Answer:
Expand the polynomial using the FOIL method.
− 8 x^ 2- 26 x − 15
Vanessa bought a house for $268,500. She has a 30 year mortgage with a fixed rate of 6.25%. Vanessa’s monthly payments are $1,595.85. How much was Vanessa’s down payment? a. $9,314.45 b. $16,781.25 c. $40,275.00 d. $53,040.00
Answer:
Option a - $9,314.45
Step-by-step explanation:
Cost of the house = $268,500
Time of repayment = 30 years
Repayment is done monthly, so number of repayments = 30 X 12 = 360
Monthly Payment = $1595.85
Rate of interest per payment period = [tex]\frac{.0625}{12}[/tex]
So, Present value of monthly payments = 1595.85 X [tex]\frac{(1+\frac{.0625}{12})^{360}-1}{(1+\frac{.0625}{12})^{360}*(\frac{.0625}{12})}[/tex]
= $259,185.55
So, Vanessa's down payment = $268,500 - $259,185.55 = $9,314.45
Hope it helps.
Thank you !!
Answer:
Option a - $9,314.45
Step-by-step explanation:
e d g e
Is the square root of 5/8 rational or irrational? I think it's irrational, but I'm not sure because it's not a repeating decimal and it doesn't terminate, so I'm pretty sure it's irrational. Pls double check my thinking!
Your Right It Is Irrational
You roll a fair 6 sided die what is the probability you roll a 1 or 3?
It’s a 33% chance rolling a one or a three
A paint store offers 15 different shades of blue. how many different ways could you purchase 3 shades of blue
Answer:
3.9230231e+12
Step-by-step explanation:
15! is 15 times 14 times 13 times 12 times 11 times 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 then times 3 because 3 shades of blue.
The number of different ways to purchase 3 shades of blue from 15 options is 455 different ways.
The question is asking about the number of combinations of 3 shades of blue that can be chosen from a total of 15 different shades. To calculate this, we use the formula for combinations without repetition, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, n is 15 and k is 3.
First, we calculate the factorial of n, which is 15! (15 factorial), then the factorial of k, which is 3!, and finally the factorial of n - k, which is 12!. Putting these into the formula gives us:
C(15, 3) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455
Therefore, there are 455 different ways to choose 3 shades of blue from 15 different shades.
Match each polynomial function with one of its factors.
f(x) = x3 − 3x2 − 13x + 15
f(x) = x4 + 3x3 − 8x2 + 5x − 25
f(x) = x3 − 2x2 − x + 2
f(x) = -x3 + 13x − 12
x − 2 -->
x + 3 -->
x + 4 -->
x + 5 -->
Answer:
[tex]x-2 => f(x)=x^{3}-2x^{2}-x+2\\x+3=>f(x)=x^{3}-3x^{2} -13x+15\\x+4=>f(x)=-x^{3}+13x-12\\x+5=>f(x)=x^{4}+3x^{3}-8x^{2}+5x-25[/tex]
Step-by-step explanation:
The value of a function will be zero if the factor is put in it. In order to check whether a factor is of a function or not we will put the value of x from that factor in the function:
So
x-2 = 0 => x=2
Putting in first function
[tex]x^{3}-3x^{2} -13x+15\\=(2)^{3}-3(2)^{2} -13(2)+15\\=8-3(4)-26+15\\=8-12-26+15\\=23-38\\=-15 \neq 0\\[/tex]
So x-2 is not a factor of first function.
Putting in second function
[tex]f(x)=x^{4}+3x^{3}-8x^{2}+5x-25\\ =(2)^{4}+3(2)^{3}-8(2)^{2}+5(2)-25\\=16+3(8)-8(4)+10-25\\=16+24-32+10-25\\=-7\neq 0[/tex]
So x-2 is also not a factor of second function.
Putting in third function:
[tex]f(x)=x^{3}-2x^{2}-x+2\\ =(2)^{3}-2(2)^{2}-2+2\\=8-2(4)-2+2\\=8-8-2+2\\=0[/tex]
So x-2 is factor of third function.
...........................
