10. angle GHI is an isosceles triangle with GI HI. IF GH is three more than x, HI is 17 less than fourtimes x, and GI is 45 less than six times x, find x and the measure of each side.

Answers

Answer 1
Answer:

Answer:

GH = 17 units

GI = 39 units

HI = 39 units

Step-by-step explanation:

We are given the following information in the question:

Triangle GHI is an isosceles triangle.

GI = HI

The measures of side are:

GH = 3 + x\nHI = 4x-17\nGI = 6x - 45

It is given that

GI = HI

4x - 17 = 6x -45\n6x - 4x = 45-17\n2x = 28\nx = 14

Thus, the measures of three sides are:

GH = 3 + x=14+3 = 17\nHI = 4x-17 = 4(14)-17 = 39\nGI = 6x - 45=6(14) - 45 = 39


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What is 678 divided by 5 with remander?

Answers

678/5 = 135 

135 is the whole number, now we need to find the remainder.

135*5 = 675

678 - 675 = 3

Our remainder is 3. 

Answer:   135 with a remainder of 3. 

How much larger is 400 than 40?

Answers

360

400 - 40 = 360

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(400)/(40) = (40)/(4) \n 10 \ times \ larger

If you mean how much larger, literally, 400-40=360

Grandma Edith uses her big punch bowl at family gatherings. The bowl is half of a sphere, with a diameter of 30 cm. Her ladle is also half of a sphere, with a diameter of 8 cm. How many ladles can Grandma Edith scoop from the punch bowl? use 3.14 to approximate pi and express your answer as a whole number. show your work.

Answers

Our first instinct is to go through every step ...

-- calculate the volume of the bowl
-- calculate the volume of the ladle
-- divide the volume of the bowl by the volume of the ladle

and we may even start down that path.  But we soon realize that
it's going to be painful and take a lot of time.  So we stop right
where we are, and consider our options. 
We have two options: 
            #1). Give up, quit, and walk away. 
            #2). Find a smarter way to do it.

Look at the formula for the volume of a sphere:

           Volume = (4/3 π) (radius³) .

Do you see that ?  The radius³ is a factor in the volume of
everysphere. That means that if you multiplythe radius
of a sphere by (a number),the volume of the sphere gets
multiplied by (the same number)³ ! 

How does that help us with this problem ?  Well, it alsomeans
that the ratio of the volumes of two spheres is

                         (the ratio of their radii)³.

Radius of the bowl  =  15 inches
Radius of the ladle  =   4 inches
Ratio of their radii  =  (15/4)  =  3.75

 
  So the bowl holds  (3.75)³  as much as the ladle holds.

  
(3.75)³  =  52.73 ...

  
The bowl holds  52.73 ... times as much as the ladle.

   After Grandma Edith scoops 52 ladle-fulls from the bowl,
there will be less than 1 ladle-full remaining in there. 

And we did it all without even knowing π .
1) we calculate the volume of the big punch bowl
Volume (half sphere)=(1/2)(4/3)πr³=2/3πr³
radius=30 cm / 2=15 cm

Volume=(2/3)π(15 cm)³=2250π cm³

2) we calculate the volume of the ladle:
radius=8 cm/2=4 cm
Volume=(2/3)π(4 cm)³=128π/3 cm³

3) we calculate the number of ladles by the rule of three.
1 ladle----------------------128π/3 cm³
x------------------------------2250π cm³

x=(1 ladle * 2250π cm³) / (128π/3 cm³)=52.73 ladles≈52 ladles

Answer: 52 ladles.

Solve the following when x=3
6x - 3x -5.

Answers

6(3)-3(3)-5 =4 just substitute it
6x - 3x -5
x = 3

Substitute and solve.

6(3) - 3(3) - 5
18 - 9 - 5
9 - 5 
4

Answer: 4

The computer lab provides black CDS for students to use. The CDS come on spindles of 100. The lab ordered 25 spindles. How many CDS were ordered in all

Answers


(25 spindles) x (100 CDs/spindle)  =  2,500 CDs .

Their color is irrelevant. 

The product would be the same if they were white,
turquoise, chartreuse, or a mixture of many colors.

Identify the constant term in 14x + 6y - 5. A. 14 B. 6y C. -5 D. 5

Answers

Answer:

D

Step-by-step explanation:

Answer:

C. -5

Step-by-step explanation:

14x and 6y both have variables attached to them

the most basic form for a function like this is ax+by+c

the definition of constant is a fixed value. the reason your constant has to be a solo number, not attached to a variable, is that these variables change the number!! so, -5, the only number that won't change in the function, is the constant.