Answer:
A
Step-by-step explanation:
First, let's label the variables:
[tex]\text{Let }x \text{ represent Kaylee's number of pens,}\\\text{Let }L \text{ represent Lou's number of pens,}\\\text{And let }I \text{ represent Ilene's number of pens.}[/tex]
The first and second sentence, Kaylee at the start has x pens. She gave half to Lou, who started out with two fewer than Kaylee.
In other words, the total Lou now has is:
[tex]L=(\frac{1}{2}x )+(x-2)[/tex]
The first term represents what Kaylee gave to Lou. The second term represents what Lou had originally (two fewer than Kaylee [x]).
Simplifying, we get:
[tex]L=\frac{3}{2}x-2[/tex]
Third sentence. Lou give half of his new total to Ilene, who started out with three fewer pens than Lou. Lou, remember, started with three fewer than Kaylee (x-2). In other words:
[tex]I=(\frac{1}{2}(\frac{3}{2}x-2) )+((x-2)-3)[/tex]
The left represents what is given to Ilene: one-third of Lou's new total. The right represents Ilene's original total: three fewer than Lou: or five fewer than Kaylee. Simplifying gives:
[tex]I=(\frac{3}{4} x-1)+(x-5)\\I=\frac{7}{4}x-6[/tex]
Finally, Ilene gives a third of this new amount to Kaylee, and Kaylee's final amount is 37. Thus:
[tex]37=x-\frac{1}{2}x+\frac{1}{3}(\frac{7}{4}x-6)[/tex]
The first term represents what Kaylee originally started with. The second term represents what she gave to Lou. And the third term represents what Ilene gave to Kaylee. Simplify:
[tex]37=\frac{1}{2}x+\frac{7}{12}x-2\\39=\frac{6}{12}x+\frac{7}{12}x \\39=\frac{13}{12}x\\ 468=13x\\x=36[/tex]
Find the value of this expression if x=3 x^2 + 3/x-1
Answer: 9
Step-by-step explanation:
[tex]3^2 + \frac{3}{3}-1\\\\=9+1-1\\\\=9[/tex]
HELPPPP The equation 2x = 3y – 5 when written in slope-intercept form is: y = 2x – 5. y = -2x + 5. y = 2x + 5. None of these choices are correct.
Answer:
Y= 2/3x +(5/3)
Step-by-step explanation:
First, have to get Y alone on one side 3y=2x+5
Second, have to get read of the 3 with the Y so divide each side by three.
In the figure, OM is perpendicular to AB. Prove that M is the the midpoint of AB.
we know by looking at the picture that m is the midpoint of AB since O to M doted lines had half into two equal parts.so M is in the midpoints of AB.
Step-by-step explanation:
to prove: M is the midpoint of AB
given: OM is perpendicular to AB
construction: joint AO and BO
proof: in the given fig,
OA and OB are joined
In Δ AOM and ΔBOM
AO = BO ( two sides of Δ AOB )
OM = OM ( common )
∴ Δ AOM ≅ Δ BOM ( by SAS rule )
∴ AM = BM ( by CPCT ) -------- 1
∴ M is the midpoint of AB ( from 1 )
⇒hence proved
HOPE THIS HELPED and PLEASE MAKE ME AS THE BRAINLIEST
A regular polygon has 10 sides. What is the measure of each interior angle of the polygon? 36° 1440° 144° 72°
Answer:
144°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 10, thus
sum = 180° × 8 = 1440°
Each interior angle = 1440° ÷ 10 = 144°
Answer:
144 deg
Step-by-step explanation:
Sum of the measures of the angles of a polygon with n sides:
(n -2)180
For a 10-sided polygon, n = 10.
The sum of the measures is
(10 - 2)180 = (8)180 = 1440
Since the polygon is regular, all angles have the same measure, so the measure of 1 angle is
1440/10 = 144
Answer: 144 deg
There are 5 orange bumper cars and 3 green bumper cars that are being tested
for safety for a ride at an amusement park. Two bumper cars are tested at
random, one at a time, without retesting the same car.
Find the probability that both cars are orange.
Enter the correct answer in the box.
Answer:
5/14
Step-by-step explanation:
I assume after testing the 1st car, it is not placed back into the pool.
So, 1st test orange is 5/8
2nd test orange is 4/7.
Both had to be true, so 5/8 x 4/7 = 5/14
if m∠2= 137 and m∠P= 22, what is m∠O? answers are 43,21,65,115
Answer:
21
Step-by-step explanation:
since it is a triangle subtract 180 by 137 and 22
180-(137+22) or 180-132-22
hope this helps
Answer:
21
Step-by-step explanation:
We khow that the sum of a triangle's angles sizes is 180°
137+22 = 159°substract the sum of the two khown angles from 180°
180°-159° = 21 °so m<0 = 21°
Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10. A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Answer:
The correct option is;
A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25
Please find attached the graphs of the table data
Step-by-step explanation:
Each of the given table data of in the tables are analysed to find direct variation;
Table 1
x, -3, -1, 2, 5, 10
y, -4.5, -3.0, -1.5, 0.0, 1.5
-4.5/-3 = 1.5 ≠ -3.0/-1 = 3
No direct variation
Table 2
x, -5.5, -4.5, -3.5, -2.5, -1.5
y, 10, 8, 6, 4, 2
10/(-5.5) = -20/11 ≠ 8/(-4.5) = -16/9
However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2
Adjusted direct variation
Table 3
x, -5.5, -5.5, -5.5, -5.5, -5.5
y, -3, -1, 2, 5 , 10
-3/(-5.5) ≠ -1/-5.5
No direct variation
Table 4
x, -3, -1, 2, 5, 10
y, -7.5, -2.5, 5.0 , 12.5, 25
-7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10
Direct variation exists
Answer:
so D
Step-by-step explanation:
Which of the following is a factor of x3+ 6x2 + 5x – 12?
A.X + 1
B. x - 3
C. x + 2
D. x + 4
1,3,4 that is the answer
Answer:
The answer is option D.Step-by-step explanation:
x³ + 6x² + 5x - 12
A factor of the polynomial is the value of x when substituted into the expression will make it zero
Choosing x + 4
x = - 4
We have
(- 4)³ + 6(- 4)² + 5(- 4) - 12
-64 + 96 - 20 - 12 = 0
Since the result is zero
x + 4 is a factor of the polynomial
Hope this helps you
PLEASE HELP A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $21. For 2 pounds of
chocolate chips and 6 pounds of walnuts, the total cost is $24. Find the cost for each pound of chocolate chips and each pound of walnuts.
Answer:
Chocolate Chips cost $2.25 and Walnuts cost $3.25 per pound each
Step-by-step explanatChocion:
Let x = cost of pounds of chocolate chip cookies and y = cost of pounds of walnuts.
From the question, we get 5x+3y = 21 and 2x+6y = 24. To solve the equation, we use substitution. From the first equation, we get y = (21-5x)/3. We substitute the y into the second equation to get 2x + 6(21-5x)/3 = 24. This turns out to be 2x+(42-10x) = 24. Adding like terms you should get 42-8x = 24. Solving for x, x = $2.25 per pound. Plugging this into the first equation, we get 5(2.25)+3y = 21. Solving for y, we get $3.25 per pound of walnuts. If we plug in the numbers into the 2 equations, we will get the right total.
It takes 4 people 2 days to paint a wall. How long would it take if we got 8 people to do it?
Answer:
if it takes 4 people for 2 days
4+4= 8
so it would only take 8 people for 1 day
Answer:
1 day
Step-by-step explanation:
4 people = 2 days
→ Work out how long 1 person takes
4 people = 2 days
( ÷ 4 ) ( × 4 )
1 person = 8 days
→ Work out how long 8 people can do it
1 person = 8 days
( × 8 ) ( ÷ 8 )
8 people = 1 day
Zach tried to solve an equation step by step. 34=z−1234+12=z−12+12Step 154=zStep 2\begin{aligned} \dfrac34&=z-\dfrac12\\\\ \dfrac34+\dfrac12&=z-\dfrac12+\dfrac12&\green{\text{Step } 1}\\\\ \dfrac54&=z&\blue{\text{Step } 2} \end{aligned} 4 3 4 3 + 2 1 4 5 =z− 2 1 =z− 2 1 + 2 1 =z Step 1 Step 2 Find Zach's mistake. Choose 1 answer: Choose 1 answer:
Question:
Zach tries to solve an equation step by step;
[tex]\frac{3}{4} = z - \frac{1}{2}[/tex]
Step 1:
[tex]\frac{3}{4} + \frac{1}{2} = z - \frac{1}{2} + \frac{1}{2}[/tex]
Step 2:
[tex]\frac{3}{4} + \frac{1}{2} = z[/tex]
[tex]\frac{5}{4} = z[/tex]
Find Zach's mistake;
Answer:
Zach didn't make any mistake
Step-by-step explanation:
Given: the steps above
At step 1, he applied addition property of equality by adding [tex]\frac{1}{2}[/tex] to both sides of the equation
Step 2 is a result of step 1 and he rightly added the fractions
Further Explanation;
[tex]\frac{3}{4} = z - \frac{1}{2}[/tex]
Add [tex]\frac{1}{2}[/tex] to both sides
[tex]\frac{3}{4} + \frac{1}{2} = z - \frac{1}{2} + \frac{1}{2}[/tex]
[tex]\frac{3}{4} + \frac{1}{2} = z[/tex]
Take LCM of fractions at the left hand side
[tex]\frac{3 + 2}{4} = z[/tex]
[tex]\frac{5}{4} = z[/tex]
Reorder
[tex]z = \frac{5}{4}[/tex]
Analyzing the steps one after the other, we can conclude that Zach didn't make any mistake;
Answer:
C: Zach did not make a mistake
Step-by-step explanation:
SO IT NOT CONFUSING
+
GOT IT ON KHAN
(p.s. can u give me brainliest?)
A track star runs twice a day. In the morning, he runs on a track that is 2 1/2 miles per lap and he runs 3 1/2 laps. In the afternoon he runs on a track that is 1 3/10 miles per lap and he runs 3 laps. How
many total miles does he run in a day?
Answer:
12.65 miles
Step-by-step explanation:
he runs on a track that is 2 1/2 miles per lap and he runs 3 1/2 laps:
2 1/2 *3 1/2= 5/2 * 7/2=35/4=8.75 miles
afternoon he runs on a track that is 1 3/10 miles per lap and he runs 3 laps
1 3/10 *3=13/10*3=39/10= 3.9
total miles he runs in a day: 8.75+3.9= 12.65 miles
One angle of an isosceles triangle is 80º. What are the other two angles?
Answer:
80 and 20
Step-by-step explanation:
80+80+20=180
pls help !!!! i do not know or understand this at all
Answer:
(3, -3)
Step-by-step explanation:
Given functions:
f(x)= x² - 5x + 3and
f(x)= -3Solution is the Intersect which is found by equalizing the two functions:
x² - 5x + 3= -3Solving for x:
x² - 5x + 6=0x² - 2x -(3x -6) =0x(x-2) - 3(x-2)=0(x-2)(x-3)= 0x= 2 and x= 3As both values of x for the first function reveal f(x) = -3, the pairs are:
(2, -3) and (3, -3)Scarlett bought an ant farm with 80 ants. Frond the following week forward, the ant population tripled every week. Let g(n) be the number on ants in scarletts farm in the nth week since she got it. G is a sequence. What kind is it? Write an explicit formula for the sequence starting with g(n)=? Need help really bad I’m stuck and can’t figure out what it is
Answer:
g(n)=80×3^(n-1)
Step-by-step explanation:
First term (a)=80
The ant population tripled every week.
So, the population of ant after 1st week will be (80 × 3) = 240
After 2 weeks, the population triples again.
We have, (240 × 3) = 720
Common ratio (r)=720/240
=3
r=3
The ants population is increasing in a geometric progression
A geometric progression is given by
g(n)=a × r^(n-1)
Substitute values of a and r to get the explicit formula
g(n)=a × r^(n-1)
g(n)=80×3^(n-1)
please help!!!!! idk how to do this
Answer:
30 seconds.
Step-by-step explanation:
So, we have the equation:
[tex]h(t)=-16t^2+h[/tex]
Where t is the time in seconds and h is the initial height.
A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:
[tex]h(t)=-16t^2+14400[/tex]
We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:
[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]
Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.
Edit: Spelling.
If a circle is dilated by a scale factor of
what will be the lenth of the new radius?
18m
12 m
9 m
36 m
27 m
Answer/Step-by-step explanation:
The scale factor is missing in the question. However, here's how to find the length of the new radius if given a known scale factor.
Length of new radius = length of the radius of the dilated circle × scale factor of dilation
Length of the radius of the dilated circle is given as 18m
Therefore,
Length of new radius = 18m × scale factor.
If the scale factor is a fraction, it means the new length would be smaller than 18m. But if the scale factor is a whole number, the new length of the radius would be greater than 18m.
