > m∠4
m∠2 > m∠4
m∠1 < m∠4
m∠3 = m∠4
Question 5 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. More than 1 solution
B. x = 5, y = -2
C. No solution
D. x = -2, y = 5
y+x=3
y-2x=-12
The solution to the system of equations is x = 5 and y = -2. Thus, the correct answer is B: x = 5, y = -2.
To find the solution to the system of equations, we can use the graphing function on a calculator. By graphing both equations and examining their intersection point, we can determine the solution.
The system of equations is as follows:
1) y + x = 3
2) y - 2x = -12
First, we rearrange equation 1) to solve for y:
y = 3 - x
Now, we can graph both equations on a graphing calculator or software. By plotting the lines representing the equations, we can see where they intersect, if at all.
Upon graphing, we observe that the two lines intersect at the point (5, -2). This means that the x-coordinate of the intersection is 5, and the y-coordinate is -2.
Therefore, the solution to the system of equations is x = 5 and y = -2. Thus, the correct answer is B: x = 5, y = -2.
It is important to note that in this case, the graphing method yields a single point of intersection, indicating a unique solution. If the two lines were parallel and did not intersect, there would be no solution (option C). Alternatively, if the two lines were coincident, overlapping each other completely, there would be infinitely many solutions (option A). However, in this scenario, the graph confirms that the system has a unique solution at (5, -2).
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The graph shows two lines, M and N.
A coordinate plane is shown with two lines graphs. Line M has a slope of 1 and passes through the y axis at negative 2. Line N has a slope of 1 and passes through the y axis at negative 2.
How many solutions are there for the pair of equations for lines M and N? Explain your answer.
Line M and line N are the same line, since they have the same slope and y-intercept. Therefore, there are infinitely many solutions for the pair of equations, since every point on the line satisfies both equations.
Solve the puzzle and add the colors
Answer:
43
Step-by-step explanation:
Green: 9 - 2(-3) = 9 + 6 = 15
Red: -2(-3) + 4 = 6 + 4 = 10
Dark blue: 7x + 5 = 19
7x = 19 - 5 = 14
x = 14/7 = 2
Light blue: 6x + 3 = 21
6x = 21 - 3 = 18
x = 18/6 = 3
Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43
