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s2008m [1.1K]
3 years ago
5

Point J is on line segment IK. Given JK = 2x – 1, IK = 3x + 2,

Mathematics
1 answer:
Serhud [2]3 years ago
4 0

Answer:

JK=7

Step-by-step explanation:

From the line segment, since J is on it ,it means the line segment is

represented as I J K

from this illustration, we can say that the longest part of the line segment is from I to K

this means that, IJ +JK =IK

making JK the subject,

JK= IK - IJ

but from the question, JK=2x-1 , IK=3x+2 and IJ=3x-5

substituting them in the expression,

2x-1 =3x+2 -(3x-5)

solving for x

2x-1 =3x+2-3x+5

2x-1 =0+7

2x-1 =7

2x=1+7

2x=8

dividing through by 2

2x/2 =8/2

x=4

but the question says we should find the numerical value for JK

but from the line segment,

JK=2x-1

but now we know the value of x to be 2

so substituting it in the formula

JK= 2(4)-1

JK=8-1

JK=7

therefore, the numerical value for JK is 7

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Answer:

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Step-by-step explanation:

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3 years ago
Of the last 24 balloons sold at a party store 6 were white. Find the experimental probability that the next balloon sold will be
Alekssandra [29.7K]

Answer: 1 out of 4

Step-by-step explanation:

If you divided the total amount of balloons that were sold by the amount of white balloons, it would be 4. The 1 comes from 1 in 4 being the probability of them being white. You can check this by multiplying the 1 and 4 by 6 and it would be 6 out of 24, which shows our answer is correct.

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3 years ago
WORTH 20 POINTS HELP
vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}

RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}

ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}

TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

QR = \frac{9 + 1}{2 + 3} = \frac{10}3

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TQ = \frac{-5+1}{-7 + 1} = \frac{2}3

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

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6 0
2 years ago
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Xelga [282]

Answer:

y =  -  \frac{ 1 }{10} {x}^{2}   +  \frac{5}{2}

Step-by-step explanation:

We want to prove algebraically that:

r =  \frac{10}{2 + 2 \sin \theta}

is a parabola.

We use the relations

{r}^{2}  =  {x}^{2}  +  {y}^{2}

and

y = r \sin \theta

Before we substitute, let us rewrite the equation to get:

r(2 + 2 \sin \theta) = 10

Or

r(1+  \sin \theta) = 5

Expand :

r+  r\sin \theta= 5

We now substitute to get:

\sqrt{ {x}^{2}  +  {y}^{2} }  + y = 5

This means that:

\sqrt{ {x}^{2}  +  {y}^{2} }=5 - y

Square:

{x}^{2}  +  {y}^{2} =(5 - y)^{2}

Expand:

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{x}^{2}  =25 - 10y

{x}^{2}  - 25 =  - 10y

y =  -  \frac{ {x}^{2} }{10}  +  \frac{5}{2}

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