Answers
The first step is to substitute values of x into each equation.
For y = x^2 + 1,
if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5
if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2
if x = 0, y = (0)^2 + 1 = 0 + 1 = 1
if x = 1, y = (1)^2 + 1 = 1 + 1 = 2
if x = 2, y = (2)^2 + 1 = 4 + 1 = 5
We would plot the corresponding values of x and y on the graph as shown below
For y = 3^(x + 1),
if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33
if x = - 1, y = 3^(-1 + 1) = 3^0 = 1
if x = 0, y = 3^(0 + 1) = 3^1 = 3
if x = 1, y = 3^(1 + 1) = 3^2 = 9
if x = 2, y = 3^(2 + 1) = 3^3 = 27
We would plot the corresponding values of x and y on the graph as shown below
Related Questions
957.55x8042x6/4x6=??
Answers
6930553.9
1) Let's rewrite and solve the expression, note that since Multiplication and Division are on the same level of priority according to PEMDAS acronym for the order of operations:
[tex]\begin{gathered} 957.55\times8042\times\frac{6}{4}\times6= \\ 957.55\times8042\times\frac{3}{2}\times6= \\ 957.55\times8042\times\frac{3}{1}\times3= \\ 69305553.90= \end{gathered}[/tex]Notice that we simplified 6/4 to 3/2 and then 6 by 2. In addition to this, note that the 2 decimal places were kept, we can write 69305553.90 or simply 69305553.9
2) Hence, the answer is = 6930553.9
4. Which of the following rules is the composition of a dilation of scale factor 2 following (after) a translation of 3 units to the right?
Answers
ANSWER
A. (2x + 3, 2y)
EXPLANATION
Let the original coordinates be (x, y)
First, there was a dilation of scale factor 2.
This means that the coordinates become:
2 * (x, y) => (2x, 2y)
Then, there was a translation of 3 units to the right. That is a translation of 3 units on the horizontal (or x axis).
That is:
(2x + 3, 2y)
So, the answer is option A.
a number, twice that number, and one-third of that number added. the result is 20. what is the number?
Answers
Answer:
6
Step-by-step explanation:
Let x = the number
2x = twice the number
1/3 x = one-third of the number
x + 2x + 1/3 x = 20
Combine like terms.
3 1/3 x = 20
Change 3 1/3 to an improper number.
10/3 x = 20
Times by 3/10 on both sides.
3/10 • 10/3 x = 20•3/10
x = 60/10
x = 6
Check:
6 + 2(6) + 1/3(6)
= 6 + 12 + 2
= 20 check!
x+2x+(1/3)x=20...multiply terms by 3
3x+6x+x=60
10x=60
x=6
Evaluate the function for the indicated values of x. (2x + 1, x 5 f(-10) = F(2) = f(-5) = f(-1) = f(8) =
Answers
Explanation
[tex]f(x)f(x)=\mleft\{\begin{aligned}2x+1\text{ if x}\leq-5\text{ } \\ x^2\text{ if -5}Step 1you need to select the correct function depending on the number
i)f(-10)
[tex]-10\leq-5,\text{ then you n}eed\text{ apply}\Rightarrow f(x)=2x+1[/tex]Let x= -10, replacing
[tex]\begin{gathered} f(x)=2x+1 \\ f(-10)=(2\cdot-10)+1 \\ f(-10)=-20+1 \\ f(-10)=-19 \end{gathered}[/tex]Step 2
Now
ii) f(2)
[tex]\begin{gathered} 2\text{ is in the interval} \\ -5Letx=2,replacing
[tex]\begin{gathered} f(x)=x^2 \\ f(2)=2^2=4 \\ f(2)=4 \end{gathered}[/tex]Step 3
iii) f(-5)
[tex]\begin{gathered} -5\text{ is smaller or equal than -5} \\ -5\leq5,\text{ then apply}\Rightarrow f(x)=2x+1 \end{gathered}[/tex]Let
x=-5,replace
[tex]\begin{gathered} f(x)=2x+1 \\ f(-5)=(2\cdot-5)+1=-10+1 \\ f(-5)=-9 \end{gathered}[/tex]Step 4
iv)f(-1)
[tex]\begin{gathered} -1\text{ is in the interval} \\ -5<-1<5 \\ \text{then apply}\Rightarrow f(x)=x^2 \end{gathered}[/tex]let
x=-1,replace
[tex]\begin{gathered} f(x)=x^2 \\ f(-1)=(-1)^2 \\ f(-1)=-1\cdot-1=1 \\ f(-1)=1 \end{gathered}[/tex]Step 5
Finally
F(8)
[tex]\begin{gathered} 8\text{ is greater or equal than 5, then apply} \\ 8\ge5\Rightarrow apply\text{ f(x)=3-x} \\ f(x)=3-x \end{gathered}[/tex]Let
x=8,replace
[tex]\begin{gathered} f(x)=3-x \\ f(8)=3-8 \\ f(8)=-5 \end{gathered}[/tex]I hope this helps you
given a quadratic equation in standard form f(x) = ax^2 + bx + c. explain how to determine if there is one real solution, two real solutions, or no real solutions (use the discriminant b^2 - 4ac)
Answers
As per given by the question,
There are given that a general form od quadratic equation.
