A cannonball is fired in the air at an angle of 45∘. How far does it travel before it is
1,700 feet above ground? (Assume the cannonball travels in a straight line. Ignore the force of gravity and wind resistance. Give your answer to the nearest foot.)

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.

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:

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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The probability the at least of the people selected from 5 is vaccinated is 0.997.

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.

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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The dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet are 4 feet and 3 feet.

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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The total of three consecutive even numbers is 312.

The correct option is A.

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.

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.

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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Answer:-3x-10y+5

Step-by-step explanation:

7x-2y-10x+5+8y

-3x-2y+5-8y

-3x-10y+5

The values of JL, EF and KM are -19units, 29 units and 22 units respectively.

13. 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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The expression for the sum of 1 cubed, 2cubed and 3 cubed is 1² + 2³ + 3³ and the value is 36.

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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The equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

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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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.

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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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

The measures of the angles are x = 40, x = 110 and y = 70

Angles are formed when two or more lines intersect

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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A random sample and a non-random sample for this situation are given below:

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 equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.

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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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

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

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

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 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]

The solution of the inequality given as 2/3(x - 9) > 8 is x > 21

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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If the measure about an angle is 3pi/4, the sentences are:

The correct option are A , D.

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.

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.

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

According to the given graph:

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 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.

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?

In linear equation , 40   is the number of  minutes until they meet again at the  starting line.

What is  linear equation?

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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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

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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Answer:

  5 + 10 + 15 = 30

Step-by-step explanation:

You want a sum of three multiples of 5 that does not end in 5.

Any 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

Answer:

A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)

B=(-4x3y2z)(  x2y3)3xy

Step-by-step explanation:

ok :)