Answer:
The rock will take about 4.5 seconds to reach the river
Step-by-step explanation:
* lets study the situation of the rock
- The rock is dropped means the initial velocity is zero
- The motion is free fall under earth gravity
- The rock dropped from a bridge 320 feet above the river
- The equation of the pathway is h = -16t² + 320
- When the rock reach to the ground the height will be zero
* Now lets substitute h by zero in the equation to find t
∵ h = -16t² + 320
∵ h = 0
∴ 0 = -16t² + 320 ⇒ add 16t² to both sides
∴ 16t² = 320 ⇒ divide both sides by 16
∴ t² = 320/16 = 20
∴ t² = 20 ⇒ take √ for both sides
∴ t = √20 = 2√5 ≅ 4.5 seconds
* The rock will take about 4.5 seconds to reach the river
The final answer is D: 4.5 seconds.
let's go through the solution in more detail.
Given the equation [tex]\( h = -16t^2 + 320 \)[/tex], where [tex]\( h \)[/tex] represents the height of the rock above the river at time [tex]\( t \),[/tex] we're trying to find out when the rock reaches the river, which means its height will be 0.
So, we set [tex]\( h \)[/tex] to 0:
[tex]\[ 0 = -16t^2 + 320 \][/tex]
To solve for [tex]\( t \),[/tex] we isolate [tex]\( t \)[/tex] by moving [tex]\( -16t^2 \)[/tex] to the other side of the equation:
[tex]\[ 16t^2 = 320 \][/tex]
Now, to solve for [tex]\( t \),[/tex] we divide both sides by 16:
[tex]\[ t^2 = \frac{320}{16} \]\[ t^2 = 20 \][/tex]
To find [tex]\( t \),[/tex] we take the square root of both sides:
[tex]\[ t = \sqrt{20} \][/tex]
Now, let's simplify [tex]\( \sqrt{20} \):[/tex]
[tex]\[ \sqrt{20} = \sqrt{4 \times 5} \]\[ \sqrt{20} = \sqrt{4} \times \sqrt{5} \]\[ \sqrt{20} = 2\sqrt{5} \][/tex]
Approximately, [tex]\( \sqrt{5} \)[/tex] is around 2.24, so [tex]\( 2\sqrt{5} \)[/tex] is approximately [tex]\( 2 \times 2.24 \),[/tex] which is approximately 4.48.
So, it will take approximately 4.5 seconds for the rock to reach the river.
Therefore, the correct answer is option D: 4.5 seconds.
Math algebra 1 plsssss helppppp!!!!
Answer:
5. He rented 7 new releases videos
6. 4 3-bedrooms units.
7. length: 37, width: 18
8. 81 dimes, 47 quarters
Step-by-step explanation:
5. Videos
X: New releases
Y: Regular titles
EQ1: x + y = 18 (he rented 18 videos)
EQ2: 3x + 2y = 43 (he paid $43 for the 18 videos)
By EQ1, we can isolate y-value as y = 18 - x
We place this y-value into EQ2:
3x + 2(18 - x) = 43 and we solve:
3x + 36 - 2x = 43
3x - 2x = 43 - 36
x = 7
He rented 7 new releases videos
6. bedroom units
X: 2-bedrooms units
Y: 3-bedrooms units
EQ1: x + y = 7 (they have 7 units)
EQ2: 450x + 650y = 3950 (their monthly renting revenues)
By EQ1, we can isolate x as x = 7 - y (since we're looking for 3-bedrooms units), and place that value in EQ2:
450 (7 - y) + 650y = 3950
3150 - 450y + 650y = 3950
200y = 800
y = 4
So, they have 4 3-bedrooms units.
7. Rectangle
X: length
Y: width
EQ1: x + y = 55 (since perimeter is 110 and includes 2x + 2y)
EQ2: x = 2y + 1 (length is twice the with, plus 1)
Since we are asked to find both values, it doesn't matter by which we begin. By EQ1, we can do x = 55 -y, and place that value in EQ2, to get:
55 - y = 2y + 1
54 = 3y
y = 18
Place y = 18 in EQ1 to find x:
x + 18 = 55
x = 37
8. Dimes and quarters
X: dimes
Y: quarters
EQ1: x = y + 34 (34 more dimes than quarters)
EQ2: 10x + 25y = 1985 (total value of the collection)
Let's place the value of x from EQ1 in EQ2:
10 (y + 34) + 25y = 1985
10y + 340 + 25y = 1985
35y = 1645
y = 47
From EQ1, we then have
x = 47 + 34 = 81
So, we have 81 dimes ($8.10) and 47 quarters ($11.75), for a total of $19.85.
