A model rocket is launched with an initial upward velocity of 65. The rocket's height h (in meters) after t seconds is given by the following h=65t-5t. Find all values of for which the rocket's height is 30 meters.

The value of angle t is 126⁰.

The value of angle x is 70⁰.

The value of angle 5 is 85⁰.

The value of each of the missing angles is calculated as follows;

angle b = 27⁰ (vertical opposite angles are equal)

The value of angle t is calculated as follows;

b + t + 27 = 180 ( sum of angles on a straight line)

27 + t + 27 = 180

54 + t = 180

t = 180 - 54

t = 126⁰

The value of angle x is calculated as follows;

x + 30 + 80 = 180 (sum of angle in a triangle and vertical opposite angles)

x + 110 = 180

x = 180 - 110

x = 70⁰

The value of angle 5 is calculated as follows;

65 + 70 + (180 - 40) + ∠5 = 360 (sum of angles in a quadrilateral)

65 + 70 + 140 + ∠5 = 360

275 + ∠5 = 360

∠5 = 360 - 275

∠5 = 85⁰

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The Surface area of figure is 396.896 unit².

We have,

x = 4 unit, y = 13 unit and z = 7 unit.

First Surface Area of Cylinder

= 2πrh

= 2(3.14)(4)(7)

=  175.84 unit²

and, Surface Area of Cone

= πrl

= (3.14)(4)(13.6)

= 170.816 unit²

Thus, the Surface area of figure is

= 175.84 + 170.816 + 50.24

= 396.896 unit²

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The given expression is

[tex]2x+x^2[/tex]

So we can write the general rule for the sequence as

[tex]T_x=2x+x^2[/tex]

Recall that the domain of a sequence is the set of natural numbers.

Let us plug in some first few natural numbers to generate the sequence.

When [tex]x=1[/tex], we obtain,

[tex]T_1=2(1)+(1)^2[/tex]

[tex]\rightarrow T_1=2+1[/tex]

[tex]\rightarrow T_1=3[/tex]

When [tex]x=2[/tex], we obtain,

[tex]T_2=2(2)+(2)^2[/tex]

[tex]\rightarrow T_2=4+4[/tex]

[tex]\rightarrow T_2=8[/tex]

When [tex]x=3[/tex], we obtain,

[tex]T_3=2(3)+(3)^2[/tex]

[tex]T_3=6+9[/tex]

[tex]T_3=15[/tex]

When [tex]x=4[/tex], we obtain,

[tex]T_4=2(4)+(4)^2[/tex]

[tex]T_4=8+16[/tex]

[tex]T_4=24[/tex]

Therefore the number sequence produced by the given expression is,

[tex]\boxed{\bold{3, 8, 15, 24.}}[/tex]

Answer:

To find the distance between a point and a line in a plane, we can use the formula:

distance = |Ax + By + C| / √(A^2 + B^2)

where A, B, and C are the coefficients of the general form of the line equation (Ax + By + C = 0), and (x,y) are the coordinates of the point.

First, we need to rewrite the given line equation in the standard form (y = mx + b):

2x - 3y = -2

-3y = -2x - 2

y = (2/3)x + 2/3

Now we can identify the slope (m) and y-intercept (b) of the line:

m = 2/3

b = 2/3

Next, we can find the equation of the perpendicular line that passes through the point (1,2), since the distance between the point and the line will be the length of the segment connecting the point to the intersection of these two lines. The slope of a line perpendicular to a line with slope m is -1/m, so the equation of the perpendicular line passing through (1,2) is:

y - 2 = (-3/2)(x - 1)

y = (-3/2)x + (7/2)

Now we need to find the intersection of the two lines by solving the system of equations:

y = (2/3)x + 2/3

y = (-3/2)x + (7/2)

(-3/2)x + (7/2) = (2/3)x + 2/3

(-13/6)x = -5/6

x = 5/13

y = (2/3)(5/13) + 2/3

y = 11/13

So the intersection point of the two lines is (5/13, 11/13). Now we can use the distance formula to find the distance between this point and the given point (1,2):

distance = √[(5/13 - 1)^2 + (11/13 - 2)^2]

distance = √[(36/169) + (25/169)]

distance = √(61/169)

distance = √61/13

The closest answer choice is (A) √13, but the simplified expression is actually √61/13. Therefore, none of the answer choices provided are completely accurate.

Step-by-step explanation:

Answer:

The total cost, C (in dollars), for driving x miles is given by:

C = 0.06x + 10.75

where x is the number of miles driven.

To find the total cost for driving a certain number of miles, simply substitute that value for x in the equation and solve for C.

Answer:

Step-by-step explanation:

There is no correlation between the two.

The graph provided is a scatter plot and the dots are to spread out to have any time of coloration

From the information provided, according to the table, if the purchase price of a car was less than $20,000, what is the probability that its Trepair costs were less than about 46%.

If a car had total repair costs of less than $10,000, what is the probability that its purchase price was more than $40.000 Express your about 20%.

Probability is a measure of the likelihood of an event happening. It is a numerical value between 0 and 1, where 0 indicates an event is impossible, and 1 indicates an event is certain.

So, calculating the probability of the events above happening in percentage is as follows:

A. 86/ (86+67+35) =

18/188 ≈ 46%.

Therefore, Blank 1 is about 46%

B. 40/(88+71+40) =

40/197 ≈ 20%.

Therefore, Blank 2 is about 20%.

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The canoe traveled approximately a distance of 21.9ft.

let the distance the canoe travels be "d".

Initial position = 65 ft

After  7s,

The Final position is 40ft away

From the given information the canoe moves =(65-40)=25ft closer

Let x=25ft

Using the tangent function

we know that, tan(50degree)=x/d

therefore, d=25/tan(50 degree)

d=21.9ft

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Answer:

The answer choice that contains only equations is:

A. 2 + H = 14 and K - 25 = 2

Explanation:

A. Both expressions are equations because they have an equal sign and a variable.

B. C-14C-14 is not an equation because it doesn't have an equal sign.

C. Both expressions are equations, but 22-y is not a complete equation (missing an equal sign).

D. Both expressions are equations, but 55= r-1 is not a complete equation (missing an equal sign).

Step-by-step explanation:

The length of the garden containing the soil is L = 24 feet

Given data ,

Volume = Length x Width x Height

Width = 4 1/2 feet

Height = 1/2 foot

Total volume of topsoil used = 18 bags x 3 cubic feet/bag = 54 cubic feet

So , the length of the garden is

54 = Length x 4 1/2 x 1/2

On simplifying , we get

54 = Length x 9/2 x 1/2

Now, let's simplify the right-hand side by multiplying the numerator and denominator by 2

54 / (9/2 x 1/2) = The length of the garden

The length of the garden = 54 /9 x 4

The length of the garden = 6 x 4

The length of the garden = 24 feet

Hence , the length of the garden bed is 24 feet

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The total number of different ways that the student can be assigned during a 4-day work week is 81 different ways.

A student is a person who is enrolled in an educational institution, such as a college, university, or trade school. Students are typically required to attend classes and complete assignments to gain knowledge and develop skills related to their field of study. Depending on their level of education, students may also be required to participate in research or internships in order to gain practical experience.

There are 3 possible floors that the student can be assigned to, so for each day of the 4-day week, there are 3 possible assignments.
Therefore, the total number of different ways that the student can be assigned during a 4-day work week is 3 x 3 x 3 x 3
= 81 different ways.

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Standard form of the equation for the circle with the following properties is (x + 7)² + (y + 6)²= 104.

A line segment through the center of a circle with its ends on the circle's circumference. Its value is twice of the radius.

An equation is a mathematical statement that asserts the equality between two expressions, typically containing one or more variables. It consists of two sides separated by an equals sign (=), indicating that the expressions on both sides have the same value. Equations are used to describe relationships, solve problems, and make predictions in various branches of mathematics, science, engineering, and other fields. They can be linear or nonlinear, and may involve arithmetic, algebraic, trigonometric, exponential, or other mathematical operations. Solving an equation involves finding the values of the variables that make the equation true.

To find the standard form of the equation for a circle, we can start by finding the center and radius of the circle using the given endpoints of a diameter.

The center of the circle is the midpoint of the diameter, which can be found by averaging the coordinates of the two endpoints. Let's denote the coordinates of the endpoints of the diameter as (x1, y1) and (x2, y2) respectively.

In this case, the coordinates of the endpoints are (x1, y1) = (-6, -1) and (x2, y2) = (-8, -11). Using the midpoint formula, we can find the center of the circle:

Center = ((x1 + x2)/2, (y1 + y2)/2)

Plugging in the values, we get:

Center = ((-6 + (-8))/2, (-1 + (-11))/2)

Center = ((-14)/2, (-12)/2)

Center = (-7, -6)

So, the center of the circle is (-7, -6).

The radius of the circle is half the length of the diameter, which can be found using the distance formula between the two endpoints of the diameter. Let's denote the distance between the endpoints as d.

The distance formula is given by:

d = sqrt((x2 - x1)² + (y2 - y1)²)

Plugging in the values, we get:

d = sqrt((-8 - (-6))² + (-11 - (-1))²)

d = sqrt((-2)² + (-10)²)

d = sqrt(4 + 100)

d = sqrt(104)

So, the radius of the circle is sqrt(104).

Now that we have the center and radius of the circle, we can write the standard form of the equation of the circle as:

(x - h)² + (y - k)²= r²

where (h, k) is the center of the circle and r is the radius of the circle.

Plugging in the values, we get:

(x - (-7))² + (y - (-6))² = (sqrt(104))²

(x + 7)² + (y + 6)²= 104

So, the standard form of the equation for the circle with endpoints of a diameter at (-6, -1) and (-8, -11) is (x + 7)² + (y + 6)² = 104

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Answer:

y = 2x

Step-by-step explanation:

If x > 5, then x - 5 is positive and x + 5 is also positive. So we can rewrite the equation as follows:

y = (x - 5) + (x + 5)

Simplifying the equation, we get:

y = 2x + 0

Therefore, the equation without using absolute value for the given conditions is y = 2x.

Hope this helps!

Without seeing the graph of the linear function, it is impossible to determine if Tom's answer of 12 is correct or incorrect. However, it is important to understand the concept of slope and how it is calculated for a linear function.

The slope of a linear function represents the rate at which the y-coordinate changes for each unit increase in the x-coordinate. In other words, it measures the steepness of the line. Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

To calculate the slope of a line given its graph, one can choose any two points on the line and find the difference in their y-coordinates and x-coordinates. The slope is then the ratio of the change in y-coordinates to the change in x-coordinates. This can be expressed as:

slope = (change in y-coordinate) / (change in x-coordinate)

Now, if Tom has correctly identified two points on the line and calculated the difference in their y-coordinates and x-coordinates, and if he has obtained a ratio of 12 for the change in y-coordinate to the change in x-coordinate, then his answer of 12 for the slope would be correct.

However, it is also possible that Tom made an error in his calculation, or that he misread the graph, and obtained an incorrect answer. Therefore, it would be necessary to verify his calculations by checking the points he used and the formula he applied.

In conclusion, without further information about the graph of the linear function and the points chosen by Tom to calculate the slope, it is impossible to determine if his answer of 12 is correct or incorrect.

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It is not appropriate to generalize the findings of the survey to the entire school population.

What is survey?

The conclusion that about 8.6% of the students in the school have a January birthday is not necessarily valid based on the information provided.

The sample size of the survey is too small (only 3 students with January birthdays) and limited to one math class, so it may not be representative of the whole school population. Additionally, the sample is not randomly selected, which introduces the possibility of selection bias.

Therefore, it is not appropriate to generalize the findings of the survey to the entire school population. A more reliable way to determine the percentage of students with a January birthday would be to collect data from a larger, randomly selected sample of students across the entire school population.

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Answer:

Use Formula nPr, to solve the following question

6P4 = 360

Answer:

171.76 Pounds

Step-By-Step Explanation:

So the explanation to how I got the answer is in the link below.

The error which Mason made was subtracting 5 from both sides.

The correct solution is x < 16 and it is shown on the number line below.

The best way to describe the temperature in the greenhouse before the heater stopped working is that it was at least 71 degrees.

An inequality that represent this situation is x + 21 ≥ 47 and the solution is x ≥ 26.

The inequalities that can be used to represent the situation are;

D. x - 7.35 ≥ 2.87

E. x ≥ 10.22

Based on the information provided about the math test, the following inequality must be solved by students;

x - 5 < 11

By adding 5 to both sides of the inequality, we have the following:

x - 5 + 5 < 11 + 5

x < 16

Therefore, the error which Mason made was subtracting 5 from both sides.

Since the temperature dropped 6 degrees before it was fixed and it was still at least 67 degrees when the heater started working again, we can model it as follows;

x - 4 ≥ 67

x ≥ 71

Since Ramiro has $21 and wants buy a skateboard that cost $47, the amount of money that he needs can be modeled by this inequality;

x + 21 ≥ 47

x ≥ 47 - 21

x ≥ 26

In conclusion, the inequalities that can be used to represent the total amount, x, Kendra needs for the bead are;

x - 7.35 ≥ 2.87

x ≥ 2.87 + 7.35

x ≥ 10.22

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A number with eight tens and one one is  = 81.

A  number with five tens and five ones is  = 55.

A number with eight tens and nine ones is 89.

A number with five tens and eight ones = 58.

A number with one ten and seven ones is 17.

A number with five tens and two ones is 52.

A  number with six tens and two ones is 62.

A number with three tens and zero ones  is 30.

A number with four tens and five ones is 45.

The phrase "eight tens and one one" denotes a numerical value featuring the digit 8 in the tens position and 1 in the ones position. This is equal to the sum of 80 and 1, resulting in a total value of 81.

Therefore "a numerical figure composed of 5 tens and 5 units" indicates a number where 5 is in the tens position while 5 is in the ones position, resulting in a total of 50 + 5, which equals 55.

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Answer:

First, we need to find out how many people are male and female in the town:

Step-by-step explanation:

Male population = 48% of 42800 = 20544

Female population = 100% - 48% = 52% of 42800 = 22256

To find out how many more females there are than males, we need to subtract the male population from the female population:

Female population - Male population = 22256 - 20544 = 1712

Therefore, there are 1712 more females than males in the town.

The values of x, y and  z of the given parallelogram are: x = 12, y = -20 and z = -32

A quadrilateral has two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.

The key properties of angles of a parallelogram are:

- If one angle of a parallelogram is a right angle, then all the angles are right angles

- Opposite angles of a parallelogram are equal (or congruent)

- Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees)

Consecutive angles are supplementary and as such:

85 + 8x - 1 = 180

8x = 181 - 85

8x = 96

x = 96/8

x = 12

Opposite angles are equal and as such:

85 = -4y + 5

-4y = 80

y = -20

Similarly:

85 - 3z - 4 = 180

3z = -96

z = -96/3

z = -32

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Answer:

Step-by-step explanation:

26/7

The inequalities that could show the weight of each horse are:

h ≤ 1248

t ≤ 352

To determine the inequalities that could show the weight of each horse, we can use the fact that the total weight of the horses and tack must be less than or equal to the capacity of the horse trailer. We can set up the following inequalities:

5h + 5t ≤ 8000

where h represents the average weight of each horse.

However, we don't know the value of t, so we need to express it in terms of h. We are given that the combined weight of the horses is 6,240 pounds, so we can write:

5h ≤ 6240

Solving for h, we get:

h ≤ 1248

This means that the weight of each horse must be less than or equal to 1,248 pounds.

Now we can substitute this upper bound for h into the first inequality to get:

5(1248) + 5t ≤ 8000

6240 + 5t ≤ 8000

5t ≤ 1760

t ≤ 352

This means that the average weight of tack per horse must be less than or equal to 352 pounds.

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Answer:

Step-by-step explanation:

The volume of the triangular prism shown below is 48 cm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The area of triangular base = (1/2) * 12 cm * 8 cm = 48 cm²

The volume of triangular prism = area of base * height

Volume = 48 cm² * 34 cm = 1632 cm³

The volume of the triangular prism is 48 cm²

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Answer:

The same, Congruent

Step-by-step explanation:

The measures of alternate exterior angles are equal when two parallel lines are intersected by a transversal line. That is, if we have two parallel lines l and m intersected by a transversal line t, then the alternate exterior angles are congruent, which means that they have the same measure. More formally, if angle 1 and angle 2 are alternate exterior angles, then:

angle 1 = angle 2

The reason for this is that when the parallel lines are intersected by the transversal line, they form a Z-shape pattern, and the alternate exterior angles are located on opposite sides of the transversal line, but outside of the two parallel lines. The angles are congruent because they are formed by a pair of corresponding angles and a pair of vertical angles.

-

The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

By Pythagoras rule we can evaluate for b as follows:

x = √(7.5² - 2.5²)

x = √50

x = x = 7.0711

f = √[(√78)² - 7²]

f = √(78 - 49)

f = √29

f = 5.3852

d = 2 × √(11² × 8²)

d = 2 × √53

d = 15.0996

Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

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answer attached

see below

please give brainliest it will be much appreciated

The limiting value or horizontal asymptote of the function y = 2x/4x-5 is y = 0.5

From the question, we have the following parameters that can be used in our computation:

y = 2x/4x-5

The limiting value or horizontal asymptote can be calculated by graph

So, we start by plotting the graph of y = 2x/4x-5

See attachment for the graph

From the graph, we can see that

The function does not have a defined value at y = 0.5

This means that the limiting value or horizontal asymptote is y = 0.5

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The height of the building is given by h = 93.5 m

Given data ,

Let the proportion be represented as A

Now , the value of A is

The height of the pole is 3.3 meters and its shadow is 1.71 meters long. We can set up a proportion to find the height of the building:

Height of pole / Length of pole's shadow = Height of building / Length of building's shadow

3.3 m / 1.71 m = x / 48.25 m

Now we can cross-multiply and solve for "x":

3.3 m * 48.25 m = 1.71 m * x

159.825 m² = 1.71 m * x

x = 159.825 m² / 1.71 m

x ≈ 93.5 m

Hence , the height of the building is approximately 93.5 meters

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