Answer:
[tex]theta = \frac{3}{2} \pi + 2k\pi[/tex]
Step-by-step explanation:
+2*k*pi is for the periodicity (if you turn 360° you get back to the same point)
What is the axis of symmetry for y = 3x^2 + x - 2
A giant pie is created in an attempt to break a world record for baking. The pie is shown below:
What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
Answer:
Area of the slice of pie = 22.09 ft²
Step-by-step explanation:
Area of the slice of pie = Area of the sector of the circle with the central angle 45°
Area of the sector = [tex]\frac{\theta}{360^{\circ}}(\pi r^{2} )[/tex] [Here, r = radius of the circle]
= [tex]\frac{45^{\circ}}{360^{\circ}}(\pi )(\frac{15}{2})^2[/tex]
= 22.09 ft²
Area of the slice of pie = 22.09 ft²
Answer:
22.08ft^2
Step-by-step explanation:
A = πr^2(x/360) d = 15
Since r is half of diameter this means that r = 15/2 =7.5
so Lets use the Area of Sector formua
A =3.14(7.5)^2 (45/360)
A =3.14(56.25) (45/360)
A = 176.625 (45/360)
A = 176.625 (0.125)
A = 22.078125
rounded to the nearest 10th would make it 22.08
At a particular restaurant, each slider has 225 calories and each chicken wing has 70 calories. A combination meal with sliders and chicken wings has a total of 7 sliders and chicken wings altogether and contains 1110 calories. Write a system of equations that could be used to determine the number of sliders in the combination meal and the number of chicken wings in the combination meal. Define the variables that you use to write the system.
Answer:
X+y=7
Step-by-step explanation:
i remember doing something like this but mines had the word onion rings .
can i get some help solving this
Answer:
A =147 cm^2
Step-by-step explanation:
A = pi r^2
The radius is 7 and let pi = 3
A = 3*7^2
A = 3*49
A =147
For this exponential function,
what is the output value (y),
when the input value (x) is 3?
y = 10.5x.
(3, [?])
Replace x with 3 and solve:
10 x 5^3
Simplify:
10 x 125 = 1250
Answer: y = 1250
(3 , 1250)
Step-by-step explanation:I got it right on my test.
It took francisco 60 minutes to walk from his house to his grandmother’s house. what is 60 written as a product of factors greater than 1? each factor can have only 1 and itself as factors.
Answer:
2 × 2 × 3 × 5
Step-by-step explanation:
Given that,
The number = 60
To find,
Factors of 60 greater than 1 = ?
Procedure:
As we know,
Any of various numbers multiplied together to form a whole.
To find the factors of a number, we will have to do its prime factorization.
So,
The prime factorization of 60:
1 * 2 * 2 * 3 * 5 = 60
Since the factors greater than 1 are asked, the factors would be;
2 * 2 * 3 * 5
Thus, 2 * 2 * 3 * 5 is the correct answer.
y=8200(0.96)^x growth or decay find
Answer:
This would be a .04 or 4% decay.....
for every "time unit" (x in this case) you will be multiplying
the amount by .96 ... in other words if you started with one dollar
the results would be 96 cents... after two "time" steps you would have
only 92 cents (.96 *.96)
Step-by-step explanation:
Emily puts away basketballs after the gym class. there are 15 basketballs, and each rack holds 4 basketballs. how many racks does Emily completely fill? How many basketballs are left?
Answer:
emily fills 3 racks
3 basketballs are Left!
Step-by-step explanation:
15/4 = 3.3
32
Two forces one is 10N and other is 6N act on a body The directions are unknown the resultant force on the body is
a. between 4 and 16N
b. more than 6N I
c. more than 1ON
d between 6 and 16N
If Forces are acting on opposite direction
[tex]\\ \rm\hookrightarrow F_{net}=F_2-F_1[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=10-6[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=4N[/tex]
If both acting on same direction
[tex]\\ \rm\hookrightarrow F_{net}=F_1+F_2[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=10+6[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=16N[/tex]
Hence
[tex]\boxed{\sf 4N\leqslant F_{net}\leqslant 16N}[/tex]
A garden is rectangular with a width of 8 feet and a length of 10 feet. If it is surrounded by a walkway 2 feet wide, how many square feet of area does the walkway cover?
Answer:
The rea of walk way is 32 ft^2.
Step-by-step explanation:
width, w = 8 feet
length, L = 10 feet
width of walkway, d = 2 feet
length of outer, L' = 10 + 2 + 2 = 14 feet
Area of outer, A' = L' x w = 14 x 8 = 112 ft^2
Area of inner, A = L x w = 10 x 8 = 80 ft^2
The area of walkway = A' - A = 112 - 80 = 32 ft^2
The rea of walk way is 32 ft^2.
What's 672 divided by 32
Suppose that d varies jointly with r and t, and d = 110 when r = 55 and t = 2. Find r when d = 40 and t = 3.
Answer:
r = 13.33
Step-by-step explanation:
d = k*r*t
Where,
k = constant of proportionality
d = 110 when r = 55 and t = 2
d = k*r*t
110 = k * 55 * 2
110 = 110k
k = 110/110
k = 1
Find r when d = 40 and t = 3
d = k*r*t
40 = 1 * r * 3
40 = 3r
r = 40/3
= 13.333333333333
Approximately,
r = 13.33
A. -5x+4y=-20
B. -5x-4y=-20
C. -5x+4y=0
D. 5x+4y=-20
b) 2x (x - y) + 3y (x - y)
Use distributive law
[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]
Now
[tex]\\ \sf\longmapsto 2x(x-y)+3y(x-y)[/tex]
[tex]\\ \sf\longmapsto 2x^2-2xy+3xy-3y^2[/tex]
[tex]\\ \sf\longmapsto 2x^2-3y^2-2xy+3x^2[/tex]
[tex]\\ \sf\longmapsto 2x^2-3y^2+xy[/tex]
Taking common
Answer: 2x (x-y) + 3y (x-y)
= ( x-y ) ( 2x-3y )
Find the values of x and y.
Answer:
I think it's 43 and 43 degrees. I just subtracted 180-94, got 86, and divided it so yea.
After 10 years, Hamid's account earned $900 in interest. If the interest rate (in decimal form) is 0.08, how much did Hamid initially invest? Without substitution, solve the formula chosen in the previous step for the unknown variable in terms of the known variable(s).
Answer:
Hamid initially invested $1,125.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After 10 years, Hamid's account earned $900 in interest.
This means that [tex]t = 10, E = 900[/tex]
Interest rate of 0.08:
This means that [tex]I = 0.08[/tex]
How much did Hamid initially invest?
We have to find P. So
[tex]E = P*I*t[/tex]
[tex]900 = P*0.08*10[/tex]
[tex]P = \frac{900}{0.8}[/tex]
[tex]P = 1125[/tex]
Hamid initially invested $1,125.
Rihanna works in a coffee shop approximately nine miles from her apartment She bikes every day from her apartment to the coffee shop and then back to her apartment in the evening. However, on her way to work, she always stops halfway through to meet her best friend at a park. If the distance from apartment to the park is (5x +2) miles and the trip from the park to the coffee shop is (25x -8) miles long, then what is the value of x?
Answer:
x = 0.5
Step-by-step explanation:
When we add up the distance between the apartment and park with the distance between the park and the coffee shop, the total will equal nine miles.
Our equation will look like this:
(5x + 2) + (25x - 8) = 9
Add up the like terms
5x + 2 + 25x - 8 = 9
30x - 6 = 9
Add 6 to both sides
30x - 6 = 9
+ 6 + 6
30x = 15
Divide both sides by the coefficient, 30, to isolate the variable, x
30x/30 = 15/30
x = 15/30
Reduce
x = 1/2
A walker has travelled 9 km along a trail. If he has completed 80% of the trail, how much further does he still have to go?
Answer:
2.25 km to go
Step-by-step explanation:
In order to get this answer, you have to figure out how many km 10% is, 0.1125. Then multiply that by the remaining 20% because he already finished 80% of the trail. So, 0.1125 x 20 = 2.25.
Hope this helps! :)
Can someone help me on this please
Given an arithmetic progression 17,13,9,..... find the number of terms required so that its sum is - 33 .
Answer:
11 terms.
Step-by-step explanation:
We are given the arithmetic sequence:
17, 13, 9, ...
And we want to find the number of terms required such that the sum is -33.
Recall that the sum of an arithmetic series is given by:
[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]
Where k is the number of terms, a is the first term, and x_k is the last term.
The desired sum is -33. The first term is 17 as well. Thus:
[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]
Simplify:
[tex]-66 = k(17 + x_k)[/tex]
We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:
[tex]x_ n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The initial term is 17 and the common difference is -4. Hence:
[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]
Then the last term is given by:
[tex]x_k = 17 - 4(k-1)[/tex]
Substitute:
[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]
Since we cannot have a negative amount of terms, we can ignore the second solution.
Therefore, the given sequence must have 11 terms such that it sums to -33.
Answer:
Here is 2 methods
Step-by-step explanation:
1) we use excel to find n=11 for lasy students
2) mathematical method
[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]
[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]
(06.01)A scatter plot is shown:
A scatter plot is shown. Data points are located at 1 and 8, 2 and 7.8, 3 and 7.4, 4 and 6.5, 5 and 5.4, 6 and 4.5, 7 and 3.1, 8 and 2, 9 and 1.
ASAP:
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
Step-by-step explanation:
If you plot those coordinates in your calculator in the stat plot function under "stat", you will see that the dots are almost but not quite in a straight line going from upper left to lower right. This indicates a strong negative linear association, third choice down.
Answer:
D. Nonlinear Negative Association
Step-by-step explanation:
sin x = 4/5, cos x = 2/5 find the value of tan x
Answer:
2 is the answer . the explanation is in the attachment .
-1/2 divided by 1/19
Answer:
-19/2 or
-9 1/2
Step-by-step explanation:
-1/2 ÷ 1/19
Copy dot flip
-1/2 * 19/1
-19/2
-9 1/2
pls pls pls pls help
Step-by-step explanation:
[tex]s = \pi \times {r}^{2} = \pi \times {6}^{2} = 36\pi[/tex]
[tex]h = 18 \times \sin(60) = 9 \sqrt{3} [/tex]
[tex]v = s \times h = 36\pi \times 9 \sqrt{3} = 324 \sqrt{3} \pi[/tex]
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
Answer:
0,1,2,3,4,5,6.......19,20
Step-by-step explanation:
in this interval 0 is included and 21 is not included. So starting from 0 up to 20, all are the solutions
(b) A shopkeeper gives 20% discount on the marked price of a television set. The VAT amount at the rate of 13% is Rs. 2,600. Find the marked price and the amount of discount.
Answer:
6.3
Step-by-step explanation:
i had the same question for school
9. Find the remainder when the polynomial: p(x) = x⁴ + 2x³- 3x² + x - 1 is divided by (x - 2)
pls it's urgent
Answer:
answer is 21..............
Explanation:
p(x) = x⁴ + 2x³- 3x² + x - 1
Factor of p(x)
x-2=0
x=2
Then by using synthetic division
which inequality is represented on the number line shown?
Answer: A x> -2
Step-by-step explanation:
please ans this question pleaseee
Answer:
[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]
Helpo pleasssse
On my hw I have a parabola that opens down with its vertex at (-3,-6)......
For the range would I say that {yER | y > -6} OR {yER | y < -6} ????
I'm just confused from the negative numbers
Answer: The range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
Explanation:
The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.
The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.
Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
This translates to "y is a real number such that y is -6 or smaller".
So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.
See below for a visual example of what's going on.