In order to be admitted for a certain ride a an amusement park, a child must be greater than or equal to 36 inches tall and less than 48 inches tall. Draw a number line to represent the following information

Answers

Answer 1
Answer:

The required number line has been attached which represents the given information.

What is Number Line?

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

We have been given that a child must be greater than or equal to 36 inches tall and less than 48 inches tall.

Let the height of the child would be x

According to the given situation, we can write the inequality would be as:

⇒ 36 ≤ x < 48

As per the above inequality, we can draw the required number line.

Thus, the required number line has been attached which represents the given information.

Learn more about the number line here:

brainly.com/question/17617832

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Answer 2
Answer:

Step-by-step explanation:

this one is easy to graph your answer on a number line draw a filled in circle on the number 36 and an open circle on the number 48 then you shaed between the two numbers


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83 tens × 2 tens =166

Answers

1 cube= 1 unit
1 Rod (Long)= 10 units
10 Rods (Longs)= 1 flat (1 flat=100 units)
10 flat =1 cube(1 cube=1000 units)
83×10= 830
2×10=20
830×20= 16,600
Just wanted to add more to help you understand why 83 is multiplied by ten and 2 is multiplied by 10. Its because when we use Base ten blocks, tens represent 1 Rod (Long)= 10 units. Hope it helps more.
That is actually not true
83 tens = 830
2 tens = 20
830x20=16600
So the answer is 16600

Given a vector with the initial point, (4,2) and the terminal point, (-3,1), find the vector in component form.

Answers

\bf (-3,1),(4,2)\implies <4-(-3)~,~2-1>\implies <4+3~~,~~2-1>\implies <7,1>

Answer:

(-7,-1)

Step-by-step explanation:

(x2- x1, y2- y1)

(-3-4,1-2)

=(-7,-1)

Cable is normally $83.47 a month. This month the bill increase by 12%. Based on the new price, how much will the cable bill cost for a year?Please help

Answers

10% is 8.35. 1% is 0.83 so 2% is 1.66. 8.35+1.66=10.01. 83.47+10.01=93.48. 93.48x12=1121.76. The bill will cost £1121.76.

Factorise x^2 - 7x + 12

Answers

Answer:

= (x-4)(x-3)

Step-by-step explanation:

Firstly, put the pronumeral in the brackets [(x)(x)].

Then, place the signs in the right positions, the sign of the constant number (12) is a positive (+), therefore the two signs must be the same. The sign of the -7x is negative (-). Place these in the brackets [(x-)(x-)].

Next, think of the factors of 12 that add up to 7 {(3 and 4) 3x4 is 12 and 3+4 is 7}. [(x-4)(x-3)].

Have a nice day!!!!!!! :-)

KA

Answer:

(x-3) (x-4)

Step-by-step explanation:

x²- 7x + 12

= x² - 3x -4x +12

=x(x-3) - 4(x-3)

=(x-3) (x-4)

Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find the value of x.

Answers

Answer:

x=4

Step-by-step explanation:

Step 1:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

AC^2 = AB^2 + BC^2

step 2:-

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

(a + b)^2 = a^2 +2ab+b^2

289 = 4x^2 +9(x^2+2x+1)

13x^2 +18x-280 = 0

finding factors  70 X 52 = 3640

13x^2 +70x-52x-280 = 0

13x^2 -52x+ 70x-280 = 0

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and 13x =-70

x=4 and x=(-70)/(13)

we can not choose negative value so x value is 4

Final answer:- x = 4

verification:-

AC^2 = AB^2 + BC^2

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

Answer:

x = 4

Step-by-step explanation:

The length of two legs of a right angle triangle are 2x and 3(x+1).  

The length of longest side is 17 units. It means measure of hypotenuse is 17 units.

According to the pythagoras theorem,

leg_1^2+leg_2^2=hypotenuse^2

(2x)^2+(3(x+1))^2=(17)^2

4x^2+9(x^2+2x+1)=289

4x^2+9x^2+18x+9=289

13x^2+18x-280=0

On splitting the middle terms we get

13x^2+70x-52x-280=0

x(13x+70)-4(13x+70)=0

(13x+70)(x-4)=0

Using zero product property we get

13x+70=0\Rightarrow x=-(70)/(13)

x-4=0\Rightarrow x=4

The value of x can not be a negaive number, because for negative value of x the value of 2x is negative and side can not be negative.

Therefore, the value of x is 4.

Jared is putting a new deck off the kitchen. The deck will be 94.45 inches deep. He will use 16 boards that are each 5.7 inches wide. He has to leave a small space between the boards. If the 15 spaces between the boards are all equal, how wide will they be?

Answers

16 boards that are 5.7 inches wide each make a total of 91.20 inches.
 
    16
x 5.7
  112
+800
 91.2 inches

Since the deck itself is 94.45 inches deep, we can subtract 91.2 from the number:

  94.45
-91.20 
   3.25 inches.

Finally, we divide 3.25 by 15, since that's the amount of spaces we want and they have to be equal:

3.25/15= .21667

We'll round that to two numbers, so we'll end up with .22.

Your final answer is .22 inches wide for each space.