When an object is projected into the air, it follows the path of a parabola. The equation always has the
same form, but the numbers change based on the data for the projectile:
If a cannonball is launched from a height of 29.4 m above the ground with an initial velocity of 24.5 m/s,
then the equation that models its path would be h(t) =
-4.9+7 + 24.5t + 29.4. This graph shows its
path: What is the height of the cannonball before it is launched,
at t=0? Remember to include units
Answer:
29.4 m
Step-by-step explanation:
From the graph
You can clearly infer from the graph that the initial height of the cannon ball, before it is launched is 29.4 mJust find t = 0, and see where the line of the graph intersects the y-axis, which represents height of the cannon ball w.r.t time.From the equation
An even simpler method is substitute t = 0 into the equation for the motion of the cannon ballh(0) = -4.9(0)² + 24.5(0) + 29.4h(0) = 29.4 mPLS HELP Solve for x
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
If two secants are drawn from a point outside a circle, then product of one secant segment and its external part equal the product of the other secant segment and its external part.
(Secant-Secant Power Theorem)
(JG)(JH) = (JM)(JK)
(16) X (7) = (8+X)(8)
112=64+8X
8X=48
X=6
A. What is 0.47 expressed as a fraction in simplest form?
B. What is 0.-47 expressed as a fraction in simplest form?
C. What is 0.--47 expressed as a fraction in simplest form?
Please show your work for each part.
25 points! and Brainliest!
Answer:
See below ~
Step-by-step explanation:
Converting a decimal to a fraction :
Multiply by 100/100 and keep in the form without divisionA. (0.47)
0.47 x 100/10047/100B. (-0.47)
-0.47 x 100/100-47/100C. (0.--47)
A minus sign multiplied by another minus sign makes a positive sign0.--47 ⇒ 0.4747/100Answer:
Part (a) = 47/100, Part (b) = -47/100, Part (c) = 47/100
Step-by-step explanation:
Step 1: Determine 0.47 as a fraction
0.47 can also be expressed as 47% which means that there is 47/100. We can see that there is no way that we can simplify the fraction even more so that is our final answer.
Step 2: Determine -0.47 as a fraction
0.47 can also be expressed as -47/100. We can see that there is no way that we can simplify the fraction even more so that is our final answer.
Step 3: Determine --0.47 as a fraction
Two negatives (-), means that they cancel out and cause a positive (+). For example, -1 * -1 gives us 1. Therefore it would just be like the first one which is 47/100.
Answer: Part (a) = 47/100, Part (b) = -47/100, Part (c) = 47/100
You decide to update your bathroom. You are going to put new tile in your shower. Your shower has three rectangular walls that need tiled. One wall is 5 feet wide and 8 feet high. The other two walls are each 4 feet wide and 8 feet high. What is the total area that you will need to tile?
[tex]\bigstar{\boxed{\pmb{Area\:of\:a\:Rectangle:\:A=LW}}[/tex]
[tex]\sf{A=8*5}[/tex]
[tex]\sf{A=40~ft^2}[/tex]
[tex]\rule{200}{2}[/tex]
[tex]\sf{A=4*8}[/tex]
[tex]\sf{A=32~ft^2}[/tex]
Now, add the areas:-
[tex]\sf{A=40+32+32~(since~there~are~2~walls~with~this~area)}[/tex]
[tex]\sf{A=72+32}[/tex]
[tex]\sf{A=104}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
The pre-image has coordinates D(-1,3),E(4,3),F(4,1),G(-1,1) What is the image of DEFG
Answer:
•SEE ABOVE ATTACHMENT•The image of DEFG forms QUADRILATERAL SHAPE
hope it helpsmark as brainliastpleas help!!! no links! According to the line plot, what is the total distance run by the runners that each ran 1/5 of a mile and 1/2 of a mile?
1 3/10 miles
1 7/10 miles
4 miles
1 1/2 miles
17/10 miles
1/5*1+1/2*3=3/2+14/10=17/10
Answer:
1/5+3/2=2/10+15/10=17/10
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution
y =4x-2
y=x+3
Answer:
[tex]\left(\dfrac53,\dfrac{14}{3}\right)[/tex]
Step-by-step explanation:
Equation 1: y = 4x - 2
Equation 2: y = x + 3
Subtract Equation 2 from Equation 1 and solve for x:
⇒ 0 = 3x -5
⇒ 3x = 5
⇒ x = 5/3
Substitute found value of x into one of the equations and solve for y:
⇒ y = 5/3 + 3
⇒ y = 14/3
Therefore, the solution of the system of equations is:
[tex]\left(\dfrac53,\dfrac{14}{3}\right)[/tex]
Solve 3x2 = -12x - 15.
