Answers
The points: (-3,-1), (6,-7)
(-7+1)/(6+3) = -6/9 = -2/3
Use equation: y = mx + b
y = -2/3x + b
Plot in any point
-1 = -2/3(-3) + b
-1 = 2 + b, b = -3
Final equation in slope intercept form:
Y = -2/3x -3
Answer:
y = -[tex]\frac{2}{3}[/tex] x - 3
Step-by-step explanation:
The general form of the equation of the line (linear equation) is:
y = ax + b
The line passes through (-3, -1) and (6, -7), i.e:
(1) (x=-3, y=-1) is a point that verifies the equation of the line, and
(2) (x=6, y=-7) also verifies the equation.
So we can put up a system of 2 equations to obtain a and b:
y = ax + b
(1) -1 = a (-3) + b
(2) -7 = a (6) + b
______________
substracting (1) - (2) we can obtain a:
-1 - (-7) = a (-3-6) ⇒ 6 = -9 a ⇒ a = -2/3
by replacing a in (1) we can obtain b:
-1 = -2/3 (-3) + b ⇒ -1 -2 = b ⇒ b = -3
so, the equation is: y = ax + b ⇒ y = -2/3 x - 3
Verification: (2) giving x= 6, let's see if y=-7 is obtained:
y = -2/3 6 - 3 ⇒ y = -4 - 3 = 7 ⇒ RIGHT!
Related Questions
A shop sells 20 different flavors of ice cream, in how many ways can a customer choose4 ice cream cones (one dip of ice cream per cone, please) if they:_________(a) are all of different flavors.(b) are not necessarily of different flavors.(c) contain only 2 or 3 flavors.(d) contain 3 different flavors.
Answers
Answer:
a.4845ways.
b. 14535ways.
c. 3990ways
d. 1140ways
Step-by-step explanation:
Given data:
No of flavors available to customers = 20.
Solution:
This is permutation and combinations problem,
(a) how many ways can the customers choose 4 different ice creams if they are all of different flavors.
20C4
= n!/(n-k)!)k!
= 20!/(20-4)!)4!
= 20!/(16)!)4!
= 4845ways.
b) are not necessarily of different flavors
Let’s say any two same flavors can be chosen.
20C4 * 3!/2!
= 4845 * 3
= 14535ways.
c) contain only 2 or 3 flavors.
= 20C3 * 3!/2!
= 1140 * 3
= 3420
20C2 * 3
= 190 * 3
= 570.
No of 2 or 3 different flavors
= 3420 + 570
= 3990ways.
d) contain 3 different flavors.
20C3
= n!/(n-k)!)k!
= 20!/(20-3)!)3!
= 1140ways.
The table gives the results of a survey of 1000 people about reducing industries' carbon emissions. Favor Oppose No Opinion TotalDemocrat 320 150 50 520Republican 125 345 10 480Total 445 495 60 1000If the group surveyed represents the people of the United States, what is the probability that a citizen selected at random will favor reducing industries' carbon emissions, given that the person is a Republican? (Enter your probability as a fraction.)
Answers
Answer:
1 / 8
Step-by-step explanation:
Given the data
_____Favor __Oppose__ No Opinion__Total
Demo 320___ 150 ______50 _______ 520
Repub 125___ 345 _____ 10 _________480
Total 445 ___495 ______60 ________ 1000
what is the probability that a citizen selected at random will favor reducing industries' carbon emissions, given that the person is a Republica
From the table provided :
n(favor n republican) / n(Total)
Number of republican who are in favor = 125
Total number of persons = 1000
Hence,
125 / 1000
= 1/8
Armon has a prepaid cell phone. This month he will like to purchase a $9 message package. The rate plan for the talk time is $0.10 per minute. Write an inequality for the maximum amount of talk time that Armon can purchase for his bill to stay under $45.
Pls show step-by-step! :)
Answers
0.10 per minute is the slope
9 would be the y intercept
Equation: 0.10x + 9 < 45
the sum of two number is 63the smaller number is 17 less than the larger number.what are the number
Answers
Answer:
The larger number is 40, and the smaller one is 23.
Step-by-step explanation:
Let x be the larger number.
Let x - 17 be the smaller number.
x + (x - 17) = 63
2x - 17 = 63
2x = 80
x = 40
Hence, the smaller number is 40 - 17 = 23.
Hope this helped!
x=40
y=23.
Explanation:
Let x be equal to the larger number.
Let y be equal to the smaller number.
Using the given information, we can come up with the following equations:
x+y=63
x-y=17
From here, we can use the method of elimination to find the value of x by adding the equations together. Please check the image attached!
