10. In the diagram of collinear points, GK=24, HJ=10, and GH=HI=IJ. Find each length.

Please show all work and not just answers.

Answer:

Height of the triangle is 6 feet and base of the triangle is 4 feet.

Step-by-step explanation:

Area of a triangle is given by the formula,

Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

Let the height of triangle = h feet

Since, base of the triangle is 2 feet less than its height then base of the triangle = (h - 2) feet

Area = [tex]\frac{1}{2}h(h-2)[/tex]

[tex]12=\frac{1}{2}h(h-2)[/tex]

h² - 2h - 24 = 0

h² - 6h + 4h - 24 = 0

h(h - 6) + 4(h - 6) = 0

(h + 4)(h - 6) = 0

h = -4, 6 feet

Since height of the triangle can not be negative, therefore, height of the triangle = 6 feet.

And base of the triangle = (h - 2) = 6 - 2

                                         = 4 feet

Height of the triangle is 6 feet and base of the triangle is 4 feet.

Answer:

The answer is H. II and III only.

Step-by-step explanation:

A simple way to tell if a relation is a function is by taking a look at the X value, which is on the left. If the X value repeats again  (ex: (0,1) (0,2) or (5,3 (5,7)) it is not a function. However, the Y value is allowed to repeat.  

x=4

subtract 8 instead of 2

Answer:

m=-1

Step-by-step explanation:

2x+3y=11............. (eqn 1)

2x-4y=-24...........(eqn 2)

Subtract eqn 1 from eqn 2

7y=35

y=5

Substitute for y in eqn 1

2x+3(5)=11

2x+15=11

2x=11-15

2x=-4

x=-2

y=mx+3

5=-2m+3

5-3=-2m

2=-2m

m=-1

Answer:Here,

Subtracting (ii) from (i),we get

2x+3y=11

- 2x+4y=24

___________

7y =35

y=5

Substituting y = 5 in (i) we get

2x+3×5=11

or,2x +15 =11

or,2x = 11- 15

or,x= -2

Now,

We know,y=mx+c

5=m ×(-2) +3

or,2=m×(-2)

or,2/-2 =m

m= -1

Answer:

I will answer in English:

We first have a rational number, the quotient between 2 positive integer numbers is 0.57....

And we want to find which number we should add in order to get 1.

Then we have:

A/B = 0.5757...

So if we have:

x = 0.5757....

we have two periodic decimals, then we multiply by 100 (the number of zeros is equal to the number of periodic decimals)

100*x = 57.575757

Now we subtract the original number:

100*x - x = 99*x = 57.575757... - 0.5757 = 57.

Then we have:

99*0.5757... = 57

0.575757... = 57/99

Now that we know the original fraction, if we want to find a fraction such that:

0.57... + a/b = 1

57/99 + a/b = 1

we should use the same denominator in both fractions:

b = 99

57/99 + a/99 = 1

57 + a = 99

a = 99 - 57 = 42

Then the fraction is 42/99

Answer:

Factors of 65: 1, 5, 13, 65. Prime factorization: 65 = 5 x 13.

Answer:

13*5*m

Step-by-step explanation:

                                                      65m

                                    13     5                           m

Answer:

3.64 hr, or 3 hr 38 min

Step-by-step explanation:

Recall that distance = (rate)(time).  Thus,

time = (distance) / (rate)

Here we have:

time = (200 km) / (55 km/hr) = 3.64 hr, or 3 hr 38 min

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

[tex]tu = tv - uv \\ tu = (14x - 8) - 5 \\ tu = 14x - 13 \: - - - (1) \\ \\ tu = 9x + 2 \: - - - (2) \\ \\ sub \: (1) \: into \: (2) \\ \\ 14x - 13 = 9x + 2 \\ 14x - 9x = 2 + 13 \\ 5x = 15 \\ x = \frac{15}{5} \\ x = 3[/tex]

AB is the answer. :)

Answer:

              [tex]\bold{(f+g)(x)=2x^2+\frac32x-5}[/tex]

Step-by-step explanation:

[tex]f(x) =\frac x2-2\quad and\quad g(x) = 2x^2 + x - 3\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=\frac12x-2+2x^2+x-3\\\\(f+g)(x)=2x^2+\frac32x-5[/tex]

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\begin{bmatrix}2x-y=0\\ x+3y=-14\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:2x-y=0:\quad x=\frac{y}{2}\\\\\mathrm{Subsititute\:}x=\frac{y}{2}\\\\\begin{bmatrix}\frac{y}{2}+3y=-14\end{bmatrix}\\\\\mathrm{Simplify}\\\\\begin{bmatrix}\frac{7y}{2}=-14\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{7y}{2}=-14:\quad y=-4\\\\\mathrm{For\:}x=\frac{y}{2}\\\\\mathrm{Subsititute\:}y=-4\\x=\frac{-4}{2}\\\\\frac{-4}{2}=-2\\\\x=-2,\:y=-4[/tex]

Answer:

(-2,-4)

Step-by-step explanation:

2x-y=0

-2(x+3y=-14)

-2x-6y=28

x terms cancel

-y+-12y=-13y

0+28=28

-7y=28

28/-7

y=-4

plug into the orginal equation

2x-(-4)=0

simply: 2x+4=0

elimante the 4

2x=-4

divide by 2

x=-2

Answer:

I am 90% sure it is D

Step-by-step explanation:

Greetings from Brasil....

As stated in the statement of the question, EF is a bisector of CD, so point G is the median point of CD, so CG = GD

5X - 1 = 7X - 13

X = 6

EF = EG + GF

6X - 4 = EG + 13      x = 6, so

6·6 - 4 = EG + 13

(see attachment)

A line segment is also a line but the line with finite length and having fixed endpoints. The length of the line segment EG is 19 unit.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

Given that EF bisects CD at point G, therefore, the line segment CD will be divided into two equal parts, CG and GD. Therefore, we can write,

CG = GD

5x - 1 = 7x - 13

-1 + 13 = 7x - 5x

12 = 2x

x = 12/2

x = 6

Further, the length of segment EG will be,

EG = EF - GF

     = 6x - 4 - (13)

     = 6x - 4 - 13

     = 6x - 17

     = 6(6) - 17

     = 36 - 17

     = 19

Hence, the length of the line segment EG is 19 unit.

Learn more about Line here:

https://brainly.com/question/21511618

#SPJ2

Answer:

C. 14%

Step-by-step explanation:

We know that Dallas's wage increased from $9 to $10.25.

Let's say the percent increase is x. Then we write the expression:

9 + x * 9 = 10.25

Divide by 9 from both sides:

1 + x = 10.25 / 9 ≈ 1.14

Subtract 1 from both sides:

x = 1.14 - 1 = 0.14

Since x is a percent, that means x = k/100, where k is an integer. So we have:

x = k/100 = 0.14

Multiply both sides by 100:

k = 0.14 * 100 = 14%

The answer is thus C.

~ an aesthetics lover

Answer:

Step-by-step explanation:

[tex]Original\:price = \$9\\New\:price =\$10.25\\\\Increase = 10.25-9\\Increase = 1.25\\\\Increase \: \% = \frac{Increase}{Original \:price} \:\times 100\\\\= \frac{1.25}{9} \times 100\\\\= \frac{125}{9}\\ \\= 13.888\\= 14\%[/tex]

Answer:

the answwr is C. the sum is zero

Answer:

y=6

then,

5x+4y=39---> plug y in to the function

5x+4(6)=39

5x+ 24=39

5x= 39-24

5x= 15

x= 15/5

x= 3

So, the value of x when y=6 in that function is 3 (D)

Answer:

A

Step-by-step explanation:

So we want to convert 59°F to Celsius using the given formula:

[tex]C=\frac{5}{9}(F-32)[/tex]

Thus, substitute F for 59:

[tex]C=\frac{5}{9}(59-32)[/tex]

Subtract:

[tex]C=\frac{5}{9}(27)\\[/tex]

Simplify:

[tex]C=\frac{135}{9}=15\textdegree F[/tex]

The answer is A

Answer:

[tex]\huge\boxed{15 \° C}[/tex]

Step-by-step explanation:

[tex]C = \frac{5}{9} ( F - 32)[/tex]

Where F = 59 °F

[tex]\sf C = \frac{5}{9} (59-32)\\C = \frac{5}{9} ( 27)\\C = 5 * 3\\C = 15 \ degrees \ Celsius[/tex]

Answer:

Step-by-step explanation:

Notice that:

● 1/2 = 0.5

● 4/5 = 0.8

0.8 is greater than 0.5.

So:

● 0.8 > 0.5

● 4/5 > 1/2

Answer:

4/5 > 1/2.

Step-by-step explanation:

4/5 is greater than 1/2.

Answer:

  No

Step-by-step explanation:

There are no real numbers that are both rational and irrational, and there are no real numbers that are neither rational nor irrational. The diagram is misleading.

___

A question is not true or false. A statement is true or false. If the statement is, "this picture represents real numbers correctly," then it is FALSE.

Answer:

-44

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3/6

Step-by-step explanation:

A coin has 2 sides

3 coins = 6 sides

3 heads 3 tails

3 chances out of 6 to get heads

3 chances out of 6 to get tails

3/6 for both

Answer:

Opposite reciprocals are two numbers that are flipped fractions of eachother. For example, the reciprocal of 2/3 is 3/2.

Answer:

An Opposite reciprocal is like a number flipped

Step-by-step explanation:

4 = 1/4

2/3 = 3/2

Answer: x=12

Step-by-step explanation:

Given

-10x-5=-125

Add 5 on both sides (addition property of equality)

-10x=-120

Divide -10 on both sides (division property of equality)

x=12

Hope this helps!! :)

Please let me know if you have any question

Answer: X=12

Step-by-step explanation:

Clear the X first to solve this problem

-10x - 5 = -125

125 - 5 = 10x

120/10 = x

12 = x

Answer:

Nocomplanar? Right because they’re not all in the same place?

Step-by-step explanation:

Answer: True

Step-by-step explanation: both equal 7

Answer:

3

Step-by-step explanation:

3 because 3 is a good number....lol

Step-by-step explanation:

(1 − cos x)(1 + cos x)

1 − cos²x

sin²x