1. You have 60 in. of molding to use as a frame around a picture you are painting. The area of the painting is giving by the function y = 30x - x^2 where x is the width in inches. What width gives the maximum area for the painting? What is the maximum area?
2. You are trying to dunk a basketball. You need to jump 2.5 ft in the air in order to dunk the ball. The height that your feet are above the ground is given by the function h = -16t^2 + 12t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?
I need a lot of help with these problems. Please answer them to the best of your capabilities. I'M GOING INSANE!!! Thanks so much!
Answers
[tex]x = -b/2a = -30/2(-1) = 15[/tex]
[tex]y = -(15)^2+20(15) y = -225+450 y = 225[/tex]
So, 15 as the width would give us the maximum area for the painting.
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2) The maximum height your feet will be above the ground is 2.25 ft.
No, you wouldn't be able to dunk the ball because the maximum height you can jump is 2.25, but you need to jump 2.5 ft to dunk.
Related Questions
WILL GIVE BRAINLIESTWhich of the following represents the ratio of the hypotenuse to the given side
Answers
The 'given' side is the one with the length marked. That's 6 .
Their ratio is
6√2 / 6 .
In simplest form, that's √2 . (B)
HELP QUICKLY
15 men and 20 women what is the experimental probability that the next person to enter the store will be a man?
Answers
15/35
which we can simplify to
3/7
The probability that the next person to enter the store will be a man is 3/7
Answer: 3/7
Women: 20
Men: 15
Total: 35
15/35 is simplified to 3/7
solve the equation. choose the answer in simplest form. 4x= 8/7 (A) 1/28 (B) 1/7 (C) 2/7 (D) 7/2
Answers
x=(8/7)÷4
x=2/7
/4 /4
x = (8/7)/4 (Keep, change, flip)
x = 8/7 * 1/4
x = 8/28
x = 2/7
can you solve x = 29 - 3(9 - 4)
Answers
The solution of expression is.
⇒ x = 14
We have to given that,
An expression,
⇒ x = 29 - 3 (9 - 4)
Now, We can solve the expression for value of x as,
⇒ x = 29 - 3 (9 - 4)
⇒ x = 29 - 3 × 5
⇒ x = 29 - 15
⇒ x = 14
Therefore, the solution of expression is.
⇒ x = 14
Learn more about the mathematical expression visit:
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150% of A is equal to $120
Answers
So, to find 150% of A, we use this equation:
1.5a = 120
We divide both sides by 1.5 to isolate a:
a = 80
150% of 80 is equal to 120
150/100A=120
Simplify
3/2A=120
A=80
The endpoints of GE are located at G(-6,-4) , and E(4,8). Using slope-intercept form, write the equation of GE.
Answers
Answer:
The line would be y = 6/5x + 26/5
Step-by-step explanation:
To find the equation, we first need to find the slope. We can do this by using the slope formula.
m(slope) = (y2 - y1)/(x2 - x1)
m = (8 - -4)/(4 - -6)
m = 12/10
m = 6/5
Now that we have the slope, we can use that and either point in point-slope form to get the equation.
y - y1 = m(x - x1)
y - 8 = 6/5(x - 4)
y - 8 = 6/5x - 24/5
y = 6/5x + 26/5
LMN≅PQR
What is the value of x in degrees?
Enter your answer in the box.
x = °
Answers
Point Q has an angle of 72, which means that point M also has an angle of 72.
Now you have two angles to find x. All interior angles of a triangle add up to 180, so you can set up the following equation to find x:
72 + 36 + x = 180
Subtract 36 from both sides.
72 + x = 144
Subtract 72 from both sides.
x = 72
The angle of point L, x, is 72.
Answer:
Step-by-step explanation:
72
120e^(2x)=75e^(3x)
Please solve with steps
Answers
[tex]120e^{2x}=75e^{3x}[/tex]
[tex]ln(120e^{2x})=ln(75e^{3x})[/tex]
Step 2. Apply product rule of logarithms [tex]ln(ab)=ln(a)+ln(b)[/tex]:
[tex]ln(120)+ln(e^{2x})=ln(75)+ln(e^{3x})[/tex]
Step 3. Apply the rule [tex]ln(e^x)=x[/tex]:
[tex]ln(120)+2x=ln(75)+3x[/tex]
Step 4. Solve for [tex]x[/tex]:
[tex]ln(120)+2x=ln(75)+3x[/tex]
[tex]ln(120)-ln(75)=3x-2x[/tex]
[tex]x=ln(120)-ln(75)[/tex]
Apply the quotient rule of logarithms [tex]ln(a)-ln(b)= ln(\frac{a}{b} )[/tex]:
[tex]x=ln( \frac{120}{75} )[/tex]
[tex]x=ln( \frac{8}{5} )[/tex]
We can conclude that the solution of our equation is [tex]x=ln( \frac{8}{5} )[/tex], which is approximately [tex]x=0.47[/tex].
what is the missing constant term in the perfect square that starts with x^2 +6x
Answers
The answer is 9
x^2 + 6x + 9 is the same thing as (x+3)^2
the rules of a contest say that there is a 5% chance of winning a prize. four hundred people enter the contest. predict how many people will win a prize
Answers
400 times 0.05 is 20
20 times 20 is 400
5 times 20 is 100
therefore, 20 people
A percentage is a way to describe a part of a whole. The number of winners in the contest is 20.
What is the Percentage?A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As it is given that the chances of winning a prize are 5%, and 400 people enter the contest, therefore, the number of people who will be winning is 5% of the number of contestants.
[tex]\text{Number of Winner} = 5\%\ \text{of the Number of Contestants}\\\\\text{Number of Winner} = \dfrac{5}{100} \times 400 = 20[/tex]
Hence, the number of winners in the contest is 20.
Learn more about Percentages:
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The base of this regular right pyramid is a square. What is its surface area?
base edge = 8in
Height = 12in
Answers
B=8^2=64 inches2
T.S.A.=1/2(32)(12)+ 64
=192+ 64
= 256 inches2
Answer:
C
Step-by-step explanation:
A rectangular jewelry box costs $125 to gold plate. Calculate the cost of gold plating a box which is similar in shape and that holds 8 times as much.
The answer is not $1,000 or $8,000 or $64,000
Answers
Volume is a three dimensional measurement, so the fact that it is 8 times larger tells us each dimension was 2 times larger (2 x 2 x 2=8).
Area is a two dimensional measurement, so the area would have been 2 x 2 or 4 times larger. This means the price would be 4 times as much.
$125 x 4 = $500.
It will cost $500 to gold plate the similar jewelry box.
PLZ HELP ASAP Using the frequency table below, find how many students received a score of 70 or better on a mathematics test.
A.19
B.12**
C.17
D.14
Score Interval Frequency
50 – 59 [2]
60 – 69 [5]
70 – 79 [5]
80 – 89 [7]
90 – 99 [2]
Answers
Here are the steps:
1. we know that 70 - 79 = 5 students 80 - 89 = 7 students 90 - 99 = 2 students.
2. ADD
3. 5 + 7 + 2= 14
4. ANSWER
A: D there are 14 students scored 70 and above!
Hope this helped! (tell me if i'm wrong or right please!!!)
Answer:
D.14
Step-by-step explanation:
To find out the answer, we need to add up all the student s that a 70 or above. 5 got 70-79, 7 got 80-89, and 2 got 90-99.Add these up and we get 14. The answer is D.14
Jonathan bought 10lb of flour at 7.50 he had a store cupon for 0.79 what was the final price for flour
Answers
The height h of an arrow in feet is modeled by h(t) = -16t^2 + 63t +4, where t is the time in seconds since the arrow was shot. what is the height of the arrow after 2 seconds?
Answers
If you substitute in the formula t = 2, you will get 66.
Hope this helps you!
What is the equivalently non equivalent
Answers
Answer:
1/2 and 5/8 are not equivalent
Explanation:
The term equivalent means that a number or term has the same numerator-to-denominator (proportional) ratio as another number.
1/2 and 2/4 would be equivalent because if you divide the numerator and the denominator of the second fraction by 2, the result is the 1/2.
If you divide the denominator of 5/8 by 4, the result is a 2, matching the denominator of 1/2. However, if you divide the numerator by 5, the result is 1.25, which does not match the numerator of 1/2.
Therefore, these two numbers are not equivalent.
you are dealt one card from a standard 52-card deck. Find the probability of being dealt a 3.
Answers
Asher pays 156 every 6 weeks for piano lessons what is the price per year for piano lessons
Answers
50.8 weeks in a year / 6 weeks = 8.48 payments
$156 x 8.48 payments = $1322.88 per year
Only 6 of the 75 trees in a park are at least 30 feet tall. What percent of the trees are under 30 feet tall?
Answers
Answer: 8%
Answer:
8%
Step-by-step explanation:
Why is a square a rectangle and a rhombus??
Answers
A square is a rhombus because it has 4 equal sides.
mrs.beluga is driving on a snow covered road with a drag factor of 0.2. she brakes suddenly for a deer. The tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet. What is the minimum speed she could have been going?
Answers
where
[tex]c[/tex] is the length of the chord
[tex]m[/tex] is the middle ordinate
We know from our problem that the tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet, so [tex]c=52[/tex] and [tex]m=6[/tex]. Lets replace those values in our formula:
[tex]r= \frac{52^2}{8(6)} + \frac{6}{2} [/tex]
[tex]r= \frac{2704}{48} +3[/tex]
[tex]r= \frac{169}{3} +3[/tex]
[tex]r= \frac{178}{3} [/tex]
Next, to find the minimum speed, we are going to use the formula: [tex]s= \sqrt{15fr} [/tex]
where
[tex]f[/tex] is drag factor
[tex]r[/tex] is the radius
We know form our problem that the drag factor is 0.2, so [tex]f=0.2[/tex]. We also know from our previous calculation that the radius is [tex] \frac{178}{3} [/tex], so [tex]r= \frac{178}{3}[/tex]. Lets replace those values in our formula:
[tex]s= \sqrt{(15)(0.2)( \frac{178}{3}) } [/tex]
[tex]s= \sqrt{178} [/tex]
[tex]s=13.34[/tex] mph
We can conclude that Mrs. Beluga's minimum speed before she applied the brakes was 13.34 miles per hour.
The minimum speed Mrs. Beluga could have been traveling when she braked suddenly on the snow-covered road is approximately 13.68 mph.
To find this, we can use the formula for determining speed from yaw marks: v = √(15 × f × R), where v is the speed in miles per hour, f is the drag factor (0.2 in this case), and R is the radius of the yaw mark.
First, we need to determine the radius of the yaw mark using the given chord length (52 feet) and middle ordinate (6 feet). The formula for R using these values is: R = (C² / 8M) + (M / 2), where C is the chord length and M is the middle ordinate.
Plugging in the values, we get:R = (52² / 8 × 6) + (6 / 2)Calculating inside the parentheses:
R = (2704 / 48) + 3This simplifies to:
R ≈ 59.42 + 3Thus, R ≈ 62.42 feet.Now, plug R and f into the speed formula:
v = √(15 × 0.2 × 62.42)Calculating inside the square root:
v = √(187.26)This yields:
v ≈ 13.68 mph.
Therefore, the minimum speed Mrs. Beluga could have been traveling was approximately 13.68 mph.
Tommy conducts an experiment where he rolls a number cube, with sides labeled from 1 to 6, and then flips a coin. This table shows the results from 12 trials. Results 1 H 4 T 1 H 5 T 2 H 3 T 6 T 2 H 3 T 5 T 3 H 4 T How do the experimental probability and theoretical probability of rolling an odd number and then flipping a tail in Tommy's trials compare? Drag and drop the values or phrases to correctly complete the sentence. The experimental probability is , which is the theoretical probability of .
Answers
The theoretical probability of rolling an odd and flipping a coin is 1/4.
1/2 x 1/2 = 1/4
Looking at the results, there are 4 occasions where an odd numbers was flipped then tails.
That is 4 out of 12 or 1/3 which is more than 1/4 for the theoretical.
Answer:
The experimental probability is greater than the theoretical probability.
Step-by-step explanation:
Edg : )
|-7 + 5| +6
________
4
Answers
The school's basketball team lost 4 times as many games as they won. They also tied 5 fewer games than they won.
If they played 43 games, how many did they lose?
Answers
If they played 43 games, the number of games that they lost is: 32
How to save algebra word problems?
Let
x represent number of games won
Let y represent number of lost games.
Thus;
y = 4x - - - - - equation (I)
Let z denote tied games.
Thus;
z = x - 5 - - - - - equation(II)
Total games played is 43.
Thus;
x + y + z = 43 (III) equation
substitute (I) and (II) in (III)
therefore
x+(4x)+(x-5)=43
6x-5=43
x=48/6
x=8
y = 4x
= 4*8 =32
The answer is 32 lost games
7.68 cal/sec to Kcal/min
Answers
first covert cal/sect o cal/min
7.68 cal/sec x 60 seconds = 460.8 cal/min
1 Kcal = 1000 cal
divide cal by 1000 to get Kcal
460.8 cal/min / 1000 = 0.4608 Kcal/min
round answer as needed
What is the value of x. Enter your answer in the box.
A triangle with 3 sides that's a right triangle the longest one is 24 then 7 then x. What is x
X=___
Answers
[tex]a^{2} + b^{2} = c^{2}[/tex]
We already know two sides, so plug those into the equation. The longest side will be c:
[tex]a = 7, c = 24[/tex]
[tex]7^{2} + b^{2} = 24^{2}[/tex]
[tex]49 + b^{2} = 576[/tex]
Subtract 49 from both sides.
[tex]b^{2} = 527[/tex]
Square root both sides to get b by itself:
[tex] \sqrt{527} = 22.9564[/tex]
[tex]b = 22.9564[/tex]
The value of x is 22.9564.
a and b are the legs, c is the hypotenuse.
Refer to the picture :) I just drew a standard right triangle, *not to scale*.
The hypotenuse is always the longest side of a right triangle, so I plugged in 24 for c. I plugged in x and 7 for a and b.
x² + 7² = 24²
Square 7 and 24.
x² + 49 = 576
Subtract 49 from both sides.
x² = 527
Square root both sides to isolate and find x.
x = 23
A computer store builds custom computers by allowing customers to choose 1 of 4 different CPUs, 1 of 8 hard drives, and 1 of 3 videos cards. How many different computers are possible?
Answers
The fundamental counting principle states that the number of total options is given by multiplying the number of possibilities for each option, or
Total choices = choices x choices x ...
4*3*8 = 96
i need your help please!!!
Answers
Area of Semicircle = ([tex] \pi 6^{2} [/tex]/2)
Area of Semicircle = (3.14 x 36/2)
Area of Semicircle = (3.14 x 18)
Area of Semicircle = 56.52[tex] in.^{2} [/tex]
Hope this helps!
[pi]r^2
So substituting...
The diameter is 12 in. And radius is half of the diameter.
12/2=6. The radius is 6 in.
To finish this, we do the r^2, which is 6^2, which is 36.
Finally, we multiply pi by 36, in this question we found pi to 3.14.
The area of the circle is 113.04 in. BUT, Half of the circle, that is being shaded, would subtract half of the circle away from the total area.
So we do 113.04/2=
56.52.
The answer is that the shaded/not shaded side of the circle is equal to 56.52 in.
solve the area of a triangle for b and use the resulting formula to find the base of a triangle with a height of 6 ft. and an area of 9 ft. ^2.
Answers
[tex]A_\Delta=\dfrac{bh}{2}[/tex]
b - a base
h - a height
We have:
h = 6ft.and A=9 ft.²
substitute:
[tex]\dfrac{6b}{2}=9\\\\3b=9\ \ \ |:3\\\\b=3\ ft.[/tex]
Answer: b = 3ft.
HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ!!!
Which of the following best describes the expression 9(x + 7)?
A. The sum of constant factors 9 and x + 7
B. The product of constant factors 9 and x + 7
C. The product of a constant factor 9 and a 2-term factor x + 7
D. The sum of a constant factor 9 and a 2-term factor x + 7
Answers
Answer:
THE ANSWER IS C NOT D
Step-by-step explanation:
The answer is C i got it correct on the test DON'T LISTEN TO THE PEOPLE THAT SAY D