A basketball player shoots a basketball with an initial velocity of 15ft/sec. The ball is released from an initial height of 6.5 feet. The function h(t)=-16t^2+v0t+h0 models the height,in feet, of an object after t seconds. v0 is the initial initial height of the object
part one right function that models the height of the basketball use your function to answer part 2 through 4
part 2 how long does it take for the basketball to hit the ground round your answer to the nearest hundredth show all your work
part 3 when does the basketball reaches maximum height round your number to the nearest hundredth show all your work and explain your answer
what is the maximum height of the basketball round your answer to the nearest hundredth and show all your work and explain your answer
PLEASE HELP
Answers
Answer:
Viewing window: [0, 1.4] × [-3, 12]
See the attachments from the TI-83 Plus graphing calculator.
1) f(t) = -16t² + 15t + 6.5
2) -16t² + 15t + 6.5 = 0
32t² - 30t - 13 = 0
t = (30 + √((-30)² - 4(32)(-13)))/(2(32))
= (30 + √2564)/64
= (30 + 2√641)/64
= (15 + √641)/32
= about 1.26 seconds
3) f'(t) = -32t + 15
-32t + 15 = 0
t = 15/32 seconds = about .47 seconds
f(15/32) = -16(15/32)² + 15(15/32) + 6.5
= about 10.02 feet
Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]
Part 2: It takes approximately 0.89 seconds for the basketball to hit the ground.
Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.
Part 1: The function that models the height of the basketball is given by:
[tex]\[ h(t) = -16t^2 + v_0 t + h_0 \][/tex]
Given:
- Initial velocity [tex](\( v_0 \))[/tex] = 15 ft/sec
- Initial height [tex](\( h_0 \))[/tex] = 6.5 feet
So, the function becomes:
[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]
Part 2: To find how long it takes for the basketball to hit the ground, we set [tex]\( h(t) = 0 \)[/tex] and solve for [tex]\( t \)[/tex]:
[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]
We can use the quadratic formula to solve for[tex]\( t \)[/tex]:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = -16 \), \( b = 15 \), and \( c = 6.5 \).[/tex]
Plugging in the values:
[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \]\[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \]\[ t = \frac{-15 \pm \sqrt{641}}{-32} \][/tex]
Using a calculator, we find:
[tex]\[ t \approx 0.89 \text{ seconds (rounded to the nearest hundredth)} \][/tex]
Part 3: To find when the basketball reaches its maximum height, we can use the formula for the x-coordinate of the vertex of a quadratic function:
[tex]\[ t_{\text{max}} = -\frac{b}{2a} \][/tex]
For our function [tex]\( h(t) = -16t^2 + 15t + 6.5 \), \( a = -16 \) and \( b = 15 \).[/tex]
[tex]\[ t_{\text{max}} = -\frac{15}{2(-16)} \]\[ t_{\text{max}} = \frac{15}{32} \]\[ t_{\text{max}} \approx 0.47 \text{ seconds (rounded to the nearest hundredth)} \][/tex]
Part 4: To find the maximum height of the basketball, we substitute the value of [tex]\( t_{\text{max}} \)[/tex] into the function [tex]\( h(t) \):[/tex]
[tex]\[ h_{\text{max}} = -16(0.47)^2 + 15(0.47) + 6.5 \]\[ h_{\text{max}} = -16(0.2209) + 7.05 + 6.5 \]\[ h_{\text{max}} = -3.5344 + 7.05 + 6.5 \]\[ h_{\text{max}} \approx 10.0156 \text{ feet (rounded to the nearest hundredth)} \][/tex]
The maximum height of the basketball is approximately 10.02 feet.
Related Questions
Subtracting 1 from which digit in the number 12,345 will decrease the value of the number by 1,000
Answers
Solve for N , I can’t get this , I’ll give brainliest to who gets it!!!
