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1 year ago

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A circle has a circumference of \blue{12}12start color #6495ed, 12, end color #6495ed. It has an arc of length \dfrac{8}{5} 5 8

start fraction, 8, divided by, 5, end fraction. What is the central angle of the arc, in degrees? ^\circ ∘ degrees

2 answers:

Lorico [155]1 year ago

7 0

Answer:

Step-by-step explanation:

its 11

Thepotemich [5.8K]1 year ago

6 0

Answer:

Therefore,

The Central Angle is 48°.

Step-by-step explanation:

Given:

Circumference = 12 units

$Arc\ length = \dfrac{8}{5}= 1.6\ unit$

To Find:

Central angle = θ = ?

Solution:

If "θ" the central angle is in degree then arc of length is given by

$Arc\ length = \dfrac{\theta}{360}\times Circumference$

Substituting the values we get

$1.6 = \dfrac{\theta}{360}\times 12\\\\\theta = 48\°$

Therefore,

The Central Angle is 48°.

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When 54,702 is divided by 25, the quotient is 2,188 R ___.

iogann1982 [59]

Hello There!

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1 year ago

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Jose wants to start a restaurant and is writing a business proposal. His rent is $1,000 per month. The monthly operating costs a

Harman [31]

Answer:

Revenue = 5( 1000 + w+ k)

Step-by-step explanation:

Lets calculate expenses first

rent = $1000

wages = w

overhead cost = k

Total cost = rent + wage+ overhead

Total cost = 1000 + w+ k

Given Jose wants his monthly sales revenue, x, to be 4 times greater than the operating costs

Let revenue be R

Thus, putting the statement mathematically

revenue - total cost = 4 * operating cost

R - ( 1000 + w+ k) = 4( 1000 + w+ k)

R = 4( 1000 + w+ k) + ( 1000 + w+ k)

R = 5( 1000 + w+ k)

Thus, revenue should be 5( 1000 + w+ k).

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2 years ago

use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1. the vertex is the . the function is inc

timurjin [86]

Answer:

The vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.

Step-by-step explanation:

The given function is

$f(x)=-x^2-2x-1$

$f(x)=-[x^2+2x+1]$

$f(x)=-(x+1)^2$ ....(1)

The general vertex form of the parabola is

$f(x)=a(x-h)^2+k$ .....(2)

Where, (h,k) is vertex and a is stretch factor.

On comparing (1) and (2), we get

$a=-1$

$h=-1$

$k=0$

The vertex of the parabola is (-1,0). Since a=-1<1 so it is a downward parabola.

The axis of symmetry is x=-1. So, before -1 the function is increasing and after -1 the function is decreasing.

The vertex of a downward parabola is the point of maxima. So, the rang of the function can not exceed 0.

Therefore the vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.

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2 years ago

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In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .

⇒ $\cos Z =\frac{3.5}{18}$

⇒ $\cos Z = 0.195$ (approx) or

$Z=\cos^{-1}(0.195)$

Therefore, the angle $\angle Z = 78.7^{\circ}$ .

The sum of the measure of the angle in the triangle is 180 degree.

In triangle XYZ.

$\angle X +\angle Y+\angle Z =180^{\circ}$

Since $\angle X=\angle Z =78.7^{\circ}$

then,

$78.7^{\circ}+\angle Y+78.7^{\circ}=180^{\circ}$

⇒ $157.4^{\circ}+\angle Y=180^{\circ}$

Simplify:

$\angle Y=22.6^{\circ}$ .

Therefore, the measure of each angle are: $\angle X=\angle Z=78.7^{\circ}$ and $\angle Y =22.6^{\circ}$

8 0

1 year ago

Dea writes the expression 0.25 + 0.76 + 0.75 + 0.24. She rewrites the expression using the commutative property. Which expressio

ipn [44]

Answer:

B ) 0.25 + 0.75 + 0.76 + 0.24

Step-by-step explanation:

<u>commutative law of addition:-</u>

According to the commutative property of addition,changing the order of the numbers.we are adding doesn't change the sum.

let a,b,c+d are two numbers

The commutative property condition in addition a+b+c+d = a+c+b+d

Given expression 0.25+0.76+0.75+0.24 = 0.25 + 0.75 + 0.76 + 0.24

conclusion:- Answer B.

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1 year ago