Answer:
[tex]D(x)= x\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex]Side = x[/tex]
Required
Represent the diagonal as a function
Using Pythagoras theorem, the diagonal is:
[tex]D^2= Side^2 + Side^2[/tex]
Substitute x for Side
[tex]D^2= x^2 + x^2[/tex]
[tex]D^2= 2x^2[/tex]
Take the square root of both sides
[tex]D= \sqrt{2x^2[/tex]
Split
[tex]D= \sqrt{2} * \sqrt{x^2[/tex]
[tex]D= \sqrt{2} * x[/tex]
[tex]D= x\sqrt{2}[/tex]
Express as a function.
[tex]D(x)= x\sqrt{2}[/tex]
A man weighing 800 N is hanging from a 2 mm diameter titanium wire with a cross-section of 3 x 10^-6 m^2. Will the wire break?
Answer:
Since stress is greater than ultimate strength, the wire will break.
Step-by-step explanation:
The titanium wire is experimenting an axial load. Ultimate strength equals [tex]2.20\times 10^{8}\,Pa[/tex]. The wire shall break if and only if stress is at least equal to ultimate strength. The equation for axial stress ([tex]\sigma[/tex]), measured in pascals, in the wire with circular cross-section is:
[tex]\sigma = \frac{4\cdot F}{\pi\cdot D^{2}}[/tex] (1)
Where:
[tex]F[/tex] - Axial force, measured in newtons.
[tex]D[/tex] - Cross-section diameter, measured in meters.
Please notice that axial force is the weight of the man hanging from wire.
If we know that [tex]F = 800\,N[/tex] and [tex]D = 0.002\,m[/tex], then the axial stress experimented by the titanium wire is:
[tex]\sigma = \frac{4\cdot (800\,N)}{\pi\cdot (0.002\,m)^{2}}[/tex]
[tex]\sigma \approx 2.546\times 10^{8}\,Pa[/tex]
Since stress is greater than ultimate strength, the wire will break.
solve the following simultaneous equations using an algebraic method.
5x + 3y = 11
2x - 7y = 29
will be grateful!
Please help will give brainliestw
Answer:
6 square units
Step-by-step explanation:
In oder to do this, you need graph paper to make it easier and then mark your graph paper with the quadrants.
I got 3 unites for the height and 4 units for the base
4 x 3 = 12 square units
however the formula for a triangle is Ab/2
so divide 12/2 = 6
So its 6 square units
Last week, labron jogged for 2 1/4 miles. This week , he plants to jog 2 times as far as last week. How many miles does Lebron Plant to jog this week?
Answer:
4.5 miles
Step-by-step explanation:
2 times as far as last week
last week was 2.25 miles
2* 2.25 = 4.5 miles
A polynomial equation with rational coefficients has roots +5 plus 12 i and −−negative 9 minus 7 i. List two more roots of the equation.
Answer:
The additional roots are: [tex]5 - 12i[/tex] and [tex]-9 + 7i[/tex]
Step-by-step explanation:
Given
Roots: [tex]5 + 12i[/tex] and [tex]-9 -7i[/tex]
Required
Determine two additional roots
For a polynomial with two rational roots, the additional roots are the conjugates of the roots.
Take for instance, the following expression:
[tex]a + \sqrt b[/tex]
The conjugate of [tex]a + \sqrt b[/tex] is: [tex]a - \sqrt b[/tex].
Having established how to determine the additional roots, we proceed to determine the roots.
The conjugate of [tex]5 + 12i[/tex] is [tex]5 - 12i[/tex] and the conjugate of [tex]-9 -7i[/tex] is [tex]-9 + 7i[/tex]
Hence, the additional roots are: [tex]5 - 12i[/tex] and [tex]-9 + 7i[/tex]
please helpppp and explain
Answer:
angle BAC=50-2x
Step-by-step explanation:
angle ACD=115+x
then, angle ACB=180-(115+x) because it is a supplementary angle
angle ABC=angle ACB because it is an isosceles triangle
angle BAC=180-2[180-(115+x)]
angle BAC=180-360+230-2x
angle BAC=50-2x
The number of incidents in which police were needed for a sample of 10 schools in one county is:
6
40
49
4
42
47
17
8
32 11
Find the first and third quartiles for the data.
Part: 0/2
Part 1 of 2
First quartile Q, is
Answer:
3Step-by-step explanation:
expand My eBay and thought you might be a good time to get the latest flash player is required for video playback is unavailable right now because this video is not available for remote playback is unavailable right now because this video is not available for remote playback is unavailable right now because this video is not available for remote playback is unavailable right for me as soon is unavailable and nice and clean this is unavailable for video for me and
Here are sketches of four triangles in each triangle the longest side is exactly 1cm the other length is given to 2 decimal places work out the value of x give your answer to 1 decimal place 4 cm 57°
If the hypotenuse is 4 cm and an angle is 57°. Then the measure of the length of the side x will be 3.36 cm.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function. The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The right triangle is given with a hypotenuse of 4 cm and an angle of 57°.
Then the value of x will be
The value of x will be given by the sine rule.
sin θ = x/h
WE have
θ = 57°
h = 4 cm
Then we have
sin 57° = x/4
x = 3.3546
x ≅ 3.36
More about the right-angle triangle link is given below.
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Can somebody help me? I need help...
Answer:
8/9
Step-by-step explanation:
your adding 1/18 each time
410 is what percent of 65?
Answer:
15.85%
Step-by-step explanation:
you know you have 65 and you have 410 so you just multiply and try and figure out the ratio and how much percentage is out of it.
The ratio of students to teachers at a school is 19 : 1. At this school, there are 400 people (teachers and students). How many of these 400 people are students? (enter number only, without the unit)
Answer:
There are 380 students and 20 teachers.
Answer:
380
Step-by-step explanation:
Let 19x = no. of students
x = no. of teachers
Then, x + 19x = 400
20x = 400
x = 20
19x = 19(20) = 380
Grapes are priced at $2.25 per pound. Which of the following equations best represents the cost, c, of buying g, pounds of grapes?
A. c=2.25g
B. c=g+2.25
C. g=c+2.25
D.g=2.25c
In triangle ABC, the sum of the measures of angle A and angle B is 120. The sum of the measures of angle B and C is 110. Find the measure of the greatest angle of the triangle.
Answer:
70
Step-by-step explanation:
the sum of the three is 180, so c is 60, a is 70, and b is 50.
two step equation -9 + 2x = .-31
Answer:
Step-by-step explanation:
Add 9 to both sides
2x = -22
Divide both sides by 2
x = -11
Is the relation a function?? Plzz helppp!!!
(1,19) , (2,23) , (3,23) , (4,29) , (5,31)
hi could you please tell me the answer to this?
Answer:
5
Step-by-step explanation:
5
please help! it would be much appreciated
Answer:
20
Step-by-step explanation:
Convert to %
1) 1/2
2) 1/4
3) 1/3
4) 3/10
5) 6.5/10
Answer:
1) 50%
2) 25%
3) 33.33 %
4) 30%
5) 65%
Mr. Brown purchased tires for his car. The tires were $75 each, including tax, plus $10 for installation. Mr. Brown paid $160 for the tires and installation. Which equation can be used to find the number of tires, t, that Mr. Brown purchased?
A. t = 160 + 75(10)
B. 75 + t(10) = 160
C. 75t + 10 =160
D. 160t - 75 = 10
Could you show your work? Thanks!
Answer:
Step-by-step explanation:
The answer is C because t = 2 so 75x2=150 and 150 + 10= 160.
9 = - 5b - 23 write your answer as a decimal
9=-5b-23
9+23=-5b
32=-5b
32/-5=b. ..(here 32/-5= 32 upon -5)
-6.4=b
The required simplified value of b for the given expression is b = -2.8.
GIven that,
To determine the simplified value of b for the expression 9 = - 5b - 23.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
the given expression,
9 = - 5b - 23
Simplifying,
-5b = 23 - 9
-5b = 14
b = -14 / 5
b = -2.8
Thus, the required simplified value of b for the given expression is b = -2.8.
Learn more about simplification here: https://brainly.com/question/12501526
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WHAT WOULD THIS BEEE!!
use Pythagoras theorem
20 units
1. Please help if possible :)
Answer:
54
Step-by-step explanation:
6x=9x-27
x=9
9*9-27=54
A petting zoo has 7 lambs, 12 rabbits, 6 goats, and 3 piglets. Find the
ratio of rabbits to the total number of animals. Write the ratio in
simplest form.
Answer:
3:7
Step-by-step explanation:
The number of rabbits is 12 while the total number of animals
7 + 12 + 6 + 3 = 28
So the ratio of rabbits to animals is 12:28 = 3:7
The track team is trying to reduce their time for a relay race. First they reduce their time by 1.2 minutes. Then they are able to reduce that time by 1/10. If their final time is 3.60 minutes, what was their beginning time?
Answer:
5.2 Minutes, or 5 minutes and 12 seconds
Step-by-step explanation:
You can solve this problem by working backward. Since our number gets smaller by a 1/10 or 0.1, in order to work backward we must multiply 3.60 by 10/9, since one tenth has been taken away already. When we do this, we get 4.0. When we add 1.2 minutes to that, we get a final answer of 5.2 minutes, or 5 minutes and 12 seconds.
Look at the information below, decide what type of substance the paint is.
ANSWER NEEDED ASAP
Answer:
A mixture?
Step-by-step explanation:
Does the point (2, 5) satisfy the equation y = 5x − 5?
Answer:
yes
Step-by-step explanation:
so x=2 and y=5
5 = 5 x 2 - 5
0=0
equation is right
I will give BRAINLIEST:)
Answer:
A'C'=AC=3
Step-by-step explanation:
Answer:
C: 3 units
Step-by-step explanation:
Just think about it... 180 degrees rotated is exactly opposite rotation degree.
If you rotate 90 degrees, the triangle will end up on quadrant 4.
Rotate 360 degrees, the triangle will stay in the same quadrant.
In conclusion, C is the best option
Joe ordered some books online and spent a total of $75 . Each book cost $6 and he paid a total of $3 for shipping . How many books did he buy ?
5 Marta designs a logo for her mother's business,
X-treme Nutrition. The logo is shown.
35°
35°
b
Which equation and solution best represents
angle b?
A b + 35 = 90; b = 55°
B b-35 = 35; b = 70°
C 6+ 70 = 180; b = 110°
D b + 35 = 180; b = 145°
Answer:
(C). b + (2 × 35) = 180; b = 110°
Step-by-step explanation:
40 is 20 of what number
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{40 is 20\% of what time number?}\\\\\\\bullet \large\bold{We\ are\ looking\ for\ your\ UNKNOWN\ number; we\ can\ the\ value}\\\large\bold{is\ \underline{a}\ for\ our\ answer!}\\\bullet\large\bold{REMEMBER: Percentages\ are\ out\ 100\ \& the\ word\ \underline{of}\ means\ \underline{multiply}}[/tex]
[tex]\huge\text{NOW LETS SOLVE FOR YOUR ANSWER!}[/tex]
[tex]\bold{Equation: 20\%\ \times \ a\ =\ 40}\\\\\bold{a = \dfrac{40}{20\%}}}\\\\\bold{20\% = \dfrac{20}{100}\rightarrow 0.2}}}\\\\\bold{Equation: a = \dfrac{40}{0.2}}\\\\\bold{\dfrac{40}{0.2}=200}\\\\\bold{a=200}\\\\\boxed{\boxed{\bold{Answer: 200}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]