The time taken by the rock to reach the lake below is 5.123 sec
t= 5.123 sec
What is quadratic equation?A quadratic equation is an algebraic expression of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2} +bx+c=0[/tex] where a, b are the coefficients, x is the variable, and c is the constant term.
It is given that,
H= [tex]-16t^{2} +32t+256[/tex], which represent the height of the rock
Also, we have given that the height of the cliff is 256 feet.
Now to find the time taken by the rock, take H=0
[tex]-16t^{2} +32t+256[/tex]=0
[tex]-16(t^{2} -2t-16) = 0[/tex]
[tex]t^{2} -2t-16 = 0[/tex]
Solve the above quadratic equation using Discriminant Method[tex]t= \frac{-(b)\pm\sqrt{(b)^{2}- 4 *a*c } )}{2*a}[/tex]
From above equation, a=1, b=-2, c=-16
So,
[tex]t= \frac{-(-2)\pm\sqrt{(-2)^{2}- 4 *1*(-16) } )}{2*1}[/tex]
[tex]t= \frac{2\pm\sqrt{(4+64 } )}{2}[/tex]
[tex]t= \frac{2\pm\sqrt{(68 } )}{2}[/tex]
There will be two value one with positive [tex]t= -2+\sqrt{(68 } )[/tex] and another with negative [tex]t= -2-\sqrt{(68 } )[/tex]
We will neglect negative value because time can't be negative.
[tex]t= \frac{2+\sqrt{(68 } )}{2}[/tex]
[tex]t= \frac{2+8.246}{2}[/tex]
[tex]t= \frac{10.246}{2}[/tex]
t= 5.123 sec
The time taken by the rock to reach the lake below is t= 5.123 sec
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can you please help me I’ll pay you £100
Answer:
The new points to the triangle will be:
[tex]A(-6, 6)\\B(-6, 3)\\C(-8, 3)[/tex]
Step-by-step explanation:
Because the reflection point is at [tex]x = -1[/tex], all x values will subtract their distances from [tex]x = -1[/tex] to get their new values. The y values remain the same.
The starting values are:
[tex]A(4,6)\\B(4,3)\\C(6,3)[/tex]
Point [tex]A[/tex] is 5 units away from [tex]x = -1[/tex], so we'll subtract 5 from -1 to get the new x value: [tex]-1 - 5 = -6[/tex], so [tex]A(-6, 6)[/tex].
Point [tex]B[/tex] is also 5 unit away from [tex]x = -1[/tex], so we'll subtract 5 from -1 to get the new x value: [tex]-1 - 5 = -6[/tex], so [tex]B(-6, 3)[/tex].
Point [tex]C[/tex] is 7 units away from [tex]x = -1[/tex], so we'll subtract 7 from -1 to get the new x value: [tex]-1 - 7 = -8[/tex], so [tex]C(-8, 3)[/tex].
Answer:
No need to pay me, its my pleasure, also its not even in my country's currency so it would be worthless to me anyways.
5,4 and 4,4
Step-by-step explanation:
help asap please bbbbb
Answer:432 whats the other option 4300
Step-by-step explanation:
A construction company needs to remove 10 tons of dirt from a construction site. They can remove 2/5 tons of dirt each hour. How long will take to remove the dirt?
Step-by-step explanation:
You can just divide 10 by 2/5 and you get 25 or try this
Set up proportions and cross multiply 2/5 / 1 = 10/x which you can read as : if 2/5 can be done in 1 hour then 10 tons can be done in x hours cross multiplying, you get 2x/5 = 10 and x = 25
Use the Pythagorean Theorem to find the distance between (3, 0) and (7,-6). Round
to the nearest tenth.
Answer:
14.4
Step-by-step explanation:
6^2+12^2=x^2
64+144+x^2
208=x^2
square root of 208= 14.4
x=14.4
Brad began working on a project at 10:15 A.M. He finished the work at 5:08 P.M.
How long did it take Brad to complete the project?
Answer:
It is a good idea to convert the times into internation time
thus, 5:08 becomes 17 08
Substraction:
17 08 - 10 15
= 16 68 - 10 15 ( I took one hour from 17 and added 60 minutes to 08)
= 6 53
he worked 6 hr 53 mins
PLEASSEWEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
46 square inches
Step-by-step explanation:
Surface Area = 2×(5×3 + 5×1 + 3×1)
Answer correctly and i give you brainliest
Answer:
B.
Step-by-step explanation: The answer is b because 65.04 is the answer we get from finding the difference of those irregular triangles and the circle.
P.S. They must be done seperately.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
48pi cm squred
Step-by-step explanation:
first find area of the circle which is pi x r^2
pi x 3^2 = 9pi
Since there are two circles...
9pi x 2 = 18pi
Then find the area of the rectangle that is wrapped around the circle by finding the circumference of the circle and then multiplying that with the height of the cylinder
circumference of the circle = 2 x pi x r
2 x pi x 3 = 6pi
6pi x 5 = 30pi
Therefore the surface area is
48pi cm squred
Hope this helps!
Part A
If Wendell creates a scale drawing using the scale 1 inch to 10 feet, what will the dimensions of the deck in the scale drawing be?
Part B
In the scale drawing, what will the length of the east side of the backyard be?
Part C
In the scale drawing, what will the length of the south side of the backyard be?
Part D
In the scale drawing, what will the length of the west side of the backyard be?
Part E
In the scale drawing, what will the length of the north side of the backyard be?
Part F
Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127º. The fourth corner forms an acute angle measuring 53º. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?
Part G
In the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?
Answer:
234
Step-by-step explanation:
Sammy was playing Games with Alex. The ratio of games Sammy won was to the number of games Alex won was 9 to 5. If Sammy won 36 games, how many games did Alex win?
-4x + 7 > x - 13 Graph the solution to this inequality on the number line
Answer:
x < - 4
Step-by-step explanation:
Draw a number line and find -4 then graph it
What is the combined length of all the buttons longer than 1 inch?
Given the recursive formula below, what are the first 4 terms of the sequence?
image
Question 3 options:
A)
17, 19, 21, 23
B)
17, –6, –3, 0
C)
17, 13, 9, 5
D)
17, 15, 13, 11
Answer:
D)
17,15,13,11
Step-by-step explanation:
From the formula
[tex]f(n) = f(n - 1) - 2 \\ f1 = 17 \\ [/tex]
we can deduce the next three terms as follows:[tex]f(2) = f(2 - 1) - 2 \\ f(2)= f(1) - 2 \\ f(2) = 17 - 2 \\ f(2) = 15\\ [/tex][tex]f(3) = f(3 - 1) - 2 \\ f(3)= f(2) - 2 \\ f(3) = 15 - 2 \\ f(3) = 13\\ [/tex][tex]f(4) = f(4 - 1) - 2 \\ f(4)= f(3) - 2 \\ f(4) = 13 - 2 \\ f(4) = 11\\ [/tex]Hence the sequence is; 17, 15, 13, 11,...What is the perimeter of the rectangle in the coordinate plane?
14 units
28 units
36 units
45 units
Answer:
45 units^2
Step-by-step explanation:
W x H = area
9 x 5 = 45 units^2
Answer:
28 units
Step-by-step explanation:
Length (l) = 9 units
Breadth (b) = 5 units
Perimeter of the rectangle will be,
→ 2(l + b)
→ 2(9 + 5)
→ 2 × 14
→ 28 units
Hence, the perimeter is 28 units.
Jerry is running a race. He knows he can run 44 feet in 3 seconds. If he maintains this rate, how many miles will he run in 1 hour?
Step-by-step explanation:
44 ft in 3 seconds
in 1 hour there are 60 minutes with 60 seconds each.
so, 1 hour = 60×60 = 3600 seconds.
in 3600 seconds there are
3600 / 3 = 1200 "packages" of 3 seconds.
so, Jerry would run
1200 × 44 = 52800 ft in 1 hour.
there are 5280 ft in 1 mile.
that means Jerry would run
52800 / 5280 = 10 miles in 1 hour.
Use the following random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question below. 3199 9288 1023 1130 0809 1770 6231 7538 8927 4761 7258 7111 0209 0916 1450 9848 4654 7579 6150 3093 9608 0061 4014 9501 0382 3052 2385 9074 1664 6551 6577 1811 3454 5870 1277 5056 1063 5697 9141 4120 9181 1343 0168 3693 0463 4842 1704 3774 4908 4161 6404 9675 2518 3988 4268 6083 0636 9634 5295 5656 1918 3133 6831 8393 6363 2452 1531 1638 1317 2279 9395 0702 2091 5269 0422 0275 3373 1424 1958 0356 5163 0743 6658 6257 2772 0570 4522 2665 0890 3560 5549 2238 2172 9715 9741 4975 6617 9034 4441 8220 Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls? Round your answer to the nearest number of groups. groups.
100:224 = 61:x, or 61/100 = x/224
Cross multiply; 100x=13664
Then, divide by 100; x=136.64, or about 137 groups would contain all girls
QUESTION 58
Calculate graduation rates using the following information: In 2012, 3,388 student entered the freshman class at
CMU. Of the 3,388 27.4% graduated in 4-years. The 5-year graduation rate (those that graduated in 5-years of
less) was 54.2%. The 6-year graduation rate was 60.9%.
How many students graduated in 4 years or less?
How many additional students (beyond the number of students who graduated in 4-years) graduated in their 5th
year?
How many additional students (beyond the number of students who graduated in 5-years) graduated in their 6th
year?
For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
Which table contains only values that satisfy the following? y = x - 1
What is the slope of the line?
Answer:
-3
Step-by-step explanation:
First, let's remind ourselves the definition of a slope.
Slope = rise/run OR the height from one point to another/ the distance from one point to another.
First, let's find two points on this graph that are marked easily.
One point that can be found is (0, -3) and the other is (0, -1).
Let's apply our formula to these points!
<------- Starting from point (0, -3), we are RISING 3 points and RUNNING -1 points.
Rise 3
------- = ----------
Run -1
3/-1 = -3
The slope of the line is -3.
Answer:
-3.
Step-by-step explanation:
1) to choose two points on the given line on the graph. For example, A(-2;3) and B(-1;0);
2) to calculate the required slope according to the rule:
[tex]slope=\frac{Y_B-Y_A}{X_B-X_A};[/tex]
3) the required slope:
slope=-3/1=-3.
Consider a triangle a
ABC like the one below. Suppose that A = 46°, C=79°, and b=61. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Answer:
A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
The sum of 6 and the product of 3 and d
Answer:
6 + 3d
Step-by-step explanation:
First, we can translate from English words to mathematical operations:
– Product: the result of multiplication
– Sum: the result of addition
So, we can rephrase the original sentence as “the result of adding 6 and (the result of multiplying 3 and d)”
When we multiply a constant like 3 by a variable like d, we usually write the two next to each other, which would be “3d” in this case. We can replace that last sentence in symbols with 6 + 3d
What is the sum of 9 7/8 plus 11 2/8?
Answer:
169/8
Step-by-step explanation:
9 7/8 = 79 / 8
11 2/8 = 90 / 8
90/8 + 79/8
The denominator (8) stays the same
90+79 = 169
169/8 or 21 1/8
from 2001 to 2012 the sales for a local doughnut store increased by about the same percent each year. The sales, S, for year t can be modeled by, S=372,300(6/5)^t. Where t=0 corresponds to 2001. What were the sales in 2001
Using the given exponential function, it is found that the number of sales in 2001 was of 327,300.
What is the exponential function in this question?It models the number of sales S in t years after 2001, given by:
[tex]S(t) = 372300\left(\frac{6}{5}\right)^t[/tex]
2001 is year 0, hence the amount is given by S(0), that is:
[tex]S(0) = 372300\left(\frac{6}{5}\right)^0 = 372300[/tex]
The number of sales in 2001 was of 327,300.
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At her Fourth of July party, Marcy serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Marcy plans to grill 4 pounds of chicken. How many cups of marinade should she use?
cups
3 number of cups will be needed to marinade 4 pounds of chicken for grill.
What is Ounce?Ounce is the small unit of weight which is generally equal to the one by 16th of the pounds.
Here we have the data from the question:-
Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.
Marcy plans to grill 4 pounds of chicken.
So total marination required will be:-
Total marination =6x4=24 ounces
Now we know that the conversion:-
1 fluid Ounce = 0.125 Cup
24 fluid ounce =0.125 Cup
Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.
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round 63,104,159,896 to the nearest hundred million
round 2,005,562,134 to the nearest hundred million
round 5,678,600,941 to the nearest hundred million
Answer:
The answer to each one is 1) 63,100,000,000
2) 2,000,000,000
3) 5,700,000,000
Energy for both renewable and nonrenewable sources originally comes from
A. Oil
B. Earth's core
C. fossil fuel
D. the sun
Answer:
d
Step-by-step explanation:
the sun is the primary source
Wanda is working on her predictions for the next few days. She calculates that there is a 20% chance of rain on Monday and a 20% chance onf rain on Tuesday. If she is correct, what is the probability that it will rain on at least one of these days?
Answer:
the answer is that 20% plus 20% equals to 40% and the probability it will rain on at least one of those days is 40% or 2/5
Find the slope on any given line please see attached photo
Answer:
-5/4
Step-by-step explanation:
Count down 5 units and then count right 4 units in order to get negative 5 over 4.
Please answer QUICK!! for brainliest!!!
Answer:
1
Step-by-step explanation:
The 2 equations have different slopes, so they have 1 solution.
solve equation 3x +4/5=8
Answer:
x=2.4
Step-by-step explanation:
3x +4/5=8
3x = 8 -4/5
3x =7.2
x = 7.2/3
x=2.4