Answer:
90+x=30-3[x]
Step-by-step explanation:
collect like terms
x+3x=30-90
4x=-260
divide both sides by 4
x=-60/4
x=-4*3*5/4
x=-[3*5/1]
x=-[3*5]
x=-15
Answer:
The number is 60.
Step-by-step explanation:
Let x = unknown number.
Now we translate the sentence into an equation, one piece at a time.
When 90 is added to a number it equals 30 less than 3 times the number.
x + 90
When 90 is added to a number it equals 30 less than 3 times the number.
x + 90 = 3x - 30
We now solve the equation for x.
Subtract 3x from both sides.
-2x + 90 = -30
Subtract 90 from both sides.
-2x = -120
Divide both sides by -2.
x = 60
The number is 60.
Check:
When 90 is added to a number it equals 30 less than 3 times the number.
Add 90 to 60:
90 + 60 = 150
We get 150.
When 90 is added to a number it equals 30 less than 3 times the number.
Now multiply 60 by 3 and subtract 30.
3(60) - 30 = 180 - 30 = 150
We also get 150.
That means our answer of 60 is correct.
Answer: 60
15pts
f(x)=(x+6)/2
g(x)=2x - 6
Show your work to evaluate g(f(x)).
Answer:
g(f(x)) = -x - 18
Step-by-step explanation:
2x - 6( (x + 6) / (2) )
2x - 3( x + 6)
2x - 3x - 18
-x - 18
12 times what equals 250?
Answer:
[tex]20.83[/tex]
Step-by-step explanation:
[tex]12 \times x = 250 \\ 12x = 250 \\ \frac{12x}{12} = \frac{250}{12} \\ x = 20.83[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The equivalent value of the equation is A = 12 x 20.833 = 250
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p
Let the second number be q
Now , A = pq
when the value of p = 12
And , when the value of q
On simplifying the equation , we get
250 = 12 x q
So , the left hand side of the equation is equated to the right hand side by the value of 12 x q
250 = 12 x q
Divide by 12 on both sides , we get
q = 250/12
On simplifying , we get
q = 20.833
Therefore , the value of q = 20.833
Hence , the expression is A = 12 x 20.833 = 250
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ6
evaluate the given expression if x=25, y=10, w=45, and z=10 (x-y)^2+10wz
Answer:
4725
Step-by-step explanation:
25-10=15
15^2=225
10*45*10=4500
225+4500=4725
A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square? What is the ratio of the areas from the larger square to the smaller square?
Answer:
The vertices are:
A' = (-3, -3)
B' = (3, -3)
C' = (3, 3)
D' = (-3, 3)
The ratio of area of larger square to smaller square is 9:1
Step-by-step explanation:
Given:
A 2 x 2 square is centered at the origin.
So, the center of the square is (0, 0)
Since it is 2 x 2 square, the side of the square is 2 units.
So, the vertices of the 2 x 2 square are A (-1, -1), B(1, -1), C(1. 1), D(-1, 1)
The above square is dilated by a factor of 3.
Let's name the dilated square A'B'C'D'
To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.
A(-1, -1) = 3(-1, -1) = A'(-3, -3)
B(1, -1) = 3(1, -1) = B'(3, -3)
C(1, 1) = 3(1, 1) = C'(3, 3)
D(-1, 1) = 3(-1, 1) = D'(-3, 3)
To find the area of the small square
the side of the small square is 2 units
so the are of the small square is [tex]2^2[/tex] = 4 square units
To find the area of the larger square
lets find the side AB of the square using distance formula
=>[tex]\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}[/tex]
=>[tex]\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}[/tex]
=>[tex]\sqrt{(3 +3)^2 +(-3 +3)^2}[/tex]
=>[tex]\sqrt{(6)^2 +(0)^2}[/tex]
=>[tex]\sqrt{36}[/tex]
=>6
AB =6 units
In a square all the sides will be equal
Now the area of the larger square will be
[tex]6^2[/tex]
36 square units
The ratio of larger square to smaller square is
=>36 : 4
=>9 : 1
What is the mean of this data set? If necessary, round your answer to the
nearest tenth.
