The equation of the line that passes through the points (2, 15) and (5, 21) is y = 2x + 11
The coordinates of the first point = (2, 15)
The coordinates of the second point = (5, 21)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (21-15) / (5-2)
= 6 / 3
= 2
The slope intercept form is
y = mx + b
Substitute the values
15 = 2(2) + b
15 = 4 + b
b = 15 - 4
b = 11
Substitute the values in the equation
y = 2x + 11
Therefore, the equation of the line in slope intercept form is y = 2x + 11
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Help please!!!!!!!!!!
Answer:
36
Step-by-step explanation:
4/9 x = 16
9/4 * 4/9 x = 16 * 9/4
x = 36
what is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2. statement (1) alone..
For the given statement about hundredth digit of the given decimal z the following statement is true:
Option E. statement (1) and (2) together are not sufficient.
As given in the question,
Let us consider decimal z is represented by k.lmn
Here hundredth digit of z is equal to m
Now,
(1) The tenths digit of 100z is 2.
100z
= 100(k.lmn)
=klm.n
This implies n = 2
(2) The units digit of 1,000z is 2.
1,000z
= 1,000(k.lmn)
= klmn
This implies n =2
From both the statements we are getting the value of n which is not sufficient to get the value of required 'm'.
Therefore, Option E is the correct answer which shows both the statements are not sufficient to get the value required hundredth digit of decimal z.
The complete question is:
What is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2.
A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.
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Richard and Teo have a combined age of 28. Richard is 13 years older than twice Teo’s age. How old are Richard and Thiago?
Richard is 23years old and Thiago is 5years old
What is word problem?
A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
From the question,
Let R stands for Richard
T stands for Teo
we were told that the combined age of Richard and Teo is 28
i.e
R + T = 28 ......eqn (i)
we were also told that Richard is 13 years older than twice Teo’s age
i.e
R = 2T + 13 .....eqn(ii)
substituting 2T + 13 for R in eqn (i)
(2T+13)+T = 28
expanding the bracket
3T + 13 = 28
collecting like terms
3T = 28 - 13
3T = 15
T = 15/3
T = 5
Teo age is 5years
From eqn (i)
R + T = 28
R + 5 = 28
R = 28 - 5
R = 23
Hence, Richard age is 23years
From eqn (ii)
R = 2T + 13
substituting for R in the eqn
23=2T+13
collecting like terms
23-13=2T
10=2T
T=10/2
T=5
Hence. Thiago age is 5years
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Find the probability of rolling a um greater than 7 given that you rolled an odd number firt
As the out comes are (3,6), (5,6), (5,3), (5,4), (5,5),(3,5) when you rolled an odd number first so the probability of rolling a sum greater than 7 is 1/6
What is probability and example?The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). it will be written as P(heads) = 1/2.
Why do we use probability?Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.
There are total 36 possible outcomes of two dices when they are rolled.
N=36
now we have to consider the out comes having sum greater than 7
which are;
(2,6),(3,5),(3,6),(4,4) ,(4,5),(4,6),(5,3),(5,4),(5,5) ,(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)
and now selecting only those having first number is odd
so they are:
(3,5),(3,6),(5,3),(5,4),(5,5),(5,6)
now using probability formula;
Probability = favorable outcomes /total outcomes
value putting;
probability = 6/36
probability =1/6
this is our required answer.
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Probability of rolling an odd number on a single die is 3/6, or 1/2. This is because there are three odd numbers (1, 3, and 5) on a standard six-sided die, and the probability of rolling any given number is 1/6.
What is meant by Probability?Probability is a metric used to determine how likely an event or result is to occur. A decimal or fraction between 0 and 1 is typically used to express it, with 0 denoting that the event will not occur and 1 denoting that it will occur without a doubt. For instance, the likelihood of rolling a 6 on a conventional six-sided die is 1/6 since there is only one scenario out of the six conceivable events that will result in rolling a 6. By dividing the number of desired outcomes by the total number of potential possibilities, one may compute probability. In general, the more likely an event is to occur, the greater its probability.
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Add 3[tex]\frac{5}{6}[/tex]+(-1[tex]\frac{1}{6}[/tex] Write your answer as a mixed number in simplest form.
