If function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
The function is
f(x) = [tex]x^2[/tex] + 4x -1
The function is the expression that represents the relationship between one variable and another variable. If one variable is dependent variable then the another variable is independent variable.
The value of g(x) = f(x+4)
First we have to find the value of f(x+4)
Substitute the values in the function
f(x) = [tex]x^2[/tex] + 4x -1
f(x+4) = [tex](x+4)^2[/tex] + 4(x+4) - 1
= [tex]x^2[/tex] + 8x +16 + 4x+16 - 1
Rearrange the terms and combine the like terms
= [tex]x^2[/tex] + 8x+4x + 16+16-1
= [tex]x^2[/tex] + 12x +31
Hence, if function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
Learn more about function here
brainly.com/question/12431044
#SPJ1
Determine the distance between the points (−4, −7) and (−8, −13).
Answer:
2[tex]\sqrt{23}[/tex]
Step-by-step explanation:
The distance between the points (-4, -7) and (-8, -13) is 2√13 units as per the concept of distance between the two points.
To determine the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is as follows:
[tex]Distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]
Given the two points (-4, -7) and (-8, -13), we can assign the coordinates as follows:
x1 = -4, y1 = -7 (coordinates of the first point)
x2 = -8, y2 = -13 (coordinates of the second point)
Now, we substitute these values into the distance formula:
[tex]Distance = \sqrt{(-8 - (-4))^2 + (-13 - (-7))^2)}\\\\= \sqrt{((-8 + 4)^2 + (-13 + 7)^2}\\= \sqrt{((-4)^2 + (-6)^2)}[/tex]
= √(16 + 36)
= √52
= 2√13
Therefore, the distance between the points (-4, -7) and (-8, -13) is 2√13 units.
To learn more about the distance between two points;
https://brainly.com/question/24485622
#SPJ2
Round 3.44570830811 to the nearest hundred-thousandth
Answer:
3.44571
Step by step explanation:
3.44570830811
8 is the number next to the place value of hundred-thousandth, so we round it up to 1 and add it to 0
please mark brainliest
Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
The property demonstrated by:
a(b+c)=(a.b)+(a.c)
Is the Distributive property
Which property is demonstrated below?Here we have the next expression:
a*(b + c) = (a*b) + (a*c)
So we have the product between a and the sum of b and c, is equal to the sum between the products of a and b, and a and c, so we "distributed" the product.
This property is called the "Distributive property".
Learn more about distributive property.
https://brainly.com/question/4077386
#SPJ1
Evelyn is thinking of constructing a swimming pool in the plot next to her house such that it is surrounded by grass as given in the figure below. The dimensions of the plot is 50 ft x 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
The area of a pool from the given situation is 816 ft².
Given that, the dimensions of plot is 50 ft and 40 ft.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, area of a plot = Length × Width
= 50 × 40
= 2000 ft²
Area of a pool = Area of a plot - Area of a grass
= 2000 - 1184
= 816 ft²
Therefore, the area of a pool from the given situation is 816 ft².
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
#SPJ1
I haven’t came across one of these questions so not sure how to solve
m∠F = 140º
1) Since that trapezoid is a quadrilateral, then we can affirm that the Sum of their interior angles is:
[tex]\begin{gathered} S_i=180(n-2) \\ S_i=180(4-2) \\ S_i=180(2) \\ S_i=360 \end{gathered}[/tex]Note that "n" refers to the number of sides:
Notice also that angle H is a right angle since this is not an Isosceles Trapezoid
So we can write out the following
9x +14x +4x + 90 = 360º
27x = 360 -90
27x = 270
x =10
Alternatively, angles between parallel lines are supplementary
2) To find out the measure of angle ∠F We'll need to plug x=10 into that expression:
m∠F = 14x
m∠F = 140º
1x + 2y = 7 and y = -2x + 3
Answer:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
Solve the system of equations:
1x + 2y = 7
y = –2x + 3
Substitute y = –2x + 3 for y in the first equation:
1x + 2y = 7
1x + 2(–2x + 3) = 7
Substract 6 from both sides:
–3x + 6 = 7
–3x + 6 – 6 = 7 – 6
–3x = 1
Divide:
–3x/–3 = 1/–3
x = –1/3
Substitute –1/3 for x in the second equation:
y = –2x + 3
y = –2(–1/3) + 3
y = 11/3
Solution:
x = –1/3 and y = 11/3
or can be written as (–1/3, 11/3)
Hope that helps! Have an amazing rest of your day! Please consider giving me the brainliest! :)
When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step? Original Equation: 5.x2 + (10x2 + 10) = 3x? First Step: 15x2 + 10 = 3.2 commutative property of multiplication commutative property of addition multiplication property of equality
The original equation is:
5 x^2 + (10 x^2 + 10) = 3 x^2 - 5
The first step the person did was:
15 x^2 + 10 = 3 x^2 - 5
so in this first step the person used the associative property of addition by associating 5 x^2 with 10 x^2 and combining them to give 15 x^2.
Please check if there is an option that states such among your options.
Show that the triangles are similar and write a similarity statement.E1427AC 18D21BZACBACEDCSo AABC ~ A
Two triangles are similar if the ratio of their corresponding side equal'
Triangle
Because
Corresponding sides are
Therefore,
Triangle
Jacob set aside (budgeted) $10 to spend on snacks at the movies. Sodas cost $1.50 each, and a box of popcorn costs $1.75. How many sodas can he buy for him and his friends if he buys 2 boxes of popcorn? Write an Inequality.
Answer:4 sodas
Step-by-step explanation:
1.75 x 2 = 3.5
10- 3.5 = 6.5
6.5 Divided by 1.50 = 4.33333333
(Round that to 4 and he will be left with cents)
On the freeway it is unsafe to drive too slowly or two quick the safest driving speeds on the freeway near Allentown worst scientifically determined to be between the minimum and maximum speed in miles per hour according to the equation X -55 in value equals 4.2 which equation can be used to determine the maximum safe driving speed
Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.
As given in the question,
Given equation :
|x – 55| = 4.2
To determine the maximum and minimum speed in miles per hour from the given equation we have,
x-55 = 4.2 or x-55 =-4.2
Add 55 both the side of the equation,
x-55 +55 =4.2+55 or x-55+55 = -4.2 +55
x =59.2 or x = 50.8
Maximum speed is 59.2 determine by equation x-55 = 4.2
Minimum speed is 50.8 determine by equation x-55 = -4.2
Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to
x -55 =4.2.
The complete question is:
On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?
Learn more about equation here
brainly.com/question/10413253
#SPJ1
Consider the following.
sin(x) + sin(3x) = 4 sin(x) cos2(x)
Prove the identity.
Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Given,
sin(x) + sin(3x) = 4 sin(x) cos²(x)
We have to prove the above given identity:
So,
sin(x) + sin(3x)
sin(x) + sin(2x + x)
By using the identity sin (A + B) we get,
sin(x) + sin (2x) cos(x) + cos (2x) sin(x)
Now use the identities:
sin 2x and cos 2x
We get,
sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)
Then,
sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)
We get,
4 sin(x) cos²(x)
Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Learn more about identities here:
https://brainly.com/question/14347010
#SPJ1
Mark Trumbo of the Arizona Diamondbacks has hit five home runs in the thirty-five times he has been up to bat. At this pace, how many at bats would he need to hit twenty-three home runs?
ASAP DUE TODAY!!
Please include answers AND an explanation. Giving branliest <3
(1) The graph is attached with the answer below.
(2)The equation of the line is y = x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The points are ( 3, 0 ) and ( 0, 3). The slope of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 3 - 0 ) ( 0 - 3 )
Slope = 1
Calculate the y-intercept,
y = mx + c
3 = 0 + c
c = 3
The equation of the line will be:-
y = x + 3
Therefore, the graph is attached with the answer below the equation of the line is y = x + 3.
To know more about an equation of the line follow
brainly.com/question/18831322
#SPJ1
the temperature at sunrise is 48°F . each hour the temperature rises 6°F write an equation that models the temperature y in degrees Fahrenheit after x hours. what is the graph of the equation.
EXPLANATION
Let's see the facts:
Temperature at sunrise = 48 °F
Rate = 6°F/h
The equation is given by the following expression:
Let's call "x" to the number of hours elapsed
y = 48 + 6x
The graph is given by the following representation:
A social scientist researched how the average working hours per worker, over a full year, for two different European countries changed since 1870. she created a scatter plot and found the regression line for each set of data. She then used the regression line to
create a table of values for the residuals. The scatter plots, regression equation, and residuals for the two countries are shown, where z represents the number of years since 1870 and y represents the average working hours per worker over a full year.
We can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.
What is a regression equation?The dependent variable's predicted value in simple linear regression is given by the equation = b₀ + b₁x. In order to minimize the total sum of squared errors, the values of b0 and b1 are calculated from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).When two variables, X and Y, are involved, there will be two regression lines: one for X on Y and one for Y on X. Lines of regression X and Y: In this configuration, the variables Y and X are independent, and the best-expected value of X is determined in accordance with the value of Y that is provided.So, according to the given image, we can easily say that Germany has a negative correlation.
Hence, option(C) and (D) are wrong.We can observe that the slope of the regression equation is negative.
Then, the wrong option will be (A) and the correct option will be (B).Therefore, we can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.
Know more about regression equations here:
https://brainly.com/question/26843436
#SPJ13
Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
Learn more about percentages on
brainly.com/question/24877689
#SPJ1
The telephone company offers two billing plans for local calls. Plan 1 charges $24 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
Answer:
plan b
Step-by-step explanation:
unless your making 120 calls or more plan B is better
24-18=6
6/0.05
=120
Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of d days that have passed. A. Write an equation for the situation.B. Find the a amount of money he began with.C. How much money does Marty have after 9 days?
Given:
Amount Marty spent per day = $3
Number of days = 14
Remaining amount = $68
Since the amount left depends on the number
Please help! Super confused!
Enter the inverse function of f(x) = -9x - 10.
Answer: [tex]f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Step-by-step explanation:
[tex]f(x)=-9x-10 \implies x=-9f^{-1}(x)-10\\\\x+10=-9f^{-1}(x)\\\\f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Which rule explains why these triangles are congruent?
Answer:
SAS Congruence Rule
A triangle is said to be congruent to each other if two sides and the included angle of one triangle is equal to the sides and included angle of the other triangle.
Answer: SAS (side side angle postulate.)
Step-by-step explanation:
can be used to prove triangles congruent.
sides and the corresponding angle of the other, then the triangles are congruent.
Please help gotta get my grade up ASAP this was due the 11th and it’s the 23rd now, super behind!!
Find f(7) if f(x) = 6x + 10. Enter DNE if the value does not exist.
f(7) =
Answer: f(7) = 52
Step-by-step explanation:
x = 7, so you would substitute x for 7
f(7) = 6(7) + 10
f(7) = 42 + 10
f(7) = 52
Hope this helps!
In the diagram below, segment PB is a tangent. IF AC = 18 and PA = 6, find PB.
Explanation
we have a secant and a tangent
To solve the question, we will apply the intersecting secant and tangent theorem
So, for the question
we have
[tex]\begin{gathered} PB^2=PA(PA+AC) \\ \\ PB^2=6(6+18) \\ \\ PB^2=6(24) \\ \\ PB=144 \\ \\ PB=12 \end{gathered}[/tex]Therefore, the value of PB is 12
Find the slope between these two points:
(3, 0), (-11, -15)
Answer:
3/4 or 0.75
Step-by-step explanation:
Round 1.9541 to the nearest tenth
Answer:
2
Step-by-step explanation:
1.9541 lets only worry about 1.95 because it rounds to this rounding up because its five will be 2
What is the slope of a line perpendicular to the line whose equation is x+6y=-24
Answer:
[tex]m[/tex]perpendicular = 6
Step-by-step explanation:
Hope this helps! :))
Determine a series of transformations that would map Figure I onto Figure J
and its not just rotate the figure 90 degrees clockwise, you have the do TWO translations
3 × 90 thus equals 280 degrees.
The figure moves onto the following quadrant of the graph with each 90 degree rotation. In order to shift Figure I to the location of Figure J, you must move the three figure quadrants in a clockwise direction. 3 × 90 thus equals 280 degrees. Only one transformation is needed.
Which transformation corresponds to turning a figure 90 degrees counterclockwise?
The coordinate transformation (x, y) (y, x) is equivalent to a rotation of the origin 90 degrees counterclockwise. The coordinate transformation (x, y) (x, y) is comparable to a 180 degree counterclockwise rotation of the origin.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, making y negative.
To learn more about the problm refer to:
https://brainly.com/question/25368661
#SPJ13
Yesterday, the temperature change for a 5-hour period of time was -degree perhour. Which statement describes this change?AThe temperature rose 5 degrees.BThe temperature rose 45 degrees.СThe temperature fell 4 degrees.DThe temperature fell 5 degrees.AB
The negative sign means that temperature decreases of fell.
Deteremine the change in temperature for 5 hours.
[tex]\begin{gathered} dT=5\cdot(-\frac{4}{5}) \\ =-4 \end{gathered}[/tex]So temperatute fell 4 degrees. Option C is correct.
#5 Pam a nurse made $93 in 6 hours determine an equation that represents how much she gets paid per hour #6 using your equation from problem 5 how much would a modern if she work for 15 hours?#7 using your equation from problem 6 how much would Pam earn if she work for 3 1/2 hours?
Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below
[tex]\begin{gathered} \text{ amount she earned per hr=}\frac{93}{6}=15.5 \\ The\text{ equation that can represent how much she earned per hour is} \\ \text{amount earned per hour = 15.5x} \\ x=\text{ hours worked} \\ \text{amount earned per hour}=15.5(1)=15.5\text{ dollars} \end{gathered}[/tex][tex]\begin{gathered} \text{amount she earned in 15 hrs=}15.5x \\ \text{amount she earned in 15 hrs}=15.5\times15=232.5dollars \end{gathered}[/tex][tex]\begin{gathered} \text{amount earned in 3}\frac{1}{2}\text{hrs}=15.5x \\ \text{amount earned in 3}\frac{1}{2}\text{hrs=15.5}\times\frac{7}{2}=\frac{108.5}{2}=54.25dollars \end{gathered}[/tex]Which of the following equations represents a proportional relationship? Select all that apply. A 5 5 = 11 11 B 3 6 = 6 3 C 2x 12 = 3x 18 D 8 15 = 4 30 E 4 6 = 10 15 F 4x 18 = x 18
The equations that represent proportional relationships are:
A. 2x/12 = 3x/18
C. 4/6 = 10/15
E. 5/5 = 11/11
How to Determine a Proportional Relationship Equation?To determine if an equation represents a proportional relationship, ensure each side of the equation gives the same value when simplified. If they do not have the same value, then the equation does not represent a proportional relationship.
A. 2x/12 = x/6
3x/18 = x/6
Therefore, 2x/12 = 3x/18 represents a proportional relationship.
B. 3/6 = 1/2
6/3 = 2
Therefore, 3/6 = 6/3 does not represent a proportional relationship.
C. 4/6 = 2/3
10/15 = 2/3
Therefore, 4/6 = 10/15 represents a proportional relationship.
D. 4x/18 = 2x/9
x/18 = x/18
Therefore, 4x/18 = x/18 does not represent a proportional relationship.
E. 5/5 = 1
11/11 = 1
Therefore, 5/5 = 11/11 represents a proportional relationship.
F. 8/15 = 8/15
4/30 = 2/15
Therefore, 8/15/2/15 does not represent a proportional relationship.
Learn more about proportional relationship equation on:
https://brainly.com/question/11688703
#SPJ1
Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope -1.
The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.
Hence,
y - y₁ = m(x - x₁)
where
m = slopey₁ and x₁ are the coordinates of the point.Therefore,
m = slope = -1
using (-12, 15)
Hence,
y - 15 = - 1(x - (-12))
Therefore,
y - 15 = - 1(x + 12)
learn more on point slope form here: https://brainly.com/question/7568466
#SPJ1