Answer:
18 racks
Step-by-step explanation:
338/19=17.78 so if you round up you get 18 racks
Ms. Sanchez needs to buy 18 coat racks to accommodate 338 coats, as each rack holds 19 coats and we round up the result of the division 338/19 to the nearest whole number.
The question asks us to determine how many coat racks Ms. Sanchez should buy if she wants to hold 338 coats and each rack holds 19 coats. To find out the number of racks needed, we divide the total number of coats by the number of coats that one rack can hold, which is a straightforward division problem.
We calculate this by dividing 338 (the total number of coats the racks need to hold) by 19 (the number of coats each rack can hold):
338 / 19 = 17.7895...
Since we cannot have a fraction of a coat rack, we round up to the nearest whole number because Ms. Sanchez needs enough racks to hold all the coats, and you cannot purchase a fraction of a rack. Therefore, Ms. Sanchez should buy 18 coat racks to accommodate all 338 coats.
The Wright family recently went out to dinner. They ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. The sales tax is 7.675 %. Mr. Wright paid with a $50 bill. Mr. Wright always leaves a 15% tip on the total bill (excluding tax). How much more money will he need in order to leave a 15% tip?
A
$ 3.00
B
$ 4.23
C
$ 6.00
D
$ 7.20
Answer:
B
Step-by-step explanation:
First
Get totals for food items:
Pizza $14.95 ×2=$29.90
Salad=$4.35
Drinks $2.49 ×4=$9.76
Total Bill
$29.90
$ 4.35
+$ 9.76
$44.21 Food Bill
Second Step
Find Tip Amount Before Tax
Total Bill $44.21 × .15=$6.63 Tip
Third Step
Find Tax on Total Food Bill
$44.21 × .07675=$3.39
Fourth Step
Find amount left from paying bill with tax.
Total Bill including tax:
$44.21 (bill) +$3.39 tax=$47.60
Cash $ 50.00
Total Bill - $47.60
$ 2.40 Change left over
Fifth Step
Find amount needed to give $6.63 tip from above.
We have $2.40 we need $6.63
Subtract $6.33 -$2.40=$4.23 more money needed for tip
The correct option is B. $ 4.23. Mr. Wright needs an additional $4.23 to leave a 15% tip.
First, we need to calculate the total cost of the meal before tax and tip. The Wright family ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. So, the cost of the pizzas is [tex]2 \times $14.95[/tex], the salad is $4.35, and the drinks are 4 \times $2.49.
Cost of pizzas: [tex]2 \times $14.95 = $29.90[/tex]
Cost of salad: $4.35
Cost of drinks: [tex]4 \times $2.49 = $9.96[/tex]
Total cost before tax: [tex]\$29.90 +\$\4.35 + \$\9.96 = \$\44.[/tex]21
Next, we calculate the sales tax, which is 7.675% of the total cost before tax.
Sales tax: [tex]\$\44.21 \times 7.675% = \$\44.21 \times 0.07675 = \$\3.39[/tex]
Now, we add the sales tax to the total cost before tax to get the total cost including tax.
Total cost with tax: [tex]\$\44.21 + \$\3.39 = \$\47.60[/tex]
Mr. Wright wants to leave a 15% tip on the total bill before tax. So, we calculate 15% of the total cost before tax.
Tip: [tex]\$\44.21 \times 15% = \$\44.21 \times \$\0.15 \times \$\ 6.63[/tex]
Mr. Wright paid with a $50 bill, so we subtract the total cost with tax from $50 to find out how much change he should receive.
Change from [tex]\$50: $50 - $47.60 = $2.40\[/tex]
To find out how much more money Mr. Wright needs to leave a 15% tip, we subtract the change he receives from the tip amount.
Additional money needed: [tex]\$6.63 - $2.40 = $4.23\[/tex]
Therefore, Mr. Wright needs an additional $4.23 to leave a 15% tip.
Solve the equation...
Answer:
D) π/2 and 3π/2
Step-by-step explanation:
The equation can be factored:
(1 -sin(x))(1 +sin(x)) = 0
The factors will be zero when ...
sin(x) = 1 ⇒ x = π/2
sin(x) = -1 ⇒ x = 3π/2
If g=26.4 and F=35° find h. Round to the nearest tenth (picture provided)
For this case we have to, by definition:
[tex]cos (F) = \frac {h} {26.4}[/tex]
This means that, the cosine of the angle F, will be equal to the leg adjacent to the angle on the hypotenuse of the triangle.
So, by clearing h we have:
[tex]h = 26.4 * cos (35)\\h = 26.4 * 0.81915204\\h = 21.6256[/tex]
Rounding out the value of h we have:
[tex]h = 21.6[/tex]
Answer:
Option B
Answer:
The correct answer is option b. 21.6
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Cos θ = adjacent side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of h
It is given that, g=26.4 and F= 35°
Cos F = adjacent side/Hypotenuse
Cos 35 = adjacent side/Hypotenuse
= FG/FH = h/g
h = g * Cos F = 26.4 * Cos 54 = 26.4 * 0.8191 = 21.62 ≈ 21.6
Therefore the correct answer is option b. 21.6
Find the domain and range of the function f(x)=-5 cos^2x
Answer:
domain: (-∞, ∞) ; range: [-5, 0]
Step-by-step explanation:
Let's begin with the basics:
The domain of cos x is (-∞, ∞); the range is [-1, 1].
The domain of cos²x is still (-∞, ∞).
Likewise, the domain of -5 cos²x is(-∞, ∞).
The range of cos²x differs: it is [0, 1] because squaring a negative number results in a positive output.
Multiplying cos²x by 5 expands the range to [0, 5].
Finally, multiplying 5 cos²x by -1 changes the range to [-5, 0].
Answer:
C
Step-by-step explanation:
Cuz edge
P(A) =0.20 P(B) = 0.25 P(A and B) = 0.10. What is P(B/A)?
A. 0.25
B. 0.40
C. 0.50
D. 0.05
Answer:
Final answer is [tex]P(B/A)=0.5[/tex]
Step-by-step explanation:
Given that P(A) =0.20
P(B) = 0.25
P(A and B) = 0.10.
Now we need to find about what is the value of P(B/A).
P(A and B) = P(A) * P(B/A)
Plug the given values into above formula:
[tex]0.10=0.20\cdot P(B/A)[/tex]
[tex]\frac{0.10}{0.20}=P(B/A)[/tex]
[tex]0.5=P(B/A)[/tex]
[tex]P(B/A)=0.5[/tex]
Hence final answer is [tex]P(B/A)=0.5[/tex]
Answer:
c is the answer
Step-by-step explanation:
5
∑ (2n-1)
n-1
Find the sum of the series. Show your work. Thanks for the help
Answer:
225
Step-by-step explanation:
15(1+15/2) *2= 240-15=225
The sum of the arithmetic series given by the terms (2n - 1) for n=1 to 5 is 25, computed using the formula for the sum of an arithmetic series.
The series in question is an arithmetic series with a difference of 2 and the sum of the first n terms can be represented by the formula for the sum of an arithmetic series, Sn = n/2[2a + (n-1)d], where 'a' is the first term and 'd' is the common difference between the terms.
In the provided series, each term is of the form (2n - 1) starting with n=1 and going till n=5. So the first term, a = 2(1) - 1 = 1, and the common difference, d = 2 since each subsequent term increases by 2.
We can compute this sum directly by evaluating S5, using the formula for an arithmetic series: S5 = 5/2[2(1) + (5-1)(2)] = 5/2[2 + 8] = 5/2[10] = 25. So, the sum of the series is 25.
The length of a rectangle is 24 units. Can the perimeter x of the rectangle be 60 units when its width y is 11 units? A. No, the rectangle cannot have x = 60 and y = 11 because x = 48 + 2y b. No, the rectangle cannot have x = 60 and y = 11 because x = 24 + 2y c. Yes, the rectangle can have x = 60 and y = 11 because x + y is greater than 48 d. Yes, the rectangle can have x = 60 and y = 11 because x + y is greater than 24
Answer:
A
Step-by-step explanation:
The formula for the Perimeter of a rectangle is P = 2W + 2L.
Let's equate this to 60 units and substitute 11 for W and 24 units for L:
2(11 units) + 2(24 units) = 22 units + 48 units = 70 units. NO (Answer A)
A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft. Approximately how long does it take for the ball to hit the ground? Acceleration due to gravity is 32 ft./s^2.
A. 2.35 seconds
B. 2.47 seconds
C. 6.46 seconds
D. 6.50 seconds
Answer:
T= 2.35 seconds
Step-by-step explanation:
⇒The question is on the time of flight.
⇒Time of flight is the time taken for a projected object to reach the ground.It depends on the projectile angle and the initial velocity of the projectile
Given;
Initial velocity of ball= 110ft./sec.
The projectile angle= 20°
Acceleration due to gravity, g=32 ft./s²
⇒Formulae for time of fright T= (2×u×sin Ф)/g
Where T=time of fright, u=initial velocity of projectile, Ф=projectile angle and g=acceleration due o gravity.
Substituting values
T= (2×u×sin Ф)/g
T=( 2×110×sin 20°) / 32
T= 2.35 seconds
Answer:
Option B - Time taken for the ball to hit the ground is 2.47 seconds.
Step-by-step explanation:
Given : A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft.
To find : How long does it take for the ball to hit the ground?
Solution :
According to question,
The equation that models the height of the ball in feet as a function of time is
[tex]h(t) = h_0 + v_0t -16t^2[/tex]
Where, [tex]h_0[/tex] is the initial height,
[tex]v_0[/tex] is the initial velocity and
t is the time in seconds.
We have given,
Initial height, [tex]h_0=4.5 ft.[/tex]
A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees.
The initial speed, [tex]v_0=110\times \sin(206\circ)[/tex]
[tex]v_0=37.62ft/s[/tex]
We have to find the time for the ball to hit the ground i.e. h(t)=0
Substitute all the values in the formula,
[tex]0 =4.5+ 37.62t -16t^2[/tex]
Applying quadratic formula to solve the equation,
The solution of quadratic general equation [tex]ax^2+bc+c=0[/tex] is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Where, a=-16 , b=37.62 , c=4.5
Substituting in the formula,
[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]
[tex]t=\frac{-37.62\±\sqrt{1703.2644}}{-32}[/tex]
[tex]t=\frac{-37.62\±41.270}{-32}[/tex]
[tex]t=\frac{-37.62+41.270}{-32},\frac{-37.62-41.270}{-32}[/tex]
[tex]t=-0.114,2.47[/tex]
neglecting the negative value
t=2.47 seconds
Therefore,Option B is correct.
Time taken for the ball to hit the ground is 2.47 seconds.
Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?
The answer is (-4x-1)(2x^2+3) when factoring this expression by grouping
Answer:
The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]-8x^3-2x^2-12x-3[/tex]
The above expression can be written as:
[tex](-8x^3-2x^2)+(-12x-3)[/tex]
Take out the greatest common factor from each group.
[tex]-2x^2(4x+1)-3(4x+1)[/tex]
Further solve the above expression.
[tex](4x+1)(-2x^2-3)[/tex]
Hence, the required expression is
[tex](4x+1)(-2x^2-3)[/tex]
The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]
Can somebody please help me.
Answer:
72
Step-by-step explanation:
The two acute angles add up to 90 degrees. That's because the given triangle is a right triangle.
So x + 4x + 90 = 180 All triangles = 180°. Combine left side terms.
5x + 90 = 180 Subtract 90°
5x + 90 - 90 = 180 - 90 Combine
5x = 90 Divide by 5
5x/5 = 90/5 Combine
x = 18
The larger angle is 4x so
The larger angle = 4*18 = 72
Elroy and Rose are at Schematic to buy a school planner. There are 333 colors (purple, red, and blue) and 222 formats (lined and unlined) offered. They each created a display to represent the sample space of randomly picking a color and a format.
Answer:
Both
Step-by-step explanation:
The total number of options that will be are 6. The representation made by both Elroy and Rose is correct.
What is the total number of options available?The total number of options available is the product of a total number of options available in different sectors.
Given that number of colors is 3 while the number of formats is two. Therefore, the total number of options that are available will be 6 which is the product of the two.
As we can see that both have pointed out each of the six options, therefore, the representation made by both Elroy and Rose is correct.
Learn more about Number of options:
https://brainly.com/question/11185799
Find the length of segment BC. Please help ASAP
BC also has length 12 because arcs DC and CE add up to 117 degrees in measure, so that arc DE is congruent to arc BC, and the chords DE and BC that respectively intercept these arcs must also be congruent.
Find the sum of the series. Include each term that leads to the final sum and show the expression for finding that term. ∑5k=3(−2k+5)
Answer:
[tex]\large\boxed{\sum\limits_{k=3}^5(-2k+5)=-9}[/tex]
Step-by-step explanation:
[tex]\sum\limits_{k=3}^5(-2k+5)\to a_k=-2k+5\\\\\text{Put}\ k=3,\ k=4\ \text{and}\ k=5:\\\\a_3=-2(3)+5=-6+5=-1\\a_4=-2(4)+5=-8+5=-3\\a_5=-2(5)+5=-10+5=-5\\\\\sum\limits_{k=3}^5(-2k+5)=-1+(-3)+(-5)=-9[/tex]
The inequality -x^2 -6 <0 has how many critical points
Answer:
See below.
Step-by-step explanation:
This inequality is < 0 for all real values of x. We see this by solving -x^2 - 6 = 0 for x:
-x^2 - 6 = 0
-x^2 = 6
x^2 = -6 for which there are no real solutions of x. So the graph does not pass through the x axis.
At x = 0. f(x) < -6 so that is the one critical value - all values of f(x) are below this value.
Answer:
0 critical points
Step-by-step explanation:
Just did it and got it right
Drag each tile to the correct box. Consider the given functions f, g, and h.
h(x)=x²+x-6
Place the tiles in order from least to greatest according to the average rate of change of the functions over the interval [0, 3].
function H function f function g
Answer:
g, f, h
Step-by-step explanation:
By definition, the average rate of change of a function f over an interval [a,b] is given by
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
So, in your case, we want to compute the quantity
[tex]\dfrac{f(3)-f(0)}{3}[/tex]
for all the three function
Average rate of change of f:
We will simply use the table to check the values for f(3) and f(0):
[tex]\dfrac{f(3)-f(0)}{3}=\dfrac{10-1}{3} = 3[/tex]
Average rate of change of g:
We will use the graph to to check the values for g(3) and g(0):
[tex]\dfrac{g(3)-g(0)}{3}=\dfrac{8-1}{3} = \dfrac{7}{3}[/tex]
Average rate of change of h:
We can plug the values in the equation to get h(3) and h(0):
[tex]h(3)=3^2+3-6=9+3-6=6,\quad h(0)=0^2+0-6=-6[/tex]
And so the average rate of change is
[tex]\dfrac{h(3)-h(0)}{3}=\dfrac{6-(-6)}{3} = 4[/tex]
Answer:
g,f,h
I just took the test and was right
Step-by-step explanation:
For the system shown below, what are the coordinates of the solution that lies in quadrant 1?
Write your answer in the form (a,b) without using spaces.
[tex]3y^2-5x^2=7\\3y^2-x^2=23[/tex]
The answer in the first quadrant is
(2,3)
Line segment AB has a slope of 4/3 and contains point A (6,-5). What is the y-coordinate of point Q(2, y) if QA is perpendicular to line segment AB.
Answers:
y = −2
y = −1
y = 2
y = −3
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~AB}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}\impliedby \textit{slope of QA} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf A(\stackrel{x_1}{6}~,~\stackrel{y_1}{-5})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-(-5)}{2-6}=\stackrel{\textit{QA's slope}}{-\cfrac{3}{4}}\implies \cfrac{y+5}{-4}=\cfrac{-3}{4} \\\\\\ 4y+20=12\implies 4y=-8\implies y=\cfrac{-8}{4}\implies \boxed{y=-2}[/tex]
PLEASE HELP Me
Thank u!!
Answer:
Length = 13
x = 80
Step-by-step explanation:
Question One
Let the width = x
Let the length = x + 5
Area = 104
Equation
Area = L * W
Area = (x+5)*x
Solution
x ( x + 5) = 104 Remove the brackets
x^2 + 5x = 104 Subtract 104 from both sides.
x^2 + 5x - 104 = 104 - 104
x^2 + 5x - 104 = 0 Factor the equation
(x + 13)(x - 8) = 0
Only x - 8 = 0 works
x = 8
The width = 8
The Length = 8 + 5 = 13
Question Two
Draw AP
<BAP = 20o The triangle (APB) is isosceles: 2 sides are radii
<BPA = 180 - 20 - 20 The three angles of a triangle = 180
<BPA = 140 Combine
Similarly <CAP = 140 Go through exactly the same steps.
<BPA + <CAP + X = 360 The total of the 3 angles in the center = 360
140 + 140 + X = 360 Combine
280 + X = 360 Subtract 280 from both sides.
x = 80
What should be done to solve the following equation?
d - 8 = 9
Subtract 8 from both sides of the equation.
Add 8 to both sides of the equation.
Add 9 to both sides of the equation.
Subtract 9 from both sides of the equation.
Add 8 to both sides of the equation.
You need to get x by itself. The only way to do that here is to do the opposite of subtracting 8, which is adding 8.
Also, when you do something to one side of the equation, you have to also do it to the other side to keep the equation equal.
Answer: Add 8 to both sides of the equation
Step-by-step explanation:
d - 8 = 9
in this equation you need to solve for d. To do that you have to get d by itself.
By adding 8 to both sides of the equation you cancel out the -8 and add 8 to 9 which solves for d.
2 fair dice are rolled. what is the probability that the sum is even given that the first die is rolled is a 2?
Wouldnt you add 6+6=12 then divide that with the probability of getting a 2?
===================================================
Explanation:
"given that the first die rolled is a 2" means we know 100% that the first die shows a 2. Either we can see the die or a friend is telling us the status. Since we know the first die is a 2, this means we can effectively ignore it. Everything will hinge on the second die. If the second die shows an odd number, something like 1, then 2+1 = 3 is the result which is also odd.
The general rule is odd+even = odd and even+even = even.
Therefore, the two dice must together be even for the sum to be even.
Of the six possible ways to roll a die {1,2,3,4,5,6}, there are 3 even values {2,4,6} so the chances of rolling an even number on the second die is 3/6 = 1/2. Again we dont need to consider the first die at all since everything practically hinges on this second die.
Answer:
50%
Step-by-step explanation:
For the total to be even, when the first number is even, the second number also has to be even.
2, 4, and 6 are even, out of 6 numbers. That is 3 numbers out of 6, which gives us that the probability is 1 out of 2, or 50%.
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Remember to be mindful of signs when adding and subtracting. 2c^2+5c+4
Ian's parents asked him to creat a budget for his $ 1,000 monthly income . He determines that he would like to save the remaining amount. What percent of his budget will go towards saving. Expense : Amount ($) Car payment $ 350 Car insurance $ 100 Fuel $ 120 Cell phone $ 80
35%
First, we need to find the amount of money that is being spent. Add all of the amounts together.
$350 + $100 + $120 + $80
$450 + $120 + 80
$570 + $80
$650
So, Ian spends $650 of his budget each month. How much does that leave for savings? Just subtract $650 from $1,000 to find that he saves $350 each month.
Now, you just need to find the percentage. The percentage is the same as the numerator in a fraction with a denominator of 100, so x% = x/100. For example, 1% = 1/100. $350 / $1000 = x / 100
How do we turn 1,000 into 100? Divide it by 10. And if you do something to the denominator of a fraction, you have to do it to the numerator as well. So, divide $350 by 10 and divide $1000 by 10, leaving you with $35 / $100 = x / 100
Multiply both sides by 100 to get x by itself. This leaves you with 35 = x, so 35% of Ian’s budget with go towards saving.
Which theorem(s) can be used to prove that the given triangles are congruent to each other with only the information shown? Select all that apply.
A. ASA similarity
B. AA similarity
C. SAS similarity
D. SSS similarity
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Which situation involves descriptive statistics?
Answer:
The median price of a new home
Step-by-step explanation:
Correlation Coefficients. Image attached for the problem.
A. 11
B. 9
C. 3
D. 5
Answer:
A
Step-by-step explanation:
y bar basically means the average of the y-values.
To get the average, we add up all the y-values in the table and divide by the total number of values (here we have 5 values). Hence,
y bar = [tex]\frac{5+7+10+15+18}{5}=11[/tex]
correct answer is A
Kahn Academy Question, Please help!
[tex]g\circ f(-9)=g(f(-9))[/tex]
By definition of [tex]f[/tex],
[tex]f(-9)=3\cdot9-8=19[/tex]
and by definition of [tex]g[/tex],
[tex]g\circ f(-9)=g(f(-9))=g(19)=\sqrt{14-19}-10=\sqrt{-5}-10[/tex]
which is undefined if [tex]f,g[/tex] are supposed to be real-valued functions. If they're complex-valued, then [tex]\sqrt{-5}=i\sqrt 5[/tex] and [tex]g\circ f(-9)=-10+i\sqrt 5[/tex].
A 12 pack of cola costs $5.46. How much does one can of cola cost?
Answer:
46¢
Step-by-step explanation:
Note that there are 12 cola's in all. The total cost is $5.46. Divide the total cost with the amount of cola's there is:
5.46/12 = 0.455
Round: 0.455 rounded to the nearest hundredths is $0.46 (You round to the nearest hundredths, for the smallest amount for US currency is a penny, which is 1/100 of a dollar bill).
Each cola costs $0.46
~
Kylie and Ethan have each saved some money. I’m their savings, each coin is worth leas then 50 cents and each bill is less then $10. Kylie has saved more money than Ethan, but he has more bills and coins than Kylie. She has one bill and seven coins. What is the amount of money each person could have?
Answer:
Kylie could have a $5 bill and seven quarters while Ethan could have two $1 bills and forty pennies.
Step-by-step explanation:
Since Kylie has seven quarters, that is seven multiplied by the value of the quarter, a quarter is 25 cents. So 7 x 25 = 125 OR $1 and 25 cents. Leaving Kylie with a total of $7 and 25 cents with the addition of the $5 bill.
Ethan has two $1 bills and forty pennies, forty multiplied by the value of the penny, a penny is 1 cent. So 40 x 1 = 40 OR 40 cents. Leaving Ethan with $2 and 40 cents with the addition of the two $1 bills from earlier.
Ethan has more bills and coins than Kylie and yet still has less money than Kylie.
70 POINTS!!!!
Find the focus, directrix, and equation of the parabola in the graph.
Answer:
Option B
Part a) The focus is [tex](1/28,0)[/tex]
Part b) The directrix is [tex]x=-1/28[/tex]
Part c) The equation is [tex]y^{2}= (1/7)x[/tex]
Step-by-step explanation:
step 1
Find the equation of the parabola
we know that
The parabola in the graph has a horizontal axis.
The standard form of the equation of the horizontal parabola is
[tex](y - k)^{2}= 4p(x - h)[/tex]
where
p≠ 0
The vertex of this parabola is at (h, k).
The focus is at (h + p, k).
The directrix is the line x= h- p.
The axis is the line y = k.
If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left
In this problem we have that the vertex is the origin
so
(h,k)=(0,0)
substitute in the equation
[tex](y - 0)^{2}= 4p(x - 0)[/tex]
[tex]y^{2}= 4p(x)[/tex]
The points (7,1) and (7,-1) lies on the parabola-----> see the graph
substitute the value of x and the value of y in the equation and solve for p
[tex](1)^{2}= 4p(7)[/tex]
[tex]1= 28p[/tex]
[tex]p=1/28[/tex]
The equation of the horizontal parabola is
[tex]y^{2}= 4(1/28)(x)[/tex]
[tex]y^{2}= (1/7)x[/tex]
step 2
Find the focus
we know that
The focus is at (h + p, k)
Remember that
[tex](h,k)=(0,0)[/tex]
[tex]p=1/28[/tex]
substitute
[tex](0+1/28,0)[/tex]
therefore
The focus is at
[tex]F (1/28,0)[/tex]
step 3
Find the directrix
The directrix is the line x = h- p
Remember that
[tex](h,k)=(0,0)[/tex]
[tex]p=1/28[/tex]
substitute
[tex]x=0-1/28[/tex]
[tex]x=-1/28[/tex]
Answer:
B
Step-by-step explanation:
Confirmed on E D G 2021
Spencer opened a savings account and deposited $10. The account pays 3.5% interest and compounds the interest monthly. How much money will Spencer have after 10 years? **n=12 because it is compounded monthly.
Answer:
[tex]\$14.18[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$10\\ r=0.035\\n=12[/tex]
substitute in the formula above
[tex]A=P(1+\frac{0.035}{12})^{12*10}=\$14.18[/tex]