2x=80
Divide both sides by 2 to isolate x
2x/2=80/2
x=40
Now, we can substitute x back into one of our original equations to solve for y.
x-y=17
40-y=17
Subtract both sides by 40 to isolate y
-y=17-40
-y=-23
y=23
Therefore, x=40 and y=23.
I hope this helps! Please comment if you have any questions :)
4x^2 - 9y^6
what patterns can be used ?
please and thank you !!!
Answers
Answer:
B. (U+V)(U-V)
Step-by-step explanation:
Factoring
The given expression is:
[tex]4x^2-9y^6[/tex]
It should be noted that both terms are perfect squares:
[tex](2x)^2=4x^2[/tex]
[tex](3y^3)^2=9y^6[/tex]
Since it's a difference of squares, we need to use the following pattern to factor the required expression:
[tex](U^2-V^2)=(U+V)(U-V)[/tex]
Thus, the answer is
B. (U+V)(U-V)
the picture is the question
Answers
Answer:
3x
Step-by-step explanation:
gradient is slope.
rise/run = 3/1x = 3x
=3/1 = 3 is the gradient
AGAIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
what is the slope of the graph in the picture
pls help it's closing in 40 minutes
pls explain how you got the answer
Answers
Answer:
-2
or
-2/1
Explanation:
**Slope = rise/run**
By counting the distance between the points, from (0,3) to (1,1) , it went down 2 units and right by 1 unit
Answer:
m= -2
Step-by-step explanation:
Pick two points and subtract the y coordinates, then subtract the x coordinates, (0,3) and (1,1) or (1,1) and (2,-1)
[tex]m = \frac{y_{2_ } - y_{1} }{x_{2} -x_{1} } = \frac{1-3}{1-0} = \frac{-2}{1} = -2[/tex] [tex]\frac{-1-1}{2-1} = \frac{-2}{1} = -2[/tex]
Petra jogs 3 miles in 30 minutes at this rate how long would it take a jog 10 miles
Answers
Answer:
100 minutes or 1 hour and 40 minutes
Step-by-step explanation:
3 miles in 30 minutes means 1 mile in 10 minutes
10 miles takes 100 minutes or 1 hour and 40 minutes.
1 hour and 40 minutes
What is the value of the expression when b= -4 and C=1
Answers
Answer:
B would equal -4
Step-by-step explanation:
Question 16
Mr. Twain asked the students in his class to draw the figure below using a scale factor of 3. Then, he asked students to tell him one of the new side lengths of the figure. Some student responses are below.
Student Response
Mark 5 in.
Samantha 6 in.
Divia 1.3 in.
Cheng 0.9 in.
Candice 11.7 in.
Select the student that answered Mr. Twain's question correctly.
A
Mark
B
Divia
C
Cheng
D
Candice
Answers
Answer:
C
Step-by-step explanation:
Your answer is C because got the question right when put C .
A tree initially measured 18 feet tall. Over the next 3 1/2 years
Answers
Answer:
5 ft/yr
Step-by-step explanation:
This is the whole question: A tree initially measured 18 ft tall. Over the next 3 1/2 years, it grew to a final height of 35 1/2 feet. During those 3 1 /2 years, what was the average yearly growth rate of the height of the tree?
The tree grew 35.5 - 18 ft = 17.5 feet in 3.5 years
This average leads to 17.5 ft / 3.5 yr = 5 ft/yr
The question is incomplete, the complete question is;
A tree measured 18 feet tall. Over the next 3 1/2 years, it grew to final height of 35 1/2 feet. During those 3 1/2 years, what was the average yearly growth rate of the height of the tree?
Answer:
5 feet per year
Step-by-step explanation:
Given that the initial height of the tree = 18 feet
Final height of the tree = 35.5 feet
Time interval = 3.5 years
Now;
Increase in length of tree = Final height of the tree - initial height of the tree
Increase in length of tree = 35.5 - 18 = 17.5 feet
Rate of growth of tree = increase in height of tree/ time taken
Rate of growth of tree = 17.5 feet/ 3.5 years
Rate of growth of tree = 5 feet per year
Can u plz help me with the number 9?
Answers
Martina ordered a set of blue and orange pins. She received 96 pins in all. 24 of the pins were
blue. What percentage of the pins were blue?
Write your answer using a percent sign (%).
Answers
Answer:
25%
Step-by-step explanation:
This is like a part over whole problem, where 24 blue pens is the part and 96 pens total is the whole.
24/96 = 0.25 * 100 = 25%
Answer:
Of the 96 pins, 25% of the pins were blue.
Step-by-step explanation:
We are given that Martina ordered 96 pins in total. We are also given that she ordered 24 blue pins.
With this, we can determine how many of the pins were not blue pins by subtracting the amount of blue pins from the number of total pins.
