Circle D is inscribed in AABC as shown.
Point E marks the intersection of the two
shapes. Which of the following statements are
true?
Statement I: DE is the radius of the
inscribed circle.
Statement II: DE is perpendicular to AC.
Statement III: Point D is equidistant from
vertices A, B, and C.

Answer:

[tex]y=-5x+2[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that the line passes through are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (1,-3) and (-3,17)

[tex]=\frac{17-(-3)}{-3-1}\\=\frac{17+3}{-3-1}\\=\frac{20}{-4}\\=-5[/tex]

Therefore the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-5x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-5x+b[/tex]

Plug in one of the given points and solve for b

[tex]-3=-5(1)+b\\-3=-5+b[/tex]

Add 5 to both sides of the equation to isolate b

[tex]-3+5=-5+b+5\\2=b[/tex]

Therefore, the y-intercept of the equation is 2. Plug this back into [tex]y=-5x+b[/tex]:

[tex]y=-5x+2[/tex]

I hope this helps!

Answer:

4, x-1

Step-by-step explanation:

The first piece of this function goes from -1 to 1. Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

The second piece of this function goes from 3 to 5. This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1. Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis). When putting this equation together we get x-1 being the second part.

The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

The first piece of this function goes from -1 to 1.

Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

so, we have,

The second piece of this function goes from 3 to 5.

This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1.

Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis).

When putting this equation together we get x-1 being the second part.

Hence, The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

To learn more on graph click:

brainly.com/question/17267403

#SPJ7

Answer:

4X+5

Step-by-step explanation:

Dan : X

Harry: X+5

Regan: 2X

X+X+5+2X

Answer:

[tex]Mean = \frac{4x + 5}{3}[/tex]

Step-by-step explanation:

Given:

Dan sold = x

Harry sold 5 more than Dan, that is = x + 5

Regan sold twice as Dan = 2x

[tex]Mean = \frac{ Total \ cars \ sold}{number\ of \ them \ sold \ it }\\\\Mean = \frac{x + ( x+ 5) +2x }{3} = \frac{4x + 5}{3}[/tex]

Answer:

x = 20

Step-by-step explanation:

The angles form a straight line so they add to 180 degrees

6x-4 + 3x+4 = 180

Combine like terms

9x=180

Divide by 9

9x/9 = 180/9

x= 20

20

Hope this helps! :)

______________

Answer: 23692929

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex](25x-4)^8[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\boxed{\text{Calculating the Answer....}}\\\\\rightarrow\sqrt{(25x-4)^{16}}\\\\\rightarrow (25x-4)^{\frac{16}{2}}\\\\\text{Recall that: }a^{\frac{b}{c}}=\sqrt[c]{a^b}\\\\\rightarrow\boxed{(25x-4)^8}\\\\\text{Side Note: }\frac{16}{2}=8[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

2015-2010=5

50÷5=10

120-50=70

2017-2015=2

2*10=20

70-20=50mg

2018=50mg

Answer:

C. a = 6√3, b = 12, c = 6√2

Step-by-step explanation:

First let's find b using the cos. The cos is the adjacent side if the angle divided by the hypotenuse. We know the value of the adjacent side and we know that cos(60°) = 1/2 = 0.5:

cos(60°) = 6/b

0.5 = 6/b

b = 6/0.5

b = 12

Now we can find a using the Pythagorean theorem:

b² = 6² + a²

12² = 6² + a²

144 = 36 + a²

a² = 144 - 36

a² = 108

a = √108

a = 6√3

And now we can find c using cos again:

cos(45°) = c/b

√2/2 = c/12

c = 12•√2/2

c = 6√2

Answer:

number of A is correct answer

Answer:

21 cm²

Step-by-step explanation:

Applying,

A = (a+b)h/2............. Equation 1

Where A = area of the trapezium, a = length of the first parallel side, b = length of the second parallel side, h = height.

From the diagram

Given: a = 5 cm (5 grids), b = 9 cm (9 grids), h = 3 cm (3 grids)

Substitute these values into equation 1

A = 3(5+9)/2

A = 3(14)/2

A = 3×7

A = 21 cm²

Answer:

19.8 m

Step-by-step explanation:

To find the height of the tree, we can use the trig ratio tangent:

θ = angle, h = height

tan θ [tex]= \frac{opposite}{adjacent}[/tex]

tan 33° = h / 30.5

h = (tan 33°)(30.5)

h = (0.6494)(30.5)

h = 19.8 m

Step-by-step explanation:

everything can be found in the picture

Answer:

The angles are 78° and 102°.

Step-by-step explanation:

Let the one angle is y and the other number if y + 24.

The sum of the angles of the linear pair is 180°.

So, according to the question

y + y + 24 = 180

2 y = 180 - 24

2 y = 156

y = 78°

So, one angle is 78° and the other is 78° + 24° = 102°.

Answer:

vertical hope this helps

Answer:

vertical, goodluck

Step-by-step explanation:

I took this

Answer:

slope

Step-by-step explanation:

The slope is the rise divided by the run

Answer: The slope.

Step-by-step explanation: That's what I think.

Answer:

The equation has 0 solutions (answer C).

Step-by-step explanation:

Starting with x = x - 9, we subtract x from both sides.  This leaves us with:

0 = -9,

which is never true.

The equation has 0 solutions (answer C).

Answer:

[tex]198\:\mathrm{m^3}[/tex]

Step-by-step explanation:

The volume of a cylinder is given by [tex]V=r^2\pi\cdot h[/tex], where [tex]r[/tex] is the radius of the cylinder and [tex]h[/tex] is the height.

What we're given:

Substituting given values, we get:

[tex]V=3^2\pi\cdot 7,\\V=9\cdot 3.14\cdot 7,\\V\approx 197.82\:\mathrm{m^3}=\boxed{198\:\mathrm{m^3}}[/tex], rounded the nearest cubic meter as requested in question.

Answer:

Volume of cylinder is 197.82 m ³.

Step-by-step explanation:

Here,

Diameter of cylinder = 6 m

So, Radius of cylinder, r = 6 / 2 = 3m

Height of cylinder , h = 7 m

Value of π = 3.14

Volume of cylinder

We know that,

Volume of cylinder = π × r ² × h

Substitute the values

Volume of cylinder = 3.14 × ( 3m ) ² × 7 m

volume of cylinder = 3.14 × 9m² × 7 m

Multiply , we get

Volume of cylinder = 197.82 m ³

Therefore, The volume of cylinder id 197.82 m ³.

Step-by-step explanation:

x-intercept => point (2, 0)

y-intercept => point (0, -4)

Answer:

27.7

Step-by-step explanation:

Pythagorean Theorem

[tex]88.3^{2}[/tex] - [tex]10.7^{2}[/tex] = [tex]x^{2}[/tex]  (10.7 comes from half of the 21.4 side)

[tex]x^{2}[/tex] = height

Answer:

(3, 1) (5, 3) (7, 5) (13, 11)

Step-by-step explanation:

There are only three of them that I know of:

(7, 5) (13, 11) (19,17)

Step-by-step explanation:

Let the increase in the size of the length and breath be 'x'.

The area of the rectangle = 12in × 8in

=96 in²

From the question,

(12+x)(8+x)=96×2 in²

or, 96+12x+8x+x²= 192

or, x²+20x+96-192=0

or, x²+20x-96=0

or, x²+24x-4x-96=0

or, x(x+24)-4(x+24)=0

or, (x-4)(x+24)=0

Either, Or,

x-4=0 x+24=0

Therefore, or, x= –24 (Which is impossible)

x=4

So the new dimensions are 12+4=16 inch and 8+4=12 inch.

Answer:

6.28km

Step-by-step explanation:

Hey,

We know that the circumfrence is the perimetert of a full circle. If we want to find the perimeter of a semicircle all we have to do is find the circumfrence and then divide it by 2 since we want to know the perimeter of half the circle.

Circumfrence is equal to 2πr. Where r is the radius and since we know the radius we an solve for the circumfrence.

2(π)(1km)=2kmπ.

The problem tells us to use 3.14 for pi so let's multiply 2 by 3.14.

6.28km is the answer!

Answer:

122 squared cm

Step-by-step explanation:

[tex]6*12=72[/tex]

[tex]10*5=50[/tex]

[tex]72+50=122[/tex]

Hope this helps

Answer:

122 squared cm

Step-by-step explanation:

First we split the figure into 2

12 x 6

And,

10 x 5

12 x 6 = 72

and

10 x 5 = 50

Now we add 72 + 50 = 122

Answer:

Option B

Step-by-step explanation:

Of those surveyed, 26 percent said free international trade helped the economy.

They claimed that trade liberalization and increase in investment in physical capital was the main reason behind the growth of the economy.

Hence, option B is correct

Answer:

Add -8

Step-by-step explanation:

Take the second term and subtract the first term

6-14 = -8

Check with the third and second terms

-2 -6 = -8

We are subtracting 8 from each side

(or adding -8)

Step-by-step explanation:

14, 6, -2, -10 , -18

ok so if you are starting at 14 then you would be add -8

14-8=6

6-8=-2

so on and so on..

But if you are starting from -18 then you would add 8

-18, -10,-2, 6, 14

-18+8=-10

-10+8=-2 so on and so on

so either one of those depending on which number your starting with

Answer:

(0,3)

Step-by-step explanation:

solve for 2y

-X-2y= -6

2y=6+2x

substitute the given value of 2y into the equation -x-2y=-6

-x-(6+3x)= -6

solve for x

x=0

substitute the given value of X into the equation 2y=6+3x

2y=6+3×0

solve for y

y=3

the solution is (0,3)

Answer:

1/7^10

Step-by-step explanation:

7^-10

=1/7^10

Answer:

2x+6>20

2x>20-6

2x/2>14/2

x>7

So your answer would be B

Answer: 10

We know that the radius of a circle is always perpendicular to the tangent. And so apply the Pythagoras theorem.

Answer:

The answer would be 10.

Step-by-step explanation:

We're doing C^2 - B^2 = A^2 since we know the hypotenus. 26 x 26 is 676 and 24 x 24 is 576. Subtract the two products to get 100. The square root of 100 is 10.

Answer: 18.84

Step-by-step explanation:

Formula for circumference of a circle is 2[tex]\pi[/tex]r. Radius is half the diameter so 6/2=3. 2(3.14)(3)= 18.84

Answer:

y=3/5x+1

Step-by-step explanation:

Hi there!

We are given the equation -3x+5y=-8 and we want to find the equation of the line that is parallel to -3x+5y=-8 and contains the point (-15,-8)

parallel lines have the same slopes, but different y intercepts.

So let's first find the slope of -3x+5y=-8

We can do this by converting the equation from standard form (ax+by=c where a, b, and c are free coefficients (numbers)) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

add 3x to both sides

5y=3x-8

divide by 5 on both sides

y=3/5x-8/5

3/5 is in the place of where m is, so that means that 3/5 is the slope of the line

we can write the equation of the new line in slope-intercept form.

Here it is so far:

y=3/5x+b

we need to find b

Because the line will pass through the point (-15,-8), we can use it to solve for b

substitute -15 as x and -8 as y

-8=3/5(-15)+b

multiply

-8=-9+b

add 9 to both sides

1=b

substitute 1 as b into the equation

y=3/5x+1

There's the equation of the line :)

Hope this helps!