Answers
Answer:
55
Step-by-step explanation:
The two shortest sides added up need to be longer then the longest angle so 48 + 55 = 103>73
[tex]\lim_{x\to \infty} \frac{\sqrt{9x^{2} +x+1} -\sqrt{4x^{2} +2x+1} }{x+1}[/tex]
Answers
Answer:
[tex]\lim _{x\to \infty \:}\left(\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}\right)=1[/tex]
Step-by-step explanation:
Considering the expression
[tex]\lim _{x\to \infty \:}\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}[/tex]
Steps to solve
[tex]\lim _{x\to \infty \:}\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}[/tex]
[tex]\mathrm{Divide\:by\:highest\:denominator\:power:}\:\frac{\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}}{1+\frac{1}{x}}[/tex]
[tex]\lim _{x\to \infty \:}\left(\frac{\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}}{1+\frac{1}{x}}\right)[/tex]
[tex]\lim _{x\to a}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\lim _{x\to a}f\left(x\right)}{\lim _{x\to a}g\left(x\right)},\:\quad \lim _{x\to a}g\left(x\right)\ne 0[/tex]
[tex]\mathrm{With\:the\:exception\:of\:indeterminate\:form}[/tex]
[tex]\frac{\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)}{\lim _{x\to \infty \:}\left(1+\frac{1}{x}\right)}.....[1][/tex]
As
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)=1[/tex]
Solving
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)....[A][/tex]
[tex]\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)[/tex]
[tex]\mathrm{With\:the\:exception\:of\:indeterminate\:form}[/tex]
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}\right)-\lim _{x\to \infty \:}\left(\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)[/tex]
Also
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}\right)=3[/tex]
Solving
[tex]\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}\right)......[B][/tex]
[tex]\lim _{x\to a}\left[f\left(x\right)\right]^b=\left[\lim _{x\to a}f\left(x\right)\right]^b[/tex]
[tex]\mathrm{With\:the\:exception\:of\:indeterminate\:form}[/tex]
[tex]\sqrt{\lim _{x\to \infty \:}\left(9+\lim _{x\to \infty \:}\left(\frac{1}{x}+\lim _{x\to \infty \:}\left(\frac{1}{x^2}\right)\right)\right)}[/tex]
[tex]\lim _{x\to \infty \:}\left(9\right)=9[/tex]
[tex]\lim _{x\to \infty \:}\left(\frac{1}{x}\right)=0[/tex]
[tex]\lim _{x\to \infty \:}\left(\frac{1}{x^2}\right)=0[/tex]
So, Equation [B] becomes
⇒ [tex]\sqrt{9+0+0}[/tex]
⇒ [tex]3[/tex]
Similarly, we can find
[tex]\lim _{x\to \infty \:}\left(\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)=2[/tex]
So, Equation [A] becomes
⇒ [tex]3-2[/tex]
⇒ 1
Also
[tex]\lim _{x\to \infty \:}\left(1+\frac{1}{x}\right)=1[/tex]
Thus, equation becomes
[tex]\frac{\lim _{x\to \infty \:}\left(\sqrt{9+\frac{1}{x}+\frac{1}{x^2}}-\sqrt{4+\frac{2}{x}+\frac{1}{x^2}}\right)}{\lim _{x\to \infty \:}\left(1+\frac{1}{x}\right)}=\frac{1}{1}=1[/tex]
Therefore,
[tex]\lim _{x\to \infty \:}\left(\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}\right)=1[/tex]
Keywords: limit
Learn more about limit form limit brainly.com/question/1444049
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Simplify .
[tex]\sqrt{x} 18[/tex]
Answers
Answer:
[tex]3\sqrt{2} \sqrt{x}[/tex]
Can someone find the total area of this poster
Answers
Answer: 1,360
Step-by-step explanation:
20 * 20 = 400
20 * 12 = 240
240 * 4 = 960
960 + 400 = 1,360
Copy the problems onto your paper, mark the givens and prove the statements asked.