[tex]96 \ \text{total pins} - 24 \ \text{blue pins} = 72 \ \text{orange pins}[/tex]
Now, we can divide the number of blue pins by the number of total pins to determine the fraction of blue pins to total pins.
[tex]\displaystyle \frac{24}{96} = \frac{12}{48} = \frac{6}{24} = \frac{3}{12} = \frac{1}{4}[/tex]
Then, we can convert our fraction to a decimal.
[tex]\displaystyle \frac{1}{4} = 0.25[/tex]
And finally, we can convert our decimal to a percentage by multiplying the determined decimal by 100.
[tex]0.25\times100 = 25\%[/tex]
Therefore, of the 96 pins that Martina ordered, 25% of them were blue.
2.1(0.2x-1.4)=1.3(0.4x—3.5)
Pls help.
Answers
Answer:
x=161/10 =16.100
Step-by-step explanation:
Combine Like Terms
PLEASE FOLLOW ME
Answer:
hope it helps..
Step-by-step explanation:
Simplifying
2.1(0.2x + -1.4) = 1.3(0.4x + -3.5)
Reorder the terms:
2.1(-1.4 + 0.2x) = 1.3(0.4x + -3.5)
(-1.4 * 2.1 + 0.2x * 2.1) = 1.3(0.4x + -3.5)
(-2.94 + 0.42x) = 1.3(0.4x + -3.5)
Reorder the terms:
-2.94 + 0.42x = 1.3(-3.5 + 0.4x)
-2.94 + 0.42x = (-3.5 * 1.3 + 0.4x * 1.3)
-2.94 + 0.42x = (-4.55 + 0.52x)
Solving
-2.94 + 0.42x = -4.55 + 0.52x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.52x' to each side of the equation.
-2.94 + 0.42x + -0.52x = -4.55 + 0.52x + -0.52x
Combine like terms: 0.42x + -0.52x = -0.1x
-2.94 + -0.1x = -4.55 + 0.52x + -0.52x
Combine like terms: 0.52x + -0.52x = 0.00
-2.94 + -0.1x = -4.55 + 0.00
-2.94 + -0.1x = -4.55
Add '2.94' to each side of the equation.
-2.94 + 2.94 + -0.1x = -4.55 + 2.94
Combine like terms: -2.94 + 2.94 = 0.00
0.00 + -0.1x = -4.55 + 2.94
-0.1x = -4.55 + 2.94
Combine like terms: -4.55 + 2.94 = -1.61
-0.1x = -1.61
Divide each side by '-0.1'.
x = 16.1
Simplifying
x = 16.1
Slope is - 1 and (0, 2) is on the line
Answers
2=-1(0)+b
2=0+b
2=b
Equation: y=-x+2
From the sum of -265 and -156 subtract the sum of 356 and -250
pls send with showing how to do the sum
Pls ASAP
Answers
Answer:
315
Step-by-step explanation:
The sum of -265 and -156:
-265 + (-156)
= -265-156
= -421
The sum of 356 and -250:
356 + (-250)
= 356-250
= 106
The sum of both:
-421 + 106
= -315
Hope this helped!
if 8 identical items together weigh 30 kg, how much does each one weigh?
Answers
Answer:
each weighs 3.75 minimum
Answer:
Each item weighs 3.75 kg, or 3 and 3/4 kg.
Step-by-step explanation:
divide the total weight by the total amount of items. 30/8=3.75
hope this helped! :)
Darnell is counting the number of vehicles that pass through an intersection per hour. Based on his count, he writes a function that approximates his data. What number set serves as the domain of Darnell's function?
Answers
Answer:
all whole numbers greater than or equal to 0
Step-by-step explanation:
Give the values of the coefficients [a], [b], and [c], regarding the product in the form of ax^2-bx + xy - cy. Use "0" if the term isn't present.
Answers
Answer:
[tex]x^{2} -6x+xy-6y[/tex]
Step-by-step explanation:
Answer:
The values of coefficients a, b and c are
a=1
b=6
c=6
Step-by-step explanation:
We need to give the values of coefficients [a],[b] and [c] regarding the product in the form of [tex]ax^2-bx + xy - cy[/tex]
The term given is: [tex](x+y)(x-6)[/tex]
First we will multiply the terms
[tex](x+y)(x-6)\\=x(x-6)+y(x-6)\\=x^2-6x+yx-6y[/tex]
Now comparing the product [tex]x^2-6x+yx-6y[/tex] with the given form [tex]ax^2-bx + xy - cy[/tex]
The values of coefficients a, b and c are
a=1
b=6
c=6
Please help ASAP! Mathematics!
Answers
Answer:
B.) See attachment below
Step-by-step explanation:
Answer:
Personally, I would say the answer is B.
