Step-by-step explanation:
Simon only used 125ml milk
250÷2=125
Craig used 375ml milk
250x1.5=275
Write in point-slope form an equation of the line through each pair of points. (-4,10) and (-6,15)
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 10) and (-6 , 15), is y - 10 = -5/2(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , 10) and (-6 , 15).
m = (y2 - y1)/(x2 - x1)
m = (15 - 10)/(-6 - -4)
m = 5/-2
m = -5/2
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = -5/2 and (x1 , y1) = (-4 , 10)
(y - 10) = -5/2(x - -4)
y - 10 = -5/2(x + 4)
To learn more about equation of line in point slope form: brainly.com/question/24907633
#SPJ4
Δ A B C has vertices A(-3,3), B(2,5) , and C(4,-3) . What are the coordinates of the centroid of ΔA B C ? Explain the process you used to reach your conclusion.
The coordinates of the centroid of Δ ABC is y = -1/3x + 2.
What is meant by the slope of the line?
The slope of the line is the rise-to-run ratio or the rise divided by the run. It expresses the slope of a line in the coordinate plane. Finding the slope of a line is similar to determining the slope between two points.
The midpoint D of AC is (-3+4/2, 3-3/2) or (1/2, 0).
Note that DB is a line that connects the vertex B and D, the midpoint of AC.
The slope of the line DB is ((5-0)/(2-1/2)) or 10/3.
The equation of DB is
y - 5 = 10/3 (x - 2)
simplifying the above equation, we get
y - 5 = 10x/3 - 20/3
y - 5 + 5 = 10x/3 - 20/3 + 5
y = 10x/3 - 5/3
Use the same method to find the equation of the line between point A and the midpoint of BC.
Therefore, the coordinates of the centroid of Δ ABC is y = -1/3x + 2.
To learn more about the slope of the line refer to:
https://brainly.com/question/16949303
#SPJ4
What is the area of the figure below?
The area of the figure is 289 square unit
What is Area of a Rectangle ?The area of a rectangle can be calculated by multiplying the length and the width of the shape.
Given that
L = 20 - xB = 3x + 8A = LBBut the length and the width have two equal opposite sides. The shape is a square
20 - x = 3x + 8
20 - 8 = 3x + x
12 = 4x
x = 12/4
x = 3
L = 20 - 3 = 17
B = 3(3) + 8
B = 9 + 8
B = 17
A = 17 x 17
A = 289 square unit
Therefore, the area of the figure is 289 square unit
Learn more about Area here: https://brainly.com/question/25292087
#SPJ1
URGENTT ! PLEASE HELP :3
Write the component form of →PQ .
The vector PQ is given by the addition of the components of the two vectors i.e. →PQ = →Q + →P
Vector is a quantity having magnitude as well as direction and is used to denote the mathematical and geometrical direction of the given quantity.
For example : Velocity, Displacement etc.
Let us first assume that,
P(x,y,z) and Q(u,v,w)
Now, we need to find the vector PQ
→PQ = →Q + →P
= (ui + vj + wk ) + (xi + yj + zk)
= (ui + xi ) +(vj + yj) + (wk +zk)
= (u+x) i + (v + y) j + (w + z)k
= →PQ
For example : Let P(1,2,1) and Q ( -1, -2,4)
Then, →PQ = →Q + →P
= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)
= (1-1) i + (2 -2) j + (1 + 4)k
= oi+0j +5j
= 5j
Hence, the vector PQ is given by the addition of the components of the two vectors.
To learn more about Vectors, here
https://brainly.com/question/24256726
#SPJ4
What are the solutions to the equation x² = 169? select each correct answer. −84.5 negative 84.5 −13 negative 13 13 13 84.5
The correct answer is A. 13.
We have been given equation. Now, to find the value of x, we will take square root. So, solving the mathematical expression now -
x = √169
Taking square root to find the value of x
x = 13
Since the number is positive. the square root of the number will also be positive.
Hence, the solution to equation is A. 13.
Further to cross check, we can also square the resultant number.
On squaring the number 13 for validation of our result, we get 169. It is the same number as in mathematical expression provided to us. Thus, our resultant solution to equation is correct.
Learn more about calculations on equation -
https://brainly.com/question/28428939
#SPJ4
The complete question is -
What are the solutions to the equation x² = 169? Choose all answers that are correct. A. 13 B. –13 C. 84.5 D. –84.5
When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent. If the path of a ball forms a 53^{\circ} angle with the floor, find \(m \angle A B C\).
The ball hits the surface at 43.5° and bounces back at 43.5°.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given that When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent.
If the path of a ball forms a 53 angle with the floor, find the angle with the floor, x
Let the angle with the floor, x
Using, to find x, setup the equation:
x+ 53 +x=180
2x+ 53 =180
2x = 127
x= 43.5°
Therefore, the ball hits the surface at 43.5° and bounces back at 43.5°.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ4
x^2(3x-1)^4 integrate by parts
Answer:
[tex]81x {}^{6} - 108 { \times }^{5} + 54 { \times }^{4} - 12 { \times }^{3} + { \times }^{2} [/tex]
A brick path is being installed around a circular pond. The pond has a circumference of 68 feet. The outer edge of the path is going to be 4 feet from the pond all the way around. What is the approximate circumference of the path? Round to the nearest hundredth.
The approximate circumference of the path Round to the nearest hundredth is 93.12 feet.
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
circumference of pond = 68 feet
⇒ 2πr = 68
⇒ r = 34/π
⇒ r = 10.82 feet
Now it is also given that, The outer edge of the path is going to be 4 feet from the pond all the way around
⇒ Radius of path, R = r + 4
⇒ Radius of path, R = 10.82 + 4
⇒ R = 14.828
So,circumference of the path = 2πR
⇒ circumference of the path = 2π*14.828 = 93.119 feet
⇒ circumference of the path Round to the nearest hundredth = 93.12 feet
Thus, the approximate circumference of the path Round to the nearest hundredth is 93.12 feet.
To learn more about circumference of circle :
brainly.com/question/13663465
#SPJ4
A scientist was in a submarine below sea level studying oceam life. Over the next ten minutes, she ascended 61.9 feet. How many feet had she been below sea level, if she was 21.6 feet below sea level after she ascended?
You can add the distance she travelled upwards to her new distance to get her old distance.
Essentially, 21.6 + 61.9 = 83.5.
This means she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.
Answer: she was 83.5 feet below sea level, before ascending 61.9 feet to 21.6 feet below sea level.
Step-by-step explanation:
The sum of three consecutive even integers is 18 more than five-halves the smallest integer. What is the product of the smallest and largest integer?
The product of the smallest and largest integer is 672
What is the product of the smallest and largest integer?Represent the smallest even integer with x.
So, the other even integers are x + 2 and x + 4
The sum is represented as
x + x + 2 + x + 4 = 18 + 5/2x
Evaluate the like terms
3x + 6 = 18 + 5/2x
Evaluate the like terms
1/2x = 12
Multiply by 2
x = 24
The largest integer is x + 4
So, we have
x + 4 = 24 + 4
x + 4 = 28
The product of the smallest and largest integer is
Product = 24 * 28
Evaluate
Product = 672
Hence, the product of the smallest and largest integer is 672
Read more about consecutive integers at:
https://brainly.com/question/10853762
#SPJ1
What is the solution of the equation 3⁻ˣ = 1/243 ?
Answer:
well done .....I hope it's helpful
Write a function rule for each relation below.
1)
X:
-2
-1
0
1
2:
Y
-2
2
6
10
14
Answer:
x | y
-2. -2
-1. 2
0. 6
1. 10
2. 14
how many numbers do we have between each number on Y? 4
Step 1
this you have to use this data to make your function
f(x)=4X
Always you have to use the spaces times X
Step 2
We have to calculate what do we need to satisfy the function, in this case we have to add 6
f(x)=4x+6
Can someone pls help me I need to know if I am correct
If you have the fraction - 8/5 (the negative sign is not on either 8 or 5) it means that both numbers are negative right?
Answer:
Yes, that means the whole fraction is negative.
Also for future note, if the negative is on the top or bottom, the fraction will still be negative. Unless it says to simplify.
Hope this helps!
Solve for d.
19d -16d-d-d-1 = 12
Answer:
d = 13
Step-by-step explanation:
19d - 16d - d - d - 1 = 12
19d + (-16 - 1d - 1d) - 1 = 12
19d + (--18d) - 1 = 12
19d - 18d - 1 = 12
1d = 12 + 1
d = 13
Check:
19*13 - 16*13 - 13 - 13 - 1 = 12
247 - 208 - 26 - 1 = 12
39 - 27 = 12
For the past 4 years, Jesse has grown 3 inches each year. He is now 15 years old and is 5 feet 6 inches tall. He predicts that when he is 20 years old, he will be 6 feet 9 inches tall. What would you tell Jesse about his prediction?
He estimates that he will stand 6 feet 9 inches tall when he is 20 years old. His prediction is correct.
How to check Jesse's prediction?Given: Growth per year = 3 inches
Height at 15 yrs of age = 5'6''
Height at 20 yrs of age = 6'9''(predicted)
We know that Jesse grows 3 inches every year.
In 5 years(15yrs - 20yrs) his growth = 5 × 3 = 15 inches.
At 15 years(present) height = 5'6''
At 20 years (future) height = 5'6'' + 15'' = 6'9'' (since, 1ft = 12 inches)
Thus, Jesse's prediction is correct
To learn more about feet and inches, refer to:
https://brainly.com/question/8019254
#SPJ4
You are choosing between two health clubs. Club A offers membership for a fee of $28 plus a monthly fee of $28. Club B offers membership for a fee of $23 plus a monthly fee
of $29. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Answer:
Step-by-step explanation:
Find the value of A if the 4-digit number 3A5A is divisible by 15.
The value of A in the 4-digit number is 5.
What is the value of A?Given the information provided in the question, the 4-digit number is a multiple of 15. A multiple of a number is the product of an integer and that number.
The multiple of a number is divisible by that number. For example, a multiple of 2 is 20. This is because 2 multiplied by 10 is equal to 20 and 20 is divisible by 2 to yield a value of 10.
The multiplies of 15 either have a unit value of 5 or 0.
If A is 5, the number becomes 3555.
3555 / 15 = 237
If A is 0, the number becomes 3050
3050 / 15 = 203.333
Thus, the value of A is 5 because 3555 is divisible by 15.
To learn more about multiples, please check: https://brainly.com/question/26030133
#SPJ1
The monthly minutes on your cell phone can add
up to no more than 700 minutes. You have used
648 minutes. Write an inequality that represents
how many more minutes m you can use during the
rest of the month.
The knowledge of how many more minutes m you can use during the rest of the month is given by the linear inequality 648 + m ≤700, where 'm' is the minutes on the cell phone or simply m ≤ 52
It is given that the monthly minutes on your cell phone can add up to no more than 700 minutes so the highest limit is 700
And You have already used 648 minutes so this is our base for the formation of linear inequality
We are provided to use 'm' for rest of the minutes on the cell phone
Hence, we can form a linear inequality using the three points as the sum of already used minutes and the maximum minutes that can be used in this month is at most 700 minutes is given by 648 + m ≤700
This can also be simplified as
m ≤ 700 - 648
m≤52
To know more about Linear inequality - https://brainly.com/question/11897796
#SPJ1
For all x,(x-7)²= ?
A x²-49
B x² + 49
C x² - 14x - 49
D x² - 14x + 49
E x² + 14x - 49
Answer:
I'm pretty sure the answer is E
If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct characters (letters or numbers)? report answer to 3 decimal places.
Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:
For the first card, all can be selected.For the second card, 48 out of the remaining 51 cards will be available, removing the three cards with the same letter or number as the first.For the third card, 45 out of the remaining 50 cards will be available, removing the six cards whose letters or numbers have already been chosen.For the fourth card, 42 out of the remaining 49 cards will be available, removing the nine cards whose letters or numbers have already been chosen.Hence the probability is given by:
p = 48/51 x 45/50 x 42/49 = 0.726.
0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
A student has some 1 bills and 5 bills in his wallet. He has a total of 15 bills that are worth 47 . How many of each type of bill does he have?
If a student has some 1 bills and 5 bills in his wallet and he has a total of 15 bills that are worth 47, then the number of 1 bills he has is equal to 7 and the number of 5 bills he has is equal to 8.
The number of bills of each type can be calculated by forming a system of equations.
Consider x to be the number of 1 bills and y to be the number of 5 bills.
The first equation can be given as,
x + y = 15
The second equation can be given as,
x + 5y = 47
The two equations can be solved by using the substitution method:
By rearranging the first equation the value of x can be calculated to be,
x + y = 15
x = 15 - y
Putting this value of x in the second equation,
x + 5y = 47
15 - y + 5y = 47
4y = 47 - 15
4y = 32
y = 32 ÷ 4
y = 8
The value of x can be determined by putting y = 8 in the first equation,
x + y = 15
x + 8 = 15
x = 15 - 8
x = 7
Hence, the number of 1 bills and 5 bills are equal to 7 and 8 respectively.
To learn more about the substitution method, click here:
https://brainly.com/question/25869125
#SPJ4
Question 2
Find the unit rate.
If there are 8 teaspoons for every 4 cups in a recipe. How many
teaspoons are there in one cup?
teaspoons
What is the value of x?
6
O 7
08
09
Answer:
7
Step-by-step explanation:
5x + 3 = 38
5x + 3 - 3 = 38 - 3
5x = 35
5x ÷ 5 = 35 ÷ 5
x = 7
In a company, the penalty for being late for work in one month
follows the table below.
Late the first 3 times
$10 total
For every additional time $8 per time
If Jane paid $42 for the penalty last month, how many times
was she late for work?
___times
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
The expression is simplified to s = -5/ 4
What are algebraic expressions?Algebraic expressions are expressions composed of terms, variables, constants, factors and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expression;
42 = 14{ 4 + 4/ 5s}
Divide both sides by 14
42/14 = 14{ 4 + 4/ 5s}/14
3 = 4 + 4/ 5s
3 = 20 + 4s/5
cross multply
15 = 20 + 4s
collect like terms
15 - 20 = 4s
-5 = 4s
Make 's' the subject
s = -5/ 4
Thus, the expression is simplified to s = -5/ 4
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
It takes Andrea 12.5 hours to drive 875 miles. What was her average Speed?
Answer:
70 miles per hour
Step-by-step explanation:
take 875mi and divide by how long it took: 12.5 hours
Question
Find the sum.
(1−5q)+2(2.5q+8)
Answer:
[tex]1 - 5q + 5q + 16 \\ = 17[/tex]
Given point Y is between X and Z, where XY = 12 and XZ = 48, What is YZ?
Answer: 36
Step-by-step explanation:
XZ=XY+YZ
48=12+YZ
48-12=12-12+YZ
YZ=48-12
YZ=36
In a company, 70% of the workers are men. If 990 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
Step-by-step explanation:
990 x 70% = 693 people
