It will take the ball 4.0625secs to stay in the air
The maximum height of the ball is 264.0625m
Given the function representing the height reached by the golf expressed as;
h(t) = -16t^2 + 130t
The velocity function is expressed as:
v(t) = -32t + 130
At maximum height, the velocity of the ball will be zero, i.e v(t) = 0
0 = -32t + 130
32t = 130
t = 130/32
t = 4.0625
Hence it will take the ball 4.0625secs to stay in the air
b) Substitute t = 4.0625 into the height function to have:
h(t) = -16t^2 + 130t
h(t) = -16(4.0625)^2 + 130(4.0625)
h(4.0625) = -264.0625 + 528.125
h(t) = 264.0625m
Hence the maximum height of the ball is 264.0625m
Learn more on velocity function here: https://brainly.com/question/10962624
Solve for x. x+12√=x√+2
[tex]x = - \frac{2 \sqrt{3} + 12 }{11} [/tex]
hope it helps
see the attachment for explanation
[tex] \: [/tex]
Help please on part b
Answer:
-0.045
Step-by-step explanation:
you first take the derivate of A(t)
A'(t)=1.4e^-0.05t X (-0.05)
A'(t)=-0.07e^-0.05t
so when t=0
amount remaining is -0.07e^-0.05(0) ---- e^0 = 1
so its -0.07
when t=9
do the same thing,
-0.07e^-0.05(9) ---use calculator
-0.045
What is the value of v?
Answer:
34 degrees
Step-by-step explanation:
If you know the 2 interior angles of a triangle, you can find the 3rd.
This is useless since this is a right triangle.
In this case:
v + 46 = 90
v = 34 degrees
You are welcome!
Kayden Kohl
8th Grade Student
Please help me ASAP this has limited time olease
Answer:
x= 67
Step-by-step explanation:
Angle CGE makes a 23 degree angle, and makes a 90 degree angle with CGB.
By subtracting 90 and 23, you get 67 degrees for the angle EGB.
Since angle EGB and angle AGF are vertical angles, they are the same. So, x would equal 67.
Answer:
x = 67°
Step-by-step explanation:
Solving for x
We know that AGC is a right angle, thus AGD has to be a right triangle as well. Angle CGE is 23°, which would mean that FGD is also 23°.
90°-23°=67°
I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 25 minutes later. How many miles did I drive?
Step-by-step explanation:
x = number of hours driven
25 minutes = 5/12 hour
remember,
1 hour = 60 Minuten
5 minutes = 60/12 minutes = 1/12 hour
25 minutes = 5×5 minutes = 5/12 hour
x hours × 40 miles/hour = (x + 5/12) hours × 30 miles/hour
the dimensions "hour" eliminate each other from the top and the bottom of the fractions leaving only miles. and the miles must be the same either way.
40x = (x + 5/12)×30 = 30x + 150/12
10x = 150/12
x = 15/12 = 5/4 hours
40 miles/hour × 5/4 hours = 40×5/4 miles = 10×5 = 50 miles.
I drove 50 miles.
The area of a triangular flower bed in the park has an area of
120 square feet. The base is six feet shorter than three times the height. What are the base and height of the triangle?
Answer:
b = 24 ft
h = 10 ft
Step-by-step explanation:
120 = ½hb
120 = ½h(3h - 6)
240 = h(3h - 6)
240 = 3h² - 6h
80 = h² - 2h
0 = h² - 2h - 80
0 = (h - 10)(h + 8)
h = 10 ft or -8 ft
we ignore -8 as it makes no sense for a triangle side length.
b = 3(10) - 6 = 24 ft
You charge $1625 on your credit card that adds 8.2% intere don't make any payments, what will your balance be after 4 years compounded continuously?"
Answer:$2227.22
Step-by-step explanation: I answered your question in your comment. If its not right report it please.
Ana is playing a quiz game and needs more than 500 points to advance to the next level. She earns 18 points for each correct answer loses 6 points foWhat is an inequality that represents all the possible combinations of c, the number of correct answers, and w, the number of incorrect answers that Ana can get and move to the next level?
if the words after " 6 points fo" is "r each incorrect answer" then the answer is
18c - 6w > 500
explanation:
if she answers one correct, she'll get 18 points, so if she gets 18 correct, she'll get 18c points, same goes for each she gets incorrect but loses 6 points is +-6w, or simplified, -6w
A family buys airline tickets online. Each ticket costs $208. The family buys travel
insurance with each ticket that costs $16 per ticket. The web site charges a fee of
$22 for the entire purchase. The family is charged a total of $1142. How many
tickets did the family buy
Answer:
5 tickets
Step-by-step explanation:
Each ticket costs $224 including the travel insurance and they are charged $22 regardless of the number of tickets they buy.
Therefore, the equation is 224x + 22 = 1142
First, you have to subtract the 22 from both sides to amount to 224x = 1120
Now, you divide 224 from 1120 to get 5
The family bought 5 tickets.
What is the slope of the line that passes through the points (6, -10) and (3, -13)?
Write your answer in simplest form.
[tex](x_1, y_1) = (6,-10),~~ (x_2, y_2) = (3,-13)\\\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-13 +10}{3 -6} =\dfrac{-3}{-3} =1[/tex]
Out of 120 customers asked at a restaurant, 38 rounded their bill up to the next whole dollar and donated the difference to the local Children's Hospital. How many consecutive customers must round up the bills so that the percentage of people who donated increases to 50%?
A. 44 customers
B. 40 customers
C. 36 customers
D. 32 customers
Using proportions, it is found that 44 consecutive customers must round up the bills so that the percentage of people who donated increases to 50%, so option A is correct.
A proportion is the number of desired outcomes divided by the number of total outcomes.
Considering that 38 out of 120 customers rounded their bill up, with x customers added, the proportion will be of 38 + x out of 120 + x.
The desired proportion is 0.5, hence:
[tex]\frac{38 + x}{120 + x} = 0.5[/tex]
[tex]38 + x = 60 + 0.5x[/tex]
[tex]0.5x = 22[/tex]
[tex]x = \frac{22}{0.5}[/tex]
[tex]x = 44[/tex]
44 customers, so option A.
A similar problem is given at https://brainly.com/question/20571459
Use the number line to answer the question below:
<—A——————-B————C—->
If AB = 7x - 24 and BC = 6x - 2, what is the value of AC?
a. 13x - 22
C. 13x - 26
b. 33
d. 46
Work Shown:
AC = AB + BC
AC = (7x-24) + (6x - 2)
AC = (7x+6x) + (-24-2)
AC = 13x - 26
This works because segment AC is split up into two parts AB and BC which don't overlap. Refer to the segment addition postulate.
4) A teacher has an annual income of $51,750. The income tax the teacher has to pay is 7%. What is the amount of income tax in dollar and cents the teacher has to pay?
A) $3,448.25
B) $3,622.50
C) $3,891.10
D) $3,933.01
9514 1404 393
Answer:
B) $3,622.50
Step-by-step explanation:
To find the tax, multiply the income by the tax rate:
$51,750 × 0.07 = $3,622.50
A proportional relationship is shown in the table below
X 0 .3 .6 .9 1.2
Y 0 1 2 3 4
What is the answer to this question?
Answer:
The answer should be A.
Step-by-step explanation:
The price of an item has risen to $343 today. Yesterday it was $140. Find the percentage increase.
Answer:
145% increase
Step-by-step explanation:
343 - 140 = 203
203/140 = 1.45
1.45 x 100 = 145
$200 is shared between Bill and Ann. Ann’s share is $50 more than Bill’s share. Calculate the size of each of their shares.
First subtract the difference between the two:
200 - 50 = 150
Now divide that by 2:
150/2 = 75
Bills share is $75
Now add the $50 to 75 to get Ann's share:
75 + 50 = $125
Ann's share is $125
Bill's share is $75
In a recent tennis tournament, women playing singles matches used challenges on 133 calls made by the line judges. Among those challenges, 31 were found to be successful with the call overturned. a. Construct a 90% confidence interval for the percentage of successful challenges. b. Compare the results from part (a) to this 90% confidence interval for the percentage of successful challenges made by the men playing singles matches: 20.9%
Using the z-distribution, it is found that the 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
31 out of 133 challenges were successful, hence:
[tex]n = 133, \pi = \frac{31}{133} = 0.2331[/tex]
90% confidence level, hence [tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 - 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.1728[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 + 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.2934[/tex]
As percentages:
0.1728 x 100% = 17.28%
0.2934 x 100% = 29.34%
The 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
A similar problem is given at https://brainly.com/question/16807970
Please tell me how much can 6 go into 14 without going over 14
A hummingbird lives in a nest that is 12 meters high in a tree. The hummingbird flies 15
meters to get from its nest to a flower on the ground. How far is the flower from the base of
the tree?
Answer:
The flower is 9 meters from the base of the tree.
Step-by-step explanation:
Use the Pythagorean theorem to solve. We are given the length of one leg and the length of the hypotenuse of a right triangle.
[tex]a^{2} +b^{2} =c^{2}[/tex]
where a and b are the legs, and c is the hypotenuse.
Plug in the given values and solve:
[tex]x^{2} +12^{2} =15^{2} \\x^{2} +144=255\\x^{2} =81\\x=9[/tex]
The flower is 9 meters from the base of the tree.
in a box of chocolate 1/5 are plain chocolate 1/3 are white chocolate the rest are white
...ok and?
finish the question
Answer:
Step-by-step explanation:
[tex]\frac{1}{5}+\frac{1}{3}+x=1[/tex]
[tex]\frac{3}{15}+\frac{5}{15}+x=\frac{1.15}{15}[/tex]
[tex]\frac{8}{15} + x=\frac{15}{15}[/tex]
[tex]\frac{8}{15} - \frac{8}{15} + x=\frac{15}{15}-\frac{8}{15}[/tex]
[tex]x=\frac{7}{15}[/tex]
I think you are missing the question but I bet you are looking for the rest of chocolate in the box.
Please help
Solve.
(5√5)^−2x+1 = 1/5 ⋅ 125^x−3
Enter your answer in the box. Enter any fraction as a simplified fraction.
Step-by-step explanation: (5√5)−2x+1=
1
5
(125x)−3
0.008x+1=
1
5
(125x)−3
Step 1: Flip the equation.
1
5
(125x)−3=0.008x+1
Step 2: Add 3 to both sides.
1
5
(125x)−3+3=0.008x+1+3
1
5
(125x)=0.008x+4
Step 3: Divide both sides by 1/5.
1
5
(125x)
1
5
=
0.008x+4
1
5
125x=0.04x+20
The value of x is 46.
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
The number of times a number is multiplied by itself is defined by the exponent. The power is an expression that displays the same number or factor being multiplied repeatedly.
Given:
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]
ow, using exponents and powers
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 5 ^{3(x-3)\\[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x - 9 - 1}[/tex]
[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x -10}[/tex]
[tex]5^{3/2(-2x+ 1)}= 5^{3x - 10}[/tex]
[tex]5^{-x+ 3/2}= 5^{3x -10}[/tex]
Now, Comparing
-x+ 3/2 = 3x- 10
-x - 3x = -10 - 3/2
-4x = -23/2
x= 46
Hence, the value of x is 46.
Learn more about Exponents and powers here:
https://brainly.com/question/15722035
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mark is paid $12.45 and hour at his job.he works a shift of 4 hours and 20minutes. how much does john earn for this shift?
Answer:
$53.95
Step-by-step explanation:
[Setting up an equation] 12.45x = y
() x is time worked and y is money made
[Plugging-in time worked] 12.45(4 [tex]\frac{1}{3}[/tex]) = y
[Multiply] 53.95 = y
[Answer] y = $53.95
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Solve please
May God bless you
Answer:
We will use a Pythagorean identity and alegbra to prove this.
sin^2 + cos^2 = 1, dividing by cos^2 gives
tan^2 + 1 = sec^2.
Now, breaking down the fraction into parts and simplifying gives:
(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4
Now use difference of squares factoring from alegbra.
= (sec^2 + tan^2)*(sec^2 - tan^2)
By rewriting our Pythagorean identity to
sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,
we can finish the problem.
= (sec^2 + tan^2) * 1 = sec^2 + tan^2
= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.
The population in millions of a city t years after 1990 is given by the equation p(t) = 2.9+0.08t in this function
Answer:
The answer would be 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.
Hope it help and if it its correct please give brainliest
Stay Safe And Healthy
Thank You
What is 3/4+1 2/3+1/2=
Answer:
Exact Form:
35/12
Decimal Form:
2.916- (6 goes on)
Mixed Number Form:
2 11/12
If z varies directly as x and inversely as y and is equal to 4 when x and y have the values 12 and 8 respectively, what is the value of z when x is equal to 6/7 and y is equal to 5/28?
Answer:
[tex]z = \frac{2}{7} [/tex] when x= [tex] \frac{6}{7} [/tex],
z= 179.2 when y= [tex] \frac{5}{28} [/tex]
Step-by-step explanation:
Let's start by writing out the two general equations for z.
Since z varies directly with x,
z= kx, where k is a constant.
Since z varies inversely with y,
[tex]z = \frac{k}{y} [/tex], where k is a constant.
When x= 12, z= 4,
4= k(12)
12k= 4
k= 4 ÷12
k= ⅓
∴ z= ⅓x
When x=[tex] \frac{6}{7} [/tex],
[tex]z = \frac{1}{3} ( \frac{6}{7} )[/tex]
[tex]z = \frac{2}{7} [/tex]
When y= 8, z= 4,
[tex]4 = \frac{k}{8} [/tex]
k= 4(8)
k= 32
[tex]∴z = \frac{32}{y} [/tex]
When y= [tex] \frac{5}{28} [/tex],
[tex]z = 32 \div \frac{5}{28} [/tex]
[tex]z = 32 \times \frac{28}{5} [/tex]
z= 179.2
Please check the mcq in the following picture and thank you
Answer 2nd one
Step-by-step explanation:
A
Triangle ABC is right-angled at A, and AD is the altitude from A to the hypotenuse BC.
Find x
Answer:
Step-by-step explanation:
5 x 6:30
50 points + brainliest answer questions 7 and 8 with work and all
Answer:
7) m∠BHE = 146°
8) m∠BAC = 25°
Step-by-step explanation:
Question 7:Given that, [tex]\displaystyle\mathsf{\overline{CD}\:||\:\overline{EF}}[/tex], and that [tex]\displaystyle\mathsf{\overline{AB}}[/tex] is a transveral.
We are also provided with the following measures of the angles: m∠DGH = 2x, and m∠FHB = 5x - 51.
∠DGH and ∠FHB are also corresponding angles, as they have corresponding positions on the same side of the transversal, [tex]\displaystyle\mathsf{\overline{AB}}[/tex]. These two angles also have the same measure.
Solve for x:In order to find the measure of ∠BHE, we could set up an equality statement on ∠DGH and ∠FHB to solve for the value of x.
m∠DGH = m∠FHB
2x = 5x - 51
Add 51 and subtract 2x from both sides of the equation:
2x -2x + 51 = 5x - 2x - 51 + 51
51 = 3x
Divide both sides by 3:
[tex]\displaystyle\mathsf{\frac{51}{3}\:=\:\frac{3x}{3}}[/tex]
x = 17
⇒ m∠DGH = 2x = 2(17) = 34°,
⇒ m∠FHB = 5x - 51 = 5(17) - 51 = 34°.
Since ∠FHB and ∠BHE are supplements (whose sum add up to 180°), we could determine the measure of ∠BHE as follows:
m∠BHE + m∠FHB = 180°
m∠BHE + 34° = 180°
m∠BHE + 34°- 34° = 180°- 34°
m∠BHE = 146°.
Therefore, the measure of ∠BHE is 146°.
Question 8:Given that ΔABC with [tex]\displaystyle\mathsf{\overline{AC}}[/tex] extended to D, and that m∠ABC = 63° and m∠BCD = 92°:
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles. In other words: ∠BCD = ∠BAC + ∠ABC.
Before we could apply the Exterior Angle Theorem, we must first find m∠BAC. Since ∠BCD and ∠BCA are supplements:
m∠BCD + m∠BCA = 180°
92° + m∠BCA = 180°
92° - 92°+ m∠BCA = 180° - 92°
m∠BCA = 88°
Solve for m∠BAC:Now that we have the measure for ∠BCA, we can find m∠BAC by applying the Triangle Sum Theorem where it states that the sum of the interior angles of a triangle is equal to 180°.
m∠BCD + m∠ABC + m∠BAC = 180°
92° + 63° + m∠BAC = 180°
125° + m∠BAC = 180°
155° - 155° + m∠BAC = 180° - 155°
m∠BAC = 25°
Therefore, the measure of ∠BAC is 25°.