But don't quote me.
Sorry if i'm wrong. Let me know if I am.
Have a great day hon.
Which congruence theorem can be used to prove △BDA ≅ △DBC?
Triangles B D A and D B C share side D B. Angles C B D and A D B are right angles. Sides C D and B A are congruent.
HL
SAS
AAS
SSS
Answers
Answer:
HL
Step-by-step explanation:
The triangles share a congruent hypotenuse as well as one side. This qualifies for the Hypotenuse leg theorem.
Answer:
A: HL
Step-by-step explanation:
Formed from sentences P and Q, the sentence P or Q is a
A) biconditional.
B) complementary.
C) conditional
D) disjunction.
Answers
Answer c I think
Step-by-step explanation:
solve for K and b. please :)
Answers
Answer:
k=-98
b=-7
Step-by-step explanation:
can i have brianliest :)
Miguel has $25. He spends $6.75 on a movie ticket, $3.70 for snacks, and $2.00 for bus fare each way.
How much money does Miguel have left?
Miguel has $_____
left.
Answers
Answer:
$12.55
Step-by-step explanation:
25-6.75=18.25
18.25-3.70=14.55
14.55-2=12.55
Miguel has $12.55 left
Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(6, 0) and line x = −6.
Answers
The equation of the graph is [tex]x = \frac 1{24}y^2[/tex]
How to determine the equation?Generally, a point is represented as:
(x,y)
The line x = -6 means that:
(-6, y)
So, we calculate the distance between (x,y) and (-6, y) as follows:
[tex]d = \sqrt{(x + 6)^2 + (y - y)^2}[/tex]
This gives
[tex]d = \sqrt{(x + 6)^2 }[/tex]
Next, we calculate the distance between (6,0) and (x, y) as follows:
[tex]d = \sqrt{(x - 6)^2 + (y - 0)^2}[/tex]
This gives
[tex]d = \sqrt{(x - 6)^2 + y^2}[/tex]
Equate both distance expressions
[tex]\sqrt{(x + 6)^2} = \sqrt{(x - 6)^2 + y^2}[/tex]
Square both sides
[tex](x + 6)^2 = (x - 6)^2 + y^2[/tex]
Expand
[tex]x^2 + 12x + 36 = x^2 - 12x + 36 + y^2[/tex]
Evaluate the like terms
[tex]12x = - 12x + y^2[/tex]
Add 12x to both sides
[tex]y^2 = 24x[/tex]
Make x the subject.
[tex]x = \frac 1{24}y^2[/tex]
Hence, the equation of the graph is [tex]x = \frac 1{24}y^2[/tex]
Read more about line equations at:
https://brainly.com/question/7098341
#SPJ1
Let f(x) = 5x + 4 and g(x) = x2 - 4. Find the following.
(gof)(-2)
Answers
Answer:
(g ￮ f)(-2) = 32
Step-by-step explanation:
Given
[tex]f(x)=5x+4[/tex]
[tex]g\left(x\right)=x^2-4[/tex]
We have to evaluate (g ￮ f)(-2), so first we will evaluate f(-2) then use this value to evaluate g(x).
Finding f(-2)
[tex]f(x)=5x+4[/tex]
[tex]f(-2) = 5(-2)+4[/tex]
[tex]= -10 + 4[/tex]
[tex]= -6[/tex]
Then
[tex]g\left(-6\right)=\left(-6\right)^2-4[/tex]
[tex]=36-4[/tex]
[tex]= 32[/tex]
Therefore,
(g ￮ f)(-2) = 32
Calculate how wide each space should be.
The lot is 41 feet wide.
The dividers are each 6 feet wide.
The dividers need to go evenly in
Answers
Answer:
Each space should be 6.83333 feet wide.
Step-by-step explanation:
a) Data and Calculations:
Lot = 41 feet wide
Dividers = 6 feet wide
For even spacing, 41/6 = 6.83333 feet
b) The quotient is equal to the dividend divided by the divisor. Since the lot is 41 feet wide, the quotient, when divided by some 6-feet wide dividers, will be equal to 6.83333 or 7 feet wide. This implies that each divider will occupy a space equivalent to 7 feet or specifically 6.83333 feet wide.
What is a number that could be placed in the blank to complete this set from least to greatest?
2/5, 1/2,----,6/8
Answers
Answer:
4/10, 5/10, 6/10
I'm guessing 6/10 simplified into 3/5
-1 1/2 minus positive 3 1/2--5/8 equals what
Answers
Answer:
[tex]2\frac{5}{8}[/tex]
Step-by-step explanation:
[tex]-1\frac{1}{2} - ( -3\frac{1}{2} ) - \frac{-5}{8} = 2\frac{5}{8}[/tex]