1. A crystal is cut into a shape formed by two square pyramids joined at the base. Each pyramid has a base
edge length of 5.7 mm and a height of 3 mm. What is the volume of the crystal to the nearest cubic
millimeter?

Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m=3, b=-7

How to write the equation in slope-intercept form?

Given:

m=3(slope)

b=-7(y -intercept)

The slope-intercept form is given by,

y=mx+b

y=3x-7

Thus, y=3x-7 is the slope-intercept form.

How to rewrite the equation in standard form?

Standard form is given by,

Ax+By=C

Since, slope-intercept form is y=3x-7

⇒3x-y=7

Thus,3x-y = 7  is the standard form.

To learn more about slope, refer:

brainly.com/question/16949303

#SPJ4

If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.

a.  0scar sits between Morgan and Phil

First step is to calculate the total distance

Total distance=2 feet+4 feet+3 feet

Total distance=9 feet

Since Morgan is 2 feet from Phil.

Hence,

P(Oscar sits between Morgan and Phil)=2/9

b. Oscar sits between Phil and Tyreese.

First step is to calculate the  distance between Phil and Tyreese

Distance= 4 feet + 3 feet

Distance =7 feet

Hence,

P(Oscar sits between Phil and Tyreese)=7/9

Therefore If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.

Learn more about probability here:https://brainly.com/question/24756209

#SPJ1

The complete question is:

Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.

a. Find the probability that 0scar sits between Morgan and Phil.

b. Find the probability that Oscar sits between Phil and Tyreese.

Answer:

2 laps

Step-by-step explanation:

The equation for circumference of a circle is 2πr.

We can use this equation to find how many ft are in a lap, then determine with the circumference how many laps need to be completed.

This is simple algebra

2πr

2π(50)

2(3.14)(50)

314.

One lap is 314 feet, so Sammy needs to walk 2 laps.

Answer: 2 laps

Step-by-step explanation:

Length of a circular path is 2πR (R=50ft)

Length of a circular path is:

2*3.14*50=

314 ft

628:314=

2 laps

Answer:5

Step-by-step explanation:

Answer:

(5,15)

Step-by-step explanation:

we know that c=12 is 5 so your answer is 5,15

Answer:  x-axis

Explanation:

The point (2,3) moves to (2, -3)

The x coordinate stays the same, but the y coordinate flipped from positive to negative. Therefore, the rule used is [tex](\text{x},\text{y}) \to (\text{x}, -\text{y})[/tex] which is a reflection over the horizontal x axis.

   The simplified value of the given expression is √6√8 / 3.

  Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

  As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.

(√6 / √3) (√8 / √3) we have a common denominator.

√6 √8/(√3)²

√6√8 / 3 is the result.

Learn more about rationalization in:

https://brainly.com/question/14261303

#SPJ4

Answer:5/25,25, 0.3

Step-by-step explanation:

Answer:

5/25 , 25% , 0.3

Step-by-step explanation:

first let's change everything into decimals

0.3 is already a decimal

25% can be changed into 0.25

5/25 can be changed into a percentage first like 25%

so:

[tex]\frac{5}{25}[/tex] × [tex]\frac{4}{4}[/tex] (you multiply both sides by 4 because you need to have the denominator as a 100 and 25 x 4 = 100)

[tex]\frac{5}{25}[/tex] × [tex]\frac{4}{4}[/tex]  = [tex]\frac{20}{100}[/tex]

this means that the percentage is 20% now lets change that into a decimal like we did with 25% earlier:

20% = 0.20

we can then order everything from least to greatest:

0.20 , 0.25 , 0.3

or

5/25 , 25% , 0.3

Answer:

Use the formula L(x)=f(a)+f'(a)(x−a) to find the linearization.

L(x)=2

Step-by-step explanation:

The possible dimensions ( width and length) plot of land are 9.5 m and 19 m.

A rectangle is a confined two-dimensional structure with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel.

Area of a rectangle

area of rectangle = l×w

where, l = length and w = width.

Thus, the perimeter for 2 side of width and 1 side of length is;

perimeter = 2w+ l

Perimeter of river = 38 m.

38 = 2w + l

l = 38  - 2w

Hence, Put the value of l in the area.

area = w(38 - 2w)

The area of the land is 140 sq.m.

140 = 38w - 2w²

-2w² + 38w - 140 = 0

-w² + 19w - 70 = 0

The equation is in the form of quadratic. Thus use the relation of coefficients and the roots to evaluate the width.

w = - b / a

Comparing the coefficients;

where,

a = -1

b = 19

w = - 19 / 2( -1)

w = 9.5 meters

Then,

l = 38  - 2w

l = 38 - 2(9.5)

l = 19 meters

Therefore, the dimensions of the plot of land are 9.5 meters and 19 meters.

To know more about the rectangle, here

https://brainly.com/question/25292087

#SPJ9

Answer:

f(- 2) = 14

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3(- 2)² + 2 = 3(4) + 2 = 12 + 2 = 14

Answer: yes it is a solution

After solving the equation, x < -3 is the value of inequality 2-3 x<11

⇒ 2-3x < 11

⇒ -3x < 11 - 2

⇒ -3x < 9

⇒ x < -9/3

⇒ x < -3

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

Answer:

a+b= (-1)

Step-by-step explanation:

4+(-5)=

4-5= (-1)

Answer:

-1

Step-by-step explanation:

a = 4

b = -5

4 + -5 = -1 ( +- turns to -)

Answer:

84 Meters^3

Step-by-step explanation:

Since this is a three dimensional object, you need to have an exponent of 3

Answer:

Step-by-step explanation: 10=-9-x > add 9 to 10 > 19=-x> divide 19 by -x> x=-19

Answer:

Step-by-step explanation:

Point slope form:

y - y1 = m(x-x1)

y - 6 = 2(x + 2)

y - 6 = 2x + 4

y = 2x +10

The values for the variables 'x' and 'y' are (3,7).

According to the question, to calculate the value of 'x' and 'y' then equate both the equations.

The given expressions are:

Equation (1): x + (1/7)y = 4 ⇒ 7x + y = 28

Equation (2): y = 3x - 2

Solving equation (1) and equation (2) by substituting the value of the 'y':

Therefore, 7x + 3x - 2 = 28 ⇒ 10x = 30 ⇒ x = 3

Now: y = 3(3) - 2 = 7

Hence, the values are: x = 3 and y = 7.

What is simplification?

Simplification of an expression can be defined as by making the complicated expression as less complicated. And through this method, it become easy to solve it and find the correct answer.

To learn more about the simplification from the given link:

https://brainly.com/question/15361818

#SPJ9

The sum of the given finite series is 100

The summation notation tells us how to sum each term in a series.

Example:

             [tex]\sum\limits^5_{n=1} {3n+1}[/tex]

means we need to evaluate the sum of (3n+1) as n moves from 1 to 5.  Here 1 is the lower limit, while 5 is the upper limit.

The given series is:

            [tex]\sum\limits^4_{n=1} {n^{3}}[/tex]

Expand this series:

          [tex]\sum\limits^4_{n=1} {n^{3}}=1^{3}+2^{3}+3^{3}+4^{3}[/tex]

1³ = 1

2³ = 8

3³ = 27

4³ = 64

Hence,

1³ + 2³ + 3³ + 4³ = 1 + 8 + 27 + 64 = 100

Learn more about finite series here:

https://brainly.com/question/24232600

#SPJ4

In the sample that is used number of viruses were 6000 times greater than the number of protozoa.

Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population.

Given the number of protozoa in the sample as 5 × 10⁵ and the number of viruses in the sample as 3x10⁹.

This is represented in the scientific notation.

To calculate the number of times the viruses in the sample is more than the protozoa in the sample we divide the amount of virus by the amount of protozoa.

∴ (3x10⁹) ÷ (5 × 10⁵)

= 6000

Therefore in the sample that is used number of viruses were 6000 times greater than the number of protozoa.

To learn more about sample visit:

https://brainly.com/question/13287171

#SPJ9

Answer:

x-int: (-12/9, 0)

y-int: (0, 6)

Step-by-step explanation:

x-int ==> on x-axis when y=0

y-int ==> on y-axis when x=0

9/4x -1/2y = -3

x-int: 9/4x -1/2(0) = -3

9/4x = -3

9x/4 = -3

9x*4/4=-3*4

9x=-12

x=-12/9 ==> x-int: (-12/9, 0)

y-int: 9/4(0) -1/2y = -3

-1/2y = -3

1/2y=3

y/2=3

y=6 ==> y-int: (0, 6)

The required value of y is 10.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx,       —-- 1

Now, find k for given x = 15 and y = 25, we need to put these values in equation 1, i.e.

25 = k(15)

k = 25 / 15

k = 5 / 3

Further calculate y for given x = 6 and constant of proportion = 5/3 i.e.

y = (6)(5 / 3)

y = 10

Hence, the required value of y is 10.

To learn more about the constant of proportion, visit the link:

https://brainly.com/question/24868934

#SPJ4

Answer:

(10 *sin(81))/sin(34)=17.66>>>17.7

Distance between the points [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex] is [tex]a[/tex]. (Option D)

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by [tex]d= \sqrt{(x^{2}-x) ^{2}+(y^{2}-y) ^{2} }[/tex]. This formula is used to find the distance between any two points on a coordinate plane or x-y plane. This formula is called distance formula.

Let A= [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and B= [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex].

Putting values in above formula:

AB=[tex]\sqrt{a^{2}[cos(0+\frac{\pi }{3})-cos(0+\frac{2\pi }{3})]^{2}+a^{2}[sin(0+\frac{\pi }{3})-sin(0+\frac{2\pi }{3})]^{2} }[/tex]

AB= [tex]a\sqrt{cos^{2}(0+\frac{\pi }{3})+sin^{2}(0+\frac{\pi }{3})+cos^{2}(0+\frac{2\pi }{3})+sin^{2}(0+\frac{2\pi }{3})}[/tex]

AB= [tex]a\sqrt{cos(0+\frac{\pi }{3})cos(0+\frac{2\pi }{3})sin(0+\frac{\pi }{3})sin(0+\frac{2\pi }{3})}[/tex]

AB=[tex]a\sqrt{1+1-2cos(0+\frac{2\pi }{3}-0-\frac{\pi }{3}) }[/tex]

AB= [tex]a\sqrt{2-2cos\frac{\pi }{3} }[/tex]

AB= [tex]a\sqrt{2-2\frac{1}{2} }[/tex]

AB= [tex]a\sqrt{2-1} =a[/tex]

Hence, the distance between the two given points is [tex]a[/tex].

To learn more about distance between two points, visit: https://brainly.com/question/24485622

#SPJ9

Answer:

Let y = length of side parallel to the side with no fence

x = length of each of the other two sides

Then, y+2x = 64. So, y = 64-2x

Area = A = xy = x(64-2x)

The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).

By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.

So, the area is maximized when x = 16 ft

y = 64 - 2x = 32 ft

Maximum area = xy = (16)(32) = 512 ft2

To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.