An object attached to a coiled spring is pulled down a distance of 10 centimeters from its rest position and then released.

Assuming that the motion is simple harmonic
with a period of 2 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds.

Also assume that the positive direction of
the motion is up. At time t=0 the object is at its resting position and moving down.

There are 180 three-digit numbers that leave a remainder of 2 when divided by 5 and 128 three-digit numbers that leave a remainder of 6 when divided by 7.

The smallest 3-digit number to leave a remainder of 2 when divided by 5 is 102.

The next number will be 107, and then 112,

The last 3 digit number to leave a remainder 2 when divided by 5 is 997

Therefore here we get an Arithmetic Progression

102, 107, 112, ..., 997

We know that for any term of an A.P

aₙ = a + (n - 1)d

where,

a = first term

n = the order number of that particular value

d = common difference

Here,

a = 102

d = 107 - 102

= 5

The number of 3 digit number for the above problem will be the value of n for 997

Hence we get

997 = 102 + (n - 1)5

or, 102 + 5n - 5 = 997

or, 5n + 97 = 997

or, 5n = 997 - 97

or, 5n = 900

or, n = 900/5

or, n = 180

Next, we need to find the no. of three-digit numbers that leave the remainder of 6 when divided by 7

The smallest 3-digit number to leave the remainder of 6 when divided by 7 is 104

The largest is 993

Therefore, just like before, we get the A.P

104, 111, 118, ..., 993

here,

a = 104

d = 7

aₙ = 993

Hence we get,

993 = 104 + (n - 1)7

or, 104 + 7n - 7 = 993

or, 97 + 7n = 993

or, 7n = 993 - 97

or, 7n = 896

or, n = 128

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The absolute value equation representing all numbers x whose distance from 5 is equal to 5 units is written as:

|x - 5| = 5

An absolute value equation where the variable is x can be written as:

|x - a| = b

This means that the distance between x and a is equal to b.

So if we want to write an equation where the distance between x and 5 is equal to 5, then we can replace:

a = 5

b = 5

And the absolute value equation will be:

|x - 5| = 5

This is what we wanted to get.

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Answer:

The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.

Answer:

b=98 and a=82

Step-by-step explanation:

b and 98 are corrisponding angles which means that they are both 98

a+b=180 because it is a straight line

a+98=180 subtract 98 from both sides a d you get a=82

Answer:

x < 1 and x > -4 (more down below)

Step-by-step explanation:

First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5                    2.  -2x -3 < 5
-2x < -2                           -2x < 8                        

x < 1                                x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4

The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1

    O-----------------------O

<---5, -4, -3, -2, -1, 0, 1, 2-->

For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.

This helps you to know what value you plug in for X makes the inequality true (shaded region)

Answer:

y= -20/9

Step-by-step explanation:

4y+5/3=y-5

3y= -(5+5/3)

3y= -20/3

y= -20/9

Answer:

Collect like terms

4y-y=-10/2-5/3

3y=-5-5/3

5-5/3

LCM=3

3/1=3×5=15

3/3=1×5=5

15-5÷3

10/3

3y=10/3÷3

3y=30/3

y=10

Answer:

C. Function, there is a unique x-value for each y-value

Answer:

x < -9

Step-by-step explanation:

2x + 4 < -14

Solve for "x"

Subtract 4 from both sides

2x + 4 < -14

2x + 4 - 4 < -14 - 4

Simplify

Subtract all the numbers

2x + 4 - 4 < -14 - 4

2x < -14 - 4

2x < -18

Divide both sides by the same factor

2x < -18

[tex]\frac{2x}{2}[/tex] < [tex]\frac{-18}{2}[/tex]

Simplify

Cancel the terms that are in both numerator and denominator

[tex]\frac{2x}{2}[/tex] < [tex]\frac{-18}{2}[/tex]

x < [tex]\frac{-18}{2}[/tex]

Divide

[tex]x < \frac{-18}{2}\\ x < -9[/tex]

The answer is [tex]x < -9[/tex]

The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

What is a regular hexagon?

It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.

Here, we let

P = it has exactly four sides.

Q = it is not an hexagon.

The negation is like this;

If it is a hexagon, then it does not have exactly four sides.

Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).

Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

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The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

According to the question,

We have the following expression:

(–5.5 + 2p)(–2)

Now, in order to simplify this expression, we will multiply -2 into the bracket:

(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)

-5.5*-2+2p*(-2)

We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.

11-4p

Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

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answer:

x = 18, 60.

step-by-step explanation:

evaulating (3x+6) = (4x-12) and solving for x gives us x = 18. you didn't include the angle, so i can't give you that. but

(3x+6) = 60

(4x-12) = 60

if those were your angles, you would have an equilalateral triangle (all sides/angles even) and your missing angle would also be 60.

Answer:

to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

Step-by-step explanation:

Step-by-step explanation:

-8(x + 7.5) ≤ 10?

expand left side:

-8x - 60 ≤ 10

subtract 60 to both sides:

-8x - 60 + 60 ≤ 10 + 60

-8x ≤ 70

dive both sides by -8: (Remember when dividing by a negative number, you flip the direction of the inequality sign)

-8x/-8 ≥ 70/-8

x ≥ -35/4

reduce right side:

x ≥ -35/4 or x ≥ -8.75 [depends on if you need fractional or decimal format]

so in set builder format: [-35/4 , ∞) or [-8.75 , ∞) [depends on if you need fractional or decimal format]

Answer:91.44  rounded is 91

Step-by-step explanation:

Answer:

2.12

Step-by-step explanation:

Discussion

The answer is given in the graph I've made for you. The distance you want is a contained in a line that is perpendicular to the given line and goes through (2,-1). If I have not interpreted this correctly please leave a comment under the question and I will edit it. I have ignored the 4.

The steps needed are

Givens

line y = -x + 4

point (2,-1)

Solution

The slope of the second line is

m1 * m2 = - 1

m1=  -1                From the given equation

m2 = ?

-1 * m2 = - 1

m2 = 1

Find the equation of the new line

x = 2

y = - 1 from the given point

-1 = 2 + b             Subtract 2 from both sides

-1 - 2 = 2-2 + b    Combine

-3 = b

Equation of the new line

y = x - 3

Intersection point of the two lines

y = -x + 4

y = x - 3              Add The xs cancel

2y = 1                  Divide by 2

y = 1/2

1/2 = -x + 4          Subtract 4 from both sides

1/2 - 4 = -x + 4 -4 Combine        

-3 1/2  = -x            Multiply both sides by - 1

3 1/2 = x

So the intersection point is (3.5, 0.5)

Find the distance between (2,-1) and (3.5,0.5)

d = sqrt( (2 - 3.5)^2 + (-1 - 0.5)^2 )

d = sqrt( (-1.5)^2 + (-1.5)^2 )

d = ( 1..5 * sqrt(2) )

d = 2.12

The correct value of the simplified expressions found using the laws of indices gives;

The laws of indices state rules that enable the simplification of the combination of expressions of numbers and variables that are given in index form or involve powers of other numbers or variables

1. [tex]3^{\frac{1}{4} } = \sqrt[4]{4}[/tex]

The radical sign is used for expressing fractional indices.

The correct option is d. [tex]\sqrt[4]{4}[/tex]

2. The radical is in its simplest form when it cannot be further simplified, which gives the radical in its simplest form as option a. [tex]\sqrt{\dfrac{5}{6} }[/tex]

3. The index of a number is the number to which the variable or number is raised

The index of x³ in [tex]\sqrt{x^3}[/tex] is d. 3

4. The given expression has y raised to the power of [tex]\frac{1}{2}[/tex], which gives;

[tex]x\cdot y^\frac{1}{2} = x\cdot \sqrt{y}[/tex]

The correct option is a. [tex]x\cdot \sqrt{y}[/tex]

5. The common index of the expression within the parenthesis is [tex]\frac{1}{2}[/tex], which gives;

[tex](x^4\cdot y^2)^\frac{1}{2} = (x^{4\times \frac{1}{2} }\cdot y^{2 \times \frac{1}{2} })=x^2\cdot y[/tex]

The correct option is b. x²·y

6. The value of all numbers raised the power of zero is 1, therefore;

[tex](2^{1/3}\cdot 3^{1/4})^0\cdot (2^{1/5}\cdot 3)^0 = 1 \times 1=1[/tex]

The correct option is b. 1

7. The given expression can be simplified as follows;

[tex]\sqrt[5]{\dfrac{1}{243} } = \sqrt[5]{\dfrac{1}{3^5} } = \sqrt[5]{\left(\dfrac{1}{3} \right)^5} = \dfrac{1}{3}[/tex]

The correct option is therefore; a. 1/3

8. The given expression [tex]\sqrt{225\cdot x^4\cdot y^8} = \sqrt{15^2\cdot x^4\cdot y^8} = 15\cdot x^2\cdot y^4[/tex]

The correct option is [tex]15\cdot x^2\cdot y^4[/tex]

9. The given expression is [tex]\sqrt[3]{216\cdot x^9\cdot y^{15}}[/tex]

[tex]\sqrt[3]{216\cdot x^9\cdot y^{15}} = \sqrt[3]{6^3\cdot x^9\cdot y^{15}} = 6\cdot x^3\cdot y^5[/tex]

The correct option is e. [tex]6\cdot x^3\cdot y^5[/tex]

10. [tex]\sqrt{\dfrac{50}{162} } = \sqrt{\dfrac{25\times 2}{81\times 2} } = \sqrt{\dfrac{25}{81} } = \dfrac{5}{9}[/tex]

The correct option is c. [tex]\frac{5}{9}[/tex]

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Answer:

Step-by-step explanation:

slope=change in y over change in x

6-2=4

6--2=6+2=8

-4/-8=1/2

Answer:

40

Step-by-step explanation:

Looking at the other examples, its shows the the second number is always 4 times bigger/ahead then/of the first number.

In the function f(2)= -5, 2 is the preimage of the function and 5 is an image of the function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

Suppose that f(a) = b

In that case, element "b" is the image of element "under the function," while element "a" is the preimage of element "under the function."

In the given function f(2)= -5

2 is the preimage of the function and 5 is an image of the function.

Hence, the 2 is the preimage of the function and 5 is an image of the function.

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The values of the interior angles, ( Angle A, Angle B and Angle C) of the triangles are 48°, 88° and 44° respectively.

Interior angle is the inner of the two angles formed where two sides of a polygon come together.

To find the measure of each interior angle of the triangle in the diagram, first, we need to find the value of x.

Recall that: The sum of the interior angles of a triangle is equal to 180°.

Using the formula,

From the triangle,

Substitute these values into equation 1

Solve for x

Therefore,

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Answer:

negative

Step-by-step explanation:

The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.

What is a standard deviation?

Data dispersion in regard to the mean is quantified by a standard deviation. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Here, we have

µ = 62 , σ = 5

P ( X < 66 )

By applying the standard deviation formula, we get

Z = ( X - µ ) / (σ/√(n)

Z = ( 66 - 62 ) / ( 5 / √50 )

Z = 5.6569

P (  ( X - µ ) / ( σ/√(n)) < ( 66 - 62 ) / ( 5 / √(50) )

P ( X < 66 ) =  P ( Z < 5.66 )

P ( X < 66 ) = 1

P ( X > 66 )  = 1 - P ( X < 66 )

By applying the standard deviation formula, we get

Z = ( X - µ ) / ( σ / √(n))

Z = ( 66 - 62 ) / ( 5 / √ ( 50 ) )

Z = 5.6569

P (  ( X - µ ) / ( σ / √ (n)) > ( 66 - 62 ) / ( 5 / √(50) )

P ( Z > 5.66 )

P ( X > 66 )  = 1 - P ( Z < 5.66 )

P ( X> 66 )  = 1 - 1

P ( X> 66 )  =  0

Hence, the probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.

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Answer: A. [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

To find the slope we must find the change in y over the change in x. Δ

Or rise over run.  [tex]\frac{rise}{run}[/tex]

In the graph, we have two "good" points. (0, -6) and (4,0)

So for Δy 0 to -6 = -6

So -6 goes on top  [tex]\frac{-6}{x}[/tex]

Now Δx goes from 4 to 0 so the change would be -4.

So now it becomes [tex]\frac{-6}{-4}[/tex]

Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]

The magnitude of earthquake on seismograph will be 3 .

What is seismograph?

A seismograph is a device that measures and records crucial data concerning earthquakes. Electromagnetic sensors in seismographs convert ground vibrations into electrical voltages. Seismograms are records that a seismograph generates and displays .

Main Body:

formula given : M = ㏒₁₀T           where T =1000

substituting the value of T in the formula

M = ㏒₁₀ 1000

M = ㏒₁₀10³

M = 3㏒₁₀           (㏒₁₀Xᵃ = a㏒₁₀)

M = 3                  (㏒₁₀10 =1)

Therefore the magnitude of the earthquake is 3.

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