Answers
Answer:
The equation of the line is [tex]y = 2\cdot x + 3[/tex].
Step-by-step explanation:
The data of the table represents a line, also known as a linear function or a first order polynomial if and only if the following property is satisfied:
[tex]\frac{y_{i+1}-y_{i}}{x_{i+1}-x_{i}} = m, m \in \mathbb{R}[/tex] (1)
Now we proceed to check if the table represents a line instead of another kind of function:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{7-5}{2-1} = 2[/tex]
[tex]\frac{y_{3}-y_{2}}{x_{3}-x_{2}} = \frac{9-7}{3-2} = 2[/tex]
[tex]\frac{y_{4}-y_{3}}{x_{4}-x_{3}} = \frac{13-9}{5-3} = 2[/tex]
[tex]\frac{y_{5}-y_{4}}{x_{5}-x_{4}} = \frac{15-13}{6-5} = 2[/tex]
Hence, the data represents a line. From Geometry we know that the equation of the line can be obtained by knowing two distinct points. The formula of the line is described below:
[tex]y = m\cdot x + b[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]b[/tex] - y-Intercept.
If we know that [tex](x_{1}, y_{1}) = (1, 5)[/tex] and [tex](x_{2}, y_{2}) = (6, 15)[/tex], then we have the following system of linear equations:
[tex]m + b = 5[/tex] (1)
[tex]6\cdot m + b = 15[/tex] (2)
The solution of the system of linear equations is: [tex]m = 2[/tex], [tex]b = 3[/tex].
The equation of the line is [tex]y = 2\cdot x + 3[/tex].
Related Questions
습
John spends $94 to buy packages of cleaning supplies for a camp. He buys t packages of
towels, each package is $6 and contains 8 towels. He also buys s packages of soap; each
package is $4 and contains 10 bars of soap. John buys 20 packages of cleaning supplies
altogether. Write a system of equations to represent the packages of cleaning supplies John
buys
Answers
Answer:
B
Step-by-step explanation:
step
it is given 5 and h + 1 are the roots of the quadratic equation x＾2 + (k - 1)x-5 = 0, where h and k are constants. Find the values of h and k.
Answers
Answer:
The values of h = -2 and 4
The value of k = -3
Step-by-step explanation:
Putting x=5 in the given equation,
x²+(k-1)x-5=0
or, 5²+(k-1)*5-5=0
or, 25+5k-5-5=0
or, 15+5k=0
or, 5k=-15
or, k=-3
putting the value of k and the other root (h+1) in the given equation,
(h+1)²+(-3-1)(h+1)-5=0
if you solve this, you'll get h = -2 and h = 4.
Answered by GAUTHMATH
State the domain and range of the function graphed below!!!!
Answers
The domain is the span of the x-values, and the range is the span of the y-values. In each, we are looking for the smallest and largest values.
Domain: x starts at -7, and goes to infinity (we cannot see an end)
(-7, infinity)
Range: y starts at negative infinity (we cannot see where it would start), and goes to 3
(negative infinity, 3)
Hope this helps!
Answer:
the domain starts at -7 ... only one answer has the domain starting at -7
domain(-7, infinity)
Step-by-step explanation:
the domain starts at -7 ... only one answer has the domain starting at -7
Can someone help me with this please!!! (Picture) I will mark brainliest no links!
Decide whether the statement below is true or false. Then fully explain why. The triangle below can be used to help with your explanation if needed.
“The sine of any acute angle is equal to the cosine of its complementary angle.”
Answers
Which equation of the solutions of x2 = -7x – 8
Answers
Answer:
x = 1, -5.56
Step-by-step explanation:
x^2 = -7x - 8
shift -7x and -8 to the other side . Remember when u shift minus changes into plus.
x^2 + 7x + 8 = 0
using quadratic equation formula
in quadratic equation one value comes positive and other comes in negative
a = 1 , b = 7 and c = 8
taking positive sign
x = (-b + [tex]\sqrt{b^2 - 4*a*c}[/tex]) /2*a
x = (-7 + [tex]\sqrt{7^2 - 4*1*8}[/tex] ) /2*1
x = (-7 + [tex]\sqrt{49 + 32}[/tex] ) /2
x = (-7 + [tex]\sqrt{81}[/tex] )/ 2
x = -7 + 9 / 2
x = 2/2
x = 1
taking negative sign
(-b - [tex]\sqrt{b^2 - 4*a*c}[/tex] ) /2*a
x = (-7 - [tex]\sqrt{7^2 - 4*1*8}[/tex] ) /2*1
x = (-7 - [tex]\sqrt{49 - 32}[/tex] ) /2
x = -7 - [tex]\sqrt{17}[/tex] / 2
x = -7 - 4.12 / 2
x = -11.12/2
x = -5.56
therefore x = 1 , - 5.56
Answer:
[tex]x = \frac{- 7 + \sqrt{17}}{2} \ , \ x = \frac{-7 - \sqrt{17}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 = - 7x - 8\\\\x^2 + 7x + 8 = 0 \\\\[/tex]
[tex]x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}\\\\[/tex] [tex][ \ a = 1 , \ b = 7 , \ c = 8 \ ][/tex]
[tex]x = \frac{-7 \pm \sqrt{49 - (4\times 8)}}{2} \\\\x = \frac{-7 \pm \sqrt{17}}{2} \\\\x = \frac{-7 + \sqrt{17}}{2} , \ , \frac{-7 - \sqrt{17}}{2}[/tex]
a = 5
an + 1 = 24, -7
Answers
I did it on my final exam. Just two days ago.
Given that X = - 2 and y = 4 , Evaluate the expression. 5y – 4x
Answers
Answer: 28
Step-by-step explanation: 5(4)-4(-2) which is 20+8 and that is 28.
Factor the following expressions completely. Show and check all work on your own paper.
x2+169
Answers
Answer:
The factor is polynomial
Step-by-step explanation:
trust me broski
If you put 700 into a savings account that's earns 1% interest compound monthly how much will you have in 5 years
Answers
Answer:
In 5 years I will have $ 1,151.71.
Step-by-step explanation:
To determine, if I put 700 into a savings account that's earns 1% interest compound monthly, how much will I have in 5 years, the following calculation must be performed:
700 x (1 + 0.01 / 12) ^ 12x5 = X
700 x (1 + 0.008333) ^ 60 = X
700 x 1.64530 = X
1,151.71 = X
Therefore, in 5 years I will have $ 1,151.71.
Saira is going to ride her bike to her friend's house that is 2.3 miles away. Then she is going to ride her bike another 3.4 miles to Starbucks before heading home, which is another 3.8 miles. She noticed on the map that her route is in the shape of a triangle. How far will Abby ride her bike altogether?
Answers
Answer:
9.5 miles
Step-by-step explanation:
Since her route is in the shape of a triangle, total distance travelled can be determined by calculating the perimeter of a triangle.
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees
The perimeter of a triangle = sum of the side lengths
The total distance travelled can be determined by adding the miles she rode
2.3 + 3.4 + 3.8 = 9.5 miles
fine the total surface area left in terms of pie
Answers
Answer:
200π cm²
Step-by-step explanation:
Applying,
TSA = πrl+πr²
TSA = π(r²+rl)............. Equation 1
Where TSA = Total surface area, r = radius of the base, l = slight height of the cone
To get l we apply pythagoras theorem
From the diagram,
l² = 15²+8²
l² = 225+64
l² = 289
l = √289
l = 17 cm
Given: r = 8 cm
Substitute these values into equation 1
TSA = π(8²+17×8)
TSA = π(64+136)
TSA = π(200)
TSA = 200π cm²
Solve for X
I’ll give BRAINLIEST to the correct answer
Answers
Answer:
[tex]x=9.91[/tex]
Step-by-step explanation:
[tex]11x-3=106[/tex]
[tex]+3[/tex] [tex]+3[/tex]
[tex]11x=109[/tex]
[tex]/11[/tex] [tex]/11[/tex]
[tex]x=9.91[/tex]
c. A 40-foot ladder reaches 38 feet up the side of a house. How far from the base of the
house is the foot of the ladder?
Answers
Answer: 12.48
Step-by-step explanation:
38x38+bxb=40x40
1444+b=1600
1600-1444=156
[tex]\sqrt156[/tex]=12.48
The base of the house is 12.48 foot far from the foot of the ladder.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
It is given that A 40-foot ladder reaches 38 feet up the side of a house.
We need to find that How far from the base of the house is the foot of the ladder.
Using Pythagoras theorem, we get;
[tex]38^2 + b^2 =40^2\\\\1444 + b^2 = 1600\\ \\b^2 = 1600 - 1444 \\\\b^2= 156\\\\b = 12.48[/tex]
Therefore, the base of the house is 12.48 foot far from the foot of the ladder.
Learn more about Pythagoras theorem;
https://brainly.com/question/343682
#SPJ2
What is the slope of the line represented by the equation y = -1/2x + 1/4?
Answers
Please mark brainliest!
Given the following equation x2 + 12x = x - 24 find the solutions.
(Show All Work)
16a) Set the equation equal to 0 by inverse operations.
16b) Place the equation in factored form.
16c) Set each factor equal to 0 and solve for x.
Answers
Answer:
OK , so I'll follow all your instructions:
x² + 12x - x + 24 = 0
x² + 11x + 24 = 0.......product = 24, sum= 11 & factors = 3 & 8
(x² + 3x ) (+ 8x + 24) =0
x ( x + 3) + 8 ( x + 3)=0
( x + 3 ) ( x + 8)=0
x +3 = 0 or x + 8= 0
x = -3. or x = -8
please help 20 pnts!!
Answers
Answer:
[tex]m^{\frac{1}{2} }[/tex] . [tex]n^{\frac{1}{2} }[/tex]
Step-by-step explanation:
Using the rules of exponents/ radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
[tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]
Given
[tex]\sqrt{mn}[/tex]
= [tex]\sqrt{m}[/tex] × [tex]\sqrt{n}[/tex]
= [tex]m^{\frac{1}{2} }[/tex] . [tex]n^{\frac{1}{2} }[/tex]
Answer:
[tex] {(mn)}^{ \frac{1}{2} } \\ {m}^{ \frac{1}{2} } {n}^{ \frac{1}{2} } [/tex]
In the diagram below, DE is parallel to XY. What is the value of y?
8
100
ya
O A. 120
B. 100
o
C. 80
o
D. 60
PREVIOUS
Answers
Answer:
100 is answer for math picture
Answer: 80
Step-by-step explanation:
180-100 = 80, y=80
Fragrant Fields Greenhouse sells rose bushes for $19.90 each. Last weekend, they made $477.60 on rose bushes. How many rose bushes did they sell?
Answers
Answer:
24 brushes
Step-by-step explanation:
Given data
cost per brush= $19.90
Amount made =$477.60
hence the number of brushes sold is given as
Number of brushes= 477.60/19.90
Number of brushes= 477.60/19.90
Number of brushes= 24 brushes
How many outfits are possible if you can choose one from each of four shirts, three pairs of pants, two pairs of shoes, and two jackets?
Answers
Answer:
40 outfits possible
Step-by-step explanation:
4 shirts * 3 pairs of pants * 2 paird of shoes * 2 jackets = 40 outfits possible
Every hour American throw away 1.2 million plastic bottles. how many plastic bottles are thrown away in one day??
need help
Answers
Answer:
the answer is 28.8 billion plastic bottles
Answer:
28.8 million
Step-by-step explanation:
24 hrs in one day - 1.2 M*24=28.8 M
The school bought 957 science books, 1054 mathematics books, and 458 reading books. Put the books in order from least to greatest.
Answers
Answer:
reading books (458), science books (957), mathematics books (1054)
Step-by-step explanation:
458 is less than 957 and 1054, while 957 is less than 1054 but more than 458, and 1054 is more than 957 and 458.
458<957<1054
Name the marked angle in 2 different ways.
Answers
∠HGF ∠EGF
Hope this helps! :)
if f(x)=8x which is the following is the inverse of f(x)
Answers
Answer:my=8x
To find the inverse, flip the x and y variables and then solve for y.
x=8y
x/8=8y/8
x/8=y
Final answer: f^-1(x)=x/8
Please help ASAP thank you
Answers
B: At sea level
Please mark brainliest when you can!
Identify the coefficient and the exponent for each term of 8x4 – 2x.
Answers
Given:
The expression is:
[tex]8x^4-2x[/tex]
To find:
The coefficient and the exponent for each term of the given expression.
Solution:
Coefficients: In the product of s number and a variable, the number is coefficient of the variable.
Exponent: The number in the power is called exponent.
We have,
[tex]8x^4-2x[/tex]
Here, the terms are [tex]8x^4,-2x[/tex].
For the term [tex]8x^4[/tex], the coefficient is 8 and the exponent is 4.
For the term [tex]-2x[/tex], the coefficient is -2 and the exponent is 1.
Therefore, the coefficients are 8 and -2, and the exponent are 4 and 1.
help mee
x=
a.8
b. 9
c. 10
Answers
Answer:
A
Step-by-step explanation:
The formula is 5*x=4*10. Then simplify to 5*x=40. Divide both sides by 5. x=8
Identify the rule that correctly describes each
sequence.
12, 8, 4, 0, -4, ...
Each term is 4 more than the previous term.
Each term is 4 less than the previous term.
Each term is 1/2 the previous term.
Each term is 2/3 the previous term.
6, 12, 24, 48, 96, ...
Each term is 6 more than the previous term.
Each term is 12 more than the previous term.
Each term is 1/2 the previous term.
Each term is 2 times the previous term.
COMPLETE
COMPLETE
here’s the answers
Answers
Answer:
Each term is 4 less than the previous term.
Step-by-step explanation:
If this helps you mark as brainlist!
Answer:
B and D are your answers for that whole page
Step-by-step explanation:
Identify the rule that correctly describes each sequence.
12, 8, 4, 0, –4, …
Each term is 4 more than the previous term.
This Is the right one: Each term is 4 less than the previous term.
Each term is 1/2 the previous term.
Each term is 2/3 the previous term.
6, 12, 24, 48, 96, …
Each term is 6 more than the previous term.
Each term is 12 more than the previous term.
Each term is 1/2 the previous term.
This is the right one: Each term is 2 times the previous term.
help pls! i cant figure it out.
Answers
[tex]\longrightarrow{\green{x\:=\:5}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
➝[tex]\: \frac{3x}{5} = \frac{x + 1}{2} [/tex]
➝[tex]\:2 \times 3x = 5(x + 1)[/tex]
➝[tex]\:6x = 5x + 5[/tex]
➝[tex]\:6x - 5x = 5[/tex]
➝[tex]\:x = 5[/tex]
To verify:-✒[tex] \:\frac{3 \times 5}{5} = \frac{5 + 1}{2} [/tex]
✒[tex]\: \frac{15}{5} = \frac{6}{2} [/tex]
✒[tex]\:3 = 3[/tex]
✒[tex]\:L. H. S. =R. H. S. [/tex]
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35☂}}}}⋆[/tex]
HELPPPPPPP PLEASEEEE
Answers
Answer:
19: x=5
20: x=13
21: y= 11
x= 11
Step-by-step explanation:
I NEED THIS NOW PLZZZ NO KINKS IT ILL REPORT
Answers
Answer:
Letter C
Step-by-step explanation:
Given:
[tex]24x-17x[/tex] ≥ [tex]13x+15[/tex]
Combine like terms
[tex]7x[/tex] ≥ [tex]13x+15[/tex]
Subtract both sides by 13x
[tex]-6x[/tex] ≥ [tex]15[/tex]
DIvide -6 from both sides
[tex]x[/tex] ≥ [tex]-2.5[/tex]
Letter C is the answer because it is at -2.5, the arrow is facing to the right, and the dot or circle is closed to indicate that it is greater than "or equal to".
Hope this helps