Given the functions f(x) = 1/x and g(x) = x⁴, the function operation ( f + g )(x) is x⁴ + 1/x.
What is the function operation ( f + g )(x)?Given the functions in the question;
f(x) = 1/xg(x) = x⁴( f + g )(x) = ?To evaluate f + g, replace the function designators in f + g with the actual functions and simplify
( f + g )(x) = f(x) + g(x)
( f + g )(x) = ( 1/x ) + ( x⁴ )
Remove the parenthesis
( f + g )(x) = ( 1/x ) + ( x⁴ )
( f + g )(x) = 1/x + x⁴
Reorder 1/x and x⁴
( f + g )(x) = 1/x + x⁴
( f + g )(x) = x⁴ + 1/x
Given the functions f(x) = 1/x and g(x) = x⁴, the function operation ( f + g )(x) is x⁴ + 1/x.
Learn more about composite function here: brainly.com/question/20379727
#SPJ1
Evaluate -2y^(3)+y^(2)-3y+4 when y=3
The value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.
How to Evaluate an Algebraic Expression?An algebraic expression contains a variable. To find the value or evaluate the algebraic expression, plug in the the value of the variable and solve accordingly.
Given the algebraic expression,
-2y³ + y² - 3y + 4, when y = 3
Substitute the value of y into the algebraic expression:
-2(3)³ + (3)² - 3(3) + 4
Evaluate the exponents in the expression:
-2(27) + 9 - 9 + 4
-54 + 9 - 9 + 4
Add together to get the value of the algebraic expression:
-54 + 0 + 4
-54 + 4
= -50
In summary, the value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.
Learn more about algebraic expression on:
https://brainly.com/question/2164351
#SPJ1
Please i need help desperately.
The minimum cost is $210.
Forgetting the situation for just a second, we can take a look atthe equation.
c(x)=x^2-40x+610
It is a parabola that opens upward and has a minimum value.
That minimum value will be the minimum cost of the taco stand.
The equation x=-b/2a gives you the axis of symmetry of theparabola. Basically, it goes right down the middle of the parabola,right through its minimum
In the equation c(x)=x^2-40x+610, a=1 and b=-40
x=-b/2a
x=-(-40/2(1)) = 20
So 20 tacos should be sold to achieve the minimum cost.
To find the cost, return to the original equation.
c(x)=x^2-40x+610
c(20)=(20)^2-40(20)+610 = 210
So the minimum cost is $210.
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
To learn more about parabola visit:https://brainly.com/question/21685473
#SPJ1
The minimum cost of the function is $210.
A function is defined as the representation of a set of variables known as the domain which are mapped onto another set of variables called the range.
The most common function is of the form y = f(x) , where x is the independent variable and y is the dependent variable and f(x) is the function.
The given function is of the form:
c(x) = x² - 40 x + 610
To find the maximum or minimum point of the function we find the second degree derivative of the function.
c'(x)=2x -40
Now we find the second degree derivative.
c"(x) = 2 > 0 so we know that c(x) is minimum at x for c'(x)=0.
Therefore c'(x) = 0
or , 2x-40 = 0
or , x = 20
Now the minimum value of the function is
c(20) = 20² - 40 (20) + 610
or, c(20) = 400 - 800 + 610
or, c(20) = 210
Hence the minimum value of the function is $210.
To learn more about function visit:
https://brainly.com/question/12431044
#SPJ1
(FUNCTIONS & RELATIONS/TRANSFORMATIONS)
f(x) = x² -2x - 1
Find the image of 3
and the image of -2
The image of 3 and the image of -2 are 2 and 7, respectively
How to find the image of 3 and the image of -2?The equation of the function is given as
f(x) = x^2 - 2x - 1
To determine the image of 3 and the image of -2, we set x to the following values
x = 3 and -2
Substitute x = 3 and -2 in the equation f(x) = x^2 - 2x - 1
So, we have
f(3) = (3)^2 - 2(3) - 1 = 2
f(-2) = (-2)^2 - 2(-2) - 1 = 7
Hence, the image of 3 and the image of -2 are 2 and 7, respectively
Read more about functions at
https://brainly.com/question/7693326
#SPJ1
The vertices of a figure are R(-7, - 5), S(-1,
- 2), and T(-1.
- 5. Find the coordinates of the
image after the figure rotates 90° counterclockwise about the origin. Then translates 3 units left and 8
units up.
The co-ordinates of the image after translation are R"(2,1),S"(-1,7) and T"(2,7).
A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
When a point is rotated 90° counter clockwise, the co-ordinates of the point say A(x ,y) changes to A"(y,-x).
The given co-ordinates are: R(-7, - 5), S(-1,- 2), and T(-1.- 5 ).
So when this co-ordinates are translated by rotating 90° counterclockwise.
R(-7, -5) →R'(5,-7)
S(-1,- 2) →S'(2,-1)
T(-1.- 5) →T'(5,-1)
Now the figure is translated 3 units left and 8 units up the new co-ordinates is given by (x-3,y+8).
So when this co-ordinates are translated the new co-ordinates are:
R'(5,-7)→R"(2,1)
S'(2,-1)→S"(-1,7)
T'(5,-1)→T"(2,7)
To learn more about translation visit:
https://brainly.com/question/12463306
#SPJ9
Consider polynomial function f.
f(x) = (x - 1)²(x + 3)³(x + 1)
Use the equation to complete each statement about this function.
The zero located at x = 1has a multiplicity of 2, and the zero located at x = -3has a multiplicity of 1
The graph of the function will touch, but not cross, the x-axis at an x-value of
Reset
Next
Answer: somehow got that v
Step-by-step explanation:
f=
x6+8x5+17x4−8x3−45x2+27
x
What is the slope of(1,-19),(-2,-7)
Answer:
Step-by-step explanation:
slope = (y2-y1) ÷ (x2-x1)
= ((-7)-(-19)) ÷ ((-2) - (1))
= 12 ÷ -3
m = -4
Big ideas math question
A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
Based on the number of people employed in education and health service industries in 2009, the number of new jobs that will be gained between 1/2009 and 1/2016 is b. 2,826,800 people.
How many jobs will be gained?The number of total jobs in 2016 can be found as:
= Number of jobs in education and health service industries x (1 + rate of increase)
= 19,200,000 x (1 + 14.8%)
= 19,200,000 x 1.148
= 22,041,600 people
The number of new jobs are:
= 22,041,600 people - 19,200,000
= 2,841,600 people
= 2,826,800 people approximate
Graph and options for the question are:
Education and Health Services - All Employees, 2000-2009 A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.
a. 21,926,800
b. 2,826,800
c. 16,273,200
d. 1,790,600
Find out more on rates of increase at https://brainly.com/question/19570909
#SPJ1
Answer:
b on edge
Step-by-step explanation:
what is the answer for 5 - ( -7) = 5 + _____
write as addition
please give explanation for this
The complete statement is 5 + 7
What is the commutative property of addition?The commutative property of addition is a mathematical rule stating that a change in the order or arrangement of the numbers being added does not affect the sum.
It is also important to note the following sign changes;
(-) (-) = +
(+) (+) = +
(-)(+) = -
(+)(-) = -
Given the expression;
5 - ( -7)
We know that the signs (-)(-) is equivalent to (+) sign
Substitute into the expression;
5 + 7
Thus, the complete statement is 5 + 7
Learn more about addition here:
https://brainly.com/question/4721701
#SPJ1
1. Clark rounded 4.359 to 4.36. He rounded to the nearest (tenths, hundredths, thousandths) Please circle.
Answer: to the nearest hundredth
I hope this helps!
Which number gives you a rational sum when you add it to 4/7 ?
Determine the function that satisfies the following conditions.
Find sin theta when cos theta= 0.319 and tan theta <0.
The value of sinФ = 0.139 for the given cosФ = 0.139 and tanФ > 0.
What is termed as the trigonometric equations?Trigonometry is a branch of mathematics that focuses on specific angle functions and their implementation to calculations. In trigonometry, there are 6 functions of an angle that are commonly used. A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is expressed as sine(sin), cosine(cos), and tangent ratios (tan), A trigonometric equation is a formula that contains a variable and a trigonometric function. A trigonometric equation is, for example, sin x + 2 = 1.The given trigonometric function is-
cosФ = 0.139.
We know the relation of sin and cos functions.
sin²Ф + cos²Ф = 1
Thus,
sinФ = √(1 - cos²Ф)
Put the value of cosФ = 0.139
sinФ = √(1 - 0.139²)
sinФ = √0.981
sinФ = 0.139
Thus, the value of the trigonometric function sinФ = 0.139.
To know more about the trigonometric equations, here
https://brainly.com/question/24349828
#SPJ9
Draw trapezoid ABCD and diagonals AC and BD. Add point E(6, 2) at the intersection of
Coordinate Geometry Graph the points A(0, 0), B(3, 3), C(9, 3), and D(12, 0).
agonals AC and BD.
Find BE and CE. What do you notice?
Answer: AED and BEC are isosceles triangles
Definition: A quadrilateral having two and only two sides parallel is called a trapezoid.
Formula: distance between two points =√(x1-x2)^2-(y1-y2)^2
Given,
ABCD is a trapezoid
AC and BD are diagonals
E is the intersection of two diagonals
A(0,0), B(3,3), C(9,3), D(12,0), E(6,2)
distance between BE=√10
distance between CE=√10
BE=CE
Similarly, AE=DE
Therefore, AED and BEC are isosceles triangles
to learn more about trapezoid visit:
brainly.in/question/21466551
#SPJ9
simplify the following absolutevalue expression |29|
PLEASE I REALLY NEED HELP ON THIS QUESTION OR I WILL FAIL PLEASE HELP!!!
A school district has paid a construction business 1.5 million to build a school, but still needs to pay the construction business 12.35 million for the total amount of work. How much will it cost to build the school?
PLEASE SHOW WORK!
Answer:
13.85 million $
Step-by-step explanation:
the man just add 12.35 and 1.5
therefore = 13.85 million $
5 Copy and complete these statements.
a √400=√x 100) = √√√√= x 10 =
=
We are struggling… assume 1st let of the statement is square root of 400 = 4x100… which equal square root 2x10… then ???
Given data,
First take work sheet 4.
[tex]\sqrt{16}[/tex]Based on the given conditions formulate :
= [tex]\sqrt{16}[/tex]
Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{4^{2} }[/tex]
Simplify the radical form,
= 4
Therefore, [tex]\sqrt{16} = 4[/tex]
[tex]\sqrt{49}[/tex]Based on the given conditions formulate :
= [tex]\sqrt{49}[/tex]
Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{7^{2} }[/tex]
Simplify the radical form,
= 7
Therefore, [tex]\sqrt{49} = 7[/tex]
[tex]\sqrt{25}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{5^{2} }[/tex]
Simplify the radical form,
= 5
Therefore, [tex]\sqrt{25} = 5[/tex]
[tex]\sqrt{144}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{12^{2} }[/tex]
Simplify the radical form,
= 12
Therefore, [tex]\sqrt{144} = 12[/tex]
[tex]\sqrt{100} +\sqrt{49}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{10^{2} } +\sqrt{7^{2} }[/tex]
Simplify the radical form,
= 10+7
= 17
Therefore, [tex]\sqrt{100} +\sqrt{49} = 17[/tex]
[tex]\sqrt{196}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{14^{2} }[/tex]
Simplify the radical form,
= 14
Therefore, [tex]\sqrt{196} = 14[/tex]
[tex]3^{2}[/tex] x [tex]\sqrt{121}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]3^{2}[/tex] x [tex]\sqrt{11^{2} }[/tex]
Simplify the radical form,
= 9 x 11
= 99
Therefore, [tex]3^{2}[/tex] x [tex]\sqrt{121} = 99[/tex]
[tex]\sqrt{169}[/tex] x [tex]\sqrt{36}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{13^{2} }[/tex] x [tex]\sqrt{6^{2} }[/tex]
Simplify the radical form,
= 13 x 6
= 78
Therefore, [tex]\sqrt{169}[/tex] x [tex]\sqrt{36} = 78[/tex]
[tex]\sqrt{16}[/tex] x [tex]\sqrt{25}[/tex]Factor and rewrite the radicand in exponential form,
= [tex]\sqrt{4^{2} }[/tex] x [tex]\sqrt{5^{2} }[/tex]
Simplify the radical form,
= 4 x 5
= 20
Therefore, [tex]\sqrt{16}[/tex] x [tex]\sqrt{25}[/tex] = 20
Given data,
First take work sheet 5.
[tex]\sqrt{400} = \sqrt{4*100} = \sqrt{4} *\sqrt{100} = 2 * 10 = 20[/tex]Therefore,
[tex]\sqrt{400} = 20[/tex]
[tex]\sqrt{2500} =\sqrt{25 * 100} =\sqrt{25} *\sqrt{100} = 5 * 10= 50[/tex]Therefore,
[tex]\sqrt{2500} = 50[/tex]
[tex]\sqrt{6400} =\sqrt{64 * 100} =\sqrt{64} *\sqrt{100} = 8 * 10 = 80[/tex]Therefore,
[tex]\sqrt{6400} = 80[/tex]
[tex]\sqrt{900} =\sqrt{9 * 100} =\sqrt{9} *\sqrt{100} = 3 * 10= 30[/tex]Therefore,
[tex]\sqrt{900} = 30[/tex]
Hence,
[tex]\sqrt{16} = 4\\\sqrt{49} = 7\\\sqrt{25} = 5\\\sqrt{144} = 12\\\sqrt{100} + \sqrt{49} = 17\\\sqrt{196} = 14\\[/tex]
[tex]3^{2}[/tex] x [tex]\sqrt{121}[/tex] = 99
[tex]\sqrt{169}[/tex] x [tex]\sqrt{36}[/tex] = 78
[tex]\sqrt{16}[/tex] x [tex]\sqrt{25}[/tex] = 20
[tex]\sqrt{400} = 20\\\sqrt{2500} = 50\\\sqrt{6400} = 80\\\sqrt{900} = 30[/tex]
Learn more about event correlation here: brainly.com/question/11257411
#SPJ9
Find the next two terms of the sequence:
5, 15, 45, 135, 405, 1215
The next two terms of the sequence are blank and blank
Answer:
3645, 10935
Step-by-step explanation:
1215*3 = 3645
3645*3= 10935
Help pls I’ll mark brainliest
Answer:
its true, true, false, false
Step-by-step explanation:
a is true b is true c is false and d is false
The price of a share of stock started the day at $20.
During the day it went down $13, up $2, down $8, and then up $5.
Which integer represents the price of a share at the end of the day?
A. 8
B. 20
C. 6
D. 5'
100 points if answered
Answer:
C. 6
Step-by-step explanation:
$20 - $13 + $2 - $8 + $5 =
= $7 + $2 - $8 + $5
= $9 - $8 + $5
= $1 + 5
= $6
(xy^4)^3 simplify simplify simplify
Answer:
[tex]x^3y^{12}[/tex]
Step-by-step explanation:
[tex]\left(xy^4\right)^3\\\left(xy^4\right)^3=x^3\left(y^4\right)^3\\=x^3\left(y^4\right)^3\\=(y^4)^3\\=(y)^{4\times 3}\\= y^{12}\\= x^3y^{12}[/tex]
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{By using the \textbf{Exponent Property}, we can simplify this.}[/tex]
[tex]\textsf{This is what it states:}[/tex]
[tex]\sf{(x^m)^n=x^{(m*n)}}[/tex]
[tex]\textsf{Multiply:}[/tex]
[tex]\sf{(xy^4)^3=x^3y^{3*4}=x^3y^{12}}[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]
Unit 3: Parallel & Perpendicular Lines Homework 6: Slope Intercept & Standard Form y= -3 and x=-6
The slope Intercept and the standard form of the equation are y = -1/2x - 3 and x + 2y = -6
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the slope Intercept and the standard form of the equation?The given parameters are
y= -3 and x=-6
The above represent the y and the x intercepts
i.e.
y-intercept = -3
x-intercept = -6
A linear equation is represented as
y = mx + c
Where
c = y-intercept = -3
So, we have
y = mx - 3
At x-intercept = -6, we have
y = 0
So, we have
0 = m(-6) - 3
This gives
m = -1/2
So, we have
y = -1/2x - 3 --- slope-intercept form
Multiply through by 2
So, we have
2y = -x - 6
Rewrite as
x + 2y = -6 ----- standard form
Hence, the slope Intercept and the standard form of the equation are y = -1/2x - 3 and x + 2y = -6
Read more about linear equations at
https://brainly.com/question/14323743
#SPJ1
Carlo is 3 2/3 years older than his sister if his sister us 18 5/6 years old how old is carlo
Answer:
[tex]\sf 22\dfrac{1}{2}\; years[/tex]
Step-by-step explanation:
[tex]\textsf{First convert all mixed fractions to improper fractions: }\\\\3\dfrac{2}{3} = \dfrac{3 \times 3 + 2}{3}= \dfrac{11}{3}\\\\18\dfrac{5}{6 } = \dfrac{18 \times 6 + 5}{6} = \dfrac{113}{6}[/tex]
Let Carlo's age be C
Carlo's age = sister's age + 11/3
[tex]\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\[/tex]
[tex]\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\\sf 6C = 113 + 22 = 135\\[/tex]
[tex]\textsf {Divide both sides by 6}\\\\\sf C = \dfrac{135}{6} \\\\\textsf {Reduce $\dfrac{135}{6}$ by dividing numerator and denominator by 3}\\\\== > C = \dfrac{135 \div 3}{6\div3} = \dfrac{45}{2}[/tex]
[tex]\textsf{So Carlo's age is $\dfrac{45}{2}$ or $22\dfrac{1}{2}$ years}[/tex]
Find the number of distinct permutations that can be formed from all the letters of each word (1) UNUSUAL.
The number of unique permutations that may be made from all of the letters in each word 210.
What is permutations?The number of alternative arrangements of such an object in different orders or sequences is referred to as its permutation. These are typically computed using factorials, as denoted by the symbol. Only natural numbers are utilized in factorials.
Assume we wish to find the number of various permutations of n objects, where p items are one type, q items are another, r items are yet another, and so on.
According to the given data:For the word 'UNUSUAL' there are 7 letters. Then there are 7! possibilities.
We have to divide this by the number of possibilities where letters would replace the same letters.
there are letter U repeated 3 time so 3!
= [tex]\frac{7!}{3!}[/tex]
= 210
the number of unique permutations that may be made from all of the letters in each word 210.
To know more about permutations visit:
https://brainly.com/question/1216161
#SPJ9
Use the Distributive Property to determine which of the following statements is equivalent to 4(8 – 1).
Answer: 4*8 - 4*1
Or you could write it as 4(8) + 4(-1)
The distributive property in general is a(b+c) = ab+ac. We multiply the outer term 'a' with each term inside.
Find the length of YZ if Y is between X and Z
Given: XY = 8a, YZ = 6a, XZ = 2a + 50
Answer:
25
Step-by-step explanation:
By the segment addition postulate,
[tex]XY+YZ=XZ \\ \\ 8a+6a=2a+50 \\ \\ 14a=2a+50 \\ \\ 12a=50 \\ \\ a=\frac{25}{6} \\ \\ \therefore YZ=6(25/6)=25[/tex]
A school has 1256 pupils write this number to the nearest 10 , 100 and 1000
The required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.
What is rounded number?A number that is easily multiplied, divided, etc., and especially a number that ends in zero.
Given:
A school has 1256 pupils write this number to the nearest 10 , 100 and 1000
According to given question we have
⇒ Round off to 10 for 1256 is 1250 or 1260 but nearest to 1256 is 1260.
⇒ So, round off to the nearest 10 is 1260.
⇒ Round off to 100 for 1256 is 1200 or 1300 but nearest to 1260 is 1300.
⇒ So, round off to the nearest 100 is 1300.
⇒ Round off to 1000 for 1256 is 1000 or 2000 but nearest to 1256 is 1000.
⇒ So, round off to the nearest 1000 is 1000.
∴ The answer is 1260,1300,1000.
Therefore, the required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.
Learn more details about rounded number here:
https://brainly.com/question/15265892
#SPJ1
40 POINTS!
Solve 2x^2 + x = 15.
x = −5 and x = 5
x = three over two and x = −5
x = 15 and x = −2
x = five over two and x = −3
Answer:
x = five over two and x = −3
Step-by-step explanation:
Let's solve your equation step-by-step.
2x2+x=15
Step 1: Subtract 15 from both sides.
2x2+x−15=15−15
2x2+x−15=0
Step 2: Factor left side of equation.
(2x−5)(x+3)=0
Step 3: Set factors equal to 0.
2x−5=0 or x+3=0
x=5/2 or x=−3
trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes
When the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes, the time when they will stop at same time is 18 minutes.
How to illustrate the information?From the information, the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes.
Therefore, the time when will they stop at same time will be the lowest common multiple for 9 and 6. This is 18. Therefore, 18 minutes is the appropriate answer.
Therefore, the the time when they will stop at same time is 18 minutes.
Learn more about factor on:
brainly.com/question/25829061
#SPJ1
Trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes. When will they stop at same time?
Write the equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point 7. y=-2x + 5; (3,-7)
Answer:
The equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14
Step-by-step explanation:
It is given that the line that is parallel to the group in each equation and passes through the given point 7y= -2x + 5; (3,-7) and we need to write the equation in slope intercept form of the same line.
Now,
The slope of parallel lines is the same. By changing the equation to slope-intercept form, get the slope in the first line;
=> 7y= -2x + 5
=> y= -2/7x + 5/7
So, the slope = -2/7
Further,
Given the point and the knowledge that the second line would similarly have a slope of -2/7 and the point is (3, -7). With these numbers, we can construct an equation in the slope-intercept form and apply it to get the y-intercept;
=> y = mx + b
=> -7 = -2/7 × 3 + b
=> -7 + 2/7 × 3 = b
=> b = -6.14
Now, put the value of y-intercept back into the equation;
=> y = -2/7x - 6.14
Therefore, the equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14
To know more about the topic, click here:
https://brainly.com/question/18442121
#SPJ9
MAKE CONNECTIONS The height h of a balloon, in feet, t seconds after it is released is given by the function h(t)=2t+6
A What is the Hight of the balloon right before released how do u know
_____ feet
t=_____ before the balloon was released and h(____)=______
Part B
d. Are there any restrictions on the values of t that can be used as inputs for the function? If so, how would this affect the graph of the function? Explain.
The values of t must be _____ because a ___ does not make sense for the given situation and would start at the _____ and only go to the _____
Using the given linear function, it is found that:
a) The initial height of the balloon is of 6 feet, as before the balloon was released t = 0 and h(0) = 6.
b) The values of t must be greater than or equal to 0, because a negative time does not does not make sense for the given situation. The graph would start at the origin and would only go to the right, in a positive direction.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the linear function is:
h(t) = 2t + 6.
From the y-intercept, it is found that:
The initial height of the balloon is of 6 feet, as before the balloon was released t = 0 and h(0) = 6.
Since time cannot be negative, the domain is t ≥ 0, and:
The values of t must be greater than or equal to 0, because a negative time does not does not make sense for the given situation. The graph would start at the origin and would only go to the right, in a positive direction.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1