In triangle PQR, what is the triangle Q? Please answer as fast as possible! 100 POINTS!!!

In Triangle PQR, What Is The Triangle Q? Please Answer As Fast As Possible! 100 POINTS!!!

Answers

Answer 1

Answer:

105 degrees

Step-by-step explanation:

The sum of the angles in a triangle add up to 180. Although we don't the know the numerical values of the angles, we can create an equation with the given expressions:

<P + <Q + <R = 180

(6x + 5) + (11x - 5) + x = 180

18x = 180

x = 10

Now, plug this value of x into the expression for Q:

<Q = 11x - 5 = 11 * 10 - 5 = 110 - 5 = 105

Thus, the measure of angle Q is 105 degrees.

Hope this helps!

Answer 2

Answer:

105 degrees

Step-by-step explanation:

The angles in a triangle must add to 180 degrees

<Q +<P + <R =180

We know <Q is 11x-5, <P is 6x+5 and <R is x, so we can substitute them in

11x-5+6x+5+x=180

Combine like terms

11x+6x+x +5 -5 =180

18x=180

Divide both sides by 18

x=10

Now we know x, and we can substitute that in to to find <Q

<Q=11x-5

<Q=11(10)-5

<Q=110-5

<Q=105


Related Questions

In the trapezoid, what is the measure of 1?

85°
115°
90°

Answers

Answer:

115°

Step-by-step explanation:

all angles of a trapezoid add up to 360° and corresponding pairs of base angles add up to 180°. this means that 65° and angle 1 would have to add up to 180°

180 - 65 = 115°

Answer:

85°

Step-by-step explanation:

Since it is a trapezoid one pair of opposite sides will be parallel.

As, AB||CD,

95°+ m<1 = 180°( co- interior angles)

m<1= 180°- 95°

m<1= 85°

A baker uses the expression 3.25c+5.75p to calculate his profit when he sells c cakes and p pies.

What is the baker’s profit, in dollars, when he sells 10 cakes and 15 pies?

Answers

Answer:

118.75

Step-by-step explanation:

I used a calculator

5. Is the equation 2x + 8 = y a
direct variation? (yes or no)

Answers

Answer:

Yes.It is

Step-by-step explanation:

A relationship between two variables in which one is a constant multiple of the other. the types of variation include direct, inverse, joint, and combined variation keep that in hand

I need help on this math problem

Answers

Answer:IS C

Step-by-step explanation:

Please help me...

1A cashier earns $8 per hour.


2.tomatoes cost $0.70 per pound

Please help me I would really appreciate it ty

Answers

Answer:

1) 2/16 |  4/32 | 5/40 | 9/72

2) 2/1.4 | 3/2.1 | 6/4.2 | 8/5.3

Step-by-step explanation:

4*8 is 32

40/8 is 5

72/8 is 9

2.1/.7 is 3

6*.7 is 4.2

8*.7 is 5.6

With the first chart all it is doing is going up by 8. So, take the time and multiply it by 8. An if you noticed the time is counting up by 2. So for the missing time just count up by 2.

For the second chart it is a little harder. The second box for the weight seems to be 3 and all you have to do for the price is take the top number and multiply it by 0.70 and you should get your answer!

Thank you for asking you question i enjoyed helping!

-MajorJax3

Find the perimeter of the quadrilateral.

If x = 2, the perimeter is
inches.

Answers

Answer:

129 inches

Step-by-step explanation:

If x=2, just substitute in the x values for each side. Your lengths are 31, 32, 22, and 44.

4(2)^2+8(2)= 16+16=32

3(2)^2-5(2)+20=12-10+20=22

7(2)+30= 14+30=44

You are given an additional side of 31.

Add the values up together.

31+32+22+44=129

Find the volume of the pool shown. It consists of two prisms.





A.
1,765 feet cubed

C.
1,620 feet cubed

B.
1,234 feet cubed

D.
1,985 feet cubed

Answers

The volume of the pool is 1,620 ft cubed
The volume of the top rectangle is 1200 ft cubed and the bottom is 420 ft cubed. In all it is 1620 ft cubed.

Daniel has read 60​% of a book. He has 28 more pages to finish. How many pages are there in the​ book? There are nothing pages in the book.

Answers

The total number of pages in Daniel's book is 70 pages.

Given that Daniel has read 60% of it and that he has 28 pages left to finish it. The remaining 28 pages represent the

40% of the book that Daniel has not read yet.

We can set up the equation where 40% of the total page number (represented as x) equals 28 pages.

0.40x = 28

x = 28 / 0.40

x = 70

There are 70 pages in the book.

To find the total number of pages in the book, we'll start by setting up an equation based on the information provided. Let's denote the total number of pages in the book as x.

Daniel has read 60% of the book, leaving 40% unread. Given that he has 28 more pages to finish, we can express this information in an equation:

0.40x = 28

This equation represents the 40% of the book that Daniel has yet to read, which equals the 28 pages remaining.

To find the total number of pages ( x ), we divide both sides of the equation by 0.40:

[tex]\[ x = \frac{28}{0.40} \][/tex]

x = 70

So, there are 70 pages in the book. This solution implies that there are 70 pages, considering that "nothing" is simply a placeholder value and doesn't affect the calculation.

Sam is baking cakes at her parent’s bakery. She gets paid 20 a week in addition to 5 for every cake she bakes. She made 50 this week. Write an equation to show how many cakes Sam baked this week

Answers

Answer:

i think it is 20 + 5x = 50    or  f(x)=2(3^x)

Step-by-step explanation:

equation to show how many cakes sam baked this week:

20 + 5x = 50

20 = 20 dollars

5 = 5 more dollars

x = number of cakes

therefore, sam earned $50 this week.

Answer:

20+5x=50

x will represent the number of cakes she baked

she gets paid $5 for every cake she bakes, this is where the 5x comes from

she makes $20 ("in addition" that's where the "+20" comes from) a week. However, in this case we're only talking about what she made in one week, hense why there is no variable attached to the 20

she makes a total of $50

20+5=50

she baked a total of 6 cakes. How?

subtract 20 from both sides so you have:

5x=30

divide both sides by 5 to get x by itself:

x=6

A construction company charges $50, per square feet for building floors. How much will it cost to build a floor with radius 10 ft. use the dollars sign in your answer. Use π = 3.14

Answers

Answer:

$15700

Step-by-step explanation:

To find the cost, you multiply $50 by the area of the floor.  The floor must be a circle ("radius"), so to find the area of a circle, use the formula[tex]A=\pi r^2 \\ A=\pi(10)^2 \\ A=(3.14)(100)=314\text{ square feet}[/tex]

Multiply 314 sq. ft. by the cost per sq. ft.

314 x 50 = 15700

Answer:

69

Step-by-step explanation:for the boys

Find an equation equivalent to r = 5/1+cos(theta) in rectangular coordinates.
a. x^2=25-10y
b. y^2=10x-25
c. x^2=10y-25
d. y^2=25-10x

Please select the best answer from the choices provided

A
B
C
D

Answers

Final answer:

By applying polar to rectangular coordinates conversion formulas, the polar equation r = 5/(1+cos(θ)) is equivalent to the rectangular coordinate equation y² = 25 - 10x, which matches option D.

Explanation:

To convert the polar equation r = 5/(1+cos(θ)) to rectangular coordinates, we use the relationships between polar and rectangular coordinates: r = √x² + y² and cos(θ) = x/r. Substituting these into the given equation, we get:

r = √x² + y²;

cos(θ) = x/r;

r(1+cos(θ)) = 5;

r + r x/r = 5;

r + x = 5;

r = 5 - x;
Substitute back in for r, we get:

(√x² + y²) = 5 - x;
Squaring both sides gives us x² + y² = (5 - x)² which can be simplified to x² + y² = 25 - 10x + x². Canceling x² from both sides and reordering the terms gives us y² = 25 - 10x, which matches option D.

HELP PLEASE PLEASE :’(

The path of a shotput thrown is represented by the following parametric equations. Distance is measured in feet and time in seconds. Rewrite the parametric equations by eliminating the time parameter.
x(t)=23t
y(t)=5+19.3t-16t^2

a. y=5+444x-10,210x^2, x>or equal to 0
b. y=5+0.84x-0.70x^2, x>or equal to 0
c. y=5+444x-16x^2, x>or equal to 0
d. y=5+0.84x-0.03x^2, x>or equal to 0


Water is dripping out of a gutter onto a splash guard that follows the path represented by the parametric equations. Rewrite the parametric equations by eliminating the parameter.
x(t)=e^t
y(t)=2e^-t

a. y= 2/x, x>or equal to 0
b. y= 2/x, x>0
c. y= 2/(x^2), x>or equal to 0
d. y= 2/(x^2), x>0

Thanks!!!!!!

Answers

Practice:

1. A.

2. D. y=5+0.84x-0.03x^2, x>=0

3. B. y=2/x, x>0

Quiz:

1. A C E. (-4,4) (0,0) (6,9)

2. A. y=-1/3x+19/3

3. D. x=2y^2-1, y>=0

4. B. y=3/x^2, x>0

For the first parametric functions the cartisian function is y = 5+ 0.84x - 0.7x², and for the second parametric function the cartisian function is y = 2/x where x>0

What are parametric equations?

A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.

For the first parametric functions:

[tex]\rm x(t)=23t \\\\y(t)=5+19.3t-16t^2[/tex]

[tex]\rm t = \dfrac{x}{23}[/tex]

Put this value in the y(t)

[tex]\rm y=5+19.3(\dfrac{x}{23})-16(\dfrac{x}{23})^2[/tex]

y = 5+ 0.84x - 0.7x²

For the second parametric functions

[tex]\rm x(t)=e^t .....(1)\\\\y(t)=2e^-^t[/tex]

Taking ln in equation (1)

lnx = t

Put this value in equation (2)

[tex]\rm y=2e^{-lnx}[/tex]

y = 2/x,   x>0

Thus, for the first parametric functions the cartisian function is y = 5+ 0.84x - 0.7x², and for the second parametric function the cartisian function is y = 2/x where x>0

Learn more about the parametric function here:

https://brainly.com/question/10271163

#SPJ2

Use the net to find the surface area of the rectangular prism. A) 168 units2 B) 192 units2 C) 220 units2 D) 224 units2

Answers

Answer:

See below.

Step-by-step explanation:

You didn't provide any dimensions to test the answers with, but here is how you could solve the problem.

A rectangular prism is just an oblong cardboard box basically. Think about how you would unfold that box. It would be made up of 3 pairs of rectangles (2 end pieces, the top and bottom, and 2 sides). To calculate its surface area you just calculate the areas of each piece and add them up.  

The overall formula ends up being:

Area = 2(LW) + 2(LH) + 2(WH)

Ac is tangent to circle o at point c what is the length of ac?

Answers

Answer:

The Answer is 12

Step-by-step explanation:

Use Pythagorean theorem. AB=8 and BO=5 We still need to find AO

AO=AB+BO

8+5

AO=13

Now solve for AC

AC^2 + OC^2= AO^2

AC^2+5^2=13^2

AC^2+ 25=169

AC^2=144

AC= 12

Find the area of the pentagon.
A)
107 inches?
B)
116 inches?
150 inches
D)
182 inches?

Answers

Where is the pentagon??

Mary spent a total of $320.91 for a party. She spent $200.39 on food, plus an additional $30.13 for
each hour of the party. How long was the party?
A.. 3 hours
B.. 4 hours
C.. 5 hours
D.. 6 hours

Answers

Answer:

The party was 4 hours long.

Step-by-step explanation:

Subtract the total by the amount already known was spent directly.

320.91-200.39= 120.52

Now, in order to figure out how many hours the part was, take how much each hour and divide it by the remainder of money.

Thus, 120.52/30.13 = 4

All things put into consideration, The party was 4 hours long.

I hope this helped!!

~ Penny

It’s 3 because I don’t know but I’m just kinda confused tho

If f(x) = 3[ x-2], what is f(5.9)

Answers

Answer:

f(x)=3[x-2]

So, f(5.9) = ?

f(5.9) = 3(5.9 - 2)

=3(3.9)

=11.7 = 12

so, the answer is 12.

Step-by-step explanation:

let me know if you need any other help:))

Answer:

9

Step-by-step explanation:

Edge 2020

THE ANSWER IS 9

~theLocoCoco

The volume of one prism is known, along with the height For the two prisms to be congruent, what must the area
of another prism. The values are shown below.
of the base be, given that the triangular bases are
congruent?
3 in 2
6 in?
12 in 2
15 in 2
15 in.
V = 90 in 3

Answers

Answer:

6in2

Step-by-step explanation:

i`m doing the assignment.

Answer:

6in^2

Step-by-step explanation:

The answer is 6in^2, I just did the assignment on Ed$ge$nuity and I got it right.

A reporter determines a baseball player’s batting average, which is a ratio of the number of hits to number of times at bat. The result is shown on a calculator as 0.212121....Write this repeating decimal as a fraction.

Answers

Answer:

21/99 or 7/33

Step-by-step explanation:

x = 0.212121

Then we multiple the decimal and x by hundred.

100x = 21.212121

Then we subtract the 21.212121 by 0.212121.

100x = 21.212121 - 0.212121

But when you are subtracting 100x, you need to subtract 100x by x because in the first step it said x = 0.212121.

100x - x = 21.212121 - 0.212121

You will have at the end is

99x = 21

Divide 99 on both side and you left with

21/99 or 7/33 simplified version

35% off $85.98 I'm having trouble with this.​

Answers

Answer:

Step-by-step explanation:

i asked siri 55.87

Answer:

The new price is $55.887

Step-by-step explanation:

Step 1:  Find the discounted price

Make an equation

85.98 * (1 - 0.35) = x

85.98 * 0.65 = x

Multiply

85.98 * 0.65 = x

55.887 = x

Answer: The new price is $55.887

PLEASE HELP ME!!!
Select the statement that correctly completes the sentence. When using more than one adjective, ________.

A. size comes after color
B. size comes after shape
C.size comes before color
D. size comes before opinion

Answers

Answer:

more comfortable

Step-by-step explanation:

Final answer:

When using more than one adjective, 'size comes before color', which is option C. Adjectives in English typically follow an established order, with the size adjective placed before the color adjective.

Explanation:

The correct statement that completes the sentence when using more than one adjective is C. size comes before color. In English, adjectives follow a specific order in which they appear before a noun. This order is generally: opinion, size, shape, age, color, origin, material, and purpose. Therefore, size should be placed before color when describing a noun with multiple adjectives.

For example, when arranging adjectives in a sentence, the phrase would be 'a small green book' rather than 'a green small book'. The adjective 'small' represents the size and 'green' represents the color, and according to the correct adjective order, size should come before color.

One letter weights 12 ounces.The mail carrier is allowed to carry 30 pounds.How many letters can he carry?

Answers

Answer:

The mail carrier can carry 40 letters.

Step-by-step explanation:

The first step is to put ounces into pounds.

1 lb = 16 oz  This is the unit rate

0.75 lbs = 12 oz

Now put the 30 lbs into ounces

30 lbs = 480 oz

Divide 480 oz by 12 oz to find how many letters equal 480 oz.

480/12 = 40 letters

If this answer is correct, please make me Brainliest!

Answer:

Hi! I am late but its 40 oz

Step-by-step explanation:

Without drawing the graphs, find the points of intersection of the lines:

11x–6y=2 and –8x+5y=3


PLZZZZZZZ HELP!

Answers

The point of intersection of the lines given by the equations [tex]\( 11x - 6y = 2 \) and \( -8x + 5y = 3 \) is \( (4, 7) \).[/tex]

To find the points of intersection of the given lines, we need to solve the system of linear equations simultaneously.

 The given equations are:

[tex]\[ 11x - 6y = 2 \quad \text{(Equation 1)} \][/tex]

[tex]\[ -8x + 5y = 3 \quad \text{(Equation 2)} \][/tex]

 We can solve this system using the method of substitution or elimination. Let's use the elimination method to find the values of [tex]\( x \)[/tex]and [tex]\( y \).[/tex]

 First, we will make the coefficients of [tex]\( y \)[/tex] the same in both equations by multiplying Equation 1 by 5 and Equation 2 by 6:

 [tex]\[ 5(11x - 6y) = 5(2) \][/tex]

[tex]\[ 6(-8x + 5y) = 6(3) \][/tex]

 This gives us:

[tex]\[ 55x - 30y = 10 \quad \text{(Equation 3)} \][/tex]

[tex]\[ -48x + 30y = 18 \quad \text{(Equation 4)} \][/tex]

 Now, we add Equation 3 and Equation 4 to eliminate [tex]\( y \):[/tex]

[tex]\[ (55x - 30y) + (-48x + 30y) = 10 + 18 \][/tex]

[tex]\[ 7x = 28 \][/tex]

 Dividing both sides by 7, we get:

[tex]\[ x = 4 \][/tex]

 Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into either Equation 1 or Equation 2 to find the value of [tex]\( y \)[/tex]. Let's use Equation 1:

[tex]\[ 11(4) - 6y = 2 \][/tex]

[tex]\[ 44 - 6y = 2 \][/tex]

 Subtracting 44 from both sides, we get:

[tex]\[ -6y = -42 \][/tex]  Dividing both sides by -6, we get:

[tex]\[ y = 7 \][/tex].

Write the numbers in order from greatest to least.
-2, 1 1⁄2, -2 3⁄4, 3⁄10

Answers

Answer:

11/2, 3/10 , -2, -2 3/4

Step-by-step explanation:

negatives are definitely on the least side. And 11/2 is 5 1/2 which is way greater 3/10. -2 3/4 means it is 3/4 more away from 0 than -2 is. So here!

The order from greatest to least is:

1 1/2  3/10  -2  -2 3/4

-2: This is a negative number, which means it is less than zero.

1 1/2 (or 1.5): A positive number greater than zero.

-2 3/4 (or -2.75): This is also a negative number and is less than -2.

3/10 (or 0.3): This is another positive number, but less than 1.

Negative numbers always rank lower than positive numbers.

Among the negative numbers, -2 is greater than -2.75.

Comparing the positive numbers:  

1.5 is greater than 0.3.

If john had 9 apples and pickles gave him ten more how much apples does John have?
(9+10)

Answers

Answer:

21

but if ur serius then 19

Step-by-step explanation:

Answer:

19 Apples

Step-by-step explanation:

If john originally had 9 apples and then added ten more to his pile, then John would have 19 apples in all.

A pole 6m high has a shadow 10 m long when the shadow of a nearby building is 220 m long. How tall is the building?

Which ratio is equal to the ratio of the height of the building to its shadow?



Answers

Final answer:

By using the similar triangles principle, the height of the building is found to be 132 meters. We find this by setting up a proportion between the known ratios of the pole's height to its shadow and solving for the building's height.

Explanation:

We can solve the problem using similar triangles. The ratio of the height of the pole to its shadow is the same as the ratio of the height of the building to its shadow. Since the height of the pole is 6m and its shadow is 10m, we have the ratio of the height to the shadow for the pole as 6/10 or 3/5.

This ratio will be equal to the ratio of the height of the building (which we'll call h) to the shadow of the building (220 m), so we can write the proportion as:

3/5 = h/220

Now we solve for h:

3/220 = h/5

h = (3/5) × 220

h = (3 × 44)

h = 132m

So the height of the building is 132m.

Rewrite the radical expression as an expression with a rational exponent.
The answer choices are in the picture!

Answers

Answer:

first one is the right answer

Answer:

[tex] = {x}^{ \frac{5}{4} } [/tex]

Step-by-step explanation:

[tex] \sqrt[4]{ {5}^{5} } \\ {5}^{(5) \times \frac{1}{4} } \\ = {5}^{ \frac{5}{4} } [/tex]

Does a dilation produce a congruent figure

Answers

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation that creates a larger image is called an enlargement. ... If the scale factor is 1, the figure and the image are congruent. The word "dilate" is often heard in relation to the human eye.

After dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

Recall:

When two figures are congruent, it means they have the same shape and size, whereby, all pairs of corresponding angles and sides of both figures are congruent or equal in measure.The image attached below shows a dilated figure.

Dilation is a transformation that enlarges a figure or reduces the figure.

After dilation, the new figure maintains the same shape of the original figure.

However, after dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

Learn more here:

https://brainly.com/question/14706073

The explicit formula for the geometric sequence -1/9, 1/3, -1, 3, -9, ... is -1/9(-3)^x-1 . What is the common ratio and recursive formula for this sequence

Answers

Answer:

r=3[tex]\left\{\begin{array}{ccc}a_1=-\frac{1}{9}\\a_n=-3a_{n-1}\end{array}\right[/tex]

Step-by-step explanation:

Given the sequence

[tex]-1/9, 1/3, -1, 3, -9, ...[/tex]

The common ratio is determined by the division of term by the previous term.

Common Ratio, [tex]r=\frac{1/3}{-1/9} =\frac{-1}{1/3} =\frac{3}{-1}=-3[/tex]

A recursive formula is a formula that defines each term of a sequence using preceding term(s).

For the given sequence, the recursive formula is:

[tex]\left\{\begin{array}{ccc}a_1=-\frac{1}{9}\\a_n=-3a_{n-1}\end{array}\right[/tex]

Answer:

−3; f(x + 1) = −3(f(x))

The answer is B.

Step-by-step explanation:

Raj paints 10 3/7 feet of his fence on Friday and 15 1/3 feet of his fence on Saturday.

How many feet of his fence did Raj paint on both days?

Answers

Answer: 25 16/21 feet

Step-by-step explanation:

10 3/7 + 15 1/3 = 25 16/21

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One letter weighs 12 ounces. The mail carrier is allowed to carry 30 pounds. How many letters is he able to carry? 16 letters 32 letters 40 letters 480 letters Stan plans to invest $100,000 in either a risk-free bond or a portfolio of 100 stocks. If he buys the bond, it will be worth $107,000 at the end of one year, for a guaranteed return of 7 percent. Alternatively, he could put $1,000 each into 100 different stocks. Each stock has a 50-50 chance of being worth either $2,300 or $0 at the end of the year, so the expected return on each stock (and the whole portfolio) is 15 percent. Which of the following should make Stan more likely to invest in the stock portfolio?The stocks are uncorrelated with each other (r = 0). How does the film industry help the local, state, national, and international economy? 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After the civil war, temperance groups worked for laws that The following box plot shows the number of years during which 20 schools have participated in an interschool swimming meet:A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.At least how many schools have participated for 6 years or more? 4 schools 5 schools 10 schools 11 schools what happens when the economy expands Yeast cells are recovered from a fermentation broth by using a tubular centrifuge. Sixty percent of the cells are recovered at a flow rate of 12 l/min with a rotational speed of 4000 rpm. Recovery is inversely proportional to flow rate. a. To increase the recovery of cells to 95% at the same flow rate, what should be the rpm of the centrifuge? How was life like for African Americans in the South? Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on a particular day, one U.S. dollar could purchase 0.8167 Euros, and one Euro could purchase 145.8038 yen. Let f (x )represent the number of Euros you can buy with x dollars, and let g (x )represent the number of yen you can buy with x Euros. In this passage, who represents the individual?Suddenly, Tessie Hutchinson shouted to Mr. Summers,"You didn't give him time enough to take any paper hewanted. I saw you. It wasn't fair!"Be a good sport, Tessie," Mrs. Delacroix called, and Mrs.Graves said, All of us took the same chance."-The Lottery,"Shirley JacksonMrs. DelacroixMrs. GravesTessie HutchinsonMr. Summers If a variable does not have a coefficient then it is either a 1 or a -1. true or false what is the area of the shaded region If just before a tee shot, a goffer shifts her attention from the length of the fairway and the direction of the wind to focusing only on the ball, her attention has shifted from to _ Do you recognize this question? You should. Did you put d" before? Recommend . Guidelines for effective eulogies include Group of answer choices explain the bad intentions they had. use a narrative organizational pattern. use a strong attention-getter for your opening. relate what you will most remember and miss about the person. For beam design, the cross section dimensions of the beam are determined: A. Based on allowable normal stress, but the allowable shear stress should always be checked to be sure it is not exceeded. B. Based on the allowable shear stress, but the allowable normal stress should always be checked to be sure it is not exceeded. C. Such that both the allowable normal stress and the allowable shear stress are reached at the same time. D. Based on the allowable normal stress. E. The allowable shear stress is not an important design consideration.