2c. We assume that the equations for ballistic motion in a vacuum apply, and the rate of downward acceleration is 32 ft/s². Then it will take ...
... (288 ft/s)/(32 ft/s²) = 9 s
for the rocket to reach its maximum height (its vertical velocity to decrease to zero).
2d. The trip down takes the same amount of time as the trip up, so the round trip time is ...
... (9 s)×2 = 18
_____
More ExplanationThe acceleration due to gravity decreases the vertical velocity by the same amount (32 ft/s) each second. An equation for that might be ...
... v = 288 -32t
When the vertical velocity is zero, the rocket is no longer going up. It has reached its maximum height. Then the equation for that looks like ...
... 0 = 288 -32t
... 32t = 288
... t = 288/32 = 9 . . . . . compare to the solution above
After 9 seconds, the rocket reaches its maximum height.
___
Simplifying the description of free-fall is a little harder. In physics terms, the potential energy the rocket has at its maximum height all gets converted to kinetic energy on the way down. At impact with the ground, the kinetic energy is the same as it was when the rocket was launched. That is, its velocity is 288 ft/s earthward at impact. The above equation for velocity still applies, but now we're solving for v = -288.
... -288 = 288 -32t
... -576 = -32t
... 576/32 = t = 18 . . . . . twice the time it took to reach maximum height.
The round trip takes 18 seconds.
Compare 9.36 to 9.359
9.36 is 0.001 more than 9.359
Both numbers round to the same value.
9.359 has greater precision.
Given: ∠A ≅∠D, ∠B ≅∠E m∠C = x, m∠F = 2x−30° Find: m∠C
This is 2 seperate triangles
ABC is one triangle and DEF is a different triangle
Answer:
[tex]m\angle c = 30^\circ[/tex]
Step-by-step explanation:
We are given the following information in the question:
ΔABC and ΔDEF
[tex]\angle A \cong \angle D\\\angle B \cong \angle E\\m\angle c = x \\m\angle F = 2x-30[/tex]
According to angle sum property of the triangle the sum of all angles of triangle is equal to 180 degrees.
Since two corresponding angles of the two triangle are equal, therefore the third angle is also equal.
[tex]x = 2x - 30\\\Rightarrow x = 30[/tex]
Thus,
[tex]m\angle c = 30^\circ[/tex]
The measure of the angle from the given information is m∠C = 2x - 30°
How to determine the measure of the angle?Given the information, we have two separate triangles: ABC and DEF.
In triangle ABC, we are given that ∠A ≅ ∠D and ∠B ≅ ∠E.
In triangle DEF, we are given that m∠C = x and m∠F = 2x - 30°.
To find m∠C, we need to find the value of x.
Since ∠A ≅ ∠D, and ∠B ≅ ∠E, we can conclude that triangle ABC is congruent to triangle DEF by the Angle-Angle (AA) congruence criterion.
Using this congruence, we can determine that m∠C = m∠F.
Therefore, we have:
m∠C = m∠F
Since we know that m∠F = 2x - 30°, we can substitute this value into the equation:
m∠C = 2x - 30°
This gives us the measure of angle C in terms of x.
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The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Is anyone good with geometry? If yes, please show your work on these questions so i can see how its done. C:
(7)
if r perpendicular to s then angles 1,2,3,4=90 deg.
if t perpendicular to s then angles 5,6,7,8=90 deg.
If two different lines intersect a third line at the same angle then they must be parallel.
r and t intersect s at the angle 2=90 deg and 6 = 90 deg, therefore r and t are parallel.
(6) use sum of angles in a triange =180 deg property.
first, the complement to 105 is an angle of 75 deg. then x=180-(24+75)=81 deg
x=81 deg
(5)
[tex]\angle STU=180-\angle STR=180- \angle SRT \\\\\4x = 180-20=160\\\\x=40[/tex]
(4) sum of angles = 180 deg
62 +45 + k = 180
k = 180 -107 = 73
k = 73
Someone please help, it will be so appreciated!
Keisha solved the following equation:
4x − 2x + 8 = 6(x + 4)
Which step has an incorrect justification? (Make sure to type only the number of the step into the blank: 1, 2, 3, 4 or 5)
Hello,
Question:
Keisha solved the following equation:
4x − 2x + 8 = 6(x + 4)
Which step has an incorrect justification? (Make sure to type only the number of the step into the blank: 1, 2, 3, 4 or 5)
Correct Solution:
x − 2x + 8 = 6(x + 4)
4x + −2x + 8 = (6) (x) + (6) (4) (Distribute)
4x + −2x + 8 = 6x + 24
(4x + −2x) + (8) = 6x + 24 (Combine Like Terms)
2x + 8 = 6x + 24
2x + 8 = 6x + 24
Subtract 6x from both sides.
2x + 8 − 6x = 6x + 24 − 6x
−4x + 8 = 24
Subtract 8 from both sides.
−4x + 8 − 8 = 24 − 8
−4x = 16
-4 x -4 = 16
x = -4
Answer:
Where keisha went wrong was forgeting to subtract 6x to both sides.
Incorrrect step is #3
The solution to the equation is correct.
on the line - 4x + 8 = 24 to the next line
- 4x = 16
4 should be Subtraction property of equality and not addition property of equality
Which is the most accurate way to estimate 33% of 52?
1/3 x 51 or 1/3 x 53?
The most accurate way to estimate 33% of 52 is explained as follows:
To find a percentage, we calculate it as follows:
a% of b [tex]=\frac{a}{100} \times b[/tex]
Now, lets convert 33% into fraction first:
33% [tex]=\frac{33}{100} =0.33[/tex]
Now,
[tex]0.33 \times 52=17.16 \approx 17[/tex]
We have two ways to calculate the same so we will compare the values of them and figure out which gives a value nearer to our actual value:
So, [tex]\frac{1}{3} \times51=17[/tex] and [tex]\frac{1}{3} \times 53=17.66[/tex]
We can see that the first method gives us a value which is far closer to the actual value.
Therefore, [tex]\frac{1}{3} \times 51[/tex] is the most accurate way to estimate 33% of 52.
6>2k+4 whats k hih9h9hhi
K=0
brainiest plz eeeeeeeeeeeeeeeeeee
The quotient of 5 times a number and 7 is equal to 10. What is the number?
A. 12
B. 13
C. 14
D. 15
The number when the quotient of 5 times a number and 7 is equal to 10 will be 15. The correct option is D.
What is a quotient?A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.
It is given that the quotient of 5 times a number and 7 is equal to 10. The number will be calculated as below:-
15 divided by 5 is 3 and 3+7 is equal to 10.
Therefore, the number when the quotient of 5 times a number and 7 is equal to 10 will be 15. The correct option is D.
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A line contains (34,12) and (32,48) what is the slope of the line in simplified form? HELP ASAPl
Answer:
[tex]m=-18[/tex]
Step-by-step explanation:
1. The line contains the points (34,12) and (32,48). Then, you need to use the slope formula, which is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
2. When you substitute values into the formula, you obtain:
[tex]y_{2}=48\\y_{1}=12\\x_{2}=32\\x_{1}=34[/tex]
[tex]m=\frac{48-12}{32-34}\\m=\frac{36}{-2}\\m=-18[/tex]
Bobby built twice as many forts as his brother. If his brother built 6 forts , how many did bobby build?
Bobby built 12 forts
Answer:
12 forts
Step-by-step explanation:
6x2=12
Ben drank 2/5 of a pitcher of lemonade Tonya drank 1/4of the lemonade. What fraction of the lemonade did they drink together?
Hello there,
So you have two fractions 2/5 and 1/4, but none of them have the same denominator... However a LCD that you can get from both of these is 20, so if you multiplied 4 on the top and the bottom for 2/5, you would get 8/20, and for 1/4, multiply 5 on the top and the bottom, and soon you end up with 5/20. If you added these two fractions together, now knowing that they have the same denominator... you would end up with 13/20 which is the answer to your problem.
Hope this was helpful for you :)
In 1970, a record 1.5 inches of rain fell in one minute at Brasse Terre, Guadalupe in the Caribbean. At this rate how much rain fell in 3 seconds or 0.05 of a minute? A 3 inches... B 0.075 inch... C 0.75 inch... D 30 inch. Pick one. Evan chose D as the correct answer. How did he get that answer?
Answer:
B. 0.075 in
Evan apparently divided by time. He might do that if he were not paying attention to units.
Step-by-step explanation:
The given rainfall rate is ...
... (1.5 in)/(60 s) = (1/40) in/s = 0.025 in/s
To find the rainfall in 3 s, you need to multiply rate by time:
... (0.025 in/s)×(3 s) = 0.075 in
If you keep the rate and time in terms of minutes, then you have:
... (1.5 in/min)×(0.05 min) = 0.075 in
_____
Evan apparently divided, instead. His number is not inches.
... (1.5 in/min)/(0.05 min) = 30 in/min² . . . . not the appropriate units for the problem
The correct amount of rain that fell in 3 seconds at Brasse Terre, Guadalupe, is 0.075 inches, as calculated by multiplying the rate of 1.5 inches per minute by 0.05 minutes. Evan made an error leading to answer D, which is incorrect.
In 1970, a record 1.5 inches of rain fell in one minute. To find out how much rain fell in 3 seconds, which is 0.05 of a minute, we need to multiply the rate of rainfall by the fraction of the minute we are interested in. The calculation is as follows:
1.5 inches/minute x 0.05 minute = 0.075 inches
Evan seems to have misunderstood the calculation, leading to answer D, but the correct amount of rain that fell in 3 seconds is 0.075 inches, which corresponds to option B.
What is the value of x?
3x−8=8x+4/2
Enter your answer in the box.
Answer:
x = -2
Step-by-step explanation:
3x -8 =8x +4/2
3x -8 =8x +2
3x -3x -8 = 8x -3x +2 (subtract 3x both sides )
-8 = 5x +2
-8-2 =5x+2 -2 (subtract 2 both sides )
-10 =5x
-10/5 = 5x/5 (divide 5 both sides)
-2 = x
$300 was deposited in a Certificate of Deposit (CD) yielding 6% interest compounded quarterly. how many years will it take the CD to reach a value of $876.34?
The future value (A) of a one-time investment of principal amount P at interest rate r compounded n times per year for t years is ...
... A = P(1 +r/n)^(nt)
Putting your given numbers into the formula, we have
... 876.34 = 300(1 +.06/4)^(4t)
Taking logarithms, this becomes the linear equation
... log(876.34) = log(300) + 4t·log(1.015)
Solving for t in the usual way, we get
... log(876.34) -log(300) = 4t·log(1.015) . . . . . . . subtract the constant term on the right
... (log(876.34) -log(300))/(4·log(1.015)) = t ≈ 18.00 . . . . divide by the coefficient of t
It will take 18 years for the $300 CD to reach a value of $876.34.
the function h(x)=g(x+2)-1, what is the value for h(2) and h(-2)
Put 2 where x is:
h(2) = g(2+2) -1 = g(4) -1
_____
Put -2 where x is:
h(-2) = g(-2+2) -1 = g(0) -1
Let f(x) = cos(x). Find the x-intercepts of f(x) on [0, 2π).
the x-intercepts of cosx are
[tex]\frac{\pi }{2}[/tex] and [tex]\frac{3\pi }{2}[/tex] on [0, 2π )
The x-intercepts of the function f(x) = cos(x) on [0, 2π) are π/2 and 3π/2.
Explanation:The x-intercepts of the function f(x) = cos(x) on the interval [0, 2π) can be found by setting f(x) equal to zero and solving for x.
cos(x) = 0
To find the values of x for which cos(x) equals zero, we need to determine when the cosine function equals zero on the given interval. The cosine function equals zero at every multiple of π/2. Therefore, the x-intercepts of f(x) are π/2 and 3π/2.
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Given the point (-1, 8), answer the questions below: After that point was translated 5 units right and 4 units up, the coordinates of this particular point would be ( , ). If this point is a part of a linear function, the parent function f(x)=x would be transformed into an equation that looks like this: g(x) = .
a) x=4 is 5 units to the right of x=-1.
y=12 is 4 units up from y=8.
Your point (-1, 8) is translated to (4, 12).
___
b) If the parent function f(x) = x is translated so it goes through (4, 12), the translated function can be written ...
... g(x) = f(x-4) +12 = (x -4) +12
... g(x) = x +8
PLZ HELP ME WITH GEOMETRY
You just need to use your test-taking skill to eliminate the wrong answers here.
There is no such thing as a "Congruent Angles Postulate," so the last two choices can be eliminated.
The AA Similarity Postulate refers to triangles, not angles, so the second choice can be eliminated.
That only leaves the (correct) first choice.
My friend needed help with this and I found the height through the theorem but can't figure out how to get the base of the overall triangle
You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
_____
Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
_____
As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
Which of the following graphs represents the function f(x) = −x2 − x + 6?
(Correct Answer will receive 30 points and be marked as Brainliest)
The function f(x) describes a parabola that opens downward. The only graph with that shape is the 2nd one.
_____
The degree of 2 on the x² term means there will be only 1 turning point (1 less than the degree). The bottom two choices have more turning points than that.
The minus sign on the coefficient of x² means the graph opens downward—that it tends toward -∞ when x gets very large in magnitude, either positive or negative.
Jeff found that 13 bag of popcorn weighed 14 pounds. How many pounds will one full bag of popcorn weigh? Express your answer in simplest form. a 112 lb b 17 lb c 37 lb d 34 lb
9g=3(-4+5g) solve for g plzzzzzzzzzzzzz
9g = 3(5g - 4)
3g = 5g - 4
3g - 5g = -4
-2g = -4
g = -4/-2 = 4/2
Answer: g = 2
Let's solve your equation step-by-step.
9g=3(−4+5g)
Step 1: Simplify both sides of the equation.
9g=3(−4+5g)
9g=(3)(−4)+(3)(5g)(Distribute)
9g=−12+15g
9g=15g−12
Step 2: Subtract 15g from both sides.
9g−15g=15g−12−15g
−6g=−12
Step 3: Divide both sides by -6.
−6g /-6=-12/-6
g=2
Answer:
g=2
Plz answer this ASAP! What is the x-coordinate of the solution for the system of equations? {y−x=910+2x=−2y Enter your answer in the box.
:) Here is your answer -7
Answer:
the answer is -7
Step-by-step explanation:
thxs person who answered before me :)
Which os larger 5.13 or 5.099? I think it's the 5.099?
5.13 is larger. Because it is closer to a whole number. That’s what I believe it is at least. Forgive me if I am wrong
list the single-digit factors of 924
The prime factorization is ...
... 2²×3×7×11
Single-digit prime factors are ... 2, 3, 7
Single-digit divisors are ... 1, 2, 3, 4, 6, 7
Which of the following must be given to prove that ΔABC is similar to ΔDBA?
a. Segment AD is an altitude of ΔABC.
b. Segment CB is a hypotenuse.
c. Segment CA is shorter than segment BA.
d. Angle C is congruent to itself.
Answer:
The correct answer is option A.
Step-by-step explanation:
For the given triangles to be similar the segment AD must be an altitude of ΔABC.
We can provide a theorem for the same:
If we draw an altitude from the right angle of any right triangle, then the two triangles formed are similar to the original triangle.
Also all the three triangles are similar to each other.
Like here, in the triangle ABC, we draw an altitude from A to the side BC, thus forming 2 triangles; ΔDBA and ΔDAC. These both will be similar to ΔABC.
So, by the theorem it is proven that ΔABC is similar to ΔDBA.
Therefore, option A is correct.
if (2k, k) and (3k, 4k) are two points on the graph of a line and k is not equal to 0, what is the slope of the line?
(2k, k) and (3k, 4k)
Slope = (4k - k )/(3k - 2k)
= 3k / k
= 3
Answer :
3
slope = 3
to calculate the slope (m ) use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2k, k) and (x₂, y₂ ) = (3k, 4k )
m = [tex]\frac{4k-k}{3k-2k}[/tex] = [tex]\frac{3k}{k}[/tex] = 3
WILL GIVE BRAINLIEST The sequence 7 21 63 189......shows the number of jumping jacks justin did each week, starting with the first week of him working out.
A. is the sequence arithmetic or geometric? how do you know?
B. What is the recursive rule for the sequence?
C. what is the iterative (explicit) rule for the sequence.
A
this is a geometric sequence since there exists a common ratio r between the terms
r = [tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = [tex]\frac{189}{63}[/tex] = 3
B
to obtain the next term in the sequence multiply the previous term by 3
[tex]a_{n+1}[/tex] = 3 [tex]a_{n}[/tex] ← recursive rule
C
the n th term of a geometric sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] [tex]r^{n-1}[/tex]
where [tex]a_{1}[/tex] is the first term in the sequence
[tex]a_{n}[/tex] = 7 × [tex]3^{n-1}[/tex] ← explicit rule
Math Write the number 63 in four different ways.
63 = 0.63×10² = 126/2 = 3×21 = √3969 = 77₈
The last is as a base-8 number.
63=60+3=31.5*2=63/100
Suzy puts 2 slices of cheese on each sandwich. she makes 4 cheese sandwich. how many slices of cheese does Suzy use in all
If she puts 2 slices in 4 sandwiches, the answer would be 8.
(4 x 2)= 8.
Hope this helps & good luck. :)
if she has 4 sandwhiches and 2 slices of chesse on each you can multiply
4*2=8