Answer:
a) 17.667 s
b) 4094 feet
Step-by-step explanation:
a) The position equation of the model is given by:
[tex]s=-16t^2+v_ot+s_o\\\\v_o=initial \ velocity = 158\ miles/hour\\\\s_o=Initial\ height=900\ ft\\\\1 \ mile = 5280\ ft, 1\ hour= 3600\ s\\\\Therefore:\\\\v_o=158\ miles/hour = 158*\frac{5280}{3600}=231.733\ ft/s\\ \\Substituting:\\\\0=-16t^2+231.733t+900\\\\16t^2-231.733t=900\\\\\\16t^2-231.733-900=0\\\\Solving\ the\ quadratic\ equation\ gives:\\\\ t=17.667\ s\ or \ t=-3.184\ s\\\\Since\ the \ time\ cannot\ be\ negative\ therefore\ t=17.667\ s[/tex]
b) The horizontal distance = Initial velocity × time = 231.733 × 17.667 = 4094 feet
An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is exactly 4 times smaller than the actual bridge. 16 ounces = 1 pound. 2,000 pounds = 1 ton. If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton?
Answer:
Yes, the bridge will hold 1 ton.
Step-by-step explanation:
The ratio of the scale of the model to the real bridge = 1:4
The test model shows the model can take 8000 ounces
The real bridge will therefore take 8000 x 4 = 32000 ounces
but,
16 ounces = 1 pound
32000 ounces = [tex]x[/tex] pounds
==> [tex]x[/tex] = 32000/16 = 2000 pounds
also,
2000 pounds = 1 ton,
therefore, the bridge will hold 1 ton
Answer:
it would be able to hold 1 ton
Step-by-step explanation:
Which numbers in Set A = (-7, 4, 2, 14, 21, 34, 42) are elements of both Set B and Set C, shown below?
Set B = {even numbers)
Set C = {multiples of 7}
-7-4214 213442
Elements of both Set B and Set C
Greetings from Brasil...
Rewriting the problem sets
A = {-7, 4, 2, 14, 21, 34, 42}
B = {...; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42;...}
C = {...; -14; -7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63; 70; 77;...}
So, according to the statement, it is desired:
A ∩ B ∩ C - the intersection between the 3 sets, that is, which numbers are present simultaneously in the 3 sets....
Looking at the sets we conclude that
A ∩ B ∩ C = {14; 42}-3/8 + 1/4 write your answer in simplest form
Answer:
-1/8
Step-by-step explanation:
Convert 1/4 into 2/8.
Then, minus -3/8 and 2/8
Answer:
-3/8 + 1/4 = 1/8
Step-by-step explanation:
-3/8 + 1/4
1/4 = 2/8
then:
2/8 - 3/8 = -1/8
Find the exact value of tan A in simplest radical form.
Answer:
[tex]tan(A) = \frac{2\sqrt{15}}{11}[/tex]
Step-by-step explanation:
Given:
Right ∆ABC
AB = 61
BC = 60
AC = 11
Required:
Value of tan A in radical form
SOLUTION:
[tex] tan(A) = \frac{opposite}{adjacent} [/tex]
Opposite = 60
Adjacent = 11
[tex] tan(A) = \frac{60}{11} [/tex]
[tex] tan(A) = \frac{\sqrt{4*15}}{11} [/tex]
[tex]tan(A) = \frac{2\sqrt{15}}{11}[/tex]
What is the midpoint of LQ?
Answer:
(-4+8) ÷ 2 = 2
uuujhhhhh
Some History teachers at Dayton High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Gruber bought 25 student tickets and 28 adult tickets, which cost a total of $984. Mr. Ellison spent $900, getting 25 student tickets and 25 adult tickets. What is the price for each type of ticket?