Ox= -4 + 2i
Ox=-4+1
Ox=-2 + 2i
Ox= -2
Answer:
x = -2 - i, -2 + i.
Step-by-step explanation:
3x2 = -12x - 15
3x^2 + 12x + 15 = 0
Divide through by 3:
x^2 + 4x + 5 = 0
x^2 + 4x = -5
Completing the square:
x^2 + 4x + 4 = -5 + 4
(x + 2)^2 = -1
x + 2 = √-1 = i
x = -2 - i, -2 + i.
What does volume measure?
a
the total distance around a figure
b
the average of the sum of all items
c
the exposed surface of a solid shape
d
the amount of space occupied by an object (its capacity)
Answer: d - the amount of space occupied by an object (its capacity)
Explanation:
[a] The total distance around a figure is the perimeter, this does not answer our question.
[b] The average of the sum of all items is the mean, this does not answer our question.
[c] The exposed surface of a solid shape is the object's surface area, this does not answer our question
[d] The amount of space occupied by an object is the object's volume, so this does answer our question.
Find the value of x. 69 30.9 38.1
Answer:
x = 30.9
Step-by-step explanation:
[tex]x = \frac{1}{2} (138 - 76.2) = \frac{1}{2} (61.8) = 30.9[/tex]
Suppose $16,250 is invested at an interest rate of 7.9%, compounded continuously. How many years will it take for the investment to double? PLEASE HELP
Answer:
4 years
Step-by-step explanation:
basically, multiple 16,250 by 107.9%, get the product and multiply that product by 107.9%+ 7.9% and keep on doing that until you eventually get to about 33,000 which is a bit more than double 16,250 but 4 years is still the minimum years it will take to get AT LEAST double. :)
The figure below is an isosceles trapezoid. Solve for x.
Note: the figure may not be drawn to scale.
Answer:
x = 3
Step-by-step explanation:
The diagonals of an isosceles trapezoid are congruent , then
4x - 1 + 4 = 2x + x + 6 , that is
4x + 3 = 3x + 6 ( subtract 3x from both sides )
x + 3 = 6 ( subtract 3 from both sides )
x = 3
100 points please help fast asap
Find the dimensions of the actual swimming pool.
A drawing plan includes a rectangular swimming pool with a length of 1/2 ft and a width of 1/4 ft. The actual pool will be enlarged by a scale factor of 80/1.
Answer:
length: 40, width: 20
Step-by-step explanation:
length = 1/2×80/1 = 40
width = 1/4 × 80/1 = 20
hope this helps =)
Space Shuttle Marion is observing the launch of a space
shuttle from the command center. When she first sees the
shuttle, the angle of elevation to it is 16°. Later, the angle
of elevation is 74°. If the command center is 1 mi from the
launch pad, how far did the shuttle travel while Marion was
watching? Round to the nearest tenth of a mile,
Using the slope concept, it is found that the shuttle traveled 3.2 miles while Marion was watching.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Initially, the angle of elevation is of 16º, with an elevation of 1 mi, hence:
[tex]\tan{16^\circ} = \frac{1}{x_1}[/tex]
[tex]x_1 = \frac{1}{\tan{16^\circ}}[/tex]
[tex]x_1 = 3.5[/tex]
Then, at the end, the angle will be of 74º, with the elevation remaining constant, hence:
[tex]\tan{74^\circ} = \frac{1}{x_2}[/tex]
[tex]x_2 = \frac{1}{\tan{74^\circ}}[/tex]
[tex]x_2 = 0.3[/tex]
The distance is:
[tex]d = x_1 - x_2 = 3.5 - 0.3 = 3.2[/tex]
The shuttle traveled 3.2 miles while Marion was watching.
More can be learned about the slope concept at https://brainly.com/question/18090623
I need help with this question for my 8th grade math test
1. Given the following coordinates, complete the listed transformations in sequence, which means you do one after the other.
