A man jogs 6 miles in 1 hour 12 minutes. Calculate the average speed.

Given:

In triangle DEF, HG is parallel to DF.

To find:

The value of x.

Solution:

In triangles DEF and GEH,

[tex]\angle DE F\cong \angle GEH[/tex]          (Common angle)

[tex]\angle EDF\cong \angle EGH[/tex]          (Corresponding angle)

[tex]\Delta DE F\sim \Delta GEH[/tex]             (By AA property of similarity)

We know that corresponding sides of similar triangle are proportional.

[tex]\dfrac{DE}{GE}=\dfrac{DF}{GH}[/tex]

[tex]\dfrac{9+(x+5)}{x+5}=\dfrac{12}{6}[/tex]

[tex]\dfrac{x+14}{x+5}=2[/tex]

[tex]x+14=2(x+5)[/tex]

[tex]x+14=2x+10[/tex]

Isolating variable terms, we get

[tex]x-2x=-14+10[/tex]

[tex]-x=-4[/tex]

[tex]x=4[/tex]

Therefore, the value of x is equal to 4.

Answer:

Step-by-step explanation:

5x5 = 10  

Answer:

35

Step-by-step explanation:

Answer:

52 when we evaluate it understand

Answer:

A 2 seconds

Step-by-step explanation:

Answer:

4 seconds

Step-by-step explanation:

Since the object is falling 16ft  per second, it would take 4 seconds for it to fall 64 ft. Because 64 divided by 4 is 16

Answer:

40 feet

Step-by-step explanation:

Answer:

40 feet tall

Step-by-step explanation:

6/2 =3

?/2 =20

*2    *2

? = 40

you do inverse operations because 6 divided by 2 is 3... the ? is the variable for how tall the building is... ? divided by 2 = 20 so you multiply 2 and 20 to get the total height

Answer:

8. [tex]-\frac{1}{9}[/tex] and 1

9. [tex]-\frac{1}{2}[/tex] and -5

Step-by-step explanation:

Hope this helps ;)

Answer:

slope intercept form is the form of y=mx+b, where the slope is m and the y intercept is b.

what you have to do is to solve the equations for y.

1) 2x+2y = 10

  2y = 10 -2x

    y = -x +5

2) 12+4y = -4x

    4y = -4x-12

       y = -x -3

lines are parallel when they have same slope and different y-intercepts. m1=m2 and b1 ≠ b2

lines are perpendicular when the multiplication of their slope gives -1

m1 x m2 = -1

here the slopes are same and y-intercepts are different so lines are parallel.

Answer:

hello your question is not well written hence i will give you a more general answer assuming a  region that is enclosed by curves y = x and y = x^3

answer : 8/21

Step-by-step explanation:

y =x , y = x^3

next determine the intersection point which is

x = x^3

x( x^2 - 1 ) = 0

therefore ; x = 0 , 1 , -1

attached below is a detailed solution

Answer:

15

Step-by-step explanation:

3*5*1=15

Answer:

[tex]1\%[/tex]

Step-by-step explanation:

Simple interest (I) = $160

Principal amount (P) = $2000

Time period (t) = 8 months

Let R denotes rate of interest.

Relation between simple interest, principal amount, time and rate of interest  is given by [tex]I=\frac{PRT}{100}[/tex]

[tex]160=\frac{2000(R)(8)}{100} \\\\160=160R\\R=1\%[/tex]

Answer:

12

Step-by-step explanation:

It would be: r = I * 100 / P * R

r = 160.67 * 100 / 2000 * 2/3

r = 16067*3 / 4000

r = 48201 / 4000

r = 12

Answer:

Its the third option

Answer:

a. root (x^2 + 64)

Step-by-step explanation:

(8^2 + x^2) = y^2

If you root both sides,

y = root (x^2 + 64)

Answer:

linear monomial

Step-by-step explanation:

Answer:

B. (–1, –1)

C. (0, 2)

E. (1, –2)

Step-by-step explanation:

plugged in the answers into (x) and (y)

The points (0, 0), (-1, -1), and (1,-2) inside the conic inequality option (B), (C), and (E) are correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Conic inequality:

8x² – 12x + 4y² + 4y – 20 ≤ 0

After plotting the above inequality on a coordinate plane we will get an ellipse:

From the graph:

The points:

(0, 0), (-1, -1), and (1,-2) inside the conic inequality.

Thus, the points (0, 0), (-1, -1), and (1,-2) inside the conic inequality option (B), (C), and (E) are correct.

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ5

Answer:

5-2x=4-2x+4+x=8-x

x=5-8=-3

Answer:

The answer is B. One solution.

Step-by-step explanation:

Given

Slope (m1) = 4

As it is said that the lines are perpendicular so we have

m1 * m2 = - 1

4 * m2 = - 1

m2 = - 1/4

The slope of the line perpendicular to line m is

- 1/4

Hope it will help :)❤

Answer:

The slope of the perpendicular line is -1/4

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

Let the slope of the perpendicular line have sloe p

m*p = -1

4 * p = -1

Divide each side by 4

p = -1/4

The slope of the perpendicular line is -1/4

Answer:

The numerator (a*c) is the product of two integers ( a and c) and the denominator (b*d) is also ( b and d). This is why multiplying rational numbers is like multiplying integers.

Step-by-step explanation:

Answer: 1. x= y/12 - 7/12

2. x=y/6 + 25/6

Step-by-step explanation:

Answer:

The correct amount of force i believe is

f= 40 newton

i got the answer by using the formula below

force = mass x acceleration

f=5kg *8.0 m/s^2

Step-by-step explanation:

Answer:

it means to add all of the numbers then divide by how many there are

so, 3+3+5+5+5+7+7+8+15+15=73

73/10=7.3

hope this helped!!

Answer:

I dont know if this question was needed to be solved

Answer:

15 student

Step-by-step explanation:

35 - 21

15

Pls mark as branlist

Answer:

64ft²

Step-by-step explanation:

trapezoid area formula is b1+b2 over 2 times the height so

(6+10)÷2×8

16÷2×8

8×8

64

Answer:

Step-by-step explanation:

ΔH + ΔJ + ΔK + ΔG = 360°

103° + 133° + 58° + X = 360°

294° + X = 360°

X = 360° - 294°

X = 66°

Answer:

-163, -180, -197

Step-by-step explanation:

-146--129=-17

the difference of them is 17 so keep adding it