A ball is thrown in the air from a ledge. Its height in feet is represented by
f(x) = –16(x2 – 6x – 7), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground.
How many seconds does it take the ball to reach the ground?
A.6
B.7
C.1
D.16

So we can write 4/6 as equivalent to 2/3

Equal is not the same as equivalent. While comparable indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is comparable to 2, even if 2 is supposed to be equal to 2.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

So , 4/6 can be written as 2*2/3*2 =  2/3

So we can write 4/6 as equivalent to 2/3

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The triangle can be constructed from sides of triangle measuring 3.5 cm 9.2 cm and 5.3 cm due to side rule of triangle.

The possibility to construct the triangle will be found out through the sum of any two sides of triangle. If the sum is greater than the remaining side of the triangle, the construction is possible. Let us assume the side a, b and c of triangle to be 3.5, 9.2 and 5.3 cm.

Now, using the side-side-side rule of triangle -

Side a + side b > side c

3.5 + 9.2 > 5.3

Add the values

12.7 > 5.3

Side b + side c > side a

9.2 + 5.3 > 3.5

Add the values

14.5 > 3.5

side c + side a > side b

5.3 + 3.5 > 9.2

Add the values

8.8 not greater than 9.2

Based on the results, the construction of triangle from mentioned sides is possible according to length rule of the triangle.

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Answer:

--------------------

Given AP with recursive formula:

As per recursive formula the first term is a₁ = 7 and common difference is d = -1.

Use the nth term formula to find the 5th term:

Therefore , as a result the solution of the given problem of expressions comes out to be the typical rate of change is -2/5 in its simplest form.

An algebraic equation must be checked by replacing each variable with a number and performing arithmetic operations. Since 8 plus 6 = 14, the reply variable in the above example is equivalent to 6. In order to test the expression, we can replace the values of the variables  with ones we already know.

Here,

Simply said, the median rate of change is -2/5.

The function's gradient or slope is its rate of change.

The slope of a function can be calculated using the formula:

=> D = dy/dx = y2, -y1, and x2, -x1.

Using the coordinates (0, 41) from the table and (15, 35)

Replace the expression with the coordinate:

=>m = 35-41/15-0

=>m = -6 /15

=>m =-2/5

As a result, the typical rate of change is -2/5 in its simplest form.

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The required equation is x×1/2+25-x ×1/4=10

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here, A math quiz has a total of 25 questions. Some questions or worth 1/2 a point and some questions or worth 1/4 point there are a total of 10 points available. let there be x 1/2 points question and 25-x 1/4 points question, then

x×1/2+25-x ×1/4=10

Hence, this is the required linear equation

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Answer:

Step-by-step explanation:

So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 22 × 3 × 5. where 2, 3 and 5 are prime numbers.

Answer: Where they bisect each other at W the 2 lines  are split in the center by one another which means both of those lines are 180

Step-by-step explanation:

Answer:

  SAS

Step-by-step explanation:

You have segments UT and VS bisecting each other at point W, and you want to show triangles UWV and TWS ae congruent.

Each half of the segment is congruent to the other half:

  UW≅TW and VW≅SW

The angles between them are vertical angles so are congruent:

  ∠UWV ≅ ∠TWS

So, you have congruent corresponding sides and the angle between. The triangles UWV and TWS are congruent by the SAS congruence postulate.

__

Additional comment

You can use substantially the same argument to say triangles UWS and TWV are congruent. The proof above shows UV≅TS. The congruence of triangles UWS and TWV shows US≅TV. Hence the figure TSUV is a parallelogram.

Answer:

27x9+57+5 / 9 = 243 + 57 + 5 / 9 = 305 / 9 = 33.89

Step-by-step explanation:

Answer:

33.89

Step-by-step explanation:

(27*9+57+5)/9=33.89

A quotient is a number created when two numbers are divided. The formula for this is Quotient = Dividend ÷ Divisor.

The division is the process of dividing one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the number that we get as a result.

Then, the quotient formula is given by Quotient = Dividend ÷ Divisor. For example, 50÷5=10. Here, 50 is the dividend, 5 is the divisor, 10 is the quotient, and 0 is the remainder.

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An equation in standard form with an x-intercept of 5 and a y-intercept of -4 is,

⇒ 5x + 4y = 20

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The x - intercept = 4 ,

So, ( 4,0) is a point on the line.

And, The y - intercept = 5,

So, ( 0, 5) is a point on the line.

Now, Slope of the line passing through the point (4, 0) and (0, 5) is,

⇒ m = (5 - 0) / (0 - 4)

⇒ m = - 5/4

So, The slope intercept form of an equation is,

⇒ y  = mx + b

Where, m = slope and b = y- intercept.

Hence, We get;

⇒ y = - 5/4x + 5

We know that;

An equation in standard form is,

⇒ Ax + By = C

So, We get;

⇒ y = - 5/4x + 5

⇒ 4y = - 5x + 20

⇒ 5x + 4y = 20

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The value of  y= 1.6667 when x= 5.

The graph is attached below.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

x= 1 when y=3, if x and y vary inversely.

Then, x = k/y

where is proportionality constant

So, k = x y

k = 3

Using Proportion

x/ y = k

5/y= 3

y= 5/3

y= 1.6667

Hence, y= 1.6667 when x= 5.

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-1.6 is the residual value of 5 for given regression table.

A residual value is the difference between the observed and expected y-values (as determined by the regression equation).

Here,

In this case, the given regression equation for the line,

y = 5.2 x - 0.4

As a result, for x = 5, the anticipated value is y = 5.2 5 - 0.4 = 26.0 - 0.4 = 25.6.

Now, according to the table,

The observed value of y = 24 for x = 5.

As a result, the residual for 5 = Observed y for 5 - Predicted y for 5

= 24 - 25.6 = - 1.6

The first option is the correct one.

The residual value of 5 for the provided regression table is -1.6.

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The complete question:

The line of best fit to model the data in the table is y = 5.2x – 0.4.

What is the residual for 5?

–1.6

–0.6

0.6

1.6

Answer:

Step-by-step explanation:

To make a parallelogram, Aston must connect the pieces of wood in the following order: 3 feet, 4 feet, 3 feet, 4 feet.

How many different parallelograms could he make with these

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Answer:

2x−15

Step-by-step explanation:

6x−7−4x−8

=6x+−7+−4x+−8

Combine Like Terms:

=6x+−7+−4x+−8

=(6x+−4x)+(−7+−8)

=2x+−15

To find the center and radius of a circle given the endpoints of its diameter, you can use the following steps:

For example, if the endpoints of a diameter are (-3, 4) and (7, -6), you can use the midpoint formula to find the center:

(x,y) = ((-3 + 7)/2 , (4 + -6)/2)

(x,y) = (2,-1)

The center of the circle is (2,-1)

To find the radius, you can use the distance formula:

d = √((7-(-3))^2 + (-6-4)^2)

d = √((10)^2 + (-10)^2)

d = √(100+100)

d = √200

d = 10√2

The radius of the circle is 10√2/2 units.

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The  amount of sales at which Company A's offer is the same as Company B's is  $600

The given parameters that will help us to understand the question are

Company A:

Base = $200

Commission = 10% of sales = .1*S

A = .1S + 200

Company B:

Base = 400

Commission = .05*S

B = .05S + 400

We're looking for the point where they're equal.

200 + .1S = 400 + .05S

Multiply by 100 to get rid of decimals

20000 + 10S = 40000 + 5S

Subtract 20000 from both sides

10S = 20000 + 5S

Subtract 5S from both sides

5S = 20000

Divide both sides by 5

S = 4000

So, at $4000 sales, the two jobs pay the same.

You have to always check your work. This can be done by plugging the values into the basic equations and determining if they check. Or we can graph the two lines and see where they cross.

Company A:

200 + .1(4000) = 200 + 400 = 600

Company B:

400 + .05(4000) = 400 + 200 = 600

Conclusively Alex (A) offers $600 as same as Company B

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Complete question:

A salesperson has two job offers. Company A offers a weekly salary of $200 plus commission of 10% of sales. Company B offers a weekly salary of $400 plus commission of 5% of sales. What is the amount of sales at which Company A's offer is the same as Company B's?

If the spring musical cost $600 for costumes and $450 for the stage materials.  the number of tickets  is 56 tickets.

Total ticket = $600 + $450

Total ticket = $1050

Now let find the number of tickets that they have to sell to profit.

Number of tickets = $1,050 - $375 / $12

Number of tickets = $675/$12

Number of tickets = 56 tickets

Therefore the number of tickets  is 56 tickets.

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The complete question is:

The spring musical cost $600 for costumes and $450 for the stage materials.

Students raised $375 from advertisements in the program. Tickets cost $12 each.

How many tickets do they have to sell to profit?

Answer:

In the case of the classification problem, the simplest way to find out whether the data is linear or non-linear (linearly separable or not) is to draw 2-dimensional scatter plots representing different classes. Here is a picture that represents the linearly and non-linearly separable dataset and how one can use scatter plots to visualize them.

Step-by-step explanation:

The value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.

The SSS similarity theorem states that if three corresponding sides of two triangles are proportional, then the two triangles are similar. This applies to all triangles, regardless of their size or shape.

To use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Once you have this information, you can use the theorem to determine if the two triangles are similar.

It's important to note that to use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Without this information, it's not possible to determine if the two triangles are similar.

Therefore the value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.

The SSS similarity theorem only states that the two triangles are similar, it doesn't tell anything about the angles of the triangles.

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To obtain 3x² + 5xy from 2x² + 2xy², you would need to add the polynomial x² + 5xy to the original expression.

In order to add two polynomials together, the terms must have the same degree and variable. In this case, we see that 2x^2 and 2xy^2 have different degrees and variables. So, we need to find a polynomial that when added to 2x² + 2xy² will give us 3x² + 5xy.

To do this, we can start by looking at the x² term in 3x² + 5xy. We can see that we need to add x² to our original polynomial. Next, we can look at the xy term in 3x² + 5xy. We can see that we need to add 5xy to our original polynomial.

So by adding x² + 5xy to 2x² + 2xy², we get the desired polynomial of 3x² + 5xy.

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The complete question is:

What should be added to 2x² + 2xy² to obtain 3x² + 5xy.

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The average rate of change from day 2 to day 10 is given as follows:

-0.75 houses sold per day.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The points of interest are given as follows:

(2,8) and (10,2).

The change in the output is of:

2 - 8 = -6.

The change in the input is of:

10 - 2 = 8.

Hence the average rate of change is obtained as follows:

r = -6/8

r = -3/4

r = -0.75 houses sold per day.

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If you want to buy fewer than 25 shirts, then prefer Shirts By Sam shop. If you want to buy more than 25 shirts, then prefer Might T Shirt shop.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Given that:

Shirts By Sam

The cost of 10 shirts is $127.5

The cost of 15 shirts is $168.75.

Assume the equation that represents total cost is y = ax+b

Putting x= 10 and y=127.5 in y = ax+b:

127.5 = 10a+b.....(i)

Putting x= 15 and y=168.75 in y = ax+b:

168.75 = 15a+b.....(ii)

Use elimination method to solve equation (i) and (ii).

Subtract equation (i) from (ii)

15a+b = 168.75

10a+b = 127.5

____________

5a = 41.25

a = 8.25

Putting a=8.25 in equation (i)

127.5 = 10×8.25+b

b = 40

The equation is y = 8.25x+40.

Might T Shirt

The cost of 8 shirts is $137

The cost of 12 shirts is $163

Assume the equation that represents total cost is y = ax+b

Putting x= 8 and y=137 in y = ax+b:

137 = 8a+b.....(iii)

Putting x= 12 and y=163 in y = ax+b:

163 = 12a+b.....(iv)

Use elimination method to solve equations (iii) and (iv).

Subtract equation (iv) from (iii)

 8a+b = 137

12a+b = 163

____________

4a = 26

a = 6.5

Putting a=6.5 in equation (iii)

137= 8×6.5+b

b = 85

The equation is y =6.5x+85.

The solution of the system of equations:

y = 8.25x+40 .....(vi)

y =6.5x+85   ......(vii)

Use substitution method to solve equations (vi) and (vii).

Subtract equations:

8.25x+40 - 6.5x-85=0

1.75x - 45 =0

x = 45/1.75

x = 25.71

Putting x = 26 in equations (vi) and (vii)

y = 8.25×26+40 = 254.5

y = 6.5×26+85 = 254

Putting x = 24 in equations (vi) and (vii)

y = 8.25×24+40 = 238

y = 6.5×24+85 = 241

Thus if you buy more than 25 shirts, then prefer Might T Shirt shop.

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Answer:  132.526

Step-by-step explanation:

Answer: 23.16%

Step-by-step explanation: 7300/9500 can be simplified to 73/95 which gives us 76.84%. subtract that from 100 and you get 23.16

N = (360/x) - 2

This formula finds the number of sides N in a regular polygon when given the measure of one interior angle x.

The formula is derived from the fact that the sum of all interior angles in a regular polygon is equal to (N-2)*180, where N is the number of sides.

Therefore, it can be rearranged to be N = (360/x) - 2.

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Solving a linear inequality step by step involves several steps including isolating the variable on one side of the inequality sign, simplifying the inequality, graphing the inequality, shading the region that include the solutions and representing the solutions in the form of an interval.

1. Isolate the variable on one side of the inequality sign: This can be done by adding or subtracting the same value from both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.

2. Simplify the inequality: This can include combining like terms, or simplifying fractions or decimals.

3. Graph the inequality: This can be done by plotting the inequality on a number line or a coordinate plane, using a solid line for "greater than" or "less than" and a dotted line for "greater than or equal to" or "less than or equal to"

4. Test a point: To test whether a point is a solution of the inequality, substitute the coordinates of the point into the inequality, and check if the statement is true.

5. Shade the region that includes the solutions: The solutions of the inequality are all the points that make the inequality statement true. The solutions of the inequality are all the points that are in the shaded region.

6. Write the solution in interval notation: Write the solution in interval notation, if needed.

Here is an example:

Solve the inequality 2x - 3 > 5.

Step 1: Isolate the variable by adding 3 to both sides: 2x > 8

Step 2: Divide both sides by 2: x > 4

Step 3: Graph the inequality on a number line. Using a solid line, draw a line at x = 4 and shade the region to the right of the line, including 4.

Step 4: Test a point, e.g. x = 5, if 5 > 4 is true.

Step 5: The solution is x > 4.

Step 6: if needed, the solution can be written in interval notation as (4, +inf)

It's important to note that solving inequalities is not always straightforward, and some inequalities may require multiple steps to be solved.

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Answer:

See below

Step-by-step explanation:

52 degrees C below  0 °  C    is just    - 53 °C

Answer:

"Substitution comes in three flavors: nominal, verbal, or clausal, depending on the item being substituted.

Step-by-step explanation:

Hope it helps!