The equation Ax + By = 14 goes through the coordinates (-7, -4) and (14, 2).
What are the values of A and B?
Answer:
A=-6
B=7
Step-by-step explanation:
We want to solve for the values of A and B.
let us substitute the values of the coordinates, that is x and y into the expression and obtain the two equations.
then we solve simultaneously
-7A-4B=14---------1
14A+2B=14--------2
-14A+-8B=28---------3
14A+2B=14------------2
0-6B=42
6B=42
B=42/6
B=7
put B=7 in eqn 1 we have
-7A-4(7)=14---------1
-7A-28=14
-7A=14+28
-7A=42
A=42/-7
A=-6
The values of A and B are 3 and -7 respectively
In order to determine the values of A and B,
First, we will determine the equation of the line passing through the coordinates (-7, -4) and (14, 2).
Using the formula for determining the equation of a line with two given points,
[tex]\frac{y-y_{1} }{x -x_{1} } =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
From the question
x₁ = -7
y₁ = -4
x₂ = 14
y₂ = 2
Putting these values into the equation,
We get
[tex]\frac{y--4}{x--7} =\frac{2--4}{14--7}[/tex]
∴ [tex]\frac{y+4}{x+7} =\frac{2+4}{14+7}[/tex]
[tex]\frac{y+4}{x+7} =\frac{6}{21}[/tex]
This becomes,
[tex]6(x+7) = 21(y+4)[/tex]
Clearing the brackets
[tex]6x + 42 = 21y + 84[/tex]
Then,
[tex]6x -21y = 84 -42[/tex]
[tex]6x -21y = 42[/tex]
Dividing through by 3
We get
[tex]3x - 7y = 14[/tex]
∴ The equation of the line that goes through the coordinates (-7, -4) and (14, 2) is [tex]3x - 7y = 14[/tex]
Now, we will compare the above equation to the equation given.
The given equation is Ax + By = 14
By comparing
A = 3 and B = -7
Hence, the values of A and B are 3 and -7 respectively
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Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
A.
{-4, 4, 14}
B.
{2, 4, 9}
C.
{-12, -4, 6}
D.
{12, 4, -6}
Answer:
The range is {12, 4, -6} ⇒ D
Step-by-step explanation:
The range of the relation is the values of y corresponding to the values given for x which is the domain of the relation
∵ The relation is 12x + 6y = 24
∵ The domain of the function is {-4, 0, 5}
→ That means x = -4, 0, 5, we need to find their corresponding values of y
∴ Substitute the values of x in the relation
∵ x = -4
∴ 12(-4) + 6y = 24
∴ -48 + 6y = 24
→ Add 48 to both sides
∴ -48 + 48 + 6y = 24 + 48
∴ 6y = 72
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{72}{6}[/tex]
∴ y = 12
∵ x = 0
∴ 12(0) + 6y = 24
∴ 0 + 6y = 24
∴ 6y = 24
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{24}{6}[/tex]
∴ y = 4
∵ x = 5
∴ 12(5) + 6y = 24
∴ 60 + 6y = 24
→ Subtract 60 from both sides
∴ 60 - 60 + 6y = 24 - 60
∴ 6y = -36
→ Divide both sides by 6 to find y
∴ [tex]\frac{6y}{6}=\frac{-36}{6}[/tex]
∴ y = -6
∵ The range is the values of y which corresponding to the domain
∴ The range is {12, 4, -6}
The answer is down below have a good day!!!
QUESTION 17
Find the coordinates of the points that are 10 units away from the origin and have an x-coordinate equal to .6
Answer:
The set of all points that are 10 units from the origin is the circle centered at (0,0) with radius 10, which has equation
x2 + y2 = 100.
So, if the y-coordinate is -6, then x2 + 36 = 100.
x2 = 64
x = ±8
The points are (8,-6) and (-8,-6).
The equation y= 10x represents a proportional relationship what is the constant of proportionality
Answer:
constant of proportionality = 10
Step-by-step explanation:
Direct proportion equation :
y = kx, where k is the constant of proportionality
* Which answer choice describes y = -3x² +7x - 2
Answer:
y = -[tex]3^{2}[/tex] + 7x - 2
Step-by-step explanation:
-9-2= -11
y = -11 +7x
+11
y+11 = 7x
/7
1.57142857143= x
What is the slope of the line that is represented by the values in the table above?
Answer:
[tex] slope (m) = 6 [/tex]
Step-by-step explanation:
To get the slope of the line of the given table of values, all we need is just 2 coordinate pairs from the table. We can pick any two.
Let's use, (-1, 0), and (0, 6).
