quadratic function with x intercepts -1 and 1:
[tex]f(x)=(x+1)(x-1)=x^2-x+x+1=x^2+1[/tex]Use the formula d = vt + 1672, where d is the distance in feet, v is the initial velocity in feet per second, and t is the time in seconds.An object is released from the top of a building 320 ft high. The initial velocity is 16 ft/s. How many seconds later will the object hit the ground?
We got to use the given formula:
[tex]d=v\cdot t+16t^2[/tex]The distance, d, given is 320 ft and the initial velocity, v, 16 ft/s. We want the time, t. So:
[tex]\begin{gathered} d=v\cdot t+16t^2 \\ 320=16t+16t^2 \\ 16t^2+16t-320=0 \\ \frac{16t^2}{16}+\frac{16t}{16}-\frac{320}{16}=\frac{0}{16} \\ t^2+t-20=0 \end{gathered}[/tex]Now, we have a quadratic equation, so we can use Bhaskara formula:
[tex]\begin{gathered} t=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-20)}}{2\cdot1}=\frac{-1\pm\sqrt[]{1+80}}{2}=\frac{-1\pm\sqrt[]{81}}{2}=\frac{-1\pm9}{2} \\ t_1=\frac{-1-9}{2}=-\frac{10}{2}=-5 \\ t_2=\frac{-1+9}{2}=\frac{8}{2}=4 \end{gathered}[/tex]Because we can't have a negative time, we consider only the second one, which it t = 4s.
The graph shows the distance ofa remote control drone above theground as it flies west to east. Thex-axis represents the distance from acentral point and the y-axis representsthe distance above the ground, in m.411-21021. What is the range of the functionand what does it represent?
Part 1
For this question we need to remember that the range is defined as:
[tex]\text{Range}=\text{Max}-Mi[/tex]And if we look at the function we see that Min =0 and Max= 5 so then we have:
[tex]\text{Range}=5-0=5[/tex]And the range represent the lenght of the codomain of a function
Part 2
The domain for this case is given by:
[tex]\text{Domain}=\left\lbrack -4,4\rbrack\right?[/tex]And it represent all te possible values of x that the function can assume
Part 3
For this case we identify two intervals where the height is increasing:
[-4,-2] and [0,4]
But the longest interval is :[0,4]
Part 4
The x intercept represent the values when the function satisfy that y=0 and we have:
x intercepts: x=-4, x=0
Part 5
The average rate of change between [-4,4] is given by:
[tex]m=\frac{3-0}{4-(-4)}=\frac{3}{8}[/tex]And then the answer for this case would be 3/8
Write the inequality statement in x describing the numbers [ 11, ∞)
The inequality [ 11, ∞) represents that value is more than or equal to 11. The interval can be expressed as,
[tex]x\ge11[/tex]In inequality, x is any variable.
So inequality statement in x is,
[tex]x\ge11[/tex]Consider the line y=4x-5.Find the equation of the line that is perpendicular to this line and passes through the point (6. 4).Find the equation of the line that is parallel to this line and passes through the point (6, 4).Equation of perpendicular line: Equation of parallel line:
Solution
gradient = 4
Slope for Perpendicular = -1/4
Slope for Parallel = 4
Equation of perpendicular line:
[tex]\begin{gathered} y-4=-\frac{1}{4}(x-6) \\ \\ 4y-16=-x+6 \\ \\ 4y+x=22 \end{gathered}[/tex]Equation of parallel line:
[tex]\begin{gathered} y-4=4(x-6) \\ \\ y-4=4x-24 \\ \\ y=4x-20 \end{gathered}[/tex]Write the polynomial function in standard form that has complex roots -2+i and -2-i
ANSWER
[tex]\text{ x}^2\text{ - 4x + 5}[/tex]EXPLANATION
Given information
The root of the polynomial function are -2 + i and -2- i
To find the standard form of the polynomial function, follow the steps below
Step 1: Express the root of the polynomial in terms of the factor
[tex]\begin{gathered} \text{ Given that the roots of the polynomial function are -2+i and -2 - i} \\ \text{ The factors of the above roots can be expressed as} \\ \text{ \lbrack x + \lparen-2 + i\rparen\rbrack and \lbrack x + \lparen-2 - i\rparen\rbrack} \end{gathered}[/tex]Step 2: Expand the factors of the polynomial in step 1
[tex]\begin{gathered} \text{ \lbrack x + \lparen-2 + i\rparen\rbrack \lbrack x +\lparen-2 -i\rparen\rbrack} \\ [x\text{ -2\rparen + i\rparen\rbrack \lbrack x -2\rparen - i\rparen\rbrack} \\ (x\text{ - 2\rparen}^2\text{ - i}^2 \\ (x\text{ - 2\rparen\lparen x - 2\rparen- i}^2 \\ x^2\text{ - 2x - 2x + 4 - i}^2 \\ x^2\text{ - 4x + 4 - i}^2 \\ \text{ Recall, that i}^2\text{ = -1} \\ \text{ x}^2\text{ - 4x + 4 - \lparen-1\rparen} \\ \text{ x}^2\text{ - 4x + 4 + 1} \\ \text{ x}^2\text{ - 4x + 5} \end{gathered}[/tex][tex]\text{ Hence, the polynomial function in standard form is x}^2\text{ - 4x + 5}[/tex]So in my class i am studying RatioThe question is:There are 7 red pens for every 10 pencils in the borrow bin So would the answer be Part to partPart to whole or Whole to part
Answer:
The ratio of red pens to pencils is 7/10
The ratio of pencils to red pens is 10/7
Step-by-step explanation:
Ratio:
The ratio of a to b is a/b
The ratio of b to a is b/a
In this question:
7 red pens
10 pencils
The ratio of red pens to pencils is 7/10
The ratio of pencils to red pens is 10/7
What is the slope of the line created by this equation? Round your answer out to two decimal places. 10x+5y=3
Given the Linear Equation:
[tex]10x+5y=3[/tex]You can write it in Slope-Intercept Form, in order to identify the slope of the line.
By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Therefore, you can rewrite the given equation in Slope-Intercept Form by solving for "y":
[tex]\begin{gathered} 5y=-10x+3 \\ \\ y=\frac{-10x}{5}+\frac{3}{5} \end{gathered}[/tex][tex]y=-2x+\frac{3}{5}[/tex]You can identify that:
[tex]\begin{gathered} m=-2 \\ \\ b=\frac{3}{5} \end{gathered}[/tex]Hence, the answer is:
[tex]m=-2[/tex]སྣ། Cookies maze -x-37 +32=2) x+4y + 3x tt 5x+2y-27=-34 -12
Step 1: Problem
-x - 3y + 3z = 21
x + 4y + 5z = -1
5x + 7y - 2z = -34
Step 2: Concept
Apply substitute method to solve the three systems of equation.
Step 3: Method
Name the system of equations
-x - 3y + 3z = 21 ------------------------------ 1
x + 4y + 5z = -1 ------------------------------- 2
5x + 7y - 2z = -34 --------------------------3
From equation 1, make r subject of relation and substitute into 2 and 3
x = -3y + 3z - 21
Next, substitute x in equations 2 and 3.
In 2
- 3y + 3z - 21 + 4y + 5z = -1
y + 8z = -1 + 21
y + 8z = 20 ----------------------------------- (4)
In 3
5(-3y + 3z - 21) + 7y - 2z = -34
-15y + 15z - 105 + 7y - 2z = -34
-8y + 13z = - 34 + 105
-8y + 13z = 71 ------------------------------------- (5)
from 4, make y subject and substitute in 5
y = 20 - 8z
In 5
-8(20 - 8z) + 13z = 71
-160 + 64z + 13z = 71
77z = 71 + 160
77z = 231
z = 231/77
z = 3
y = 20 - 8(3)
y = 20 - 24
y = -4
x = -3y + 3z - 21
x = -3(-4) + 3(3) - 21
x = 12 + 9 - 21
x = 0
Step 4: Final answer
x = 0, y = -4 z = 3
Want to check if I got the correct answer, thank you
To find:
The division of the polynomial.
Solution:
The division in given in the image below:
Thus, the result is:
[tex]x^3+3x^2-1x-5-\frac{11}{x+3}[/tex]Option D is correct.
The longest runaway at an airport has the shape of rectangle and an area of 2,057,000 square feet. This runaway is 170 feet wide how long is the run away ? The length of the runaway is ?
The runway is 12100 ft long
Explanation:The area of a rectangle is given as:
A = wl
Where w is the width and l is the length
Given that A = 2, 057,000 sq. ft
w = 170 ft
Using these, we can easily find l
2,057,000 = 170l
l = 2,057,000/170
= 12100
I NEED HELP FINDING THIS ANSWER ASAP PLEASE AND THANK YOU
The coordinates of triangle after being reflected across y-axis: X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
Given that the coordinates of triangle X(4, -5), Y(4, -2), Z(5, -4)
ΔXYZ is reflected across the line x = 3 and then reflects the image across the y-axis.
We need to find the coordinates of triangle after mentioned geometric transformation.
i) when ΔXYZ is reflected across the line x = 3
the coordinates of ΔX'Y'Z' are:
X'(2, -5), Y'(2, -2), Z'(1, -4)
The green triangle in the following graph.
ii) when ΔX'Y'Z' is reflected across the y-axis
the coordinates of ΔX"Y"Z" are:
X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
The orange triangle in the following graph.
Therefore, the coordinates of triangle after being reflected across y-axis: X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
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Simplify the following expression(-2v)^4
We have
[tex]\mleft(-2v\mright)^4[/tex]In order to simplify this expression, we will use the next rule
[tex]\mleft(ab\mright)^m=a^mb^m[/tex]We use the rule and we simplify
[tex](-2)^4v^4=16v^4[/tex]Evaluate 2^5.32251016
32
Explanation:The given expression is:
2⁵
This means the product of 2 in 5 places
That is,
2⁵ = 2 x 2 x 2 x 2 x 2
2⁵ = 32
Each chef at "Sushi Emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On Tuesday, each customer ate 2 regular rolls and 3 vegetarian rolls. By the end of the day, 4 regular rolls and 1 vegetarian roll remained uneaten.
How many chefs and how many customers were in "Sushi Emperor" on Tuesday?
Please Help!
Answer: 13 customers and 2 chefs
Step-by-step explanation:
I vaguely remember how to do this although I am familiar with all. All I need is a quick review explanation and I’ll be good. Thanks!
We have to calculate the perimeter of a pen that has an area expressed as
A = 3x²-7x+2.
We assume it is a rectangular pen, so it will have two different sides.
The area will be the product of this two side lengths, while the perimeter will be 2 times the sum of the lengths of the two sides.
Then, we start by rearranging the expression of A as a product of two factors.
We can do it by factorizing A.
To do that, we calculate the roots of A as:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot3\cdot2}}{2\cdot3} \\ x=\frac{7\pm\sqrt[]{49-24}}{6} \\ x=\frac{7\pm\sqrt[]{25}}{6} \\ x=\frac{7\pm5}{6} \\ \Rightarrow x_1=\frac{7-5}{6}=\frac{2}{6}=\frac{1}{3} \\ \Rightarrow x_2=\frac{7+5}{6}=\frac{12}{6}=2 \end{gathered}[/tex]Then, we can now express A as:
[tex]\begin{gathered} A=3(x-\frac{1}{3})(x-2) \\ A=(3x-1)(x-2) \end{gathered}[/tex]Then, we can consider the pen to be a rectangle (or maybe square, depending on the value of x) with sides "3x-1" and "x-2".
Then, we can now calculate the perimeter as 2 times the sum of this sides:
[tex]\begin{gathered} P=2\lbrack(3x-1)+(x-2)\rbrack \\ P=2(3x-1+x-2) \\ P=2(4x-3) \\ P=8x-6 \end{gathered}[/tex]Answer: we can express the perimeter as 8x-6.
Lynette is covering shapes with wrapping paper to make a design for the school carnival how much paper and square feet will Lynette need to cover the figure shown below
The area of paper needed is;
[tex]7\frac{1}{2}ft^2[/tex]Here, we want to get the square feet of paper needed
What we have to do here is to get the area of the parallelogarm
Mathematically, that would be the product of the base of the parallelogram and its height
We have the base as 3 3/4 ft which is same 15/4 ft and the height as 2 ft
Thus, we have the area calculated as follows;
[tex]\frac{15}{4}\times\text{ 2 = }\frac{30}{4}\text{ = 7}\frac{1}{2}ft^2[/tex]Enter the exponential function using t (for time) as the independent variable to model the situation. Then find the value of the function after the given amount of time. The value of a textbook is $65 and decreases at a rate of 14% per year for 13 years. The exponential function that models the situation is y =__After 13 years, the value of the textbook is $__
Please, give me some minutes to take over your question
_________________________________
For my practice review, I need help to determine if these are functions or not.
Answer:
1: no
2: no
3: yes
4: no
5: yes
6: yes.
Step-by-step explanation:
Think of a vertical line sweeping across the graph from left to right. If ever this line crosses two points of the graph at the same time, it cannot be a function, since a function can only have max. 1 result per x value.
2) sin X Z 45 36 X 27 Y A) B) no+ D)
Explanation
For the angle α, the sine function gives the ratio of the length of the opposite side to the length of the hypotenuse.
[tex]\sin \alpha=\frac{\text{opposite side}}{\text{hypotenuse}}=\frac{y}{z}[/tex]then, Let
[tex]\begin{gathered} \text{opposite side= 36} \\ \text{hypotenuse =45} \\ \text{angle}=\angle x \end{gathered}[/tex]Now, replace
[tex]\begin{gathered} \sin \alpha=\frac{\text{opposite side}}{\text{hypotenuse}} \\ \sin \angle x=\frac{36}{45}=\frac{12}{15}=\frac{4}{5} \\ \sin \angle x=\frac{4}{5} \end{gathered}[/tex]so, the answer is
[tex]B)\frac{4}{5}[/tex]I hope this helps you
I need help with this practice problem Having trouble solving it If you can use Desmos to graph it
The graph of the function:
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]is shown below:
By graphing at least one full period of the function, we would take the limit of the function as:
[tex]-\pi\le x\le\pi[/tex]Hence, the graph of at least one full period is:
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer: [tex]48^{\circ}[/tex]
Step-by-step explanation:
Coterminal angles differ by integer multiples of [tex]360^{\circ}[/tex].
So, an angle coterminal with an angle of [tex]408^{\circ}[/tex] is [tex]408^{\circ}-360^{\circ}=48^{\circ}[/tex], which lies within the required interval.
Plot the image of point C under a reflection across line n.Click to add points
We can find the image of point C reflected across line n by finding the distance d (perpendicular) from point C to line n, and then placing point C', the image, at an equal and perpendicular distance d on the other side of the line.
We can graph this as:
I need help with 5 and 6. The exponent for part 5 if you can't see it well 2/3
5.
Given the equation to solve for x:
[tex]3(x+1)^{\frac{2}{3}}=12[/tex]The steps for the solution are as follows:
[tex]\begin{gathered} 3(x+1)^{\frac{2}{3}}=12 \\ \frac{3(x+1)^{\frac{2}{3}}}{3}=\frac{12}{3} \\ (x+1)^{\frac{2}{3}}=4 \\ \lbrack(x+1)^{\frac{2}{3}}\rbrack^{\frac{1}{2}}=(4)^{\frac{1}{2}} \\ \lbrack(x+1)^{\frac{1}{3}}\rbrack=\pm2 \\ \lbrack(x+1)^{\frac{1}{3}}\rbrack^3=(\pm2)^3 \\ x+1=\pm8 \end{gathered}[/tex]From the above equation, we have x + 1 = 8 and x + 1 = -8. These imply x = 7 and x = -9.
Check for extraneous solutions:
If x = 7, then the left-hand side of the equation is:
[tex]3(x+1)^{\frac{2}{3}}=3(7+1)^{\frac{2}{3}}=3(4)=12[/tex]Thus, the equation holds true at x = 7.
If x = -9, then the right-hand side of the equation is:
[tex]3(x+1)^{\frac{2}{3}}=3(-9+1)^{\frac{2}{3}}=3(4)=12[/tex]Thus, the equation holds true at x = -9.
There is no extraneous solution. The solutions of the given equation are x = 7 and x = -9.
6.
Given an equation to solve for x:
[tex]\sqrt[]{3x+2}-2\sqrt[]{x}=0[/tex]The steps of the solution are as follows:
[tex]\begin{gathered} \sqrt[]{3x+2}-2\sqrt[]{x}=0 \\ \sqrt[]{3x+2}=2\sqrt[]{x} \\ (\sqrt[]{3x+2})^2=(2\sqrt[]{x})^2 \\ 3x+2=4x \\ 2=4x-3x \\ 2=x \end{gathered}[/tex]Thus, the solution of the equation is x = 2.
Suppose that the functions h and f are defined as follows h(x)=x^2 +2f(x)=7/9x, x ≠0Find the compositions h• h and f•f Simplify your answers as much as possible (h•h)(x)=(f•f)(x)=
1) First we compute:
[tex](h\circ h)(x)=h(h(x))=h(x^2+2)=(x^2+2)^2+2.[/tex]Simplifying we get:
[tex](h\circ h)(x)=x^4+4x^2+4+2=x^4+4x^2+6.[/tex]2)Computing the composition we get:
[tex](f\circ f)(x)=f(f(x))=f(\frac{7}{9x})=\frac{7}{(9(\frac{7}{9x}))}=\frac{7}{\frac{7}{x}}=x.[/tex]Answer:
[tex]\begin{gathered} (h\circ h)(x)=x^4+4x^2+6, \\ (f\circ f)(x)=x. \end{gathered}[/tex]The original price of a riding lawn mower is $1250. Paul bought his for $1000. What percent was the discount?
we get that the percentage he paid was
[tex]\frac{1000}{1250}\cdot100=80\text{ \% }[/tex]so the percentage of discount is 20%
I really need help I can’t seem to understand this at all
Given the sequence below
[tex]8,12,18,27[/tex]The sequence above is a geometric series, therefore the formula for the common ratio(r) is
[tex]r=\frac{2ndterm}{First\text{ term}}=\frac{Thirdterm}{2nd\text{ term}}[/tex]Therefore,
[tex]\begin{gathered} r=\frac{12}{8}=\frac{18}{12} \\ r=\frac{3}{2}=\frac{3}{2} \end{gathered}[/tex]Hence, the answer is
[tex]\frac{3}{2}\text{ \lparen Option 3\rparen}[/tex]120+m=203d+59=33c-87=-42
Let's solve the following equation
c - 87 =42
Adding 87 at both sides:
c - 87 + 87 = -42 + 87
c = 45
The steps for deriving the Quadratic formular are shown. Which best choose for the missing reason?
In the part inside the yellow circle, we multiplied by 1 the term -c/a, that is
[tex]-\frac{c}{a}=-\frac{c}{a}\times1=-\frac{c}{a}(\frac{4a}{4a})=-\frac{4ac}{4a^2}[/tex]where 1 was written as 4a/4a.
Since we must add this result to
[tex]\frac{b^2}{4a^2}[/tex]the answer is option C, change to LCD ( Least Common Denominator) because both terms must have the same denominator, which is 4a^2.
choose equation of a line perpendicular to the given equation and passing through the point p x-axis; P =(6,2)
To solve the question you have find the equation of the line that is perpendicular to the y axis and passes through the point (6,2), so in this case the equation of the line is y=2 as you can see in this picture
Remember that two lines are perpendicular when they form an 90 degrees angle between them
What is the approximate area they will have to paint to fill in this tree?
The area is 18. 8 ft².
From the question, we have
Area of a triangle = 1/2 base × height
= 1/2 × 5 × 3
= 1/2 × 15
= 7. 5 ft²
In trapezoid,
a = 4ft
b = 0. 2ft
h = 5ft
Area of trapezoid = 1/2*(a+b)*h
= 1/2*(4+0.2)*5
= 1/2*4.2*5 = 10. 5 ft²
Area of rectangle = length × width
= 0. 2 × 4
= 0. 8 ft²
Total area of tree = area of triangle + area of trapezoid + area of rectangle
= 7. 5 + 10. 5 + 0. 8
= 18. 8 ft²
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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