The standard form equation for the line through the points (3,-4) and (6,-2) is -2/3 x + y = 4.
What is the equation of the line passing through the two-point?
To find the equation for the line through two points we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) is one of the points, and m is the slope of the line. The slope of the line is equal to the change in y over the change in x, which can be calculated as:
m = (y2 - y1) / (x2 - x1)
where (x2, y2) is the other point.
Substituting the given points and the formula for the slope into the formula for the equation of the line, we get:
y - (-4) = ((-2) - (-4)) / (6 - 3) (x - 3)
This simplifies to:
y + 4 = -2/3 (x - 3)
To write the equation in standard form, we can distribute the -2/3 and then rearrange the terms:
-2/3 x + y = 4
Hence, the standard form equation for the line through the points (3,-4) and (6,-2) is -2/3 x + y = 4
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Simplify: 3/8(4a-5)-5/12(3a-4)=1/6
Answer:
Step-by-step explanation:
3/8(4a-5)-5/12(3a-4)=
9/24(4a-5)-10/24(3a-4)=1/6 | x24
9*(4a-5)-10(3a-4)=4
36a-45-30a+40=4
6a=9
a=3/2
In this activity, you will create a function from two points that satisfy it. A linear function passes through the points ( - 2 , 3 ) and ( - 3 , 5 ) . Complete the following tasks to find the equation of the function. Part A To find the equation, first find the rate of change. What is the rate of change for the linear function that passes through the two points?
The linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
Given that linear function passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 3
x₂ = -3, y₂ = 5
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 3 = (5 - 1)/(-3 - (-2))[x -(-2)]
⇒ y - 3 = (4)/(-1)[x +2]
⇒ y - 1 = -4(x +2)
⇒ y = -4x - 8 + 1
⇒ y = -4x - 7
Therefore, the linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
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Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.
Draw the solution above.
Write the solution as a compound inequality
4
The solution to the inequality (x - 4)(x - 5) < 0 is given as follows:
4 < x < 5.
The test values are given as follows:
x < 4 -> x = 3: false.4 < x < 5 -> x = 4.5: true.x > 5 -> x = 6: false.The graph of the inequality is given by the image shown at the end of the answer.
How to solve the inequality?The inequality in this problem is given as follows:
(x - 4)(x - 5) < 0
The inequality is a product, meaning that there is two cases for when it is negative, which are:
x - 4 > 0 and x - 5 < 0.x - 4 < 0 and x - 5 > 0.For the first case, the solution is given as follows:
x > 4 and x < 5 -> 4 < x < 5 (intersection).
For the second case, the solution is given as follows:
x < 4 and x > 5 (impossible).
Hence the compound inequality that gives the solution is of:
4 < x < 5.
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2. Find the 72nd term in the arithmetic sequence 2,
-8, -18, -28, ..
Answer:
The 72nd term is -708
Step-by-step explanation:
Find how long it takes a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set on 80 mph.
When time is also known, distance—the measurement of how far something has travelled in a straight line—can be used to determine speed.
Step-by-step explanation:Speed can be calculated using distance—the amount of distance something has travelled in a straight line—when time is also known.Distance, D = 260 miles
Velocity, V = 80 miles/hour
Time taken, t = distance/velocity
= D/V
= 260/80
= 3.25 hours
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Shelby and Aisha baked homemade dog treats to sell. They baked 116 dog treats in all.
Shelby baked 3 times as many treats as Aisha.
4) How many dog treats did Aisha bake?
Answer:
87
Step-by-step explanation:
If Shelby and Aisha baked a total of 116 dog treats to sell, and Shelby baked 3 times as many dog treats that Aisha, then we need to figure out what 3/4 of 116 dog treats is.
116 ÷ 4 = 29
29 × 3 = 87
Shelby baked 87 dog treats.
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
Answer:
This is a function
Step-by-step explanation:
For every input there is only one output.
Suppose that the functions g and h are defined for all real numbers x as follows.
g(x)=x-6
h(x)=4 x+3
By using the concept of function, it can be calculated that-
(h.g)(x) = 4x - 21
(h + g)(x) = 5x - 3
(h - g)(-1) = 6
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
g(x)= x - 6
h(x) = 4x + 3
(h.g)(x) = h(g(x)) = 4(x - 6) + 3 = 4x - 21
(h + g)(x) = h(x) + g(x) = 4x + 3 + x - 6 = 5x - 3
(h - g)(x) = h(x) - g(x) = 4x + 3 - x + 6 = 3x + 9
(h - g)(-1) = 3 [tex]\times[/tex] (-1) + 9 = 6
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If the lengths of two sides of a triangle are represented by 2x + 5 and 3x + 7 (in which x is positive), describe in terms of x the possible lengths of the third side whose
length is represented by y.
Answer:
x + 2 < y < 5x + 12
Step-by-step explanation:
given 2 sides of a triangle then the third side y is within the limits
difference of 2 sides < y < sum of 2 sides
3x + 7 - (2x + 5) < y < 3x + 7 + 2x + 5
3x + 7 - 2x - 5 < y < 5x + 12
x + 2 < y < 5x + 12
A wire is first bent into the shape of a rectangle with width 5cm and length 16 cm . Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?
Hello,
I hope you and your family are doing well!
To find the length of each side of the triangle, we can use the formula for the perimeter of a rectangle: perimeter = 2 * (width + length). In this case, the perimeter of the rectangle is 2 * (5cm + 16cm) = 42 cm. Since each side of the triangle has the same length, and the perimeter of the triangle is equal to the perimeter of the rectangle, the length of each side of the triangle is 42cm / 3 = 14 cm.
Therefore, the length of each side of the triangle is 14 cm.
---
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We want to determine if [u, v, w is linearly independent. To do that we write the vectors as columns of a matrix A and row reduce that matrix To check this we add We then add We then add We conclude that times the first row to the second. times the first row to the third. times the new second row to the new third row. OA. The set [u, v, w} is linearly dependent. O B. The set {u, v, w] is linearly independent. C. We cannot tell if the set [u, v, w] is linearly independent or not.
Option C, If your row reduces the matrix A and obtains a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly dependent.
This is because the row of all zeros except for a 1 in the rightmost column indicates that one of the vectors in the set can be expressed as a linear combination of the other vectors.
On the other hand, if your row reduces the matrix A and does not obtain a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly independent. This is because the absence of such a row indicates that none of the vectors in the set can be expressed as a linear combination of the other vectors.
If you are unable to row reduce the matrix A for any reason, then it is not possible to determine if the set {u, v, w} is linearly independent or not.
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At the school fair, students used a scatter plot to compare the number of T-shirts sold
with the number of jars of jam sold. What can you conclude about the relationship
between the sales of the T-shirts and the jars of jam?
Answer: The jars of jam sales and the T-shirt sales have a positive correlation, but neither may cause the other.
Step-by-step explanation:
The correlation is a positive slope but selling T-Shirts and Jam shouldn't correlate to each other.
You are playing a game that involves tossing a single die. If you roll a one, you win $50.
If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?
Answer:
the answer is: 01111001 01101111 01110101 00100000 01101000 01100001 01110110 01100101 00100000 01101000 01100001 01110110 01100101 00100000 00110011 00110000 00100101 00100000 01100011 01101000 01100001 01101110 01100011 01100101 00100000 01101111 01100110 00100000 01110111 01101001 01101110 01101110 01101001 01101110 01100111 00100000 01100001 01110011 01110011 01110101 01101101 01101001 01101110 01100111 00100000 01110100 01101000 01100101 00100000 01100100 01101001 01100011 01100101 00100000 01101000 01100001 01110011 00100000 00110110 00100000 01110011 01101001 01100100 01100101 01110011 00101110 . do a bit of work decoding it to get the right answer
Step-by-step explanation:
I need help completing the proving Statement
This looks like a fill-in the blanks question for a two column proof :]
3. CPCTC
The reasoning for this is that because triangle ABC and EDC are congruent, their corresponding parts are also congruent, (CPCTC; Corresponding Parts of Congruent Triangle are Congruent) or AC = EC
4. ACE
Because AC = EC, triangle ACE is isosceles
5. Base Angles Theorem
The base angles of a isosceles triangle are congruent
:]
The number of bacteria in a certain population increases Accor to a continuous growth model,with a growth parameter of 9.6% per hour. How many hours does it take for the size of the sample to double
The required number of hours does it take for the size of the sample to double is 11 hours.
What is percentage?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, in the event that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:Let initial population be x.
As question says number of bacteria increases by 9.6% per hours.
9.6% of x takes 1 hours,
So, in 11 hours size of sample become 105.6%, means almost double of initial size.
Thus, 11 hours will be taken to make size double.
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5 + w - 9 = 8
How do I solve this equation? Please explain step by step
Answer:
w=12
Step-by-step explanation:
w+5-9=8
w-4=8
w=12
Answer:
w = 12
Step-by-step explanation:
Subtract the numbers.
5 + w - 9 = 8
-4 + w = 8
Rearrange terms
-4 + w = 8
w - 4 = 8
Add 4 to both sides
w - 4 = 8
w - 4 + 4 = 8 + 4
Add
w - 4 + 4 = 8 + 4
w = 8 + 4
Add
w = 8 + 4
w = 12
Cindy bought 7/8 yard of ribbion at the craft store. Jacob bought 4/5 the length of ribbon as Cindy. How many yards of ribbon did jacob buy?
Fill in the chart on paper,
then list the coefficient
of the "x" term.
4x
-10
3x²
-8x
+2
Enter
Answer:
2
Step-by-step explanation:
add 2 by 6 to get 02
Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.
A line parallel to one side of a triangle divides the other two sides proportionally.
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let ΔADE and ΔABC are two triangles.
Given: DE∥BC
To prove: DB/AD = EC/AE
ΔADE and ΔAC share ∠A
∠A ≅∠A reflexive property
DE∥BC is given
∠ADE ≅ ∠B because they are corresponding angles when transversal
AB cuts parallel lines DE and BC
ΔADE ∽ ΔABC a pair of angles in each are congruent.
AB / AD = AC / AE
because corresponding sides of similar triangle's are proportional.
Now subtract 1 from each side
AB / AD - 1 = AC / AE - 1
Combining fractions,
(AB - AD) / AD = (AC - AE) / AE
⇒ DB / AD = EC / AE
Hence, a line parallel to one side of a triangle divides the other two sides proportionally.
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Geometric figure:
A rectangular solar panel has a length that is 11 inches shorter than 4 times it’s width. If the perimeter of the panel is 178 inches, what are the dimensions of the panel?
The width of the panel is *blank* inches.
Answer:
The width of the panel is 20 inches----------------------
Let the width be x, then the length is 4x - 11.
The perimeter of the rectangle is:
2(x + 4x - 11) = 178Solve it for x:
2(5x - 11) = 1785x - 11 = 895x = 100x = 20X
Y
If L=4, Y=30 and Z=14. Solve for X. (round to 2 decimal places)
L
N
Answer:
Y+Z/Z = X/L
X= (44/14)4 = 12.57(nearest 2 decimal
Jonah ran 1 Taps on Monday, 21 laps on Tuesday, and 6 laps on Wednesday.
How much farther did he run on Wednesday than on the other two days
combined? Show your work.
Jonah runs 2 (19/20) laps more than the remaining two days
Adding Fractions:The fractions that have the same denominator are like fractions, to add like fractions directly, But if the denominators are not the same then we need to change their denominators to the same then we can add the fractions.
To make denominators as same we need to take the LCM of denominators of two fractions.
Here we have
Jonah ran 1(3)/(4) laps on Monday
=> 1 3/4 = 7/4 laps
On Tuesday he ran 2(3)/(10) laps
=> 2 3/10 = 23/10 laps
On Wednesday he ran 6(1)/(5) laps
=> 6 1/5 = 31/5 laps
The total number of laps ran combining Monday and Tuesday
= 7/4 laps + 23/10 laps
= (35 + 46)/20 [ take Lcm of 4, 10 i.e 20 ]
= 81/20
From the above calculations,
Jonah ran 81/20 laps on combining Monday and Tuesdays
The difference between Wednesday's counted laps and Monday, and Tuesday's counted laps
= 31/5 - 81/20
= (140 - 81)/20 [ Take Lcm of 5, 20 i.e 20 ]
= 59/20
= 2 (19/20)
Therefore,
Jonah runs 2 (19/20) laps more than the remaining two days
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Complete Question:
Jonah ran 1(3)/(4) laps on Monday, 2(3)/(10) laps on Tuesday, and 6(1)/(5) laps on Wednesday. How much farther did he run on Wednesday than on the other two days combined? Show your work.
A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
a) The constant of proportionality of the given problem is; 4
b) An equation that represents the relationship is; y = 4x
c) The graph is as attached.
d) The gallons of water that are needed for 10 scoops of drink mix is; 2.5 gallons
How to find the proportional relationship?The general equation for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope of line which tells us the unit rate of change of y with respect to x
c is the y - intercept
Now, it is pertinent to note that y = mx also represents direct proportionality. Making m the subject gives;
m = y/x
Thus, with proportion, we can say;
y₁/x₁ = y₂/x₂
The proportional relationship will be written as;
y = kx
where k is constant of proportionality
From the question, we can say that;
2 scoops require 0.5 gallon of water
6 scoops require 1.5 gallon of water
a) Thus;
k = 2/0.5
k = 2/(1/2)
k = 2 * 2 = 4
b) Equation that represents the relationship can be written as;
y = 4x + c
Since 2 scoops require 0.5 gallon of water, then;
2 = (4 * 1/2) + c
2 = 2 + c
c = 0
The equation will be; y = 4x.
c) Graph of y = 4x is attached at the end.
d) For 10 scoops of water;
10 = 4x
x = 2.5 gallons of water required.
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Solve for x Round to the nearest tenth, if necessary.
Answer:
1.7
Step-by-step explanation:
tan30°=1/XX=1/tan30°X=1/0.57741.73191.7(to the nearest tenth)Are the triangles congruent, if so which triangles?
S
3 in
AD
Q
4 in
R
X
3 in
4 in
O Yes, A RSQ =A XÚC
O Yes, AUXC = AQRS
O Yes, A XCU A SRQ
O No, these triangles are not congruent
O Yes, AUXCAQSR
Answer:
Yes, [tex]\triangle UXC \cong \triangle QRS[/tex]
Step-by-step explanation:
The triangles are congruent by SAS.
2. Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
The theoretical probability of rolling a two with one standard die in three equivalent form is 1/6, 0.167 and 16.7%
How to determine the theoretical probability?From the question, we have the following parameters that can be used in our computation:
The rolling of a standard die
In this case, we assume that the standard die is a fair die
i.e. the faces have equal chance of appearing
This means that the sample space of the die is
Sample space = {1. 2. 3. 4. 5. 6}
In this sample space, we have
Number of occurrence of 2 = 1
Number of items in the sample space = 6
The theoretical probability of 2 is then calculated as
Probability = Number of occurrence of 2/Number of items in the sample space
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/6 --- in fraction
Evaluate the quotient
Probability = 0.167 -- in decimal
Express as percentage
Probability = 16.7%
Hence, the probability is 16.7%
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what is the area of a circle with a radius of 2 cm anda circle with a radius of 4 cm
Answer:
Step-by-step explanation:
area = pi * r^2
area = pi * 2^2
area = 4pi
area = pi * 4^2
area = 16pi
Consider the piecewise function shown on the graph, which is composed of polynomial, constant, and exponential pieces.
10
-10-8-6-4-2 02 4
O
2
D. (-00, 4)
-2.
-6-
-8
-10-
Over which interval of the domain is the function increasing?
A. (1,4)
OB. (-00, 1)
OC. (-00,-4)
10
4
"Increasing" means the y-values are increasing as x-values increase. Or visually, if you were walking along the graph, from left-to-right, where would you be walking uphill?
The uphill portion is from (-infty, -4). Once you get to an x-value of -4, then it levels off (so it's "constant") until you get to x = 1, when it goes downhill (the function is decreasing).
The interval of the domain in which the function is increasing is(-∞, -4). so option C is correct.
What is a piecewise function?A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.
Given that,
The piecewise function which is discontinuous at x =1
In the interval
(-∞, -4) the value of the function is increasing.
[-4, 1) the value of the function is constant.
(1, ∞) the value of the function is decreasing.
Hence, the function is increasing in the domain (-∞, -4)
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Select the correct answer.
What is the y-intercept of f(x) = 3x+2?
Ο Α.
OB.
O C.
OD.
(9, 0)
(0, 9)
(0, -9)
(9,-9)
4
Answer:
C, (0, 9)
Step-by-step explanation:
The y-intercept is when the x-value is 0. We pug in 0 for x, getting f(0) = 3^2=9. The x-coordinate must be 0, and the y-value is 3^2, or 9. The correct answer is (0, 9)
Anita Jacobs could deposit R600 every 3 months in her credit union which pays 12% interest compounded quarterly. How much more would she have in her account at the END of 4 years if she deposited the R600 at the BEGINNING of each quarter rather than at the END of each quarter?
Answer: 1890
Step-by-step explanation: