Answer:
b=43/3
Step-by-step explanation:
2/3+5=20-b
2/3+15/3=20-b
17/3=20-b
b=20-17/3
b=60/3-17/3
b=43/3
How many solutions does this system have?
Answer:
Infinitely many solutions.
Step-by-step explanation:
3x-5y=15
6x-10y=30
----------------
simplify 6x-10y=30 into 3x-5y=15
Answer:
C, Since there is is more then one solution
Step-by-step explanation:
What is the sum of the interior angles of an equilateral triangle?
A. 60°
B. 90°
C.180°
D.360°
Answer:
c
Step-by-step explanation:
simplify the following (y^2 -3y+4) (5y-3)
Answer:
y = 7/8 = 0.875
Step-by-step explanation:
hope it helps ^^
A local library bought 54 books. Some cost $32 each and some cost $44 each. The total cost of the books was $1,968. How many of the $32 books were purchased?
Answer:
Step-by-step explanation:
I think the answer is 34
To find the number of $32 books purchased, we can set up a system of equations. Solving the system using substitution, we find that the library purchased 34 of the $32 books.
Explanation:To solve this problem, we can set up a system of equations. Let's call the number of $32 books x and the number of $44 books y. We know that x + y = 54, since the library bought a total of 54 books. We also know that the total cost of the books is $1,968, which can be expressed as 32x + 44y = 1968. Now, we can solve this system of equations to find the value of x.
One way to solve this system is by substitution. Solving the first equation for x, we get x = 54 - y. Plugging this into the second equation, we have 32(54 - y) + 44y = 1968.
Expanding and simplifying, we have 1728 - 32y + 44y = 1968. Combining like terms, we get 12y = 240. Dividing both sides by 12, we find that y = 20. Plugging this back into the first equation x + 20 = 54, we get x = 34.
Therefore, the library purchased 34 of the $32 books.
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Which function represents the sequence: 4, 7, 10, 13, 16,...
Answer:
3n + 1
Step-by-step explanation:
Note the sequence has a common difference between consecutive terms, that is
7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3
This indicates that the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 4 and d = 3, thus
[tex]a_{n}[/tex] = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1
Answer:
[tex]\large\boxed{a(n)=3n+1}[/tex]
Step-by-step explanation:
It's an arithmetic sequence:
[tex]a(1)=4\\\\a(2)=a(1)+3=4+3=7\\\\a(3)=a(2)+3=7+3=10\\\\a(4)=a(3)+3=10+3=13\\\\a(5)=a(4)+3=13+3=16\\\vdots[/tex]
An explicit formula of an arithmetic sequence:
[tex]a(n)=a(1)+(n-1)d[/tex]
d - common difference
We have
[tex]a(1)=4,\ d=3[/tex]
Substitute:
[tex]a(n)=4+(n-1)(3)[/tex] use the distributive property
[tex]a(n)=4+3n-3[/tex]
[tex]a(n)=3n+1[/tex]
A carpenter wants to cut a 6 foot board into pieces 2/3 foot long . How many pieces can the carpenter make
Answer:
The carpenter can make 9 pieces.
Step-by-step explanation:
6/(2/3)=(6/1)(3/2)=18/2=9
7. 6h - 18 < 6h + 1
Answer:
Explanation:In this exercise we have to solve the following inequality:
[tex]6h-18<6h+1[/tex]
Step 1. Subtract 6h from both sides:
[tex]6h-18-6h<6h+1-6h[/tex]
Step 2. Simplify:
[tex]6h-6h-18<6h-6h+1 \\ \\ -18<1[/tex]
This is always true because -18 is a number less than 1. Therefore, for any real h-value the inequality is always true.
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The cost
y
y
(in dollars) to rent a kayak is proportional to the number
x
x
of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours.
a. Write an equation that represents the situation.
An equation that represents the situation is
y=
y=
.
Question 2
b. Which is the best Interpretation of the slope?
It costs $9 every 3 hours to rent a kayak.
It costs $9 per hour to rent a kayak.
It costs $81 per hour to rent a kayak.
It costs $24 per hour to rent a kayak.
Question 3
c. How much does it cost to rent the kayak for 5 hours?
It costs $ ? to rent the kayak for 5 hours.
a. An equation that represents the situation is y = 9 x
b. The best Interpretation of the slope is " It costs $9 per hour to rent a kayak " ⇒ 2nd answer
c. It costs $45 to rent the kayak for 5 hours
Step-by-step explanation:
Proportional relationship means two quantities vary with each other
If y varies directly as x, then
y ∝ x y = k xk is called the constant of proportionality You can find k by using the initial values of x and yThe cost " y " in (dollars) to rent a kayak is proportional to the
number of hours " x " that you rent the kayak
∵ y ∝ x
∴ y = k x , where k is the constant of proportionality
∵ It costs $27 to rent the kayak for 3 hours
∴ y = 27 and x = 3
- Substitute these value in the equation above
∴ 27 = k (3)
- Divide both sides by 3
∴ 9 = k
∴ y = 9 x
a. An equation that represents the situation is y = 9 x
∵ The slope is the unit rate of the cost
∵ The slope = 9
∴ The unit rate is $9 per hour
b. The best Interpretation of the slope is " It costs $9 per hour to rent a kayak "
∵ y = 9 x
∵ x = 5 hours
- Substitute x by 5 in the equation above
∴ y = 9 (5) = $45
c. It costs $45 to rent the kayak for 5 hours
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Final answer:
The equation representing the situation is y = 9x. The slope indicates that it costs $9 per hour to rent the kayak. For 5 hours of rental, the cost is $45.
Explanation:
If the cost (y) to rent a kayak is proportional to the number (x) of hours the kayak is rented, and it costs $27 to rent the kayak for 3 hours, we can use this information to write a linear equation that represents the situation. The cost is $9 per hour since $27 ÷ 3 hours = $9 per hour. Our equation is thus y = 9x.
For the interpretation of the slope, since we've determined the cost is $9 per hour, the correct interpretation of the slope is that it costs $9 per hour to rent the kayak.
To find out how much it costs to rent the kayak for 5 hours, we simply plug in x = 5 into our equation y = 9x. So, it costs y = 9 × 5 = $45 to rent the kayak for 5 hours.
Which statement is true for the tables?
1) Both Table A and Table B represent functions.
2) Both Table A and Table B do not represent functions.
3) Table A does not represent a function, but Table B represents a function.
4) Table A represents a function, but Table B does not represent a function.
Answer:
Table A represents a function, but Table B does not represent a function.
Step-by-step explanation:
We have to select the correct option among the given 4 options after judging the given two tables attached to this question.
The first table shows that for each x values there is only one y value. Therefore, this is a function.
But in the second table shows that for each x value there are multiple y values since we are getting y = 1 and 2 for x = 5.
Hence, table B is not a function. it is just a relation. (Answer)
Answer:
d.
Step-by-step explanation:
Solve by factoring 2x^2+13x-7=0
Answer:
x=-7 and (1/2)
Step-by-step explanation:
An astronaut weighs 49 kg on earth. On the moon, an
object's weight is 1/6 of its weight on earth. On Mars, an
object's weight is 0.38 of its weight on earth. What is the
difference between the astronaut's weight on Mars and her
weight on the moon? Round your answer to the nearest
tenth. *
approximately 10.4 kg
approximately 1.4 kg
approximately 104 kg
approximately 49 kg
Answer:
The correct answer is A. Approximately 10.4 kg.
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Weight of the astronaut on Earth = 49 kg
Weight of the astronaut on the moon = 1/6 * 49 kg
Weight of the astronaut on Mars = 0.38 * 49 kg
2. What is the difference between the astronaut's weight on Mars and her weight on the moon? Round your answer to the nearest tenth.
Weight of the astronaut on the moon = 1/6 * 49 kg
Weight of the astronaut on the moon = 8.2 kg
Weight of the astronaut on Mars = 0.38 * 49 kg
Weight of the astronaut on Mars = 18.6 kg
Difference between the astronaut's weight on Mars and her weight on the moon = 18.6 - 8.2
Difference between the astronaut's weight on Mars and her weight on the moon = 10.4 kg
(X+5) with exponent 1/2 equals (5-2x) with exponent 1/4
Answer: x=-2
Step-by-step explanation: Eliminate the fractional exponent by raising both sides of the equation by the reciprocal of the exponent.
Hope this helps you out! ☺
Answer:
x = -2.
Step-by-step explanation:
(x + 5)^1/2 = (5 - 2x)^1/4
Taking both sides to the power of 4:
(x + 5)^2 = 5 - 2x
x^2 + 10x + 25 = 5 - 2x
x^2 + 12x + 20 = 0
(x + 10(x + 2) = 0
x = -2, -10
Test for extraneous roots.
When x = -10
(-10 + 5)^1/2 = (-5)^1/2 which is not real.
When x = -2
(-2+5)^1/2 = 3 ^1/2
(5 - 2*(-2)) ^1/4 = 9 ^ 1/4 = 3^1/2
so x = -2 is a root.
GETS BRAINILIST!!!!What number should be placed in the box to help complete the division calculation? long division setup showing an incomplete calculation. 13 is in the divisor, 3302 is in the dividend, and 2 hundreds and 5 tens is written in the quotient. 2600 is subtracted from 3302 to give 702. An unknown value represented by a box is being subtracted from 702. Numerical Answers Expected! Answer for Blank 1:
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
Long division setup showing an incomplete calculation
13 is in the divisor3302 is in the dividend2 hundreds and 5 tens is written in the quotient2600 is subtracted from 3302 to give 702An unknown value represented by a box is being subtracted from 702We need to find this number
Lets write the steps above
∵ The dividend = 3302
∵ The divisor = 13
- 2 hundreds means 200 and 5 tens means 50
∵ The quotient = 200 + 50 + x
∵ Dividend = divisor × quotient
∴ (13 × 200) + (13 × 50) + (13 × x) = 3302
∵ 13 × 200 = 2600
- Subtract 2600 from the dividend
∴ 3302 - 2600 = 702
∵ 13 × 50 = 650
∴ 702 - 650 = 52 ⇒ 650 is the unknown value
∵ 13 × x = 13x
∵ 52 - 13x = 0
- Add 13 x to both sides
∴ 52 = 13x
- Divide both sides by 13
∴ x = 4
∴ 3302 ÷ 13 = 200 + 50 + 4
∴ 3302 ÷ 13 = 254
∴ From the steps above the missing number subtracted from
702 is 650
The unknown value is being subtracted from 702 is 650
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Answer:
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
Long division setup showing an incomplete calculation
13 is in the divisor
3302 is in the dividend
2 hundreds and 5 tens is written in the quotient
2600 is subtracted from 3302 to give 702
An unknown value represented by a box is being subtracted from 702
We need to find this number
Lets write the steps above
∵ The dividend = 3302
∵ The divisor = 13
- 2 hundreds means 200 and 5 tens means 50
∵ The quotient = 200 + 50 + x
∵ Dividend = divisor × quotient
∴ (13 × 200) + (13 × 50) + (13 × x) = 3302
∵ 13 × 200 = 2600
- Subtract 2600 from the dividend
∴ 3302 - 2600 = 702
∵ 13 × 50 = 650
∴ 702 - 650 = 52 ⇒ 650 is the unknown value
∵ 13 × x = 13x
∵ 52 - 13x = 0
- Add 13 x to both sides
∴ 52 = 13x
- Divide both sides by 13
∴ x = 4
∴ 3302 ÷ 13 = 200 + 50 + 4
∴ 3302 ÷ 13 = 254
∴ From the steps above the missing number subtracted from
702 is 650
The unknown value is being subtracted from 702 is 650
Step-by-step explanation:
p = $14,300
r = 7 1/2%
t = 4
What is i?
$4,290.00
$429.00
$4.29
Answer:
Value of I is $4290
Step-by-step explanation:
We have been given that,
Formula for simple interest is given by
Plugging the known values
On simplifying, we get
Hence, value of I is $4290
In a finsh tank, 75% is female finshes. The rest are male. Female fishes are also 5 more than twice
of the male fishes. How many female and male fishes in the tank?
(Set up the rational equation, and solve for x!) PLEASE HELP ME
Answer:
5 Male fishes, and 15 Female fishes
Step-by-step explanation:
We have two unknowns: The number of lady fishes (let's represent this number with "L"), and the number of male fishes (let's name this unknown number "M"). So now we need to create two equations to help us solve for these unknowns.
Use the actual sentences they give you to create the equations:
a) "75% of the total number of fishes are female"
Notice that the total number of fishes is the addition of the number of ladies plus the number of males; that is the total is "L+M". According to the sentence, 75% (which in math terms is written as "0.75") of this total number equals the number of lady fishes:
[tex]0.75 \,*\,(L+M)=L[/tex]
now we work a little the algebra indicated in this equation to simplify it a bit:
[tex]0.75 \,*\,(L+M)=L\\0.75\,L+0.75\,M=L\\0.75\,M=L-0.75\,L\\0.75\,M=0.25\,L\\L=\frac{ 0.75\,M}{0.25}\\L=3\,M[/tex]
which tells us that the number of lady fishes is 3 times thenumber of male fishes.
b) Now the second equation based on the words:
"Lady fishes are 5 more than twice the male fishes"
"Twice the male fishes" can be written as: "2M"
so now we write this sentence as:
[tex]L=2\,M+5[/tex]
Now we combine the two equations by using in the second one the replacement for "L" in terms of "M" that we found in the first equation (that is: "L = 3 M") , so we obtain an equation with just one unknown (M) and we can solve for it:
[tex]L=2\,M+5\\3\,M=2\,M+5\\3\,M-2\,M=5\\M=5[/tex]
Which tells us that the number of male fishes in the tank is "5".
We can use now our first simplified equation to find the number of lady fishes:
[tex]L=3\,M\\L=3\,(5)\\L=15[/tex]
So, there are 15 female fishes in the tank.
The shorter leg of a right triangle is 6 feet shorter than the longer leg. The hypotenuse is 6 feet longer than the longer leg. Find the side lengths of the triangle.
The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.
Step-by-step explanation:
Let,
Longer leg = a = x
Shorter leg = b = x - 6
Hypotenuse = c = x + 6
As the triangle is right angles, therefore, using pythagoras theorem;
[tex]a^2+b^2=c^2\\(x)^2+(x-6)^2=(x+6)^2\\x^2+(x^2-12x+36)=x^2+12x+36\\x^2+x^2-12x+36=x^2+12x+36\\ 2x^2-12x+36=x^2+12x+36[/tex]
Adding (-x² - 12x-36) on both sides
[tex]2x^2-12x+36-x^2-12x-36=x^2+12x+36-x^2-12x-36\\x^2-24x=0[/tex]
Taking x common;
[tex]x(x-24)=0\\[/tex]
Either,
x=0
or,
x-24 = 0 => x=24
As length cannot be 0 therefore,
Longer leg = x = 24 feet
Shorter leg = x-6 = 24-6 = 18 feet
Hypotenuse = x+6 = 24+6 = 30 feet.
The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.
Keywords: triangle, addition
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A pool gained 10 gallons of water on Friday due to rain. How could the owner of the pool bring the water level back to its previous level? Select all that apply.
A) Let her kids play in the pool and splash out 10 gallons
B) Let 10 gallons of water evaporate
C) increases the amount of water by 10 gallons due to rain
D) add 10 gallons of water with hose
E) drain 10 gallons of water from the pool
F) fill 10 old milk gallons with water and dump them into the pool
Answer:
A) B) E)
Step-by-step explanation:
I had this question on one of my tests and I got it right :)
The length of the long leg of a right triangle is 16 inches more than four times of the shorter leg. The length of the hypotenuse is 17 inches more than four times the length of the shorter leg. Find the side lengths of the triangle.
Answer:
The side lengths of the triangle, in order, are 11 inches, 60 inches, 61 inches.
Step-by-step explanation:
Let the shorter leg be x, the longer leg, y and the hypotenus, z.
y = 16 + 4x
z = 17 + 4x
By Pythagoras rule,
z^2 = x^2 + y^2
(17+4x)^2 = x^2 + (16+4x)^2
that is,
x^2 - 8x - 33 = 0 (A quadratic equation)
By factorising,
(x+3)(x-11)=0
either x = -3 or x = 11.
But length cannot be negative. Hence, -3 is dicarded.
x = 11 inches
y = 16 + 4x = 60 inches
z = 17 + 4x = 61 inches
Final answer:
To find the side lengths of the triangle, assume the shorter leg as 'x' inches. Use the given information about the longer leg and hypotenuse to write equations. Simplify the equation and solve for 'x' to find the side lengths of the triangle.
Explanation:
To find the side lengths of the triangle, let's assume that the shorter leg of the right triangle is 'x' inches.
According to the problem, the longer leg is 16 inches more than four times the shorter leg, so it can be written as '4x + 16' inches.
The hypotenuse is 17 inches more than four times the length of the shorter leg, so it can be written as '4x + 17' inches.
Applying the Pythagorean theorem (a² + b² = c²) to the triangle, we get (x² + (4x + 16)² = (4x + 17)²).
Simplifying the equation and solving for 'x', we find that the shorter leg is 15 inches, the longer leg is 76 inches, and the hypotenuse is 77 inches.
20% of the students in the class play an instrument. If there are 35 students in class, how many play an instrument?
Answer: 7
Step-by-step explanation:
35 x 0.20 = 7
Find the measure of the supplement of a 95 degree angle
Answer: it is 85 degrees
Step-by-step explanation:
anybody help me to solve this question.
Answer:
[tex]\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)} are\ in\ AP[/tex]
Step-by-step explanation:
Given that [tex](b-c)^2, (c-a)^2 , (a-b)^2[/tex] are in AP
To prove: [tex]\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}[/tex] are in AP
From given as we know if p , q, r are in AP then 2q= p+r.
[tex]2(c-a)^2= (b-c)^2+(a-b)^2\\\\\Rightarrow 2(c^2+a^2-2ac)=b^2+c^2-2bc+a^2+b^2-2ab\\\\\Rightarrow 2c^2+2a^2-4ac= 2b^2+c^2+a^2 -2bc-2ab\\\\\Rightarrow a^2+c^2-2b^2-4ac= -2bc-2ab\\\\\Rightarrow a^2-2b^2+c^2= 4ac-2bc-2ab[/tex]
Now
[tex]\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}2\dfrac{1}{(c-a)} =\dfrac{1}{(b-c)}+\dfrac{1}{(a-b)}\\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-b+b-c}{(b-c)(a-b)} \\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-c}{(b-c)(a-b)} \\\\\Rightarrow2(b-c)(a-b) = (c-a)(a-c) \\\\\Rightarrow 2(ab-b^2-ac+bc)= -(a-c)^2\\\\\Rightarrow 2ab- 2b^2-2ac+2bc = -a^2-c^2+2ac\\\\\Rightarrow a^2-2b^2+c^2=4ac-2ab-2bc[/tex]
Which is the result of AP
.
Hence proved
Angle addition and angle bisectors. Can someone help me with this please?
Answer:
ABE is 75
Step-by-step explanation:
If ABD = 108, that is the entire picture.
CBD is the part that is bisected. Bisector line BE cuts the angle in half.
Since CBD is 66, half of it is what is pictured on both sides of line BE.
Half of 66 is 33.
Angles EBE and EBD are both 33.
Angle ABE is ABC + CBE.
Angle ABE is also ABD - EBD.
ABE = ABD - EBD
ABE = 108 - 33
ABE = 75
What is the measure of < c
45°
56°
60°
66°
Answer:
c = 56
Step-by-step explanation:
The two angles 'c' and '124' form a straight angle. They add to 180
c+124 = 180
c+124-124 = 180-124 ... subtract 124 from both sides
c+0 = 56
c = 56
Answer:
56 <3
Step-by-step explanation:
Mrs. Martini is 6 years more than 3 times as old as Tony. Eight years ago, she
was 2 years less than 9 times as old as he was then. Find each of their ages.
Mrs Martini age is 42 years and Tony age is 12 years
Step-by-step explanation:
The given is:
Mrs. Martini is 6 years more than 3 times as old as TonyEight years ago, she was 2 years less than 9 times as old as he was thenAssume that Tony is x years old now
∵ Mrs. Martini is 6 years more than 3 times as old as Tony
∵ Tony is x years old
- Multiply the age of Tony by 3 and add 6 to the product
∴ The age of Mrs Martini = 3 x + 6
8 years ago
- Subtract 8 from the age of each one
Tony age = (x - 8)
Mrs Martini age = (3 x + 6) - 8 = 3 x + 6 - 8 = 3 x - 2
∵ Eight years ago, Mrs Martini was 2 years less than 9 times as old
as Tony was then
- Multiply Tony age by 9 and subtract 2 from the product
∵ Tony age from 8 years ago = x - 8
∵ Mrs Martini age from 8 years ago = 3 x - 2
∴ 9(x - 8) - 2 = 3 x - 2
- Simplify the left hand side
∴ 9 x - 72 - 2 = 3 x - 2
- Add like terms
∴ 9 x - 74 = 3 x - 2
- Subtract 3 x from both sides
∴ 6 x - 74 = -2
- Add 74 to both sides
∴ 6 x = 72
- Divide both sides by 6
∴ x = 12
∵ x represents the age of Tony
∴ Tony is 12 years old
∴ 3 x + 6 is the age of Mrs Martini
- Substitute x by 12
∵ 3(12) + 6 = 36 + 6 = 42
∴ Mrs Martini is 42 years old
Mrs Martini age is 42 years and Tony age is 12 years
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define the solution to a system of linear inequalities.
The solution to a system of linear inequalities is the set of values that satisfy all the inequalities at once, graphically represented as the overlapping shaded region on a coordinate plane.
Explanation:The solution to a system of linear inequalities is defined as the set of values that satisfy all inequalities in the system simultaneously. To find this solution set, each inequality is graphed on the same coordinate plane to determine the region where all inequalities overlap. Within this region, any point represents a solution to the system. If an inequality is non-strict (less than or equal to or greater than or equal to), the boundary line is included in the solution set and is usually drawn as a solid line. If the inequality is strict (less than or greater than), the boundary line is not included in the solution set and is depicted as a dashed line. The solutions are typically represented graphically by shading the area of the plane that satisfies all conditions.
A series of books has 30 volumes, each with 700 pages. What is the total number of pages in the series?
Answer:
Step-by-step explanation:
Here we have to multiply to find the total...
30 volumes, then each individual book with 700 pages, therefore, the answer would be 21,000 pages
To calculate the total number of pages in the series, multiply the number of volumes (30) by the pages per volume (700) to get a total of 21,000 pages.
Explanation:The question asks for the total number of pages in a series of books, assuming each of the 30 volumes has 700 pages. Therefore, the calculation we need to perform is: 30 volumes × 700 pages per volume.
The formula to calculate the total number of pages is:
Total Pages = Number of Volumes × Pages per Volume
By inserting the given values into the formula:
Total Pages = 30 × 700 = 21,000 pages.
Hence, the total number of pages in the series is 21,000.
Which statements are true given the histogram? Check
all that apply.
The histogram is symmetrical.
The histogram is evenly distributed.
The cluster from 4 p.m.-10 p.m. means that most of
the texts were sent in the afternoon and evening.
U More texts were sent from 6 p.m.-8 p.m. than from 8
p.m.-10 p.m.
The peak from 4 p.m.-6 p.m. means that the highest
number of texts was sent during this interval.
10 pm-1159
Answer:
C and E
Step-by-step explanation:
The cluster from 4 p.m.–10 p.m. means that most of the texts were sent in the afternoon and evening.
The peak from 4 p.m.–6 p.m. means that the highest number of texts was sent during this interval.
What is
The equation of the line that passes through the points (5,-1) and (4,-5)
For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have two points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 5, -1)\\(x_ {2}, y_ {2}) :( 4, -5)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5 - (- 1)} {4-5} = \frac {-5+ 1} {- 1} = \frac {-4} {- 1} = 4[/tex]
Thus, the equation is of the form:
[tex]y = 4x + b[/tex]
We substitute one of the points and find b:
[tex](x,y):(5,-1)\\-1=4(5)+b\\-1=20+b\\-1-20=b\\b=-21[/tex]
Finally, the equation is:
[tex]y = 4x-21[/tex]
Answer:
[tex]y = 4x-21[/tex]
What is the value of x in the equation? 5 5/6 x + 2 2/3 = 12
Answer:
The value of x is 8/5
Step-by-step explanation:
(35/6)x + (8/3) = 12
(35/6)x = 28/3 (cross multiplication)
105x = 168
x = 8/5
Answer: 1 3/5 or 8/5
Step-by-step explanation:
what is the force of an object with the mass of 27 kg and an acceleration of 4.75m/s?
Answer:
F = 128.25 Newtons
Step-by-step explanation:
The force of an object is the combination of its mass and its acceleration. The formula is:
F = ma
Where
F is the force in Newtons
m is the mass in (kilograms)
a is the acceleration (in m/s^2)
Given,
m = 27
a = 4.75
We now need to find the force, so we plug the known information and solve easily:
F = ma
F = 27 * 4.75
F = 128.25 Newtons