Find the total surface area of this cuboid.
5 cm
4 cm
6 cml

Answer:

Given: QR = QS (by given)

We are to prove: LS = ZR

Proof:

Since QR = QS, by the SAS (Side-Angle-Side) congruence postulate, we know that triangle QRS is congruent to triangle QSZ (both have two equal sides and included angle).

By the AAS (Angle-Angle-Side) congruence postulate, we know that if two angles of one triangle are congruent to two angles of another triangle, and the included side is congruent, then the two triangles are congruent.

Therefore, by using AAS congruence, we can say that triangle QRS is congruent to triangle QSZ.

By the CPCTC (Corresponding parts of congruent triangles are congruent), we know that if two triangles are congruent, then their corresponding sides are congruent.

Therefore, LS is congruent to ZR.

Therefore, we have proved LS = ZR

Note: The above proof uses the properties of congruence of triangles, if the student is not familiar with this, it might be challenging for them.

Independent system of linear equations that do not rely on each other for the algebraic or graphic form of equations.

The collection of two or more linear equations involving the same variables is known as a system of linear equations. The number of orders in a system of linear equations can range from one to n.

If a consistent system only has one solution, it is regarded as independent.

Elimination or substitution are two algebraic methods for solving a system of linear equations. and was also graphically solved.

Hence Independent system of linear equations that do not rely on each other for the algebraic or graphic form of equations.

to more learn about click here.System of linear equations.

https://brainly.com/question/20379472

#SPJ4

From the given line equation, the closet point to the origin is (-6/5, 3/5).

Here we have given that the point on the line y=2x+3 that is closest to the origin.

As we all know that the closest point from origin will be the perpendicular distance from origin to the line.

Here we need to find an equation of the perpendicular from (0,0) on y = 2x + 3.

As we all know that the standard form of the equation is in slope-intercept form is written as,

=> y = mx + c

While we comparing this with the given equation, then we get the value of the Slope that is m = 2 and the Slope of the perpendicular is calculated as,

=> - (1/m) = -1/2

Now, we have to write the equation of the perpendicular is found by using the formula,

=> (y - y1) = m (x - x1)

Apply the value on the equation, then we get,

=> y - 0 = (-1/2) (x - 0)

=> y = (-1/2)x

therefore, the resulting perpendicular equation is written as,

=> 2y + x = 0 ----------------(2)

When we solving (1) and (2), then we get,

=> 5y = 3

Therefore, y = 3/5

And the value of x is calculated as

=> x + 2(3/5) = 0

=> x = -6/5

So the point on the line is (-6/5, 3/5).

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

Check the picture below.

so, let's notice the angle made by the hand from 2pm to 4:45pm, well, it goes around twice, 2 revolutiions, then it goes 270° more after that, and we know the "radius" is 10.5"

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =\stackrel{360+360+270}{990~\hfill }\\ r=10.5 \end{cases}\implies s=\cfrac{(990)\pi (10.5)}{180} \\\\\\ s=\cfrac{231\pi }{4}\implies s\approx 181.43~in[/tex]

The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.

The maximum deflection of the simply supported beam is given by:

Maximum deflection = (5PL^3)/(384EI)

where P is the load applied to the beam, L is the length of the beam, E is the Young's Modulus of the beam material, and I is the moment of inertia of the beam.

Substituting the given values into the equation, we get:

Maximum deflection = (5*P*L^3)/(384*200*10^9*39.9*10^6)

= (5*P*L^3)/(1536.3*10^15)

= (5*P*L^3)/1536.3*10^15 m

The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.

Learn more about maximum here

https://brainly.com/question/29156925

#SPJ4

2y - z + z^2 is an algebraic expression. It represents a mathematical operation that includes three different terms: 2y, -z and z^2. It can be simplified depending on the context and the values of y and z.

In the given expression, 2y is the coefficient of y, which is multiplied by y. -z is subtracted from 2y and z^2 is added to the result.

In order to simplify this equation, you could combine like terms, which means combining the same variable or powers of the same variable with each other.

This expression does not have any like terms, so it can't be simplified anymore.

It can be evaluated by replacing y and z with specific values and then performing the mathematical operations in the given order.

The length that needs to cover all 3 sides of both book ends will be √208 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Sylvie realizes the container will be 8 inches long and the level will be 12 inches.

Then the length is given as,

H² = 12² + 8²

H² = 144 + 64

H² = 208

H = √208 inches

Then the length that needs to cover all 3 sides of both book ends will be √208 inches.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ1

The velocity of the trainee is 94.2/m m/s and 0.15 x m rev/s.

The centripetal force (Fc) felt by the trainee can be calculated using the following equation:

Fc = mv2/r

Where m is the mass of the trainee, v is the velocity and r is the radius of the circle.

Therefore, the velocity (v) required to produce a centripetal force of 7.85 times the mass of the trainee can be calculated as follows:

v =√(Fc x r/m)

=√(7.85 x 12.0/m)

=√(94.2/m)

For a given mass, the velocity is therefore 94.2/m m/s.

Converting to revolutions per second (rev/s), the velocity can be calculated as follows:

v = (2πr)/T

= (2π x 12.0)/(94.2/m)

= (14.14 x m)/94.2

= 0.15 x m rev/s

Therefore, the velocity of the trainee is 94.2/m m/s and 0.15 x m rev/s.

Learn more about velocity here:

https://brainly.com/question/29253175

#SPJ4

By analyzing the given graph, we can see that the rate of change of the linear equation is 8.

A general linear equation can be written as:

y = a*x + b

Where a is the slope (also known as the rate of change, this is what we are looking for here) and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can see the points:

(1, 28) and (2, 36) and we can use these two to find the slope.

a = (36 - 28)/(2 - 1)

a = 8

So the slope (thus, the rate of change) is 8.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

Step-by-step explanation:

Volume of cuboid = AC x CD x CG. (Cuboid formula is l x b x h)

Now, given, area of ABCD is 25.

Area of square = a² or AC x CD

Therefore, substituting that in the first line, we get,

25 x CG = volume,

or 25 x 12 = 300 cm³. (Given CG is 12cm)

Step-by-step explanation:

Square the 3 first, which gives you 9 (use the 9 as the denominator), then do 2 X 1/9. Which leaves you with 2/9

The formula to compute the total weekly in cell H2 is H2=D2+G2

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

(a).By using formula we get;

Regular gross pay= Regular Hours x Hourly Rate

D2=B2*C2

(b) By using the formula we get;

Overtime Hours = Hours Worked -Regular Hours

E2=A2-B2

(c) By using the formula we get;

Time-and-a-half overtime

hourly rate = Hourly rate 1.5

F2=C2x1.5

(d) By using the formula we get;

Total overtime pay

=Overtime Hours x Overtime rate

G2=E2 x F2

(e) By using the formula we get;

Total weekly pay =  Regular pay + Overtime pay

H2=D2+G2

Therefore, the unitary answer will be H2=D2+G2

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ1

Answer:

15

Step-by-step explanation:

x + 2y

Putting x = 7, y = 4, we have

7 + 2(4)

= 7 + 8

= 15

Hope it helps.

If you have any query, feel free to ask.

Step-by-step explanation:

It's saying x = 7 and y = 4, which means everywhere there is an x, you'll place a 7 and everywhere there is a y, you'll place a 4

x + 2y turns into (7) + 2(4)

Now we can answer the bottom question

2(4) = 8

7 + 8 = 15

so...

If x =7 and y=4, then x+2y= 15

The total displacement of the car after 5hrs is 0km.

                s =sf– si

where, s = displacement.

In the given graph, there is the change in distance covered with the time that is:

Thus, the displacement will be 0 km as the final point and initial point are the same.

Read more about displacement:

https://brainly.com/question/28370322

#SPJ4

The expression describing how many songs are played by the radio station in H hours is 12H

The phrase used to describe how many songs the radio station plays in H hours is Number of songs = 12 xH

288 songs are played in a 24-hour period.

60 nonstop songs are played over the course of 5 hours.

Given

Every hour, a radio station plays 12 songs.

Compose an expression that indicates how many songs the radio station plays in H hours.

There are 12 songs performed throughout an hour.

Then,

Number of songs=  songs played in one-hour x songs played in H hour

Number of songs=12H

The expression describing how many songs are played by the radio station in H hours is 12H

The phrase used to describe how many songs the radio station plays in H hours is 12H

To know more about Equation

brainly.com/question/12895249

#SPJ4

Out of 400 band-aids, 200 were used yesterday. Therefore, the percentage of band-aids used yesterday is 50%.

You started with 4 boxes × 100 band-aids per box

= 400 band-aids.

You ended with 2 boxes × 100 band-aids per box

= 200 band-aids

So you used

400 band-aids - 200 band-aids = 200 band-aids yesterday.

To find the percentage of band-aids used, you can divide the number of band-aids used by the total number of band-aids you started with and multiply by 100:

= (200 band-aids / 400 band-aids) × 100

= (1/ 2) × 100

= 50%

Therefore, 50% of the band-aids were used yesterday.

To know more on percentage

https://brainly.com/question/29284499

#SPJ4

Answer:

720 Should be the answer I think.

The ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.

The amount of water, sucrose, and the saline solution used can be expressed as a ratio in its simplest form by finding the greatest common divisor (GCD) of the three quantities and dividing each by it.

1l of water = 1000 ml of water.

Let's find the GCD of the three quantities:

GCD(199,271,1000) = 1

So we can express the amount of water, sucrose, and saline solution needed as a ratio in its simplest form by dividing each of the three quantities by 1

Water : Sucrose : Saline solution = 1000 : 199/1 : 271/1 = 1000:199:271

Hence, the ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.

Read more about Ratio:

brainly.com/question/2914376

#SPJ4

Answer:

Step-by-step explanation:

Pull FG together, and assume FG is 11. HJ, must be the same as FG, so it is 11. Our answer is 121.

According to the given statement the area of shaded region is is 20 units squared.

As an outcome, an isosceles triangle has two equal sides as well as two equal angles. As from Greek words iso (same) and skelos, the phrase is formed (leg). Except for a right triangle, which has quadrilateral on all sides, a scalene triangle lacks equal sides on each side.

The slope of the line connecting the bottom right vertex of something like the triangle to the top left vertex of both the square is equal to -1/2.

This line's equation is y = (-1/2)x + 10. (1)

The point at the triangle's top vertex is (15, 10)

The slope of the segment between (10, 0) and (15, 10) is 10/5, which equals two.

The line connecting these two locations has the equation y = 2(x - 10) y = 2x - 20. (2)

You may get the x coordinate of the point where these lines cross by putting (1) = (2) 

(-1/2)x + 10 = 2x - 20 

30 = [5/2]. x x equals 12 and y equals 2(12) - 20 = 4.

Therefore, the triangle's shaded area's height is 4 and its base is 10.

Its area is therefore (1/2)(4)(10) = 20 units squared.

To know more about Isosceles triangle visit:

https://brainly.com/question/12479957

#SPJ4

Answer:d

Step-by-step explanation:

Therefore , area and capacity of volume values equal f2 f 2 and f3 f 3, respectively, if the curve is f, f, and also the rim step size is f, f.

When we enlarge a shape by a scale factor, we multiply the area of the shape by the square of the scale factor. When we enlarge a shape by a scale factor, we multiply the volume of the shape by the cube of the scale factor. The scale factor is the proportional relationship that exists between the sides of similar figures.

Here,

Similar geometric shapes' edges, areas, and volumes are also connected to the scale factor.

The peripheral scale factor is f, f if the curve is f, f, and the surface and volume ratios are f2 f 2 but also

f3, f 3, respectively, if the correction factor is f, f.

Therefore , area and capacity values equal f2 f 2 and f3 f 3, respectively, if the curve is f, f, and also the rim step size is f, f.

To know more about volume visit:-

brainly.com/question/1578538

#SPJ1

The wood fragment is 11,460 years old by C-14 dating if only 25% of the amount the tree had when it was alive is left.

The process of carbon-14 dating can be used to determine the age of an organic material such as wood. Carbon-14 is a radioactive isotope of carbon that is present in all living organisms. When an organism dies, the carbon-14 begins to decay at a known rate, and the amount of carbon-14 in the material decreases over time. By measuring the amount of carbon-14 remaining in a sample, it is possible to determine how long ago the organism died.

If the analysis shows that the C-14 has been reduced to 25% of the amount the tree had when it was alive, it means that 75% of C-14 has decayed, and the material is therefore 75% of its way through its radioactive decay.

Carbon-14 has a half-life of 5,730 years, which means that after 5,730 years, half of the carbon-14 in a sample will have decayed. To find the age of the wood fragment, you would need to multiply the sample's decay percentage (75%) by the material's half-life (5730 years) to get the number of years that have passed.

[tex]t = \frac{5730\ ln(0.25)}{-ln2}[/tex]

Where t is the number of years to decay to 25%.

t = 5730 × ( ln(4)/ ln(2))

t = 5730 × 2

t = 11,460

To know more on C-14 dating

https://brainly.com/question/16192875

#SPJ4

Answer:

1/1-mpc and 1-mps

Step-by-step explanation:

to get the multiplier effect you use the formula

M=1/1-MPC

Therefore , the solution of the given problem of pie chart comes out to be the amount he spent on living expenditures was $1634.5.

A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarize a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. Each segment stands for a specific category.

Here,

living expenses are 35% of the monthly budgeted income of $4670.

Next, we must utilize the rule of four:

4670 $ => 100%

x=> 35%

Clearing x:

=> x=(35/100)*(4670)

=> x=1634.5$

The amount he spent on living expenditures was $1634.5.

Therefore , the solution of the given problem of pie chart comes out to be the amount he spent on living expenditures was $1634.5.  

To know more about pie chart , visit

https://brainly.com/question/30145769

#SPJ1

Answer:

Step-by-step explanation:

Answer: 72 in = 182.88cm

Step-by-step explanation:

The measure of the angle subtended at the center of this circle is 78°.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know the angle subtended at the center of a circle is twice the measure of any angle subtended at any point of the circumference of the circle.

Given, The measure of the angle subtended at the circumference of this circle is 39°.

Therefore, The measure of the angle subtended at the center is,

= (2×39)°.

= 78°.

learn more about circles here :

https://brainly.com/question/29142813

#SPJ1