Which measurement could be a surface area measure? 18 ft. 64.5 m3 27.9 mm2 50 g
Answer:
27.9 mm2
27.9 mm2 = 2.79 × 10^ -5 m2
bill ran 400 m in 54s. joe ran 300m in 43s. who ran faster
Answer:
Bill
Step-by-step explanation:
Answer:
Bill ran faster than Joe.
Step-by-step explanation:
On average Bill ran each 100m in 13.50s while Joe ran each 100m in 14.33s.
Which values are the solutions to the inequality below
Answer:
option B 5
option D -6
Step-by-step explanation:
Given in the question an inequality
x² > 16
Step 1
Take square root on both sides of inequality
√x² > ±√16
x < -√16 or x > √16
x < -4 or x > 4
Step 2
-4 > x > 4
x = 5 x > 4 accepted
x = -6 x < -4 accepted
Step 3
x = 4 rejected
x = -1 rejected
25 POINTS + BRAINLIEST
Use the net to find the surface area of the prism.
A. 22 m^2
B. 276 m^2
C. 522 m^2
D. 968 m^2
Answer:
C. 522 m^2.
Step-by-step explanation:
The area of the 3 rectangles in the net
= 10 * (9 + 16.6 + 14)
= 10 * 39.6
= 396. m^2.
The area of the 2 triangles
= 2 * 1/2 * 14 * 9
= 126 m^2.
Total surface area = 522 m^2.
Please help me with this question I would really appreciate it:Hilda has 72 half dollars.how much is her coin collection worth?
Answer:
36
Step-by-step explanation:
half dollar equals 50 cents.
72/2=35
Answer:
36
Step-by-step explanation:
divide it by two since it says that each are half a dollar meaning 50 cents each.
If x+y = 6, y+z = 7, and z+x = 9, what is the average (arithmetic mean) of x, y, and z?
Answer:
11/3 . . . or . . . 3 2/3
Step-by-step explanation:
Adding the three equations will give 2x+2y+2z:
(x +y) +(y +z) +(z +x) = 6 +7 +9
2x +2y +2z = 22
Dividing by 2 gives the sum of three variables:
x +y +z = 11
The average of x, y, and z is their sum divided by 3:
(x +y +z)/3 = 11/3
Which of the following histograms would best be approximated by a normal distribution?
Answer:
Choice B is correct
Step-by-step explanation:
The normal distribution has extensive applications in statistics. The distribution is characterized by a symmetric bell-shaped density curve. Most of the observations or data points fall in the middle of the distribution while both the right and left tails are equally longer.
The histogram that can be approximated by a normal distribution must meet the above conditions.
The histogram in alternative A is skewed to the right since most of the values fall in the lower end of the distribution. A skewed distribution is not symmetric.
The histogram in choice C is approximately uniformly distributed since most of the observed values have an approximately equal frequency. Each of the values is approximately equally likely. The uniform distribution is not symmetric.
The histogram in D follows no know pattern and nevertheless it lacks the symmetric property.
The histogram in B is approximately symmetric in distribution since most of the observed data values fall in the middle of the distribution while the left and right tails are nearly equal. This histogram can thus be approximated by a normal distribution.
Drag the values to order them from least to greatest, with the least at the top.
[tex]\bf 4\pi \qquad \approx \qquad 12.57 \\\\[-0.35em] ~\dotfill\\\\ \sqrt{79}+\sqrt{63}\qquad \approx \qquad 8.89 + 7.94\implies 16.83 \\\\[-0.35em] ~\dotfill\\\\ \sqrt{143}\qquad \approx \qquad 11.96 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{11.96}{\sqrt{143}}\qquad \stackrel{12.57}{4\pi }\qquad \stackrel{16.83}{\sqrt{79}+\sqrt{63}}~\hfill[/tex]
[tex]4\pi = 1.27323954474\\\sqrt{143} = 11.9582607431\\\sqrt{79} + \sqrt{63} = 16.8254483505[/tex]
Enter your answer and show all the steps that you use to solve this problem in the space provided.
f(x)+9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4
What is f(x)-g(x)?
Show all of your steps and write your final answer in factored form.
I would like it if you put down all the steps and explanation for I do not understand it. Thank you so much for your help in advance!
Answer:
[tex]\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}[/tex]
Step-by-step explanation:
f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4
Step 1. Calculate the difference between the functions
(a) Write the two functions, one above the other, in decreasing order of exponents.
ƒ(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
(b) Create a subtraction problem using the two functions
ƒ(x) = 9x³ + 2x² - 5x + 4
-g(x) = -(5x³ - 7x + 4)
ƒ(x) -g(x)=
(c). Subtract terms with the same exponent of x
ƒ(x) = 9x³ + 2x² - 5x + 4
-g(x) = -(5x³ - 7x + 4)
ƒ(x) -g(x) = 4x³ + 2x² + 2x
Step 2. Factor the expression
y = 4x³ + 2x² + 2x
Factor 2x from each term
y = 2x(2x² + x + 1)
[tex]\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}[/tex]
Find the area of the composite figure and round the nearest tenth
Answer:
The area of the composite figure is 1360 ft.
Step-by-step explanation:
First, you should split up the composite figure into separate shapes.
So to find area of the triangle all the way on the left, you multiply base x height then divide by 2.
30 x 34 = 1020 ÷ 2 = 520.
Then, moving on to next shape, we can break up the trapezoid into a rectangle and a triangle.
To find area of the rectangle you multiply length x width.
16 x 30 = 480.
Finally, we have the last triangle right above the rectangle. Keep in mind that the rectangle does not have a length of 40!
You have to subtract 40 - 16 which equals 24.
30 x 24 = 720 ÷ 2 = 360.
Now that we have all 3 numbers, we simply add them all together and you will get an answer of 1360 ft.
Remember to label your answer!
Answer:
1080 ft^2
Step-by-step explanation:
We are given a composite figure that consists of a triangle and a trapezoid.
We know that the area of these two shapes is given by the following formulas so we will put in the given values to get:
Area of triangle = [tex]\frac{1}{2} \times b \times h[/tex] = [tex]\frac{1}{2} \times 16 \times 30[/tex] = 240 ft^2
Area of trapezoid = [tex]\frac{a+b}{2} h[/tex] = [tex]\frac{16+40}{2} 30[/tex] = 840 ft^2
Area of composite figure = [tex]240+840[/tex] = 1080 ft^2
The circumference of a circle is 50.24 centimeters. Find the area of the circle. (Use 3.14 for π.)
Answer:
help me first
Step-by-step explanation:
Answer:
200.96
Step-by-step explanation:
First, divide 50.24 by the pi (3.14)
50.24 / 3.14 = 16
Second, divide 16 by two (so that the radius is found).
16 / 2 = 8
Now that we have the radius length, solve for the area.
area of circle = πr^2
Area of circle = (3.14) (8^2)
Area of circle = 3.14 x 64
Area of circle = 200.96
use unit multipliers to convert 14 yards per minute to inches per second
Answer:
8.4 in. per seconds
Step-by-step explanation:
14yd=42ft.
42ft=504in per min
504/60=1 min / 60
8.4=1 sec.
Answer:
8.4 inches/second
Step-by-step explanation:
1 yd = 3 ft
1 ft = 12 inches
1 minute = 60 seconds
These are the conversion factors we need to convert 14 yds /minutes to inches per second
14 yds 3 ft
-------- * -------------
minutes yd
The yds cancel and we are left with
42 ft
--------
minutes
42 ft 12 inches
-------- * ------------------
minutes 1 ft
The feet cancel
504 inches
-------------------
minutes
504 inches 1 minute
------------------- *--------------
minutes 60 seconds
The minutes cancel
504 inches
------------------
60 seconds
Simplifying the numbers
8.4 inches
----------------
second
HELP HELP 20 points,,,,,,,
Answer:
B) y+3=-1/4(x-8) hope this helps! :D
Step-by-step explanation:
point-slope formula is y-y1=m(x-x1)
y1 and x1 are coordinates, aka a point
The answer ur looking for is B
can someone plz help me now plz
Answer:
Step-by-step explanation:
Write down what you have for each pizza size.
small: s
Medium: (3/2) s
Large: (5/2) s
The only way I can see to do this is
s = L - M
s = 5/2 s - 3/2 s
s = 2/2 s
This of course is not exactly what you are looking for. There is no explicit formula that will tell you exactly how much dough is in a small pizza.
See the comment below posted by SqdanceFan. He is saying that M/L = (3/2)//(5/2) = 3/5
Also (M)/( S + M) = 3/5
But neither gives you an explicit formula for small, but it is a relationship. The fact that equality is achieved when both are zero is also true, but it does not solve the question. I don't think there's a good answer to this question.
There are 858 calories in 13 servings of cereal. If a bowl holds 2 servings, how many calories are in the bowl?
Answer:
132 calories in a bowl that holds 2 servings
Step-by-step explanation:
In order to find what 1 serving equals, you have to divide 858 by 13 and you get 66, but since the bowl holds 2 servings you have to multiply 66 by 2 and you get 132
Answer:
78
Step-by-step explanation:
Subtract 2 serving out of 13 and the then divide 858 by the number.
Last year Jonathan was 6034 inches tall. This year he is 6514 inches tall. How many inches did he grow?
Answer:
480 in
BTW: Who could be that tall other than "Jonathan" of course?
Step-by-step explanation:
If you use subtraction...
6514-6034=480
to solve this problem subtract 6034 from 6514 to get 480
So he grew 480 inches which is equivalent to 40 feet
What is the value of the function f(x)=3/2x-1/2 when x=6?
Answer:
Option 1
Step-by-step explanation:
In order to find the value of the function at x=6, we have to replace x by 6 in the given function.
[tex]f(x)=\frac{3}{2}x -\frac{1}{2}[/tex]
Replacing(Substituting) x = 6 in above equation we get:
[tex]f(6)=\frac{3}{2} (6) -\frac{1}{2}\\\\f(6)=9-\frac{1}{2}\\\\ f(6)=\frac{18}{2}-\frac{1}{2}\\\\ f(6)=\frac{17}{2}\\\\ f(6)=8\frac{1}{2}[/tex]
Thus, 1st option gives the correct answer.
Answer:
The correct answer is option 1
8 1/2
Step-by-step explanation:
It is given that,
f(x) = 3x/2 - 1/2
We have to find f(x) when x = 6
To find the value of f(6)
we have, f(x) = 3x/2 - 1/2
when x = 6
f(x) = f(6)
f(6) = (3 * 6)/2 - 1/2
= 18/2 - 1/2
= (18 - 1)/2 = 17/2
= 8 1/2
Therefore the correct answer is first option
Which of the following function is graphed below?
Answer:
C
Step-by-step explanation:
We can see that there is a closed dot and the function is going left and it is a cubic function.
Additionally, the only one with a [tex]x^3+n\leq 2[/tex] inequality is C.
HELP PLEASE WILL GIVE BRAINLIEST TO WHOM CAN ANSWER CORRECTLY A lawn-care specialist chooses a random sample from the yard and determines the number of weeds in the sample. The results of the sample are shown in the table below.
look at attachment
Which explains whether or not this is a representative sample?
Yes, this is a representative sample because each type of weed is represented in the sample.
Yes, this is a representative sample because each type of weed is represented approximately the same number of times in the sample.
No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
No, this is not a representative sample because each type of weed should be represented exactly the same number of times in the sample.
Answer: No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
Step-by-step explanation:
A representative sample has to be in proportion, and the diagram shows that the greater part is not represented in proportion. Because it is not represented in proportion, it is not a representative sample.
Answer: C
Answer:
Letter C because the sample size is not in proportion to the rest of the weeds in the grass.
Step-by-step explanation:
Also, I use Ed_genuity too did u rlly need to blur out time left lol
What is the quadratic regression equation that fits these data?
Option: A is the correct answer.
The quadratic equation that fits these data is:
A. [tex]y=2.09x^2+0.33x+3.06[/tex]
Step-by-step explanation:We are given a table of values as:
x y
-4 35
-3 20
-2 12
-1 6
0 2
1 6
2 10
3 24
4 38
From the given data values we see that the points follow a parabolic path this means that the line of best fit will has a quadratic equation.
Also, the line that best represents these data points as is done by the regression calculator is:
A. [tex]y=2.09x^2+0.33x+3.06[/tex]
Janice completed the following polynomial addition. Find her error and correct her work.
Answer:
Option B. [tex]9x^{3}-2x^{2}-4x-2[/tex]
Step-by-step explanation:
we have
[tex]7x^{3}-2x^{2} +5[/tex]
[tex]2x^{3}-4x-7[/tex]
Adds the polynomial
Group terms that contain the same variable
[tex](7x^{3}+2x^{3})-2x^{2}-4x+(5-7)[/tex]
Combine like terms
[tex]9x^{3}-2x^{2}-4x-2[/tex]
Janice's error was
[tex]-2x^{2} +5-4x-7=6x^{2}-12[/tex]
so
[tex]-2x^{2}-4x=6x^{2}[/tex]
instead
[tex]-2x^{2}-4x=-2x^{2}-4x[/tex]
and
[tex]5-7=-12[/tex]
instead
[tex]5-7=-2[/tex]
Answer:
B
Step-by-step explanation:
Edge 2022
What is the result of this operation?
the answer is B because you will add and subtract each element with it's corresponding one
The result of this operation is option B. This is obtained by using matrix addition and subtraction.
What is the result of this operation?Adding and subtracting the terms of the matrix since these are matrices with same order. Hence we get,
[tex](\left[\begin{array}{ccc}13&10&7\\6&8&1\\2&5&0\end{array}\right] -\left[\begin{array}{ccc}3&-2&6\\14&-6&11\\8&-12&9\end{array}\right] ) +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}10&12&1\\-8&14&-10\\-6&17&-9\end{array}\right] +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]
=[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex]
Thus the required matrix is option B.
Learn more about matrix addition and subtraction here:
brainly.com/question/34923885
#SPJ2
help me plzz show work plz
Answer:
B
Step-by-step explanation:
Use the formula for radius and circle circumference.
[tex]d=2r \\ \\ C=2\pi r[/tex]
Since we know the diameter, if we divide that by 2, we can get the radius.
[tex]29.5/2=14.75[/tex]
Now we can plug that value into the circumference formula to get the circumference.
[tex]C=2(14.75)\pi \\ \\ C=29.5\pi \\ \\ C=93[/tex]
*Since we're rounding to the nearest inch.
1. z²-9z=66
2. y²+16y=17
3. 2h²-5h=-1
Hello,
Starting with problem one:
Subtract 66 from both sides.
z2−9z−66=66−66
z2−9z−66=0
Use quadratic formula with a=1, b=-9, c=-66.
z = 9/2+1/2√345
Problem two:
Subtract 17 from both sides.
y^2+16y−17=17−17
y^2+16y−17=0
Factor left side of equation.
(y−1)(y+17)=0
Set factors equal to 0.
y−1=0 or y+17=0
y=1 or y=−17
ANSWER: y=1 or y=−17
Problem 3:
2h^2−5h−(−1)=−1−(−1)
2h^2−5h+1=0
Use quadratic formula with a=2, b=-5, c=1.
ANSWER: h=5/4+1/4√17
Have an amazing day.
Need help plz .You have $2500 to invest in two different accounts. In order to save the money you need for college, you need to average 7% interest. If the two accounts pay 7.5% and 6% interest, how much should you invest in each account? Round to the nearest dollar amount.
A)$1667 in 7.5%, $833 in 6%
B)$1833 in 7.5%, $667 in 6%
C)$667 in 7.5%, $1833 in 6%
D)$833 in 7.5%, $1667 in 6%
Answer:
A)$1667 in 7.5%, $833 in 6%
Step-by-step explanation:
Let amount of money invested 6% account = x
Let amount of money invested 7.5% account = y
Then we get equations:
x+y=2500
or x=2500-y ...(i)
6% of x+7.5% of y=7% of (2500)
or 0.06x+0.075y=0.07(2500)
or 60x+75y=175000...(ii)
plug (i) into (ii)
60x+75y=175000
60(2500-y)+75y=175000
150000-60y+75y=175000
-60y+75y=175000-150000
15y=25000
y=$1666.66666667
or y=1667
plug into (i)
x=2500-y=2500-1667=833
Hence final answer is A)$1667 in 7.5%, $833 in 6%
confused can someone help pls
For this case, we have that by definition, be given two functions f (x) and g (x). So:
[tex](f-g) (x) = f (x) -g (x)[/tex]
We have:[tex]f (x) = - 3x-5\\g (x) = 4x-2[/tex]
So:
(f-g) (x) = - 3x-5- (4x-2)
We have to:
[tex]- * + = -\\(f-g) (x) = - 3x-5-4x + 2[/tex]
Equal signs are added and the same sign is placed while different signs are subtracted and the sign of the greater is placed
[tex](f-g) (x) = - 7x-3[/tex]
Answer:
Option D
You are to demonstrate that you understand what represents a function and what does not represent a function. You may do this by either writing a paragraph using complete sentences or drawing pictures with labels.
We know that functions are mathematical entities that assign unique outputs to given inputs. In other words, a function can't have repeated values in the input repeated x-value.
For example consider the relation {(1,4), (1,5), (2,6), (3,7), (4,8), (5,9)}.
We see that above relation has repeated x-value "1" which is assigned to two different output values 4 and 5. So by definition of function, above relation can't be a function.
Stephaine has 3 3/4 bags of soil to put in her garden. Each bag of soil will cover 125.3 ft^2. How many square feet will Stephanie. be able to cover if she uses all these bags of soil?
Answer:
[tex]125.3 \times 3 = 375.9[/tex]
[tex]125.3 \times \frac{3}{4} = 93.975[/tex]
[tex]375.9 + 93.975 = 469.875[/tex]
which of exercises 14-19 could you solve mentally
Answer:
piccctures?
Step-by-step explanation: