Considering the vertex of the quadratic equation, it is found that the scuba diver reaches maximum depth after 6 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the depth is given by:
D(x) = -x² + 12x + 4.
Which means that the coefficients are a = -1, b = 12, c = 4, hence:
[tex]x_v = -\frac{b}{2a} = -\frac{12}{-2} = 6[/tex]
The scuba diver reaches maximum depth after 6 seconds.
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How much would you have after 4 years if you invested $1250 with a quarterly compounding interest rate of 5%?
Using compound interest, it is found that you would have $1524.86.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem, we have that the values of the parameters are given by: P = 1250, r = 0.05, n = 4, t = 4. Hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(4) = 1250\left(1 + \frac{0.05}{4}\right)^{4 \times 4} = 1524.86[/tex]
Tou would have $1524.86.
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She says that the coffee cup fountain actually holds about 400 gallons of coffee.
The newscaster claims that if the coffee fountain really broke, the 400 gallons of coffee would cover the
equivalent of half a city block.
You look up some information.
• One gallon of water covers about 13.8 square feet.
• Near the mall, an average city block is about 300 feet by 300 feet.
Assume the fountain holds 400 gallons of coffee. Using the information given, determine whether the
newscaster's claim is correct.
• Construct an argument that supports or refutes the newscaster's claim.
Include mathematics to support your argument.
https://www.perfection-events.com/content/back-basics-coffee-essentials
Since the area 400 gallons will cover, 5520 square feet is less than the area of half a city block which is 45000 square feet, the Newscasters claim is wrong.
What is the area of the city block?The area of the city block is calculated from the product of the dimensions provided:
The city block is in form of a square, hence it's area = side × side
Dimension of city block = 300 feet by 300 feet.
Area of city block = 90000 square feet
Half of area of city block = 45000 square feet
1 gallon covers 13.8 square feet
400 gallons will cover = 400 × 13.8 = 5520 square feet
The area 400 gallons of coffee will cover is less than 45000 square feet.
Therefore, the news caster's claim is wrong.
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Help me do this question :)
Answer:
[tex]y = \frac{1}{8}x -7[/tex]
Step-by-step explanation:
Slope formula: [tex]y=mx+b[/tex]m = slope[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]Find the slope using (8, -6) and (-8, -8):
[tex]m=\frac{-8-(-6)}{-8-8} \\\\m=\frac{-8+6}{-8-8} \\\\m=\frac{-2}{-16}\\\\m=\frac{2}{16}\\\\m=\frac{1}{8}[/tex]
[tex]y=mx + b\\\\y = \frac{1}{8}x + b[/tex]
Now, we use either of our points (8, -6) OR (-8, -8) to find b.
I will be using (8, -6):
[tex]y = \frac{1}{8}x + b\\\\-6=\frac{1}{8}(8) + b\\\\-6=1+b\\\\-1 \ \ -1\\\\-7=b[/tex]
[tex]y = \frac{1}{8}x + b== > y = \frac{1}{8}x -7[/tex]
Check your answer manually: (-8, -8)
[tex]y = \frac{1}{8}x -7\\\\-8 = \frac{1}{8}(-8) -7\\\\-8=-1-7\\\\-8=-8[/tex]
This statement is correct.
*You can also view the attached graph to verify the answer, meaning that those two points should lie on the same line.*
Hope this helps!
Wendell wants to make a wooden lid for a decorative box. The lid needs to be 612inches wide and 812inches long with sides 2 inches deep. Part A Part B Wendell has a square piece of wood that has a side length of 12 inches. Based on your answer to Part A, does Wendell have enough wood to make the lid? Explain. Wendell has enough wood to make the lid because the surface area of his piece of wood is larger than the surface area of the wood needed. Wendell does not have enough wood to make the lid because the longest piece needed for the lid is longer than the side of his piece of wood. Wendell has enough wood to make the lid because each dimension of the box is less than the side length of his piece of wood. Wendell does not have enough wood to make the lid because the surface area of his piece of wood is smaller than the surface area of the wood needed
Answer:
Step-by-step explanation:
A
The cities of fayetteville, raleigh and durham form a triangle. they are building a new
baseball stadium. how should they determine where to place the stadium so it is the
same distance from all three cities to the stadium? assume a direct path.
Answer:
it should be built at the centre
PLEAASE SOMEONE HELP ME IM SO STUCK
finish the table using the equation y= x/2
Julian has a points card for a movie theater. He receives 85 rewards points just for signing up. He earns 3.5 points for each visit to the movie theater. He needs 120 points for a free movie ticket. Which equation or tape diagram could be used to represent the context if xx represents the number of visits Julian must make to earn a free movie ticket?
Answer:
an equation that can be used to represent the number of visits needed to earn a free movie ticket is
3.5x+85=120
Step-by-step explanation:
you would multiply 3.5 by the number of visits (x) to determine how many points Julian would have earned in total. you would add 85 to the product of 3.5(x) because he had started with 85 points.
if you want to find how many times Julian would need to visit the movie theater to get a free movie ticket you can subtract 85 from 120, to find out how many visits are necessary before adding the extra 85 points. subtracting that leaves you with 35, and if you divide that by 3.5, the number of points per visit, you are left with 10. Julian would need to visit the theater 10 times before earning a free movie ticket.
if you want to check to see if that's right, you can just do the equation in reverse. rather than 85-120=35/3.5=10, you can do 10*3.5=35+85=120
hope this helps
ASAPPPPPPPPPPPP!!!!!!
Answer:
angle C measures 31 degrees.
Step-by-step explanation:
because when they are complementary, the two angles add up to 90 degrees and you know the measure of part of that 90 already, so its as simple as subtracting 90-59=31
Answer:
31
Step-by-step explanation:
complementary angles equal 90
90-59=31
A and b are supplementary angles. angle a measures 67° what is the measure of angle b
Answer:
113°
Step-by-step explanation:
because supplementary angles add up to 180°
thus if a is 67° then we subtract 67° from 180° and b will be 113°
the diameter of a circle is 13.8cm. Find the length of its radius
Hello!
R = D/2
R= 13,8/2 => 6,9cm
The length of the circle's radius is 6.9 cm.
The diameter of a circle is twice the length of its radius. So, to find the length of its radius (r), you can divide the diameter (d) by 2.
Given: Diameter (d) = 13.8 cm
Length of radius (r) = d / 2
r = 13.8 cm / 2
r = 6.9 cm
The length of the circle's radius is 6.9 cm.
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please help with this math problem
Step-by-step explanation:
please mark me as brainlest
Answer:
10 mm
Step-by-step explanation:
You can find the missing dimension using the triangle area formula with the dimensions you know.
A = 1/2bh
40 mm² = 1/2(b)(8 mm)
b = 40 mm²/(4 mm) = 10 mm . . . . . . . divide by the coefficient of b
The triangle's base is b = 10 mm.
hello, please answer the question, please show work
Jaden is looking up at the top of a 56 Foot
rock climbing wall
. If Jaden is standing 15 feet
from the base of the wall,
what is the angle
of elevation from Jaden to the top of the wall?
noooooooooooooooooooolo
Multicultural Studies!
HELP PLEASE
Gisela didn't say anything when her friend made a joke about the texture of
Black people's hair. What is Gisela showing?
O A. Assertive behavior toward racism
B. Institutional racism
C. Passive acceptance of racism
D. Intolerance toward racism
Answer:
It is Passive acceptance of racism, There was no reason why she needed to say black people unless she wanted to downplay them. She is being racist because she saying that only black people have this type of texture. If her friend made a joke like this then she would do worse jokes like calling black people monkeys (aka N's that the definition of the N-word monkey).
A (2, 2)
b (0,3)
c (2, 4)
rhombus abcd has the coordinates listed. find the coordinates of point d.
es )
a)
)
(4.3)
b)
(3,4)
c)
(3.3)
d)
(4.4)
Answer:
I think its 3,4 maybe
Step-by-step explanation:
try it out but I'm not sure
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $1.90. Today they made $78.60 from the 57 wraps sold. How many of the wraps so ld were vegetarian?
Two basketballs fell, without bouncing, from a net and a chair at the same time. The ball which fell from the net rolled 30 feet. Note: Figure is not drawn to scale The horizontal and vertical distances traveled by the balls formed similar triangles. How far did the second ball roll from the chair? A. 6 feet B. 22 feet C. 4 feet D. 3 feet
Answer:
c
Step-by-step explanation:
The bearing of a point K from a point L is 084 degrees. What is the bearing of L from K
Answer:
if point bearing of k-l is 084 degree so the bearing of point l-k is 84 degree
The bearing of a point L from a point K is 264 degrees.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The bearing of a point K from a point L is 084 degrees.
Now,
Since, The bearing of a point K from a point L is 084 degrees.
Hence, The bearing of a point L from a point K = 180° + 84°
= 264°
Thus, The bearing of a point L from a point K is 264 degrees.
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what is 1 half multiplied by (4+8) equal
Answer:
6
Step-by-step explanation:
What is 1 half (1/2) multiplied by (4+8) equal?
1/2*(8+4) <== add the number in the parenthesis
1/2*12 <== multiply the numbers, half of 12 is 6
6 <== final answer
Hope this helps!
6
Step-by-step explanation:
Hope the pic will help
HELPPP 50 pointsss
An equation is shown below:
8(2x – 14) + 13 = 4x – 27
Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)
Part B: What value of x makes the equation true? (4 points)
Answer:
x = 6
Step-by-step explanation:
8(2x – 14) + 13 = 4x – 27
Lets go in the order of PEMDAS (Parantheses, Exponents, Multiplication, Division, Addition, Subtraction)
First, distribute 8.
8(2x – 14)
[tex]8*2x=16[/tex]
[tex]8*-14=-112[/tex]
So now our equation is:
16x – 112 + 13 = 4x – 27
Now we can add. We will add 13 to -112.
[tex]-112 +13=-99[/tex]
Now our equation looks like this:
16x – 99 = 4x – 27
Now we have to try to get the variable (x) on one side of the equation.
To do this, we will subtract 4x from both sides of the equation.
16x – 99 = 4x – 27
-4x -4x
12x - 99 = -27
Now we can add 99 to -27.
[tex]99 + (-27) = 72[/tex]
Now we have
12x = 72
Our last step is to divide both sides by 12:
[tex]\frac{12x}{12}= \frac{72}{12}[/tex]
We get x = 6.
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
−Kallmekrish
Answer:
Step-by-step explanation:
A.
8(2x – 14) + 13 = 4x – 27
Step 1: Distribute 8, meaning multiply 2x and -4 using 8
8(2x – 14)
8(2x) + 8(-14)
16x - 112
New equation:
16x - 112 + 13 = 4x – 27
Step 2: Add any numbers or like terms:
16x - 112 + 13 = 4x – 27
16x - 109 = 4x - 27
New equation:
16x - 99 = 4x - 27
Step 3: Isolate the variable on one side
16x - 99 = 4x - 27
-4x -4x
12x - 99 = - 27
+ 99 + 99
12x = 72
Step 4: Divide both sides by 12
12x = 72
/12 /12
x = 6
B.
Check your answer:
8(2x – 14) + 13 = 4x – 27
8(2(6) - 14) + 13 = 4(6) - 27
8(12 - 14) + 13 = 4(6) - 27
8(-2) + 13 = 24 - 27
-16 + 13 = 24 - 27
-3 = -3
This statement is correct
Therefore, our answer (x = 6) is correct.
Hope this helps!
use the muliplier method to increase 88 pound by 14% show your working
Answer:
100.32
Step-by-step explanation:
Since the question is asking to INCREASE, you want to multiply 88 by 1.14
This is because a percent is a number multiplied by 100 (For example 0.1 is 10%)
Whenever you want to increase by a percent, you add 100% to the number.
So:
88 * 1.14 =
100.32
A bottle is launched from a bottle launcher. The height of the bottle is modeled by the equation h(t) = –16t2 + 78t + 10. How long does it take the bottle to reach the ground?
A.
10 seconds
B.
5 seconds
C.
4.7 seconds
D.
1.1 seconds
Answer:
C: 4.7
Step-by-step explanation:
Axis of symmetry: -b/2a
a=-16
b=78
-78/2(2(-16))= 4.875 seconds in the air.
Pls help i will give 5 starts and brainliest question is down below 9:22
Answer:
D
Step-by-step explanation:
I have done this before
Top row units is 8 i then multiplied both sides so 5*2 which = 10 then multiplied 8*10 to get 80
Answer:
80 square units (D)
Step-by-step explanation:
Base is 16 units, height is 5 units. 16 * 5 = 80
Mrs Smith visits THE SCHOOL - outfitters to buy school clothes for the new school year.
The price of a school dress is R350 and a blazer is R650.
Calculate the percentage profit the shop makes if the cost price per dress is R280.
The shop makes 25% profit if the cost price per dress is R280.
In how many years will $1,000 yield an interest of
$6000 at 60% simple interest?
Answer:
10 years
Step-by-step explanation:
The simple interest formula tells you the relationship between interest, principal, interest rate, and time. When the given values are put into the formula, it can be solved for the unknown time.
__
I = Prt . . . interest earned on principal P at rate r for t years
6000 = 1000·0.60·t . . . . use the given values for I, P, r
6000/600 = t = 10 . . . . divide by the coefficient of t
$1000 will yield an interest of $6000 in 10 years.
What are the factors of 2x2 3x – 54? Select two options. 2x – 9 2x – 6 2x 6 x – 6 x 6.
The factors of expression [tex]2x^{2} +3x-54[/tex] are (x+6) and (2x-9).
The given expression is: [tex]2x^{2} +3x-54[/tex]
What is a factor?A factor is a number that divides another number leaving no remainder.
We can rewrite the given expression as:
[tex]2x^{2} +12x-9x-54[/tex] (middle term has been splitted)
Take 2 as common from first two terms while take -9 as common from last two terms.
[tex]2x(x+6)-9(x+6)[/tex]
Take (x+6) as common
[tex](x+6) (2x-9)[/tex]
So, we got the factors (x+6) and (2x-9)
Therefore, The factors of expression [tex]2x^{2} +3x-54[/tex] are (x+6) and (2x-9).
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Does the budgeted amount cover the actual amount for expenses, savings, and emergencies?
A)
No, it's short $207.00,
No, it's short $227,00,
o
Yes, there's a surplus of $207.000
D)
Yes, there's a surplus of $227.00,
Answer:
No its short 207
Step-by-step explanation:
Took the test on UsaTestPrep got it right :)
Bye loves <3
Answer:
the one b4 is wrong its a surplus of 207 .-.
Step-by-step explanation:
this is correct usatestprep also lol
SUB - Mathematics
Grade - 9th
Q.1) Visualise 3.765 on the number line , using Succescive Magnification.
Note:-
• Kindly Don't spam
• Need Genuine Answer
• Don't need plagiarised answer .
• Spam/wrong/short answers will be reported....
• Don't be greedy for points.
Step-by-step explanation:
Introduction:-Successive magnification:
In this process, we use to represent real numbers and visualize them on the number line such as by the magnifying glass, due to this we refer it as successive magnification.
Solution:-Since, we're given to visualize 3.765 on the number line, we take the number line from between 3 and 4Then, in between 3 and 4, we then visualize the portion of 3.7 and 3.8Again, in between 3.7 and 3.8, we visualize the portion of 3.76 and 3.77.At last, we point out the required number for visualizing that is 3.765, in between 3.76 and 3.77.What do I have to major in to become an astronomer and approximately how long would I have to stay in college?
Can someone please answer & show work? Thanks.