The rocket hit the ground is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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A kangaroo hopped directly toward a lake at a constant velocity for 30seconds. In one-third of that time, the kangaroo hopped 60meters. What was the kangaroo's velocity?
Answer: The animal hopped 60 meters in 10 seconds
6 m/s (lol)
Step-by-step explanation:
First off ok and second off bye <3
if traingle PAG is comgruent to riangle DEN, use words numbers and or symbols to state two conclsuions that can be made based upon cpctc
s: One skis fast.
Express the statement One does not ski fast symbolically.
The given statement can be expressed as ~S.
What is a negation of a statement?
A negation of a statement is a statement that is the opposite of the original statement. In other words, a negation of a statement is a statement that is true if and only if the original statement is false, and vice versa.
To express the statement "One does not ski fast" symbolically, we can use the negation symbol
Using the symbol "S to represent the statement "One skis fast", we can express the statement "One does not ski fast" symbolically as:
~S
This can be read as "Not S" or "It is not the case that S."
Hence, the given statement can be expressed as ~S.
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What is the m∠ c? Enter your answer as a number.
The measure of angle c is m ∠c = 103°.
What is triangle?
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle with the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane.
180 degrees is the sum of the triangle's three angles.
Let Δabc is given with m ∠a = 30° and m ∠b = 37°
We have to find the measure of angle c.
Since the sum of three angles of triangle is 180 degree.
⇒ m ∠a + m b + m ∠c = 180°
30° + 37° + m ∠c = 180°
77° + m ∠c = 180°
m ∠c = 180°- 77°
m ∠c = 103°
Hence, the measure of angle c is m ∠c = 103°.
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Find the volume of a cube if one face of which has an area of 64 sq.metre
The volume of a cube is 512 m3.
Given,
The one-face area is nothing but the area of a square since it is a cube.
So, (a2) = 64 m2.
Then, a = 8m
Hence, the side of the cube is 8 m.
Formula to calculate the volume of the cube :
The volume of the cube = a3
Volume = (8)3
Volume = 512m3
Therefore, the volume of the cube is 512m3.
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the confidence interval approach is the correct method by which to determine sample size. true false
The confidence interval approach is the correct method by which to determine sample size. True
Confidence Interval:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.
In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
Your desired confidence level is usually one minus the alpha (α) value you used in your statistical test:
Confidence level = 1 − α
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what is the slope if the line that passes through the points (10,8) and (7,14)? write your answer in simplest form
Answer:
-2
Step-by-step explanation:
we use the y2-y1/x2-x1 fomrula to find slope
14-8/7-10
6/-3
-2 is the slope
hopes this helps
Problem 5 Claire is planning to buy a phone plan for two cell phones that costs $350 for the phones themselves and $65 per month for service. Claire's daughter offers to chip in $125 for her phone and $12 per month for her phone. Write as many expressions as you can to represent the cost to Claire of the two phones and their service for m months.
The cost to Claire for the phones and their service for m months is $350 + $65*m.
The cost to Claire for the two phones is $350, and the cost for the service for m months is $65m, for a total cost of $350 + $65m.
What are expressions to represent the cost to Claire?Generally, Claire will pay a total of $350 + $65*m for the two phones and their service for m months.
The total cost for Claire for the two phones and their service for m months is $350 + $65*m.
The cost of the phones and service for m months to Claire is $350 + $65*m.
Claire will pay $350 for the phones and $65m for the service for a total of $350 + $65m for m months.
The cost to Claire for the two phones and their service for m months is $350 + m*$65.
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We need help please.
Answer:
The slope is 3 or 3/1.
Step-by-step explanation:
I figure this out by finding out the two beginning points with this: (x1, y1) , (x2, y2). The two beginning points (-3, -5) , ( -2,-2). Then from there you are counting by 3 to get to the next point. I hope this helps.
x − 3y = −12 2x − y = 1 (1 point) a line includes points 0 comma 1 and negative 3 comma negative 4. A line includes points 0 comma negative 4 and negative 6 comma negative 2 a line includes points 0 comma 4 and 1 comma 3. A line includes points negative 2 comma 2 and negative 4 comma 0 a line includes points 0 comma negative 1 and 1 comma negative 3. A line includes points 6 comma negative 10 and 3 comma negative 11 a line includes points 0 comma 4 and 3 comma 5. A line includes points 1 comma 1 and 2 comma 3
By graphing the system of equations, we can see that the solution is (3, 5).
How to solve the system of equations?
I assume we want to solve the following system of equations graphically:
x - 3y = -12
2x - y = 1
To do so we only need to graph both the lines on the same coordinate axis and find the point where the lines do intersect. The graph can be seen below.
There we can see that the intersection is at (3, 5), so that is the solution of the system of equations.
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Number 49. Please help Graphing inequalities? Why is the answer A? Please do a step by step explanation for each answer choice.
I don't see the picture. Can you send it in the message.
Go step by step to reduce the radical
Answer:
[tex]3 \sqrt{8} [/tex]
Step-by-step explanation:
1. we are find which factors which when multiplied will give us 192
2. so i took 3 and 64
3. now square root both factors
like this
[tex] \sqrt{3} \times \sqrt{64} [/tex]
4. then you will be left with 3 and a 8
so then we will write that as the answer given above
What is the area of triangle lmn? round to the nearest square meter. 3 square meters 9 square meters 28 square meters 34 square meters
9 square meters is the area of triangle LMN. Using the concept of Heron's formula.
What is Heron's formula?Heron of Alexandria is credited with creating Heron's formula, which determines a triangle's area by dividing the lengths of its sides. if the side lengths are represented in symbols by a, b, and c.
According to Heron's formula the area = √s (s - a)(s - b)(s - c)
A triangle's semi-perimeter, whose area has to be calculated, is represented by the letter s in Heron's formula. s = (a+b+c)/2 is the formula for the triangle's semi-perimeter, which is the sum of its three sides.
a triangle with three sides, a, b, and c.
given data was LM = 7,MN = 6 and perimeter was given by 16m
As we know perimeter is the sum of all the sides
so, Perimeter=LM + MN + NL
NL=Perimeter-(LM+MN)
NL=16 - 7 - 6
NL= 3
By Heron's formula,
Area = √[(s(s-a)(s-b)(s-c)].
where s = perimeter/2
so, s = 16/2 = 8
area = √[(8(8-7)(8-6)(8-3)]
area = 8.94427191 ≈ 9 square meters.
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Answer: 9m
Step-by-step explanation:
write 987.6 in scientific notation
987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]
What is scientific notation?
Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.
When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].
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which statement must be true?
Answer:
DF=FE
Step-by-step explanation:
first to make it easier we can find the angles to each side
the sum of all angles of a triangle equal 180 degrees so to find x we set all the angles equal to 180
(3x+5)+(4x-15)+(2x+10)=180
9x+0=180
/9. /9
x=20
now we can find each angle
3(20)+5
60+5
D=65 degrees
4(20)-15
80-15
E= 65 degrees
2(20)+10
40+10
F=50 degrees
Angle D and E are the only angles equal to each other so answer C and d ARE INCORRECT
Since there are 2 of the same angles this is an isosceles triangle
the 2 of the same angles are the base so the side going up are connecting to the top angle F so the sides will be DF and FE and these are equal
hopes this helps
5. Which of the following is an arithmetic
sequence?
A
B
C
D
-2, -5, -8, -11, -14, -17, ...
0,5, 0, 10, 0, 15, ...
2, 4, 8, 16, 32, ...
5, 11, 17, 23, 29, 36, ...
Answer:
A. -2, -5, -8, -11, -14, -17, ...
Step-by-step explanation:
The difference between consecutive terms is constant.
What is 213 divided? Also how do you break 23 into tens and ones?
Answer:
What is 213 divided? 2 I think
Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones
I have this question can anyone solve
The double bar graph collected from the survey is given by the image presented at the end of the answer.
How to build the double bar graph?A bar graph shows the number of times that each observation appears in the data-set.
The double bar graph means that for each input on the bar graph, there are going to be two bars.
The meaning of each bar is given as follows:
Number of people who like watching the sport.Number of people who like participating in the sport.The colors for each bar are given as follows:
blue bar: people who like watching the sport.red bar: people who like participating in the sport.Then the data of the table is used to give the height of each bin in the double bar graph.
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what is infinity times infinity (it was a bonus question)
Answer: infinity
Step-by-step explanation:
Just answer it, dont have to show work
The equations that are false for all real numbers of x are given as follows:
x² + 4 = 0.square root of x - 1 = -2.2(x - 4) = 2x - 4.How to obtain the equations which are false?To obtain the equations which are false, we have to consider the domain and the range of the functions in this problem.
We start at the first equation, given as follows:
x² + 4 = 0.
Isolating x², we have that:
x² = -4.
However, the range of the function y = x² is composed only by non-negative numbers, meaning that y = x² will never assume a value of -4, meaning that this statement is false for all real numbers.
The same holds true for the third item, which is the square root of x - 1 = -2. The range of the square root function is also composed by non-negative numbers, thus the statement is also false for all real numbers.
The final statement that is false is given as follows:
2(x - 4) = 2x - 4.
Applying the distributive property, we have that:
2x - 8 = 2x - 4
0x = 4
x = 4/0 (division by zero does not exist on the real set).
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What values of b and c make AGHI AZYX?
G
b
||
CE
48
I
b
H
X
17
Y
8c
Z
The value of b = 17 and c = 6 makes ΔGHI ≅ ΔZYX.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
If and only if two angles have equal measurements, they are said to be congruent. If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
Here, we have
Given the sides of both the triangle and
we have to find the value of b and c that makes ΔGHI ≅ ΔZYX
b = 17 and,
48 = 8c
c = 6
Hence, the value of b = 17 and c = 6 that makes ΔGHI ≅ ΔZYX.
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Solve for j
1 - j/4 = 3
Answer:
j = - 8
Step-by-step explanation:
1 - j/4 - 3
1 is also 4/4
so
4/4 - j/4 = 3
4 - j/ 4= 3
multiply by 4 on both sides
which gets you
-j + 4 = 12
minus 4 from both sides
-j = 8
j = -8
Answer:j=-8 I hope this helps
Step-by-step explanation:
1-j/4=3
Multiply both sides of the equation by 4
which gives you
4-j=12
Move the constant to the right-hand side and change its sign
-j=12-4
Subtract the numbers
-j=8
Change the signs on both sides of the equation
j=-8 - This is your answer
Which is the equation for a line that passes through
the points (-6, -13) and (-12, 5)?
Answer:
y = -3x - 31
Step-by-step explanation:
y = mx + b
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex] m=\frac{5-(-13)}{-12-(-6)} [/tex]
[tex] m=\frac{18}{-6} [/tex]
m = -3
y = -3x + b
-13 = -3(-6) + b
-13 = 18 + b
b = -13 - 18
b = -31
Alonso went to the market with \$55$55dollar sign, 55 to buy eggs and sugar. He knows he needs a package of 121212 eggs that costs \$2.75$2.75dollar sign, 2, point, 75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money. The sugar he likes comes in boxes that each cost \$11.50$11.50dollar sign, 11, point, 50
The number of boxes of sugar that Alonso can buy are 4.5 boxes.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.
The money remaining after buying 12 eggs : {r} = $(55 -2.75).
Cost of one box of sugar = $11.5
The number of boxes that he can buy are -
n = (55 - 2.75)/11.5
n = 4.5 boxes {approx.}
Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.
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If a fair die is rolled 4 times, what is the probability, rounded to the nearest thousandth, of getting at least 3 twos?
7.08 is the probability, rounded to the nearest thousandth.
What does the math term "probability" mean?
The simple definition of probability is the likelihood that something will occur.
We can discuss the probabilities of various outcomes to determine how likely they are whenever we are uncertain about the result of an event. Statistics describes the examination of events subject to probability.
Probability of getting a six on rolling a dice = 1/3
Here ,
n = 4 , p = 1/3
So, For P(X <= 1) = P(X = 0) + P(x = 1)
4C0 * (1/6)^0 * (1 - 1/3)^(4-0) + 4C1 * (1/3)^1 * (1-1/3)^(4-1)
= 1 * 1 * (5/3)^4 + 4 * (1/3) *
= 5.75 + 1.33
= 7.08
= 7.08 (nearest thousandth)
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A beetle is moving along a straight line at a constant rate. It moves 23 of a foot in 15 of a minute.
What is the average speed of the beetle?
The average speed of the beetle is 1.53 feet per minute.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, it moves 23 of a foot in 15 of a minute.
Here, the average speed
= 23/15
= 1.53 feet per minute
Therefore, the average speed of the beetle is 1.53 feet per minute.
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12. A typical large recycling tote can hold 10 kilograms of plastic yogurt containers. What volume is
needed to hold this amount of plastic?
A typical large recycling tote can hold 10 kilograms of plastic yogurt containers. the volume is 0.01 m^3
What volume is needed to hold this amount of plastic?Generally, To determine the volume needed to hold 10 kilograms of plastic yogurt containers, you would need to know the density of the plastic and the size and shape of the containers.
The density of a material is a measure of its mass per unit volume. It is usually expressed in kilograms per cubic meter (kg/m^3). The density of plastic can vary depending on the specific type of plastic and any additives that are present.
Once you know the density of the plastic, you can use the following formula to calculate the volume needed to hold a certain mass of the material:
Volume = Mass / Density
For example, if the density of the plastic is 1000 kg/m^3 and you want to hold 10 kilograms of it, the volume needed would be:
Volume = 10 kg / 1000 kg/m^3
Volume = 0.01 m^3
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THE COMPLETE QUESTION WAS NOT FOUND
True or false. When y is positive, the value of y^2 is always greater than the value of y. Why?
however if you have 0.5^2 which is 0.25 is that not smaller than 0.5
Answer: False
Step-by-step explanation:
If [tex]y=0.5[/tex], then [tex]y^2=0.25[/tex], whereas [tex]y=0.5[/tex].
Therefore, this is a counterexample. Hence, the statement is false.
5/7 of.... is 1/7. What is the missing number?
The missing number is [tex]\frac{1}{5}[/tex]
Let the missing number be x.
now, [tex]\frac{5x}{7}[/tex] = [tex]\frac{1}{7}[/tex]
on cross multiplying we get,
x= [tex]\frac{7}{35}[/tex]
on simplifying,
x= [tex]\frac{1}{5}[/tex]
Hence, the missing number is [tex]\frac{1}{5}[/tex]
What is cross multiplying?
An equation involving a variable as a component of two fractions set equal to one another can be solved by cross multiplying. Cross-multiplying lowers the proportion to one straightforward equation, enabling you to solve for the variable in issue. The variable serves as a placeholder for an unknowable number or quantity.
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A circle has a diameter of 14 inches. A central angle of 85° intercepts an arc of the circle.
What is the intercepted arc length to the nearest tenth of an inch?
The intercepted arc measures 11.78 to the closest tenth of an inch.
What is intercepted arc?Remember that an arc is a portion of a circle's circumference.
Therefore, an intercepted arc is an arc that is created when one or more chords or line segments intersect a circle and come together at a vertex.
It's vital to keep in mind that the lines or chords can come together inside, outside, or in the center of a circle.
An interrupted arc and the inscribed and central angles of a circle have some intriguing correlations.
An inscribed angle is created in geometry between chords or lines that cut through a circle.
The center angle is a joint created by the intersection of two radii.
According to our question-
angel/360=arc/circumference
85/360=
d= 14 inches
Hence, The intercepted arc measures 11.78 to the closest tenth of an inch.
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