The value of the function at x = 0 will be 1.
What is a function?
A statement, principle, or rule that creates a relationship between two variables is known as a function. Functions are abundant in mathematics and are required for the creation of complex relationships.
When the required parameters and natural laws are given values, the expression yields the calculation result that the mathematical model represents.
The table represents a function.
x f(x)
-3 1
-1 8
0 1
3 0
6 13
9 -3
In the above table, we can see that at the value of x = 0 in the function the value of the whole function is 1.
Let's learn more about the function
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A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant.
Answer in the form of a polynomial equals a constant:
2w^3-4w^
Find the equation of a line perpendicular to y +1 = -x that passesthrough the point (-8, 7).
Two lines are perpendicular if the product of their slopes is equal to -1.
Find the slope of the given line. Then, use that result to find the slope of a line perpendicular to it. Use the slope of the line perpendicular to the given line to find the equation of the one that passes through the point (-8,7).
To find the slope of the given line, write it in slope-intercept form by isolating y:
[tex]\begin{gathered} y+1=-x \\ \Rightarrow y=-x-1 \end{gathered}[/tex]The coefficient of x is -1. Then, the slope of the given line is -1.
Let m be the line perpendicular to y+1=-x.
Since the product of the slopes of perpendicular lines is equal to -1, then:
[tex]\begin{gathered} -1\times m=-1 \\ \Rightarrow m=\frac{-1}{-1} \\ \therefore m=1 \end{gathered}[/tex]The equation of a line with slope m that passes through the point (a,b) in slope-point form is:
[tex]y=m(x-a)+b[/tex]Replace m=1, a=-8 and b=7 to find the equation of the line perpendicular to y+1=-x that passes through the point (-8,7):
[tex]\begin{gathered} y=1(x-(-8))+7 \\ \Rightarrow y=(x+8)+7 \\ \therefore y=x+15 \end{gathered}[/tex]Therefore, the equation of the line perpendicular to y+1=-x that passes through (-8,7) is:
[tex]y=x+15[/tex]need help for mathhh
Using implicit differentiation, the rates are given as follows:
2. dV/dt = 144π cm³/sec.
3. dh/dt = 2/5π cm/s.
4. dr/dt = -0.2/π cm/day.
What is the rate of change of the volume of an sphere?The volume of an sphere of radius r is given by the following equation:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Applying implicit differentiation, differentiating both variables relative to t, the rate of change is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
For item 2, the parameters are given as follows:
[tex]\frac{dr}{dt} = 2, r = 4[/tex]
Hence the rate is given as follows:
dV/dt = 4π x 4² x 2 = 144π cm³/sec.
For item 4, the parameters are:
[tex]\frac{dV}{dt} = -0.2, r = 5[/tex]
Negative because the orange is shrinking.
Hence the rate of the radius can be found as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]-0.2 = 4\pi (5)^2\frac{dr}{dt}[/tex]
dr/dt = -0.2/100π
dr/dt = -0.2/π cm/day.
What is the rate of change of the volume of an cylinder?The volume of a cylinder of radius r and height h is given as follows:
[tex]V = \pi r^2h[/tex]
The rate of change of the volume as a function of time is given by:
[tex]\frac{dV}{dt} = 2\pi rh\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]
For item 3, the parameters are given as follows:
[tex]r = 5, \frac{dV}{dt} = 10, \frac{dr}{dt} = 0[/tex]
The radius is of 5 as r² = 25, due to the area of the base.
Hence the rate of change of the height is found as follows:
[tex]\frac{dV}{dt} = \pi r^2\frac{dh}{dt}[/tex]
10 = 25π dh/dt
dh/dt = 10/25π
dh/dt = 2/5π cm/s.
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Identify the pre-image and the image. Then determine if the transformation is a rigid motion or not
The pre-image is the figured formed by the points VWUST and the image is V'W'U'S'T'.
To produce the image from the pre-image a rotation is performed around the point (2, -2). A rotation doesn't change the dimensions of the figure, therefore it is not a rigid motion.
c(n) = -6 (-1/3) *n-1What is the 2nd term in the sequence ?
We are given the following sequence
[tex]c(n)=-6(-\frac{1}{3})^{n-1}[/tex]We are asked to find the 2nd term of the above sequence
Let us substitute n = 2 into the given sequence
[tex]\begin{gathered} c(2)=-6(-\frac{1}{3})^{2-1} \\ c(2)=-6(-\frac{1}{3})^1 \\ c(2)=6\cdot\frac{1}{3} \\ c(2)=2 \end{gathered}[/tex]Therefore, the 2nd term of the given sequence is 2
(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)
From the given information, we know that the decreasing function values is
[tex]V(t)=3600(3^{-0.15t})[/tex]and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have
[tex]1200=3600(3^{-0.15t})[/tex]By dividing both sides by 3600, we get
[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]So we have the equations
[tex]3^{-0.15t}=\frac{1}{3}[/tex]From the exponents properties, we know that
[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]so we have
[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]or equivalently,
[tex]3^{0.15t}=3[/tex]This means that
[tex]0.15t=1[/tex]Then, by dividing both sides by 0.15, we obtain
[tex]t=\frac{1}{0.15}=6.6666[/tex]So, by rounding to the nearest hundreadth, the answer is 6.67 years
the side opposite the right angle measures 8 in. what is the measurement of the side opposite of the 60 degree angle (draw and label the triangle before solving)
1) The best way to tackle this question is by sketching out the triangle:
2) Considering that 60º angle we can write out the following trig ratio:
[tex]\begin{gathered} \sin (60^{\circ})=\frac{x}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{8} \\ 2x=8\sqrt[]{3} \\ x=\frac{8\sqrt[]{3}}{2} \\ x=4\sqrt[]{3} \end{gathered}[/tex]Note that if we had drawn the 60º angle to the lowe right in that triangle we would find the same measure, by using the cosine of (30º) instead.
And that's the answer
Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=
1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.
a²=b²+c²
4²=b²+3²
16=b²+9
16-9=b²
b=√7
2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:
[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:
[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:
[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]Given l ∥ m ∥ n, find the value of x.
Answer:
[tex]x = \frac{ - 23}{3} [/tex]
Step-by-step explanation:
everything u need is in the picture
Scientific notation of 100+6*10^2
Answer: The answer is 700
Step-by-step explanation:
is that the answer you're looking for?
Answer:
7e2
Step-by-step explanation:
10^2=100
100*6=600
600+100=700
there are 2 zeros in 700 so
7e2
on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers
Solution:
Given the points below
[tex]p\left(4,2\right)and\text{ }q\left(8,12\right)[/tex]To find the distance between two points, the formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where point p represents coordinates 1 and point q represents coordinates 2
Substitute the coordinates into the formula above
[tex]\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}[/tex]Since, 1 unit represents 1 kilometer on the map,
Hence, the answer is
[tex]2\sqrt{29}\text{ km}[/tex]2. A membership to the theme park is $48 per year. Marcos cancelled his membership early and is only required to pay for 0.25 of a year. How much will he need to pay?
Marcos needs to pay $12 for 0.25 of a year due to cancelling the membership
Membership cost to the theme park per year = $48
Payment required to be made by Marcos = 0.25 of a year
When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. However, as we proceed to the right following the decimal point, we obtain the fractional portion of the decimal number.
Converting the decimal into a fraction we get:
=0.25
= 25/100
= 1/4 of a year
So, Marcos needs to pay the membership fees for only 1/4 of a year
According to which we get: 48*1/4 = $12
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In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.
We are given a distribution graph.
The mean of the distribution is the center that is 125.
[tex]\operatorname{mean}=\mu=125[/tex]The standard deviation is given by
[tex]std=\sigma=153-125=28[/tex]Therefore, the mean of the distribution is 125 and the standard deviation is 28.
Use inverse matrices to find the solution to the system of equations represented by this matrix equation
if you replace it in that order, it should give you the answer
[tex]\begin{bmatrix}{2} & {-3} \\ {-3} & {5}\end{bmatrix}[/tex]PLS HELP WILL MARK YOU BRAINLIEST!!
Point B is the midpoint of AC. AB=2x and AC=3x+20.
What is the value of x?
x=-20
x=20
x=4
x=6
Answer:
X=4
Step-by-step explanation:
i got the answer on a different app
Answer: The correct answer is 20 or -20
Step-by-step explanation:
its between 20 and -20 since i selected x=6 and x=4 and they were both wrong lol
Could you please help me with this exercise? Thanks for your help!
ANSWER
• Distance:, 7.81
,• Midpoint: ,(-4.5, -6)
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean Theorem,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2_{}}[/tex]In this problem, the points are (-7, -9) and (-2, -3),
[tex]\begin{gathered} d=\sqrt[]{(-7-(-2))^2+(-9-(-3))^2} \\ d=\sqrt[]{(-7+2)^2+(-9+3)^2}\text{ } \\ d=\sqrt[]{(-5)^2+(-6)^2}=\sqrt[]{25+36} \\ d=\sqrt[]{61}\approx7.81 \end{gathered}[/tex]Hence, the distance between P1 and P2 is 7.81 units.
To find the midpoint, we have to find the average between the coordinates of the points,
[tex](x_m,y_m)=\mleft(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\mright)[/tex]The midpoint in this problem is,
[tex](x,y)=\mleft(\frac{-7-2}{2},\frac{-9-3}{2}\mright)=\mleft(\frac{-9}{2},\frac{-12}{2}\mright)=(-4.5,-6)[/tex]Hence, the midpoint between P1 and P2 is (-4.5, -6).