The equation is,
[tex]f(x)=ax^2+bx+c[/tex]Now,
For determine the one real solution, two real solution, and no real solution;
There are apply the condition for all these three.
So,
First for one real solution.
If
[tex]b^2-4ac=0,\text{ then}[/tex]The given quadratic equation has one real solution.
If,
[tex]b^2-4ac>0,\text{ then;}[/tex]The given quadratic equation has two real solution.
And,
If,
[tex]b^2-4ac<0,\text{ then;}[/tex]The given quadratic equation has no real solution.
solve using the quadratic formulax^2+2x-17=0
Answers
Determine m such that the line through points (2m,4) and (m-3,6) has a slope of -5.
Answers
We have to use the formula of the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=2m,x_2=m-3,y_1=4,y_2=6,m=-5[/tex]Replacing all these values, we have
[tex]-5=\frac{6-4}{m-3-2m}[/tex]Now, we solve for m
[tex]\begin{gathered} -5=\frac{2}{-m-3} \\ -m-3=\frac{2}{-5} \\ -m=-\frac{2}{5}+3 \\ m=\frac{2}{5}-3=\frac{2-15}{5}=\frac{-13}{5} \end{gathered}[/tex]Therefore, m must be equal to -13/5 in order to meet the given characteristics.Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
Answers
Answer: [tex]\frac{5}{2\sqrt{5x+3\\} }[/tex]
Step-by-step explanation:
First, use the chain rule to quickly find the answer so that you can check after you go through the ridiculous process that is the bane of every calculus 1 student's existence.
f(x) = (5x + 3)^(1/2)
(d/dx) (5x + 3)^(1/2) =
(1/2)(5x + 3)^(-1/2) * (5) =
5/[2(5x+3)^(1/2)]
Now, we enter the first gate of hell:
f'(x) = the limit as h approaches 0 of [(f(x+h) - f(x))/h]
lim as h -> 0 of [(5(x+h)+3)^(1/2) - (5x+3)^(1/2)/h]
lim as h -> 0 of [(5x+5h+3)^(1/2) - (5x+3)^(1/2) / h]
Multiply numerator and denominator by the conjugate of the numerator, which is (5x+5h+3)^(1/2) + (5x+3)^(1/2).
lim as h -> 0 of
[√(5x+5h+3) - √(5x+3) ] [√(5x+5h+3) + √(5x+3) ]
______________________________________
h[√(5x+5h+3) - √(5x+3) ]
Simplify the numerator via FOIL:
5x+5h+3 + √(5x+5h+3)√(5x+3) - √(5x+3)√(5x+5h+3) - (5x+3)
The remaining radicals in the numerator cancel each-other, giving us:
5x + 5h + 3 - 5x - 3
Simplify Further:
5h
Now that we have simplified our numerator, let's continue:
lim as h -> 0 of (5)(h)/[(h)((5x+5h+3)^(1/2) + (5x+3)^(1/2))]
The h in the numerator cancels the h in the denominator.
lim as h -> 0 of 5/[(5x+5h+3)^(1/2) + (5x+3)^(1/2)]
Now, we directly substitute h with 0 in the equation.
5/[ (5x+3)^1/2 + (5x+3)^(1/2) ]
In the denominator, both sides of the addition sign are the same, so we can simplify it further to:
5/[ 2(5x+3)^(1/2) ]
This is the same answer we received using the chain rule, so it is correct!
3.) Write the explicit formula for the arithmetic sequence. 50, 47, 44, 41,...
