eight out of 10 dentist prefer Crest toothpaste.What is the ratio of dentist whi prefer Crest to those who do

1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is $(2x+10)^\circ$ , so the measure of arc DF is

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

$170-2x=64\implies106=2x\implies\boxed{x=53}$

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2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

$m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}$

7 0

2 years ago

Please help!!! ill mark brainliest

Vesnalui [34]

3x - 1 = 3x + 1

subtract 3x from both sides to get (-1 = 1). This is a false statement so it is: CONTRADICTION

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4x - 11 = 7

add 11 to both sides and then divide both sides by 4 to get $(x = \frac{18}{4} = \frac{9}{2})$ . This statement is true only when x = $\frac{9}{2}$ so it is: CONDITIONAL

*************************************************

2 - 8x = 2 - 8x

add 8x to both sides to get (2 = 2). This is a true statement so it is: IDENTITY

*************************************************

x + 1 = -x + 4

add x to both sides, subtract 1 from both sides, and divide both sides by 2 to get $(x = \frac{3}{2} )$ . This statement is true only when x = $\frac{3}{2}$ so it is: CONDITIONAL

Answer: B, A, C, A

6 0

3 years ago

The diagram shows a track composed with a semicircle on each end. The area of the rectangle is 8,400 square meters. What is the

MrRa [10]

Answer:

468.4 meters

Step-by-step explanation:

Find the width of the rectangle.

The area of a rectangle is A=length*width. Substitute the values of length and area and solve for width.

A=length*width

8,400=140*width

60= width

Use the width of the rectangle to find the circumference of the semicircles. Since each semicircle is half of a circle, the perimeter of the two semicircles is equal to the circumference of one circle.

The circumference of a circle is equal to pid, where d is the diameter. The diameter of the semicircle is the same as the width of the rectangle.

So, the diameter is 60 meters. Substitute the diameter into the formula for the circumference and simplify using 3.14 for pi.

≈188.4

(2 times 140)+ 188.4

So, the perimeter of the track is 468.4 meters.

7 0

3 years ago

Jon goes to a flea market and sells comic books for 3 dollars each. He starts the night with 20 dollars in

Rudiy27

So what you have to do to figure this out is 47-20 to get 27, then take 27 and divide it by 3 to get the answer of 9 comic books were sold by John.

5 0

2 years ago

Find several points that are on the graph of the function y = x^2 + 1. Plot the points in a coordinate plane.

beks73 [17]

Answer:

Below.

Step-by-step explanation:

Plot following points.

Calculate the point by plugging in values of x into x^2 + 1

for example When x = 0, y = 0^1 + 1 = 1.

So plot plot (0, 1),

Make a table of points to plot:

x -3 -2 -1 0 1 2 3

y 10 5 2 1 2 5 10

When you plot the points you'll see the graph is U shaped.

The function is of second degree (as it contains x^2) so it wont be linear.

8 0

3 years ago