Let's assume any of the following scale factors was what was given in the question:
*If scale factor given is ½, new radius length = 18m × ½ = 9m
*If scale factor given is 2, new radius length = 18m × 2 = 36m
can someone answer the underlined question? (number 9)
Answer:
Slope = -6/7
Step-by-step explanation:
You need to use the formula m = y2 - y1 ÷ x2 - x1
The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1
So,
m = 2 - 5 ÷ 3/2 - (-2)
m = -3 ÷ 7/2
m = -6/7
Hope this helps :)
Simplify. Your answer should contain only positive exponents.
9) 3^-1 • 3^0
Answer:
1 / 3^1
Step-by-step explanation:
3^-1 • 3^0
When multiplying exponents with the same base, we add the exponents
3^ (-1+0)
3 ^-1
We know that a^ - b = 1/a^b
3 ^ -1 = 1/3^1
The slope of the line below is -3 which is the following is the point - slope from the line ?
Answer:
D. y + 6 = -3(x - 2)
Step-by-step explanation:
To find the equation in point-slope form, you need to use the slope and a point from that line. The slope is -3 and the point given is (2, -6).
Point-slope form is y - y₁ = m(x - x₁). Plug in the slope and point.
y - (-6) = -3(x - 2)
y + 6 = -3(x - 2)
Answer:
D. [tex]y - 2 = -3(x+6 )[/tex]
Step-by-step explanation:
Well point slope form is,
[tex]y - y_{1} = m(x-x_{1} )[/tex]
So we already have slope meaning we can plug that in for m.
[tex]y - y_{1} = -3(x-x_{1} )[/tex]
And with the given point (2,-6),
we can create point slope form.
[tex]y - 2 = -3(x+6 )[/tex]
Therefore,
the answer is d. [tex]y - 2 = -3(x+6 )[/tex].
Hope this helps :)
URGENT!!!!!!
Identify the sequence graphed below and the average rate of change from n = 0 to n = 3 . (2, 10) (3, 5) (4, 2.5) (5, 1.25)
A) a_n=8(1/2)^(n-2); average rate of change is -3
B) a_n=10(1/2)^(n-2); average rate of change is -(35/3)
C) a_n=8(1/2); average rate of change is 3
D) a_n=10(1/2)^(n-2); average rate of change is 35/3
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
=======================================================
Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
Find the value of x.
Answer:
x = 84°Step-by-step explanation:
A radius to the tangent point always forms a right angle with the tangent.
m∠OAB = m∠OCB = 90°
[tex]m\angle AOC=\stackrel{\big{\frown}}{ADC}=96^o[/tex]
The sum of the angles in the quadrilateral is 360°, so:
x = 360° - 2•90° - 96° = 84°
10 pts
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the
building. How many feet away from the building is the base of the ladder? Write only the number
rounded to the nearest tenth of a foot.
Answer:
13.2 ft
Step-by-step explanation:
We are given a ladder, a building, and an angle. Let's construct a right triangle (see attachment).
In this right triangle, we know that the hypotenuse (the ladder) is 25 feet, while the angle made between the top of the ladder and the building is 32°. Since we want to find the number of feet between the building and the base of the ladder, we will use the trigonometric function sine, which is opposite divided by hypotenuse.
Here, the opposite side is the value we want to find, while the hypotenuse is the length of the ladder.
We have:
sin(32°) = opposite / hypotenuse = x / 25
x = 25 * sin(32°) ≈ 13.2 ft
The answer is thus 13.2 ft.
~ an aesthetics lover
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting: at least three the same color?
Answer:
We shall need to pick at least 4 balls to be sure that we are getting balls with the same color
Step-by-step explanation:
Here, we want to know the least number of balls to be taken out of the box to be sure that we have all the three colors represented.
We know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know we have all the colors of balls represented, we will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that we have taken all the colors since we would have exhausted picking other balls at this point.
So we shall be needing at least 4 balls picked to ensure that we have all the colors represented
Please help me.. please
Hey there! :)
Answer:
$10 balcony
$15 orchestra
Step-by-step explanation:
We can solve for the prices of each seat by creating an algebraic expression:
Let 'x' be the cost of a balcony seat:
and 'x + 5' be the cost of an orchestra seat.
200 of both seats were sold, therefore:
200(x) + 200(x + 5) = 5000
Distribute:
200x + 200x + 1000 = 5000
Combine like terms:
400x + 1000 = 5000
Subtract 1000 from both sides:
400x = 4000
Divide:
x = $10 for the balcony seat.
Substitute this value of x to solve for the cost of an orchestra seat:
(10) + 5 = $15.
Therefore:
$10 balcony
$15 orchestra
Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 3/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?
