The system of equations are y = ( 5/4 )x and y = 6 - 3x where the value of x and y are 1.4117 and 1.765 respectively
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first equation be P
y = ( 5/4 )x be equation (1)
Let the second equation be Q
y = 6 - 3x be equation (2)
Substituting the values in the equation , we get
( 5/4 )x = 6 - 3x
Adding 3x on both sides of the equation , we get
6 = ( 5/4 + 3 ) x
( 17/4 )x = 6
Multiply by 4 on both sides of the equation , we get
17x = 24
Divide by 17 on both sides of the equation , we get
x = 24/17 = 1.4117
Substitute the value of x in equation (1) , we get
y = ( 5/4 ) ( 24/17 )
y = ( 30/17 )
y = 1.765
Hence , the equations are solved and the value of x and y are 24/17 and 30/17 respectively
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Teacher's name Height with the heels Height without the heels
Ms. Mathey 190 cm 182.4 cm
Mrs. Meansy 162.5 cm 156 cm
Ms. Cool 140 cm 134.4 cm
Miss Petite cm 155.1 cm
Ms. Lora cm
159.8 cm
The required complete table of heights of teachers is shown in the image attached.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To calculate the height without heels, we need to subtract 4% of the height with heels from the height with heels. This can be done by multiplying the height with heels by 0.96 (which is equivalent to subtracting 4%):
Height without the heels = Height with the heels x 0.96
Using this formula, we can fill in the chart for each teacher.
Thus, the required complete table has been shown in the image attached.
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A zookeeper is preparing to care for snakes in an exhibit. For every
feeding, she needs three mice and an additional two mice for each
snake. How many mice are needed if the number of the snakes is:
A- 10
B-6
C- x
The number of mice needed is given as follows:
a) 10 snakes: 23 mice.
b) 6 snakes: 15 mice.
c) x snakes: (3 + 2x) mice.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For every feeding, she needs three mice and an additional two mice for each snake, hence the slope and the intercept of the function are given as follows:
m = 2, b = 3.
The function is then defined as follows:
y = 2x + 3.
For 10 snakes, the number of mice is given as follows:
y = 2(10) + 3
y = 23 mice.
For 6 snakes, the number of mice is given as follows:
y = 2(6) + 3
y = 15 mice.
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14. 15x5y
= -20
-3x + y = 4
Answer:
The answer is: y=4+3x
Step-by-step explanation:
I know this because I believe we are solving for the system of equations or solving by the system of subtraction.
I will say I am not completely sure this is right but I hope I helped out a little :)
what is 65kgs in lbs ?
Since, 01 kilogram is approximately equal to 2.2046226218 lbs.
Therefore, 65 Kilogram is 143.3 lbs.
Pound:
Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.
Kilogram:
The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.
According to the Question:
To find how many pounds are in kilograms, you can convert kg to pounds using this formula:
X(lb) = Y(kg) / 0.45359237
Now,
Converting 65 kg to lbs:
To convert 65 kg to pounds:
⇒ X(lbs) = 65(kg) / 0.45359237
⇒ 143.3005 lbs
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Can someone pls help me
Answer:10 or 25
Step-by-step explanation:
just add both or times them
5+5 or 5x5
A gopher is in a hole that is 12% in. below the surface of the ground. It then
digs 2½ in. deeper. What is the gopher's new elevation relative to the surface
of the ground?
-14%
-10%
10%
14%
The gopher’s new elevation relative to the surface of the ground will be
13¹/₄ inches.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that a gopher is in a hole that is 6¹/₄ in. below the surface of the ground. and, Then digs 7¹/₂ in. deeper.
The gopher’s new elevation relative to the surface of the ground will be calculated as;
⇒ 6¹/₄ + 7¹/₂
⇒ 25/4 + 15/2
Make denominators the same as;
⇒ 25/4 + 30/4
⇒ (25 + 30) / 4
⇒ 55 / 4
⇒ 13¹/₄ inches.
Thus, the gopher’s new elevation relative to the surface of the ground will be 13¹/₄ inches.
The complete question is given below,
A gopher is in a hole that is 6 1/4 in. below the surface of the ground. It then digs 7 1/2 in. deeper. What is the gopher’s new elevation relative to the surface of the ground? Show your work.
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Special Triangle Segments......
3. Find the value of the variable given the triangles are similar. Answer the additional questions. Show all work. Name the property you used in your problem.
The value of x is 20 and the property is similar triangle
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Since ∆ ADC and IJH are similar, the ratio of their corresponding sides are equal.
Therefore,1.2/12 = 2/x
1.2x= 12×2
x = 24/1.2
x = 20
Therefore the value of x is 20
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction barts).
In the given diagram, ARST is a right triangle with MPL ST. Segment RT is divided into 5 equal parts.
R(4.3,7.4)
T(-8.5,-2.2)
M
S(4.3,-2.2)
The coordinates of point O are (
), and the coordinates of point M are (
The coordinates of P are (-0.82, 3.56).
The coordinates of M are (-2.1, -2.2).
What is a midpoint of a line segment?The midpoint of a line segment is written as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) are the coordinates of the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
R = (4.3, 7.4)
T= (-8.5, -2.2)
S = (4.3, -2.2)
Segment RT is divided into 5 equal parts.
So,
TP : PR = 3 : 2 = m : n
The coordinates of P.
T= (-8.5, -2.2) = (a, b)
R = (4.3, 7.4) = (c, d)
x = [tex]\frac{mc + na}{m + n}[/tex]
x = [tex]\frac{3\times4.3 + 2\times-8.50}{5}[/tex]
x = [tex]\frac{12.9 - 17}{5}[/tex]
x = [tex]\frac{-4.1}{5}[/tex]
x = -0.82
And,
y = [tex]\frac{md + nb}{m + n}[/tex]
y = [tex]\frac{3\times7.4 + 2\times-2.2}{5}[/tex]
y = [tex]\frac{22.2 - 4.4}{5}[/tex]
y = 3.56
The coordinates of P are (-0.82, 3.56).
Now,
T= (-8.5, -2.2)
S = (4.3, -2.2)
M is the midpoint of TS.
So,
M = (x, y)
x = [tex]\frac{(4.3 - 8.5)}{2}[/tex] = [tex]\frac{x-4.2}{2}[/tex] = -2.1
y = [tex]\frac{-2.2 - 2.2}{2}[/tex] = [tex]\frac{-4.4}{2}[/tex] = -2.2
M = (x, y) = (-2.1, -2.2)
Thus,
The coordinates of P = (-0.82, 3.56).
The coordinates of M = (-2.1, -2.2).
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Answer:
The answer is (-3.38,1.64),(-0.82,-2.2)
Step-by-step explanation:
I just got it right on the test
how to convert m/s to rad/s?
By using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).
Using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).
The equation reads: Radius divided by linear velocity gives you the angular velocity (). (r) where R is in metres, V is in m/s, and is in rad/s.
Direct conversion from m/s to rad/s is not possible if the radius is omitted. The aforementioned formula can be used to determine the missing value and then convert m/s to rad/s if you know the radius or the angular velocity. You can use the formula to determine the angular velocity in rad/s, for instance, if you know the linear velocity v in m/s and the radius r in metres.
ω = v / r
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A ping-pong ball rolls forward 6 meters, and bounces backward 3 meters. It traveled a total distance of:.
The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.
Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.
When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.
When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.
The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as
=> d = d1 + d2 = 6 + (-3) = 3 meters.
In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.
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Which expression is equivalent to 10+5 to the fourth power?
The expression [tex](3 \times 5)^4[/tex] is equivalent to 10+5 to the fourth power.
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
We need to find the expression into an equivalent form 10+5 to the fourth power
Therefore,
This expression 10+5 to the fourth power could also be given as;
10 + 5 = 15
That is [tex]15^4[/tex]
We can also write as;
[tex](3 \times 5)^4[/tex]
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can u help me with I J and L please!!!
ABC PON 30 36 12 8 20 24 determine if the following triangles are similar?
Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12
What is Properties of Similar Triangles?The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.
here, we have,
Given that ΔABC and ΔDEF are similar triangles, therefore:
Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.
Let, x, y, and z be the sides of ΔDEF.
Let z = 18
Thus:
a/x = b/y = c/z
Substitute
6/x = 8/y = 12/18
Find x using 6/x = 12/18:
6/x = 12/18
Cross multiply
x = 18*6/ 12
x = 9
Find x using 8/y = 12/18:
8/y = 12/18
Cross multiply
x = 18*8/12
x = 12
Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12
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In a perfectly symmetrical distribution:
a. the range equals the interquartile range.
b. the interquartile range equals the mean.
c. the median equals the mean.
d. the variance equals the standard deviation.
In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. So , the correct option is C.
In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. The mean and median are both measures of the central tendency of a distribution and in a symmetrical distribution, they are the same value.
Option (a) is false because the range is the difference between the largest and smallest values in a distribution, whereas the interquartile range is the difference between the first quartile (25th percentile) and the third quartile (75th percentile), which are measures of variability.
Option (b) is false because the interquartile range is always smaller than the mean in any distribution, symmetrical or not.
Option (d) is false because in a symmetrical distribution, the variance and standard deviation may be equal, but this is not always the case.
So , the correct option is c.
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What is the area of the shape for the quilt block? ninety-four and one half in2 one hundred sixty-six and one half in2 189 in2 333 in2
The area of the shape for the quilt block is 166.5 in²
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape
Given that, a quilt has blocks of design on it, we need to find the area of the block,
To find the area of the block = sum of the areas of the right triangle and the rectangle,
Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²
Hence, the area of the shape for the quilt block is 166.5 in²
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The figure is unavailable is the question is solved for the figure attached
What are the measures of angles Q and R?
187/17 is 11, so x = 11. Substituting 11 in for x gives you 93 for the measure of angle Q and 87 for the measure of angle R.
Mr. Lee's house has two stories and an attic. The first floor is
9½ feet high, the second floor is 8 3/4 feet high, and the entire
house is 24 7/12 feet high. What is the height of the attic?
The height of the attic in Mr. Lee's house is 6 1/3
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Mr. Lee's house has two stories and an attic. Therefore:
Height of entire house = height of first floor + height of second floor + height of attic
The first floor is 9½ feet high, the second floor is 8 3/4 feet high, and the entire house is 24 7/12 feet high
9 1/2 = 19/2; 8 3/4 = 27/4; 24 7/12 = 295/12. Let x represent the height of the attic. Substituting:
x + 19/2 + 35/4 = 295/12
x = 19/3
x = 6 1/3
The height of the attic is 6 1/3
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A video game randomly chooses your
car color and type. The probability of
getting a red car is 0.25, and the probability of getting a convertible is 0.40.
Event A = You get a red car.
Event B = You get a convertible.
B A and B are independent events if
• A. The probability of getting a red car or a convertible is 0.10.
• B. The probability of getting a red convertible is 0.
•
C. The probability of getting a red convertible is 0.10.
• D. The probability of getting a red car or a convertible is 0.65.
A and B are independent events if, the probability of getting a red convertible is 0.10
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, in a video game, the probability of getting a red car is 0.25 (event A), and the probability of getting a convertible is 0.40 (event B).
We need to identify the condition for events A and event B being independent events.
We know that,
The events in probability two are independent if event one does not affect the other one.
The formula for independent events =
P(A∩B) = P(A) x P(B).
So,
P(A) = 0.25 and P(B) = 0.40
P(A∩B) = P(A)xP(B)
= 0.25 x 0.4
= 0.10
Hence, the events A and B are independent events if, the probability of getting a red convertible is 0.10
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I think I have the answer, but it keeps saying I'm incorrect.
Answer:
B.
D.
Step-by-step explanation:
B is actually 141, not 14.1
(204 plus 98) is more than 250.7
This means that multiplying it by 8.3 would not even make it near 250.7
It would actually be 2506.6
Answer: Your answers are B and D.
stuart sold 8 couches and 11 armchairs at his furniture store yesterday he made a 10$ loss on each couch and a 12$ profit on each armchair what was his overall profit or loss
The overall profit of what Stuart sold is 52 dollars.
How to find loss and profit ?Stuart sold 8 couches and 11 armchairs at his furniture store yesterday and he made a 10 dollars loss on each couch and a 12 dollars profit on each armchair.
Therefore, the overall profit or loss can be calculated as follows:
Total loss on the couch = 8 × 10 = 80 dollars
Total profit on the armchairs = 11 × 12 = 132 dollars
Therefore,
Overall profits = 132 - 80
Overall profits = 52 dollars
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True or false a square is a parallelogram
True (but a parallelogram is not always a square). This is because a parallelogram is a quadrilateral with 2 pairs of parallel sides, and a square fits the requirements.
How to find a vector equation and parametric equations for the line segment that joins p to q?
The vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.
We have P(0, -1, 1), Q(1/2, 1/3, 1/4)
We have to find a vector equation and parametric equations for the line segment that joins P to Q.
Vector equation of a line segment joining the points with position vectors r0 and r1 is given by
r =(1 - t)r0 + tr1
Where, t ∈ [0, 1]
Here, r0 = (0, -1, 1) and r1 = (1/2, 1/3, 1/4)
So, r(t) = (1 - t)(0, -1, 1) + t(1/2, 1/3, 1/4)
r(t) = [((1 - t)(0) -1(1 - t) + 1(1 - t)] + [t/2, t/3, t/4]
r(t) = [0, (t - 1), (1 - t)] + [t/2, t/3, t/4]
On simplification,
r(t) = [(t/2 + 0), (t + t/3 - 1), (1 - t + t/4)]
r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)]
Where, t ∈ [0,1]
The parametric equations for the line segment are
x = t/2, y = -1 + 4t/3, z = 1 - 3t/4
Where, t ∈ [0, 1]
Therefore, the vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.
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The given question is incomplete, complete question is:
Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4).
What is the length of segment AC
(Please explain how you got your answer)
The length of the segment AC is 40 units
How to determine the length of the segment ACFrom the question, we have the following parameters that can be used in our computation:
The quadrilateral ABCD is a rhombus
The diagonals of rhombus bisect each other
Using the above as a guide, we have the following:
AC = 2 * EC
Substitute the known values in the above equation, so, we have the following representation
AC = 2 * 20
Evaluate
AC = 40
Hence, the length is 40 uints
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A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall, then how long will the maple tree's shadow be?
The length of the shadow of the maple tree will be 15 meters.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall.
Let 'S' be the shadow of the maple tree. Then the equation is given as,
16 / 30 = 8 / S
0.533 = 8 / S
S = 8 / 0.533
S = 15 meters
The length of the shadow of the maple tree will be 15 meters.
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Solve 1/11 divided by 4
a
one forty fourth
b
44
c
four forty fourths
d
one fifteenth
Answer:
a ) one by forty fourth
Step-by-step explanation:
1/11 ÷ 4
= 1/11 x 1/4
= 1/44
therefore, the answer is one by forty fourth
Hope it's helpful..
Solve for x. -6 + 14 < -28 AND 3x + 28 <25
A) x < - 1 or x >7
B) -1 < x < 7
C) x < 7
D) There are no solutions.
E) All values of x are solutions
The option representing the solution of the inequality is given as follows:
D) There are no solutions.
How to solve the inequality?The inequality for this problem is defined as follows:
-6x + 14 < -28 and 3x + 28 < 25.
The and operation means that we must solve each inequality, and then obtain the intersection of the two solutions.
The solution to the first inequality is given as follows:
-6x + 14 < -28
6x - 14 > 28
6x > 42
x > 7.
The solution to the second inequality is given as follows:
3x + 28 < 25.
3x < -3
x < -1.
There is no intersection between x > 7 and x < -1, hence the system has no solutions.
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how to calculating rf values?
Answer:
Step-by-step explanation:
Rf values (retention factor values) are used in thin layer chromatography (TLC) to measure the separation of components in a mixture. They are calculated as follows:
Rf = (distance traveled by the solute) / (distance traveled by the solvent)
The distance traveled by the solute is measured from the origin (the spot where the sample was applied) to the final position of the solute on the TLC plate. The distance traveled by the solvent is measured from the origin to the solvent front (the point where the solvent stops moving up the plate).
It is important to note that Rf values are unique to each solute and are dependent on the solvent used, the type of TLC plate, and the conditions of the experiment (such as the temperature and humidity). To ensure accurate comparison of Rf values, it is necessary to standardize the conditions of the experiment.
Calculating Rf values is a crucial step in the interpretation of TLC data, as it allows for the identification of the components of a mixture based on the unique Rf values of each solute.
Mrs. Chen wrote two checks and made a deposit of $1,987.09 since her october statement. The october statement shows a balance of $3,611.08, and her checkbook shows she currently has $2,778.09. What is the total amount of the checks that Mrs. Chen wrote?
2. An apartment is 8m in length, 5m in width and 3M in height. How many people can be invited to a party if each person requires 5m³ of air space?
The apartment can accommodate 24 people if each person requires 5 cubic meters of air space.
Solution:
Given,
Dimension of apartment
l = 8m
b = 5m
h = 3m
So, the volume of the apartment will be,
l*b*h = 8*5*3 = 120 cubic meters
Each person requires 5 cubic meters of air space,
Hence, the total number of persons = 120/5 = 24
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Can somebody explain how to solve -4(2a+7)+3a+18? What type of polynomial is it?
Simplified form of the polynomial -4(2a+7)+3a+18 is -5a - 10. It is a binomial.
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given expression,
-4(2a+7)+3a+18
using distributive property
-4(2a) -4(7) + 3a + 18
-8a - 28 + 3a + 18
Solving like terms
-5a - 10
The solved polynomial is a binomial, since it has two terms.
Hence, simplified form of the given polynomial is -5a - 10, it is a binomial
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