The slope of the line containing (4,2) and (4,-3) is Infinity.
The slope of a straight line can be written as follows,
m = [tex](y_{2} -y_{1} ) / (x_{2} -x_{1} )[/tex] equation1
The line is containing the points (4,2) and (4,-3). So, we can write
[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = 2 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = 4 .
On substituting the values of variables in equation1, we will get
m = ( (-3)-(2) ) / ( (4)-(4) ) = (-6/0) = Infinity
As the slope of a line is Infinity, so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (4,2) and (4,-3) is Infinity.
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2/106 = x/901 what is x?
x=567
Step-by-step explanation:
Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. (Lesson 10-1) C=78 ft
The diameter and radius of circle is 24.84 feet and 12.42 feet.
We are given the circumference of circle. So, using the formula of circumference, we will find the diameter. As we know, the radius of circle is half of its diameter.
Performing calculation now -
Circumference = π×d, where d stands for diameter of circle.
Taking the value of π as 3.14.
Keep the values in formula to find the diameter of circle
Diameter = 78÷3.14
Performing division
Diameter = 24.840
Rounding to nearest hundredth -
Diameter = 24.84 feet
Now, calculating radius by the formula -
Radius = diameter÷2
Radius = 24.84÷2
Performing division to find the radius of circle
Radius = 12.42 feet
Hence, the diameter and radius of circle is 24.84 feet and 12.42 feet.
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The average of the five numbers in a list is 54. the average of the first two numbers is 48. what is the average of the last three numbers?
The average of the last three numbers is 58 if the average of the five numbers in a list is 54. the average of the first two numbers is 48.
What is average?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that:
The average of the five numbers in a list is 54. and the average of the first two numbers is 48.
54 = sum of the five numbers/5
54x5 = sum of the five numbers
270 = sum of the five numbers
48 = sum of the two numbers/2
48x2 = sum of the two numbers
96 = sum of the two numbers
Sum of three numbers = 270 - 96
Sum of three numbers = 174
The average of the last three numbers = 174/3 = 58
Thus, the average of the last three numbers is 58 if the average of the five numbers in a list is 54. the average of the first two numbers is 48.
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Write an equation in slope-intercept form for each line described.
passes through (6,2) , parallel to y=-2/3x+1 .
The equation in slope-intercept form is y = -2/3x + 6
Given,
Points (x, y) = (6, 2)
Parallel to y = -2/3x + 1
Now,
Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "-2/3" (the coefficient that accompanies "x").
Therefore the equation of a parallel line has to be of the form:
y = -2/3x + b
2 = -2/3(6) + b
2 = -12/3 + b
2 = -4 + b
b = 6
So the equation now becomes:
y = -2/3x + 6
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Solve each system by substitution. Check your answers.
x + 12y = 68 , x=8y-12
By substitution, the solution of the system of equations, x + 12y = 68 and x = 8y - 12, is (20 , 4).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + 12y = 68 (equation 1)
x = 8y - 12 (equation 2)
Since the second equation is already expressed in x in terms of y, substitute the value of x to the first equation.
x + 12y = 68 (equation 1)
(8y - 12) + 12y = 68
8y - 12 + 12y = 68
Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.
8y - 12 + 12y = 68
8y + 12y = 68 + 12
20y = 80
y = 4
Substitute the value of y in the second equation and solve for x.
x = 8y - 12 (equation 2)
x = 8(4) - 12
x = 32 - 12
x = 20
Hence, the solution of the given system of equations is (20 , 4).
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Write a flow proof.
Given: RQ ≅ ST and RQ || ST
Prove: Δ R U Q ≅ ΔT U S
We can say that ΔRUQ ≅ ΔTUS under RHS condition.
What exactly does this mean by the congruency of a triangle?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.These triangles can be moved, rotated, flipped, and turned to look exactly the same.They will coincide if they are repositioned.Two triangles are congruent if they satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Given: RQ ≅ ST and RQ || ST
To Prove: ΔRUQ ≅ ΔTUS
∠RUQ = ∠SUT = (Inversely proportional)(RHS)RQ = ST = (Given: parallel and as ∠U is same in front of the lines, so the lines will also be same)So, RU = TU = (RHS condition)So, we can say that ΔRUQ ≅ ΔTUS under RHS.
Therefore, ΔRUQ ≅ ΔTUS.
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If you throw a dart, what is the probability of
hitting the area of the shaded region?
Use 3.14 for T. Round answers to nearest Hundredth(two decimal places).
The probability of hitting the area of the shaded region is 0.21 (in the form of two decimal places) when you throw a dar.
What is probability?The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have been given that the radius of the circle = 2cm
So one side of square = 2+2 = 4cm
Area of circle = πr² = (3.14) ×(2)²= (3.14)×4 = 12.57cm²
Area of square = (a)² = (4)² =16cm²
Then the area of the shaded region = 16−12.57 = 3.43cm²
So the probability of hits in the shaded region = 3.43/16 = 0.2144
Round to the nearest Hundredth (two decimal places).
The probability of hits in the shaded region = 0.21
Hence, the probability of hitting the area of the shaded region is 0.21 (in the form of two decimal places) when you throw a dar.
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What is the product of all the common factors of 16 and 24?
Answer:
The GCF of 16 and 24 is 8. To calculate the GCF (Greatest Common Factor) of 16 and 24, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 16 and 24, i.e., 8.
Step-by-step explanation:
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If z varies directly with the product of x and y(z=k x y) , then z is said to vary jointly with x and y .
c. Suppose z varies jointly with x and y , and x varies directly with w . Show that z varies jointly with w and y .
The value of z varies jointly with w and y.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation
let k be the constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx
Given relation is z = kxy —-- 1
Also x varies directly with w i.e. x = k'w, where k' is constant of variation for x and w
Using in equation 1, we have,
z = k(k'w)y
z = kk'wy
z = Kwy, where K is constant of variation i.e. K = kk'
It shows that z varies directly with w and y.
Hence, z varies jointly with w and y.
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Given the rule what is the new coordinate? Show all of your work.
Rule: (x, y) → (x − 7.5, y + 6.8)
-
Original coordinate: (5, 3)
Using translation concepts, the new coordinates of the point are given as follows:
(-2.5, 9.8).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
For this problem, the translation rule for each point is given as follows:
(x, y) → (x - 7.5, y + 6.8)
This translation rule means that the figure is shifted:
7.5 units left, because x -> x - 7.5.6.8 units up, because y -> y + 6.8.The original coordinate is given by:
(5,3), meaning that x = 5 and y = 3.
Applying the rule to the original coordinates, we have tat:
5 - 7.5 = -2.5.3 + 6.8 = 9.8.Hence the new coordinates, after the rule is applied to the original coordinates, are given as follows:
(-2.5, 9.8).
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Two cyclists, 80 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
The speed of the faster car is 15 miles per hour.
How to find the speed of the faster cyclist?Two cyclists, 80 miles apart, start riding toward each other at the same time.
One cycles 3 times as fast as the other. If they meet 4 hours later
speed = distance / time
distance = speed × time
let
speed of the slower cycle = x
speed of the faster cycle = 3x
Therefore,
4x + 3x(4) = distance
4x + 3x(4) = 80
4x + 12x = 80
16x = 80
divide both sides by 16
x = 80 / 16
x = 5
Therefore, the speed of the faster car is 15 miles per hour.
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Are the lines perpendicular?
no, because the slopes of the lines are equal
no, because the slopes of the lines are not opposite reciprocals
yes, because the slopes of the lines are equal
yes, because the slopes of the lines are opposite reciprocals
Please help my head hurts to much right now to think!!
Answer:
A) y=10x-4
Step-by-step explanation:
There are 10 full boxes which means 10x (since x is the boxes of pizza)
but there are 4 already eaten slices in one, which can be subtracted at the end, making the equation y=10x-4.
Hope this helped and feel better soon! :)
Given ABCD, solve for x. We
The local gym holds three 45-minute workout sessions and two 30-minute sessions each week. Judy attended all of the sessions this week but left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions. How many total minutes did Judy work out for the week?
The local gym holds three 45-minute workout sessions and two 30-minute sessions each week. Then the, total number of minutes Judy worked out for the week was 155 minutes.
We are to determine the total number of minutes Judy worked out for the week.
The gym holds three 45-minute workout sessions and two 30-minute sessions each week
So,
We can write,
The total number of minutes the gym holds workout sessions is
3 × 45 + 2 × 30
= 135 + 60
= 195 minutes
Also, from the information,
Judy left 5 minutes early during the 30-minute sessions and 10 minutes early during the 45-minute sessions.
The total number of minutes Judy didn't attend is
= 3 × 10 + 2 × 5
= 30 + 10
= 40 minutes
Then,
The total number of minutes Judy worked out for the week was,
= 195 minutes - 40 minutes
= 155 minutes
Therefore,
The total number of minutes Judy worked out for the week was 155 minutes.
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Which line on the graph below has an undefined slope?
On a coordinate plane, line Q is horizontal, line P has a positive slope, line R is vertical, and line S has a negative slope.
P
Q
R
S
The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.
Which line among the given answer choices is that which has an undefined slope?It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.
Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.
The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.
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Answer:
Step-by-step explanation:
The answer is R
In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.
c. Verbal Draw another circle and repeat parts a and bfb . Make a conjecture about arcs of a circle that are cut by two parallel chords.
Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.
When two chords of a circle are parallel are the arcs?
Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.
The lengths of the arcs connecting two parallel chords of a circle are equal. Similarly, if the lengths of the two arcs connecting two distinct chords are the same, the chords are parallel. If two chords have the same length, the arcs between their endpoints will have the same measure.
The term "parallel" refers to how each note in the chord rises or falls by the same interval.
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Omar deposits $300 in an account earning 3% interest compounded annually. How much will be in the account after 1 year if he makes no withdrawals?
Answer: 100 $
Step-by-step explanation:
300 divided by 3 is 100
Find the distance between each pair of points.
R(8,0), S(-9,6)
The distance between the points R and S is 18.03 units.
We know that for points P(x1, y1) and Q(x2, y2) the distance between points is given as:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this question, we have been given two points R(8,0), S(-9,6)
We need to find the the distance between the points R(8,0) and S(-9,6)
Let R(8,0) = (x1, y1) and S(-9,6) = (x2, y2)
Using distance formula the distance between the points R and S is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d=\sqrt{(-9-8)^2+(6-0)^2} \\\\d=\sqrt{(-17)^2+6^2}\\\\ d=\sqrt{289+36}\\\\ d=\sqrt{325}\\\\d=18.03~~units[/tex]
Therefore, the distance between the points R and S is 18.03 units.
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I need help with 19-22
Answer:
4
[tex]4x6 \div 17 \\ [/tex]
Answer:
Step-by-step explanation:
19-22= -3 becuase
22-19=3 but the other way around is -3
find the equation of locus of all points equidistant from the point +2,4 )and y-axis
Answer:
Let P(h,k) be the point which is equidistant from the point (2,4) and the y-axis. The distance of point P(h,k) from the y-axis is h. ∴h=√(h−2)2+(k−4)2⇒h2−4h−4+k2−8k+16=h2⇒k2−4h−8k+20=0.
Hence,the locus of (h,k)is y2−4x−8y+20=0.
Step-by-step explanation:
find two consecutive odd integers whose product is the same as fifteen more than three times their sum
The find two consecutive odd integers is 7 and 9
Linear functionsThese are functions that has a linear degree of 1. Let the two consecutive odd numbers be 2x + 1 and 2x + 3
If their product is the same as fifteen more than three times their sum, then;
(2x+1)(2x+3) = 3(2x+1+2x+3) +15
4x²+6x+2x+3 = 3(4x+4) +15
4x²+8x+3 = 12x+12 + 15
4x² - 4x + 3 = 27
4x² - 4x - 24 = 0
x² - x - 6 = 0
On factorizing, the value of x is 3 and -2
First number = 2(3) + 1 = 7
Second number = 2(3) + 2 = 9
Hence the find two consecutive odd integers is 7 and 9
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Which of the following numbers is an imaginary number?
A. -3²
B. (-5)2
C. √5
D. √-49
E. -√36
Answer:
B
Step-by-step explanation:
-3^2 =+8999999999999999999999(9())))))))(-"""&+(()))))(&&%422222222222223
A certain standardized test's math scores have a bell-shaped distribution with a mean of 525 and a standard deviation of 105
105. Complete parts (a) through (c).
a ) What percentage of standardized test scores is between 210 and 840?
b)What percentage of standardized test scores is less than 210 or greater than 840 ?
c)What percentage of standardized test scores is greater than 735?
A. The percentage of standardized test scores is between 210 and 840 is 99.7%
B. The percentage of standardized test scores that is less than 210 or greater than 840 is 0.3%.
C. The percentage of standardized test scores that is greater than 735 is 2.2%.
How to calculate the percentage?a) The z score for 210 will be:
= (210 - 525)/105
= -3
The score for 840 = (840 - 525)/105 = 3
Hence,
Percentage between 210 and 840 will be:
= P(-3 < z < 3)
= 99.7%
b) The percentage of standardized test scores is less than 210 or greater than 840 will be:
= 100% - P(Between 210 and 840)
= 100% - 99.7%
= 0.03%
c) The z score for 735 = (735 - 525)/105
= 2
Hence, the percentage greater than 735
= P(z > 2)
= 2.2%
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Solve each system by elimination.
