Solve:(6x^2+5x+1)÷(x+2)​

The obtained stress which is acting from every direction is at 45 degree.

The transformation equations will be used to calculate the stresses acting on an inclined element.

(σ x+σ y )/2  =75 MPa

(σ x-σ y )/2  =35 MPa

Tor xy = 28 MPa

sin 2θ = sin 90° = 1          

cos 2θ = cos 90° = 0

Substituting these values into Eqs

σ x1 =(σ x+σ y )/2+ (σ x-σ y )/2 cos2θ+ τxy sin2θ      

= 130 MPa

τ x 1 y 1 =  (σ x-σ y )/sin2θ + τxy cos2θ

σ y 1=  (σ x+σ y )/2- (σ x-σ y )/cos2θ+ τxy sin2θ    

= 47Mpa

Elements of stress

We can easily obtain the stresses acting on all sides of an element oriented at = 45° from these results.

The arrows indicate the true directions of the stresses. Take special note of the shear stress directions, which all have the same magnitude. Also, keep in mind that the sum of the normal stresses remains constant at 150 MPa.

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Answer:

1

Step-by-step explanation:

The points go rise:1 up:1 so the slope is 1.

Answer:

hey!! we can taIk here

Step-by-step explanation:

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Step-by-step explanation:

Easier to just realize that the largest area will be a square

 three sides of which will sum to 600 ft    ( yes, a square is a rectangle)

     600 / 3 =   200 ft per side

  area is then 200 x 200 = 40 000 ft^2

Answer:

2.5

Step-by-step explanation:

for example, if you take two of the value of x's -- 5/2, it equals 2.5

2 x 2.5 = 5

Answer:

2nd and 3rd options are correct

Step-by-step explanation:

the altitude (height) slips the main triangle into 2 snake triangular that are both similar to the original main triangle.

since R is the original right angle, T must be the right angle for the similar triangles and therefore in the middle of the vertex triple, as R is in the middle of vertex triple of the main triangle.

triangle SRQ ~ triangle RTQ

triangle SRQ ~ triangle RTS

it is confusing as the problem description phrased it as if there is only one correct answer. but there are 2.

The value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

The value of angle x and angle y is calculated by applying principle of angles formed by parallel lines as follows;

The value of angle adjacent x = 102⁰

The value of angle x   is calculated as;

x = 180 - 102 ( sum of angles on a straight line)

x = 78⁰

The value of angle y is calculated as follows;

y = 115⁰ (corresponding angles are equal)

Thus, the value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

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Answer:

\(6\sqrt{3}\)

Step-by-step explanation:

because of the 90-60-30 theorem

which \(6*\sqrt{3}=6\sqrt{3}\)

a) The coefficients are the costs of the respective shirts.

b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)

c) 3 solutions are:

(0, 25), (30, 0), (25, 4)

Here we know that:

And we have the linear equation:

10x + 12y = 300

The first coefficient is the one in the term "10x"

The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.

The second coefficient is on the term "12y"

And 12 means the cost in dollars of each long-sleeved shirt.

b) The graph of the linear equation can be seen on the image at the end.

The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.

The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.

c) 3 possible solutions can be seen on the graph, some examples are:

(0, 25), (30, 0), (25, 4)

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Answer: 100

Step-by-step explanation:

2(4x7)+2(4x2)+2(7x2)=?

2(28)+2(8)+2(14)=?

56+16+28=100

Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

Width=10 ft

Lenth=14 ft

Explanation

Step 1

Let

length(L)

Width(W)

The length of a rectangle is six feet less than twice the width,it is

Also, the perimeter of the rectangle is 48,the perimeter is given by:

Step 2

using equation (1) and (2), find L and W

a)

replace equation (1) in equation (2)

b) replace the value fo W in equation (1) to find L

I hope this helps you

Answer: y= 1.75$ x= .75 *x

Answer:

y= 1.75$ x= .75 *x

Step-by-step explanation:

Your welcome

The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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Answer:

8 and 7

Step-by-step explanation:

8 -7 = 1

8*7 = 56

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

y=-8x+4/5

Step-by-step explanation:

the formula for slope intercept is y=mx+b so you just plug in the numbers. m is slope and b is the y intercept

sorry if this is wrong :)

Answer:

The answer will be listed below!

Step-by-step explanation:

The equation would be y=-8x+4/5. Slope intercept form is y=mx+b. m would be the slope while b is the y-intercept so in the end, you get y=-8x+4/5.

Answer:

−6 x + 4

Step-by-step explanation:

Hence the product of the functions in standard form is - 16x² + 38x - 21

Given the functions

f(x) = 2x - 3

g(x) = 7 - 8x

The product of the functions is expressed as

f(x) g(x) = (2x - 3)(7 -8x)

f(x) g(x) = 14x - 16x² - 21 + 24x

Rearrange in standard form

f(x) g(x) = -16x² + 24x + 14x - 21

f(x) g(x) = -16x² + 38x - 21

Hence the product of the functions in standard form is - 16x² + 38x - 21

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In quarter 2 revenue of east is  €32 million and revenue of west is  €88 million using substitution method.

Substitution method:

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

For example -

x +y = 2 , x = 2-y

3x+3y = 6

substituting value of x in equation 2 we get

y =1

x = 1

According to the given information:

Sales revenue by quarter:

Quarter 1: €120 million

Quarter 2: €110 million (decreased by €10 million from Quarter 1)

Sales revenue by region:

East: €78 million in Quarter 1 (accounting for 65% of total sales in Quarter 1)

West: €42 million in Quarter 1 (accounting for 35% of total sales in Quarter 1), €42 million + €46 million = €88 million in Quarter 2 (accounting for 80% of total sales in Quarter 2)

Percentage of sales revenue by region:

In Quarter 1:

East: (€78 million / €120 million) x 100% = 65%

West: (€42 million / €120 million) x 100% = 35%

In Quarter 2:

East: (€32 million/ €110 million) x 100% = 29%

West: (€88 million / €110 million) x 100% = 71%

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Such probability is calculated by dividing the number of mystery books by a total number of books:

    --> \(\frac{16}{32} = \frac{1}{2}\)

Thus the probability that the book is a mystery book is 1/2.

Hope it helps!

Answer:

points-

(0,2)

(5,3)

(10,4)

I hope this is good enough:

Answer:

Step-by-step explanation:

points-

(0,2)

(5,3)

(10,4)

She has to swim \(3\frac{3}8\) miles to reach her weekly goal

The weekly goal is given as:

\(Weekly = 7 miles\)

The distance covered on Monday and Tuesday are given as:

\(Monday = 1\frac 78\)

\(Tuesday = 1\frac 34\)

The total distance covered is then calculated as:

\(Total = Monday + Tuesday\)

This gives

\(Total = 1\frac 78 + 1\frac 34\)

Express as improper fractions

\(Total = \frac{15}8 + \frac 74\)

Take LCM

\(Total = \frac{15+14}8\)

\(Total = \frac{29}8\)

The remaining distance is the difference between the weekly goal and the total distance covered.

So, we have:

\(r = 7 - \frac{29}8\)

Take LCM

\(r = \frac{56-29}8\)

\(r = \frac{27}8\)

Express as mixed number

\(r = 3\frac{3}8\)

Hence, she has to swim \(3\frac{3}8\) miles to reach her weekly goal

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Answer:

Both equal sides have a length of 29 cm.

The third inequal side is 9 cm.

Step-by-step explanation:

System of Equations

With the data provided in the problem, we can form a system of two equations with two unknowns.

Let's call x to each equal side of the isosceles triangle and y to the other side. One condition states that each equal side is 2 cm more than three times the other side. It can be written as:

\(x=3y+2\)

We also know the perimeter of the triangle is 67 cm. Since we have to equal sides to x:

\(x+x+y=67\)

\(2x+y=67\)

Let's put together both equations:

\(x=3y+2\)

\(2x+y=67\)

To solve the system, we can use the x from the first equation and replace it into the second equation:

\(2(3y+2)+y=67\)

Operating:

\(6y+4+y=67\)

Joining like terms:

\(7y=67-4=63\)

Solving for y:

\(y=63/7=9\)

The third inequal side is 9 cm. Now find the value of x.

\(x=3y+2=3(9)+2=27+2=29\)

Both equal sides have a length of 29 cm.

Answer:

3

Step-by-step explanation:

3 x 3 = 9

11 x 2 = 22

4 x 7 = 28

9 + 22 = 31

31 - 28 = 3

hope this helps :)

The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.

Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.

The Pythagorean theorem formula is:

R ² = 6.5 ² + 4 ²

R ² = 42. ²25 + 16

R ² = 58.25

R = 7. 63 ft

There are two ropes so the length would be :

= 7. 63 + 7. 63

= 15. 3 ft

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