Answers
all the terms are 3 less than its preceding term, simple!
So, the formula would be:
[tex]a_n=a+(n-1)d[/tex]Where
a is the first term
d is the common difference (diff in 2 terms)
From the sequnce,
first term (a) is 50
common difference (d) = 47 - 50 = -3
So, we have:
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_n=50+(n-1)(-3_{}) \\ a_n=50-3n+3 \\ a_n=53-3n \end{gathered}[/tex]Explicit Formula:
[tex]a_n=53-3n[/tex]7. Find the perimeter of the rectangle with length 33 yards and width 59 yards.A.92 ydB.1,947 ydC.125 ydD.184 yd
Answers
Solution
We are given
Length (l) = 33 yards
Width (w) = 59 yards
To find the perimeter
Note: Perimeter of a Rectangle
[tex]Perimeter=2(l+w)[/tex]solve a system of equations to solve the problem question 8
Answers
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Reflects the given the coordinates points across the y - axis
Answers
Answer:
Explanation:
The reflection over the line y = x gives the following transformation of coordinates
[tex](x,y)\to(y,x)[/tex]therefore, for our case the transformation gives
[tex]\begin{gathered} S(-2,5)\to S^{\prime}(5,-2) \\ T(-3,0)\to T^{\prime}(0,-3) \\ U(1,-1)\to U^{\prime}(-1,1)_{} \end{gathered}[/tex]which are our answers!
The graphical representation of a point and its reflection about the line y =x is the following:
If a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle040 3113O 22
Answers
The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]Substitute 70 for P, x for l and (x - 9) for w in the formula to determine the value of x.
[tex]\begin{gathered} 70=2(x+x-9) \\ 35=2x-9 \\ 2x=35+9 \\ x=\frac{44}{2} \\ =22 \end{gathered}[/tex]So value of x is 22.
Can u please help me solve? I'm reviewing for finals.
Answers
Given:
Consider the given graph as a reference of the solution.
To find:
[tex]-3(u\cdot v)[/tex]Explanation:
By analyzing the graph, we can define the coordinate of vector u and v:
[tex]\[\begin{align} & \vec{u}=(-8,-9)-(0,0)=(-8,-9) \\ & \vec{v}=(3,7)-(0,0)=(3,7)\end{align}\][/tex]Now, let perform the dot product of two vectors,
[tex]\begin{gathered} u\cdot v=(-8,-9)\cdot(3,7) \\ u\cdot v=(-8)(3)+(-9)(7) \\ u\cdot v=-24-63 \\ u\cdot v=-87 \end{gathered}[/tex]Now, perform the required operation,
[tex]\begin{gathered} -3(u\cdot v) \\ =-3(-87) \\ =261 \end{gathered}[/tex]Final answer:
Hence, the required solution is:
[tex]-3(u\cdot v)=261[/tex]What is the measure of m?n20m5m = [?]✓=Give your answer in simplest form.Enter
Answers
STEP - BY - STEP EXPLANATION
What to find?
The value of m.
To find the value of m, we take the proportion of the sides of the triangles.
That is;
adjacent of the bigger triangle/hypotenuse of the bigger triangle = adjacent of the smaller triangle / hypotenuse of the smaller triangle.
That is;
[tex]\frac{m}{20+5}=\frac{5}{m}[/tex][tex]\frac{m}{25}=\frac{5}{m}[/tex]Cross-multiply
[tex]m^2=25\times5[/tex]Take the square root of both-side of the equation.
[tex]m=\sqrt[]{25\times5}[/tex][tex]m=5\sqrt[]{5}[/tex]NO LINKS!! Show all work where necessary to get full credit
Answers
16. Circle F
You name a circle using the center.17. BF
A radius connects the center to a point on the circumference of the circle.18. CD
A chord is a segment connecting two points on the circumference of the circle.19. BE
A diameter is a segment that passes through the center while also connecting two points on the circumference of the circle.20. FA
See 17 and 19.Answer:
16. F
17. FA
18. CD
19. BE
20. FA
Step-by-step explanation:
Question 16
A circle is named by its center.
The center of the given circle is F, therefore the name of the given circle is F.
Question 17
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
FA, FB and FE.Question 18
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
BE and CD.Question 19
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameter of the given circle is:
BE.Question 20
As the diameter is BE, it contains the radii FB and FE.
Therefore, the radius that is not contained in the diameter is:
FA.Suppose a certain company sells regular keyboards for $82 and wireless keyboards for $115. Last week the store sold three times as many regular keyboards as wireless. If total keyboard sales were $5,415, how many of each type were sold?how many regular keyboards?how many wireless keyboards?
Answers
Given:
A set 3 regular and 1 wireless keyboard,
Regular keyboards = $ 82
Wireless keyboards = $ 115
Total keyboards sales = $ 5415
Find-:
(a) how many regular keyboards?
(b) how many wireless keyboards?
Explanation-:
A set of 3 regular and 1 wireless keyboard would sell for:
[tex]\begin{gathered} =3\times82+115 \\ \\ =246+115 \\ \\ =361 \end{gathered}[/tex]For, the given sales, the number of sets sold:
Total keyboard sales = $5415
[tex]\begin{gathered} =\frac{5415}{361} \\ \\ =15 \end{gathered}[/tex]Since there are 3 regular keyboards in each set,
The regular keyboard is:
[tex]\begin{gathered} =3\times15 \\ \\ =45\text{ Regular Keyboards} \end{gathered}[/tex]The regular keyboard is 45.
Wireless keyboard is 15.
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was5%, and the tax in the second city was 6%. The total hotel tax paid for the two cities was $552.50. How much was the hotel charge in each city before tax?Note that the ALEKS graphing calculator can be used to make computations easier.
Answers
SOLUTION
Let us represent the hotel charge with different variables x and y:
Let the hotel charge before tax in the first city be x
Let the hotel charge before tax in the second city be y
Now, let us represent the word problem in equation form:
First, we were told that the charge before tax in the second city is $500 more than the charge before tax in the first city, this can be represented thus:
[tex]y=x+500\ldots\text{.eqn 1}[/tex]Going forward in the question, we were told the tax for the first city (x) is 5%(0.05), and the tax for the second city is 6%(0.06). The total tax from both cities is $552.5, this expression can be written mathematically as:
[tex]0.05x+0.06y=552.5\ldots\ldots\text{eqn 2}[/tex]Now, by solving equation 1 and equation 2 simultaneously, we will obtain the hotel charge in each city before tax. (that is the value of x and y).
[tex]\begin{gathered} y=x+500 \\ 0.05x+0.06y=552.5 \\ \end{gathered}[/tex]Using, the substitution method of solving simultaneous equation, we will solve further:
[tex]\begin{gathered} \text{substitute equation 1 into equation 2} \\ 0.05x+0.06(x+500)=552.5 \\ 0.05x+0.06x+30=552.5 \\ 0.11x+30=552.5 \end{gathered}[/tex][tex]\begin{gathered} 0.11x=552.5-30 \\ 0.11x=522.5 \\ x=\frac{522.5}{0.11} \\ x=4750 \end{gathered}[/tex]The hotel charge before tax in the first city is $4750.
Now, substitute the value of x into equation 1 to get the value of y (hotel charge before tax in the second city)
[tex]\begin{gathered} y=x+500 \\ x=4750 \\ y=4750+500 \\ y=5250 \end{gathered}[/tex]The hotel charge before tax in the second city is $5250.
Graph the line that passes through the points (9,4) and (9,1) and determine the equation of the line.
Answers
Both points of the given points have the same x-coordinate. This is only possible if we have a vertical line. The vertical line have the format
[tex]x=k[/tex]Where k represents the x-coordinate of all points of the line. The x-coordinate of our points is 9, therefore, the equation of the line is
[tex]x=9[/tex]And its graph is
which fraction remains in the quotient when 4,028 is divided by 32
Answers
We get that
[tex]\frac{4028}{32}=\frac{1007}{8}=\frac{1000}{8}+\frac{7}{8}=125+\frac{7}{8}[/tex]so the fractions that remains is 7/8
Solve the equation. Select the correct answer below, and, if necessary, fill in the answer box to complete your choice.
Answers
Explanation
[tex]\begin{gathered} \frac{4}{y}+\frac{3}{4}=\frac{4}{4y} \\ Multiply\text{ through by the lowest common multiple }\Rightarrow4y \\ 4y\times\frac{4}{y}+\frac{3}{4}\times4y=\frac{4}{4y}\times4y \\ 16+3y=4 \\ 3y=4-16 \\ 3y=-12 \\ y=-\frac{12}{3} \\ y=-4 \end{gathered}[/tex]Answer= y=-4
i inserted a picture of the question please state whether the answer is a b c or d please don’t ask questions, yes i’m following.
Answers
Solution
- We are asked to find the complement of rolling a 5 or 6 given a cube numbered 1 - 6.
- The complement of an event is defined as every other event asides the event in context.
- Other than rolling a 5 or 6, we can also roll a 1, 2, 3, or 4. This constitutes the complement of rolling 5 or 6.
Final Answer
The complement of rolling a 5 or 6 is:
{Rolling a 1, 2, 3, or 4} (OPTION B)
Dave has a collection of 60 DVDs. One quarter of them are action mc
What is the ratio of the number of action DVDs to all ofner genres?
Answers
Answer:
15:45 i think
Step-by-step explanation:
25% of 60 is 15
60-15=45
15:45
what is the area of the triangle below with a side length of 4
Answers
All angles of triangles is equal means that that triangle is equailateral triangle with side of a = 4 in.
The formula for the area of equilateral triangle is,
[tex]A=\frac{\sqrt[]{3}a^2}{4}[/tex]Substitute 4 for a in the formula to determine the area of the triangle.
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}\cdot(4)^2 \\ =4\sqrt[]{3} \end{gathered}[/tex]So area of triangle is,
[tex]4\sqrt[]{3}[/tex]James types 50 words per minute. He spends 20 minutes typing his homework. What is the domain of this situation?
Answers
Answer:
You answer is B, from 0 to 20 and including 0 and 20.
Step-by-step explanation:
translate the following verbal statement into an algebraic equation and then solve: demetrius paid 9$ for a matinee movie. this is 1$ less than the price in the evening what is the price of the movie at night?use x for your variable equation ________x=______
Answers
Answer:
x = price of the movie at night
x = $9 + $1
Explanation:
We need to find the price of the movie at night, so, let's call x the price of the movie at night.
Then, the price of the matinee movie $9 is $1 less than the price in the evening. Therefore, we can write the following equation:
9 = x - 1
Solving for x, we get:
x = 9 + 1
if the slope of a line and a point on the line are known the equation of the line can be found using the slope intercept form y=mx+b. to do so substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b. using the above technique find the equation of the line containing the points (-8,13) and (4,-2).
Answers
The general equation of a line is;
[tex]y\text{ = mx + b}[/tex]m is the slope and b is the y-intercept
To find the slope, we use the equation of the slope as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (-8,13)} \\ (x_2,y_2)\text{ = (4,-2)} \\ \\ m\text{ = }\frac{-2-13}{4-(-8)}\text{ = }\frac{-15}{12}\text{ = }\frac{-5}{4} \end{gathered}[/tex]We have the partial equation as;
[tex]\begin{gathered} y\text{ = }\frac{-5}{4}x\text{ + b} \\ \\ \text{Substitute the point (-8,13)} \\ \text{x = -8 and y = 13} \\ \\ 13\text{ = }\frac{-5}{4}(-8)\text{ + b} \\ \\ 13\text{ = 10 + b} \\ b\text{ = 13-10 = 3} \end{gathered}[/tex]We have the complete equation as;
[tex]y\text{ =}\frac{-5}{4}x\text{ + 3}[/tex]4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
Answers
These 2 lines perpendicular to each other on the graph.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
To know more about perpendicular lines ,visit:
brainly.com/question/18271653
#SPJ13
Eight less than a number n is at least 10
Answers
Answer:
n - 8 ≥ 10
n ≥ 18
Step-by-step explanation:
Hello!
8 less than the number n can be represented as n - 8.
To be atleast 10, we can have values greater than 10 and equal to 10, but cannot be less than 10 . We can use the ≥ symbol to represent this.
The inequality would be n - 8 ≥ 10
Solving for n:n - 8 ≥ 10n ≥ 18n has to be greater than or equal to 18
Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. (Round your answers to the nearest integer. If an answer does notexist, enter DNE.)
Answers
Given:
[tex]f(x)=4x-2x^2[/tex]Required:
To find the relative minimum and relative maximum values of the function.
Explanation:
Consider
[tex]f(x)=4x-2x^2[/tex]The graph of the function is
The relative maximum is at (1,2).
There is no relative minimum.
Final Answer:
The relative maximum : (1,2).
The relative minimum : DNE.