Correct option is A. The value of f(3) is -11
What is a piece-wise function?A piece wise-defined work could be a work characterized by different sub-functions, where each sub-function applies to a diverse interim within the domain. Piece-wise definition is really a way of communicating the work, instead of a characteristic of the work itself.The value of x = 3 corresponds to the following function on the piece wise
[tex]f(x) = -3x -2[/tex]
Substitute 3 for x
[tex]f(3) = -3(3) -2[/tex]
Expand
[tex]f(3) = -9 -2[/tex]
Evaluate -9 -2
[tex]f(3) = -11[/tex]
Hence, the value of f(3) is (a) -11
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Answer: A.) -11
Step-by-step explanation: i hope this helps :)
A person is looking up to the top of a pole at an angle of elevation of 32°. If their line of sight is at 6 ft, find the total height of the pole from the ground to the top. (HINT: you must find "h" first in order to find the total height): (Do not do any rounding during your calculations, just round your final answer)
The total height of the pole from the ground to the top is 3.2 added to the height of the person
How to determine the height of the pole?The given parameters are:
Elevation angle = 32 degreesLine of sight, L = 6 ftThe question is an illustration of elevation
Where the height of the building is the sum of the height of the person and the height from the person's sight to the top of the building (h)
Start by calculating the value of h using the following sine function
[tex]\sin(\theta) = \frac{h}{L}[/tex]
Substitute the values of L and ∅ in the above equation
sin(32) = h/6
Multiply both sides by 6
h = 6 * sin(32)
Evaluate sin(32)
h = 6 * 0.5299
Evaluate the product
h = 3.1794
Approximate
h = 3.2
Hence, the total height of the pole from the ground to the top is 3.2 added to the height of the person
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Elise is buying a new car selling for
$21,450. The rate of depreciation on this
type of car is 8% per year. On the graph
of a function that represents this
situation, where does the line cross the y
axis?
Answer: 21450
Step-by-step explanation:
That is the initial price.
The line cross the y axis at 21450.
The correct option is (C)
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Elise is buying a new car selling for $21,450.
The rate of depreciation on this type of car is 8% per year.
Using f(x) = A [tex](1+r)^x[/tex]
A= $21,450. and r = -8% (depreciated)
So, f(x) = A [tex](1+r)^x[/tex]
f(x) = 21450 [tex](1- 8/100)^x[/tex]
= 21450 x [tex](0.92)^x[/tex]
Thus, the line cross the y axis at
= 21450 ( initial point)
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Under his cell phone plan, christopher pays a flat cost of $59 per month and $3 per gigabyte. he wants to keep his bill at $62.90 per month. how many gigabytes of data can he use while staying within his budget?
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
How many gigabytes of data can he utilize while staying within his budget?The number of gigabytes of data that Christopher can use while staying within his budget is 1.8 gigabytes.
Based on the information, we get
59 + (3 × g) = 62.90
59 + 3g = 62.90
simplifying the equation, we get
3g = 62.90 - 59
3g = 3.9
Divide both sides by 3, and we get
3g/3 = 3.9/3
g = 1.3
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
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please help i dont know to do it please help
Answer:
5/10
Step-by-step explanation:
0.5 is 5/10 as a decimal. Any number that can be written as a fraction or a ratio is a rational number, so, since 0.5 can be written as 5/10, it’s a rational number.
If y° and 48° are a pair of complementary angles then find y°
Answer:
y = 42 and/or x = 36
Step-by-step explanation:
y + 48 = 90
y = 42 (subtracted 48 from 90)
3x + 2x = 180 (angles are linear pairs)
5x = 180 (combine like terms)
x = 36 (divided by 5 on both sides)
I didn't know which question you needed help with, I hope this makes sense :)
❄ Hi there,
the sum of complementary angles is always 90°.
If we know one of these angles, we can set up an equation –
[tex]\triangleright\sf{y+48=90}[/tex]
and then solve for y...
[tex]\triangleright \ \sf{y=42}[/tex]
That's it!
❄
please help! look at the photo linked
Answer:
3; 1
Step-by-step explanation:
when there are six spots we can see that there are 2 eyes
so
divide both sides by 2
6:2
6 / 2 : 2 / 2
3 : 1
that is your answer
Which inequality explains why these three segments cannot be used to construct a triangle? ef fd > de ed ef < df ed ef > df ef fd < de
We have the segments EF, FD, and DE.
Therefore, the correct answer is
ED + EF < DF
EF + FD < DE
What is Triangle Inequality Theorem?
The Triangle Inequality Theorem states that the totality of any side of a triangle must be greater than the measure of the third side in this problem.
We have the segments EF, FD, and DE.
To construct a triangle three inequalities must be met
case 1: EF + FD > DE
case 2: FD + DE > EF
case 3: EF + DE > FD
Therefore, the correct answer is
ED + EF < DF
EF + FD < DE
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Use a calculator to find tan 24°, round to the nearest hundredth.
Hi :)
To find the tan of a number, just type the number into your calculator and press [tex]\boxed{\tan}[/tex].
[tex]\tan 24=0.45[/tex], Rounded to the nearest hundredth, or 2 numbers after the decimal point, just like you asked
[tex]\textit{\textbf{Learn\;More;Work\;Harder}}[/tex]
:)
An ANOVA procedure is applied to data obtained from four distinct populations. The samples, each comprised of 15 observations, were taken from the four populations. The degrees of freedom for the numerator and denominator for the critical value of F are ________.
The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
The samples, each comprised of 15 observations, were taken from the four populations.
How to find the degrees of freedom?The determine the degrees of freedom for the numerator and denominator for the critical value of F is given below:
k = 4
n = 15
Total degree of freedom;
= nk - 1
= 59
For numerator, it is
= k -1
= 4 - 1
= 3
For denominator it is
= T - (k -1 )
= 59 - 3
= 56
The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
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The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15
Answer:
2.57
Step-by-step explanation:
The mean absolute deviation(MAD) of a data set is given by the formula
[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]
n = number of data set values. Here n=7
[tex]\bar{x}=[/tex]mean of the data set values = [tex](20+16+21+16+22+16+ 15)/7 = 126/7 = 18[/tex]
[tex]x_{i}[/tex] are the n individual values
Substituting in the summation we get
MAD = [tex]\frac{1}{7} |20-18| + |16-18| + |21-18| + |16-18| + |22-18| + |16-18| + |15-18|\\= (2 + 2 + 3 + 2 + 4+ 2 + 3)/7\\= 18/7 = 2.571428 \\[/tex]
Rounded to the nearest hundredth, the answer is 2.57
A study of the annual population of bees in a county park shows the population, B(t), can be represented by the function B(t)=182(1.065)t, where the t represents the number of years since the study started. Based on the function, what is the growth rate?
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
From the function [tex]B(t) = 182(1.065)^t[/tex]:
b = 1.065
Growth rate = 1.065 - 1 = 0.065 = 6.5%
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
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In the circle below, O is the center, MP is a diameter, and m angle M O L equals 45 degrees. Find the measure of L N M.
Check the picture below.
The length of a rectangular field is 9m longer than its width, if the perimeter of the field is 270m find its width.
==================================================
Work Shown:
width = w
length = w+9
perimeter = 2*(length + width)
P = 2(w+9+w)
P = 2(2w+9)
P = 4w+18
4w+18 = P
4w+18 = 270
4w = 270 - 18
4w = 252
w = 252/4
w = 63 meters is the width
w+9 = 63+9 = 72 meters is the length
Check:
perimeter = 2*(length + width)
perimeter = 2*(72 + 63)
perimeter = 2*(135)
perimeter = 270
The answer is confirmed.
29% of a university's freshman class are majoring in Economics. If 2668 students in
the freshman class are Economics majors, how many students are in the freshman
class?
The number of students in the class is 9200.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The percent of students pursuing economics is 29%.
And, the number of students pursuing economics is 2688.
Suppose the total number of students are x.
Then, the following equation can be written for the given case,
29% of x = 2668
=> 29/100 × x = 2668
=> x = 2668 × 100/29
= 9200
Hence, the total number of students in the freshman class is 9200.
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The midpoint of EF is (-6, 1). One endpoint is E(-9, 7). Find the coordinates of endpoint F.
Answer:
Step-by-step explanation:
here is an solution :
Answer:
Its (-3,-5)
Step-by-step explanation:
Hope This Helps:))
Several properties are used to evaluate this expression. identify the property used in each step. 21 + (19 + 36): (21 + 19) + 36:
21 + (36 + 0 + 19) Equals 76.
What is the property of addition?A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.
Equation to be used: 21 + (36 + 0 + 19)
The identity property of addition states that a + 0 = a.21 + (36 + 0 + 19) = 21 + (36 + 19)Using the commutative property of addition, a + b equals a + b.21 + (36 + 19) Equals 21 + (19 + 36)By using the associative property of addition, the formula is: a + (b + c) = a + b + c.21 + (19 + 36) Equals (21 + 19) + 36Put two more numbers within the bracket now.(21 + 19) + 36 = 40 + 36A + B Equals C, any number, using the closure property of addition.40 + 36 = 76Hence 21 + (36 + 0 + 19) Equals 76.To know more about property of addition visit:
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I understand that the you are looking for is :
Several properties are used to evaluate this expression. Identify the property used in each step.
21 + (36 + 0 + 19)
21 + (36 + 19):
21 + (19 + 36):
(21 + 19) + 36:
40 + 36
76
18
An open-faced box is to be constructed by cutting squares out of the corners of a 7in by 7in
sheet of tin and folding up the sides. Which of the following describes the surface area of such
a box? (Let h represent the side length of the cut out squares. * (5 Points)
O The surface area of the box is given by (7 - 2h)² + 4h (7-2h) in².
The surface area of the box is given by 2(7 - 2h)² + 4h² in².
O The surface area of the box is given by h(7 - 2h)² in².
O The surface area of the box is given by 4(7-2h)² + h² in².
O I don't know.
Answer:
a
Step-by-step explanation:
S.A for open-faced box= lb + 2(bh+lh)
= (7-2h)(7-2h) + 2[h(7-2h)+h(7-2h)]
= (7-2h)² + 2[2h(7-2h)]
= (7-2h)² + 4h(7-2h) in²
Determine the factors of x2 − 8x − 12. (x − 6)(x 2) (x 3)(x − 4) prime (x 6)(x − 2)
The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.
What is a quadratic equation?
In a quadratic equation ax² + bx + c = 0
when (b² - 4ac) exists a perfect square only then we can factorize the equation.
In the given equation x² - 8x - 12 we have to determine the value of
b² - 4ac
From the equation, we get b = -8 and c = -12
b²- 4ac = (-8)² - 4(1)(-12)
= 64 + 48 = 112
Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.
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Compute the surface area obtained by rotating the curve y = 3 x , for x is in [1, 125] about the y-axis
Answer:
Given,
y=x³ ,0≤x≤2
We have to find the surface area of the surface by rotating the curve about the x axis.
For rotation about the x axis, the surface area formula is given by-
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
let u=1+9x⁴
du=36x³dx
dx/36x³
Substituting u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
therefore, the exact surface area is 203.06 square units.
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Answer:
In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.
Given: y=3x, for x is in [1,125] about the y axis.
y=x³ ,0≤x≤2
Lets find the surface area of the rotating curve,
Finding surface area for rotation along x-axis,
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
Assuming u =1+9x⁴
du=36x³dx
=dx/36x³
Substituting respective values of u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
hence, the surface area is 203.06 square units.
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How many faces, edges and vertices does the shape below have?
Faces:
Edges:
Vertices:
Solve the proportion.
A. 12
B. 2
C. 8
D. 16
D. 16
Cross multiply, to cancel the denominator; so if you multiple by 6 on one side, to cancel the division of 6 - you must also multiply the other side by 6 & vice versa.
You get:
8(x-4) = 6x
Expand bracket to get:
8x - 32
Now solve for x :
8x - 32 = 6x
- 8x
- 32. = - 2x
÷ - 2
16 = x
Or
8x - 32 = 6x
+ 32
8x. = 6x + 32
- 6x
2x. = 32
÷2
x =16
Check:
16 - 4 = 12, then ÷ 6 is 2
16/8 = 2
Hope this helps!
Which type of function describes f(x)? exponential logarithmic polynomial rational
The category of the function f(x) shown in the graph is a (B) linear function.
What are linear functions?In mathematics, the word linear function refers to two distinct but related concepts.In calculus and related fields, a linear function is one whose graph is a straight line, that is, a polynomial function of degree zero or one.
To find which type of function describes f(x):
How do determine the graph?
A linear graph is any graph that is represented by a straight line.Because the graph is represented by a straight line, the above statement implies that it is a linear graph.Therefore, the category of the function f(x) shown in the graph is a (B) linear function.
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The complete question is given below:
Which type of function describes f(x)?
(A)exponential
(B) linear
(C) logarithmic
(D) polynomial
(E) rational
cuanto da (9+4m)² cuadrado de binomio ayudaaaaa
Answer:
16m^2 + 72m + 81
Step-by-step explanation:
you expand it, by (9+4m)(9+4m), using distributive property you get
81 + 36m + 36m + 16m^2, simplifying you get the answer
Write the following expression using exponents -3x7x7x7x7x7x7
Solution -:
[tex] \bold{ \underline{ \underline{Given}}}[/tex]
-3x7x7x7x7x7x7
[tex]\bold{\underline {\underline{lets \: begin}}}[/tex]
We have,,
[tex] -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} [/tex]
exponent and shortcut to express a multiplication of number by itself several times explain us how many time we should multiply the number by itself this process of using exponent is called raising to a power where the exponent is the power.Law of exponent -: a ⁰ = 1 a ^ m × a ^ n (a^m)^na^m × b^ mAs like example→ 2⁴
here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.
• Evaluate the expression 16n+4 when n=5
Answer:
84
Step-by-step explanation:
substitute n = 5 into the expression
16n + 4
= 16(5) + 4
= 80 + 4
= 84
Answer:
The expression will have the value of 84
Step-by-step explanation:
Greetings ![tex]16n + 4[/tex]
given expression
Thus, plug n=5
[tex]16(5) + 4 \\ 80 + 4 = 84[/tex]
Finally, we get the value 84
How to name a angle in 4 different ways?
First answer and correct answer gets to be brainliest!
Hey there!
4 ways to name angles⇒ Use the vertex as the middle letter, and the point from each side (<ABC or <CBA)
⇒ Use the vertex only (<B)
⇒ Use a number (<1)
Classify angles according to their measure.⇒ Acute angle: less than 90°
⇒ Right angle: exactly 90°
⇒ Obtuse angle: between 90° and 180°
⇒ Straight angle: exactly 180°
Thank you,
Eddie
See the attachment for a visual!
please answer my question
Considering the box-plots, the means for the data-sets are given as follows:
Data-set A: 5.5Data-set B: 5.What does a box-plot shows?Each shows the number of times each measure appears.
Hence, the mean of data-set A is given as follows:
mA = (3 + 4 x 3 + 5 x 2 + 6 x 2 + 7 x 3 + 8)/(1 + 3 + 2 + 2 + 3 + 1) = 5.5.
For data-set B, the mean is:
mB = (2 x 4 + 2 x 5 + 2 x 6)/(2 + 2 + 2) = 5.
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Can someone help me this is Algebra 2 thank you
Answer:
Order of exponentiation can be swapped here, and the fractional power written as a root.
Step-by-step explanation:
The commutative property of multiplication and the rules of exponents apply.
Product of exponentsThe rule is ...
(a^b)^c = a^(bc)
ApplicationThe given expression can be rearranged to ...
[tex]\left(3^\frac{1}{5}\right)^2=3^{\frac{1}{5}\cdot2}=3^{2\cdot\frac{1}{5}}=\left(3^2\right)^\frac{1}{5}\\\\=9^\frac{1}{5}=\boxed{\sqrt[5]{9}}[/tex]
number 7 please and don t care abt others lol
Answer:
The question does not make a lot of sense to me but I think this is how its supposed to be done
so there are 15 shirts
2 are sold at 3.90, 2 x 3.90 = 7.8
15-2= 13 t shirts
13 sold at 4.70, 13 x 4.70 = 61.1
amount of money made is = 7.8 + 61.1
= 68.9
What are the steps to my answer?
Answer:
f[g(x)] = 4x²+6x-3Step-by-step explanation:
f[g(x)]=(2x)²+3(2x)-3...substitute the values of g(x) into the function f(x)f[g(x)]=4x²+6x-3...simplified