Answer:
The height, h, of the rock as a function of the horizontal distance from Jeremy's hand is h = -13/784·(x - 28)² + 17
Step-by-step explanation:
The given parameters are;
The height of the rock above the water when it leaves Jeremy's hand = feet
The maximum height of the rock = 28 feet
The horizontal distance at maximum height = 17 feet
Therefore, the given coordinates of the maximum height = (28, 17)
The equation of a parabola in vertex form is f(x) = a(x - h)² + k
Taking the maximum point as the vertex of the parabola, we have;
(h, k) = (28, 17)
Substituting the values gives;
f(x) = a·(x - 28)² + 17
At x = 0, the height = 4, we have;
f(0) = 4 = a·(0 - 28)² + 17
4 - 17 = a×28²
-13 = 784 × a
a = -13/784
Therefore, the height of the rock, f(x) = h, as a function of the horizontal distance from Jeremy's hand is therefore;
f(x) = h = -13/784·(x - 28)² + 17
Jack's family left home at 9:00 AM and drove to the amusement park at 60 mph. They spent 7 hours at the park and then drove back home. On the way home, traffic was bad and they drove 20 mph slower than in the morning. They got home at 8:00 PM. How far is the amusement park from Jack's home?
Answer:
96 miles
Step-by-step explanation:
The distance from the amusement to jack's home is x (mile, x>0)
jack's family went to the amusement park at: 9 + x/60
On the way home, traffic was bad and they drove 20 mph slower than in the morning⇒ they drove: 60 - 20 = 40 mph
they left the amusement park at: 20 - x/40
have the following equation:
(20 - x/40) - (9+ x/60) = 7
⇔ 4 = x/40 + x/60
⇔ x = 96
so the distance from the amusement park to jack's home is 96 miles
What is m∠PQR?
The PS is line segment. Q is the point between segments PS. QR is another line segment passes through segment PS. The angle PQR is (3x + 5) degree and angle SQR is (x + 3) degree.
Answer: m∠PQR = 134°
Step-by-step explanation:
Given: PS is line segment. Q is the point between segment PS. QR is another line segment passes through segment PS.
That means ∠PQR and ∠SQR are linear pair [Linear pair is a pair of two angles made on one line and their sum is 180°]
⇒ ∠PQR + ∠SQR = 180° (i)
Since, ∠PQR is (3x + 5)° and ∠ SQR is (x + 3)° [given]
Put this in (i), we get
(3x + 5)° + (x + 3)° = 180°
⇒ 3x + 5 + x + 3 = 180
⇒ 4 x + 8 = 180
⇒ 4 x = 180-8
⇒ 4 x = 172
Divide both sides by 4
⇒ x= 43
So, ∠PQR= (3(43) + 5)° = 134°
Hence, m∠PQR = 134°
The measure of m ∠PQR is 134 degrees.
GivenPS is a line segment.
Q is the point between segment PS.
QR is another line segment that passes through segment PS.
Which property of the triangle is used to solve the value of x?The sum of two angles made on one line is equal to 180 degrees.
[tex]\angle \rm PQR + \angle SQR = 180[/tex]
Where the angle QPR is (3x + 5) degree and angle SQR is (x + 3) degree.
Substitute all the values in the equation
[tex]\angle \rm PQR + \angle SQR = 180\\\\(3x+5) + (x+3) =180\\\\3x+5+x+3=180\\\\4x+8=180\\\\4x=180-8\\\\4x=172\\\\x = \dfrac{172}{4}\\\\x =43[/tex]
The value of x is 43 degrees.
Therefore,
The measure of m ∠PQR is;
[tex]\rm m \angle PQR = 3x+5 = 3(43) + 5= 129+5=134[/tex]
Hence, the measure of m ∠PQR is 134 degrees.
To know more about the Properties of triangles click the link given below.
https://brainly.com/question/9404288
A submarine descends at a rate of 2.6 kilometers per hour.
If the ocean floor is 6.24 kilometers below sea level, how long will it take the submarine to descend to the ocean floor?
Round your answer to the nearest tenth. Enter your answer in the box.
Answer:
6.24/2.6 = 0.24
0.2 is the answer
Step-by-step explanation:
Answer:8.84 if you add -3.63 when sub 14.976 when multiplyed and 0.2 when devided
Step-by-step explanation:
i just use a simple mdethod and it was to do all the pfroblems then do what ever to them to get my answer
The square root of 215 is between which two whole numbers?
Answer:
14 and 15
Step-by-step explanation:
14.6628782986, this is the square root.
Will mark brainliest‼️
every year 20 fewer students eat in the school cafeteria. assuming this trend continues, write a multiplication expression to show the change in the number of students over the next 4 years. Express this change as an integer.
Answer:
ㅎㄹㅊㅊㅎ초ㅗ초초쳧쳐ㅗ채ㅓㅓ호퐃러ㅗㅏㅗㅎ초하ㅗㅓㅠㅗㅍㅊ호허ㅠㅓㅠㅓㅏㅑㅗㅗㅍㅎㅊㅎ처ㅏㅜㅣㅓㅓㅎ
Hello. What are the vertices, foci, endpoints of the conjugate axis, and the equation of the asymptote of 7x^2-9y^2-14x+72y-200=0?
Answer: is ( 1,4 )
Step-by-step explanation:
What is the domain of this exponential function?
Show work please I have no clue how to do this.
BRAINIEST IF ANSWERED !!If mZBNO = 85, then what is m
solve the inequality:
-|x-2| + 9 > 6
Answer:
− 1 < x < 5
Step-by-step explanation:
HURRT PLEASE HELP!
Which sequence of transformations could be used to
map parallelogram ABCD onto A"B"C"D"?
ry-axis T(0.4)
TO, -4) ºry-axis
T-5, -1) ºrx-axis
rx-axis o T-5, -1)
Answer:
its C T(-5,-1) rx-axis
Step-by-step explanation:
right on edge
answer quick please, appreciate it
A number line graph is shown:
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Based on the graph, which inequality is correct for a number that is to the right of -4?
0-2 <-4
O-3>-4
0 1 <-4
-5 >-4
Answer:
1<-4
Step-by-step explanation:
Answer:
-3 > -4 i believe i hope this helps!!
Step-by-step explanation:
What is a greater slope 3 or 8
Answer:
8
Step-by-step explanation:
it goes up steeper
Answer:
3
Step-by-step explanation:
Because on a graph it is wider and less vertically stretch
3. Simplify i41. (2 points)
0
-1
O
-1.
O
1
Maria made 4 pies for the school carnival. She cut each pie into 8 slices. If she sold 27 slices, how many slices did she have leftover?
Answer:
She had 5 slices left over
Step-by-step explanation:
8 times 4 is 32 so then subtract 27 and you get 5
how can you find odd numbers that u can put as a fraction
Answer:
Fractions are not even numbers or odd numbers, because they are not whole numbers. They are only parts of numbers, and can be written in different ways.
Step-by-step explanation:
Giving brainlist SO PLZ HELP
Select the situation below that models the following equation: -3(8) = -24.
A. A diver who was in the water wanted to see a school of colorful fish below. She dove at a depth of three feet per second. If she started diving at sea level, what is her position after eight seconds?
B. The temperature outside dropped a total of three degrees in eight hours. What was the temperature after those eight hours?
C. At the football game, Tyrice gained eight yards on one play and then lost three yards on the next play. How many total yards did he gain or lose over those two plays?
D. Gunner wants to see a movie that costs $8.00. He sees the movie with three of his friends. How many times did he see the movie?
Answer:
a
Step-by-step explanation:
-3 feet every second x 8 seconds
Solve for x in the following equation:
kx = m + nx
Answer:
x = [tex]\frac{m}{k-n}[/tex]
Step-by-step explanation:
Given
kx = m + nx ( subtract nx from both sides )
kx - nx = m ← factor out x from each term on the left side
x(k - n) = m ← divide both sides by (k - n)
x = [tex]\frac{m}{k-n}[/tex]
Solving for x in the equation, kx = m + nx, we would make x the subject of the formula to solve for x as: [tex]\mathbf{x = \frac{m}{k - n}}[/tex]
Given:
kx = m + nx
We are require to make x the subject of the formula.Thus:[tex]kx = m + nx[/tex]
Subtract nx to both sides of the equation[tex]kx - nx = m + nx - nx\\\\kx - nx = m[/tex]
Factor out x on the left side[tex]x(k - n) = m[/tex]
Divide both sides by (k - n)[tex]\frac{x(k - n)}{k - n} = \frac{m}{k - n} \\\\x = \frac{m}{k - n}[/tex]
Therefore, solving for x in the equation, kx = m + nx, we would make x the subject of the formula to solve for x as: [tex]\mathbf{x = \frac{m}{k - n}}[/tex]
Learn more here:
https://brainly.com/question/21727387
Determine if JK and LM are parallel, perpendicular, or neither: J(13,-5), K(2,6), L(-1,-5), M(-4,-2)
Answer:
Parallel
Step-by-step explanation:
mjk=-1
mlm=-1
Write an equation in slope-intercept form passing thru the points (-2,2)
and (-3,4)
Put a pic of your self while you answer I need it to make edits you can see it tomorrow on my Instagram ill comment on it, thx for the help guys
Pls make it to you because people can tell.
can someone help me figure out how to do unit cube finding volume please?
Answer:
the Volume of a cube Given the length of one side, call it the volume of a cube can be found by using the following formula: Volume of any cube = a 3 = a × a × a Examples showing how to find the volume of a cube.
Step-by-step explanation:
Yesterday Christopher sold 35 pounds of apples and 34 pounds of bananas for a total revenue of $163.50. Today he sold 15 pounds of apples and 17 pounds of bananas for a goal revenue of $76.75. Determine the price of each pound of apples and the price of each pound of bananas
Answer:
Step-by-step explanation:
35 a + 34 b = 163.50 (given)
15 a + 17 b = 76.50 (given) multiply this equation by -2
-30 a - 34 b = -153.00 now add this equation to the first equation t get
5 a = 10.50 solve this for a (apple's price) then sub this value into one of the equations to find banana price, b.
Find the lenght of side BC. give your answer to 3 significant figures
Answer:
BC ≈ 19.4 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos71° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{6.3}{BC}[/tex] ( multiply both sides by BC )
BC × cos71° = 6.3 ( divide both sides by cos71° )
BC = [tex]\frac{6.3}{cos71}[/tex] ≈ 19.4 cm ( to 3 significant figures )
What is the answer pls help
Answer:
a 180* clockwise rotation
Step-by-step explanation:
It is being flipped 180*.
Can someone please help me with my Imagine Math? My teacher assigned are class to do this even though we haven't learned about this yet.... I don't understand this at All!
QUESTION:
Drag each graph to show whether it is a function of x or not a function of x. If there is not enough information to tell, drag the graph into the box under “Not Enough Information.”
When you tell me the answers type it in this format:
this graph goes in "function" OR this graph goes in "Not a function" OR this graph goes in "Not enough information"
Answer:
first graph is not a function, second graph is a function, 3rd is not enough information, 4th is a function, 5th is not a function, 6th is a function
Step-by-step explanation:
Answer:
I got all of them right on Imagine Math!
Step-by-step explanation:
Hope this helps!
HELP ME PLZZZ WILL MARK YOU BRAINLIEST!!! HURRY
Answer:
[tex]\boxed {r = \frac{31}{3}}[/tex]
Step-by-step explanation:
To find the value of [tex]r[/tex], write an expression by using the following measurements of both [tex]\overline {DG}[/tex] and [tex]\overline {GM}[/tex], then you solve for [tex]r[/tex]:
[tex]\overline {DG} = r + 3[/tex]
[tex]\overline {GM} = 4r - 28[/tex]
[tex]r + 3 = 4r - 28[/tex]
Solve for [tex]r[/tex]:
[tex]r + 3 = 4r - 28[/tex]
[tex]x + 3 - 4r = 4r - 4r - 28[/tex]
[tex]-3r + 3 = -28[/tex]
[tex]-3r + 3 - 3 = -28 - 3[/tex]
[tex]-3r = -31[/tex]
[tex]\frac{-3r}{-3} = \frac{-31}{-3}[/tex]
[tex]\boxed {r = \frac{31}{3}}[/tex]
So, the value of [tex]r[/tex] is [tex]\frac{31}{3}[/tex].
Mario volunteered 1,386 minutes each month for 36 months. How many minutes did Mario volunteer in total???
Answer:
49,860
Step-by-step explanation:
Mario volunteered 49,860 in total.
seven apples cost five dollars. How many apples can I buy for $8?
Answer:
11 apples
Step-by-step explanation:
7/5=1.4
1.4x8=11.2
11.2 rounded to 11
Help me solve this inequality!