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3 years ago

Using the triangle find x and y

Mathematics

1 answer:

Elenna [48]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

Since the base angle are congruent, both 44° then the triangle is isosceles.

Then the 2 legs are congruent, that is

4x - 7 = 2x + 1 ( subtract 2x from both sides )

2x - 7 = 1 ( add 7 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Thus legs are both 4x - 7 = 4(4) - 7 = 16 - 7 = 9 and base = x + 3 = 4 + 3 = 7

As a check 9 + 9 + 7 = 25 → correct

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the base angles from 180 for y, that is

y = 180 - (44 + 44) = 180 - 88 = 92

Finally

x = 4

y = 92

angles are 92°, 44° and 44°

sides are 9, 9 and 7

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The center of a circle lies on _____.

algol [13]

<h2>Answer:</h2>

A) every diameter

<em>The center of a circle lies on </em><em>every diameter.</em>

<h2>Explanation:</h2>

B) The circle: A circle is a two-dimensional shape where all points are the same distance from the center. So this definition doesn't match the definition of the center of the circle. The center is just a point not several ones.

C) A tangent line: obviously this definition is false. A tangent line is a line not a point.

D) Every chord: A chord is any line segment between two points on a circle. The only chord that passes through is the diameter. So this definition does not include all the chords of a circle

A) Every diameter: This is the correct option! A diameter is any chord that <em>passes through the center</em>.

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3 years ago

g Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 7yi + xzj + (

Sati [7]

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

where $S$ is any oriented surface with boundary $C$ . We have

$\vec F(x,y,z)=7y\,\vec\imath+xz\,\vec\jmath+(x+y)\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-7)\,\vec k$

Take $S$ to be the ellipse that lies in the plane $z=y+9$ with boundary on the cylinder $x^2+y^2=1$ . Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+9)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

Then we have

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\big((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+2)\,\vec k\big)\cdot\big(-u\,\vec\jmath+u\,\vec k\big)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(3u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{3\pi}$

5 0

3 years ago

A scarf takes 20 feet of yarn to make. If 1 foot = 12 inches, how many inches does it take to make the scarf

mestny [16]

Answer:

240

Step-by-step explanation:

20 times 24 is 240

20 x 24 = 240

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2 years ago

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Vikki [24]

Answer:

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Step-by-step explanation:

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3 years ago

What is the solution to this system of equations, and what does it mean to the contractor? The solution (0, 20) tells the contra

oksano4ka [1.4K]

The question is incomplete. Here is the complete question:

A contractor has two choices for billing a completed job.

· $500 flat rate, regardless of the number of hours worked

· $20 per hour worked

The graph shows the relationship between pay per hour and number of hours worked for both scenarios.

What is the solution to this system of equations, and what does it mean to the contractor?

A.The solution (0, 20) tells the contractor the minimum amount that can be charged.

B.The solution (0, 500) tells the contractor the maximum amount that can be charged.

C.The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

D.The solution (20, 25) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

Answer:

The graph is attached below.

C.The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

Step-by-step explanation:

As per the graph, the x-axis represents the number of hours worked and the y-axis represents the rate in dollars per hour.

The hourly rate is given as $20.

The solution to the given lines drawn on the graph is the point of intersection of the two curves.

As we observe from the graph, the point of intersection of the two curves is at (25,20). The point tells the contractor that when the hourly rate is $20, then the number of hours worked will be 25.

So, when the hourly rate is same for both the billings, then the number of hours worked will be 25.

Hence, the correct option is (C).

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2 years ago

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