Answer:
Student Ticket: $8
Adult $28
Step-by-step explanation:
To find out the price of each ticket create 2 equations, then solve for x & y
x = student tickets
y = adult tickets
25x + 28y = 984
25x + 25y = 900
To do this first put x on one side of the equation
25x = 900 - 25y
x = 36 - y
Now substitute this equation in x for the first equation
25(36 - y) + 28y = 984
Now distribute 25 in 36 - y, 900 - 25y + 28y = 984
After this combine like term, then subtract 900 from each side, 3y = 84
Then divide 3 on each side, y = 28
Lastly substitute 28 for y in any equation to solve for x, x = 8
x & y are the price of each ticket
What is the correct definition of a line segment?
O A a figure in which every point is a fixed distance from a given center
B a figure that connects two points and has a fixed distance
C a figure that extends in two directions on forever
Da figure that has one endpoint and extends in one direction
Answer:
B
Explanation:
Line segments do not extend or extract, they come together to form 1 line instead of going in one/two directions forever.
Keith bought a soft drink for three dollars and eight candy bars. He spent a total of twenty-seven dollars. How much did each candy bar cost?
Answer:
$3 Each
Step-by-step explanation:
27 Spent Toatal.
Soft Drink for 3.
27-3 = 24
He bought eight candy bars, so divide 24 by 8.
24/8 = 3
So each was 3 dollars.
Amna can type 710 words in 15 minutes,Sara can type 810 word in 18 minutes and Uzma can type 780 words in 20 minutes.who is the fastest typist?
Answer:
Amna is the fastest typist.
Step-by-step explanation:
Amna = 710 words/15 minutes = 47.3 words per minute
Sara = 810 words/18 minutes = 45 words per minute
Uzma = 780 words/20 minutes = 39 words per minute
HELP PLEASE
Through any ________ non collinear points there is exactly one plane.
If two points lie in a plane, then _______
If two planes intersect; they intersect in exactly one _______
Answer:
a.three
b.the line containing them lies in the plane.
c.one point
v() and () are inverses of one another and drawn on the same graph with the same scale on both the horizontal and vertical axis. Which of the following would be true?
A.
By rotating () 90° clockwise around the origin you would get ().
B.
By rotating () 180° clockwise around the origin you would get ().
C.
By reflecting the entire coordinate grid over the line =, () would land on ().
D.
() is the same as (), translated up 3 units.
Answer:
Answer C: Reflecting over the line y = x
Step-by-step explanation:
A function and its inverse have always symmetry around the line y = x (called also the identity line)
Therefore answer C seems to be the only answer that addresses such.
Choose your three favorite ice cream flavors. If you want a cone with two dips, how many different combinations of flavors could you have?
Answer:
6
Step-by-step explanation:
3 x 2
The graph represents the heights of two climbers on a
climbing wall over a 12-minute time period.
How high did Abby climb above their original starting
position?
The Climbing Wall
24
O 8 feet
O 15 feet
O 18 feet
22
20
18
O 22 feet
16
14
2
Height (feet)
Abby's climb
8
Brynn's dimb
6
4
2
+
7
1 2 3
4
5
6
8
9
10
11
12
Time (min
Answer22:
Step-by-step explanation:
edge2021
The height Abby climb above their original starting position is 20 feet.
How do we make graph of a function?Suppose the considered function whose graph is to be made is
f=f(x) f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f=f(x) f(x)
are plotted on the vertical axis.
They are together plotted on the point
f(x)) (x,y) = (x, f(x))
This is why we usually write the functions as:
f(x) y = f(x)
We are given that;
Time= 12min
Now,
To find how high Abby climbed above their original starting position, we need to look at the graph and find the highest point of Abby’s climb.
We can see that Abby’s climb is represented by the blue line on the graph.
The highest point of Abby’s climb is at (6, 22), which means that after 6 minutes, Abby reached a height of 22 feet.
Since the original starting position is at (0, 2), which means that at the beginning, Abby was at a height of 2 feet, we can subtract 2 from 22 to find how high Abby climbed above their original starting position.
Abby climbed 22 - 2 = 20 feet above their original starting position.
Therefore, by the graph the answer will be 20 feet.
Learn more about graphing functions here:
https://brainly.com/question/14455421
#SPJ7
A Girl Scout camp served half of their granola with breakfast. After dinner, they put the remaining 6{,}250 \text{ g}6,250 g6, comma, 250, start text, space, g, end text of granola on top of their yogurt dessert. How many kilograms of granola did the Girl Scout camp start with?
Answer:
12.5 kilograms
Step-by-step explanation:
Given:
Half of the granola served with breakfast.
Let the amount of Granola present initially = [tex]x[/tex] kg
Half of it ([tex]\frac{x}{2}[/tex]) served with breakfast, so remaining granola :
[tex]x-\dfrac{x}{2} = \dfrac{x}{2}[/tex]
After dinner, the remaining granola 6,250 gm granola was served with yogurt dessert.
First of all, let us convert it to kilogram because the answer is required in Kilograms.
We know that:
1000 gms = 1 kilograms
1 gms = 0.001 kilograms
6250 gms = 6250 [tex]\times[/tex] 0.001 = 6.250 kilograms
Now, as per given question statement:
[tex]\dfrac{x}{2} = 6.250\ kg\\\Rightarrow x = 2 \times 6.250\\\Rightarrow \bold{x = 12.5\ kg}[/tex]
So, the answer is:
Girl scout camp started with 12.5 Kilograms of granola.
Help!!!!!!!!!!!!!!!!!!!!
Answer: Light blue
Step-by-step explanation:
Answer:
2x+10≤25Step-by-step explanation:
[tex]2\$ on \:each \:game\\10\$ on food\\Let \:x \:be the \:no \:of \:games \:he \:plays\\\\2x +10\\Must\: be \:less\: than\: or \:equal \:to\: 25\$\\\\= 2x+10\:\le 25[/tex]
The following map shows the location of a mall, library, and school in a city: Mike traveled from the school to the mall and then from the mall to the library. Henry traveled from the school to the library. How many more miles did Mike travel than Henry?
A.) 10
B.) 12
C.) 34
D.) 46
Mike: From the school to the mall, we could count out 16 units. From the mall to the library, we could count out 29 units. When we add 16 and 29, we get the distance Mike traveled: 45 units.
Henry: He traveled from the school to the library. To find out how long this distance is, we look at our previous numbers. From the school to the mall: 16. From the mall to the library: 29
To solve, we need to know the Pythagorean Theorem. We use the formula a^2 + b^2 = c^2. Here, 16 is a and 29 is b. We need to square both numbers and add them together to get c^2.
[tex]16^2=256\\29^2=841\\256+841=1097\\1097=c^2[/tex]
Then, we have to square 1097 to find c.
√1097 ≈ 33
Total: We subtract Henry's distance from Mike's to get our final answer.
45 - 33 = 12
Mike traveled 12 more units than Henry.
If two of these shapes are randomly chosen, one after the other without replacement, what is the probability that both chosen will be triangles?
Answer:
[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]
Step-by-step explanation:
From the comments in your question; we have
Stars = 4
Triangles = 5
Circles = 3
Squares = 3
Required
Determine the probability of both shapes being triangles
First, calculate the total
[tex]Total = 4 + 5 + 3 + 3[/tex]
[tex]Total = 15[/tex]
Next, calculate the probability of the first selected shape being a triangle;
P(T₁) = Number of triangles divided by total number of shapes
[tex]P(T_1) = \frac{5}{15}[/tex]
[tex]P(T_1) = \frac{1}{3}[/tex]
Next, calculate the probability of the second selected shape being a triangle;
P(T₂) = Number of triangles divided by total number of shapes
Because it's probability without replacement. the number of triangle left is 4 and the number of shapes left is 14;
So:
[tex]P(T_2) = \frac{4}{14}[/tex]
[tex]P(T_2) = \frac{2}{7}[/tex]
Hence:
[tex]P(T_1\ n\ T_2) = P(T_1) * P(T_2)[/tex]
[tex]P(T_1\ n\ T_2) = \frac{1}{3} * \frac{2}{7}[/tex]
[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]
Hence, the required probability is [tex]\frac{2}{21}[/tex]
Answer:
2/21
Step-by-step explanation:
There are 4 stars, 5 triangles, 3 circles, and 3 squares
For the first drawing there are 5 triangles and a total of 15 shapes.
p(first triangle) = 5/15 = 1/3
Since there is no replacement, for the second drawing, and one triangle has been taken, now there are 4 triangles left and 14 total shapes left.
p(second triangle) = 4/14 = 2/7
p(two triangles) = p(first triangle) * p(second triangle)
p(two triangles) = 1/3 * 2/7
p(two triangles) = 2/21
Help urgently wanted
Find x
Answer:
[tex] \boxed{ \bold{x = 4.54}}[/tex]Step-by-step explanation:
[tex] \sf{Given}[/tex]
[tex] \sf{hypotenuse = 5}[/tex]
[tex] \sf{base = 2.1}[/tex]
[tex] \sf{perpendicular = x}[/tex]
Now, Let's find the value of x
Using Pythagoras theorem
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Plug the values
⇒[tex] \sf{ {5}^{2} = {x}^{2} + {2.1}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{25 = {x}^{2} + 4.41}[/tex]
Swap the sides of the equation
⇒[tex] \sf{ {x}^{2} + 4.41 = 25}[/tex]
Move constant to R.H.S and change it's sign
⇒[tex] \sf{ {x}^{2} = 25 - 4.41}[/tex]
Calculate the difference
⇒[tex] \sf{ {x}^{2} = 20.59}[/tex]
Squaring on both sides
⇒[tex] \sf{x = 4.54}[/tex]
Hope I helped!
Best regards!!
Find the area of each square. And input each area
Answer:
16m²
25m²
9m²
Step-by-step explanation:
4 × 4 = 16m²
5 × 5 = 15m²
3 × 3 = 9m²
Average rate of change from the function from 0 to 2.
===========================================
Plug in x = 0
f(x) = 2x^2 + 5
f(0) = 2(0)^2 + 5
f(0) = 5
Plug in x = 2
f(x) = 2x^2 + 5
f(2) = 2(2)^2 + 5
f(2) = 13
Now use the formula below to find the average rate of change (AROC) from x = a to x = b
AROC = ( f(b) - f(a) )/( b-a )
AROC = ( f(2) - f(0) )/( 2-0 )
AROC = ( 13 - 5 )/( 2 - 0)
AROC = 8/2
AROC = 4
-----------------
This is the same as finding the slope of the line through (0,5) and (2,13)
m = (y2 - y1)/(x2 - x1)
m = (13-5)/(2-0)
m = 8/2
m = 4
can someone please help me with these couple questions I don’t really understand how to read this graph
1. How many hours does the heater run on Tuesday?
2. Which object runs 11 hours on Saturday?
3. Which object has the biggest difference between weekdays and weekends?
4. If this graft is for winter electricity usage, how do you think it would be different for summer?
Answer:
1. 7.5 hours
2. TV
3. Computer
4. All electronic usage except for the heater would decrease because summer is usually when people go outside and don't really stay indoors. While in winter, most people stay inside their houses.
fill in the power 4 _ =64
Answer:
the 3'd power
Step-by-step explanation:
4x4=16 16x4=64
Answer:
[tex]\Huge \boxed{\mathrm{3}}[/tex]
Step-by-step explanation:
Let the power be x.
[tex]\mathrm{4^x=64}[/tex]
Take log of both sides.
[tex]\mathrm{log(4^x)=log(64)}[/tex]
[tex]\mathrm{x \cdot log(4)=log(64)}[/tex]
Divide both sides by log(4).
[tex]\displaystyle \mathrm{x=\frac{log(64)}{log(4)} }[/tex]
[tex]\mathrm{x=3}[/tex]
A 2-liter bottle of juice costs $2.80. A box containing six 12-liter bottles sells for $3.90. Which option has a higher cost per liter? What is that cost? A. 2-liter bottle; $1.40 B. Box of six 12-liter bottles; $1.30 C. 2-liter bottle; $2.80 D. Box of six 12-liter bottles; $3.90
Step-by-step explanation:
It is given that,
A 2-liter bottle of juice costs $2.80.
It means that 1 liter bottle of juice costs $1.4.
A box containing six 12-liter bottles sells for $3.90.
(6×12)l i.e. 72 liter bottles sells for $3.9
1 liter bottles sells for $0.05416
It is clear that "A box containing six 12-liter bottles sells for $3.90." have higher cost per liter. Its cost is $0.05416 per liter. Hence, the correct option is (D).
Answer:
D
Step-by-step explanation:
Which of the following is an equivalent expression of 76543−4? Question 1 options: 176543−4 765434 1765434 765436
Answer:
[tex] \frac{1}{76543^4} [/tex]
Step-by-step explanation:
We are given base that is raised to a negative power of 4, [tex] 76543^{-4} [/tex].
Another way to rewrite this is as indicated as follows: thus, [tex] a^{-x} = \frac{1}{a^x} [/tex], where, a is the base, and x is the exponent.
Therefore, an equivalent expression of [tex] 76543^{-4} [/tex] = [tex] \frac{1}{76543^4} [/tex]
Plz HELP ME.ASP
How many unique, line segments are visible in the figure below?
Answer:
7
Step-by-step explanation:
h,n
m,n
n,o
j,k
k,l
k,i
"One less than triple a number"
So in this case "number" will be "x"
Triple means multiply by 3 = 3x
1 less means minus 1.
3x-1
Find the value of x. Can someone please help me, i’ve been stuck for hours
Answer: Hi!
The value of the variable is 11.
The angles will be equal, as the lines intersect and make an X. To find the value of the angle, we would first subtract 2 from 35 and then divide by 3 to fill in the expression.
35 - 2 = 33
33 ÷ 3 = 11
The value of x is 11.
Hope this helps!
Drag each number to the correct location on the image. Each number can be used more than once, but not all numbers will be used.
Answer:
5 3
6 4
4 2
Step-by-step explanation:
x(2y-5z+1)= show work plz
Answer:
[tex]2xy-5xz+x[/tex]
Step-by-step explanation:
I'm going to assume you wanted to multiply these terms.
To do this, we distribute [tex]x[/tex] into each term in the parentheses.
[tex]2y \cdot x = 2xy\\\\-5x \cdot x = -5xz\\\\1 \cdot x = x[/tex]
Combining these terms, we get [tex]2xy-5xz+x[/tex].
Hope this helped!
A y = 1/2x + 5 B y = 1/2x + 7 c y = 2x + 5 D y = y = 2x + 7
Answer:
[tex]y=-\frac{2}{3}x+12[/tex]
Step-by-step explanation:
Step 1: Rule out answers
The answer cannot be B or D because the y-intercept is at 12(b = 12) and in a linear equation y=mx+b, b is the y intercept.
B has the y intercept at 18
D has the y intercept at 18
Step 2: Find the slope
The slop is the change in y over the change in x. We can also write this as [tex]\frac{rise}{run}[/tex]
We see it lowers by 2 so we will put -2 as the numerator
We also the x value increase by 3 every time it gets lowered by 2 so the run is 3
Therefore the slope is [tex]-\frac{2}{3}[/tex]
Step 3: Plug in the the variables to get the linear equation
[tex]y=mx+b[/tex]
[tex]y=-\frac{2}{3}x+12[/tex]
Therefore the answer is A. [tex]y=-\frac{2}{3}x+12[/tex]
Answer:
[tex]\Large \boxed{{y=-\frac{2}{3}x +12}}[/tex]
Step-by-step explanation:
y = mx + b (slope-intercept form of a line)
m is slope
b is y-intercept
The y-intercept of the line is (0, 12) or 12.
y = mx + 12
The slope of the line can be found through rise over run.
(0, 12) and (18, 0) are two points on the line.
m = (y2-y1)/(x2-x1)
m = (0-12)/(18-0)
m = -12/18
m = -2/3
The slope of the line is -2/3.
y = -2/3x + 12