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Klio2033 [76]
3 years ago
11

Maya designed two intersecting roads. She drew the roads so that one of the angles at the intersection was 45 degrees. What are

the three other angle measures formed by the intersection? Draw a picture and explain your answer.
Mathematics
1 answer:
Citrus2011 [14]3 years ago
4 0
The sum of opposite angles are equal, so two of the angles are 45°.  The sum of all angles about the intersection of two lines is 360°.  So the remaining two angles are found by:

α=(360-2*45)/2

α=135°  thus all four angles are:

45°,135°,45°,135°
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professor wrote the following inequalities for N number of students in his lecture. N <10, N>10, N<22, N>22. Turns o
m_a_m_a [10]

Answer:

There are N students in the class.

We know that ONLY ONE of the inequalities is true:

N < 10

N > 10

N < 22

N > 22

We want only one of these four inequalities to be true.

Remember that if we have:

x > y

y is not a solution, because:

y > y is false.

Then:

If we take N = 10, then:

N < 22

Is the only true option.

While if we take N = 22

N > 10

is the only true option.

So there are two possible values of N.

8 0
3 years ago
Consider the following region R and the vector field F. a. Compute the​ two-dimensional curl of the vector field. b. Evaluate bo
Shalnov [3]

Looks like we're given

\vec F(x,y)=\langle-x,-y\rangle

which in three dimensions could be expressed as

\vec F(x,y)=\langle-x,-y,0\rangle

and this has curl

\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle

which confirms the two-dimensional curl is 0.

It also looks like the region R is the disk x^2+y^2\le5. Green's theorem says the integral of \vec F along the boundary of R is equal to the integral of the two-dimensional curl of \vec F over the interior of R:

\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA

which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of R by

\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle

\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt

with 0\le t\le2\pi. Then

\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt

=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0

7 0
3 years ago
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount o
Len [333]

Answer:

<u>V</u><u>=</u><u>8</u><u>.</u><u>5</u>

Step-by-step explanation:

o=oil. vinegar=v. furniture polish=f

O=3v

34= 3v + v

Using a system of guessing and checking if that number fits equation you can tell that 8 causes the equation to be unequal and also 9. You can learn V must be between 8 and 9 so 8.5 might fit the equation. <u>8.5</u><u>=</u><u>V</u>

6 0
3 years ago
Write an inequality that represents the situation. Jon can do less than 25 sit-ups on an exercise ball. How many sit-ups might J
o-na [289]

The inequality is x<25, when Jon cam do less than 25 sit-ups on an exercise ball.

Given that,

Jon can do less than 25 sit-ups on an exercise ball.

We have to find an inequity to illustrate the circumstance.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

The inequality is

Take the exercise balls as x

x<25

Therefore, the inequality is x<25, when Jon cam do less than 25 sit-ups on an exercise ball.

To learn more about inequality visit: brainly.com/question/28823603

#SPJ9

5 0
1 year ago
How much gift wrap is needed to cover a box which measures 3 feet by 2 feet by 3 feet?
ankoles [38]
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3 0
3 years ago
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