It travels 2404 feet before it is 1,700 feet above ground;
The given question can be represented in the form of equation;
y = tan(45°)x + c;
Since it is launched from ground; c = 0;
thus; y = x is the equation of motion of cannonball;
According to question; y = 1700 feet
x = 1700 feet;
The distance travelled by cannonball will be
√(x² + y² = √(1700² + 1700²) (∵ it is a right angled triangle;
using Pythagoras theorem)
= 2404.16 feet
≅ 2404 feet
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Write the equation of a line that is parallel y = 4x - 7 and goes through the point (4,1).
The equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.
How do we find the equation of a line when two lines are parallel?We can infer that the two lines are parallel because they are distinct and share the same slopes. We can determine whether any two lines are parallel using this characteristic.Then we determine the equation of the line by point-slope form.A point on the line and the slope of the line are required in the point-slope version of the equation of a line. The line's slope is m, and the referred point on the line is (x₁,y₁).Given line: y = 4x - 7
Slope of line m₁ = 4
Two lines are parallel lines when the slopes of the lines are the same.
so, m₁ = m₂
m₂ = 4
Now, the equation of a line with slope 4 and passing through the point (4,1) is:
⇒ y - y₁ = m (x - x₁)
⇒ y - 1 = 4(x - 4)
⇒ y - 1 = 4x -16
⇒ y = 4x - 15
Hence the equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.
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Will give brainlyiest 50 points
Answer:4
Step-by-step explanation:4(5x+6) = 4[tex]x[/tex]5x=20x 4[tex]x[/tex]6=24
Answer:
The answer is 4.
4 * 5x = 20x
4 * 6 = 24
So the result we get is 20x + 24
A school board member surveys parents to learn how they feel about the new school boundaries. What are a random sample and a non-random sample for this situation?
A random sample and a non-random sample for this situation are given below:
Mrs.Donovan could have taken opinions from the first 50 parents to answer.Mr.Giles could have taken 10 Parents from each grade in the school and used that as his example.What is a Random Sample?This refers to the statistical population where there is an equal chance of being selected by members of a population.
Hence, we can see that a random sample and a non-random sample for this situation are given above and this shows that each of them have equal chances of being selected (random sampling)
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the 2nd and 5th terms of a gp are 1/18 and 4/243 respectively. Find
Answer:
Step-by-step explanation:
The third term of the geometric progression will be 1 / 27 with common ratio 2 / 3.
We are given that:
2nd term of geometric progression = 1 / 18
5th term = 4 / 243
Now, we can also write it as:
2nd term = a r ( where r is the common ratio and a is the initial term.)
a r = 1 / 18
5th term = a r⁴
a r⁴ = 4 / 243
Now divide 5th term by 2nd term, we get that:
a r⁴ / a r = ( 4 / 243 ) / ( 1 / 18 )
r³ = 72 / 243
r³ = 8 / 27
r = ∛ (8 / 27)
r = 2 / 3
3rd term = a r²
a r² = a r × r
= 1 / 18 × 2 / 3
3rd term = 1 / 27
Therefore, the third term of the geometric progression will be 1 / 27 with common ratio 2 / 3.
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Your question was incomplete. Please refer the content below:
The 2nd and 5th term of a GP are 1/18 and 4/243 respectively find the 3rd term
Find the volume of a sphere with a diameter of 6 centimeters.gi
12 cubic centimeters
288 cubic centimeters
97 cubic centimeters
O 367 cubic centimeters
Answer:V≈113.1
Step-by-step explanation:
d Diameter 6
V=4
3πr3
d=2r
Solving forV
V=1
6πd3=1
6·π·63≈113.09734
Draw a rotation of segment CD 189 degrees around point D.
Rotation of a point through 189° about the origin When a point C(h, k) is rotated through 180° in either an anticlockwise or clockwise direction about the origin O, it takes the new position D(-h, -k).
The rotation formula will give us the precise location of a point after a finite degree of rotation. The rotation formula is determined by the type of rotation applied to the point in relation to the origin. A geometric two-dimensional shape can undergo four major types of transformation.
The rotation formula describes how a point rotates with respect to the origin. The rotation formula is used to determine the position of a point after it has been rotated. A rotation is a circular motion around a specific axis or point of rotation. In general, rotation can be done in two ways: clockwise and anti-clockwise or counter-clockwise.
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If DF=9c -39 then x = and DF =
Answer: x=16
DF=105
Step-by-step explanation:
DF=DE+EF
9x-39=47+3x+10
9x-39=57+3x
9x=96+3x
6x=96
x=16
DF=9x-39
DF=9(16)-39
DF=144-39
DF=105
If you use a graph and a table to solve an equation that shows two expressions equal to one another, how can you use algebra to check your answer?
Answer:If you use a graph and a table to solve an equation that shows two expressions equal to one another, how can you use algebra to check your answer? Choose the correct answer below. A. Rewrite the equation as two new equations, with the expression on each side of the original equation set equal to the answer you are checking, which is an estimate. Check to see if solving each of the new equations gives values of x that are close to each other. If they are too far from each other, you may need to reexamine the table and graph. B. Input the answer into each expression and simplify. Check to see if the result gives exactly the same number on each side. If the numbers are not exactly equal, you may need to reexamine the table and graph. C. Input the answer into each expression and simplify. Check to see if the result, which is an estimate, gives numbers on each side which are close to each other. If they are too far from each other, you may need to reexamine the table and graph. D. Rewrite the equation as two new equations, with the expression on each side of the original equation set equal to the answer you are checking. Check to see if solving each of the new equations gives exactly the same values of x . If they are not equal, you may need to reexamine the table and graph.
Step-by-step explanation:
which number is irrational an integer and a real number?
A.0
B. there is no such number
C.-4/2
D. 4
Answer:
B
Step-by-step explanation:
None of the provided options are irrational. Irrational numbers are those which cannot be expressed as the ratio of two integers. In other words, if represented in decimal form, they would continue indefinitely after the decimal point, such as the value of π. This also means, by definition, they cannot be both irrational and an integer.
They are all real numbers as they can represent a distance along a line (they could all be plotted on a number line or graph, for instance).
Only 0 and 4 out of the provided options are integers (whole numbers). As mentioned above, all integers are rational by definition.
find the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet
The dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet are 4 feet and 3 feet.
How to calculate the value?From the information, we are given that the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet.
It should be noted that the number will be:
= 4 × 3 = 12 ft²
It should be noted that 4² + 3² = 25 and the square root will give 5 which is also the diagonal.
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I hate my school for giving me all of this in one day <3
Answer:
A.
Step-by-step explanation:
[tex]0.75 > 7/12(0.58)[/tex]
Answer:
A
Step-by-step explanation:
0.58= 7/12 so 0.75 is more then -.8 so that is true.
benjamein writes an expression for the sum of 1 cubed, 2cubed and 3 cubed. what is the value of the expression
The expression for the sum of 1 cubed, 2cubed and 3 cubed is 1² + 2³ + 3³ and the value is 36.
How to compute the value?It should be noted that the information is to find the expression for the sum of 1 cubed, 2cubed and 3 cubed.
This will be:
= 1³ + 2³ + 3³
= 1 + 8 + 27
= 36
Therefore, the correct answer is 36.
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T(x,y,z)=x^2yz^3 với M(1,1,1)
Answer:
A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)
B=(-4x3y2z)( x2y3)3xy
Step-by-step explanation:
ok :)
In AOPQ, PQ = 19, QO = 11, and OP = 20. Which statement about the angles of AOPQ
must be true?
The true statement about the angles of the triangle OPQ is the third statement that is m∠P < m∠O < m∠Q.
It is given that:-
In triangle OPQ,
PQ = 19
QO = 11
OP = 20
We have to find which one of the six statements given in the question is correct.
We know that, in a triangle, if one side of the triangle is longer than the other side, then the angle opposite to the longer side will be larger than the angle opposite the shorter side.
Hence,
In triangle OPQ,
Angle opposite to side OP = ∠Q
Angle opposite to side PQ = ∠O
Angle opposite to side QO = ∠P
As,
QO < PQ < OP , Hence,
m∠P < m∠ O < m∠Q
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The sum of three consecutive even integers is 312. Find the integers.
OA. 103, 104, 105
OB. 100, 102, 104
OC. 104, 106, 108
D. 102, 104, 106
The total of three consecutive even numbers is 312.
The correct option is A.
Briefing:Three numbers totaling 312 are consecutive, one of which being 104. Take one of the other numbers from 104=103 and add one to 104=105 for the third.
103 + 104 + 105 = 312.
What are consecutive even integers?Consecutive even numbers are consecutive even integers that differ by 2. If x is an even number, then x + 2, x + 4, and x + 6 are also even numbers. The difference between consecutive even numbers is two.
How do you find a series of consecutive integers?The formula for successive integers is quite simple. If x is the first consecutive integer, x+1 is the next, x+2 is the third, x+3 is the fourth, and so on. Consider the following example. 45 is 'x if it is the first consecutive integer in either a series of numbers.
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Find the points on the curve y = 2x3 + 3x2 − 12x + 3 where the tangent line is horizontal.
the tangent is only horizontal at the critical points of the equation, so
[tex]y=2x^3+3x^2-12x+3\implies \cfrac{dy}{dx}=6x^2+6x-12\implies \cfrac{dy}{dx}=6(x^2+x-2) \\\\\\ \stackrel{\textit{setting the derivative to 0}}{0=6(x^2+x-2)}\implies 0=x^2+x-2 \\\\\\ 0=(x+2)(x-1)\implies \boxed{x= \begin{cases} -2\\ 1 \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ y=2(-2)^3+3(-2)^2-12(-2)+3\implies y=-16+12+24+3\implies \boxed{y=23} \\\\\\ y=2(1)^3+3(1)^2-12(1)+3\implies y=2+3-12+3\implies \boxed{y=-4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \text{\LARGE (-2~~,~~23)\qquad (1~~,~~-4)}~\hfill[/tex]
9
)
14+(−9)+(−9)14, plus, left parenthesis, minus, 9, right parenthesis, plus, left parenthesis, minus, 9, right parenthesis.
The value of (9)14+(−9)+(−9)14 is -9
The concept is used to Solve is BODMAS
(9)14+(−9)+(−9)14
126-9-126=-9
BODMAS, also known as the order of operations, is a series of operations in an arithmetic statement. Math is all about logic and certain common principles that help us with our calculations. So BODMAS is one of the basic principles for simplifying multi-operator formulations.
An expression or equation in arithmetic has two components:
Numbers \Operators
A character that combines two integers to form an expression or equation is known as an operator. The most popular operators in mathematics are Addition (+), Subtraction (-), Multiplication (), and Division (). Finding the solution to mathematical statements or equations with only one operator is rather straightforward.
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The length of a rectangle parking area is three times the width.The perimeter is 280 yd.Find the length and width of the parking are.
Answer:
length = 105 yd
width = 35 yd
Step-by-step explanation:
Let L = length and W = width.
L = 3W
perimeter = 2(L + W)
280 =2(L + W)
L = 3W
We have a system of 2 equations. Let's use the substitution method to solve it. Substitute 3W for L in the first equation.
280 = 2(3W + W)
140 = 4W
W = 35
L = 3W = 3(35) = 105
length = 105 yd
width = 35 yd
Write an equation of a parabola in vertex form. Vertex (0,-3) and passes through (-8,5)
The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3.
The vertex form of the equation of a parabola is:
y = a(x-h)² + k
where the vertex = (h, k)
The given vertex, (h, k) = (0, -3)
The line passes through the (-8, 5)
x = -8, y = 5
Substitute x = -8, y = 5, h = 0, y = -3 into the equation to solve for a
y = a(x - h)² + k
5 = a(-8-0)² + (-3)
5 = a(-8)² - 3
-8a = 5+3
-8a = 8
a = 8/-8
a = -1
Substitute a = -1, h = 0, k = -3 into y = a(x - h)² + k
y = -1(x - 0)² - 3
The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3
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Cassie and Amy are playing a card flash game. Cassie has a card with the fraction - 2/7 and Amy has a card with the fraction - 3/4. Write an equation to represent the product of theirs fractions then solve that equation.
( The minus is not plain -3 or -2 it’s the whole fraction)
The equation representing the product of theirs fractions is -
(- 2/7) x (- 3/4) and on solving this expression, we get 3/14.
What is a Fraction?In mathematics, fractions are represented as a numerical value, which defines a part of a whole.
Given that Cassie and Amy are playing a card flash game such that Cassie has a card with the fraction - 2/7 and Amy has a card with fraction - 3/7.
The equation that represent the product of their fractions is -
(- 2/7) x (- 3/4)
Now, solving the above expression, we get -
(- 2/7) x (- 3/4)
(1/7) x (3/2)
3/14
Therefore, the equation representing the product of theirs fractions is -
(- 2/7) x (- 3/4) and on solving this expression, we get 3/14.
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Find a counterexample to show that the following statement is false.
The sum of three multiples of 5 will always end in a 5.
Answer:
5 + 10 + 15 = 30
Step-by-step explanation:
You want a sum of three multiples of 5 that does not end in 5.
Multiples of 5Any odd multiple of 5 will end in 5. An even multiple will not.
In order for the sum to not end in 5, the total of the multipliers must be even:
1×5 +2×5 +3×5 = 6×5 = 30
5 +10 +15 = 30 . . . . . . three multiples of 5 whose sum does not end in 5
Greatest Common Factor and Least Common Multiple
Juan and Joe start walking around a track at the
same time and at the same place. It takes Joe 8
minutes to walk around the track, and it takes Juan
10 minutes. After how many minutes will they reach
the starting point at the same time?
In linear equation , 40 is the number of minutes until they meet again at the starting line.
What is linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Juan walks 1/8 of a lap in one minute
joe walks 1/10 of a lap in one minute
The LCM of 8 and 10 = 40 = the number of minutes until they meet again at the starting line
In that time Juan walks (1/8) * 40 = 5 laps
And Juan walks (1/10)*40 = 4 laps
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Express the solution graphically 2/3(x-9)>-8
The solution of the inequality given as 2/3(x - 9) > 8 is x > 21
How to express the solution graphically?The inequality is given as
2/3(x - 9) > 8
Multiply both sides by 3/2
So, we have
x - 9 > 12
Add 9 to both sides of the inequality
So, we have
x > 21
Hence, the solution of the inequality given as 2/3(x - 9) > 8 is x > 21
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Which of the following polynomials have a GCF of 2x. (SELECT ALL THAT APPLY)
3x² - 6x
02x³+4x²
2x² - 4x
6x² + 2x
If the measure of angle is 3pi/4 , which statements are true?
If the measure about an angle is 3pi/4, the sentences are:
sinθ = sin135 = √2/2cosθ = cos135 = √2/2The correct option are A , D.
What is a trigonometric function?a function of an arc or angle represented most simply in terms of the ratios of pairs of sides of a right-angled triangle (such as the sine, cosine, tangent, cotangent, secant, or cosecant). also known as a circular function.
Why do we utilize trigonometric functions?Trigonometry is used to set directions such as north, south, east, and west; it tells you which direction to go using the compass to get on a straight path. It is used in trace to locate a location. It is also used to determine the distance between the shore and a point in the water.
According to the given data:Investigation trigonometric function:
θ = 3π/4
= 3/4 * 180
= 135
tanθ = sin135/cos135
= -1
sinθ = sin135 = √2/2
cosθ = cos135 = √2/2
The reference angle for stuff in Q2 is 180 - theta = 180 - 135 = 45 degrees.
If the measure about an angle is 3pi/4, the sentences are:
sinθ = sin135 = √2/2
cosθ = cos135 = √2/2
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I understand that the question you are looking for is:
If the measure of angle 0 is 3pi/4 which statements are true (multiple choice)
A. sin(0)=sqrt2/2
B. The measure of the reference angle is 45
C. The measure of the reference angle is 30
D. The measure of the reference angle is 60
E. cos(0)=sqrt2/2
F. tan(0)=1
100 points hellpppp look at the image below
The values of JL, EF and KM are -19units, 29 units and 22 units respectively.
How to determine the values13. From the diagram shown, we have;
JL = JK + KL
where;
JK = x + 2
KL = 4x - 16
JL = 6x - 13
Substitute the expressions
6x - 13 = x + 2 + 4x - 16
collect like terms
x = -1
JL = 6x - 13 = 6(-1) - 13 = -6 -13 = -19 units
14. EG = 2x + 13
EF = x + 14
FG = 14
2x + 13 = x + 14 + 14
collect like terms
x = 15
EF = 15 + 14 = 29 units
15. KL = 6
LM = 2x
KM = 3x - 2
3x - 2 = 6 + 2x
collect like terms
x = 8
KM = 3x - 2 = 22 units
Thus, the values of JL, EF and KM are -19units, 29 units and 22 units respectively.
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in the diagram, CD || EF, G, -70° and HI - HG. Calculate the values of x, y and z
The measures of the angles are x = 40, x = 110 and y = 70
What are angles?Angles are formed when two or more lines intersect
How to calculate the values of x, y and z?The figure represents the given parameters
On the figure, we have the following highlights
Angle 3 and angle y are corresponding angles.
Corresponding angles are congruent
So, we have
y = Angle 3
From the figure
Angle 3 = 70
So, we have
y = 70
The angle on a straight line is 180 degrees
So, we have
x + y = 180
This gives
x + 70 = 180
Evaluate the like terms
x = 110
The triangle is an isosceles triangle.
So, we have
y = Angle 2
This means that
Angle 2 = 70
The sum of angles in a triangle is 180
So, we have
z + y + Angle 2 = 180
This gives
z + 70 + 70 = 180
Evaluate
z = 40
Hence, the measures of the angles are x = 40, x = 110 and y = 70
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In a large population, 53 % of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
The probability the at least of the people selected from 5 is vaccinated is 0.997.
What is meant by the binomial distribution?The binomial distribution is a statistical probability distribution that summarizes the likelihood of a value taking one of two independent values under the specific set of assumptions or assumptions.
The likelihood that at least one person has been vaccinated = 1 - the likelihood that nobody has been vaccinated. In a large population, the probability of a randomly selected person NOT being vaccinated is 1 - 0.53 = 0.47.Because the five randomly chosen people are independent, the probability that they're all unvaccinated is (0.47)⁵,
The probability that at least one among them 5 has been vaccinated is;
= 1 - (0.47)⁵
= 0.997
Therefore, the probability that at least one of the five people chosen is vaccinated is 0.997.
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twenty professiional athlets were asked what age did you graduate from college the responses are displayed in the histogram below
According to the given graph:
Age at graduation (in years) between 45 to 50 years.Age at graduation (in years) between 20 to 25 years.What is histogram?A histogram is a data representation that looks like a bar graph that bins a variety of classifications into columns and along the horizontal x-axis. The number count or percentage of occurrences inside this data for each column is represented by the vertical y-axis. Columns can be utilized to display data distribution patterns.
When should a histogram be used?When you're taking continuous measurements and you want to understand the distribution of results and look for outliers, use histograms. These graphs divide your continuous measurements into value ranges known as bins.
According to the given data:Based on these data, the numbers below appear to represent the smallest.:
= Age at graduation (in years) between 45 to 50 years.
Based on these data, the numbers below appear to represent the largest.
= Age at graduation (in years) between 20 to 25 years.
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I understand that the question you are looking for is:
Twenty professional athletes were asked, “What age did you graduate from college?” The responses are displayed in the histogram below.
Frequency 20 30 Age at graduation (in years) 40 50
(a) Which of the statistics below appear to be the smallest based on these data?
(b) Which of the statistics below appear to be the largest based on these data?
7x-2y-10x+5+8y simplified please show steps
Answer:-3x-10y+5
Step-by-step explanation:
7x-2y-10x+5+8y
-3x-2y+5-8y
-3x-10y+5