HELP! Write the equation of the line using function notation.
f(x) = -3x + 3
f(x) = 3x + 3
f(x) = 2x + 3
f(x) = 1/3x + 3
Answers
f(x) = 3x + 3
Solution:
Let us take f(x) = y.
The points indicated in the graph are (0, 3) and (–2, –3).
Slope(m) of the line passing through two points formula:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points in the above formula,
[tex]$m=\frac{-3-3}{-2-0}[/tex]
[tex]$=\frac{-6}{-2}[/tex]
m = 3
constant is the y-intercept which implies c = 3.
The equation of a line standard form is y = mx + c.
y = 3x + 3
The equation of a line is
f(x) = 3x + 3
Related Questions
Can you please help me with the problem in the image below?
Answers
Given data:
m∠P = m∠R and TP = SR
To prove that ΔQTP ≅ ΔQSR:
Consider ΔQTP and ΔQSR,
m∠P = m∠R (given angle)
TP = SR (given side)
m∠Q = m∠Q (common angle)
∴ ΔQTP ≅ ΔQSR (by ASA congruence rule)
Hence ΔQTP and ΔQSR are congruence triangles by Angle - Side - Angle congruence rule.
For all values of x, which expression is equivalent to x + 1 − x + 2x + x + 1?
Answers
Answer:
3x+2
Step-by-step explanation:
We want to find an expression that is equivalent to:
[tex]x+1-x+2x+x+1[/tex]
We regroup similar terms to get:
[tex]x-x+2x+x+1+1[/tex]
We now combine the similar terms to obtain:
[tex]3x+2[/tex]
Therefore the expression that is equivalent to: x + 1 − x + 2x + x + 1 is [tex]3x+2[/tex]
Answer:
3x + 2
Step-by-step explanation:
3x + 2
Solve by simplifying the given expression OR substitute 1 for x in each expression.
x + 1 − x + 2x + x + 1 → x − x + 2x + x + 2 → 3x + 2
OR
x + 1 − x + 2x + x + 1 → 1 + 1 − 1 + 2(1) + 1 + 1 = 5
3x + 2 → 3(1) + 2 = 5
7x + 2(6x + 9) = 170
Answers
Answer:
x = 8
Step-by-step explanation:
7x + 2(6x + 9) = 170
2(6x + 9) = 12x + 18
7x + 12x + 18 = 170
19x = 152
152/19 = 8
x = 8
Which value of n makes the equation true? 6n − 2(4n + 7) + 4 = -2
Answers
Answer:
n = - 4
Step-by-step explanation:
Given
6n - 2(4n + 7) + 4 = - 2 ← distribute and simplify left side
6n - 8n - 14 + 4 = - 2
- 2n - 10 = - 2 ( add 10 to both sides )
- 2n = 8 ( divide both sides by - 2 )
n = - 4
To solve the equation 6n - 2(4n + 7) + 4 = -2, we apply the distributive property and combine like terms to simplify. The solution is n = -4.
To solve the equation 6n - 2(4n + 7) + 4 = -2, we need to apply the distributive property and combine like terms to simplify.
Distribute the -2 to both terms inside the parentheses: -2(4n + 7) = -8n - 14.Combine like terms: 6n - 8n - 14 + 4 = -2.Combine like terms again: -2n - 10 = -2.Next, we isolate the variable n by adding 10 to both sides: -2n - 10 + 10 = -2 + 10.Simplify: -2n = 8.Finally, solve for n by dividing both sides by -2: n = 8 / -2.Therefore, the value of n that makes the equation true is n = -4.
Learn more about Solving equations here:
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I don’t understand how to get the answer
Answers
x = –5 or x = 3
Solution:
Given expression:
[tex]|-1-x|=4[/tex]
[tex]\Rightarrow |-x-1|=4[/tex]
⇒ –x – 1 = 4 or –x – 1 = 4
First take –x – 1 = 4.
Add 1 on both side of the equation.
⇒ –x – 1 + 1 = 4 + 1
⇒ –x = 5
Divide by –1 on both side of the equation, we get
⇒ x = –5
Now take –x – 1 = –4.
Add 1 on both side of the equation.
⇒ –x – 1 + 1 = –4 + 1
⇒ –x = –3
Divide by –1 on both side of the equation, we get
⇒ x = 3
x = –5 or x = 3
Hence the two values of x are –5 or 3.
what is the answer to 10+7x
Answers
Answer:if u I simplified then 17x
Step-by-step explanation:
Like terms are 10+7=17+x=17x
Answer please! True or false!
Answers
Answer:
a. False
b. False
c. False
d. True
e. False. (any number above 14.5 is a solution).
Step-by-step explanation:
12 + 6y > 99
6y > 87
y > 14.5.
False
False (the answers are equal and therefore it’s not larger than 99)
True
False (there can be multiple answers but it needs to be above 14.5)
Equivalent expressions 3.7r - 1.5r =
Answers
Answer:
2.2r
Step-by-step explanation:
3.7r - 1.5r =
= r(3.7 - 1.5)
= r×2.2
= 2.2r
Yo sup??
given expression: 3.7r-1.5r
3.7r-1.5r
=3.7r+(-1.5r)
=2.2r
Hope this helps.
if ABCD is a rombus with side length 15 mm and if BD=24 mm, then find the length of the other diagonal, AC. Draw a diagram and show work.
Answers
Answer:
AC = 18 mm
Step-by-step explanation:
See the attachment for a diagram.
Since length BD = 24 mm, length BO = 12 mm. Then ΔBOC is a right triangle with one leg 12 and hypotenuse 15. The other leg (OC) is given by the Pythagorean theorem:
OC² +OB² = BC²
OC = √(BC² -OB²) = √(225 -144) = √81
OC = 9
Diagonal AC is twice the length of OC, so is ...
AC = 2·9 = 18 . . . . mm
_____
It can save a little time if you recognize that the given sides of triangle BOC have the ratio 4:5. This suggests you're dealing with a 3:4:5 right triangle, and that side OC is (3/5)·(15 mm) = 9 mm.
Find a pair of numbers that is a member of both y=-3x-27 and y=5+x
Answers
Answer:
(x, y) = (-8, -3)
Step-by-step explanation:
If all you want is a quick solution, I find a graphing calculator to be very handy. The one used in the attachment shows the solution to be (x, y) = (-8, -3).
_____
You can use one equation to substitute for y in the other equation:
-3x -27 = 5 +x
-32 = 4x . . . . . . add 3x-5 to both sides
-8 = x . . . . . . . . divide by 4
y = 5 +(-8) = -3 . . . . . use the second equation to find y
The pair of numbers that satisfies both equations is ...
(x, y) = (-8, -3)
What does x equal in
-0.4 (x+3)=4
Answers
Answer:
x=-13
Step-by-step explanation:
1. Divide both sides by -0.4
2. Subtract -3 on both sides.
3. -10-3=-13
what is the solution ? Please help with this !!
Answers
Answer:
the answer is c
Step-by-step explanation:
see picture
What is the range of the equation ?
Answers
Option D:
all real numbers
Solution:
Definition of domain:
The domain of the function is the set of all possible
x-values (independent variable).
Definition of range:
The range of a function is the set of all possible resulting values
of y-values (dependent variable).
i.e The range of a function is the resulting y-values we get after substituting all the possible x-values.
Given function: [tex]y=\log_8x[/tex]
Domain of y: (0, ∞) (or) {x | x > 0}
Range of y: (–∞, ∞) (or) {y | y > R}
i.e all real numbers
Option D is the correct answer.
Hence the range of y is all real numbers.
what is 1% of 12.54?
Answers
Answer:
0.1254
Step-by-step explanation:
(Divide by 100 to get 1%)
Answer:
Step-by-step explanation:
0.1254
is 28 √6 rational or irrational
Answers
Answer:
68.58571279792898674952395409176495897504652945838676359611.....
Irrational
Step-by-step explanation:
Answer:
It is irrational
Step-by-step explanation:
28sqrt6=sqrt(28^2*6)=sqrt(784*6)=sqrt(4704)=68.5857128...
Since the decimals go on forever, 28sqrt6 is irrational
Hope this helped!
20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability that the first is a Man's card and the Second, A woman's card?
5/19
14/19
1/4
9/10
Answers
Answer:
First choice:
[tex]\large\boxed{\large\boxed{5/19}}[/tex]
Explanation:
The probability that the first is a man's card and the second, a woman's card is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards in the hat has changed.
In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.
1. Probability that the first is a man's card
Number of cards in the hat = 20 (the 20 business card)Number of man's card in the hat: 10Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.2. Probability that the second is a woman's card
Number of cards in the hat = 19 (there is one less card in the hat)Number of wonan's card in the hat: 10Probability = favorable oucomes / possible outcomes = 10/19.3. Probability that the first is a man's card and the second, a woman's card
(1/2) × (10/19) = 5/19That is the first choice.
Answer:
5/19
Step-by-step explanation:
I know this isn't as good as the other persons answer but I wanted to reassure you that it was correct and my proof is that I took a test on this and got it right with this answer. I hope I helped! :>
What is 8x to the second power plus 10x
Answers
hope this helps!
The expression [tex]8x^2 + 10x[/tex] factors to [tex]2x(4x + 5)[/tex] and has solutions x = 0 and x = -5/4.
We first need to understand what it represents. In this expression, [tex]x[/tex] is the variable, and the terms [tex]8x^2[/tex] and [tex]10x[/tex] are polynomial terms where:
[tex]8x^2[/tex] indicates that the variable [tex]x[/tex] is raised to the power of 2, meaning it is multiplied by itself ([tex]x \times x[/tex]) and then scaled by a factor of 8.
[tex]10x[/tex] means that the variable [tex]x[/tex] is multiplied by 10.
The first term is [tex]8x^2[/tex].
The second term is [tex]10x[/tex].
In this case, the terms are not like terms because one is [tex]x^2[/tex] and the other is [tex]x[/tex]. Therefore, they cannot be combined further. The expression is simplest as it stands, which is: [tex]8x^2 + 10x[/tex]
Factoring out [tex]2x[/tex] gives us:
[tex]2x(4x + 5)[/tex]
Thus, [tex]8x^2 + 10x[/tex] can also be expressed as [tex]2x(4x + 5)[/tex]. This is useful if you are trying to find the roots of the equation (setting it equal to zero) since it can help identify the values of [tex]x[/tex] that satisfy the equation [tex]8x^2 + 10x = 0[/tex].
This gives two possible solutions for x:
2 * x = 0 which leads to x = 0
4 * x + 5 = 0 which leads to x = -5/4
total area of the trapezoid
meters. What is the length of
2 The trapezoid below is made up of a square and a triangle. The total area of the
is 57.5 square meters. The area of the triangle is 32.5 square meters. What is the
a side of the square?
A 5 meters
B 25 meters
C 90 meters
D Not enough information is given.
Answers
Answer:
A 5 meters
Step-by-step explanation:
57.5 - 32.5 = 25
25 cubed is 5
If PQR measures 75°, what is the measure of SQR?
Answers
Answer: the measure of SQR is 53°
in the rectangle below ac=48 units what is de
Answers
Answer:
24
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The diagonals of a rectangle are congruent, thus
DB = AC = 48
The diagonals also bisect each other, thus
DE = 0.5DB = 0.5 × 48 = 24 → B
how do you do number 5 please.
Answers
Answer:
2.4 kg
Step-by-step explanation:
Given
dog eats 0.3 kg of dog food each day
hence we can say that the unit rate is 0.3 kg per day
1 day ------> eats 0.3 kg
8 days -------> eats 0.3 kg x 8 = 2.4 kg
Answer:
2.4 kilogram
Step-by-step explanation:
If
1 day = 0.3kg
8day =
0.3 multiply by number of days
0.3kg * 8= 2.4kg
Questions 32 help plz with explanation. 15 points!!
Answers
Answer:
The man's son
Step-by-step explanation:
"Brothers and sisters I have none, but that man's father is my father's son" the part where he says "that man's father is my father's son" implies that he is looking at his son.
help asap please!!!!!!!
Answers
Answer:
VW=30, WX=20, YW=30,ZX=20
Step-by-step explanation:
solve for x.
Brainlest for anyone who helps!!
thanks you
Answers
================================================
Explanation:
If points F and E are the midpoints of segment VU and segment ST respectively, then segment FE is the midsegment of the trapezoid. The midsegment is parallel to the bases, and the midsegment's length is found by adding up the bases VS and UT, then dividing by 2.
(VS + UT)/2 = FE
(29 + x+17)/2 = 23 ... plug in given info; isolate x
(x+46)/2 = 23
x+46 = 23*2 ... multiply both sides by 2
x+46 = 46
x = 46-46 ... subtract 46 from both sides
x = 0The lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel. If $\angle BAE=54^{\circ}$ and $\angle DCE=25^{\circ}$, what is the measure of $\angle AEC$?
Use an asymptote convertor if needed:
[asy]
size( 200 ) ;
pair A = (0,0) ;
pair B = (0,2) ;
pair C = (3,0.5) ;
pair D = (3,2.5) ;
pair ptE = extension( A , A+dir(90-54) , C , C+dir(90+25) ) ;
draw( (0,-0.5)--(0,3) , linewidth(1.3) ) ;
draw( (3,-0.5)--(3,3) , linewidth(1.3) ) ;
draw( A--ptE--C ) ;
dot(Label( "$A$" , A , W )) ;
dot(Label( "$B$" , B , W )) ;
dot(Label( "$C$" , C , E )) ;
dot(Label( "$D$" , D , E )) ;
dot(Label( "$E$" , ptE , N )) ;
label( "$54^{\circ}$" , A , 5dir(70) ) ;
label( "$25^{\circ}$" , C , 8dir(100) ) ;
[/asy]
Answers
Answer:
79°
Step-by-step explanation:
Label the intersection of AE and CD point F. Then angle CFE is an alternate interior angle with angle BAE, so is congruent. The angle of interest is an exterior angle to triangle CFE, so is the sum of remote interior angles CFE (54°) and DCE (25°). That sum is ...
m∠AEC = 54° +25° = 79°
Based on the definition of alternate interior angles, the measure of ∠AEC is: 79°
What are Alternate Interior Angles?Interior angles that are alternating each other on a transversal are congruent, and are called alternate interior angles.
Thus:
m∠AEC = m∠BAE + m∠FCE
Substitute
m∠AEC = 54° + 25°
m∠AEC = 79°
Therefore, based on the definition of alternate interior angles, the measure of ∠AEC is: 79°
Learn more about alternate interior angles on:
https://brainly.com/question/20344743
The graph at the right shows the relationship between distance and time for a car driven at a constant speed.
1. What is the speed?
2. Is this a function relationship?
3. If this is a function, write a rule to represent it.
Answers
Answer:
1. 60 miles per hour
2. Yes, linear
3. Y=60x
Step-by-step explanation:
1. Speed is 60 miles per hour.
2. A function relationship is a relationship between two variables.
3. The rule to represent the function is Distance = 60t.
1. What is the speed?
The speed of the car is the rate at which it is traveling. It is calculated by dividing the distance traveled by the time taken to travel that distance.
Speed = Distance / Time
From the graph, we can see that the car travels 120 miles in 2 hours. Therefore, the speed of the car is:
Speed = 120 miles / 2 hours = 60 miles per hour
2. Is this a function relationship?
A function relationship is a relationship between two variables where each input value has only one output value. In other words, for every value of the independent variable (in this case, time), there is only one corresponding value of the dependent variable (in this case, distance).
We can see from the graph that the distance traveled by the car increases linearly with time. This means that there is a one-to-one relationship between the two variables, and therefore the relationship is a function.
3. If this is a function, write a rule to represent it.
A rule for a function is a mathematical expression that shows how the dependent variable is related to the independent variable. In this case, the rule for the function would be:
Distance = Speed * Time
Substituting the speed of the car into the rule, we get:
Distance = 60 miles per hour * Time
Therefore, the rule to represent the function is:
Distance = 60t
where t is the time in hours.
What are all possible functions from 1 to 9
Answers
Answer:
In mathematics, a function (f) is a relationship between a given set X (called domain) and another set of elements Y (called codomain) so that each element x of the domain corresponds to a single element f (x) of the domain (the that form the route, also called scope ranking).
See: Relations and functions
In everyday or simpler language, we will say that mathematical functions are equivalent to the common logical process that is expressed as "dependent on."
Mathematical functions can refer to everyday situations, such as: the cost of a phone call that depends on its duration, or the cost of sending a parcel that depends on its weight.
As an example, what would be the rule that relates the numbers on the right with those on the left in the following list ?:
1 --------> 1
2 --------> 4
3 --------> 9
4 --------> 16
The numbers on the right are the squares of those on the left.
The rule is then to "square":
1 --------> 1
2 --------> 4
3 --------> 9
4 --------> 16
x --------> x 2.
To refer to this rule we can use a name, which is usually the letter f (of function). So, f is the rule "square the number".
Usually two notations are used:
x --------> x 2 or f (x) = x 2.
Thus, f (3) means applying the rule f to 3. Doing so results in 3 2 = 9.
Then f (3) = 9. Similarly f (2) = 4, f (4) = 16, f (a) = a 2, etc.
18.
[Algebra - Expansion]
Expand 3(x + 2)
Answers
Answer:
Step-by-step explanation:
3(x + 2) = 3*x + 3*2
= 3x + 6
3x+6
Then divide 3x on both sides (3x divided by 3x and 6)
Your answer should be x=2
a teacher has 64 students to divide into small groups greater than 2 with no remaimder. how many ways can this be done?
Answers
To divide 64 students into small groups greater than 2 with no remainder, you would use the concept of combinations, specifically 62C3, resulting in 3,992 possible ways.
Explanation:A teacher has 64 students to divide into small groups greater than 2 with no remainder. To solve this, we can use the concept of combinations, denoted as nCr, where n is the total number of students and r is the size of each group. In this case, the calculation would be 62C3, which equals 3,992 ways of dividing the students into groups.
1/2 = 1/3 − |x−3/6 +x|
Answers
Answer:
No solution exist!
Step-by-step explanation:
Answer:
It is impossible to have an arithmetic answer. No Solutions, or ø