In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement ∠Q ≅ ___

Answer:

x = 4

Step-by-step explanation:

Given that DE is parallel to AC then DE divides the sides proportionally, so

[tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex] , substitute values

[tex]\frac{x+2}{x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3x = 2(x + 2) ← distribute

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

4 option

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rate of increase = r = 25%

n = number of years = 6

P = Current population = 3000

Population after n years = [tex]P*(1 + \frac{r}{100})^{n}[/tex]

            [tex]= 3000 * (1 +0.25)^{6}\\\\= 3000 * (1.25)^{6}\\\\= 3000 * 3.8\\\\= 11400=[/tex]

Answer:

m = 3 , n = 4

Step-by-step explanation:

Using Section Formula.

[tex]If \ the \ line \ segment \ AB \ where \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \ the \ points \ of \ P \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}[/tex]

   [tex]Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x = -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3[/tex]

  [tex]y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4[/tex]

Answer:

$27

Step-by-step explanation:

Thomas rents a car for his vacation. The mileage include with the rental is 54 miles. For every mile he drives over 54 miles, he needs to pay $1 4/5. If he drives 69 miles, how much extra does he need to pay?

Total mileage included with the rental = 54 miles

Additional cost per mile after 54 miles = $1 4/5

Total miles Thomas drives = 69 miles

Extra miles Thomas drives = 69 miles - 54 miles

= 15 miles

how much extra does he need to pay?

Extra cost Thomas needs to pay = Additional cost per mile after 54 miles * Extra miles Thomas drives

= $1 4/5 * 15 miles

= 9/5 * 15

= (9 * 15) / 5

= 135/5

= 27

Extra cost Thomas needs to pay = $27

Answer:

option A

Step-by-step explanation:

22 : 15 + 10hours = 8 : 15

                              8 : 15 + 35 minutes = 8 : 50

Therefore the difference = 10 hours 35 minutes

Answer:

The measure of each angle will be 7 degrees. It is because a bisector divides an angle in two equal halves. 14 / 2 = 7

Answer:

[tex]delta = {b}^{2} - 4ac = {p}^{2} - 4 \times 3 \times 3 = {p}^{2} - 36[/tex]

The equation has no real roots if delta <0

that is -6<p<6

Answer:

Is that it's not about the answers and the questions

Answer:

stars: triangles

3  : 1

Step-by-step explanation:

There are 3 starts and 1 triangle

stars: triangles

3  : 1

Answer:

3:1

Step-by-step explanation:

3 Stars and 1 Triangle

Answer:

The length of each ribbon is 1.6 inches

Step-by-step explanation:

From the question, we are told that:

Kenedi has a piece of ribbon that measures 24 inches long. She cuts the ribbon into 15 equal pieces to attach to her dance costume

Hence, the expression that can be used to show how to calculate the length of each piece of ribbon is given as:

24 inches ÷ 15 pieces

= 24 ÷ 15

= 1.6 inches

Therefore, the length of each ribbon is 1.6 inches

Answer:

3

Step-by-step explanation:

3

Answer:

7.5 as an improper fraction in its simplest form would be 15/2

Answer:

{2, 4, 6, 8,10}

Step-by-step explanation:

GIven U={1,2,3,.............,10} A={2,4,6,8,10} and B= {1,3,5,7,9);

Required

A-B = AnB'

B' = {2, 4, 6, 8,10}

AnB' are elements common to both A and B'.Hence;

AnB' = A- B = {2, 4, 6, 8,10}

3+2=5

Milk =3/5×640 = 384

Curd 2/5×640 = 256

Answer:

z = -74

Step-by-step explanation:

12 = (2+z) / -6

Multiply each side by -6

-6 * 12 = (2+z)/ -6 * -6

-72 = 2+z

Subtract 2 from each side

-72-2 = 2+z-2

-74 =z

Answer:

f(6) = 24

Step-by-step explanation:

To evaluate f(6) substitute x = 6 into f(x) , that is

f(6) = 6² - 2(6) = 36 - 12 = 24

Answer:

∠AEC ≅ ∠BED by vertical angles theorem

Answer:

Answer:

∠AEC ≅ ∠BED by vertical angles theorem

Step-by-step explanation:

Answer:

The length of the equal sides of the isosceles triangle with a perimeter of 34 cm perimeter is 12 cm

The length of the equal sides of the isosceles triangle with a perimeter of 82 cm perimeter is 36 cm

The base length of both triangles is 10 cm

Step-by-step explanation:

The given parameters are;

The base length of the triangles are equal

The base length of one of the triangle = The base length of the other triangle

The equal sides of one of the triangles = 3 × The length of the equal sides of the other

The perimeter of the triangles are; 34 cm and 82 cm

Let 'b' represent the base length of each triangle, let 'a' represent the length of an equal side of the smaller triangle with a perimeter of 34 cm and let 'c' represent the length of an equal side of the larger triangle with a perimeter of 82 cm

For the smaller triangle, we have;

b + 2·a = 34..(1)

For the other triangle;

b + 2·c = 82...(2)

Given that the side length of the larger triangle are larger than those of the smaller triangle, and that the side length of the larger triangle is 3 times the side length of the smaller triangle, we get;

c = 3·a

By the substitution method, from equation (2) we get;

b + 2·c = b + 2 × 3·a = b + 6·a = 82

∴ b + 6·a = 82...(3)

Subtracting equation (1) from equation (3) gives;

b + 6·a - (b + 2·a) = 82 - 34 = 48

b - b + 6·a - 2·a = 48

4·a = 48

a = 48/4 = 12

The length of the equal sides of the 34 cm perimeter (smaller) isosceles triangle, a = 12 cm

From c = 3·a, and a = 12, we get;

c = 3 × 12 = 36

The length of the equal sides of the 82 cm perimeter (larger) isosceles triangle, c = 36 cm

From equation (1), we get;

b + 2·a = 34

∴ b + 2 × 12 = 34

b = 34 - 2 × 12 = 10

The base length of both triangles, b = 10 cm

Answer:

The standard equation is 7x + y = 9

Step-by-step explanation:

Equations given are:  

7x + 3 = 5 and y - 1 = 6

Set both given equations equal to zero, then combine them into one standard form equation

Set the equations to zero by moving the constant from R.H.S to L.H.S

7x + 3 - 5 = 0

7x - 2 = 0 ---- eq 1

y - 1 = 6

y - 1 - 6 = 0

y - 7 = 0 ----- eq 2

We have to combine eq 1 and eq 2

7x - 2 + y - 7 = 0

7x + y - 9 = 0

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

Thus the standard equation is:

7x + y - 9 = 0

7x + y = 9

Thus the standard equation is 7x + y = 9

Solution :

As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis. The first block then should be negative x-axis if r is positive and in the positive x-axis if r is negative.

My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence, which would mean an interference from the above statements, from the drag phase you have given the interference would be positive x-axis.

Answer:

50.24 sq cm

Step-by-step explanation:

radius is 4 (half of 8)

A=(3.14)4^2

A=50.24

Answer:

B) 50.24 sq.cm

Step-by-step explanation:

equation for area of circle is [tex]\pi r^{2}[/tex]

radius is half of diameter

radius = 4 cm

[tex]\pi (4)^2[/tex] = 50.24 sq.cm

well, let's keep in mind that the SAS postulate, so if one Side and the Angle next to it and the following Side after the angle are equal on both triangles, both triangles are congruent.  Now, we have the angle 30° with sides and 9 and 2x and sides 9 and x + 4, well, the 9's are equal, dohh, you know, if only the 2x  = x + 4, we'd be golden

[tex]2x = x + 4\implies 2x - x = 4\implies \boxed{x = 4}[/tex]

Answer:

Given

To find f(x + 2) substitute x with x + 2 in the given function:

f(x+2)= 4(x + 2)² + 2(x + 2) - 4

         = 4(x² + 4x + 4) + 2x + 4 - 4

         = 4x² + 16x + 16 + 2x

         = 4x² + 18x + 16

f(x+2)

Answer:

5

Step-by-step explanation:

AC=AB+BC

so 16=x+1+x+7

which simplifies to 16=2x+8

subtract eight from both sides to get 8=2x

then divide by 2 to get that x=4

AB=x+1, which substitutes into 4+1=5