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Anit [1.1K]
3 years ago
10

Finding missing angles 33 33 x

Mathematics
1 answer:
Levart [38]3 years ago
5 0
Answer:

x + 33 = 180

x = 180 - 33

x = 147


Explanation:

The angle x and the angle 33 are supplementary angles. Supplementary angle are two angle side-by-side one another, and when added, give you 180 degrees.
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113.1in³ should be tge volume
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3 years ago
Find the solution to this system.<br><br> Is it (1,2)?
tester [92]
2 lines intersect at (1,2)
so answer is Yes.
(1,2) is the solution to the system.
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3 years ago
A police cruiser is traveling at 20.0 m/s when the officer spies a speeder. The cruiser accelerates at 3.0 m/s^2 for 5.0 seconds
Tema [17]

For the first 5.0 seconds, the cruiser covers a distance of

\left(20.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2=137.5\,\mathrm m

At this point, the cruiser will have achieved a velocity of

\left(20.0\dfrac{\rm m}{\rm s}\right)+\left(3.0\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)=35\dfrac{\rm m}{\rm s}

The cruiser will take

\left(35\dfrac{\rm m}{\rm s}\right)-\left(5.0\dfrac{\rm m}{\mathrm s^2}\right)t=0\implies t=7.0\,\mathrm s

to come to a stop as it decelerates. It will have covered a total distance of

(137.5\,\mathrm m)+\left(35\dfrac{\rm m}{\rm s}\right)(7.0\,\mathrm s)+\dfrac12\left(-5.0\dfrac{\rm m}{\mathrm s^2}\right)(7.0\,\mathrm s)^2=\boxed{260\,\mathrm m}

8 0
3 years ago
In the trapezoid ABCD (AB∥CD) point M∈AD, so that AM:MD=3:5. Line L ∥AB and going through point M intersects diagonal AC and leg
siniylev [52]

Answer:

\dfrac{AP}{PC}=\dfrac{3}{5}

\dfrac{BN}{CN}=\dfrac{3}{5}

Step-by-step explanation:

Consider triangles AMP and ADC. In these triangles,

  • angle A is the common angle, so \angle MAP\cong \angle DAC by reflexive property;
  • angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.

Hence, triangles AMP and ADC are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{AM}{AD}=\dfrac{AP}{AC}\\ \\\dfrac{3x}{3x+5x}=\dfrac{AP}{AC}\\ \\\dfrac{AP}{AC}=\dfrac{3}{8}\Rightarrow AP=\dfrac{3}{8}AC\\ \\PC=AC-AP=AC-\dfrac{3}{8}AC=\dfrac{5}{8}AC,

so

\dfrac{AP}{PC}=\dfrac{\frac{3}{8}AC}{\frac{5}{8}AC}=\dfrac{3}{5}

Consider triangles ACB and PCN. In these triangles,

  • angle C is the common angle, so \angle ACB\cong \angle PCN by reflexive property;
  • angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.

Hence, triangles ACB and PCN are similar by AA similarity theorem.

Similar triangles have proportional corresponding sides, thus

\dfrac{CP}{AP}=\dfrac{CN}{CB}\\ \\\dfrac{5x}{3x+5x}=\dfrac{CN}{CB}\\ \\\dfrac{CN}{CB}=\dfrac{5}{8}\Rightarrow CN=\dfrac{5}{8}CB\\ \\BN=BC-CN=BC-\dfrac{5}{8}BC=\dfrac{3}{8}BC,

so

\dfrac{BN}{CN}=\dfrac{\frac{3}{8}BC}{\frac{5}{8}BC}=\dfrac{3}{5}

4 0
3 years ago
Michael has 12 yards of yellow fabric and 6 yards of purple fabric. how many inches of yellow and purple fabric does Kelly have.
jasenka [17]

Answer:

648 inches

Step-by-step explanation:

12 + 6 = 18 yards

there are 36 inches in 1 yard

so there is 648 inches in 18 yards

5 0
2 years ago
Read 2 more answers
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