Answer:
Cantidad que Lupe dejó en casa con inicialmente = 127.5 soles.
Amount that Lupe left home with initially = 127.5 soles.
Step-by-step explanation:
Pregunta correcta
Lupe va al mercado y compra abarrotes con los 2/5 de su dinero ; luego va a la seccion de carnes y compra con los 1/3 de lo que le queda ; si gasta 3 soles en pasaje de ida y vuelta ; ¿con cuanto dinero salio de su casa si llega de regreso a su casa con 48 soles?
Solución
Deje que la cantidad de dinero que Lupe dejó en casa sea x soles.
Lupe compra comestibles con 2/5 de su dinero. Es decir, Lupe gasta (2/5) × x = (2x/5)
En este punto, Lupe se queda con
x - (2x/5) = (3x/5) soles.
Lupe luego gasta 1/3 de lo que queda en la carne
(1/3) de lo que queda = (1/3) × (3x/5) = (x/5)
Lo que significa que Lupe gasta (x/5) soles en la sección de carne.
Cantidad restante después de la sección de carne = (3x/5) - (x/5) = (2x/5)
Lupe gasta 3 soles en el viaje de ida y vuelta al mercado y se queda con 47 soles después de todo.
(2x/5) - 3 = 48
(2x/5) = 48 + 3 = 51
2x = 5 × 51 = 255
2x = 255
x = (255/2) = 127.5 soles
¡¡¡Espero que esto ayude!!!
English Translation
Lupe goes to the market and buys groceries with 2/5 of her money; then he goes to the meat section and buys with 1/3 of what he has left; if you spend 3 soles on a round trip ticket; How much money did you leave your home with if you arrive home with 48 soles?
Solution
Let the amount of money Lupe left home with be x soles.
Lupe buys groceries with 2/5 of her money
That is, Lupe spends (2/5) × x = (2x/5)
At this point, Lupe is left with
x - (2x/5) = (3x/5) soles.
Lupe then spends 1/3 of what is left on meat
(1/3) of what is left = (1/3) × (3x/5) = (x/5)
Meaning that Lupe spends (x/5) soles at the meat section.
Amount left after the meat section = (3x/5) - (x/5) = (2x/5)
Lupe spends 3 soles on round ticket trip to market and is left with 47 soles after everything.
(2x/5) - 3 = 48
(2x/5) = 48 + 3 = 51
2x = 5 × 51 = 255
2x = 255
x = (255/2) = 127.5 soles
Hope this Helps!!!
Suppose your car has hhh liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is ggg liters.
Answer:
g = (h+a) - l
None of them
Step-by-step explanation:
Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them
Let
h = liters of oil in the morning
l= liters that has leaked
a= liters that were added during the day
g= amount of liters at the end of the evening
Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked
Substituting each variable into the formula, we have
g = (h+a) - l
Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.
Answer:
Step-by-step explanation:
Since we're given a time at which the height is maximum, we can use a cosine function for the model.
The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.
The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.
The period is given as 3 seconds, and the right shift is given as 1.31 seconds.
This gives us enough information to write the function as ...
H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)
H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm
Cheryl is planning to go to a four-year college in two years. She develops a monthly savings plan using the estimates shown. What should her monthly savings be? (rounded to the nearest cent)
Answer:
$541.67 per month
Step-by-step explanation:
Tuition and other expenses = $8,250 per semester.
There are two semesters in a year
She has 4 years to spend
Total semester=4years*2semesters
=8 semesters
4 years in college which is a total of 8 semesters.
Total Tuition and other expenses = $8,250 * 8
= $66,000
She needs a total of $66,00 to complete her college
Assistance from parents=$15,000
Financial aid(per semester)=$4750
Total financial aid=$38,000
Total assistance=
Assistance from parents+ financial aid
=$15000+$38,000
=$53,000
Total savings=Total amount needed - Total assistance
=$66,000 - $53,000
=$13,000
She needs to save $13,000 in two years
There are 12 months in one year
2 years=2*12=24 months
Monthly savings=Total savings/24 months
=$13,000/24
=$541.666666
To the nearest cent
=$541.67
Answer: $541.67
Step-by-step explanation: Got it right on TTM.
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
A. g(x) = -x2 + 2
B. g(x) = -X2 - 2
C. g(x) = (-x)2 - 2
D. g(x) = (-x)2 + 2
B. [tex]-x^2-2[/tex].
Hope this helps.
Answer:
i think its g(x)=-x^2-2
Step-by-step explanation: