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love history [14]
1 year ago
13

point I is on line segment HJ. GIVEN IJ = 3× + 3, HI = 3× - 1, and HJ = 3× + 8, determine the numerical length of HJ.

Mathematics
1 answer:
Vedmedyk [2.9K]1 year ago
4 0

Given, IJ = 3x + 3, HI = 3x - 1, and HJ = 3x + 8.

Since I is a point on line segment HJ, we can write

HJ=HI+IJ\begin{gathered} 3x+8=(3x-1)+(3x+3) \\ 3x+8=6x+2 \\ 8-2=6x-3x \\ 6=3x \\ 2=x \end{gathered}

Put x=2 in HJ=3x+8.

\begin{gathered} HJ=3\times2+8 \\ HJ=6+8 \\ =14 \end{gathered}

Therefore, the numerical length of HJ is 14.

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Lily bought 25.29 pounds of grapefruit. The lightest grapefruit weighed 1.4 pounds. The heaviest grapefruit weighed 1.6 pounds.
Gemiola [76]

Answer:

B

Step-by-step explanation:

GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.

This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.

recall that : average weight = total weight / number of fruit

we are given than total weight = 25.29 lb, so

average weight = 25.29 / number of fruit

Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.

Choice A: number of fruit = 19

average = 25.29 / 19 = 1.33  (outside of range, not the answer)

Choice B: number of fruit = 17

average = 25.29 / 17 =1.49   (within range , possible answer)

Choice C: number of fruit = 10

average = 25.29 / 10 = 2.529 (outside of range, not the answer)

Choice D: number of fruit = 50

average = 25.29 / 50 = 0.5058  (outside of range, not the answer)

From the above, we can see that only B gives an average between 1.4 and 1.6 lb.

5 0
3 years ago
Desperate<br> please Hurry<br> Question Down Below
aliina [53]

Answer:

4

Step-by-step explanation:

6+10=16

2+2=4

16/4 = 4

8 0
2 years ago
Read 2 more answers
Find the slope of the line passing through the points (-3,-8) and (5,6)
Mkey [24]

Slope is the change in Y over the change in X:

Slope = (6 - -8) / (5 - -3)

Slope = (6+8) / (5+3)

Slope = 14/8

Slope = 7/4

7 0
3 years ago
Read 2 more answers
The table shows the price for different numbers of board games:
zlopas [31]

Answer:

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

  = 7/2

  = 3.5

For the point (4, 14)

k = y/x

   = 14 / 4

   = 7/2

    = 3.5

For the point (5, 17.50)

k  = y/x

   = 17.5 / 5

   = 3.5

For the point (9, 31.50)

k  = y/x

   = 31.50 / 9

   = 3.5

From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

  = 7

The price of 4 board game

y = 3.5 (4)

  = 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

6 0
2 years ago
Find the distance between the points (0,-9) and(4,-6)
Len [333]

Answer:

d=5

Step-by-step explanation:

1. use the distance formula: d=\sqrt{(x_{2} - x_{2} )^{2} +(y_{2} -y_{1} )^{2}

2. plug in the points: d=\sqrt{(0-4)^{2} +(-9+6)^{2}

3. solve problem inside parentheses: d=\sqrt{(-4)^{2} +(-3)^{2}

4. square -4 and -3: d=\sqrt{16+9

5. add:d=\sqrt{25

6. find square root: d=5

8 0
3 years ago
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