Find the missing variables in the triangle below. Leave your answer in simplest radical form.

The range is 5 feet

The path of the rocket can be modeled by the equation

h(t) = -16t² + 80t

We know that the range of a projectile is nothing but the horizontal distance the projectile travels from the time it is launched to the time it comes back down to the same height at which it is launched.

To find the horizontal distance we find the distance between the points on the horizontal axis.

i.e., to find the value of t for which h(t) = 0

Let us assume that the value of equation h(t) = 0

h(t) = 0

-16t² + 80t = 0

t(-16t + 80) = 0

t = 0   OR   -16t + 80 = 0

t = 0   OR  -16t = -80

t = 0   OR  t = 5

So, the range would be,

R = 5 - 0

R = 5 feet

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So, Amy used 30 stamps of 41-cent stamps and 17 stamps of 7-cent stamps.

This is a system of equations problem. We can call the number of 41-cent stamps x and the number of 7-cent stamps y.

The two equations are:

x + y = total number of stamps used

0.41x + 0.07y = 1.79 (the total cost of the postage in dollars)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = total number of stamps used - x

Then we can substitute this into the second equation:

0.41x + 0.07(total number of stamps used - x) = 1.79

Solving for x,

x = (1.79 - 0.07*total number of stamps used) / 0.41

We can substitute this into the first equation to solve for total number of stamps used.

x + y = total number of stamps used

x + (total number of stamps used - x) = total number of stamps used

2x = 1.79/0.41 + 0.07/0.41

x = (1.79/0.41 + 0.07/0.41)/2

x = (1.79 + 0.07)/(0.41*2)

So, x = 30 stamps of 41-cent stamps

and y = (total number of stamps used - x) = (total number of stamps used - 30) = (1.79/0.48 - 30) = 17 stamps of 7-cent stamps

So, Amy used 30 stamps of 41-cent stamps and 17 stamps of 7-cent stamps.

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The simplified form of the expression is option C. (3)^5/12 * (4)^2/3.

An exponential expression is one which has the value of the power of one of its terms to be greater than 1 or in a fraction form. Thus some laws are required to simplify a given exponential expression. These laws are sometimes referred to as the law of indices.

Considering the given question;

(3^2/3 * 3^3/2)^5/12  x (4^2/3)

Simplifying this expression requires applying required laws, so that;

(3^2/3 * 3^3/2)^5/12 = (3^6/6)^5/12

                                 = (3^1)^5/12

                                 = 3^5/12

(3^2/3 * 3^3/2)^5/12 = 3^5/12

Therefore, we have;

(3^2/3 * 3^3/2)^5/12  x (4^2/3) = (3)^5/12 x (4)^2/3

Thus the simplified form is option C.

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1001 ways are there to distribute the money of Uncle Henry to his nieces and nephews.

He may donate the entire sum to one child (five ways).

He could give each youngster two bucks (one way).

He may offer $0.00, $1.00, $2.00, $3.00, and $4.00 in five different ways.

Henry will put the dividers on the left and the banknotes on the right. Money to the left of the first divider goes to the youngest kid, money between the first and second dividers goes to the child after that, and so on.

For example, the first kid receives $1, the second receives $2, the third receives $1, the fourth receive nothing, and the fifth receives $6.

It is merely a matter of selecting the number of arrangements of 10 bills and four dividers using this model:

[tex]\frac{14 !}{(10 !)(4 !)}=1,001, \text { or: } 14 C 4=1,001[/tex]

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There are 1001 ways to distribute Uncle Henry's money to his nieces and nephews.

He might give one youngster the full amount (five ways).

He could give each child two dollars (one way).

He can make five separate offers of $0.00, $1.00, $2.00, $3.00, and $4.00.

Henry will arrange the banknotes on the right and the dividers on the left. The youngest child receives the money to the left of the first divider, the following child receives the money between the first and second dividers, and so forth.

The first child gets $1, the second gets $2, the third gets $1, the fourth gets nothing, and the fifth gets $6, for instance. Using this model, it is only a matter of choosing the quantity of arrangements of 10 bills and 4 dividers.

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It is possible to have a rational function where the denominator can have no zeroes and thus the function itself will have no singularity. Such a function will have no vertical asymptotes.

A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = x / (x - 3). The denominator has only one zero, x = 3.

Given, In a rational function, R(x): = P(x)/Q(x)

p/q is a form of rational function.

q is not zero since divisor cannot be 0.

If we divide any function by 0 the operation is considered as undefined.

A rational function has at most one horizontal or oblique asymptote, and possibly many vertical asymptotes.

First, factor both the numerator and the denominator. Then, cancel out any common factors. A common factor does not give rise to a vertical asymptote, but it does create a hole if the zero of the common factor is real. Next, find the zeros for all of the remaining factors in the denominator after canceling out the common factors. For each zero in the denominator, there will be a vertical asymptote at that zero.

Therefore, The simples example I can give you for such a rational function would the f(X) = X, defined over the real numbers.

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Answer: (0, -1)

Step-by-step explanation:

Hello! One method you can use to solve a system of equations is the elimination method.  Here are the steps to use the elimination method in this equation:

 -4y + x = 4               -4y - (-6y) = -4y + 6y = 2y, x -x = 0, 4 - 6 = -2
- (-6y + x = 6)
_________
2y = -2
__    __
2       2

y = -1

You now know that y = -1 for both lines to intersect.  Let's now find x using the substitution method.

Use the equation -4y + x = 4.  Substitute -1 for y in the equation.

-4(-1) + x = 4
4 + x = 4
-4      =  -4
x = 0.  

You now know that x = 0 and y = -1.  Coordinate pairs are represented as (x, y).  Substitute 0 in for x and -1 in for y.  Your answer is (0, -1).

1. The product of 653.2 x 4.6 lie between A. Between 2,612 and 3,265.

2. The value of 147 x 3 will be B. 441

3. The product of 6.84 x 57 will be 389.88.

4. The number of plants in 7 gardens is A. 1652.

5. The value of 16 × 103 to nearest number is B. 1600.

6. The amount for 75 drinks is A. 223.50

7. The option that best describes the estimate for 1.2 x 1.2 is B. The answer will be greater than 1 because the decimals are greater than 1.

8. The product of 2,456 x 38 is B. 93328.

The product of 653.2 x 4.6 will be:

= 653.2 × 4.6

= 3004.72

The value of 147 x 3 will be:

= 147 × 3

= 441

The product of 6.84 x 57 will be:

= 6.84 × 57

= 389.88.

The number of plants in 7 gardens is:

= 236 × 7

= 1652.

5. The value of 16 × 103

= 16 × 103

= 1600 approximately.

The amount for 75 drinks is:

= $2.98 × 75

= $223.50

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Answer:

1) False

2)True

3)True

4)False

The 9th term of the geometric sequence is 2304.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

9, -18, 36

First term = 9

Common difference = -18/9 = -2

Now,

The nth term of a geometric sequence.

= a[tex]r^{n-1}[/tex]

For n = 9,

= 9 [tex](-2)^{9 - 1}[/tex]

= 9 x [tex](-2)^8[/tex]

= 9 x 256

= 2304

Thus,

The 9th term is 2304.

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The Dimension of parallelogram is 7.57 inches . A special type of quadrilateral known as a parallelogram has opposite sides that are parallel and equal.

A parallelogram is a two-dimensional shape with four sides. The sides of this particular example of a quadrilateral are parallel and equal. The area of a parallelogram is the space enclosed by its four sides. The area of a parallelogram is calculated by multiplying its height by its length.

Area of Parallelogram = b × h

area is 63.9 in x in.

Area of Parallelogram = b × h 63.9

               = x+6.5 × x 63.9-6.5

                       = 57.4 x

                    = 7.57 inches x

height = dimension = 7.57 inches

Because it can be rearranged into a rectangle with the same area, the area of a parallelogram is the base times the height. A particular kind of parallelogram is a rectangle.

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Answer:

To solve a system of equations by substitution, we can use one equation to solve for one variable in terms of the other variable, and then substitute that expression into the other equation.

Given the system of equations:

10x + 2y = 4

.-9x + 3y = 18

We can start by isolating y in one of the equations. For example, we can use the first equation:

10x + 2y = 4

To solve for y, we can divide both sides by 2:

y = -5x + 2

Now we can substitute this expression for y into the second equation:

-9x + 3(-5x + 2) = 18

-9x - 15x + 6 = 18

-24x + 6 = 18

-24x = 12

x = -0.5

Now that we know x = -0.5, we can substitute this value back into the original expression we found for y:

y = -5(-0.5) + 2

y = 2.5

So the solution of the system of equations is (x, y) = (-0.5, 2.5).

The function that represents their household income if they work the same number of hours is 52x + 25.

Therefore the answer is B. (r + s)(x) = 52x + 25

Rhonda's paycheck is modeled by the function r(x) = 22x + 50, where x is the number of hours worked.

Shalene's paycheck is modeled by the function s(x) = 30x – 25, where x is the number of hours worked.

The function that represents their household income if they work the same number of hours can be determined by adding their individual income

(r + s)(x) = 22x + 50 + 30x - 25

(r + s)(x) = 52x + 25

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The arithmetic sequence is x+4n -55.

Given that,

20th term is = x + 25

a20 = a +19d = x + 25,

40th term is = x + 105

a40 = a +39d = x + 105,

now subtract a20 by a40,

a40 - a20

a + 19d - (a + 39d) =  x + 25 - (x + 105)

20d =  x + 25 -x - 105

20d = 80

d= 4.

a1 = a20 - 19d

a1 = x+ 25 - 19 x 4

a1 = x -51

so,

an = a1 + (n-1)d

an = x- 51 + (n-1)4

an = x- 51 + 4n - 4

an = x + 4n -55.

so, The arithmetic sequence is x+4n -55.

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The angles of the triangle are ∠Q=59°, ∠R=90°,∠S=31°.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle are less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As sum of all angles of triangles=180°

90+2x+33+5x-34=180

7x=90+1

x=13

Therefore,

                 ∠Q=59°, ∠R=90°,∠S=31°

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It will take approximately 197.36 minutes for the sample to reach 100,000 bacteria.

Calculate the growth rate of bacteria in each 40 minute interval by dividing 3 (the amount of growth) by 40 (the time interval):
Growth rate = 3/40 = 0.075
Calculate the number of growth periods necessary to get from 38 to 100,000 bacteria. To do this, divide the desired number of bacteria (100,000) by the initial number of bacteria (38):
Growth Periods = 100,000/38 = 2,631.57
Calculate the total time required for the sample to reach 100,000 bacteria by multiplying the growth rate (0.075) by the number of growth periods (2,631.57):
Total Time = 0.075 x 2,631.57 = 197.36 minutes
Therefore, it will take approximately 197.36 minutes for the sample to reach 100,000 bacteria.

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Answer:

A. Total number of Birds: G + D + C + E + S or B + L + F

B. [tex]\frac{L}{B+L+F}[/tex]

C. [tex]\frac{G+D}{B+L+F}[/tex]

Step-by-step explanation:

first divide you duck by one two three and then subtracted by 578

Answer:189/2

Step-by-step explanation:

The height of right circular cylinder is 8.4 cm.

Given that,

The radius = r = 2.4 cm

Volume      =  152 cubic cm

Let height of right circular cylinder = h

We know that,

The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centres of the cylinder's two bases. This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.

And we know that,

Volume of right circular cylinder = πr²h

                                              152  = 3.14 x 2.4 x 2.4 x h

⇒ h = 8.4 cm

Hence, height is 8.4 cm.

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Answer:

672

Step-by-step explanation:

1. Multiply the length, width, and height of the triangle.

14 x 12 x 8 = 1,344

2. Divide by 2.

1,344/2 = 672

Answer:

672 Feet^3

Step-by-step explanation:

Volume of a triangle = 1/2 (B)(H)(L)

B = base

H = height

L = length

I see you've found the numbers for B, H, and L so great start.

B = 12

H = 8

L = 14

So now its just plug and play

(12)(8) = 96

(96)(14) = 1344

And lastly (1/2)(1344) = 672 cubic feet

35% of the circle would represent the food budget.

The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics

Given are the vacation expenses budgets labeled in a circle graph.

We can write the total budget as equivalent to the Area of the circle as -

${600 + 450 + 270} → πr²

$1320 → πr²

$1 → πr²/1320

$450 →  πr²/1320 x 450 = 0.35 πr²

Therefore, 35% of the circle would represent the food budget.

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The variance of the ages of this population is equal to 28.33.

Mathematically, the mean for the ages of these siblings (mean age) would be calculated by using this formula:

Mean = [F(x)]/n

Total age, F(x) = 3 + 4 + 6 + 9 + 15 + 17

Total age, F(x) = 54.

Therefore, the mean age is given by:

Mean age = [F(x)]/n

Mean age = 54/6

Mean age = 9

Next, we would calculate the standard deviation by using this formula:

Standard deviation, SD = √(1/n × ∑(xi - u₁)²)

Standard deviation, SD = √(1/6 × [(3 - 9)² + (4 - 9)² + (6 - 9)² + (9 - 9)² + (15 - 9)² + (17 - 9)])

Standard deviation, SD = √(1/6 × [36 + 25 + 9 + 0 + 36 + 64])

Standard deviation, SD = √170/6.

Standard deviation, SD = 5.32

In Statistics, the standard deviation of a data set is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 5.32²

Variance = 28.33.

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Complete Question:

The ages of the siblings in a family are 3, 4, 6, 9, 15, 17. The variance of the ages of this population is?

A person who purchases his/her own policy can exclude the benefits from gross income. It's also good to note that statutory limitations exist for the following amounts:

Benefits that have been collected under the employer's plan

Premiums that have been paid by the employer

benefits that have been collected from the individuals' policy. Therefore the amount Valentino may exclude will be calculated as follows;

Daily statutory amount in 2020 (380 * 61)  

= $23180.

Actual cost of care                                    $27816         $23180

Less: Amount received from Medicare                           ($16690)

Equal amount of exclusion                                              ($6490)

Thus:

Valentino must include (30598 - 6490)=$6800 of the long-term care benefits received in his gross income.

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Answer:

Step-by-step explanation:

78,500 x 0.02 = 1,570--year 1 raise

(78,500 + 1,570) x 0.02 = 1,601.4--year 2 raise

(78,500 + 1,570+ 1,601.4) x 0.02 = 1,633.428--year 3 raise

(78,500 + 1,570+ 1,601.4+1,633.428) x 0.02 = 1666.1--year 4 raise

(78,500 + 1,570+ 1,601.4+1,633.428+1666.1) x 0.02 = 1699.42--year 5 raise

just keep doing this till you get to year 10 and then add up the total of money gained to the initial salary

If the baseball player went up to bat 250 times in a season and hits the ball 100 times then the rate of balls hits to times at bat is 2/5 .

the number of times the player went up to bat is = 250 times ;

the number of times he hits the ball is = 100 times ;

So , the rate of balls hit to times at bat is calculated as :

= (number of times he hits the bat)/(number of times player went to bat)

substituting the required values in formula ,

we get ;

= 100/250 ;

writing the fraction in the simplified form ,

we have ⇒ 2/5 .

Therefore , the rate of balls hit to times at bat in simplified fraction is 2/5 .

The given question is incomplete , the complete question is

A baseball player went up to bat 250 times in a season. he hit the ball 100 times. find the rate of balls hit to times at bat. express as a simplified fraction.

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Answer:

Given that RS bisects MO at N, we know that:

RN = RO (by definition of a bisector)

MN + NO = MO (by the angle bisector theorem)

Given that MN = 5x + 8 and NO = 10 + 3x, we can substitute these values into the second equation to find the value of x.

MN + NO = MO

(5x + 8) + (10 + 3x) = MO

8x + 18 = MO

Now we can use the first equation to find the value of x.

RN = RO

5x + 8 = 10 + 3x

3x = 2

x = 2/3

Therefore, the value of x is 2/3.

Considering the 12-face diagonals of a rectangular block, 30 pairs of these diagonals are skew lines.

In a rectangular block, there are a total of 12 face diagonals. These diagonals are formed by connecting the opposite vertices of each face of the block. To determine the number of pairs of skew lines among these diagonals, we can consider the following:

There are 6 faces in a rectangular block, each with 2 diagonals.

Every diagonal on one face is unique and does not intersect with any other diagonal on the same face.

However, diagonals on opposite faces are parallel to each other and therefore, do not form skew lines.

So, we will be selecting one diagonal from one face, so we have 6 options, then we select another diagonal from another face, which would be 5 options, and we repeat this process until we exhaust all the diagonals. This will give us 6*5 = 30 pairs of skew lines.

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The measure of angle C of the given triangle is 42.8°.

To find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,

sin A / a = sin B / b = sin C / c

where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.

Given ∠A = 61°, c = 35, a = 45

∴( sin A)/a = (sin C)/c

(sin 61° )/ 45 = (sin C) / 35

sin c = ((sin 61°) / 45) × 35

sin c = 0.68

c ≈ 42.8°

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Complete question:

You have given a triangle ΔABC, where ∠A = 61°, c = 35, a = 45. Solve for measurement(s) of angle c.

The all the measurements that are equivalent to 48 centimeters are (a) 0.48 m and (c) 480 mm.  .

the number is 48 centimeter , we  have to express the number in various units ,

For (a)  and (d) ; we know the conversion that 100 cm = 1 m , so , 48 cm will be = 48/100 = 0.48m .

For (b) and (c) ; we know that 1 cm = 10 mm , so , 48 cm = 48 × 10 = 480 mm

For

For (e) , we know that 100000 cm = 1  km , so , 48 cm = 48/100000 km

= 0.00048 km .

Therefore , the equivalent measurements are (a) 0.48 m and (c) 480 mm.

The given question is incomplete , the complete question is

Select all the measurements that are equivalent to 48 centimeters.

(a) 0.48 m

(b) 4.8 mm

(c) 480 mm

(d) 4,800 m

(e) 48,000 km

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Answer:

  1.5 < x < 34.7

Step-by-step explanation:

You want a compound inequality describing possible lengths (x) for the third side of a triangle with sides 18.1 and 16.6.

The shortest side cannot be any shorter than the difference of the two known sides:

  18.1 -16.6 = 1.5

The longest side cannot be any longer than the sum of the two known sides:

  18.1 +16.6 = 34.7

The possible lengths of the third side are given by ...

  1.5 < x < 34.7

__

Additional comment

If the third side is exactly equal to the sum or the difference, then the "triangle" looks like a line segment. It has zero area. That possibility is usually disallowed. If you want to allow it, then change < to ≤ in the inequality.