12, 16, 22, 23, 34, 44, 46, 47, 48, 64, 67, 73, 83, 88, 89
Answer:
50.4
Step-by-step explanation:
First, add the values. You will get 756. The you divide the sum by the number of data values, which is 15. You will end up with 50.4
Answer: 50.4
Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many number are in the set.
So to find the mean of the data set shown here, let's begin by adding the numbers.
12 + 16 + 22+ 23 + 34 + 44 + 46 + 47 + 48 + 64 + 67 + 73 + 83 + 88 + 89 = 756
756 will be divided by how many numbers are in the set which is 15 which gives us 50.4.
50.4 is already rounded to the nearest tenth.
If F(x) = 2x-5 and G(x) = x + 1, what is G(F(x)) ?
A Chemist needs to mix a 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution. How many liters of each acid solution must be used?
Please explain well!!
Answer:
8 Liters of 20% acid and 7 Liters of 50% acid
Step-by-step explanation:
Let we mix "x" liters of 20% acid, and
"y" liters of 50% acid
Total is 15 liters, so we can write:
x + y = 15
or x = 15 - y
Then,
We mix x liters of 20% (20/100=0.2) and y liters of 50% (50/100=0.5) acid solution to make 15 liters of 34% (34/100=0.34) solution, we can write:
0.2x + 0.5y = 0.34(15)
This becomes:
[tex]0.2x + 0.5y = 5.1[/tex]
We replace x with what we got in 1st equation and solve for y:
[tex]0.2x + 0.5y = 5.1\\0.2(15-y) + 0.5y = 5.1\\3-0.2y+0.5y=5.1\\0.3y=5.1-3\\0.3y=2.1\\y=\frac{2.1}{0.3}\\y=7[/tex]
We know x = 15 - y, so
x = 15 - 7
x = 8
So, we use 8 Liters of 20% acid and 7 Liters of 50% acid
Final answer:
To find out how many liters of each acid solution (20% and 50%) a chemist needs to mix to get 15 liters of a 34% acid solution, a system of equations using the volumes and concentrations is set up and solved to determine the exact volumes needed.
Explanation:
To solve the problem of mixing a 20% acid solution with a 50% acid solution to get 15 liters of a 34% acid solution, we can set up a system of equations based on the volumes and concentrations. Let's define x as the number of liters of the 20% solution and y as the number of liters of the 50% solution. The first equation is based on the total volume: x + y = 15. The second equation is based on the total amount of pure acid: 0.20x + 0.50y = 0.34 × 15. Solving this system gives us the volumes needed for each solution.
Steps to Solve the System of Equations:
Write the two equations:
x + y = 15 (the volume equation)
0.20x + 0.50y = 5.1 (the acid equation, since 0.34 × 15 = 5.1)
Solve one of the equations for x or y. For instance:
x = 15 - y
Substitute into the second equation and solve for y:
0.20(15 - y) + 0.50y = 5.1
Solve for y, which represents the volume of the 50% solution:
Substitute the value of y back into any of the original equations to solve for x, which represents the volume of the 20% solution:
By following these steps, the chemist can determine precisely how many liters of each acid solution must be used to obtain the final mixture.
3 - 0.3y = 5.1
y = 7 liters
x = 8 liters
What is x ?
x + 5 + 2x = x + 15
Answer:
x = 5Step-by-step explanation:
[tex]x+5+2x=x+15\qquad\text{combine like terms}\\\\(x+2x)+5=x+15\\\\3x+5=x+15\qquad\text{subtract 5 from both sides}\\\\3x+5-5=x+15-5\\\\3x=x+10\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x-x=x-x+10\\\\2x=10\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{10}{2}\\\\x=5[/tex]
If you know it, get the brainliest answer.
Answer:
[tex]2x^4+4x^2-3[/tex]
Which of the following is the missing justification?
Step Justification
one fifth times x plus six equals five Given
x + 30 = 25
x = −5 Subtraction Property of Equality
A Multiplication Property of Equality
B Distributive Property
C Addition Property of Equality
D Division Property of Equality
Answer:
No idea what the other person who answered was trying to say since it has to be 1 answer but i think its multiplication because to get 1/5 to be 1 so x you multiply by 5 and it matches because to get 6 to be 30 you multiply by 5 and to get 5 to be 25 you multiply by 5
ANSWER A
Step-by-step explanation:
A local farmer built a rectangular pen for her goats using 20 meters of fence. She used part of one side of her barn as one length of the rectangular pen. She maximized the area using 20 meters of fence. She then built a rectangular pen for her hogs using 24 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of the goat pen. The width of her pen was 1 meter more than the width of the goat pen. How much larger is the hog pen than the goat pen?
The farmer's hog pen, with length of 12 meters and a width of 11 meters, is 32 square meters larger than the goat pen which has a length and width of 10 meters.
Explanation:First, let's establish the dimensions of both pens. For the goat pen, given that the farmer used 20 meters of fencing and one side was provided by the barn, the fence was distributed between two sides. If we assume these two sides to be equal (maximizing the area), each side would be 10 meters long.
On the other hand, the hog pen had 24 meters of fence distributed between two sides, with the length being 2 meters more than the goat pen and the width being 1 meter more than the goat pen. So, the length of the hog pen is 12 meters and width is 11 meters.
To find the difference in areas, we subtract the area of the goat pen from the hog pen. The area of a rectangle is calculated by multiplying the length by the width. For the goat pen, the area is 10m * 10m = 100m² and for the hog pen, the area is 12m * 11m = 132m². Thus, the area of the hog pen is 32m² larger than the goat pen.
Learn more about Mathematics Problem here:https://brainly.com/question/34294735
#SPJ3
A students grade goes from a 95 to a 60 in 3 weeks. Calculate the students rate of grade change.
Answer: The rate of change is 11.6666...
Step-by-step explanation:
You subtract 95 by 60 and you get 35.
You divide it by 3 because it happened over 3 weeks.
After dividing your answer is 11.6666...
To calculate the rate of grade change, subtract the final grade from the initial grade, then divide the result by the number of weeks. In this case, the rate of grade change is 11.67, meaning the grades are dropping at a rate of 11.67 points per week.
Explanation:To calculate the rate of grade change, we should subtract the final grade from the initial grade and divide the result by the number of weeks. In this case, the initial grade is 95 and the final grade is 60. Therefore, the grade change is 95 - 60 = 35. The number of weeks is 3 according to your question.
So, the rate of grade change can be calculated as follows:
Rate of Grade Change = Grade Change / Number of weeks
Substituting the given values:
Rate of Change = 35 / 3 = 11.67
This means, grades are dropping at a rate of 11.67 points per week.
Learn more about Rate of Change here:https://brainly.com/question/20816247
#SPJ2
Choose the abbreviation of the postulate or theorem that supports the conclusion that WAS NOT. Given: W = N, S = T, WA = NO.
SSS
SAS
ASA
AAS
Answer:
AAS I just answered this question and I got it right.
Final answer:
Given W=N, S=T, and WA=NO, no congruence theorems (SSS, SAS, ASA, AAS) demonstrate that triangles WAS and NOT are congruent, so the triangles are not congruent.
Explanation:
The student is asking which postulate or theorem supports the conclusion that triangle WAS is not congruent to triangle NOT. Given that W = N, S = T, and WA = NO, we can determine that the two triangles are not congruent. The four options provided are abbreviations for congruence theorems in geometry: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS).
However, none of these congruence theorems apply here because those would be used to prove congruence, not the lack thereof. In this case, if we look at the information given, we see that we have two pairs of sides and one pair of angles that are congruent. But the postulated congruent angles, A in triangle WAS and O in triangle NOT, are not included between the sides of the triangles that are known to be congruent. Therefore, none of the listed congruence postulates or theorems (SSS, SAS, ASA, AAS) can be used to conclude that the triangles are congruent. As a result, it can be concluded that the triangles are not congruent without needing to invoke a specific congruence theorem.
Please help I really need your help
Answer:
1. [tex]1200 \ kg/m^3[/tex]
2.
a)
35 cm = 0.35 meters
11 dm = 1.1 meters
15 mm = 0.015 meters
b)
Volume = 0.005775 cubic meters
Mass = 15.5925 kilograms
Step-by-step explanation:
1.