Given ∠E ≅ ∠T, M − midpoint of TE Prove: MI ≅ MR
Answers
MI ≅ MR proved by using ASA postulate of congruence
Step-by-step explanation:
Let us revise the cases of congruence
SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ AAS ⇒ 2 angles and one side in the 1st Δ ≅ 2 angles and one side in the 2nd Δ HL ⇒ hypotenuse leg of the 1st right Δ ≅ hypotenuse leg of the 2nd right Δ∵ M is the mid-point of TE
∴ MT = ME
In Δs TMI and EMR
∵ ∠T ≅ ∠E ⇒ given
∵ ∠TMI ≅ EMR ⇒ vertical opposite angles
∵ MT = ME ⇒ proved
∴ Δ TMI ≅ ΔEMR by ASA postulate of congruence
- From congruence, corresponding sides are equal
∴ MI ≅ MR
MI ≅ MR proved by using ASA postulate of congruence
Learn more;
You can learn more about the cases of congruence in brainly.com/question/6108628
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The question is about a geometry proof related to congruent angles and midpoints, but additional information is needed to provide a specific solution.
Explanation:The question appears to be a geometry proof involving congruent angles and midpoints. The goal is to prove that two line segments MI and MR are congruent given ∠E ≅ ∠T, and M is the midpoint of TE.
To prove this, one would need to provide more information about the points I and R, such as their positions relative to point E, T, and M.
Without this additional information, it is difficult to give a specific proof. However, typical proof strategies might involve showing that triangles EMI and TMR are congruent by Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS) postulates, depending on the position of points I and R.
It takes 1 1/4 minutes to fill a 3 gallon bucket at this rate how long will it take to fill a 50 gallon tub
Answers
It will take [tex]20\frac{5}{6}[/tex] minutes to fill a 50 gallon tub.
Step-by-step explanation:
Time taken to fill 3 gallons bucket = [tex]1\frac{1}{4}=\frac{5}{4}\ minutes[/tex]
We have to find time required to fill 50 gallons tub.
3 gallons = [tex]\frac{5}{4}\ minutes[/tex]
1 gallon = [tex]\frac{5}{4}*\frac{1}{3}\ minutes[/tex]
1 gallon = [tex]\frac{5}{12}\ minutes[/tex]
To find the time required for 50 gallons;
50 gallons = 50 * Time per gallon
50 gallons = [tex]50*\frac{5}{12}[/tex]
50 gallons = [tex]\frac{250}{12}[/tex] = [tex]\frac{125}{6}[/tex]
50 gallons = [tex]20\frac{5}{6}\ minutes[/tex]
It will take [tex]20\frac{5}{6}[/tex] minutes to fill a 50 gallon tub.
Keywords: fraction, division
Learn more about fractions at:
brainly.com/question/11007026brainly.com/question/11207748#LearnwithBrainly
Final answer:
It takes approximately 20.83 minutes to fill a 50 gallon tub if it takes 1 1/4 minutes to fill a 3 gallon bucket, considering a constant rate of filling.
Explanation:
The question asks us to determine how long it will take to fill a 50 gallon tub if it takes 1 1/4 minutes to fill a 3 gallon bucket. To solve this, we can set up a proportion since the rates of gallons per minute will be the same for both the bucket and the tub.
First, let's convert the time from minutes to seconds to match the unit for seconds provided in the example. There are 60 seconds in a minute, so 1 1/4 minutes is equal to 75 seconds.
Now, we know it takes 75 seconds to fill 3 gallons. Let's calculate the number of seconds it takes to fill 1 gallon, and then we will use that rate to find out how many seconds it will take to fill 50 gallons.
We divide 75 seconds by 3 gallons, to get 25 seconds per gallon. Then we multiply this rate by 50 gallons to find the total time needed to fill the tub:
25 seconds/gallon × 50 gallons = 1250 seconds.
Finally, to convert seconds back to minutes, we divide 1250 seconds by 60:
1250 seconds ÷ 60 seconds/minute = 20 5/6 minutes or approximately 20.83 minutes.
So, it takes approximately 20.83 minutes to fill a 50 gallon tub at the given rate.
5. A hummingbird feeder holds 2/3 of a cup of hummingbird solution. A bottle of solution will fill the feeder 8 times. How much hummingbird solution is in the bottle.
Answers
Answer:
1.26 liters.
Step-by-step explanation:
Given that, a hummingbird feeder holds [tex]\frac{2}{3}[/tex] of a cup of hummingbird solution.
Again, a bottle of solution will fill the feeder 8 times.
Therefore, a bottle of solution will measure [tex](\frac{2}{3}\times 8) = \frac{16}{3} = 5.33[/tex] cups of hummingbird solution.
Now, one cup is equivalent to 0.236588 liters.
So, 5.33 cups is equal to (0.236588 × 5.33) = 1.26 liters. (Answer)
Mrs.Lohens made curtains for her children’s bedrooms. She used 4 3/4 yards of fabric for Nickys room and 6 5/8 yards for Linda’s room. How much fabric did she use in all?
Answers
Answer:
[tex]11\frac{3}{8}\ yd[/tex]
Step-by-step explanation:
we know that
To find out the total yards of fabric used, add up the yards of fabric used for Nickys' room and the yards of fabric used for Linda's room
so
[tex]4\frac{3}{4}+6\frac{5}{8}[/tex]
Convert mixed number to an improper fraction
[tex]4\frac{3}{4}\ yd=4+\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}\ yd[/tex]
[tex]6\frac{5}{8}\ yd=6+\frac{5}{8}=\frac{6*8+5}{8}=\frac{53}{8}\ yd[/tex]
Adds the fractions
[tex]\frac{19}{4}+\frac{53}{8}=\frac{2*19+53}{8}= \frac{91}{8}\ yd[/tex]
Convert to mixed number
[tex]\frac{91}{8}\ yd= \frac{88}{8}+ \frac{3}{8}= 11\frac{3}{8}\ yd[/tex]
In the triangle below, what is the sine of 30°?
Answers
Answer:
There's no picture. Is it D.√3 / 2
Step-by-step explanation:
What is the answer to 13d+25=8d
Answers
13d + 25 = 8d
13d - 8d = -25
5d = -25
d = -5
so the answer is (-5)
Answer:
Step-by-step explanation:
13d + 25 = 8d
13d = 8d -25
13d - 8d = -25
5d = -25
d = -5
Can someone please answer this question please answer it correctly and show work please
Answers
Answer:
42) 122.72 square inches
43) 212.83 additional feet of fabric
Step-by-step explanation:
42)
Diameter = [tex]12\frac{1}{2}[/tex] = 12.5 inches
Radius = (1/2) * Diameter = (1/2) * 12.5 = 6.25 inches
The formula for calculating the area of a circle is π * Radius²
π * Radius²
Substitute radius and pi into formula
3.14159265359 * 6.25²
Solve exponent
3.14159265359 * 39.0625
Multiply
122.7184630309
Round to the nearest hundredth
122.72 square inches
43) Clarissa needs 500 feet of fabric
She has these pieces
3 pieces of fabric that are each 18 yards long
1 piece of fabric that is [tex]16\frac{1}{2}[/tex] yards long
1 piece of fabric that is [tex]75\frac{2}{3}[/tex] feet long
Convert all yard measurements to feet and all fractions to decimals
(1 yard = 3 feet)
3 pieces of fabric that are each 54 feet long
1 piece of fabric that is 49.5 yards long
1 piece of fabric that is 75.67 feet long
Add all lengths
3(54) + 49.5 + 75.67
162 + 49.5 + 75.67 = 287.17
Subtract from 500 to find missing length
500 - 287.17 = 212.83
212.83 additional feet of fabric
Hope this helps :)
Let y=f(x) be the particular solution to the differential equation dy/dx=(x^2+1)/e^y with the initial condition f(1)=0. What is the value of f(2) ?
Answers
[tex]\( f(2) = \ln \left( \frac{14}{3} \right) \)[/tex]. You can calculate this value to get a numerical result.
To find the particular solution [tex]\( y = f(x) \)[/tex] to the given differential equation [tex]\( \frac{dy}{dx} = \frac{x^2 + 1}{e^y} \)[/tex] with the initial condition [tex]\( f(1) = 0 \)[/tex] and then evaluate [tex]\( f(2) \),[/tex] we can follow these steps:
1. Separate variables:
[tex]\[ e^y dy = (x^2 + 1) dx \][/tex]
2. Integrate both sides:
[tex]\[ \int e^y dy = \int (x^2 + 1) dx \][/tex]
[tex]\[ e^y = \frac{1}{3} x^3 + x + C \][/tex]
3. Apply the initial condition [tex]\( f(1) = 0 \):[/tex]
[tex]\[ e^0 = \frac{1}{3} (1)^3 + 1 + C \][/tex]
[tex]\[ 1 = \frac{1}{3} + 1 + C \][/tex]
[tex]\[ C = \frac{2}{3} \][/tex]
So, the particular solution is:
[tex]\[ e^y = \frac{1}{3} x^3 + x + \frac{2}{3} \][/tex]
4. Solve for y :
[tex]\[ y = \ln \left( \frac{1}{3} x^3 + x + \frac{2}{3} \right) \][/tex]
Now, we need to find f(2), which means finding the value of y when x = 2:
[tex]\[ y = \ln \left( \frac{1}{3} (2)^3 + 2 + \frac{2}{3} \right) \][/tex]
[tex]\[ y = \ln \left( \frac{8}{3} + 2 + \frac{2}{3} \right) \][/tex]
[tex]\[ y = \ln \left( \frac{14}{3} \right) \][/tex]
buzz makes 75% of her free throws.If she whats to set the record of making 48 free throws in 5 minutes,how many free throws does she have to make?
Answers
Answer:
63
Step-by-step explanation:
Answer:
65
Step-by-step explanation:
75% of 65 = 48
Which statement describes the graph of f(x) = x² - 6x + 9 ?
a line with an x-intercept of (-3, 0)
a parabola with an x-intercept of (-3, 0)
a line with an x-intercept of (3, 0)
a parabola with an x-intercept of (3, 0)
Answers
Answer:
About
step 1 highlight numbers
step 2 do ctrl+f
step 3 type in 9
ENJOY
1051541451431641621571721571511441234567881234567812345678123678326470547 2999999259923478990124999995689902993413269916749953349999914649932724997 2994567809912568990139956799809929936781467998299634699818991169966144990 2999994569970124995699801323459999012615302799995324993243699019923412993 2994567801993569980299356780239999456725634569974326992644399243992369936 2994567801992689901239967899029939945745315319931253399436998011992349950 2998012345299999388352999991039953991232012479934673289999982640499999415l
Step-by-step explanation:
lines AD and BE intersect at point C, as shown. create an expression that represents the measure of the angle DCE in terms if X
part 2 of question: using your expression, solve for the missing value of X if DCE was 120 degrees.
Answers
Answer:
Please, find the image with the diagram of the lines corresponding to this question:
The answers are:
Equation: m ∠ DCE = 180º - x
Value of x = 60º
Explanation:
First question:
You must use the fact that the angles DCE and BCD are adjacent angles, because they share the vertex (C) and have a common side (CD).
Thus, as a first fact, the measure of the angle BCE is equal to the sum of the measures of the angles BCD and DCE.
On the other hand, BE is a straight line, thus the measure of angle BCE is 180º.
Hence, you can write:
m ∠ DCE + m ∠ DCB = 180ºm ∠ DCE + x = 180ºm ∠ DCE = 180º - xSecond question:
Solve for x:
Given: m ∠ DCE = 180º - xAdd x to both sides: m ∠ DCE + x = 180º Subtract m ∠ DCE from both sides: x = 180º - m ∠DCESubstitute m ∠DCE with 120º:
x = 180º - 120º = 60ºHence, for m ∠DCE = 120º, x = 60º.
