write the equation of the circle given a center of (1,3) and a point on the circle at (-2,7)

Answer:

Joe's present age = 36 years

Vika's present age = 20 years

Step-by-step explanation:

Let us represent the present age of

Joe = x

Vika = y

Joe's age exceeds by Vika's age by 16 years.

x = y + 16...... Equation 1

Four years ago, Joe was twice as old as Vika.

x - 4 = 2(y - 4)

x - 4 = 2y - 8........ Equation 2

We substitute y + 16 for x

y + 16 - 4 = 2y - 8

Collect like terms

16 - 4 + 8 = 2y - y

y = 20 years

We solve for x

x = y + 16...... Equation 1

x = 20 + 16

x = 36 years

Therefore, Joe's present age = 36 years

Vika's present age = 20 years

Answer:A

Step-by-step explanation:

Dotted line means less than so it has to be A

Answer:

Step-by-step explanation:

Answer:

The rhombus because is the same shape

Answer:

Well, seems this'll be a long answer... *ahem*

So, the properties of a Kite are that they have

-Two pairs of consecutive sides

-No opposite sides

-Perpendicular diagonals

-One set of equal angles

The properties of a Trapezoid are that

-It has exactly 1 pair of opposite sides parallel

-It has congruent lower base angles

-Congruent upper base angles (both of these apply only if isosceles)

-Any lower base angle is supplementary to any upper base angle (applies to all)

The properties of a Square are that it has:

-Parallel opposite sides

-Congruent opposite sides

-Congruent opposite angles

-Bisecting diagonals

-Congruent diagonals

-Perpendicular diagonals

-All sides are congruent

-Consecutive angles are supplementary

-Contains four right angles

The properties of a Parallelogram are

-Parallel opposite sides

-Congruent opposite sides

-Congruent opposite angles

-Bisecting diagonals

-Consecutive angles are supplementary

The properties of a Rectangle are

-Consecutive angles are supplementary

-Contains four right angles

-Has all the properties of a parallelogram

The properties of a Rhombus are

-Has all the properties of a parallelogram

-Four sides are equal in length

-Diagonals are perpendicular

-Diagonals bisect each pair of opposite angles

Step-by-step explanation:

Hope you have a wonderful day, and also that this helped! (Even though I know it's quite long) :D

Answer:

3.5

Step-by-step explanation:

3.5 + 3.5 = 7

Answer:

75+3x=180

Step-by-step explanation:

Answer:

75 + 3x = 180

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

45 + 30 + 3x = 180

75 + 3x = 180

Answer:

y=6/7x

Step-by-step explanation:

You need to find the slope.  The rise is 18 and the run is 21.  18/21 simplifies to 6/7

Answer:

c

Step-by-step explanation:

Answer: 27.625 fl oz

Step-by-step explanation:

8.25*3.5= 27.625 fl oz

Answer:

22.407 < 22.416 because the value of the 0 in the hundredths place is less than the value of the 1.

SHOW ANSWER

Step-by-step explanation:

Answer:

The last answer choice

Step-by-step explanation:

22.407 < 22.416

Answer:

5. 2=1+1

6. 0= -3*0

7.2=3*0+2

Answer:

B

Step-by-step explanation:

3(d+2)-12d-2

3d+6-12d-2

3d+6-12-2

3d+4-12d= -9+4

Answer:

1. =−2

2.

3.

4. a=1

5. x=-1/2

6. x=4.2

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Honestly when I did the math I got closest to b so I think it's B hope his helps

Answer: [tex]\dfrac{14}{10}\ kg[/tex]

Step-by-step explanation:

Given

Henry has [tex]\frac{5}{10}\ kg[/tex] of flour and [tex]\frac{9}{10}\ kg[/tex] of sugar

If henry added the two amounts, the net weight of the two is

[tex]\Rightarrow W_{net}=\dfrac{5}{10}+\dfrac{9}{10}\\\\\Rightarrow W_{net}=\dfrac{5+9}{10}=\dfrac{14}{10}\ kg\ \text{or}\ \dfrac{7}{5}\ kg[/tex]

Answer:

559.70 ft

Step-by-step explanation:

Let D be the distance between building and Bianca.

Height of building H = 150 ft

Let there be a triangle ABC where, AC = height of building H= 150ft, AB = distance between Alice and Bianca and BC = D and therefore, ∠ABC = 15°.

Now in Triangle ABC , tanB = AC/BC

therefore, tan15° = 150/D

D = 150/tan15° = 559.70 ft

Therefore, the distance between building and Bianca D = 559.70 ft

Answer:

J

Step-by-step explanation:

Answer:

x = 58

Step-by-step explanation:

that is a 90 degree angle - 32 degrees = 58 degrees

Answer:

x = 27

Step-by-step explanation:

Hello There!

The first thing we want to do is find the measure of arc AD

remember the circumference of a circle in degrees is 360

so to find the measure of arc AD we subtract the given arc measures (97 and 112) from 360

360 - 112 - 97 = 151

so arc AD = 151

now to find x

if you didnt know an included angle formed by tangent lines is equal to one half of its major arc minus its minor arc

For this problem to be more specific ∠B = 1 half of (arc AD - arc AC)

Now what we want to do is plug in the known information and solve for angle B

∠B = 1/2 ( 151 - 97 )

151 - 97 =54

54/2=27

so we can conclude that x = 27

Hey there!

The answer is 13 boys and 16 girls.

We can do this by making an equation, using "x" to represent boys. Knowing there are 3 more boys than girls, we can set up the following equation:

(x + 3) + x = 29

NOTE: "x + 3" represents the number of girls, since there are 3 more girls than boys. "x" represents the number of boys. Now we can solve the equation:

x + 3 + x = 29

Add like terms:

2x + 3 = 29

Subtract 3 from both sides:

2x = 26

Divide both sides by 2:

x = 13

Therfore, there are 13 boys. To figure out girls, we simply add 3, giving us 16.

Have a terrificly amazing day! :D

Answer:

12

Step-by-step explanation:

6x12=72

3x12=36

36+36=72

Answer: 23.

Step-by-step explanation:

Answer:  

The opposite sides of a parallelogram are congruent, then

19x - 9 = 13x + 15 ( subtract 13x from both sides )

6x - 9 = 15 ( add 9 to both sides )

6x = 24 ( divide both sides by 6 )

x = 4

---------------------------------------------

Consecutive angles are supplementary, sum to 180° , that is

10y - 37 + 4y + 7 = 180

14y - 30 = 180 ( add 30 to both sides )

14y = 210 ( divide both sides by 14 )

y = 15

Then

∠ R = 10y - 37 = 10(15) - 37 = 150 - 37 = 113°

Then

∠ P = 113° ( opposite angles are congruent )

Step-by-step explanation:

Answer:

At least 16 service technicians

Step-by-step explanation:

Given

[tex]C(t) = -0.0625t^4 + t^3 - 6t^2 + 16t[/tex]

Required

Number of service technician to be online at 12 noon

First, we calculate the value of t

[tex]t = 12\ Noon - 8:00AM[/tex]

[tex]t = 4[/tex]

Substitute [tex]t = 4[/tex] in [tex]C(t) = -0.0625t^4 + t^3 - 6t^2 + 16t[/tex]

[tex]C(4) = -0.0625 * 4^4 + 4^3 - 6 * 4^2 + 16 * 4[/tex]

[tex]C(4) = 16[/tex]

This implies that there are 16 customers online at 12 noon.

If 16 customers are online, then there should be at least 16 service technicians online.

Answer:

this would be a right triangle with the legs being 8 miles and 6 miles. using the Pythagorean theorem, the hypotenuse would be 10 miles long. therefore, he would be walking a total of four miles less if he walked diagonally.

Step-by-step explanation:

Answer:23

Step-by-step explanation:

Answer:

the answer is y^3+11y^2+22y-6

Answer:

y³ + 11y² + 22y - 6

Step-by-step explanation:

(y + 3)(y² + 8y - 2)

y(y² + 8y - 2)+ 3(y² + 8y - 2)

y³ + 8y² - 2y + 3y² + 24y - 6

y³ + 11y² + 22y - 6

Answer:

Answer:

-35π/18 radians

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

Let number of pages=x

60% of x=114

x=114×100/60=190

pages left=190-114=76

Answer:

2262 in³

Step-by-step explanation:

Given that:

Height, h = 20 inches

Radius, r = 6 inches

Volume of a cylinder is given as :

V = πr²h

V = π * 6² * 20

V = π * 36 * 20

V = 2261.9467 in³

Hence, Nicholas pot can hold about 2262 in³ of soup