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwise
b) Dilation by a scaling factor of 2
c) Reflect across the x-axis
d) Translation 2 Up and 5 to the Left
Transforming the points involves changing their coordinates
The image of the points are: (3, 6), (-11, 12) and (-3, -12)
How to complete the transformations?The coordinates of the points are given as:
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwiseThe rule of this transformation is:
(x, y) to (y, -x)
So, we have:
X' = (4, -2)
Y' = (-3, -5)
Z' = (1, 7)
b) Dilation by a scaling factor of 2The rule of this transformation is:
(x, y) to (2x, 2y)
So, we have:
X'' = (8, -4)
Y'' = (-6, -10)
Z'' = (2, 14)
c) Reflect across the x-axisThe rule of this transformation is:
(x, y) to (x, -y)
So, we have:
X''' = (8, 4)
Y''' = (-6, 10)
Z''' = (2, -14)
d) Translation 2 Up and 5 to the LeftThe rule of this transformation is:
(x, y) to (x -5, y + 2)
So, we have:
X'''' = (3, 6)
Y'''' = (-11, 12)
Z'''' = (-3, -12)
Hence, the image of the points are: (3, 6), (-11, 12) and (-3, -12)
Read more about transformation at:
https://brainly.com/question/4289712
PLS HELPPPPPPP
A, B and C line up randomly to buy tickets. Find the probability that A is beside C in the queue
Answer:
Sample Space = {(ABC), (ACB), (BAC), (BCA), (CAB), (CBA)}
= 6
Instances when A is besides C {(ACB),( BAC),( BCA), ( CAB)}
=4
P( A is besides C)= 4/6
= 2/3MARK ME AS BRAINLISTI think of a number . If I subtract six from it and multiply the difference by 4 the result is 36. Evaluate the number that I thought of.
Answer:
15
Step-by-step explanation:
First we can make an equation by replacing the unknown number with x :
First step of problem:
x-6
Second part of problem:
4(x-6)
Third part of the problem:
4(x-6)=36
First we can expand the bracket to give us:
4x-24=36
Now we add 24 to both sides:
4x = 60
Now we divide both sides by 4 for our final answer of
x= 15
To check this answer we can put it back into the problem:
4(15-6)=36
4(9)=36
✅
Therefore our answer that was thought was 15.
The length, breadth and height of a rectangular room are in the ratio of 3:2:1. If the room contains 3072 cubic meter of air, find the length, breadth and height of the room.
Answer:
length: 24 mbreadth: 16 mheight: 8 mStep-by-step explanation:
Let k represent the multiplier of the ratio units that will give actual dimensions. The the height can be represented by k, the breadth by 2k, and the length by 3k. The volume of the room will be ...
V = LBH
V = (3k)(2k)(k) = 6k³
3072 m³ = 6k³ . . . . . use known volume
512 m³ = k³ . . . . . . . divide by 6
8 m = k . . . . . . . . . take the cube root
The height of the room is 8 m, its breadth is 16 m, and its length is 24 m.
Answer:
See below ↓↓↓
Step-by-step explanation:
Given :
Length, breadth, and height in the ratio 3 : 2 : 1Room contains 3072 cubic meter of air [refers to volume]Solving :
Let the length, breadth, and height be 3x, 2x, and x respectivelyMultiply them and equate to the volume(3x)(2x)(x) = 30726x³ = 3072x³ = 512x = 8Solution :
Length = 3x = 24 mBreadth = 2x = 12 mHeight = x = 8 mi do not understand this please help
Answer: 7.4.
Step-by-step explanation: To find the area of a triangle, you need the base, height, and then divide the results by two. The following is done below:
A = h x b / 2, where h is the height, b is the base, and A is the area of the triangle.
A = 3.7 x 4 = 14.8.
Next, 14/8 / 2 = 7.4.
Therefore, 7.4 is your answer.
Hope this helps! :)
pls help me to answer this
Answers:
Sample Variance = 31.03
Sample Standard Deviation = 5.57
See the table below.
===================================================
Explanation:
M refers to the midpoint of each interval. The midpoint is [tex]M = \frac{a+b}{2}[/tex] where a,b are the left and right endpoints.
For example, [tex]M = \frac{0+4}{2} = \frac{4}{2} = 2[/tex] in the first row.
Multiply the frequency with the midpoint to get the third column. Summing this column of values leads to 4+49+180+153+154 = 540 shown at the bottom of that column.
Divide this sum over the sum of the frequencies (2+7+15+9+7 = 40) and we arrive at [tex]\overline{x} = \frac{540}{40} = 13.5[/tex] which is the sample mean xbar.
--------------------------------------------------------------------------
After we determine xbar, we subtract it from each value of M. Then we square the result to get [tex](M - \overline{x})^2[/tex]. Multiply that with the column f to get the new column [tex]f(M-\overline{x})^2[/tex].
This column is added to arrive at 1210 shown in the table below. Divide this over the sum of the frequencies minus 1. So we divide by n-1 = 40-1 = 39 to get roughly 31.03
This is the sample variance.
The square root of this is sqrt(31.03) = 5.57 and this is the approximate sample standard deviation.
A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. The radius of the dartboard is 13in, and the radius of the shaded region is 4in.
Use the value 3.14 for π. Round your answer to the nearest hundredth.
Answer:
The first thing you need to do is:you have a square whose area is 11^2 = 121 square inches.then we are going to multiply the radius to the PI which is 3.14 the area of the circle with radius 4 is equal to 3.14 * 4^2 = 3.14 * 16 = 50.24you need to divide the calculated radius times pi (3.14) you can get the answer and you need to round your answer to the nearest hundredththe probability that the dart will hit within the circle is equal to 50.24 / 121 = 0.4152066116 which is rounded to .04152 or 41.52%this assumes the dart will always hit the square at least.
Step-by-step explanation:
Which steps could be part of the process in algebraically solving the system of equations, y 5x = x2 10 and y = 4x – 10? select two options. y = x2 5x 10 y 5x = x2 10 4x – 10 0 = x2 – 9x 0 = x2 – 9x 20 one x-value of a solution to the system is 4.
Answer:
That would be :
4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substitute for y)
PROOF: y + 5x = x² + 10
(4x - 10) + 5x = x² + 10
4x - 10 = x² -5x + 10
0 = x2 – 9x + 20 (liked terms are grouped and simplified)
PROOF: 4x - 10 = x² -5x + 10
4x = x² -5x + 10 + 10
0 = x² -5x -4x + 20
0 = x² - 9x + 20
Solving:
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
(x - 5) (x - 4) = 0
⇒ x = 4 (as question says) OR x = 5
Step-by-step explanation:
hope this helps
Answer:
D,E
Step-by-step explanation:
HELP 80 POINTS
Solve the right triangle.
Round your answers to the nearest tenth
answer:
A=46°
a=17.983 (tenths- 18, hundredths- 17.98)
b=17.366 (tenths- 17.4, hundredths- 17.37)
explanation:
1. find angle A
it shows that the angle corresponding with the side length of 25 is a right angle, meaning it's 90°. using that information and the angle given to us (44°), we're able to find the missing angle. since all the angles in a triangle always add up to 180°, we can add the two angles together and then subtract that from 180° to find the missing angle.
90°+44°=134°
180°-134°=46°
A=46°
2. find side a
using the law of cosines, we're able to find the length of side a. cosine of an angle equals [tex]\frac{adjacent}{hypotenuse}[/tex]. we'll be using angle B (44°) for our angle. after we plug in the values, we can just solve the equation to find side a.
cosine44°=[tex]\frac{a}{25}[/tex]
(multiply both sides by 25)
25cosine44°=a
a=17.983
3. find side b
finding the length of side b is very similar to how you found side a. you can use the law of cosines again (make sure you use the right side lengths and angles!), but i used the law of sines. the sine of an angle equals [tex]\frac{opposite}{hypotenuse}[/tex]. we're going to be using the same angle for this.
sine44°=[tex]\frac{b}{25}[/tex]
(multiply both sides by 25)
25sine44°=b
b=17.366
--
if this helped, please consider giving brainliest !
What number am I?
Elmo wants his answer please
Answer:
8
Step-by-step explanation:
Im not sure but i think it might be correct.
Answer:
8
Step-by-step explanation:
An African bush elephant weighs 5½ tons. How many pounds does this elephant weigh?
HELP GUYS!
Answer:
11000 pounds
Step-by-step explanation:
1 US ton=2000 pounds
multiply the mass value by 2000
5.5ton x 2000pound
=11000pounds
PLEASE HURRYYYYYYYYYYYYYYYYY!!!!!!!
Answer:
y = 2/5 x + 4/5
Step-by-step explanation:
First, we find the slpe of the line that is shown.
We go from point (-2, 2) to (0, -3).
We go 5 down, or a rise of -5.
Then we go 2 right, or a run of 2.
slope = m = -5/2
The perpendicular line has slope 2/5.
y = (2/5)x + b
2 = (2/5)(3) + b
10/5 = 6/5 + b
b = 4/5
y = 2/5 x + 4/5
a community service program, students earn points for two tasks: painting over graffiti and picking up trash. The
following constraints are imposed on the program.
1) A student may not serve more than 10 total hours
per
week.
2) A student must serve at least 1 hour per week at each task.
Let g = the number of hours a student spends in a week painting over graffiti.
Let t = the number of hours a student spends in a week picking up trash.
Write a system that represents the imposed constraints.
The system of equations that represents the imposed constraints is given as follows:
[tex]g + t \leq 10[/tex][tex]g \leq 1, t \leq 1[/tex]What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
g = the number of hours a student spends in a week painting over graffiti.t = the number of hours a student spends in a week picking up trash.A student may not serve more than 10 total hours per week, hence:
[tex]g + t \leq 10[/tex]
A student must serve at least 1 hour per week at each task, hence:
[tex]g \leq 1, t \leq 1[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Solve the following ⇒ 8x-5=5(x-4)
Answer:
x = -5
Step-by-step explanation:
Given:
[tex]\displaystyle \large{8x-5=5(x-4)}[/tex]
Distribute 5(x-4):
[tex]\displaystyle \large{8x-5=5x-20}[/tex]
Add both sides by 5:
[tex]\displaystyle \large{8x-5+5=5x-20+5}\\\displaystyle \large{8x=5x-15}[/tex]
Subtract both sides by 5x:
[tex]\displaystyle \large{8x-5x=5x-15-5x}\\\displaystyle \large{3x=-15}[/tex]
Divide both sides by 3:
[tex]\displaystyle \large{\dfrac{3x}{3}=\dfrac{-15}{3}}\\\displaystyle \large{x=-5}[/tex]
Therefore, your solution is x = -5
Answer:
x = -5
Step-by-step explanation:
8x - 5 = 5(x - 4)Distributing the value in the RHS
5(x - 4)5(x) - 5(4)5x - 20Equating to the RHS
8x - 5 = 5x - 20Bring x terms to the left and numbers to the right.
8x - 5x = -20 + 53x = -15Divide both sides by 3.
3x/3 = -15/3x = -54) Good Work Company charges by the word to run classified ads. This company charges $12 for
the first 15 words and $0.55 for each additional word.
a. How much would a 25-word classified ad cost?
b. How much would a 50-word classified ad cost?
Equation::
Rate of change=0.55$If words be x
Equation in slope intercept form
y=12+0.55x, x≥15So
#1
More words=25-15=10
Cost:-
y=12+0.55(10)=12+5.5=17.5$#2
Extra words=50-15=35
Cost:-
y=12+0.55(35)=12+19.25=29.25$Answer:
a. $17.50
b. $31.25
Step-by-step explanation:
a.
For $12 you get 15 words.
For a 25-word ad, you need 10 more words than the 15 you get for $12, so you must add 10 words at $0.55 per word.
cost = $12 + 10 × $0.55
cost = $12 + $5.5
cost = $17.50
b.
50 words is 25 words more than 25 words, so you must pay for 25 words more than the cost of the 25-word ad in part a.
cost = $17.50 + 25 × $0.55
cost = $17.50 + $13.75
cost = $31.25
Solving the System of Equations
Examine the system of equations.
4.2x + 8y = 41.8
–4.2x + y = 19.4
Use the linear combination method to solve the system of equations. What is the value of x?
–3
–1
1.7
6.8
Answer:
x= -3
Step-by-step explanation:
Solve the following system:
{8 y + 4.2 x = 41.8
y - 4.2 x = 19.4
In the second equation, look to solve for y:
{8 y + 4.2 x = 41.8
y - 4.2 x = 19.4
y - 4.2 x = y - (21 x)/5 and 19.4 = 97/5:
y - (21 x)/5 = 97/5
Add (21 x)/5 to both sides:
{8 y + 4.2 x = 41.8
y = 1/5 (21 x + 97)
Substitute y = 1/5 (21 x + 97) into the first equation:
{4.2 x + 8/5 (21 x + 97) = 41.8
y = 1/5 (21 x + 97)
4.2 x + (8 (21 x + 97))/5 = ((168 x)/5 + 776/5) + 4.2 x = 37.8 x + 776/5:
{(37.8 x + 776/5) = 41.8
y = 1/5 (21 x + 97)
In the first equation, look to solve for x:
{37.8 x + 776/5 = 41.8
y = 1/5 (21 x + 97)
37.8 x + 776/5 = (189 x)/5 + 776/5 and 41.8 = 209/5:
(189 x)/5 + 776/5 = 209/5
Subtract 776/5 from both sides:
{(189 x)/5 = -567/5
y = 1/5 (21 x + 97)
Multiply both sides by 5/189:
{x = -3
y = 1/5 (21 x + 97)
Substitute x = -3 into the second equation:
Answer: {x = -3, y = 34/5
Answer:
A) -3
Step-by-step explanation:
