A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft. what is the period of simple harmonic motion?

The type of transformations that maps triangle ABC onto Triangle prime ABC is a  Reflection across the line y=x ; translation 10 units to the right and 4 units up.

Note that: Triangle ABC has vertices at points  which are:

A(-6,2), B(-2,6) and C(-4,2).

Therefore, the reflection across the line y=x has the rule of"

(x, y) ---(y, x).

Hence:

A(-6,2) -- A''(2,-6);

B(-2,6)--- B''(6,-2);

C(-4,2)----C''(2,-4).

2. The translation 10 units to the right and 4 units up is:

(x, y)----(x+10,y+4).

Hence

A''(2,-6)----A'(12,-2);

B''(6,-2)----B'(16,2);

C''(2,-4)----C'(12,0).

Therefore, Points A'B'C' are said to be exactly of the vertices of that of triangle A'B'C'.

Hence, The type of transformations that maps triangle ABC onto Triangle prime ABC is a  Reflection across the line y=x ; translation 10 units to the right and 4 units up.

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Answer:

Step-by-step explanation:

You answer

The equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]

The fraction is given as:

[tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex]

Take the LCM

[tex]\frac{y + 1}{y} \div \frac{y-1}y[/tex]

Express as products

[tex]\frac{y + 1}{y} \times \frac{y}{y-1}[/tex]

Evaluate the product

[tex]\frac{y + 1}{y-1}[/tex]

Hence, the equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]

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Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

No directions given here. What exactly do you need to be done with this trigonometric function?

Answer:

37.44 cm²

Step-by-step explanation:

To find the width, follow these steps.

10.4*2=20.8

28-20.8=7.2

7.2/2=3.6

The width is 3.6.

To find the area, multiply the width and the length together.

10.4*3.6=37.44

The area of the rectangle is 37.44 cm²

Hope this helps!

Answer:

In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .

Step-by-step explanation:

Answer:

53 degrees

Step-by-step explanation:

If the two lines intersected by a transversal are parallel then the same side interior angle should add up to 180 degrees.

180-127 = 53 degrees

Answer:

150 [tex]m^{2}[/tex]

Step-by-step explanation:

Consider the figure as an isosceles triangle and a rectangle combined.

ISOSCELES TRIANGLE

[tex]A = \frac{1}{2} bh[/tex]

[tex]A = \frac{1}{2} *15*12[/tex]

A = 90

RECTANGLE

[tex]A=lw[/tex]

[tex]A = 5*12[/tex]

[tex]A = 60[/tex]

60 + 90 = 150

Answer:

150m

Step-by-step explanation:

break up the polygon into a triangle and a rectangle.

Triangle:

to find the height of the triangle, subtract 5 from 20

height = 15m     base = 12m

[tex]area=\frac{1}{2}bh\\ A=\frac{1}{2} (12)(15)\\A=6(15)\\A=90m[/tex]

rectangle:

[tex]A=bh\\A=12(5)\\A=60m[/tex]

Add both areas together:

[tex]90+60=150m[/tex]

Answer: Isosceles Trapezoid

Step-by-step explanation:

See the graph of the quadrilateral.

Answer:

D

Step-by-step explanation:

Answer:

First, use the distributive property and distribute 8 to the [tex](x,2)[/tex] in the first part of the equation to get [tex]8x + 16[/tex].

Next, also use the distributive property to distribute the 4 to the [tex](2x+9)[/tex] in the second part of the equation to get [tex]8x+36[/tex].

The simplified equation looks like this: [tex]8x+16=8x+36[/tex].

The probability of not drawing a black marble is 4/5

The probability of drawing a red marble is 3/10

Probability determines the odds of the occurrence of a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of not drawing a black marble = total marbles that are not black / total number of marbles

(5 + 3) / (5 + 3 + 2) = 8/10 = 4/5

The probability of drawing a red marble = total number of red marbles / total number of marbles

= 3/10

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Answer:

See image

Step-by-step explanation:

Plato

The constant of proportionality is 2.5.

First, There is a proportional relationship

Two values x  and y are said to be in a proportional relationship if y=kx, where x and y are variables and k is a constant.

y = kx

The constant k is the constant of proportionality

As shown that ,

A 2-column table with 3 rows.

Column 1 is labeled x with entries 2, 4, and 5.

Column 2 is labeled y with entries 5, 10, and 12.5.

According to the Above statement, the calculation is as follows:

5/2 = 2.5 , here we get is 2.5

10/ 4 = 2.5 so Here we get 2.5 and so on

Hence, The constant of proportionality is 2.5.

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Considering the linear functions on the graph, the inequality that matches the situation is:

B.

A linear function is modeled by:

y = mx + b

In which:

The lower bound of the interval is a linear function with y-intercept of b = 2, that also passes through (2,3), hence the slope is:

m = (3 - 2)/(2 - 0) = 1/2.

Hence the inequality is:

[tex]y \geq \frac{1}{2}x + 2[/tex]

The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:

m = (5 - 1)/(2 - 0) = 2.

Hence the inequality is:

[tex]y \leq 2x + 1[/tex]

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The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7

7/11 = x/9

7 × 9 = 11 × x

63 = 11x

x = 63/11

x = 5.72727272727272

Approximately,

x = 5.7

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a) The variables are:

b)

x + y ≥ 12

x*$0.75 + y*$1.25 ≤ $15

a) First we need to define the variables, in this case we have:

b) Now we want to write the system, we know that he must buy at least 12 items, then:

x + y ≥ 12

And he can spend, at most, $15, then:

x*$0.75 + y*$1.25 ≤ $15

These two inequalities conform the system of inequalities:

x + y ≥ 12

x*$0.75 + y*$1.25 ≤ $15

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The side LO is congruent to the side MN, the diagonal LN is congruent to the diagonal MO, and the angle L is congruent to the angle M in an isosceles trapezoid, denoted by the symbols LMNO.

What are the conditions for an Isosceles Trapezoid?

The conditions listed below demonstrate that any trapezoid is an isosceles trapezoid:

When these conditions are met by the given trapezoid LMNO, it will be referred to as an isosceles trapezoid. Hence, the following conditions of trapezoid LMNO need to be fulfilled,

LN ≅ MO

LO ≅ MN

∠L ≅ ∠M

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✔ (A.) LN ≅ MO

✔ (C.) LO ≅ MN

✔ (E.) ∠L ≅ ∠M

Answer:

12

Step-by-step explanation:

Well they are similar I assume so 5 / 3.5 = roughly 1.43 and 8.4 x this number gives you 12 so I would say 12

Answer:

y = 27

Step-by-step explanation:

The given are two similar triangles.

We can use the following equation to find the variables:

[tex]\frac{y-3}{32} = \frac{18}{24}[/tex]

Cross multiply fractions

32*18 = 24(y-3)

576 = 24y - 72

add 72 to both sides

648 = 24y

divide both sides by 24

27 = y

The smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5

The given number is 29160

Note that:

29160 can be factored into 5832

That is, 29160 = 5832 x 5

Take the cube of 5832:

[tex]\sqrt[3]{5832}=18[/tex]

Since it has been confirmed that 5832 is a perfect cube, the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5

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F is located on the number 4.5 on the number line.

We know that point D is at -6

Point E is at 8.

Point F is between D and E, such that the ratio:

DF:FE is 3:1

So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.

First, the distance between E and D is:

distance = 8 - (-6) = 14 units.

Now, if we divide that by 4, we get:

14/4 = 3.5

Then we have:

DF = 3*(3.5) = 10.5

This means that F is at 10.5 units to the right of D, then:

F = D + 10.5 = -6 + 10.5 = 4.5

F is located on the number 4.5 on the number line.

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Answer:

4.5 is the answer :D

Step-by-step explanation:

The y-value of the terminal point of the vector is 3.

In this question we must apply a matricial form of rotation, which is a kind of rigid transformation. This transformation is defined by the following formula:

[tex]\vec A' = \vec T\cdot \vec A[/tex], where [tex]\vec A' , \vec A \in \mathbb{R}_{1 \times 2}[/tex], [tex]\vec T \in \mathbb{R}_{2 \times 2}[/tex]

If we knw that [tex]\vec A = \left[\begin{array}{c}- 4\\3\end{array}\right][/tex] and [tex]\vec T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], then the transformed vector column is:

[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}-4\\3\end{array}\right][/tex]

[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}4\\3\end{array}\right][/tex]

The y-value of the terminal point of the vector is 3.

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The correct statement comparing the theoretical and experimental probabilities is given as follows:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:

T(H) = 1/4.

The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:

E(H) = 28/100 = 7/25.

Hence the correct statement is:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

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Answer:

D. continuous

The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.

First, we will find the equations showing the level of mercury in each body of water.

For the first water body:

Initial measure of mercury = 0.05 ppb.

Rate of rising = 0.1 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.05 + 0.1y.

For the second water body:

Initial measure of mercury = 0.12 ppb.

Rate of rising = 0.06 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.12 + 0.06y.

We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.

As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:

0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.

Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

The measure of angle 3 from the figure is 110 degrees

An angle is the intersection between two lines. From the given figure, we have the following parameters

m∠1= 40°,

m∠2= 70°.

Required

Measure of angle 3

The sum of the interior angles of the triangle is equal to the exterior

Sum of interior = <1 + <2

Sum of interior = 40 + 70

Sum of interior =110 degrees

Hence the measure of angle 3 from the figure is 110 degrees

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Step-by-step explanation:

the equation in the standard form is :

( x - 2 ) 2+ ( Y + 3 ) 2 = 18

the center is at the point ( 2, - 3 ).

its radious is : /18 = 3/ 2 units

The length of the side QR in the task content can be determined as; 12.22cm.

It follows from the task content that 2 lengths and one included angle are given in the task content. It therefore follows that the length of side QR can be evaluated by the cosine rule as follows;

QR² = 13² + 4² - (2×4×13×cos70)

QR = √149.4

QR = 12.22cm

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By definition of surface area, the composite figure reports an area of 233.6 square centimeters.

In this question we need to determine the surface area of a composite figure, which is the sum of all the areas of the faces, which are combinations of triangles and quadrilaterals. Now we proceed to calculate the surface area:

A = 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (3.6 cm) + 2 · (8 cm) · (2 cm) + 4 · (1/2) · (3 cm) · (2 cm)

A = 233.6 cm²

By definition of surface area, the composite figure reports an area of 233.6 square centimeters.

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