Estimate by rounding the largest number to hundreds and then multiplying.
691 x 4 is approximately
Answers
Answer:
approximately 2,800
Step-by-step explanation:
you would round 691 to 700 then multiply by 4
Answer:
2,800
Step-by-step explanation:
In saying "largest number," I believe the question means that you should round 691 up to 700 (nearest hundreds). Multiple 700 by 4, and you will get 2,800! Hope this helps! :)
Afon read pages in 30 minutes.
Find the number of minutes read per page and the number of pages read per minute.
I need help im bad at 7th grade math!!!!!!!!
Answers
Answer:
Therefore Afon can read 0.75 pages per minute.
Step-by-step explanation:
Afon read 22 1/2 pages in 30 minutes
Therefore Afon read 22.5 pages in 30 minutes.
Therefore the number of pages Afon can read in 1 minute
[tex]= \dfrac{22.5}{30} = \dfrac{45}{60} = \dfrac{9}{12} = \dfrac{3}{4} = 0.75 pages[/tex]
Therefore Afon can read 0.75 pages per minute.
Please help I'm a little confused!
Eight is less than or equal to the quotient of a number and negative four.
Answers
I will have "x" represent the unknown number, or you could use a "?", doesn't matter.
[tex]8\leq \frac{x}{-4}[/tex] [8 is less than or equal to (≤) the quotient (÷) of a number and -4, so the number is being divided by -4]
If you need to solve this, you need to isolate/get the variable "x" by itself in the inequality:
[tex]8\leq \frac{x}{-4}[/tex] Multiply -4 on both sides to get rid of the fraction and get "x" by itself
[tex](-4)8\geq \frac{x}{-4} (-4)[/tex] When you multiply/divide by a negative number, you flip the sign (< >)
-32 ≥ x [-32 is greater than or equal to x, or x is less than or equal to -32]
Find the cube root of 3357
Answers
Jim is 2 years older than 3 times his little brother Tommy. Together their ages add up to 18. How old is each?
Answers
Final answer:
By setting up an equation based on the given information that Jim is 2 years older than 3 times Tommy's age and their combined ages are 18, we find that Tommy is 4 years old and Jim is 14 years old.
Explanation:
The question is about finding the ages of Jim and his younger brother Tommy given that Jim is 2 years older than 3 times Tommy's age and together their ages add up to 18. Let's denote Tommy's age as T years. Therefore, Jim's age would be 3T + 2 years. According to the problem, if we add both ages, the sum is 18. So, we can set up the following equation to find their ages:
T + (3T + 2) = 18
Simplifying this equation gives:
4T + 2 = 18
4T = 16
T = 4
Thus, Tommy is 4 years old. To find Jim's age, we substitute Tommy's age back into the equation for Jim's age:
Jim's age = 3(4) + 2 = 12 + 2 = 14
Therefore, Tommy is 4 years old, and Jim is 14 years old.
What do you know about two different integers that are opposites?
Answers
Only if they are each the same distance away from zero, but on opposite sides of the number line.
Hope this help! :)
Answer:If you add a negative and a positive you do the the integers step by changing the add operation to a subtraction.
Step-by-step explanation:-4+3
integers property -4 - 3 = 1
negative plus a positive is a positive.
Divide using polynomial long division
(x^2+x-17)/(x-4)
Answers
The solution for (x^2+x-17) / (x-4) is (x + 5) + 3/(x-4)
Step-by-step explanation:
The given polynomial is (x^2+x-17) divided by (x-4)
Steps for long division method :
check the polynomial is written in descending order of power (x^3, x^2, and so on).To make the first term zero, multiply the divisor with one power lesser than the first term. For eg. To divide x^2, multiply the divisor with x.Subtract and bring down the next term.The above two steps are repeated until the last term gets divided.The term remaining after the last subtract step is the remainder. The final answer must be written in quotient and remainder as a fraction with the divisor.Using long division method :
x + 5
x-4 | x^2 + x - 17
(-)(x^2 - 4x)
5x - 17
(-)(5x -20)
3
The quotient is (x+5).
The remainder is 3.
The solution is written in the form of quotient + remainder/ divisor
∴ The final answer is (x^2+x-17) / (x-4) = (x + 5) + 3/(x-4)
Final answer:
To divide (x²+x-17) by (x-4) using polynomial long division, divide the highest order term of the dividend by the highest order term of the divisor, multiply the divisor by the result, subtract the result from the dividend, and repeat until there are no more terms or the remainder has lower degree. The quotient is x+5 and the remainder is -3.
Explanation:
To divide (x²+x-17) by (x-4) using polynomial long division:
Write the dividend (x²+x-17) and the divisor (x-4) in the division format.
Divide the highest order term of the dividend (x²) by the highest order term of the divisor (x). The result is x.
Multiply the entire divisor (x-4) by the result from step 2 (x) and write the result below the dividend.
Subtract the result from step 3 from the dividend.
Repeat steps 2-4 until there are no more terms to bring down or the degree of the remainder is less than the degree of the divisor.
The final quotient is x+5 and the remainder is -3.
Please solve for me!!
During a trip , Jonathan had driven a total of 75 miles by 6:20 PM and a total of 85 miles by 6:40 Pm. He drove at the same rate for the entire trip. At what time had he driven a total of 140 miles?
Answers
Answer:
8:30 PM
Step-by-step explanation:
Let's say that x is minutes since 6:20 PM, and y is position in miles.
Since Jonathan drives at a constant rate, the position vs time graph is linear. Two points on the line are (0, 75) and (20, 85). The slope of the line is:
m = Δy / Δx
m = (85 − 75) / (20 − 0)
m = ½
So the equation of the line is:
y = ½ x + 75
We want to find x when y is 140.
140 = ½ x + 75
65 = ½ x
x = 130
So 130 minutes after 6:20 PM is when Jonathan's position will be 140 miles. 130 minutes is 2 hours and 10 minutes. So the time will be 8:30 PM.
By calculating the speed at which Jonathan was driving and applying that rate to the total distance, it can be concluded that Jonathan would have driven a total of 140 miles by about 8:30 PM.
Explanation:Jonathan drove 10 miles from 6:20 PM to 6:40 PM, giving a 20-minute duration. We can say the rate of speed he was driving at is 10 miles/20 minutes. We can simplify this rate down to 1 mile/2 minutes to make it easier to work with.
To calculate when he would've driven a total of 140 miles we follow these steps:
Subtract the 75 miles he had already driven from the total of 140 miles we want to find out about, which gives us 65 miles.
Divide these 65 miles by the rate he's driving at (1 mile/2 min), which gives us 130 minutes.Add these 130 minutes to the original time of 6.20 PM. The result is approximately 8.30 PM.Therefore, Jonathan would've driven a total of 140 miles by about 8:30 PM.
Learn more about Rate Calculation here:https://brainly.com/question/16549128
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10 times a number, then add 20
Answers
Answer:
10x+20
Step-by-step explanation:
Answer: The equation is 10x+20
(x is a variable, not a multiplication symbol)
Step-by-step explanation:
10 times a number, that is unknown, plus 20.
x is the unknown number.
10x plus 20.
10x+20
Please answer this question.
Answers
Answer:
2
Step-by-step explanation:
There are 26 students in Mrs. Augello’s math class. The number of boys is three less than the number of girls. Write a system of equations that represents the number of boys and girls.
Answers
Answer:
[tex]b+g=26[/tex]
[tex]b=g-3[/tex]
Step-by-step explanation:
Let the number of boys be reprented by [tex]b[/tex]
Let the number of girls be represented by [tex]g\\[/tex]
↓ Total number of boys + girls must be 26
[tex]b+g=26[/tex]
↓ Number of boys is 3 less than the number of girls
[tex]b=g-3[/tex]
The system of equations that represents the number of boys and girls are [tex]x+y=26[/tex] and [tex]x = y-3[/tex] and this can be determined by forming the linear equation.
Given :
There are 26 students in Mrs. Augello’s math class. The number of boys is three less than the number of girls.The following steps can be used in order to determine the system of equations that represents the number of boys and girls:
Step 1 - Let the total number of boys be 'x' and the total number of girls be 'y'.
Step 2 - So, the linear equation that represents the total number of students in Mrs. Augello's math class is:
[tex]x+y=26[/tex] --- (1)
Step 3 - The linear equation that represents the situation "number of boys is three less than the number of girls" is:
[tex]x = y-3[/tex] --- (2)
For more information, refer to the link given below:
https://brainly.com/question/11897796
and then you have to graph it but im stuck on graphing f(2) so please help
Answers
[tex](-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )[/tex]
Solution:
Given [tex]f(x)=6\left(\frac{2}{3}\right)^{x}[/tex]
Domain = {–1, 0, 1, 2, 3}
Substitute the given values in the function.
At x = –1,
[tex]f(-1)=6\left(\frac{2}{3}\right)^{-1}[/tex]
[tex]=6 \times \frac{3}{2}[/tex]
= 9
[tex](x, f(x))=(-1, 9)[/tex]
At x = –0,
[tex]f(0)=6\left(\frac{2}{3}\right)^{0}=6[/tex]
[tex](x, f(x))=(0,6)[/tex]
At x = 1,
[tex]f(1)=6\left(\frac{2}{3}\right)^{1}=4[/tex]
[tex](x, f(x))=(1,4)[/tex]
At x = 2,
[tex]f(2)=6\left(\frac{2}{3}\right)^{2}[/tex]
[tex]=\frac{24}{9}[/tex]
[tex]=2\frac{6}{9}[/tex] (Cancel the common terms)
[tex]=2\frac{2}{3}[/tex]
[tex](x, f(x))=(2, 2\frac{2}{3} )[/tex]
At x = 3,
[tex]f(3)=6\left(\frac{2}{3}\right)^{3}[/tex]
[tex]=\frac{48}{27}[/tex] (Cancel the common terms)
[tex]=\frac{16}{9}[/tex]
[tex]=1\frac{7}{9}[/tex]
[tex](x, f(x))=(3, 1\frac{7}{9} )[/tex]
Plot the points in the graph.
The image of the graph is attached below.
which plane is closer to the base of the airplane tower? explain. The distance for Plane A, to the nearest tenth, is ____ kilometers. The distance for Plane B, to the nearest tenth, is _____ kilometers. help!!
Answers
Answer:
Plane B is closer.
The distance for Plane A is 7.9 km.
The distance for Plane B is 7.4 km.
Step-by-step explanation:
To find the distance to the tower, altitude must be converted to kilometers. Each 1000 ft is 0.3048 km, so the heights of the planes are ...
-- Plane A: (20 thousand ft)*(0.3048 km/thousand ft) = 6.096 km
-- Plane B: (8 thousand ft)*(0.3048 km/thousand ft) = 2.4384 km
The Pythagorean theorem can be used to find the distance from each plane to the tower:
-- distance = √((ground distance)² + (height)²)
-- Plane A distance = √(5² +6.096²) ≈ √62.16 ≈ 7.9 . . . km
-- Plane B distance = √(7² +2.4384²) ≈ √54.95 ≈ 7.4 . . . km
The distance for Plane B is shorter, so Plane B is closer to the tower.
A 25-foot flag pole casts a shadow of 40 feet. What is the approximate height from the top of the flag pole to the top of the shadow? 45 47 65
Answers
Answer:45
Step-by-step explanation:
it is 45
Step-by-step explanation: