Evaluate the given function. The values of the independent variable are approximate.
f(x) = 3x² - 3x, find f(3.52) and f(-8.77)
The values of f(3.52)=26.61 and f(-8.77)=257.05
An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.
The given function is f(x) = 3x²-3x =3x(x-1)
f(3.52)=3*(3.52)(3.52-1)
=26.61
f(-8.77)=3*(-8.77)(-8.77-1)
=257.05
Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05
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URGENT
due in 1 hour! For 50 points!!
Pic is the question
Answer:
21 grandchildren
Explanation:
2/7ths + 5/7th = all
5/7ths = 15 <- divide both sides by 3 to get 1/7th
1/7th = 3 (multiply both sides by 7 to get "1")
7/7ths = 21
so, eva has 21 grandchildren
Answer:
21
Step-by-step explanation:
If 2/7th of Eva's grandchildren live in one location, we know that 5/7th (the remaining portion of Eva's grandchildren) must live in the other location
Wales + Australia = all of the kids (100% = 1/1 (which is equal to 7/7) )
Wales + Australia = 7/7ths
{x is the total number of kids}
Australia = 5/7ths
15 = [tex]\frac{5}{7}x[/tex] {multiply both sides by 7 to get rid of fraction}
105 = 5x {divide both sides to find 1x}
21 = x
check:
2/7th of 21 = 6
5/7th of 21 = 15 {which we know}
6 + 15 = 21
21 = 21
(TRUE)
So, Eva has 21 grandchildren
hope this helps!!
(9x³+5)/(2x - 3)
How do I divide these using long division
(9x³+5)/(2x - 3)
split up (9x³+5)
9x³/2x-3 + 5/2x-3
attached solution.
Some children research their classmates' favourite colour. They show the results in a pie chart. 40 children were asked about their favourite colour. How many children chose each colour? red = green = blue =
Step-by-step explanation:
Can you attach the questions please? Thanks
Classify this triangle. (image down below)
(Acute scalene triangle. (Obtuse isosceles triangle. (Right isosceles triangle (Right scalene triangle?
Answer: Right iscoleces triangle
Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.
Answer:
right isosceles
Step-by-step explanation:
the right angle and the two sides that are equal make the triangle a right isosceles
Find the equation of a line passing through the points (-1,5) and (3,17).
Answer:
y=3x+8
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
you find the slope by using this formula:
then we figure out it is 3
then graph to find the y-intercept which is 8
Answer:
y = 3x + 8
Step-by-step explanation:
Below is the image for the formula of the slope.
1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.
Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).
When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8
Therefore, the equation is y = 3x + 8
Steps are very much required they should be clear and neat please i need to understand this I'm taking a practice test for my future sats
ill report in inappropriate answers
Answer:
2nd option
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{4x+5+7x-6-8x+2}{3}[/tex]
= [tex]\frac{3x+1}{3}[/tex]
= [tex]\frac{3x}{3}[/tex] + [tex]\frac{1}{3}[/tex]
= x + [tex]\frac{1}{3}[/tex]
if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
60200 cm^2
Step-by-step explanation:
I believe I've answered this question on another post: https://brainly.com/question/27987703
1,000f= 4,135.135135...
what is the answer in fraction form?
Answer:
f = 4 [tex]\frac{5}{37}[/tex]
Step-by-step explanation:
divide 1000 on both sides.
f = 4.135 repeating (the 135 is repeating.)
Put the .135135135... over 999 because it is repeating. F becomes 4[tex]\frac{135}{999}[/tex]
Simplify. f = [tex]4\frac{5}{37}[/tex]
what is the number you must add to complete the square x^2 - x
lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol
Using a rounded version of a conversion ratio allows for a quick estimate of a unit conversion
using mental math or paper and pencil (no calculator or phone). Show an example of a unit cuz
conversion estimation using this strategy.
The conversion ratio that can be illustrated will be converting 2030m to kilometers.
How to illustrate the conversion?The unit conversion that can be illustrated based on the information can be convert 2030m to kilometers.
It should be noted that 1000 meters makes 1 kilometer. Therefore, rounding up 2030m mentally will be 2000m and the conversion to kilometers will be:
= 2000/1000
= 2 km
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Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A' is at (−2, 2) and the image of D' is at (−3, 0). Which transformation can be used to show that ABCDE and its image are congruent?
The transformation that can be used to show that ABCDE and its image are congruent is a 90° counterclockwise.
How to depict the transformation?It should be noted that when we rotate a point through 90° counterclockwise, the mapping will be: (x, y) to (-y, x).
In this situation, it van be deduced that the x and y coordinates swapped positions. This illustrates a 90° counterclockwise rotation about the origin..
In this situation, since the rotation is a rigid motion, the two shapes are congruent.
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1-
-5-4-3-2-11₁
H
5
4
3
2
Mark this and return
-2+
-3+
AWN
-4
-5
]
[
C
1 2 3 4 5 x
]
What is the range of the function on the graph?
all the real numbers
O all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
The range of the function on the graph is C. all the real numbers greater than or equal to –3 .
How to get the range?We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .
So, the range contain all the real numbers greater than or equal to –3 .
Therefore, the range contain all the real numbers greater than or equal to –3 .
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The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 12, y = 3
1
y =
?
x
►
Enter
Answer:
1/4
Step-by-step explanation:
Since y/x = 3/12 = 1/4, the answer is 1/4.
Find the distance between the points (2, −3) and (−4, −7).
-------------------------------------------------------------------------------------------------------------
Answer: [tex]7.21[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(2, -3) and (-4, -7)}[/tex]
Find: [tex]\textsf{Find the distance between the two points}[/tex]
Solution: Use the distance formula and the two points that were provided to determine the distance.
Plug in the values
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]d = \sqrt{(-4-2)^2+(-7-(-3))^2}[/tex]Simplify and expand
[tex]d = \sqrt{(-6)^2+(-7+3))^2}[/tex][tex]d = \sqrt{(-6)^2+(-4))^2}[/tex][tex]d = \sqrt{36+14}[/tex][tex]d = \sqrt{52}[/tex]If we are using square root we use the square root of 52 but if we simplify it to a decimal point we would use 7.21
I need help pls help
Answer:
550g
Step-by-step explanation:
total g in 1 kg is 1000
so 1000 - 550 =450
Consider the given density curve.
A graph goes from (0, 0) to (5, one-half).
Suppose that the mean value is 3.67. What is the best approximation for the median?
3.2
3.4
3.6
3.8
Picture posted below
The best approximation for the median is 3.6.
An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).
For the given density curve, the area under the density curve is
A=(1/2)×5×(1/2)=5/4
now, for the median, the area on the left and the area on the right of the median.
Let the median be x, then
The area criteria we get
(1/2)x(x/10)=(5/4)/2
⇒x²=5*20/4=25/2
So, we get x=5/([tex]\sqrt2[/tex])=3.5 ≈ 3.6
Hence the required answer is option 3.6
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find the zeros of following quadratic polynomial and verify the relationship between the zeros and the coefficient of the polynomial f(x)=5x-4√3+2√3x²
Answer:
[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]
To find the zeros, set the function to zero and solve for x using the quadratic formula.
[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]
Quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore,
a = 2√3b = 5c = - 4√3Substituting the values into the quadratic formula:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]
[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
The sum of the roots of a polynomial is -b/a:
[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]
The sum of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]
The product of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Answer:
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
To find the zeros, set the function to zero and solve for x using the quadratic formula.
Quadratic formula:
Therefore,
a = 2√3
b = 5
c = - 4√3
Substituting the values into the quadratic formula:
The sum of the roots of a polynomial is -b/a:
The sum of the found roots is:
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
The product of the found roots is:
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Find the equation of the line that is perpendicular to the graph of y=1/6x+3 and passes through (6.-6)
Answer:
y=−6x−36
Step-by-step explanation:
ez math
CAN SOMEONE PLS HELP ME WITH BOTH OF THESE QUESTIONS
EXPLANATION IS NOT NEEDED
WILL MARK BRAINLIEST
The amount in the new checking account is 600 dollars
The operation (5 α 3) + (7 α 5) is 46.
How to find the amount in the checking account?She had 1000 dollars in her checking account. she had a loan of 800 dollars to pay.
After paying her loan form her checking account the balance of the loan reduce to half.
Therefore, she paid 800 / 2 = 400 dollars for her loan
Hence,
Her new checking account = 1000 - 400 = 600 dollars
How to find value of an operation?
a α b = ab - a + b
Therefore,
(5 α 3) + (7 α 5)
(5 α 3) = 5(3) - 5 + 3 = 13
(7 α 5) = 7(5) - 7 + 5 = 33
Therefore,
(5 α 3) + (7 α 5) = 13 + 33 = 46
Note: I can't use the at symbol because it is a swear word.
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Tim go to school.His age is a cube number.His age is double 1 square number and half a different square number.How old is Tim?
Answer:
Tim is 8 years old.
Explanation:
8 is the cube number of 2, as 2 × 2 × 2 = 8. Additionally, 8 is double 4, which is the square number of 2, and half of 16, which is the square number of 4.
Tim who goes to school is 8 years old.
Why numerical ability is important ?Good numerical ability describes your ability to think and conclude logical thoughts in your daily life also in your working role how you handle data in form of numbers, graphs, statements etc.
According to the given question Tim goes to school.
His age is a cube number let that number be x therefore age of Tim would be x³.
His age can also be defined as double of 1 square number which is 2x² and half of a different square of a numbers.
Let us equate x³ = 2x² and by hit and trial we get to know that x = 2 satisfies this condition.
So, Age of Tim could be 8 years,Now lets check our third statement half a different square number 16 is square of 4 so half of 16 is also 8.
Thus Tim is 8 years old.
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Item 2
A container holds 54.6 gallons of liquid. The container leaks 8.4 gallons per hour.
How many hours will it take for the container to empty?
Enter your answer as a decimal in the box.
Answer:
54.6 ÷ 8.4 = 6.5 hours
6 hours, 30 minutes:)
Input 1,2,3,4,5, n output 2,-1,-4,-7, ?please help me find the linear function!
Answer:
f(x) = -3x + 5
Step-by-step explanation:
The slope of the function is -3 as the outputs decrease by three for each iteration.
The constant is 5 and can be determined if you plug in 1 as an x value and solve for c in an equation like this: -3(1) + c = 2
1/a + 1/b = 1/2 (solve for a)
Answer:
1/a+ 1/b = 1/2
Adding the fractions we get
b+a/ab=1/2
cross Multiplying the denominator we get,
b+a=ab/2
a= ab/2 -b
Answer:
a = 1/(1/2 + 1/b)
Step-by-step explanation:
1/a + 1/b = 1/2
1/a = 1/2 - 1/b
1 = a(1/2 - 1/b)
1/(1/2 + 1/b) = a
Think about all of the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and a parabola can intersect.
00
1
2
03
04
05
DONE
There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle and a parabola:
As we know the standard form of a circle:
[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]
The standard form of the parabola:
[tex]\rm y = a(x-h)^2+k[/tex]
If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)
The solution of the quartic equation will be 4.
Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
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Use the Factor Theorem to determine whether x−1 is a factor of 4x^3−6x^2+2x+1.
The sum of the first n terms of a geometric series is 364? The sum of their reciprocals 364/243. If the first term is 1, find n and common ratio
If the geometric series has first term [tex]a[/tex] and common ratio [tex]r[/tex], then its [tex]N[/tex]-th partial sum is
[tex]\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}[/tex]
Multiply both sides by [tex]r[/tex], then subtract [tex]rS_N[/tex] from [tex]S_N[/tex] to eliminate all the middle terms and solve for [tex]S_N[/tex] :
[tex]rS_N = ar + ar^2 + ar^3 + \cdots + ar^N[/tex]
[tex]\implies (1 - r) S_N = a - ar^N[/tex]
[tex]\implies S_N = \dfrac{a(1-r^N)}{1-r}[/tex]
The [tex]N[/tex]-th partial sum for the series of reciprocal terms (denoted by [tex]S'_N[/tex]) can be computed similarly:
[tex]\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}[/tex]
[tex]\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}[/tex]
[tex]\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}[/tex]
[tex]\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}[/tex]
We're given that [tex]a=1[/tex], and the sum of the first [tex]n[/tex] terms of the series is
[tex]S_n = \dfrac{1-r^n}{1-r} = 364[/tex]
and the sum of their reciprocals is
[tex]S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}[/tex]
By substitution,
[tex]\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243[/tex]
Manipulating the [tex]S_n[/tex] equation gives
[tex]\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363[/tex]
so that substituting again yields
[tex]r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}[/tex]
and it follows that
[tex]r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}[/tex]
Which of the following is the difference of two squares?
A. 100m^2+9n^2
B.9x^2-12y^2
C. 16g-49h
D. 25a^2-36b^6
The difference of two squares expression is (d) 25a^2-36b^6
How to determine the difference of two squares?The difference of two squares is represented as:
x^2 - y^2
Where x and y are perfect square expressions.
From the list of options, we have:
25a^2-36b^6
The terms of the above expression are perfect squares
i.e.
25a^2 = (5a)^2
36b^6 = (6b^3)^2
Hence, the difference of two squares expression is (d) 25a^2-36b^6
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PLEASE HELP what does -4=<X<4 mean?
Suppose that the function fis defined for all real numbers as follows. Graph the function f. Then determine whether or not the function is continuous.
Answer:
the value of x is between -4 and 4
PLEASE HELP!! ANSWER AND EXPLANATION NEEDED URGENTLY!!
Using it's concept, it is found that the probability that the button is either pink or blue is:
[tex]p = \frac{26}{29}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
There are x yellow buttons.There are y blue bottons.There are z pink buttons.There are six times as many pink buttons as yellow books, hence:
z = 6x.
Considering the ratio of yellow buttons to blue buttons, we have that:
[tex]\frac{x}{y} = \frac{3}{8}[/tex]
3y = 8x
[tex]y = \frac{8x}{3}[/tex]
The total number of buttons is given by:
[tex]T = x + \frac{8x}{3} + 6x[/tex]
[tex]T = \frac{29x}{3}[/tex]
The number of pink or blue is given by:
[tex]y + z = \frac{8x}{3} + 6x = \frac{26x}{3}[/tex]
Hence the probability is given by:
[tex]p = \frac{\frac{26x}{3}}{\frac{29x}{3}} = \frac{26}{29}[/tex]
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