Answer:
C. 29
Step-by-step explanation:
[tex]f(x) = -3x^3 + 2x^2 +24[/tex]
• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:
[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]
⇒ [tex]-3(-1) +2(1) + 24[/tex]
⇒ [tex]3 + 2 + 24[/tex]
⇒ [tex]29[/tex]
[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]
We have this equation:
[tex]f(x)=-3x^3+2x^2+24[/tex]
Substitute [tex]x=-1[/tex]:
[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]
Simplify to find the final answer:
[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]
In the notation “t(x)=…,” what does “t(x)” represents
The notation "t(x)" represents the statement t is a function of x
How to interpret the notation?The notation is given as:
t(x) = ....
The above notation is a function notation, and it used to relate one element to another
For instance:
f(x) means f is a function of x
Similarly, "t(x)" represents the statement t is a function of x
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2. David determines that 3 sqrt 2 cis(7pi/4) = -3+3i. When he considers the graphical representation of these numbers, he knows he made an error. Clearly explain in complete sentences what David observed, and where David made his mistake. State the correct rectangular equivalence of 3 sqrt 2 cis(7pi/4).
The correct rectangular equivalence of 3sqrt(2)·cis(7pi/4 ) is:
3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.
Where did David go wrong?David mistakenly interchanged the Sin function and the Cos function when he was calculating the problem.
Hence the correct rectangular equivalence is:
3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.
What is rectangular equivalence?An equation is rectangular in form when it is comprised of Variables like X and Y and can be represented on a Cartesian Plane.
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Find the midpoint of the line segment with the given endpoints: (-1, -6) and (-6, 5).
Answer:
Step-by-step explanation:
First, we will find the midpoint for the x - coordinate first.
Midpoint (x) = [tex]\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5[/tex]
Now we will find the midpoint for the y - coordinate.
Midpoint (y) = [tex]\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5[/tex]
Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)
The "int()" operator in your calculator is the "greatest integer function." It returns the greatest integer less than or equal to the operand and is written using square brackets: [x] or [[x]]. For example, it would give back 82 for [[82.976]]. In Smalltown, AZ the students receive grade points as follows: 4.0 for any grade 90% or higher. [90,100) 3.0 for any grade 80% or higher. [80,90) 2.0 for any grade 70% or higher. [70,80) 1.0 for any grade 60% or higher. [60,70) (Notice: students NEVER fail! And students never get 100%!)
The function that correctly returns grades from 60 percent to a 100 percent is f(x) = [[(x - 50)/10]]
How to determine this functionThe question tells us that the students do not fail and they do not get a 100 percent score either.
Hence there is no need for worry if the grade is at 5.0 or less than 1.
For example we have
x = 82.976
f(82.976) =[[(82.976-50)/10]
This would then be 3.29
This is then = 3.0
This function is not an odd function and it is not an even function. This is because the domain does not have negative values.
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What is the slope of the line that passes through (0,5) and (10,0)?
Answer:
-1/2
Step-by-step explanation:
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex]m = \dfrac{0 - 5}{10 - 0} = \dfrac{-5}{10} = -\dfrac{1}{2}[/tex]
Answer: slope = -1/2
A rectangular plot of land is to be fenced in using two types of fencing. Two opposite sides will use heavy-duty fencing selling for $4.50 a foot. The two remaining sides will use standard fencing selling for $3 a foot. How much of the heavy-duty and standard fencing should be used so that the greatest area can be fenced in at a cost of $18,000?
The amount of heavy-duty fencing to be used is 2000 ft for $9000 and the amount of standard fencing to be used is 3000 ft for $9000 in order to make a total cost of $18000.
How do we determine the area of a rectangular plot?The area of the rectangular plot is denoted by the length multiplied by the width.
Let us assume that the length = x and the width = y.
