Given:
The net value of the bakery (in thousands of dollars) t months after its creation is modeled by
[tex]v(t)=2t^2-12t-14[/tex]
Paul wants to know what his bakery's lowest net value will be.
To find:
The function in a different form (factored or vertex) where the answer appears as a number in the equation.
Solution:
Factor form is used to find the x-intercepts and vertex form is used to find the extreme values (maximum or minimum). So, here we need to find the vertex form.
We have,
[tex]v(t)=2t^2-12t-14[/tex]
[tex]v(t)=2(t^2-6t)-14[/tex]
Adding and subtract square of half of 6 in the parenthesis, we get
[tex]v(t)=2(t^2-6t+3^2-3^2)-14[/tex]
[tex]v(t)=2(t^2-6t+3^2)+2(-9)-14[/tex]
[tex]v(t)=2(t-3)^2-18-14[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]v(t)=2(t-3)^2-32[/tex]
Vertex form:
[tex]f(x)=a(x-h)^2+k[/tex]
where, (h,k) is vertex.
On comparing this equation with vertex form, we get the of the function is (3,-32).
Therefore, the vertex form is [tex]v(t)=2(t-3)^2-32[/tex] and the function has minimum value at (3,-32). It means, minimum net value of the bakery is -32 after 3 months.
Answer:
v(t) = 2(t - 3)^2 - 32. and -32
Please mark the other one Brainiest.
Hope that this helps!
Rita is hiking along a trail that is 13.7 miles long. So far she has hiked ond tenth of the trail.
How far has rita hiked
Answer: 1.37 miles
Step-by-step explanation:
13.7=100%
13.7/10=1.37=10%=1/10
Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Which pair (x, y) represents hours that Leah could work to meet the given conditions? Select all that apply.
A.
(2.5, 15)
B.
(5, 20)
C.
(7.5, 12.5)
D.
(17.5, 5)
E.
(19, 1)
Answer:
A,B and C
Step-by-step explanation:
Solve the compound inequality. 3x − 4 > 5 or 1 − 2x ≥ 7 A. x ≤ −3 or x > 3 B. x −3 or x ≤ 3
Answer: B
Step-by-step explanation:
Answer i guess its b then
Step-by-step explanation:
The ratio of apples to oranges is 3 to 9. What is the percent of the oranges?
Answer:
I think its 33.333333333333%
Step-by-step explanation:
1. 3(6a); for a=3
2. 5d(4); for d=-2
Answer:
Step-by-step explanation:
1. Solution for 3(6a)a=3 equation:
Simplifying
3(6a) * a = 3
Remove parenthesis around (6a)
3 * 6a * a = 3
Multiply 3 * 6
18a * a = 3
Multiply a * a
18a2 = 3
Solving
18a2 = 3
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Divide each side by '18'.
a2 = 0.1666666667
Simplifying
a2 = 0.1666666667
Take the square root of each side:
a = {-0.408248291, 0.408248291}
2.Solution for 5d(4)d=-2 equation:
Simplifying
5d(4) * d = -2
Reorder the terms for easier multiplication:
5 * 4d * d = -2
Multiply 5 * 4
20d * d = -2
Multiply d * d
20d2 = -2
Solving
20d2 = -2
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Divide each side by '20'.
d2 = -0.1
Simplifying
d2 = -0.1
Reorder the terms:
0.1 + d2 = -0.1 + 0.1
Combine like terms: -0.1 + 0.1 = 0.0
0.1 + d2 = 0.0
Leon receives a birthday gift of $50 from his parents. Each week he saves $5.00. How many weeks will it take for him to save $120? Select and equation from below that will help him determine how much he needs to save every week to save $120.00.
A) 5x + 50= 120.00
B) 50x +5.00 = 120
C) 120x + 50= 1200.00
D) 5x + 120.00= 50.00
Answer:
14 weeks. the equation would be a.
Step-by-step explanation:
120-50=70 70/5=14 it will take him 14 weeks to get 120 if he saves 5 a week on top of the additional 50 he already has.
Answer:
14 weeks
Step-by-step explanation:
45 POINTS IF YOU STEAL POINTS IM REPORTING YOU I NEED THE ANSWER
Caisha has a circular garden with a radius of 4 ft. She needs to put a layer of soil on top. Each bag of soil covers 9.42 square feet. How many bags of soil will she need to buy? 5 bag 6 bags 7 bags 8 bags
Answer:
5
Step-by-step explanation:
A = 50.2654825
idk it could be 6
PLEASE HELP I AM TIMED!
Answer:
i believe it would be 45 is greater than or equal to 3x + (3x-1) + [(3x-1)-4]
I hope you pass. Plz correct me If I am wrong
Step-by-step explanation:
What is an equation of the line that passes through the points (-4, -1)and (3, -8)
Put your answer in fully reduced form.
Grant saved $1,325 to purchase a lawn tractor that costs $1,600. Last month the tractor was on sale for 20% off. Grant did not buy the tractor last month because he spent $360 to go bungee jumping. Decide if the decision is financially responsible.
Answer:
No, he is not financially responsible
Step-by-step explanation:
Given that:
Amount saved for tractor purchase = $1325
Original cost of tractor = $1600
Amount spent on bungee jumping = $360
Discounted price of tractor :
$1600 - (1600 * 0.2) = $1280
Saved amount left after bungee jumping :
$1325 - $360 = $965
The saved amount had exceeded the discounted price, hence, the discount served as an opportunity to make the purchase, However, spending $360 from the saved amount meant that the amount left could not afford the tractor despite the discount. Hence, Missing out on such opportunity due to jumping shows lack of financial responsibility.
idk men PLEASE HELP!
Mr. Villamayor rented a construction crane for five hours and a backhoe for seven hours. The total amount he paid is less than Php 9,000. Suppose the hourly rate for the crane is Php 800. What is the maximum amount he paid for the backhoe to the nearest hundreds?
Answer:
Let 7x be the rent paid for backhoe for seven hours.
Step-by-step explanation:
Keyword: maximum amount, the most
Inequality symbol: ≤
(800 × 5) + 7x ≤ 9,000
4,000 + 7x ≤ 9,000
7x ≤ 9,000 - 4,000
7x ≤ 5,000
7x ÷ 7 ≤ 5,000 ÷ 7
x ≤ 714.29
To the nearest hundreds:
x ≤ 700
ANSWER: The maximum rental fee per hour of backhoe is Php 700.00 (rounded off to the nearest hundreds).
To check if he paid less than 9,000 for the total rent:
(800 × 5) + (700 × 7) < 9,000
4,000 + 4,900 < 9,000
8,900 < 9,000 (True)
Worth 25 points!
Simplify these equations with steps please.
√-48
√-63
√-72
√-24
√-84
√-99
Answer:
1) [tex]\sqrt{-48}=4\sqrt{3} \ i[/tex]
2) [tex]\sqrt{-63}=3\sqrt{7} \ i[/tex]
3) [tex]\sqrt{-72}=6\sqrt{2} \ i[/tex]
4) [tex]\sqrt{-24}=4\sqrt{6} \ i[/tex]
5) [tex]\sqrt{-84}=2\sqrt{21} \ i[/tex]
6) [tex]\sqrt{-99}=3\sqrt{11} \ i[/tex]
Step-by-step explanation:
We need to simply the following :
Note: For all questions given we know that [tex]\sqrt{-1}=i[/tex] using it in all the given questions.
1) [tex]\sqrt{-48}[/tex]
Factors of 48 are: 2x2x2x2x3
[tex]\sqrt{-48}\\=\sqrt{48}\sqrt{-1} \\=\sqrt{2\times2\times2\times2\times3}\ i\\= \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i[/tex]
2) [tex]\sqrt{-63}[/tex]
Factors of 63 are: 3x3x7
[tex]\sqrt{-63}\\=\sqrt{63}\sqrt{-1} \\=\sqrt{3\times3\times7}\ i\\= \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i[/tex]
3) [tex]\sqrt{-72}[/tex]
Factors of 72 are: 2x2x2x3x3
[tex]\sqrt{-72}\\=\sqrt{72}\sqrt{-1} \\=\sqrt{2\times2\times2\times3\times3}\ i\\= \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i[/tex]
4) [tex]\sqrt{-24}[/tex]
Factors of 24 are: 2x2x2x3
[tex]\sqrt{-24}\\=\sqrt{24}\sqrt{-1} \\=\sqrt{2\times2\times2\times3}\ i\\= \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i[/tex]
5) [tex]\sqrt{-84}[/tex]
Factors of 84 are: 2x2x3x7
[tex]\sqrt{-84}\\=\sqrt{84}\sqrt{-1} \\=\sqrt{2\times2\times3\times7}\ i\\= \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i[/tex]
6) [tex]\sqrt{-99}\\[/tex]
Prime factors of 99 are: 3x3x11
[tex]\sqrt{-99}\\=\sqrt{99}\sqrt{-1} \\=\sqrt{3\times3\times11}\ i\\= \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i[/tex]
how do solve slope and for the y axis?
Answer:
Slope = rise/run or y2-y1/x2-x1 (change in y over change in x)
Y-intercept (I'm assuming you mean y-intercept instead of y axis) = if there's a graph, find where the line intersects the y axis, if there isn't a graph, use y=mx+b to solve for b, the y-intercept.
Hope this helps!
I need help on both please and thank youuu
PLEASE HELP WILL GIVE BRAINLIEST IF CORRECT
figure out the miles per hour (mph)
1. what is the mph if the time is 1 hour 42 min and the distance is 935 miles?
2. what is the mph if the time is 36 min and the distance is 330 miles?
Answer:6.67 for number 1
Step-by-step explanation:
Answer:
Answer 1 is 550
and 2 is also 550
Step-by-step explanation:
Triangle QRS is transformed as shown on the graph. Which rule describes the transformation?
Answer:
270°
Step-by-step explanation:
(x , y) --> (y, -x)
90° clockwise rotation
270° anti-clockwise rotation
PLEASE HELP ME ANSWER THESE 2 QUESTIONS PLEASE PLEASE PLEASE ASAP
Answer:l
Step-by-step explanation:
HELP ASAP PLEASE WILL MARK BRAINIEST
Answer:
40
Step-by-step explanation:
In one month, a cell phone company charges $50 and additional $0.05 for each text message. The company charged Christian $80 for October. How many text messages did Christian send in October?
Answer:
He has 1000 text messages.
Step-by-step explanation:
50 for a month and 0.05 for every text message
0.05x100=5
0.05x1000=50
Helpppp with this plssss
Answer:
26.411
Step-by-step explanation:
In 3a+bc-c you have to substitute
a=8.6, b=2.3, c=0.47
3*8.6 + 2.3*0.47 - 0.47 first do the multiplication then addition and subtraction
25.8 + 1.081 - 0.47=
26.411
Pumpkin pie is on sale for $12.50. How much will it cost to buy enough to feed 20 people? Please help me!
Answer:
$37.05
Step-by-step explanation:
thats what i got so it might not be right
The area of on field is 16 acres, the area of the second field is 1 1/4 times bigger. A barn of wheat on the first field makes up 37 1/2 thousands pounds per acre, and on the second 1 2/15 as much per acre, how much more was gathered on the second field than the first?
Answer:
250 thousand pounds
Step-by-step explanation:
Given that:
Area of field 1 = 16 acres
Area of field 2 = 1 1/4 bigger than field 1
Barn of wheat on field 1 = 37 1/2 thousands pounds per acre
Barn of wheat on second field = 1 2/15 as much as field one per acre
Total pounds gathered on field 1 :
37 1/2 * 16 = 600 thousand pounds
Area of second field :
1 1/4 * 16 = 5/4 * 16 = 20 acres
Barn of wheat per acre = 1 2/15 * 37 1/2
= 17/ 15 * 75/2 = 42 1/2 thousand pounds per acre
Total = 42 1/2 * 20 = 850 thousand pounds.
850 - 600 = 250 thousand pounds
pls help will give brianly for help Find the quotient:
–20 ÷ 5
Answer:
The answer is -4 :)
Step-by-step explanation:
Answer:
-20 divided by 5 = -4
Step-by-step explanation:
Write the expanded form of the expression
-6.4(-n+2+4.9n)
Answer:
6.4n - 12.8 - 31.36n
Step-by-step explanation:
multiply each term by -6.4
Use the following pattern to answer the questions.
24.3, 24, 23.7, 23.4, _____, _____
Part A
What is the rule for the pattern?
A.
Add 0.3 to each term.
B.
Subtract 0.3 from each term.
C.
Add 0.03 to each term.
D.
Subtract 0.03 from each term.
Part B
Complete the next two terms in the pattern.
24.3, 24, 23.7, 23.4,
Choose...
,
Choose...
This does not make sense to me
[tex]\frac{3}{11}[/tex]
Find the slope of the line that passes through (7,2) and (3,3)
Answer:
1 over 4
Step-by-step explanation:
Answer:
the answer is [tex]\frac{1}{-4\\}[/tex]
Step-by-step explanation:
slope= [tex]y_{2}[/tex]-[tex]y_{1}[/tex]
[tex]x_{2}[/tex]-[tex]x_{1}[/tex] so 3-2=1 and then 3-7=-4
If a 90°degree angle is bisected, the two angles created by the bisector will equal?
Answer:
45 degrees
Step-by-step explanation:
when an angle is bisected both angles formed are equal, so 90/2=45
Select the correct answer.
Which statement is false?
A.
The inequality sign always opens up to the larger number.
B.
The greater number in an inequality is always above the other number on the vertical number line.
C.
The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
D.
The inequality sign always opens up to the smaller number
Answer:
I think it might be C or B
Step-by-step explanation:
Hope this helped have a nice day :)
Somebody please help not that much time left