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2 years ago

Find the value of x. (Type an integer or decimal.)

Mathematics

1 answer:

SOVA2 [1]2 years ago

6 0

Answer:

Step-by-step explanation:

An angle formed by 2 tangent lines is equal to one half the measure of the major arc minus the measure of the minor arc.

we are given the minor arc ( 110 ) however we are not given the major arc.

Because circles make a 360 degree rotation we can find the major arc by subtracting the measure of the minor arc from 360

Thus, major arc = 360 - 110 = 250

Now that we have identified the major and minor arc we can find x

Recall that x = 1/2 ( major arc - minor arc )

Thus, x = 1/2 ( 250 - 110 )

250 - 110 = 140

140 / 2 = 70

Hence, x = 70

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Joaquin and Trisha are playing a game in which the lower median wins the game. Their scores are shown below. Joaquin's scores: 7

alekssr [168]

Answer:

Step-by-step explanation:

Given

Joaquin's score is $75,72,85,62,58,91$

and Trisha's score is $92,90,55,76,91,74$

Arranging score in order of value we get

Joaquin's : $58,62,72,75,85,91$

Trisha's : $55,74,76,90,91,92$

as no of values is even therefore their median is

Joaquin's $=\frac{72+75}{2}=73.5$

Trisha's $=\frac{76+90}{2}=83$

Therefore median of Joaquin's is lower

Thus Joaquin wins the game

5 0

2 years ago

Read 2 more answers

Sqareroot 12 - (sqr. 3) = ?

Brrunno [24]

1.73 is the answer >:-)............................

7 0

2 years ago

∆ABC has vertices A(–2, 0), B(0, 8), and C(4, 2)

Natali [406]

Answer:

Part 1) The equation of the perpendicular bisector side AB is $y=-\frac{1}{4}x+\frac{15}{4}$

Part 2) The equation of the perpendicular bisector side BC is $y=\frac{2}{3}x+\frac{11}{3}$

Part 3) The equation of the perpendicular bisector side AC is $y=-3x+4$

Part 4) The coordinates of the point P(0.091,3.727)

Step-by-step explanation:

Part 1) Find the equation of the perpendicular bisector side AB

we have

A(–2, 0), B(0, 8)

step 1

Find the slope AB

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{8-0}{0+2}$

$m=4$

step 2

Find the slope of the perpendicular line to side AB

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=-\frac{1}{4}$

step 3

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+0}{2},\frac{0+8}{2})$

$M(-1,4)$

step 4

Find the equation of the perpendicular bisectors of AB

the slope is $m=-\frac{1}{4}$

passes through the point $(-1,4)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$4=(-\frac{1}{4})(-1)+b$

solve for b

$b=4-\frac{1}{4}$

$b=\frac{15}{4}$

$y=-\frac{1}{4}x+\frac{15}{4}$

Part 2) Find the equation of the perpendicular bisector side BC

we have

B(0, 8) and C(4, 2)

step 1

Find the slope BC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-8}{4-0}$

$m=-\frac{3}{2}$

step 2

Find the slope of the perpendicular line to side BC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=\frac{2}{3}$

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{0+4}{2},\frac{8+2}{2})$

$M(2,5)$

step 4

Find the equation of the perpendicular bisectors of BC

the slope is $m=\frac{2}{3}$

passes through the point $(2,5)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$5=(\frac{2}{3})(2)+b$

solve for b

$b=5-\frac{4}{3}$

$b=\frac{11}{3}$

$y=\frac{2}{3}x+\frac{11}{3}$

Part 3) Find the equation of the perpendicular bisector side AC

we have

A(–2, 0) and C(4, 2)

step 1

Find the slope AC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-0}{4+2}$

$m=\frac{1}{3}$

step 2

Find the slope of the perpendicular line to side AC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=-3$

step 3

Find the midpoint AC

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+4}{2},\frac{0+2}{2})$

$M(1,1)$

step 4

Find the equation of the perpendicular bisectors of AC

the slope is $m=-3$

passes through the point $(1,1)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$1=(-3)(1)+b$

solve for b

$b=1+3$

$b=4$

$y=-3x+4$

Part 4) Find the coordinates of the point of concurrency of the perpendicular bisectors (P)

we know that

The point of concurrency of the perpendicular bisectors is called the circumcenter.

Solve by graphing

using a graphing tool

the point of concurrency of the perpendicular bisectors is P(0.091,3.727)

see the attached figure

5 0

2 years ago

Determine the slope of a line that goes through (2,7) and (11,10)

tia_tia [17]

Answer:

1/3

Use the slope formula and simply the fraction.

4 0

2 years ago

Suppose a population of deer in the state is 10, 289 and is growing 1% each year. Predict the population after 5 years

eimsori [14]

Answer: the population after 5 years is 10814

Step-by-step explanation:

The population growth of the deer is exponential. We would apply the formula for determining exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

n represents the period of growth

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 10289

r = 1% = 1/100 = 0.01,

t = 5 years

Therefore,

A = 10289(1 + 0.01)^5

A = 10289(1.01)^5

A = 10814

3 0

3 years ago