For x+3
x+3=0
x=-3
First function:
[tex]f(x)=x^{3}-3x^{2} -13x+15\\=(-3)^{3}-3(-3)^{2} -13(-3)+15\\=-27-3(9)+39+15\\=-27-27+39+15\\=-54+54\\=0\\[/tex]
So x+3 is a factor of first function.
.............................
For x+4
x+4=0
x=-4
As we have already found the factors of first and third function, we will now only check second and fourth function.
[tex]f(x)=x^{4}+3x^{3}-8x^{2}+5x-25\\ =(-4)^{4}+3(-4)^{3}-8(-4)^{2}+5(-4)-25\\=256+3(-64)-8(16)-20-25\\=256-192-128-20-25\\-109\neq 0[/tex]
So x+4 is not a factor of second function.
Putting in fourth function:
[tex]f(x)=-x^{3}+13x-12\\ =-(-4)^{3}+13(-4)-12\\=64-52-12\\=64-64\\=0\\[/tex]
So x+4 is a factor of fourth function
..........................
For x+5=0
x=-5
Since only one function is remaining we'll only check for that.
[tex]f(x)=x^{4}+3x^{3}-8x^{2}+5x-25\\ =(-5)^{4}+3(-5)^{3}-8(-5)^{2}+5(-5)-25\\=625+3(-125)-8(25)-25-25\\=625-375-200-25-25\\=0\\[/tex]
The result of multiplying two or more numbers is called
The numbers you are multiplying are called the factors the result is called the product.
Answer: Product?
Step-by-step explanation:
Adding: Sum
Subtracting: Difference
Dividing: Quotient
Multiplying: Product
Hope this helps
56% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.
(a) ≈ 0.202, (b) ≈ 0.878, (c) ≈ 0.376, calculated using binomial probability formula with 56% chance for baseball fans.
To solve this problem, we can use the binomial probability formula since we have a fixed number of trials (selecting 10 men) and each trial (man) has two possible outcomes (considering themselves a baseball fan or not).
The binomial probability formula is:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
- [tex]\( P(X = k) \)[/tex] is the probability of getting exactly \( k \) successes,
- [tex]\( n \)[/tex] is the number of trials (in this case, 10 men),
- [tex]\( k \)[/tex] is the number of successes we are interested in (number of men considering themselves baseball fans),
- [tex]\( p \)[/tex] is the probability of success on each trial (in this case, 56% or 0.56),
- [tex]\( \binom{n}{k} \)[/tex] is the binomial coefficient, representing the number of ways to choose [tex]\( k \)[/tex] successes from [tex]\( n \)[/tex] trials.
Let's solve each part of the problem:
(a) Finding the probability of exactly five men considering themselves baseball fans:
[tex]\[ P(X = 5) = \binom{10}{5} \times (0.56)^5 \times (1 - 0.56)^{10 - 5} \][/tex]
(b) Finding the probability of at least six men considering themselves baseball fans. This is the sum of probabilities of having 6, 7, 8, 9, or 10 successes:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
(c) Finding the probability of less than four men considering themselves baseball fans. This is the sum of probabilities of having 0, 1, 2, or 3 successes:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
Let's calculate each part:
(a)
[tex]$\begin{aligned} & P(X=5)=\left(\begin{array}{c}10 \\ 5\end{array}\right) \times(0.56)^5 \times(1-0.56)^{10-5} \\ & =\left(\begin{array}{c}10 \\ 5\end{array}\right) \times(0.56)^5 \times(0.44)^5 \\ & \approx 0.202\end{aligned}$[/tex]
(b)
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \]\[ = \sum_{k=6}^{10} \binom{10}{k} \times (0.56)^k \times (0.44)^{10 - k} \]\[ \approx 0.878 \][/tex]
(c)
[tex]$\begin{aligned} & P(X < 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3) \\ & =\sum_{k=0}^3\left(\begin{array}{c}10 \\ k\end{array}\right) \times(0.56)^k \times(0.44)^{10-k} \\ & \approx 0.006+0.034+0.111+0.225 \\ & \approx 0.376\end{aligned}$[/tex]
So, the probabilities are:
(a) [tex]\( \approx 0.202 \)[/tex]
(b) [tex]\( \approx 0.878 \)[/tex]
(c) [tex]\( \approx 0.376 \)[/tex]
Find the volume of the cone shown below.
Answer:
D
Step-by-step explanation:
The formula for volume of cone is [tex]V=\frac{1}{3}\pi r^2 h[/tex]
Where
V is the volume
r is the radius of the circular base
h is the height of the cone
In the diagram shown, we can clearly see that height is 12, radius is 9. We can simply plug them into the formula and get our exact answer (leaving pi as pi):
[tex]V=\frac{1}{3}\pi (9)^2(12)\\=324 \pi[/tex]
correct answer is D
What is the phase shift of y = cos(3x - 3pi/4 )?
Use the form
a
cos
(
b
x
−
c
)
+
d
acos(bx-c)+d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
4
a=4
b
=
3
b=3
c
=
π
4
c=π4
d
=
0
d=0
Find the amplitude
|
a
|
|a|
.
Amplitude:
4
4
Find the period using the formula
2
π
|
b
|
2π|b|
.
Tap for more steps...
Period:
2
π
3
2π3
Find the phase shift using the formula
c
b
cb
.
Tap for more steps...
Phase Shift:
π
12
π12
Find the vertical shift
d
d
.
Vertical Shift:
0
0
List the properties of the trigonometric function.
Amplitude:
4
4
Period:
2
π
3
2π3
Phase Shift:
π
12
π12
(
π
12
π12
to the right)
Vertical Shift:
0
0
i think ;-;
Answer:
[tex]\frac{\pi }{4}[/tex]
Step-by-step explanation:
The standard form of the cosine function is
y = a cos(bx + c)
where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and
phase shift = - [tex]\frac{c}{b}[/tex]
here b = 3 and c = - [tex]\frac{3\pi }{4}[/tex], hence
phase shift = - [tex]\frac{-\frac{3\pi }{4} }{3}[/tex] = [tex]\frac{\pi }{4}[/tex]
Subtraction:
57 - 28 = ? Show how to solve it step by step.
Answer:
29
Step-by-step explanation:
50 - 20 = 30
7 - 8 = -1
30 - 1 = 29
Express 4.54545454545... as a rational number, in the form pq where p and q are positive integers with no common factors.
Answer:
the final answer is 50/11
Step-by-step explanation:
Here let's regard the first number of this geometric series as 0.54, holding the 4 to include later. The next is 0.0054, the next 0.000054, and so on.
Thus, the common ratio is 1/100. Then the sum of the infinite series, not including that 4, is
a 0.54 0.54
-------- = ------------ = ------------
1 - r 1 - 1/100 99/100
54
Multiplying both 0.54 and 99/100 by 100 results in ------- and this
99 0.545454....
Now add the 4 back in, obtaining 4 54/99, or (396 + 54) / 99.
This is the same as 450 / 99. You can readily check with a calculator to see whether this is equivalent to the given 4.54545454545...
Note that 450/99 is in the form p/q (not pq), where p and q are positive integers. But also note that 450/99 can be reduced to 150/33, or
50/11. A calculator will show you that 50/11 is equivalent to the given 4.54545454545...
Hence, the final answer is 50/11 (in the form p/q, NOT pq).
The number 4.54545454545... can be expressed as a rational number in the form of p/q as 50/11.
Explanation:To express the given number 4.54545454545... as a rational number in the form p/q, we need to use the concept of repeating decimals.
Let x = 4.54545... We can then write 100x = 454.54545... Subtracting the first equation from the second, we get 99x = 450. Solving for x gives us x = 450/99.
This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor. In this case, 450 and 99 share a common factor of 9. Dividing both numbers by 9 gives us 50/11, which is the simplest form of this fraction.
Therefore, 4.54545454545... as a rational number in the form p/q is 50/11.
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A series of transformations on quadrilateral S resulted in quadrilateral T.
~The angle measures of quadrilaterals T are congruent to those of quadrilateral S
~The side lengths of quadrilateral T are twice as long as those of quadrilateral S
Which transformation on quadrilateral S must be included to result in quadrilateral T?
A) Dilation
B) Rotation
C) Reflection
D) Translation
Dilation since one image is bigger than the other
A dilation transformation must be included to result in quadrilateral T.
Explanation:To result in quadrilateral T, a dilation transformation must be included. A dilation is a transformation that changes the size of the figure without changing its shape. In this case, the side lengths of quadrilateral T are twice as long as those of quadrilateral S, indicating a scaling factor of 2. Therefore, a dilation is needed to scale up the size of quadrilateral S by a factor of 2 to obtain quadrilateral T.
A cone has a volume of $12288\pi$ cubic inches and the vertex angle of the vertical cross section is 60 degrees. what is the height of the cone? express your answer as a decimal to the nearest tenth.
Answer:
The height of the cone is [tex]48\ in[/tex]
Step-by-step explanation:
step 1
Find the radius of the base of cone
we know that
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]V=12,288\pi\ in^{3}[/tex]
[tex]tan(30\°)=\frac{r}{h}[/tex] ---> remember that the vertex angle of the vertical cross section is 60 degrees
so
[tex]r=(h)tan(30\°)[/tex]
[tex]r=(h)\frac{\sqrt{3}}{3}[/tex]
substitute the values and solve for h
[tex]12,288\pi=\frac{1}{3}\pi ((h)\frac{\sqrt{3}}{3})^{2} h[/tex]
[tex]36,864=\frac{h^{3}}{3}[/tex]
[tex]h^{3}=110,592[/tex]
[tex]h=48\ in[/tex]
Of the 500000 people (age 16+) in a particular country 300000 people are in the labor force. of the 240000 are employed and 60000 are unemployed what is the unempoyment rate
Answer:
12%
Step-by-step explanation:
60000 people are unemployed, out of 500000 people.
That means that 60000/500000 of the population is unemployed.
Simplify: 60000/500000 = 6/50 = 0.12 = 12%
The overall unemployment rate is will be 12% based on the given data.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Total people = 5000000
40000 are employed and 60000 are unemployed out of 300000 people are in the labor force.
The % unemployment rate = (60000)/500000 x 100 = 12%
Hence "The overall unemployment rate is will be 12% based on the given data".
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2(x + 7) + 3x = 12
What is the first step in solving this equation for x?
A) 2x + 14 + 3x = 12
B) 2x + 7 + 3x = 12
C) 2x + 14 = 9
Eliminate
D) 5x = -2
A would be the very first step in solving the equation for x
You have to distribute 2 to x and 7.
2(x + 7) + 3x = 12
2x + 14 +3x = 12
Answer:
A) 2x + 14 + 3x = 12
Step-by-step explanation:
The first step is to distribute the 2
2(x + 7) + 3x = 12
2x+14 +3x =12
Then we combine like terms
5x+14 =12
Subtract 14 from each side
5x+14-14=12-14
5x = -2
Then divide each side by 5
5x/4 = -2/5
x = -2/5
The manager of a local basketball arena wants to survey fans attending a game at the arena about other sports they enjoy.
Select Yes or No to tell whether each method results in a random sample of the population.
Answer:
Yes, no, no, no
Step-by-step explanation:
The first method is random. There's no bias in selecting fans spaced out evenly as they enter.
The second method is not random. It is biased towards those who hear the announcement and wish to participate.
The third method is not random. It is biased towards those in the biggest rush to leave.
The fourth method is not random. It is biased towards those with the best seats.
I AM OFFERING 50 POINTS FOR THIS ANSWER. PLEASE HELP ME !
Answer:
question 8: 30975
question 9:
I don't know if it wants me to find the interest from the bond or the quote price of the bond.
If it is the bond it would be $1400 interest.
If it is the quote price of the bond, it would be $1,239 interest.
use de moivres theorem to write the complex number in trigonometric form.
[sqrt(2)(cos(10)+isin(10)]^6
By DeMoivre's theorem,
[tex](\sqrt2(\cos10^\circ+i\sin10^\circ))^6=(\sqrt2)^6(\cos60^\circ+i\sin60^\circ)[/tex]
[tex]=8(\cos60^\circ+i\sin60^\circ)[/tex]
The answer is 8(cos60° +isin 60°)
Demoivre's theorem:, De Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it holds that (cosx + i sinx)^n= cosnx + i sinnx.
where i is the imaginary unit (i2 = −1).
By DeMoivre's theorem:
[sqrt(2)(cos(10)+isin(10)]^6
(√2 (cos 1o° + isin 10°))^6 = (√2)^6(cos 60° + isin 60°)
=8(cos60° +isin 60°)
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evaluate the function for an input of 0
Answer:
4
Step-by-step explanation:
The table clearly shows that if x = 0, y = 4.
The required output for the input of 0 in the function is 4.
Given that,
A table is shown the input and output value of the function, we have to determine the output value of the function for the corresponding input value 0.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the table,
f(x) shows the output for the corresponding input x,
In the given question for x = 0 {input} there is f(0) = 4 in the table,
Thus, the required output for the input of 0 in the function is 4.
learn more about function here:
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The standard size of a rectangular placemat is 14 inches by 16 inches. How much fabric is needed to make 6 standard placemats?
90 in²
224 in²
672 in²
1,344 in²
Answer:
D. 1,344 in^2
Step-by-step explanation:
The area of the standard placemats is 84 in^2. To make 6 we need to multiply that by 6. 84 in^2*6 is 1,344 in^2. Please rate brainliest. It would really help!
Answer:
Option D
Step-by-step explanation:
The standard size of the rectangular placemat is 14 inches by 16 inches.
So fabric needed to make a placemat = Length × Width
= 14 × 16
= 224 inch²
Now for 6 placemats fabric required = 6 × 224
= 1344 inch²
Option D is the answer.
Nicole runs a farm stand that sells bananas and peaches. Each pound of bananas sells for $2 and each pound of peaches sells for $3.25. Nicole sold 3 more pounds of bananas than pounds of peaches and made $231.75 altogether. Write a system of equations that could be used to determine the number of pounds of bananas sold and the number of pounds of peaches sold. Define the variables that you use to write the system.
Answer:
The required system of equations is:
2x + 3.25y = 231.75
x = y + 3
where x is the number of pounds of bananas and y is the number of pounds of peaches
Explanation:
1- Defining the variables:
Assume that the number of pounds of bananas sold is x
Assume that the number of pounds of peaches sold is y
2- Setting the system of equations:
We are given that:
i. Each pound of bananas sells for $2
Money gained from selling x pounds of bananas is 2x
ii. Each pound of peach sells for $3.23
Money gained from selling y pounds of peaches is 3.25y
iii. Nicole made $231.75 in total. This means that:
2x + 3.25y = 231.75 .................> equation I
iv. Nicole sold 3 more pounds of bananas than pounds of peaches. This
means that:
pounds of bananas = pounds of peaches + 3
x = y + 3 ..................> equation II
3- Solving the equations (if required):
In equation II, we have: x = y + 3
Substitute with equation II in equation I and solve for y as follows:
2x + 3.25y = 231.75
2(y+3) + 3.25y = 231.75
2y + 6 + 3.25y = 231.75
5.25y = 231.75 - 6
5.25y = 225.75
y = 43
Substitute with y in equation II to get x:
x = y + 3
x = 43 + 3 = 46
Based on the above:
Number of pounds of bananas = x = 46 pounds
Number of pounds of peaches = y = 43 pounds
Hope this helps :)
A town doubles its size every 30 years. If the population is currently 10,000, what will the population be in 60 years?
Answer: 20,000
Step-by-step explanation:
every 30 years 10,000 adds to the population
30 years=10,000 people
60 years=20,000 people
Help with this question, please!! I don't understand it!!
Answer:
BC = 52
Step-by-step explanation:
The point of the question is to have you recognize and use the fact that the tangent segments from the same point are of equal length. That lets you write the equation ...
4x +8 = 2(3x -7) . . . BC = BA
2x +4 = 3x -7 . . . . . divide by 2
11 = x . . . . . . . . . . . . add 7-2x
The length of segment BC is computed using this value of x:
BC = 4x +8 = 4·11 +8
BC = 52
I am begging someone to help me.
Answer:
B. The sum of the squares of the two smaller sides is equal to the square of the third side.
Step-by-step explanation:
It can be helpful to recognize that the given side lengths, 12, 16, 20 are in the ratio 3:4:5, a recognizable Pythagorean triple. That is, you may know already that the triangle is a right triangle and the sum of squares of the short sides is equal to the square of the longest side (choice B).
In case you aren't aware of common Pythagorean triples, or didn't recognize these numbers, you can try the options to see which fits.
A. The sum of the two smaller sides is 12 +16 = 28. It is NOT equal to the third side, 20.
__
B. The sum of the squares of the two smaller sides is 12^2 + 16^2 = 144 + 256 = 400. This IS equal to the square of the third side: 20^2 = 400.
__
C. The absolute value of the difference between the squares of the two smaller sides is |256 -144| = 112. This is NOT equal to the square of the third side, 20^2 = 400.
__
D. The sum of the squares of the two smaller sides is 400 (as above). It is NOT equal to the third side, 20.
___
The only answer choice that fits is choice B.
Match each curve to the area under it on the interval [-1, 5]. y = x2 + 16 42 square units y = -x2 + 7x 72 square units y = 4x + 26 204 square units y = -0.5x + 13 138 square units
Answer:
1. [tex]\boxed{y=x^2+16\to138sq.\:units}[/tex]
2. [tex]\boxed{y=-x^2+7x\to42sq. \:units}[/tex]
3. [tex]\boxed{y=4x+26\to 204sq.\:units}[/tex]
4.[tex]\boxed{y=-0.5x+13\to72sq.\:units}[/tex]
Step-by-step explanation:
1. The first curve is [tex]y=x^2+16[/tex]
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {x^2+16} \, dx[/tex]
We integrate to obtain:
[tex]\frac{1}{3}x^3+16x|_{-1}^5[/tex]
We evaluate to obtain:
[tex]\frac{1}{3}(5)^3+16(5)-(\frac{1}{3}(-1)^3+16(-1))=138sq.\:units[/tex]
[tex]\boxed{y=x^2+16\to138sq.\:units}[/tex]
2. The second curve is [tex]y=-x^2+7x[/tex].
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {-x^2+7x} \, dx[/tex]
We integrate this function to obtain:
[tex]-\frac{1}{3}x^3+\frac{7}{2}x^2|_{-1}^5[/tex]
This evaluates to
[tex]-\frac{1}{3}(5)^3+\frac{7}{2}(5)^2-(-\frac{1}{3}(-1)^3+\frac{7}{2}(-1)^2)=42[/tex] square units.
[tex]\boxed{y=-x^2+7x\to42sq. \:units}[/tex]
3. The third curve is [tex]y=4x+26[/tex]
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {4x+26} \, dx[/tex]
We integrate this function to obtain:
[tex]2x^2+26x|_{-1}^5[/tex]
We evaluate the limits of integration to obtain:
[tex]2(5)^2+26(5)-(2(5)^2+26(5))=204sq.\:units[/tex]
[tex]\boxed{y=4x+26\to 204sq.\:units}[/tex]
4. The fourth curve is [tex]y=-0.5x+13[/tex]
The area under this curve on the interval [-1, 5] is given by:
[tex]\int\limits^5_{-1} {-0,5x+13} \, dx[/tex]
We integrate this function to obtain:
[tex]-0.25x^2+13x|_{-1}^5[/tex]
We evaluate the limits of integration to obtain:
[tex]-0.25(5)^2+13(5)-(-0.25(-15)^2+13(-1))=72sq.\:units[/tex]
[tex]\boxed{y=-0.5x+13\to72sq.\:units}[/tex]
Which situation can be modeled by the inequality 50−12x≥8?
The situation that can be modeled by the given inequality is required.
Option D. is correct.
Let [tex]x[/tex] be the number of T shirts bought
The initial amount of money is $50
The savings should be at least $8 so more than or equal to $8.
The required inequality is [tex]50-12x\geq 8[/tex]
The inequalities of the other options that are not correct are
C. [tex]50-12x<8[/tex]
Here, [tex]x[/tex] is number of weeks
B. [tex]50-12x\geq 8[/tex]
Here [tex]x[/tex] is the number of packages bought.
So, [tex]12x[/tex] will be the total number of pretezels[/tex]
A. [tex]50-8x<12[/tex]
Here [tex]x[/tex] is the number of weeks.
So, option D. is correct.
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Convert the exact rectangular coordinates to polar coordinates.
if the rectangular coordiante is (x,y) and the polar coordinate is (R,t), then they are related as follows:
R^2=x^2+y^2
tant=y/x
1.(pi,pi/4)
here, R=
[tex] \sqrt{ {\pi}^{2} + { (\frac{\pi}{4} })^{2} } = \sqrt{ \frac{17 {\pi}^{2} }{16} } = \frac{\pi}{4} \sqrt{17} \\tant = \frac{ \frac{\pi}{4} }{4} \\ t = {tan}^{ - 1} \pi = 89.682[/tex]
therefore the polar form of Q.1 is
(pi sq. root 17/4,89.682°)
you can do 2 in similar way.
I need help with a pre-calc problem I really don't understand how to solve it
(the answer is: 101.496936 feet above the ground.)
And please explain how you got the answer step-by-step, thank you:))
Answer:
Step-by-step explanation:
We know a maximum point on the height vs. time curve is at t=16 seconds. Then the height function can be written by filling in the known values in ...
h(t) = (center height) + (wheel radius)·cos((frequency)·2π·(t -(time at max height)))
Since t is in seconds, we want the frequency in revolutions per second. That will be ...
(3.2 rev/min)·(1 min)/(60 sec) = 3.2/60 rev/sec = 4/75 rev/sec
Then our height function is ...
h(t) = 59 + 45·cos(8π/75·(t -16))
9 minutes is 9·60 sec = 540 sec, so we want to find the value of h(540).
h(540) = 59 + 45·cos(8π/75·(540 -16))
= 59 +45·cos(4192π/75)
≈ 59 + 45·0.944376 . . . . . calculator in radians mode
≈ 101.496937 . . . . feet
_____
The cosine function is a maximum when its argument is zero. We used the process of function translation to translate the maximum point to t=16 from t=0. That is, we replaced t in the usual cosine function with (t-16).
We can also evaluate the cosine function by subtracting multiples of 2π from the argument. When we do that, we find that Shirley's height at 9 minutes is the same as it is after 15 seconds. Some calculators evaluate smaller cosine arguments more accurately than they do larger argument values.
In the figure, m∠1 = m∠2 = 22 and m∠3 = m∠4 = 123. From this, you can conclude that m∠TKL = _____
a. 22.
b. . 57.
c. 35.
d. 47.
Answer:
57°
Step-by-step explanation:
Angle 3 is supplementary to angle TKL. That means they add up to 180°. Therefore, 180° - 123° = 57°
Answer:
57°
Step-by-step explanation:
You can notice that by putting ∠3 and ∠TKL together you have a flat angle.
A flat angle has 180 degrees.
so, you can say that m∠3 and m∠TKL add 180 degrees, then they are supplementary angles.
Remember: Two angles are supplementary if they add 180 degrees.
Then, as you know m∠3=123°:
m∠3 + m∠TKL=180°
123 + m∠TKL=180°
m∠TKL=180° - 123°
m∠TKL=57°
Johan used the table below to show the sample space for choosing an outfit for school.
Which outfit is part of Johan’s sample space?
·black pants, white shirt
·gray pants, green shirt
·blue pants, brown shirt
·white pants, white shirt
Black pants , white shirt
Answer:
·black pants, white shirt
Step-by-step explanation:
Shirt Colors : Yellow Purple Gray Green white
Pant Colors = Blue Green Black Brown
Combinations can be:
(Shirt color, Pant color)
(Yellow,Blue)
(Yellow,Green)
(Yellow,Black)
(Yellow,Brown)
(Purple,Blue )
(Purple,Green)
(Purple,Black)
(Purple,Brown)
(Gray,Blue)
(Gray,Green)
(Gray,Black)
(Gray,Brown)
(Green,Blue)
(Green,Green)
(Green,Black)
(Green,Brown)
(White,Blue)
(White,Green)
(White,Black)
(White,Brown)
Now we are given that Which outfit is part of Johan’s sample space
Option A : ·black pants, white shirt
True . It belongs to sample space
Option B : gray pants, green shirt
False . It does not belongs to sample space.
Option C : ·blue pants, brown shirt
False . It does not belongs to sample space.
Option D : white pants, white shirt
False . It does not belongs to sample space.
Hence Option A is true