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2 years ago

Suppose given a trapezoid ABCD with bases BC=5 and AD=8, and leg CD=3. The lines AB and CD meet at a point P. Find DP

Mathematics

2 answers:

LUCKY_DIMON [66]2 years ago

6 0

Answer:

8 units

Step-by-step explanation:

Consider triangles BPC and APD. These two triangles are similar, because

∠DAP≅∠CBP (as corresponding angles);
∠BCP≅∠ADP (as corresponding angles);
∠APD≅∠BPC (by reflexive property of congruence).

Then, by AA theorem, $\triangle BCP\sim \triangle ADP.$

Similar triangles have proportional sides lengths:

$\dfrac{BP}{AP}=\dfrac{CP}{DP}=\dfrac{BC}{AD},\\ \\\dfrac{BP}{AP}=\dfrac{CP}{CP+3}=\dfrac{5}{8}.$

The last proportion gives you

$8CP=5(CP+3),\\ \\8CP=5CP+15,\\ \\3CP=15,\\ \\CP=5\ un.$

Then $DP=CP+CD=5+3=8\ un.$

Luba_88 [7]2 years ago

5 0

Answer:

Step-by-step explanation:

ΔPBC ~ ΔPAD so ...

... BC/AD = CP/DP

... 5/8 = (DP-3)/DP

... 5·DP = 8(DP -3) . . . . multiply by 8·DP

... 24 = 3DP . . . . . . . . . add 24-5·DP

... 8 = DP . . . . . . . . . . . . divide by 3

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Students at a high school were polled to determine the type of music they preferred. There were 1940 students who

Reika [66]

Answer:

students preferred alternative music

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6 0

2 years ago

1. Mac is about to sue his contractor who promised to install a water tank that holds 1880 gallons of water. Mac knows that 1880

zzz [600]

Answer:

option C.

Yes, the water tank is about 245 cubic feet too small

Step-by-step explanation:

step 1

Determine the volume of the cylindrical tank

we know that

The volume of a cylinder is equal to

$V=\pi r^{2} h$

Remember that

$1\ ft=12\ in$

we have

$r=6\ ft\\h=2\ ft\ 2\ in=2+(2/12)=\frac{13}{6}\ ft$

assume

$\pi =3.14$

substitute

$V=(3.14)(6)^{2}(\frac{13}{6})$

$V=244.92\ ft^3$

Compare with 251 cubic feet

$244.92\ ft^3 < 251\ ft^3$

therefore

Yes, the water tank is about 245 cubic feet too small

8 0

2 years ago

RQ is tangent to Circle S. Use the diagram below to find the measure of QRS. mQRS < 90 mQRS > 90 mQRS = 90 not enough info

Masteriza [31]

Given that you did not include the diagram showing the circle, the tangent line and the points Q, R, and S, I am going to give you the explanation to answer the question.

1) The tangent lines to a circle form a 90° angle with the radius at the point of intersection.

2) Therefore, if the point of intersection of the tangent line and the circle is named R, and the points S and Q are one the center of the circle and the other is on the line RQ, then you know that the segment SR is a radius and the line RQ is the tangent, which means that they are perpendicular, i.e. the angle QRS is measures 90°.

In this case the answer is m angle QRS = 90°.

3) Otherwise the angle is different to 90° and you need to observe the figure to conclude whether it is greater than 90°, less than 90° or there is not enough information.

7 0

2 years ago

All of the following are equivalent ratios except... a) AR:RC b) BS:BC c) AR:AC

kiruha [24]

We know that

in the figure equivalent ratios are
BS/BC
and
AR/AC

therefore

AR/RC is not equivalent

the answer is
AR/RC

6 0

2 years ago

The plot of land illustrated in the accompanying diagram has a perimeter of 34 yards. Find the length, in yards, of each side of

noname [10]

Answer:

Length of x+3= 6.75

Length of 4x=15

Length of 3x-1=10,25

Step-by-step explanation:

First make an equation and find x x+3+3x+1+4x=34
Then solve for x, answer will be 3,75
3,75 represents x

3 0

1 year ago