Four of the twelve members of the panel were late for
the meeting. What fraction of the members were on
time?
Answer:
2/3
Step-by-step explanation:
If 4 were late, then 8 were on time.
8/12 Divide the top and bottom by 4
2/3
Shiori is working on a stem project and her model is represented by the quadratic function below. She eventually wants to build a 3D model si she needs to understand each part of the function . She is trying to find the coordinate of the vertex of the following function and determine whether the graph opens up or down. F(x)=3x^2-2x-71. What are the coordinates of the vertex of the parabola of the function. There are several wars to determine this answer but state clearly all the steps you look to find the solution.2.Just by looking at the equation (without graphing it) does the graph open up or down(How do you know).3.what does the -7 tell you about the parabola specifically.
1) To get the vertex of the function, the formulae is given as:
[tex]x=-\frac{b}{2a}[/tex]This gives the x coordinate of the vertex. Where a and b are the coefficients of the 1st and 2nd terms respectiely.
[tex]x=\frac{-(-2)}{2(3)}=\frac{1}{3}=0.333333[/tex]To get the y coordinate, we substitute this x value into the original equation.
[tex]f(x)\text{ = 3(}\frac{1}{3})^2-2(\frac{1}{3})-7=\frac{-22}{3}=-7.333333[/tex]The coordinates of the the vertex (0.33, -7.33)
2) The graph opens upwards. Because the coefficient of the 2nd power of x is a negative number.
3) The -7 tells us that the graph cuts the vertical axis at -7.
Find the indicated angle 0. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 120 and c = 136. Round your answer to two decimal places.)
Base on the given data, the triangle is shown below.
Apply law of sine to this triangle implies,
[tex]\sin \theta=\frac{a}{c}[/tex]Given that, a=120 and c=136. Thefore, the given equation becomes,
[tex]\begin{gathered} \sin \theta=\frac{120}{136} \\ \sin \theta=0.88 \end{gathered}[/tex]Take the inverse to find the the measure of indicated angle.
[tex]\begin{gathered} \theta=\sin ^{-1}0.88 \\ \theta=61.64 \end{gathered}[/tex]Therefore, the angle is 61.64 degree.
Write the inequality shown by the shaded region in the graph with the boundary line y = -3x +5
Inequality is an inequality comparison of numbers or expressions.
Given inequality:
y < -3x+5, y < x+2, y < -1
Graph the above inequality using Geogebra's online graphing calculator.
Answer:
...................... Hoffe er u
Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
As per the given percentage, there are 147 students are not take French their freshman year.
Students:
The students are the person formally engaged in learning, especially one enrolled in a school or college.
Given,
Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students.
Here we need to find the number of students who are not take French as their freshman year.
Let x be the total number of students in the freshman year.
So according to the given question, we know that,
72% of x = 378
Therefore, we have to find the value of x, so we have to move the others,
Then we get,
x = 378/72%
x = 378 x 100/72
x = 525
So, the total number of students are 525.
Then the students who are not taken French is,
=> 525 - 378 = 147
Therefore, the students who are not taken French is 147.
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Jolie is redesigning a water bottle to fit better in her cup holder. The diameter will have to be no larger 2.5 in. The water bottle is straight up and down. What would the height of the bottle be if she wants it to have a 99.34 in3 volume. (Round to nearest whole number)
20in
Explanations:The water bottle in question is known to be cylindrical in shape. The formula for calculating the volume of a cylinder is expressed as:
[tex]V=\pi r^2h[/tex]where;
r is the radius
h is the height
Given the following parameters
diameter = 2.5in
radius = 2.5/2 = 1.25in
volume = 99.34 in^3
Required
Height of the water bottle
Substitute the given parameters intothe formula
[tex]\begin{gathered} 99.34=3.14(1.25)^2\times h \\ 99.36=4.90625h \\ h=\frac{99.36}{4.90625} \\ h=20.25\approx20in \end{gathered}[/tex]The height of the water bottle will be 20in
You are dressing a mannequin for a clothingstore display. You have 4 types of shoes, 5necklaces, 10 tops, and 7 bottoms to choosefrom. How many distinct outfits can youcréate? >
Given:
• Types of shoes = 4
,• Number if necklaces = 5
,• Number of tops = 10
,• Number of bottoms = 7
Let's find how many distinct outfits you can create.
To find the number of distinct outfits you can create, we have:
[tex]\begin{gathered} n=4*5*10*7 \\ \\ n=1400 \end{gathered}[/tex]Therefore, the number of distinct outfits you can create is 1400.
ANSWER:
1400
Identify a solution to the system of equation
-4x+ 3y=23
x - y =7
x = - 44 and y = - 51
How are the linear equations solved?
-4x+ 3y=23 ---(1)
x - y =7 ----(2)
4*(2) => 4x- 4y =28 ---- (3)
(3) + (1)
4x- 4y =28 (+)-4x+ 3y=23
- y = 51
y = -51
Substituting y in (2)
x - y =7
x + 51 = 7
x = -44
What are linear equations ?
A linear equation is one in which the variable's maximum power is consistently 1.A one-degree equation is another name for it. A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero. Due in part to the fact that linear equations are typically good approximations for non-linear systems, linear equations are ubiquitous in all mathematics and their applications in physics and engineering.To learn more about linear equations, refer:
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Answer: x = -2
y = 5
Step-by-step explanation:
-4x+3y=23
x-y= -7
First take x-y= -7 and make it x=-7+y place it into the first equation
-4 (-7+y)+3y = 23
28-4y+3y = 23
28-y = 23
+y +y
28=23+y
-23 -23
5=y
Not that you have y you can replace it into the original
-4x+3(5)=23
-4x+15=23
-15=-15
-4x = 8
x= -2
The answer would be (-2,5)
Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4
Given the trigonometry equation below,
[tex]\tan (x)(\tan (x)-1)=0[/tex]Solving each part separately
[tex]\begin{gathered} \tan \mleft(x\mright)=0\quad \mathrm{or}\quad \tan \mleft(x\mright)-1=0 \\ x=\tan ^{-1}0\text{ or tan(x)=1} \\ x=\pm n\pi\text{ }or\text{ }x=tan^{-1}1 \\ x=\pm n\pi\text{ or x=45} \\ x=\pm n\pi\text{ or x=}\frac{\pi}{45}\pm n\pi \end{gathered}[/tex]Therefore,
[tex]x=\pm n\pi,\text{ x=}\frac{\pi}{45}\pm n\pi[/tex]Hence, Option D is the correct answer.
I dont know how to answer this pls help
The hedgehog's total change in weight is -2.5 ounces.
What is the total change in weight?A relationship is proportional if the ratio of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.
Ratio = change in weight / days of hibernation
-0.18 / 9 = -0.02
-0.56 / 28 = -0.02
-1.44 / 76 = -0.02
-1.96 / 98 = -0.02
Weight when the day of hibernation is 125 = number of days x ratio
125 x -0.02 = -2.5
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Choose the equation that represents a line that passes through points (−3, 2) and (2, 1)
5x + y = −13
5x − y = 17
x − 5y = −13
x + 5y = 7
The equation that represents a line that passes through points (−3, 2) and (2, 1) is x + 5y = 7.
How to find the equation of a line?The equation of the line passes through the points (−3, 2) and (2, 1). The equation of the line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope using (−3, 2) and (2, 1)
m = slope = 1 - 2 / 2 + 3
m = - 1 / 5
Therefore,
slope = - 1 / 5
Let's find the y-intercept of the line using (2, 1)
y = - 1 / 5 x + b
1 = - 1 / 5 (2) + b
b = 1 + 2 / 5
b = 5 + 2/ 5
b = 7 / 5
Therefore, the equation of the line can be represented as follows:
y = - 1 / 5 x + 7 / 5
5y = -x + 7
5y + x = 7
x + 5y = 7
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All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having a vowel written on it?
Let:
A = Get a paper having a vowel written on it
N = Total number of letters = 11
a = Number of vowels = 4
so:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{4}{11} \\ P(A)\approx0.36 \end{gathered}[/tex]Answer:
36%
The product of the digits of a five-digit number is 6! (factorial). How many such numbers are there
There are 720 of such numbers that consists of five-digits which their product is 6! by permutation.
What is permutation?The mathematical term permutation can simply be defined as a process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.
We can apply the formula for permutation;
[tex]p(n,r) = \frac{n!}{(n - r)!} [/tex]
where n = total number of object and r = number of objects selected.
We can calculate the arrangement by applying the permutation formula as follows
[tex]p(6,5) = \frac{6!}{(6- 5)!}[/tex]
[tex]p(6,5) = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1!}[/tex]
[tex]p(6,5) = \frac{720}{1}[/tex]
[tex]p(6,5) = 720[/tex]
Hence, with good application of the formula for permutation, we can say that there are 720 arrangement of such numbers which their product is 6!.
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Find f(g(3)).f(x)=2x-5g(x) = 1 + x²f(g(3)) = [?]
To find the value of the given composition of functions you follow the next steps:
1. Find g(3):
[tex]\begin{gathered} g(3)=1+3^2 \\ g(3)=1+9 \\ g(3)=10 \end{gathered}[/tex]2. Find f(g(3)) or f(10):
[tex]\begin{gathered} f(g(3))=f(10) \\ f(g(3))=2(10)-5 \\ f(g(3))=20-5 \\ f(g(3))=15 \end{gathered}[/tex]Then, f(g(3)) is equal to 15