How can the triangles be proven similar by the SSS similarity theorem?

The shear and moment throughout the beam as functions of x are V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft and V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft

The ability to construct shear force diagrams (SFD) and bending moment diagrams (BMD) is essential for any student studying statics, mechanics of materials, or structural engineering. Both a long and a short route can be used to complete them. The extended method is more thorough and yields formulas for the internal shear and internal bending moments in beams in terms of x: V(x) and M(x), respectively. In introductory statics classes, this is typically the approach required to demonstrate understanding of the situation. The rapid method eliminates the need for calculations in terms of x and instead employs a more visual method that you may use to highlight the crucial areas on the diagrams before simply connecting the dots.

How to solve?

For 0 ≤ x ≤ 6 ft,

∑ Fy = 0

30 - 2 x - V = 0

V = ( 30 - 2x ) kip

∑M = 0

M + 216 + 2 x ( x / 2 ) - 30 x = 0

M = ( - x² + 30 x - 216 ) kip ft

For 6 ≤ x ≤ 10 ft,

∑ Fy = 0

V - 8 = 0

V = 8 kip

∑ M = 0- M - 8 ( 10 - x ) - 40 = 0

M = ( 8 x - 120 ) kip ft

the shear and moment throughout the beam as functions of x are :

V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft

V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft

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Answer:

Below

Step-by-step explanation:

acceleration =  Δv /  Δt =  - 5/6   m/s^2  

                     ( negative sign shows it to be a deceleration)

F = ma

 =  30 ( -5/6)  = -25 N      or 25 N in the direction opposite of the velocity ( like a frictional force)

the Total deposit will be $935.2.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Luna Brennan's is depositing $320 in currency, currency, $1.55 In coins, a check for $213.40, and a check for $400.25.

So Total deposite will be $320+$1.55+ $213.40+$400.25 = $935.2

Hence the Total deposit will be $935.2

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Apple pies are $5 and pumpkin pies are $15

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

5a+12p=205............(1)

2a+1p=25.................(2)

Now, Multiply (2) by -12 to get

-24a-12p=-300

and, 5a+12p=205

-24a-12p=-300

Adding above Equations together

-19a=-95

a= 5

and, 2(5)+p=25

10+p=25

p=15

Hence, Apple pies are $5 and pumpkin pies are $15

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Answer:

[tex](6,1)[/tex]

Step-by-step explanation:

When reflecting over [tex]y=x[/tex], [tex](x,y) \longrightarrow (y, x)[/tex].

Answer:

1, 2, and 3

Step-by-step explanation:

5% = 0.05 = 1/20

The first expression is equal, as 5% is equal to 1/20.

The second expression is equal, as 5% in decimal form is 0.05.

The third expression is equal, as 5% is 5/100 in fraction form, which can be simplified to 1/20.

The fourth expression is NOT equal, as it is 20%, not 5%. 1/5 = 0.2.

The fifth expression is NOT equal becauase 0.5 is one half (1/2), which is not equal to 0.05.

Answer:

x = 3

Step-by-step explanation:

First, distribute the 3.

3(x - 5) + 2x = 0

3x - 15 + 2x = 0

Next, combine the x's.

(3x + 2x) - 15 = 0

5x - 15 = 0

Then, add 15 to both sides.

5x = 15

Finally, divide by  5 on both sides.

x = 3

The results most probably be invalid because the subjects were voluntary sample.

What is sample in statistics?

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The function that represents the cost of David's bike rental plan, B(t) is C. B(t) = 0.6t + 5

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, David pays a flat rate of $5 and and extra $0.6 per day to rent his bike. The cost of David's bike rental plan, B(t). Let the extra day be illustrated by t.

This will be:

B(t) = 5 + (0.6 × t)

B(t) = 5 + 0.6t

The correct option is C.

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Complete question

David pays a flat rate of $5 and and extra $0.6 per day to rent his bike. The cost of David's bike rental plan, B(t), can be represented by which of the following functions?

A. B(t) = 5(0,6)^t

B. B(t) = 5(1 + 0.6)^t

C. B(t) = 0.6t + 5

D. B(t) = -0.6t + 5

Answer:

y=-2x+10

Step-by-step explanation:

Just use the formula y=mx+b and replace the letters with the numbers.

Answer: y = -2x + 10

Step-by-step explanation:

y = mx + b

m = -2

b = 10

x = unknown number

y = m(-2)x + b( 10)

The outcome is Reject H0 and make a Type 1 error

What is H0?

When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H0.

Here type 1 error is defined as Rejecting H0 when H0 is true.

Therefore, the outcome is Reject H0 and make a Type 1 error.

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1.42 is the base of the equation and equation [tex]y = 51 (1.42)^t[/tex] represents the exponential function

An exponential function is a function which can be defined as f(x) = aˣ, Where 'x' is a variable and 'a' is a constant.

The given equation is,

[tex]y = 51 (1.42)^t[/tex]

The given function is in exponential power of t.

Since, the 1.42 is the base of the given function

And equation [tex]y = 51 (1.42)^t[/tex] represents the exponential function.

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To determine whether the mean weight of two distinct turtle species is equal. It would take too much time and money to weigh each turtle because there are thousands of them in each group.

A two-sample t-test is used to determine whether or not genuine population means are equal.

The accompanying null hypothesis is usually used in a two-sample t-test:

[tex]H_0[/tex]: The two population averages are equivalent when 1 = 2.

The alternative hypothesis might have two tails, a left or right tail, or none at all:

Two-tailed [tex]H_1[/tex]: μ1 ≠ μ2 Neither of the two population means is equal.

(Left-tailed) [tex]H_1[/tex]: Population 1 mean is lower than population 2 mean by a factor of 1.

[tex]H_1[/tex] (right-tailed): Populations 1 and 2 have mean values that are higher than each other.

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Answer:1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

7/10-x+3/2=6/5

7/10-x=6/5-3/2

7/10-x=-3/10

-x=-10/10

x=1

[tex]\cfrac{7}{10}-x+\cfrac{3}{2}=\cfrac{6}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{7}{10}-x+\cfrac{3}{2} \right)=10\left( \cfrac{6}{5} \right)}\implies 7-10x+15=12 \\\\\\ 22-10x=12\implies 22=10x+12\implies 10=10x\implies \cfrac{10}{10}=x\implies 1=x[/tex]

Answer:

Step-by-step explanation:

Answer: $4/sandwich

The unknown value that has the solution as c = 4 of the given algebraic equation is; 2

The given algebraic expression for which we want to input a value and solve is given as; 5(2c − ?) =2(c + 11)

Now, we want to find the unknown value that has the solution as c = 4. Thus, we will plug in 4 for c into the given equation to get;

5(2(4) − ?) =2((4) + 11)

5(8 − ?) = 30

divide both sides by 5 to get;

(8 − ?) = 6

Add -6 + ? to both sides to get;

8 − ?  - 6 + ? = 6 - 6 + ?

? = 2

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Complete question is;

Complete the equation so that it has the solution c = 4.

5(2c − ?) =2(c+11)

Answer

Step-by-step explanation:

The one which uses Sir Ronald Fisher's F-distribution for the test statistic is to compare several population means simultaneously.

The F-distribution was developed by Sir Ronald Fisher to study the behavior of two variances from random samples taken from two independent normal populations. The F-distribution allows us to use a F statistic to compare two populations.

The F-distribution is also known as a right-skewed distribution used commonly in another statistical test called an Analysis of Variance (ANOVA). For ANOVA tests we can use the F-distribution to check whether the variance among the means of two populations significantly differ. The F-distribution can also be used in regression analysis to compare the fit of different models.

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The average of the new list of 4 numbers is 94.

If the average of the original list of 4 numbers is 90, then the sum of these 4 numbers is:

4 x 90 = 360

If the 4th number in the original list is 80, then the sum of the first 3 numbers in the original list is:

360 - 80 = 280

If the first 3 numbers in the new list are the same as in the original list then the sum of these new first 3 numbers is also:

280

If the 4th number in the new list is 96 then the sum of the 4 numbers in the new list is:

280 + 96 = 376

Therefore, the average of the new list of 4 numbers is:

376 / 4 = 94

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The triangle is an Equilateral triangle.

What is an equilateral triangle?

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In an equilateral triangle, all three angles are 60 degrees.

Angle bisector means a bisector which divides an angle into two equal parts. A perpendicular bisector is a line which makes 90 degrees with the base and divides it into two equal parts.

In the case of an equilateral triangle, the angle bisector of each angle of a triangle and the perpendicular bisector of the opposite side is the same.

Hence the answer is an equilateral triangle.

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The number of shirts to be left for folding is 7 and the equation is F+N=22.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Boris has 22 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating N to F.

The equation will be written as,

N + F = 22

N + 15 = 22

N = 22 - 15

N = 7

Therefore, the number of shirts to be left for folding is 7 and the equation is F+N=22.

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The total standard time required to processed for one hundred units as per given setup and run time is equal to 1120minutes.

As given in the question,

Number of units to be processed = One hundred units

Conversion used:

1 hour = 60 minutes

Time required for setup = 2 hours

                                        = 2 ( 60) minutes)

                                        = 120 minutes

Run time per piece = 10 minutes

⇒ Run time required for 100 units = 100 × 10

                                                        = 1000 minutes

Total standard time for 100 units is equal to

= Run time for 100 units + set time

= 1000 + 120

= 1120 minutes

Therefore, the total standard time required to processed 100 units is equal to 1120 minutes.

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Answer:

A. Linear

B. Non-linear

C. Linear

Step-by-step explanation:

A linear line has a consistent slope either going down (negative) or going up (positive.)

A. The x values are increasing by a constant rate of 1, and the y values are decreasing at a constant rate of 1. Therefore it is a linear relation.

B. The x values are increasing by a constant rate of 1, but the y-value repeats itself twice in the second and third column. Therefore it does not have a consistent slope and is not a linear relation.

C. The x values are increasing by a constant rate of 1, and the y- values increase by a constant rate of 2 except in column 4 making it a non-linear relation.

Answer:

x=1, y=-3

Step-by-step explanation:

We first see there is a 3y in both equations. We can completely eliminate the y term by subtracting the equations.[tex](4x+3y=-5)-(-x+3y=-10)[/tex]. This gives us (4x--x)=(-5--10), which is 5x = 5. So, x = 1.

Now we can plug this value in to solve for y. Let's plug it in to [tex]-x+3y=-10[/tex]. We get [tex]-1 + 3y=-10[/tex], so 3y = -9 and y = -3. Hope this helps!

The phrase "given that they completed the homework" indicates that we're only looking at the students who completed the homework.  We're ignoring those students who didn't complete the homework.

Of the 19 students who completed the homework, 16 of those passed the test.

This gives us the fraction 16/19 which is about 0.842105263157895 or about 84.2%.

That's your probability that a student passed the test given that they completed the homework.

Answer:

140 degrees

Step-by-step explanation:

first we have to find x by setting these 2 angles equal to each other

x+28=2x+16

-x.       -x

28=x+16

-16.    -16

12=x

Now we need to find the x+28 angle

12+28

40

And since PTR is next to it we subtract 180 from this

180-40

140 degrees

Hopes this helps

1. Simplified Solution: [tex]a^9[/tex]

2. Simplified Solution: [tex]x^1^0[/tex]

3. Simplified Solution: [tex]1024a^1^0b^1^5[/tex]

4. Simplified Solution: [tex]x^2[/tex]

5. Simplified Solution: [tex]\frac{1}{x^3}[/tex]

6. Simplified Solution: [tex]1[/tex]

7. Simplified Solution: [tex]\frac{4a^6}{b^8}[/tex]

8. Simplified Solution: [tex]32768x^1^0[/tex]

9. Simplified Solution: [tex]\frac{1}{x^1^2y^2^1}[/tex]

10. Simplified Solution: [tex]x^1^4y^1^1[/tex]

11. Simplified Solution: [tex]-\frac{3}{x^4}[/tex]

12. Simplified Solution: [tex]\frac{xy^1^1}{4}[/tex]

13. Simplified Solution: [tex]x^7[/tex]

14. Simplified Solution: [tex]xy^2[/tex]

15. Simplified Solution: [tex]1[/tex]

16. Simplified Solution: [tex]\frac{1}{1000x^1^5y^9}[/tex]

17. Simplified Solution: [tex]\frac{y^3}{x^2}[/tex]

18. Simplified Solution: [tex]\frac{1}{16x^4y^1^0}[/tex]

19. Simplified Solution: [tex]\frac{xy^2}{3}[/tex]

20. Simplified Solution: [tex]-\frac{y^1^2}{9x^4}[/tex]

21.Simplified Solution: [tex]3x^2y^2[/tex]

____________________________________________________

Hope this helps! And good luck! :D

Answer:

Below

Step-by-step explanation:

Expand the parentheses to get

1/5 b   - 2a + 1/2 b     + 4a          gather like terms to get

2a  + 7/10  b

If Greg is at work for 10 hours a week, he spends 30 hours traveling to work.

Explanation

No of hours he works in a week = 10

No of hours he spends on travelling = 3 * no of hours he works in a week

=10 x 3 =

30 hours

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.

The repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

In addition to addition, subtraction, and division, multiplication is a mathematical operation. The four fundamental arithmetic operations are taught to students in their primary classes.

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