Apply the formula, [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex], where,
[tex] (-1, 0) = (x_1, y_1) [/tex]
[tex] (0, 6) = (x_2, y_2) [/tex]
Thus:
[tex] m = \frac{6 - 0}{0 - (-1)} [/tex]
[tex] m = \frac{6}{1} [/tex]
[tex] slope (m) = 6 [/tex]
Please help I would appreciate
Answer:
the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative
Define the following terms:
HURRY PLEASE HELP
What is the approximate distance from the origin to the point (−10, −4, 5)? Round to the nearest tenth. 4.4 units 10.4 units 11.9 units 19.0 units
The answer is 11.9 units
First you must set up the distance formula.
[tex]\sqrt[]{ (-10-0)^2+(-4-0)^2+(5-0)^2}[/tex]
Then, simplify like terms.
[tex]\sqrt{(-10)^2+(-4)^2+(5)^2}[/tex]
Next, simplify exponents.
[tex]\sqrt{100+16+25}[/tex]
Then, add like terms.
[tex]\sqrt{141}[/tex]
Finally, round to the nearest tenth.
11.9
Graph the line that passes through the coordinates below and determine which statement is true.
(2,3) (3,4.5) (4,6) (6,9)
A.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
D.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
Answer:
the correct answer is: C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
Step-by-step explanation:
A straight line passing through the points (1, 2), (3, 4), (5, 6) and (7, 8) does not pass through the origin, as shown on the graph below.
Therefore, the line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
Answer:
The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin--the correct answer is B.
Step-by-step explanation:
You first graph the coordinates shown, then you repeat the same pattern until the answer is revealed which is shown in the column above. Also, a reminder to all a proportional line is a line that goes through the origin ((0,0)).
I'm still figure is a rectangular prism identity which one of the line segment in the given figure is perpendicular to HG
Answer: so, its pretty simple so just figure it it so, its pretty simple so just figure it it
Step-by-step explanation: so, its pretty simple so just figure it it so, its pretty simple so just figure it it!
Is the square root of 14 +6.2 less than 3 pi - 8.2?
Answer:
No. √14 + 6.2 is more than 3π - 8.2
Step-by-step explanation:
√14 + 6.2
√20.2
≈ 4.494
π ≈ 3.14159
3(3.14159) - 8.2
9.42577 - 8.2
1.22477
Therefore, the answer is no.
1 3 Divide - 2 +7=Explain each step you used to find the quotient. 9 5 What is the first step in finding this quotient? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a fraction. Use a comma to separate answers as needed.) O A. Multiply the whole parts of the mixed numbers. The product is OB. Multiply the fraction parts of the mixed numbers. The product is OC. Convert the mixed numbers to fractions. The fractions are OD. Find the reciprocal of the dividend. The reciprocal is
Answer: 15 an ummm fine
Step-by-step explanation:
Answer:
15 is the correct answer
find an equation for the line that passes through the point (7,1) and is perpendicular to the line x-3y+25=0
Answer:
y + 3x = - 20
Step-by-step explanation:
x - 3y + 25 = 0
- 3y = - 25 - x
3y = 25 + x
y = ( 25 + x )/3
y = ( 1/3 )x + 25/3
Y= mX+ c
m= gradient= 1/3
The perpendicular gradient should be the negative reciprocal of the gradient we have now.
which is : -1÷(1/3) = -3
Now for the perpendicular line equation, we have:
y = 1
x= 7
m= -3
y - y1 = m ( x - x1 )
y - 1 = -3 ( x + 7 )
y-1 = -3x -21
y + 3x = -20
The mapping diagram shows a functional relationship.
A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (8, 4), (negative two-thirds, 3), (11, negative 1), (4, one-half).
Complete the statements.
Answer:
do you have the diagram
Step-by-step explanation:
Answer:
yes ido
Step-by-step explanation:
I toss a coin 60 times. It lands on tails 24 times. What percent of the time does it land on tails?
Cualquiera de las dos rectas puede ser la de pendiente 1 o pendiente 2, sólo hay que
conservarla hasta el final de la operación.
BLO
Fórmula que vamos a aplicar:
m-m
1+m-m
tan 0=
Pendiente de la recta 3x - 4y + 8 = 0
Pendiente de la recta 2x + 3y - 23 = 0
Sustitución de datos
tan 0 =
Al realizar la operación de la fórmula se obtiene la tangente del ángulo, por lo que hay
que buscar el inverso de la tangente, que es el valor del ángulo de intersección entre
las rectas dadas.
tan 8 =
El valor del ángulo e es
These are the weekly wages paid to staff in a hotel.
£245
£140
£525
£163
£195
£174
£140
What is the range of these wages?
What is the mean wage?
Answer:
range is 525-140=385
The mean of a set of numbers is the sum divided by the number of terms. Mean= 226
Step-by-step explanation:
hope that helper, have a good one
Range = 525 - 140 = 385
Mean =
[tex](140 + 140 + 163 + 174 + 195 + 254 + 525) \div 7 = 226[/tex]
____ is 22 more than 88
Answer:
110
Step-by-step explanation:
88+22=110
One number exceeds another by 1. The sum of the numbers is 23. What are the numbers?
Answer:
the numbers are 11 and 12
Step-by-step explanation:
Hansel's age is one less than three times Gretel's age. The sum of their ages is 43.
Answer: Hansel is 32
Step-by-step explanation: 11x3-1=32, 32+11=43
-3.6 divided by -0.75
Answer:
4.8
Step-by-step explanation:
the two negatives cancel each other
Answer:
4.8
Step-by-step explanation:
Since both numbers are in negative form and a division is supposed to occur, take away the negative so that the division can properly occur:
3.6 ÷ 0.75
Now simplify:
4.8
If you found my answer helpful
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The ratio of a number x and four added to two
Answer:
hope it helps...
Step-by-step explanation:
The ratio of a number x and four added to two:
= 4x + 2 = 0
= 4x = -2
= 4x/4 = -2/4
= x = -2/4
= x = -1/2
A box contains three types of fruits:
apples, bananas, and pears. There are
20 pieces of fruit in all. Of these, 3 are
apples and 11 are bananas. What is the
ratio of pears to bananas?
A 6: 11
B 11 : 6
C 3:11
D 11:3
Answer:
A
Step-by-step explanation:
divide 25.84 divide by 4
Answer:
25.84 divide by 4 Is 6.46.
An electrician needs to buy 600 centimeters of electrical tape. How many rolls of tape should
the electrician order if there are 200 centimeters of tape on each roll?
Answer:
3 rolls of tape
Step-by-step explanation:
600 diveded by 200 is 3
Find f(5). f(x) = x2 + 2x
Help please
Answer:
Your answer is: 15
Your equation would have f(5) = x^2 + 2x
Substitute the given value into the function and evaluate.
Step-by-step explanation:
Hope this helped ; )
If 24 divided by 4 is 6 what is the remainder?
The remainder from the given division is 0.
Given that, 24 divided by 4 is 6.
The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here,
4|24|6
24
______
0
So, the remainder is 0.
Therefore, the remainder from the given division is 0.
To learn more about the division visit:
https://brainly.com/question/1575906.
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Suppose that Haley encounter two traffic lights on her commute to GGC campus. Based on
her past experience, she judge that the probability is 0.35 that the first light will be red when she gets to it,
0.45 that the second light will be red, and 0.20 that both lights will be red. Let R1 denote the event that the
first light is red, and let R2 denote the event that the second light is red.
a) Determine the probability that at least one light will be red. (Show how you calculate this.)
b) Determine the conditional probability that the second light will be red given that the first light is
red. (Show how you calculate this.)
c) Are the events R1 and R2 independent? Justify your answer numerically.
d) Are the events R1 and R2 disjoint (mutually exclusive)? Justify your answer numerically.
Answer:
Explained below.
Step-by-step explanation:
The information provided is,
P (R₁) = 0.35
P (R₂) = 0.45
P (R₁ ∩ R₂) = 0.20
(a)
Compute the probability that at least one light will be red as follows:
P (at least one light will be red) = P (R₁ ∪ R₂)
= P (R₁) + P (R₂) - P (R₁ ∩ R₂)
= 0.35 + 0.45 - 0.20
= 0.60
Thus, the probability that at least one light will be red is 0.60.
(b)
Compute the conditional probability that the second light will be red given that the first light is red as follows:
[tex]P(R_{2}|R_{1})=\frac{P(R_{1}\cap R_{2})}{P(R_{1})}[/tex]
[tex]=\frac{0.20}{0.35}\\\\=0.571428\\\\\approx 0.57[/tex]
Thus, the conditional probability that the second light will be red given that the first light is red is 0.57.
(c)
If two events, say A and B are independent then:
P (A|B) = P (A).
The value of P (R₂ | R₁) = 0.57.
And the value of P (R₂) = 0.45
P (R₂ | R₁) ≠ P (R₂)
Thus, the events R₁ and R₂ are not independent.
(d)
If two events, say A and B are mutually exclusive then:
P (A ∩ B) = 0
The value of P (R₁ ∩ R₂) = 0.20.
Thus, the events R₁ and R₂ are not mutually exclusive.
If anyone is willing to try and answer this go ahead
Answer:
X intercept: x = 4 or in point form (4,0)
Zero for the function at (4, 0)
Y intercept : y = 160 or in point form (0,160)
slope = -40 mph
Step-by-step explanation:
The y-intercept, x-intercept are directly obtained from the graph by noticing the points on the axes where the line crosses them.
The slope is calculated using the points (0, 160) and (4, 0) and the formula for the slope of the segment that joins them:
slope = (y2 - y1)/(x2 - x1) = (160 - 0) / (0 - 4) = -160/4 = -40
and the units of the slope are miles over hour (that is miles per hour or mph)