Answer: 2 2/3 or 8/3
Step-by-step explanation:
3 5/6 = 23/6
-1 1/6 = -7/6
23/6-7/6
16/6
simplify
8/3
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
3 [tex]\frac{5}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{5}{6}[/tex] = [tex]\frac{23}{6}[/tex] ( [tex]\frac{6}{6}[/tex] is the same one)
1 [tex]\frac{1}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex]
Adding a negative number is like subtracting a positive number.
[tex]\frac{23}{6}[/tex] - [tex]\frac{7 }{6}[/tex] = [tex]\frac{16}{6}[/tex] 6 goes into 16 2 times with 4 left over
2 [tex]\frac{4}{6}[/tex] Divide the top and bottom by 2 to get
2 [tex]\frac{2}{3}[/tex]
A line with a slope of 0 passes through the point (9, 8). What is its equation in slope-intercept form?
Answer: y = 0x + 8
Step-by-step explanation:
The slope-intercept form is y=mx + b
The slope is 0, and y-intercept is at (0,8)
So our equation is
y = 0x + 8
There are more than 360 different breed of dog recognized worldwide. Which inequality repreent thi tatement?
x > 360
x < 360
x ≥ 360
x ≤ 360
Answer:
should be the first one, x > 360
Step-by-step explanation:
im sorry if its wrong :*(
finding x??????????????????????????
Answer:
x = 12.5
Step-by-step explanation:
The inside angles of a triangle should sum 180°
then
2x + (7x+5) + (180 - (11x-25)) = 180
2x + 7x + 5 + 180 - 11x -25 = 180
-2x - 25 = 0
2x = -25
x -25/2
x = 12.5
helppp i need helpppp
Yo’s hi and Mariam are both driving from Chicago to Columbus yo’s hi leaves at 8:00 and averages 60 mph on the way.Mariam leaves at 8:15 and averages 65 mph on the way. The situation is modeled by this system, where x is the number of hours after Mariam leaves and y is the distance each will travel: y=60x+15
Y=65x
How long after Miriam leaves will she pass Yoshi, and how far will they each travel?
Answer:
x = 3
y = 195
Step-by-step explanation:
y = 60x + 15
y = 65x
65x = 60x + 15
5x = 15
x = 3
y = 65(3)
y = 195
Hope it helps!
What is the domain of this function?
Use the information in the table f (x), the graph g (x)and equation h (x) to evaluate the following expressions.
Drag and drop the most appropriate answer in the box provided.
Question 1
[tex](f \circ g)(-2)=f(-2) \cdot g(-2)=10 \cdot 3=\boxed{30}[/tex]
Question 2
[tex](g \circ h)(1)=g(1) \cdot h(1)=2(1^2 -9)=\boxed{-16}[/tex]
Question 3
[tex](g/f)(0)=\frac{g(0)}{f(0)}=\frac{0^2 -9}{6}=\boxed{-3/2}[/tex]
Question 4
[tex](h/f)(-3)=\frac{h(-3)}{f(-3)}=\frac{3^2 -9}{12}=\boxed{0}[/tex]
Write the linear equation of the following graph in slope-intercept form.
y =-1/2x
y=1/2x
y=-2x
y=2x
please help!!!!
The linear equation of the following graph in slope-intercept form will be; y=1/2x
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The slope of the line is calculated as follows:
m = Δy/Δx
To find the linear equation of the following graph in slope-intercept form.
Therefore, the slope of the line is;
m = Δy/Δx
m = 1/2
When we simplify it, then we get the equation as;
y=1/2x
Hence, The linear equation of the following graph in slope-intercept form will be; y=1/2x
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Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $264.00. On her second business trip she drove 200 miles in 3 days, and paid $165.00 for the rental. Find the daily fee, and find the mileage charge.
of the 360 people that attended a town meeting 96 were senior citizens what percent of the people that attended the town meeting are senior citizens if necessary round to the nearest tenth (1 point)
Will give brainliest need now
Answer: 0.26666667 (0.3)
A room is 9 feet by 12 feet. How far is it across from opposite corners?
A. 17
B. 14
C. 15
D. 11
the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams. what is the probability that the next report will weigh less than 45 grams?
The probability that the next report will weigh less than 45 grams = 0.106
In this question, we have been given the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams.
We need to find the probability that the next report will weigh less than 45 grams.
