f(x)=2x-1
we repleace the x with the number -4
f(-4)=2(-4)-1=-8-1=-9
f(-4)=-9
Identify the independent and dependent variables for each relation below.1. "The more hours Maribel works at her job, the larger her paycheck becomes."Independent Variable =Dependent Variable =1. "Increasing the price of an itpunt of people willing to buy it."hours workedIndependent Variable =size of paycheckDependent Variable =
First relation.
Independent variable: Hours worked.
Dependent variable: Size of paycheck
Second relation:
Independent variable: Price of an item
Dependent variable: Number of people willing to buy.
Now, this comes from the fact the the independent variable can be change witho
calculate the difference quotient and use your results to find the slope of the tangent line
Approximate Slope of a Function
We are given the function:
[tex]H(x)=8\ln x+3[/tex]We will find the approximate value of the slope at (e,11).
It's required to use 3 possible values of the approximation differential h.
Let's use h=0.1 and evaluate the function at x = e + 0.1 = 2.8182818
Compute:
[tex]H(e+0.1)=8\ln 2.8182818+3=11.2890193[/tex]Compute the difference quotient:
[tex]H^{\prime}=\frac{11.2890193-11}{0.1}=2.890193[/tex]Now we use h=0.01:
[tex]H(e+0.01)=8\ln 2.728281828+3=11.02937635[/tex]The difference quotient is:
[tex]H^{\prime}=\frac{11.02937635-11}{0.01}=2.9376353[/tex]Finally, use h=0.001:
[tex]H(e+0.001)=8\ln 2.719281828+3=11.00294249[/tex][tex]H^{\prime}=\frac{11.00294249-11}{0.001}=2.9424943[/tex]The last result is the most accurate, thus the slope of the tangent line is 2.94
The following data are the final exams scored on the 13th student in a small calculus class
The following data set for the final exam score in a calculus class
(a) The data set represents a sample data
(b) Range
[tex]\begin{gathered} \text{Range = Highest mark - Lowest mark} \\ \text{Range = 98-60} \\ \text{Range = 38} \end{gathered}[/tex](c) Variance
[tex]\text{Variance = }\frac{\sum ^{}_{}(x-\bar{x})^2}{n}=\frac{2796.36}{13}=215.105[/tex](d) Standard Deviation
[tex]\begin{gathered} S\mathrm{}D\text{ = }\sqrt[]{variance} \\ S\mathrm{}D\text{ = }\sqrt[]{215.105} \\ S\mathrm{}D\text{ = }14.666 \end{gathered}[/tex]Need help with this math homework has a couple steps just need someone to guide me through itConstruct the line that is perpendicular to the directrix and passes through the focus this line will be the axis of symmetry of the para bola what are the coordinates of the point of intersection A of the access of symmetry and the directrix of the para bola explain how you can locate the vertex V of the para bola with the given focus and directrix write the coordinates of the vertex When done which way were the para bola open and can you find the value of P is it positive or negative write the equation of the parabola in vertex form
Part A)
The equation of the directrix is x=-5+8=3, x=3
Part B)
After using 'Perpendicular line' tool and 'Intersect' tool, we obtain the purple line and point A. A=(3,2)
The vertex V has to be on the axis of symmetry, halfway between points A and F. Vertex is V=(-1,2)
Part 3)
The focus is to the left of the vertex; therefore, the parabola opens to the left.
In general,
[tex]\begin{gathered} Vertex:\left(h,k\right) \\ Focus:\left(h+p,k\right) \end{gathered}[/tex]Then, in our case,
[tex]\begin{gathered} \Rightarrow\left(h,k\right)=\left(-1,2\right) \\ and \\ \left(h+p,k\right)=\left(-5,2\right) \end{gathered}[/tex]Thus, p=-4
Finding the equation in vertex form,
[tex]\begin{gathered} x=\frac{1}{4*-4}\left(y-2\right)^2-1 \\ \Rightarrow x=-\frac{1}{16}\left(y-2\right)^2-1 \end{gathered}[/tex]The answer is x=-(y-2)^2/16-1
16.2-(3×4) + (14÷2) I have to tell how many terms the expression has.
The expression we have is:
[tex]16.2-(3\times4)+(14\div2)[/tex]A term in an expression in every part of the said expression, for example, in the expression 10+3, 10 and 3 are terms.
For the case of our expression, each number is a term:
16.2, 3, 4, 14, and 2 are terms.
So in total, we have 5 terms.
Answer: 5 terms
−6x−y=9−2x+10y=−28 please help me
We have to solve the linear system:
-6x - y = 9
-2x + 10y = -28
Multiply both sides of the first equation by 10:
-60x - 10y = 90
-2x + 10y = -28
Now sum both equations, we get:
-60x - 2x -10y + 10y = 90 - 28
-62x + 0 = 62
-62x = 62
x = 62 / -62
x = -1
Now lets find y. I'm going to use the first equation since it is easier to do the math:
-6x - y = 9
-6(-1) - y = 9
6 - y = 9
-y = 9 - 6
-y = 3
y = -3
So the solution of the linear system is x = -1, y = -3 or simply (-1, -3).
Answer: x = -1 ; y = -3
The domain of a quadratic function is all real numbers. The range of the quadratic function is determined by the vertex of the parabola. If the parabola has a minimum value than the range will be all outputs (less than or greater than) that maximum value. If the parabola has a maximum value then the range will be all outputs (equal to or less than) that maximum value.
Answer:
If the parabola has a minimum value, the range will be all outputs greater than the maximum value. If the parabola has a maximum value then the range will be all outputs less than that maximum value.
Explanation:
The range of a function is the set of values that the y-variable can take. If the parabola has a minimum value, the y-variable can take values greater than or equal to the minimum.
In the same way, if the parabola has a maximum value, the y-variable can take values less than the maximum.
Therefore, the answers are:
If the parabola has a minimum value, the range will be all outputs greater than the maximum value. If the parabola has a maximum value then the range will be all outputs less than that maximum value.
____years will be spent on working and ___years will be spent on eating food
In the graph, we can see the following:
We know that a person will devote 28 years working and eating from the word problem. Also, the number of years working will exceed the number of years eating by 20. Then, we have:
[tex]\begin{gathered} \text{Number of years working }+\text{Number of years eating }=28 \\ 24+4=28 \end{gathered}[/tex]Therefore, a person will be spent 24 years working and 4 years eating food.
You have quarters and dimes that total $2.80 your friend says it is possible that the number of quarters is 8 than the number of dimes. Is your friend correct? Let d represent the number of dimes. An equation that models this situation is ____ = 2.80
If d is the amount of dimes and the number of quarters is 8 times the number of dimes, then, you have 8d number of quarters.
Moreover, due to the total amount of money is $2.80, then, you have the following expression:
d + 8d = 2.80 simplify like terms left side
9d = 2.80
Hence, the equation is 9d = 2.80
To determine if your friend is correct, solve the equation for d by dividing by 9 both sides:
d = 2.80/9 =
Error Analysis .... Your friend knows that <1 and <2 are complementary and that <1and <3 are complementary. He concludes that <2 and <3 must becomplementary. What is his error in reasoning? *
In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the problem to find the error.
Data
∠1 + ∠2 = 90
∠1 + ∠3 = 90
Step 02:
∠1 = 25
25 + ∠2 = 90
∠2 = 90 - 25
= 65
∠1 = 25
25 + ∠3 = 90
∠3 = 90 - 25
= 65
∠2 + ∠3 = 130
The answer is:
∠2 = ∠3
Angle 2 and angle 3 are equal, but they are not always complementary.
What is the value of y in this simplified expression?11-4= 119118
Hello can you help me with this. 4/10 = 1/X. it for a Recipe for Salt
We solve it as follows:
[tex]\frac{4}{10}=\frac{1}{x}\Rightarrow x=\frac{1\cdot10}{4}\Rightarrow x=\frac{5}{2}[/tex]So, the value of x is 5/2.
In which quadrant or ok which axis does the point lie ?
Explanation
We are given the following point:
[tex](-5,-3)[/tex]We are required to determine the quadrant, or the axis it lies on a coordinate plane.
We start by plotting the point thus:
Hence, the answer is:
[tex]III[/tex]The last option is correct.
The international club at school has 125 members, many of whom speak multiple languages, the most commonly spoken languages in the club are English, Spanish and Chinese.55 students speak Spanish30 students speak Chinese89 students speak English15 students speak Spanish and Chinese20 students speak Chinese and English33 students speak Spanish and English8 students speak allCreate a Venn Diagram
8 students speak all, so it is in the intersection of the three
15 speak Spanish and Chinese, but 15-8=7 do not speak English
20 speak Chinese and English, but 20-8=12 do not speak Spanish
33 speak Spanish and English, but 33-8=25 do not speak Chinese
55 speak Spanish, but 55-25-8-7=15, do not speak English or Chinese
30 speas chinese, but 30-12-8-7=3 do not speak English or Spanish
89 speak English, but 89-12-8-25=44 do not speak Spanish or Chinese
To end our diagram, we add
[tex]44+25+15+7+8+12+3=114[/tex]Then 125-114=11 students don't speak English, Spanish or Chinese
л IX +6 ІІ 2 someone please help
Given,
[tex]\frac{x}{5}+6=2[/tex]This can be further solved as, by multiplying with 5 on all the terms,
[tex]x+30=10[/tex]Thus x can be calculated as
[tex]undefined[/tex]1) What is the greatest common factor (GCF) of 9 and 27? 1 3 9 27
GCF = 9
Explanations:To find the Greatest Common Factors of 9 and 27:
Step 1: Find the factors of 9 and 27
Factors of 9 = 1, 3, 9
Factors of 27 = 1, 3, 9, 27
Step 2: Find the Common Factors of 9 and 27
That is, the factors that are common to both 9 and 27
Common Factors of 9 and 27 = 1, 3, 9
Step 3: Find the Greatest Common Factor
The Greatest Common Factor (GCF) is the greatest of all the common factors in step 2
Greatest Common Factor = 9
Which facts are true for the graph of the function below? Check all that apply.F(x) = log8x
EXPLANATION
Given the function f(x) = log_8 x.
The facts that apply are:
B. The x-intercept is (1,0)
F. It is increasing.
I am going to attach a photo of the question. as you can tell the question has already been answered but my teacher wants me to show how she got the answer.
Answer:
The ratio of their surface area is;
[tex]25\colon9[/tex]Explanation:
Given the length of the slant height of the cone as;
[tex]\begin{gathered} l_A=35\text{ in} \\ l_B=21\text{ in} \end{gathered}[/tex]since the cones are similar, the ratio of their sides is;
[tex]\begin{gathered} A\colon B \\ =35\colon21 \\ l^{}_A\colon l^{}_B=5\colon3 \end{gathered}[/tex]The ratio of the total surface area is the square of the ratio of the sides.
[tex]\begin{gathered} S_A\colon S_B=l^2_A\colon l^2_B \\ S_A\colon S_B=5^2_{}\colon3^2_{} \\ S_A\colon S_B=25\colon9 \end{gathered}[/tex]Therefore, the ratio of their surface area is;
[tex]25\colon9[/tex]A house was valued at $302,000. over several years, the value increased by 9% given the house in new value.
It is given that a house was valued at $302,000.
Let old value =$302,000.
Over several years, the value increased by 9%.
New value=9 % of old value+old value
[tex]\text{New value=}\frac{9}{100}\times302000+302000[/tex][tex]\text{New value=}\frac{9}{100}\times302000+(1)\times302000[/tex]Taking out 302000 as common, we get
[tex]\text{New value=(}\frac{9}{100}+1)\times302000[/tex][tex]\text{Use }\frac{\text{9}}{100}=0.09,\text{ we get}[/tex][tex]\text{New value=(0.09+1)}\times302000[/tex][tex]A\text{dding 1 and 0.09 , we get 1+0.09=1.09}[/tex][tex]\text{New value=1.09}\times302000[/tex][tex]\text{New value=\$}329180[/tex]Hence the new value of the house is $329180.
Help me please . And have a good day :D
Correct option is A, 0 to 0.25
and E, 15 to 20.
Given:
a data of f(x) and g(x) corresponding to the values of x is given.
Find:
we have to find the interval in ehich g(x) grows faster than f(x).
Explanation:
from the given data, it is clear that g(x) growing faster than f(
Solve the expression for x = -2.2x + 4[x - 2(3 + x)]
ANSWER
[tex]-20[/tex]EXPLANATION
To solve the expression for x = -2, substitute -2 for x in the expression and simplify:
[tex]2x+4\mleft\lbrace x-2(3+x)_{}\mright\rbrace[/tex]That is:
[tex]\begin{gathered} 2(-2)+4\mleft\lbrace-2-2(3+(-2))\mright\rbrace \\ -4+4\mleft\lbrace-2-2(3-2)\mright\rbrace \\ -4+4\mleft\lbrace-2-2(1)\mright\rbrace \\ -4+4\mleft\lbrace-2-2\mright\rbrace \\ -4+4\mleft\lbrace-4\mright\rbrace \\ -4-16 \\ -20 \end{gathered}[/tex]That is the solution of the expression for x = -2.
2 Which function represents a translation of the graph of 1 = x by 8 units to the right? O A. V=(x-8) O B. v = (x+8) O c. v=872 =x2+8
Given function is,
[tex]y=x^2[/tex]For the function
[tex]y=f(x)[/tex]If we shift the graph b units to the right, the new function is
[tex]y=f(x-b)[/tex]Now, if we shift the graph of the given function 8 units to the right, the equation is
[tex]y=(x-8)^2[/tex]Hence, the correct option is (A)
Solve the following Equation:-5k=12
k = -2.4
Explanation:[tex]-5k\text{ = 12}[/tex]Divide both sides by -5:
[tex]\begin{gathered} \frac{-5k}{-5}=\frac{12}{-5} \\ \end{gathered}[/tex]Division of same sign gives positive number. Division of opposite signs give negative number.
[tex]\begin{gathered} k\text{ = -12/5} \\ k\text{ = -2.4} \end{gathered}[/tex]base: 5 ft 5 area: 5-ft?
area of the triangle is
[tex]A=\frac{1}{2}bh[/tex]then solve for h:
[tex]\begin{gathered} 5\frac{5}{6}=\frac{1}{2}(5)h \\ \frac{35}{6}=\frac{5}{2}h \\ \frac{35}{6}\times\frac{2}{5}=\frac{5}{2}\times\frac{2}{5}h \\ h=\frac{70}{30}=\frac{7}{3} \\ h=2\frac{1}{3} \end{gathered}[/tex]answer: h = 2 1/3
I don't know how to shade for the 2nd one please help
Answer: Your result (without simplifying) is actually 2/36, so you would shade two boxes out of the 36 shown.
NOTE: For problem #19, you have 6 boxes for shading, so each box represents 3 increments (3x6=18 boxes). For your result of 5/18, you should only shade the first box and 2/3 of the next box (the other four boxes should be unshaded).
Hope this helps!
Step-by-step explanation:
Solve for 3+y/2=-212
You have the following equation:
[tex]3+\frac{y}{2}=-212[/tex]In order to solve the previous equation for y, proceed as follow:
3 + y/2 = -212 subtract 3 both sides
y/2 = -212 - 3 simplify right side
y/2 = -215 multiply by 2 both sides to cancel the denominator left side
y = -215(2)
y = -430
Hence, the solution for y in the given equation is y = -430
Hernando’s salary was $47,500 last year. This year his salary was cut to $38,475. Find the percent decrease
To determine the percentage of decrease that Hernando's salary was cut, we first calculate the total value, then the ratio of this value to the initial one, then we multiplicate by 100, to get it in percent, as follows:
[tex]\begin{gathered} 47,500-38,475=9,025 \\ \frac{9,025}{47,500}=0.19 \\ 0.19\times100=19\text{ \%} \end{gathered}[/tex]From the solution we developed above, we are able to conclude that the salary of Hernando was cut by 19 %14. The measure of one side of an equilateral triangle is (s+6) inches long. Write 2 different, equivalent
expressions to represent the perimeter of the triangle.
Perimeter of the equilateral triangle = 3(s + 6) inches
Perimeter of the equilateral triangle = 3s + 18 inches
Explanation:Given:
One of the sides of an equilateral triangle = (s + 6)
To find:
2 different equivalent expressions that represent the perimeter of the triangle
To determine the expression, we need to apply the formula for the perimeter of an equilateral triangle
[tex]\begin{gathered} Perimeter\text{ of equilateral triangle = sum of all 3 sides} \\ since\text{ all sides of an equilateral triangle are equal,} \\ Perimeter\text{ = 3}\times\text{ one of the side} \end{gathered}[/tex][tex]\begin{gathered} one\text{ of the side = s + 6} \\ \\ Perimter\text{ = 3 }\times(s\text{ + 6\rparen} \\ Perimeter\text{ of the equilateral triangle = 3\lparen s + 6\rparen inches} \end{gathered}[/tex]Another expression for the perimeter:
[tex]\begin{gathered} Perimeter\text{ = 3\lparen s + 6\rparen} \\ Expanding\text{ the parenthesis using distributive property:} \\ Perimeter\text{ = 3\lparen s\rparen + 3\lparen6\rparen} \\ Perimeter\text{ of the equilateral triangle = 3s + 18 inches} \end{gathered}[/tex]?In the table below, y is a linear function of x.X-214710y09182736What is the y intercept of the function
y intercept : (0,6)
Explanation:
Use the formula:
. y = mx + b
Find m (the slope), using 2 random points of the graph: (-2,0) and (1,9)
. m = (y-y1) / (x-x1)
m = (0-9) / (-2-1)
m = -9 / -3
m = 3
Replace m in the equation:
. y = 3x + b
Find b by replacing y and x by a random point of the graph: (1,9)
. 9 = 3*1 + b
b = 9 - 3
b = 6
Replace b in the equation:
. y = 3x +6
To find the y-intercept replace x by 0 in the equation:
. y = 3*0 +6
y = 0+6
y = 6
=> y-intercept : (0,6)
Find the quotient. Write your answer in standard form. 3+ O A. + COLO O B.-1 O C. 1-1 OD. llo 011
Option A is correct.
The given complex number is
[tex]\frac{3+i}{3-i}[/tex]Multiply the numerator and denominator by 3+i and solve as follows:
[tex]\begin{gathered} \frac{3+i}{3-1}\times\frac{3+i}{3-i}=\frac{(3+i)^2}{3^2-i^2} \\ =\frac{3^2+i^2+6i}{9+1} \\ =\frac{9-1+6i}{10} \\ =\frac{8+6i}{10} \\ =\frac{8}{10}+\frac{6}{10}i \\ =\frac{4}{5}+\frac{3}{5}i \end{gathered}[/tex]