8y + 10 = 6x , 8y - 4x = -12
Using elimination method, the solution of the given system of equations is (-1, -2)
A system of equations can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations is:
8y + 10 = 6x ..... (1)
8y - 4x = -12 ...... (2)
Re-arrange equation (1) to
8y - 6x = -10 ........ (3)
To eliminate variable y, subtract equation (3) from equation (2):
8y - 4x = -12
8y - 6x = -10 –
2x = -2
x = -1
Substitute x = -1 into equation (2)
8y - 4x = -12
8y - 4. (-1) = -12
8y + 4 = -12
Add (-4) to both sides:
8y = -16
y = -2
Hence, the solution is (-1, -2)
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Finding the initial amount and rate of change given a table for a linear function
Answer: X=Time(Minutes) Y=Gallons Y= 8x+70. I used slope intercept form: My example point would be (6, 118) (9, 142) 142-118/9-6=24/3=8. Therefore 8 is your slope. or you cold see that it increases by 24 everytime it skips 3 times.
Step-by-step explanation:
((6+x))/(3)=(x)/(4)+4
Answer:
x = 24
Step-by-step explanation:
[tex]\frac{6+x}{3}[/tex] = [tex]\frac{x}{4}[/tex] + 4 Multiply though by 12 to clear the fraction
4(6 + x) = 3x + 48 Distribute the 4)
24 + 4x = 3x + 48 Subtract 3x from both sides of the equation
24 + x = 48 Subtract 24 from both sides.
x = 24
How do I Evaluate this expression
|-3d-6|+|-5-d²| for d = -3
After evaluating the expression | - 3 d - 6 | + | - 5 - d² | for d = - 3, we get that the result is 17.
We are given the expression:
| - 3 d - 6 | + | - 5 - d² |
We need to evaluate the expression for d = - 3
Put the value of d as - 3 in the expression, we get that:
| - 3 ( - 3 ) - 6 | + | - 5 - ( - 3 )² |
Solving the expression further, we get that:
| 9 - 6 | + | - 5 - 9 |
| 3 | + | - 14 |
= 3 + 14
= 17
Therefore, after evaluating the expression | - 3 d - 6 | + | - 5 - d² | for d = - 3, we get that the result is 17.
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Find the magnitude and direction of the following vector.
-JK : J<8,1>and K(2,5)
The magnitude of the vector JK is estimated to be 2√13.
The given vector JK's direction is - Ф = 33.69° (angle lies in the fourth quadrant with having direction in clockwise)
What is the definition of a distance formula?The algebraic demonstration of the coordinate-based distances between two points (in coordinate system). Using rectangular coordinates, the Pythagorean theorem is employed to determine distances among points in 2- and 3-dimensional Euclidean space.
Now, in answer to your questioning;
J and K have coordinates of (8,1) & (2,5), respectively.
The following is the distance formula for the points J & K:
JK² = (x₂ - x₁)² + (y₂ - y₁)²
JK = √[(x₂ - x₁)² + (y₂ - y₁)²]
The given of coordinates of J and K's are-
(x₁,y₁) = (8,1) and (x₂,y₂) = (2,5).
Substituting the given values in the distance formula;
JK = √[(2 - 8)² + (5 - 1)²]
JK = √[(-6)² + (4)²]
JK = √[36 + 16] = √52
JK = 2√13 (magnitude of the vector JK)
Now, estimate the vector JK's direction.
The angle formed by a vector with a horizontal line defines its direction.
Use one of the given equation to find the direction of a vector.
tan Ф = Δy/Δx
Where, x = horizontal change
and, y = vertical change
tan Ф = (y₂ - y₁)/(x₂ - x₁)
= (5 - 1)/(2 - 8)
tan Ф = 4/(-6) = -2/3
Ф = 33.69° (angle lies in the fourth quadrant with having direction in clockwise)
As a result, the distance between J and K is found to be 2√13, that is the same as a magnitude of the given vector JK.
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Please help meee
Approximate negative seventeen plus square root of sixty to the nearest tenth. −9.3 −7.7 7.7 9.3
The approximate value of negative seventeen plus square root of sixty to the nearest tenth is -9. 3 . Option A
How to determine the valueFrom the information given, we have;
negative seventeen, this is written as = - 17square root of sixty, this is written as = √60Substitute the values into the expression, we have;
- 17 + √60
Find the square root of 60 and add to the expression;
-1 7 + 7. 7459
Find the sum of the values
-9. 3
Thus, the approximate value of negative seventeen plus square root of sixty to the nearest tenth is -9. 3 . Option A
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