We know
Density = Mass/Volume
Given
Mass = 90 kg
Volume = 0.075 cubic meters
The SI unit for density is kilograms per cubic meters. Our dimensions are just that, so we just need to plug in the numbers into the formula and get our answer. Shown below:
Density = [tex]\frac{90}{0.075}=1200 \ kg/m^3[/tex]
The Density of asphalt block = [tex]1200 \ kg/m^3[/tex]
2.
a)
We need to express 35cm, 11dm, and 15mm in meters
We know
100 cm = 1 meters, so
35 cm = 35/100 = 0.35 meters
We know 1 dm = 0.1 meters, so
11 dm * 0.1 = 1.1 meters
We know, 1mm = 0.001 meters, so
15 mm * 0.001 = 0.015 meters
b)
Volume of the Slab is length * width * height, in meters, that would be:
Volume = 0.35 * 1.1 * 0.015 = 0.005775 cubic meters
THe mass would be found by the formula:
Density = Mass/Volume
2700 = Mass/0.005775
Mass = 0.005775 * 2700 = 15.5925 kilograms
Adam writes 18y to simplify an expression with three like terms. What could the expression be?
Answer:
Step-by-step explanation:
5y + 6y + 7y = 18y......any numbers that add(or subtract) to equal 18, stick them before the y....
or it could be : 10y + 10y - 2y = 18y or 5y + 10y + 3y or 30y - 20y + 8y....I could go on forever...lol
3x-4y>12
which order pair (x,y) satisfies the inequality?
For this case we have the following inequality:
[tex]3x-4y> 12[/tex]
We must find an ordered pair of the form [tex](x, y)[/tex] that meets the inequality.
Example:
Pair 1: [tex](x, y) :( 0,0)[/tex]
[tex]3 (0) -4 (0)> 12\\0> 12[/tex]
This pair does not satisfy the inequality.
Pair 2: [tex](x, y) :( 6,1)[/tex]
[tex]3 (6) -4 (1)> 12\\18-4> 12\\14> 12[/tex]
This pair satisfies the inequality!
Thus, the pair[tex](x, y) :( 6,1)[/tex] meets the inequality.
Answer:
[tex](x, y) :( 6,1)[/tex]
An alloy composed of nickel, zinc, and copper in a 4:1:2 ratio. How many kilograms of each metal are needed to make 35 kg of this alloy?
The required amount of nickel is
kg .
The required amount of zink is
kg .
The required amount of copper is
kg .
Step-by-step explanation:
The total number of parts is 4 + 1 + 2 = 7.
Nickel is 4/7 of the mass: 4/7 × 35 kg = 20 kg.
Zinc is 1/7 of the mass: 1/7 × 35 kg = 5 kg.
Copper is 2/7 of the mass: 2/7 × 35 = 10 kg.
Answer:
15g 5g 10g
Step-by-step explanation:
A book is on sale for $8.93. The sale price is 15% off the original price. What was the
original price?
Answer:
i think 10.30 according to my calculation
Answer:
10.30
Step-by-step explanation:
Kelli makes $13 an hour working at the bakery and her boss gave her a 7% raise.
How much is Kelli's raise per hour:
Answer:
She gets a raise of 91 cents per hour. So that means each hour, she makes $13.91
Kelli's raise per hour is $13.91.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Kelli makes $13 an hour working at the bakery,
and her boss gave her a 7% raise.
That means,
Kelli's raise per hour = 13 + 13 x 7/100
= $13.91
Therefore, $13.91 raise per hour.
To learn more about the percentage;
https://brainly.com/question/24159063
#SPJ5
(-5x²-9x-6)+(6x²+10)
Answer:
x^2-9x+4
Step-by-step explanation:
(-5x^2-9x-6)+(6x^2+10)
-5x^2+6x^2-9x-6+10
x^2-9x+4
Answer:
x^2 - 9x + 4.
Step-by-step explanation:
(-5x²-9x-6)+(6x²+10)
= -5x² - 9x - 6 + 6x² + 10
= -5x² + 6x² - 9x - 6 + 10
= x^2 - 9x + 4.
Olivia bought a piece of ribbon priced at $0.56 per yard. The total cost was $1.54. How many yards did she buy?
Answer:
2.75 or 2 3/4
Step-by-step explanation:
Divide the total cost by the price of each ribbon.
$1.54 ÷ $0.56/yard = 2.75 yards
If the answer needs to be in mixed fractional form, convert 0.75 to a fraction.
3/4 = 0.75
The fraction form of 2.75 is 2 3/4.
Therefore Olivia bought 2 3/4 yards of ribbon.
Find the distance between points P(9,6) and Q(3,2) to the nearest tenth
Answer:
[tex]\large \boxed{7.2}[/tex]
Step-by-step explanation:
You could use the distance formula to calculate the length of PQ. I prefer a visual approach, because it requires less memorization.
Draw a vertical line from P and a horizontal line from Q until they intersect at R (9, 2).
Then you have a right triangle PQR, and you can use Pythagoras' theorem to calculate PQ.
[tex]\begin{array}{rcl}PQ^{2} & = & PR^{2} + QR^{2}\\& = & 4^{2} + 6^{2}\\ & = & 16 + 36\\& = & 52\\PQ& = & \sqrt{52}\\& = & \mathbf{7.2}\\\end{array}\\\text{The distance between P and Q is } $\large \boxed{\mathbf{7.2}}$}[/tex]
Use the calculator to find the product of 4.17 and 2.3 x
106. Which statements are true about finding the
product?
Check all that apply.
A) 4.17 is equivalent to 4.17 x 100
B) 4.17 is equivalent to 4.17 x 10^1
C) The product has a positive exponent.
D) The coefficient is 6.
E) The E in the product is the indicator that the
solution is in scientific notation.
F) The exponent of the product is the product of the
original exponents.
Answer: 1st 3rd and 5th trust me
A) 4.17 is equivalent to 4.17 x 100
C) The product has a positive exponent.
E) The E in the product is the indicator that the solution is in scientific notation.
Given that,
The product of 4.17 and 2.3 x 106.For this, we can say that the first option, third option and the fifth option should be correct. And, the other options are wrong.learn more: https://brainly.com/question/864553?referrer=searchResults
A chess player won 48 of the games he played. If the ratio of wins to loses was 8:7, how many games did he play total?
Answer:
the answer would be 90
Step-by-step explanation:
first you multiply 8 until you get 48, which would be 6 times, then do the same thing for 7 (7x6), which would be 42 and just add it all together and you get 90
The chess player played a total of 56 games.
Explanation:To find the total number of games the chess player played, we need to determine the ratio of wins and losses. The ratio of wins to losses is given as 8:7. This means for every 8 wins, there are 7 losses. Since the player won a total of 48 games, we can set up the following proportion:
8/7 = 48/x
Cross-multiplying, we get 8x = 7 * 48. Solving for x, we find that the player played a total of 56 games.
In 1 minute alex can type 44 words at the same rate how long would it take him to type 176 words
Final answer:
It will take Alex 4 minutes to type 176 words at his current typing speed of 44 words per minute.
Explanation:
The question asks how long it would take for Alex to type 176 words if he can type 44 words in one minute. To find the answer, we utilize a simple rate calculation by dividing the total number of words (176) by Alex's typing speed (44 words per minute).
176 words ÷ 44 words/minute = 4 minutes
Therefore, it will take Alex exactly 4 minutes to type 176 words at the rate of 44 words per minute.
How many solutions over the complex number system does this polynomial have?
3x6 – x3 - 4x2 + 3x + 52 = 0
Enter your answer as an integer. Can somebody plzzzzzzzzz help me plzzzzzzzz I really need help with this plzzzzzzz can anyone help??????????
Answer:
6 complex numbers
There are 6 solutions to the polynomial over the complex number system.
The given equation is 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.
What is the complex number system of a polynomial?The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system. A further theorem, in some cases referred to as the Linear Factorization Theorem, states that a polynomial of degree n has exactly n linear factors, and each can be written in the form (x - c), where c is a root. These n complex roots are counted with multiplicity.
In polynomials, the number of roots or highest power is equal to the degree of the polynomial.
Here, 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.
We can see that the polynomial is a sixth-degree polynomial.
Therefore, there are 6 solutions to the polynomial over the complex number system.
Learn more about polynomials here:
brainly.com/question/27343162
#SPJ2
Can someone answer this please
Answer:
0 hours = $40
1 hours = $75
2 hours =$110
3 hours =$145
4 hours =$180
5 hours =$215
Step-by-step explanation:
C=Cost in dollars,
n=hours.
Calculating Cost for 0 hours
[tex]C=35n+40[/tex]
[tex]C=(35\times 0)+40[/tex]
[tex]C=0+40[/tex]
[tex]C=40[/tex]
Cost for 0 hours=$40
Calculating Cost for 1 hours
[tex]C=35n+40[/tex]
[tex]C=(35\times 1)+40[/tex]
[tex]C=35+40[/tex]
[tex]C=75[/tex]
Cost for 1 hours=$75
Calculating Cost for 2 hours
[tex]C=35n+40[/tex]
[tex]C=(35\times 2)+40[/tex]
[tex]C=70+40[/tex]
[tex]C=110[/tex]
Cost for 2 hours=$110
Calculating Cost for 3 hours
[tex]C=35n+40[/tex]
[tex]C=(35\times 3)+40[/tex]
[tex]C=105+40[/tex]
[tex]C=145[/tex]
Cost for 3 hours=$145
Calculating Cost for 4 hours
[tex]C=35n+40[/tex]
[tex]C=(35\times 4)+40[/tex]
[tex]C=140+40[/tex]
[tex]C=180[/tex]
Cost for 4 hours=$180
Calculating Cost for 5 hours
[tex]C=35n+40[/tex]
[tex]C=(35\times 5)+40[/tex]
[tex]C=175+40[/tex]
[tex]C=215[/tex]
Cost for 5 hours=$215
Find the sum the interior angle angle measures of a 17-gon
Answer:
2700 degrees.
Step-by-step explanation:
The external angles add up to 360 degrees
So 1 external angle in a regular 17-gon = 360/17
= 21.176 degrees
The internal angle = 180 - 21.176
= 158.824 degrees
Sum of internal angles = 158.824 * 17
= 2700 degrees.
Answer:
Step-by-step explanation:
Every closed curve called a polygon can be separated into a specific number of triangles. Then, because the sum of the interior angles of a triangle is 180, you take the number of triangles and multiply by 180 to get the sum of the interior angles of the n-gon. To find the number of triangles that exist within an n-gon, subtract 2 from the number of sides. If our figure is a 17-sided polygon, then the number of triangles within it is 17 - 2 = 15. 15 triangles, each with a sum of 180 for its angles. 15 * 180 = 2700.
Each central angle is 360 divided by 17 to get 21°10'35"
Each interior angle is 2700 divided by 17 to get 158°49'24"
A line containing the points (3,0) and (-2,-2) is graphed on a coordinate grid. Which of these
points is a solution to the equation that represents this line?
(-12,-6)
(-4,-3)
(0.5,-1)
(5,0.8)
(9,3)
(18,6)
Answer: (-12,-6)
Step-by-step explanation:
If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its equation:
Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]
Point 2: [tex](x_{2},y_{2})=(-2,-2)[/tex]
Slope equation:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-2-0}{-2-3}[/tex]
[tex]m=\frac{2}{5}[/tex] This is the slope of the line
Now, the equation of the line is:
[tex]y=mx+b[/tex]
We already know the slope, now we have to find [tex]b[/tex] with any of the given points. Let's choose Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]
[tex]0=\frac{2}{5}(3)+b[/tex]
Isolating [tex]b[/tex]:
[tex]b=-\frac{6}{5}[/tex]
Then, the equation of the line is:
[tex]y=\frac{2}{5} x-\frac{6}{5}[/tex]
With this equation we can find which point is a solution. Let's begin with the first point (-12,-6):
[tex]-6=\frac{2}{5} (-12)-\frac{6}{5}[/tex]
[tex]-6=-\frac{24}{5} -\frac{6}{5}[/tex]
[tex]-6=-6[/tex] Since both sides of the equation are equal, (-12,-6) is the point that fulfills the solution of the equation.
HELP ASAP 15 points
Select the equation of the line that passes through the point (–2, –1) and has slope 5 in point-slope form. a (y + 1) = 5(x + 2) b (x + 2) = 5(y – 1) c (y – 1) = 5(x – 2) d (x – 2) = 5(y + 1)
Answer:
y+1=5(x+2)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1)=5(x-(-2))
y+1=5(x+2)