Area = xyThen, for two opposite with heavy fencing for $4.50 a foot and the standard fencing for $3 a foot, we have:
2x (4.50) + 2y(3) = 18000 ---- (1)
⇒ 9x + 6y = 18000
Make (y) the subject, we have:
[tex]\mathbf{y = \dfrac{18000-9x}{6}}[/tex]
Replace the value of y with the area of the rectangle, and we get:
[tex]\mathbf{Area =x(\dfrac{18000 - 9x}{6})}[/tex]
Area = x(3000 - 1.5x)
Area = 3000x - 1.5x²
For the area to be maximum, we take the differentiation of the Area:
dA/dx = 0
dA/dx = 3000 - 3x
x = 3000/3
x = 1000 ft
From equation (1)
2x (4.50) + 2y(3) = 18000
x (4.50) + y(3) = 9000
1000(4.50) + 3y = 9000
3y = 9000 -4500
y = 4500/3
y = 1500 ft
So, there are (1000× 2)ft = 2000ft heavy duty fencing for $9000, and (1500 ×2)ft = 3000ft standard fencing for $9000 to make a cost of $18000.
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The question is down below
Answer:
108 cmStep-by-step explanation:
The ratio is 1 : 3, so we multiply the numbers by 3
4 * 3 = 12
3 * 3 = 9
So, the length is 12 and the width is 9.
12 * 9 = 108
So the area is 108
Hope this helps!
what fraction is 40cm of 2cm
2/40 = 1/20.
We are able to simplify by dividing 2 and 40 by the greatest common factor (GCF), which was 2. We know this because 2 and 40 can be divided by 2.
2cm is 1/20th of 40cm.
The following data set is given: 122, 130, 145, 154, 165, 178
Adding which number to the set will increase its mean?
140
A)
B)
C)
D)
148
149
150
Answer:
150
Step-by-step explanation:
Mean is average, so adding any number above the original mean would increase the mean.
On October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos.
(a) On that date, how many pesos was 81.35 dollars worth?
Round your answer to the nearest hundredth of a peso.
0 pesos
(b) On that date, how many dollars was 91.03 pesos worth?
Round your answer to the nearest hundredth of a dollars. I need help with both of these math problems.
Taking into account the rule of three, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.
Rule of threeThe rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following expression must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Amount of Mexican pesos in this casesOn October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos. So, you can apply the following rules of three:
If 1 dollar is equal to 13.65 Mexican pesos, 81.35 dollars is equal to how many Mexican pesos?1 dollar ⇒ 13.65 Mexican pesos
81.35 dollars ⇒ x
So: [tex]x=\frac{81.35 dollarsx13.65 Mexican pesos}{1 dollar}[/tex]
Solving:
x= 1110,4275 Mexican pesos
f 13.65 Mexican pesos is equal to 1 dollar, 91.03 Mexican pesos is equal to how many dollars?13.65 Mexican pesos ⇒ 1 dollar
91.03 Mexican pesos ⇒ x
So: [tex]x=\frac{91.03 Mexican pesosx 1 dollar}{13.65 Mexican pesos}[/tex]
Solving:
x= 6.67 dollars
In summary, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.
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Graph f(x) = 3/4x - 2
The equation of the function is the graph of line.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The function is given below.
f(x) = (3/4)x – 2
The function is an equation of line.
The graph of the function is given below.
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equation
3/8 + 5/12 =
Answer:
19/24
Step-by-step explanation:
3/8=36/96
5/12=40/96
36/96+40/96=76/96
76/96=19/24
a = 2√3 ft.;c = 4 ft.
A = 8√3 sq. ft.
True
False
False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².
Area of the triangleGiven:
a = 2√3 ft,
c = 4 ft,
Lengths of the sides of a right triangle = a and b
Hypotenuse= c
Hence:
Using Pythagorean theoremc²=a²+b²
4²=(2√3)²+b²
16=12+b²
4=b²
b=2
Area of triangle
A=1/2×a×b
A=1/2×2√3×2
A=4√3÷2
A=2√3 sq.ft
The Area of the triangle is 2√3 ft².
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5,679 is invested, part at 12% and the rest at 7%. If the interest earned from the amount invested at 12% exceeds the interest earned from the amount invested at 7% by $407.50, how much is invested at each rate? (Round to two decimal places if necessary.)
The amount of money invested at 12% was $4327 while $1442 was invested at 7%.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount invested at 12% and y represent the amount invested at 7%, hence:
x + y = 5679 (1)
Also:
0.12x = 0.07y + 407.5 (2)
From both equations:
x = 4327, y = 1442
The amount of money invested at 12% was $4327 while $1442 was invested at 7%.
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NO LINKS!! Find an nth-degree polynomial function with real coefficient satisfying the given conditions.
n= 4
-1, 3, and 2+ 4i are zeros;
f(1)= -136
n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.
Since these are solutions
x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.
We have (x-2)(x-5i)(x+5i) = 0
Now,
f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.
f(-1) = (-3)(26) = -78.
But -78 x -2 = 156, so our polynomial becomes
Y= -2x (x - 2 ) x (x to the power of 2 + 25) = 0
Answer:
[tex]f(x)=2x^4-12x^3+50x^2-56x-120[/tex]
Step-by-step explanation:
Complex Conjugate Theorem
For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs. So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.
Given zeros:
-1, 3, and (2 + 4i)
As one of the given zeros is a complex number, (2 - 4i) is also a zero.
Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:
[tex]\begin{aligned}f(x) & =a(x+1)(x-3)(x-(2+4i))(x-(2-4i))\\& = a(x+1)(x-3)(x-2-4i)(x-2+4i)\\& = a(x+1)(x-3)(x^2-2x+4ix-2x+4-8i-4ix+8i-16i^2)\\& = a(x+1)(x-3)(x^2-4x+4-16i^2)\end{aligned}[/tex]
Remember that [tex]i^2=-1[/tex], therefore:
[tex]\begin{aligned}f(x)&=a(x+1)(x-3)(x^2-4x+4-16(-1))\\&=a(x+1)(x-3)(x^2-4x+4+16)\\&=a(x+1)(x-3)(x^2-4x+20)\end{aligned}[/tex]
To find the value of the leading coefficient (a), use the given [tex]f(1)=-136[/tex] :
[tex]\begin{aligned}f(1) & = -136\\\implies a(1+1)(1-3)(1^2-4(1)+20) & = -136\\a(2)(-2)(17) & = -136\\-68a & = -136\\\implies a & = 2\end{aligned}[/tex]
Therefore, the polynomial in factored form is:
[tex]f(x)=2(x+1)(x-3)(x^2-4x+20)[/tex]
Finally, expand the brackets:
[tex]\begin{aligned}f(x) & =2(x+1)(x-3)(x^2-4x+20)\\& =2(x^2-2x-3)(x^2-4x+20)\\& =2(x^4-4x^3+20x^2-2x^3+8x^2-40x-3x^2+12x-60)\\& =2(x^4-4x^3-2x^3+20x^2+8x^2-3x^2-40x+12x-60)\\& =2(x^4-6x^3+25x^2-28x-60)\\& =2x^4-12x^3+50x^2-56x-120\end{aligned}[/tex]
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trigonometry question
worth 100 points!
desperately need help
Answer:
Height is 40√2 m or 56.57 m
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are the legs and 'c' is the hypotenuse
Here given:
a = 20 meterb = heightc = 60 meterSubstitute values:
(20)² + (h)² = 60²
400 + h² = 3600
h² = 3600 - 400
h² = 3200
h = √3200
h = 40√2
h = 56.6 meter
Solve for x in the triangle. Round your answer to the nearest tenth.
[tex]x = 12.9[/tex]
Step-by-step explanation:Note:
The following is sin formula:
[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]
1) Using the sin formula
[tex]sin(59) = \frac{x}{15} [/tex]
2) Multiply both sides by 15
[tex]15 \sin(59) = \frac{x}{15} \times 15[/tex]
3) Divide both sides by sin(59)
[tex] \frac{15 \sin(59) }{ \sin(59) } = \frac{x}{ \sin(59) } [/tex]
4) Find the value of x
[tex]x = 15 \sin(59) [/tex]
[tex]x = 12.9[/tex]
What is the slope of the line graphed below?
OA. -
OB.
312
O c. //
C.
O D. 23/0
10
(-3,-1)
(0, 1)
Answer:
Your answer is -2/-3
The formula to calculate slope is y2-y1/x2-x1
I think it will help you
Oh no! The principal can't unlock her phone, because she can't remember how to solve the puzzle for her password.
At least two numbers that do NOT work, with an explanation of why they don't work.
Your best guess for a number that does work (or almost works).
A reminder of the puzzle:
The number is between 8,500 and 8,800.
When multiplied by 8, the result is a whole number.
The digit in the hundreds place is ¾ the digit in the thousands place.
The sum of all digits in the number is 26.
The digit in the hundredths place is 200% of the digit in the tenths place.
There are no zeros in the decimal places.
The numbers are:
8,640.1258,604.1258,622.1258,613.1258,631.125What is number system?
A number system is defined as a system of writing to express numbers.
First, the number between 8,500 and 8,800.
So, the thousands place digit is 8.
Second, When multiplied by 8, the result is a whole number.
So, multiplying by 8, the decimal has to end in 5.
Because there is no zeroes in the decimal place..
options are:
8 times 0.5
8 times 0.25
8 times 0.125
Now, The digit in the hundredths place is 200% of the digit in the tenths place
considering digit in the hundreds place is ¾ the digit in the thousands place.
So, choose 0.125.
Now, The digit in the hundreds place is 3/4 the digit in the thousandths place.
Digit in Thousandth Place = 5
Digit in Hundreds place=3/4*2=6
Our number now is:86_ _.125
As, The sum of all the numbers is 26
8+6+1+2+5=22
26-22=4
The possible numbers are:
8,640.125
8,604.125
8,622.125
8,613.12
8,631.125
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In the following figure AEDC is a square, BA= BC and AE = AC. The area of AEDC is 25 cm² and angle B=90°, Calculate the length of AB.
A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The area of AEDC is 25 cm². Therefore,
AEDC = AC²
25 cm² = AC²
AC = 5 cm
In ΔABC,
AB² + BC² = AC²
Since AB=BC,
2(AB²) = AC²
AB² = 25/2
AB = 5/√2 cm
Hence, the length of side AB is 5/(√2) cm.
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-6-5
A. 2
C. 3
3
2
A
1
4-3-2-10
-1
-21B
-3
C
E
D
F
1 2 3
In the similarity
transformation of AABC
to ADFE, AABC was dilated by
a scale factor of [? ], reflected
across the [ ], and moved
through the translaton [ ].
B. 1/2
D. 1/3
Answer: A
Step-by-step explanation:
Following the first two steps of the sequence of transformations,
[tex]A(-4,-2) \longrightarrow (-2,-1) \longrightarrow (-2,1)[/tex]
We need to map this onto D(1,1), which involves a translation 3 units right.
In the similarity transformation of ΔABC to ΔDFE, ΔABC was dilated by a scale factor of [1/2 ], reflected across the [x-axis ], and moved through the translation [(X+3, Y+0)].
So, correct option is: A.
Here, we have,
from the given fugre we get,
A =( -4, -2)
Following the first two steps of the sequence of transformations,
Dilated by a factor of 1/2 => A' = ( -2, -1)
reflected across the X-axis => A''=( -2, 1)
and moved through the translation becomes D = ( 1,1)
We need to map this onto D(1,1), which involves a translation 3 units right.
so, translation=> ( -2 + 3, 1+0) => (X+3, Y+0)
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Determine the amount of interest the principal in each account had earned. (From Example 2)
3. On March 3, Raul Avila deposited $10,000 in a savings account that pays 5.5% interest compounded daily until June 21.
4. On March 26, Samuel Griffin deposited $20,000 in a savings account that pays 5.5% interest compounded daily until July 24.
The amount of interest that the principal in each account had earned is as follows:
Raul Avila = $167.12
Samuel Griffin = $364.91
How is compound interest computed?The compound interest can be calculated using the compound interest formula:
A = P(1 + \frac{r}{n})^{nt}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It can also be computed using an online finance calculator as follows:
Data and Calculations:Raul Avila:N (# of periods) = 110 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $10,167.12
Total Interest = $167.12
Samuel Griffin:N (# of periods) = 120 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $20,000
PMT (Periodic Payment) = $0
Results:
FV = $20,364.91
Total Interest = $364.91
Thus, using the online finance calculator, the compound interests for each principal have been computed as $167.12 and $364.91, respectively.
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I need help with this please!!!
Answer: 3/11
The question is just asking you to select three people out of the group of eleven. And because we don't know there ages, the probability they are the oldest three in the group would be 3/11 or 3 out of 11.
PLEASE I BEG HELP ASAP PLEASE
Claus used this picture to explain why the area of a circle is equal to 2
π
r
2
. What is NOT true about the parallelogram he formed?
Answer:
The perimeter of the parallelogram is 2πr
Step-by-step explanation:
The area of the circle should be the same as the area of the parallelogram. Therefore, the area of the circle cannot equal the area of the parallelogram.
Hope this helps. (:
The following formula gives the total surface area S of a cylinder with radius r and height h.
S=2πr(r+h)
Find the total surface area of a cylinder with radius 4 and height 8. Enter an exact answer in terms of π. Do not include S= in your answer.
The total surface area of a cylinder with radius 4 and height 8 is 96π.
Surface area of a cylinderIt follows from the task content that the total surface area of the cylinder is to be determined. The total surface area of the cylinder is given by the formular;
S=2πr(r+h)
where,S = surface arear = radius = 4h = height = 8S=2πr(r+h)
= 2 × π × 4(4 + 8)
= 2 × π × 4(12)
= 2π × 48
= 96π
Hence, the total surface area of the cylinder in terms of π is; 96π.
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an airplane flies 3300 miles with the wind in 3 hours 18 minutes. it takes 4 hours and 24 mins to make the return flight against the same wind. find the speed of the airplane and the speed of the wind.
Answer:
The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Step-by-step explanation:
Let’s assume the speed of the plane =x miles/hr
And let the speed of wind =y miles/hr
So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr
Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr
We know that, distance=speed×time
Then according to the given conditions, we have
3300=(x+y)×(3+(18/60))
here convert 18mins to hour by dividing by 60 and add to 3hrs.
⇒x+y= 3300/3.3
⇒x+y=1000 … (i)
And,
3300=(x-y)×(4+(24/60))
here convert 24mins to hour by dividing by 60 and add to 4hrs.
⇒x-y= 3300/4.4
⇒x-y=750 … (ii)
Adding equation (i) and (ii), we get
2x=1750
⇒x= 1750/2
=875
Substituting the value of x in equation (ii), we get
875−y=750
⇒y=875-750
⇒y=125
Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Use Interval notation to indicate all real numbers between and including -3,8
The interval notation for all real numbers between -3 and 8 is:
[-3, 8].
How to list all real numbers between a and b?There are an infinite number of real numbers between a and b, hence we list all them in interval notation, as follows:
[a,b]: including a and b.(a,b): excluding a and b.In this problem, we include -3 and 8, hence the notation is:
[-3, 8].
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pls help quickly pls
Step-by-step explanation:
if I understand your comment correctly, then you need the mean value of the lifetime of these light bulbs.
1. get the midpoint of each interval.
2. multiply each frequency with its midpoint.
3. sum all frequencies.
4. sum all multiplication results if 2. (of frequencies and midpoints).
5. divide 4. by 3.
lifetime midpoints :
(25 + 50)/2 = 75/2 = 37.5
(50 + 100)/2 = 150/2 = 75
(100 + 150)/2 = 250/2 = 125
(150 + 200)/2 = 350/2 = 175
(200 + 250)/2 = 450/2 = 225
(250 + 300)/2 = 550/2 = 275
(300 + 350)/2 = 650/2 = 325
multiply frequencies with their midpoints :
37.5 × 47 = 1762.5
75 × 86 = 6450
125 × 45 = 5625
175 × 36 = 6300
225 × 0 = 0
275 × 37 = 10175
325 × 50 = 16250
sum all frequencies
47+86+45+36+0+37+50 = 301
sum all multiplication results of 2.
1762.5+6450+5625+6300+0+10175+16250 = 46,562.5
divide 4. by 3.
the mean value is
46,562.5 / 301 = 154.692691... hours ≈
≈ 154.69 hours
Given the data set in the image, which of the following equations best represents a line of best fit?
Answer:
C.
Step-by-step explanation:
what is the answer (3^3/3^4)^5
Answer:
Exact Form:
1/243
Decimal Form:
0.00411522…