We have mean= 60 grams
Standard Deviation = 12 grams
First we convert 45 to z score.
45 converted to z score for given mean and standard deviation will be:
z = (45 - 60)/12
z = -1.25
So, from standard normal table a P-value:
P(x<45) = 0.10565
Therefore, the probability would be 0.10565
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A fair spinner has 12 equal sections: 3 red, 5 blue and 4 green.
It is spun twice.
What is the probability of getting not green then green?
Answer:
2/9 = approximately 0.22.
Step-by-step explanation:
There are a total of 12 possible outcomes when the spinner is spun once, so the probability of getting a result that is not green is 8/12, or 2/3. Similarly, the probability of getting green on the second spin is 4/12, or 1/3.
To find the probability of getting a result that is not green on the first spin and green on the second spin, you can multiply the probabilities of each individual event. Therefore, the probability of getting not green then green is (2/3) * (1/3) = 2/9 = approximately 0.22.
Alternatively, you could also use the principle of complementary probabilities to calculate the probability of getting not green on the first spin and green on the second spin. The probability of getting not green on the first spin is 1 - (4/12) = 8/12 = 2/3, and the probability of getting green on the second spin is still 4/12 = 1/3. Multiplying these probabilities gives a result of (2/3) * (1/3) = 2/9 = approximately 0.22.
8 1/2 - 6 1/4 = ? I would like to know the anwer of thi equation becaue i’m having trouble olving it. Thank you
Answer:
2 1/4
Step-by-step explanation:
Subtract the whole numbers first:
8 - 6 = 2
To subtract the fractions, change 1/2 to 2/4 since they equal the same thing and 2/4 has the same denominator as 1/4:
2/4 - 1/4 = 1/4 <--- all we needed to do was subtract the numerators
Your final answer is 2 1/4.
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
Answer:
B) 10
Step-by-step explanation:
The triangles are congruent by HL. Thus, by CPCTC, [tex]x=10[/tex].
13 Which situation could be modeled by a linear function?
(1) The value of a car depreciates by 7% annually.
(2) A gym charges a $50 initial fee and then $30 monthly.
(3) The number of bacteria in a lab doubles weekly.
(4) The amount of money in a bank account increases by 0.1%
monthly.
The situation could be modeled by a linear function is
(2) A gym charges a $50 initial fee and then $30 monthly.
What is a linear function?A linear function in mathematics is one that has either one or two variables and no exponents.
2) Let y be the total amount charged by the gym to a person for x months.
as the initial amount for every person is $30.
The gym charges [tex]50+30x[/tex] $ after x months.
Hence this is a linear equation.
The remaining situations cannot be expressed as a linear equation because they include percentages in them.
Every situation that has a percentage is an exponential function.
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Solve the system. Explain your answer using words, symbols, or both.
x+2y=8
x+y=2
Answer:
Using substitution method for to solve, X = -4 and Y = 6
Step-by-step explanation:
1) x+2y = 8
2) x+y = 2
solve 2)
x = 2-y
Then replaced it in 1)
(2-y) + 2y = 8
2 + y = 8
y = 6
then
x = 2 - 6
X = -4
h(a)=5a²
What is h(6)?
Answer:
h(6) = 180
Step-by-step explanation:
h(a)=5a²
for a=6
h(6) = 5(6)²
h(6) = 5*36
h(6) = 180
he graph shows the number of pages in each chapter of a book that Josh is reading. A number line going from 2 to 28. 1 dot is above 2. 0 dots are above 4. 0 dots are above 6. 0 dots are above 8. 2 dots are above 10. 0 dots are above 12. 3 dots are above 14. 2 dots are above 16. 1 dot is above 18. 2 dots are above 20. 2. dots are above 22. 0 dots are above 24. 1 dot is above 16. 0 dots are above 28. Which statement is true about the effect of the 2-page introduction chapter? The outlier of 2 increases the median page count. The outlier of 2 increases the mean page count. The outlier of 2 decreases the median page count. The outlier of 2 decreases the mean page count.
The outlier of 2 decreases the mean page count.
What is mean and median?
The mean is that the variety you get by dividing the total of a collection of values by the quantity of values within the set.
In distinction, the median is that the middle variety in an exceedingly set of values once those values square measure organized from smallest to largest.
Main Body:
From the picture we can know that outlier of 2 does not effect the median page count.
But outlier of 2 decreases the mean page count.
it can be found out by taking mean
(1+2+3+2+1+2+2+1)/8= 1.75
and if we remove outlier of 2 ,then
(1+3+2+1+2+2+1)/7 = 1.86
Hence ,the outlier of 2 decreases the mean page count.
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Answer:
the answer is d
Step-by-step explanation:
Which division equation represents the situation?
Answer: 6 divided by 2/3
Step-by-step explanation:
The division equation which represents the situation is 6 ÷ 2/3 = 9.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Division equation is the equation involving the operation of division.
The model shows there are 9 pieces that are each 2/3 feet long.
We can calculate the total length of the pieces using the multiplication equation.
9 × 2/3 = 6
Total length = 6 feet
Length of each piece = 2/3 feet
Number of pieces can be found using the division equation,
6 ÷ 2/3 = 9
Hence the division equation for the given situation is 6 ÷ 2/3 = 9.
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3. Apply Math Models Cynthia earns $680 in
commissions and is paid $10.25 per hour. Javier
earns $410 in commissions and is paid $12.50 per
hour. What will you find if you solve for x in the
equation 10.25x + 680 = 12.5x +410?
The earnings for both Cynthia and Javier are same for x hours.
What is commission?
When an employee completes a task, typically selling a certain volume of goods or services, they are compensated financially. Sales commissions are occasionally used by employers as incentives to boost employee productivity. It is possible to receive a commission in place of or in addition to a salary.
Given:
Cynthia earns $680 in commissions and is paid $10.25 per hour.
Javier earns $410 in commissions and is paid $12.50 per hour.
So, the equation is
10.25x + 680 = 12.5x + 410
To simplify this equation for x.
10.25x+ 680 =12.5x +410
680 ‐ 410 = 12.5x ‐ 10.25x
270 = 2.25x
x = 270/2.25
x = 120
If we plug x = 120 in both the values 10.25x + 680 and 12.5x + 410 then we will get the same values.
Hence, the earnings for both Cynthia and Javier are same for x hours.
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What is the approximate perimeter of this triangle?
Answer:
Step-by-step explanation:
perimeter = hypotenuse + side a + side b
sin = opposite / hypotenuse
tan = opposite/adjacent
find the hypotenuse
let x = hypotenuse
sin(55 deg) = 56 / x
x * sin(55 deg) = 56
x = 56 / sin(55 deg) use a calculator
x ~ 68.36
find the side adjacent to 55 degrees
let x = adjacent leg
tan(55 deg) = 56 / x
x * tan(55 deg) = 56
x = 56 / tan(55 deg) use a calculator
x ~ 39.21
add them together
perimeter = 56 + 68.36 + 39.21
perimeter ~ 163.57 or 164
Which of these represents the graph of x + 3y = 6
Answer:
PLEASE ADD A DANG PICTURE
Step-by-step explanation:
A line a pae through point (-3,5) and (0,0) and line b paed through point (3,5) and (0,0). Are line a and b parallel, perpendicular, or neither? Explain your anwer
A line 'a' and line 'b' are perpendicular to each other.
We know that the formula for the slope of line passing through two points (x1, y1) and (x2, y2) is,
m = (y2 - y1)/(x2 - x1)
A line 'a' passes through points (-3,5) and (0,0)
Let m1 be the slope of line 'a'
m1 = (0 - 5)/(0 - (-3))
m1 = -5/3
A line 'b' passes through points (3,5) and (0,0).
Let m2 be the slope of line 'b'
m2 = (0 - 5)/(0 - 3)
m2 = (-5)/(-3)
m2 = 5/3
We can observe that, m1 * m2 = -1
Since the product of slopes of the lines is -1, the lines a and b are perpendicular.
Therefore, the lines are perpendicular.
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Jessica and Anthony are trying to finish a large pizza all by themselves. If Jessica ate 7/12 of the pizza and Anthony ate 3/12 of the pizza, what fraction of the pizza is left? A pizza cut into 12 equal pieces.
ANSWER ASAP
Answer:
2/12 of the pizza is left.
Step-by-step explanation:
7/12 plus 3/12 is 10/12, then minus that from 12/12 and you get 2/12.