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allochka39001 [22]
2 years ago
7

Points ), K and L are collinear with J between L and K. IF KJ = 28 - 3, LK = 9x + 7 and LJ = 4x - 8,

Mathematics
1 answer:
babymother [125]2 years ago
6 0

J, K, and L are collinear

J is between K and L

LK = KJ + LJ

LK = 9x + 7

KJ = 2x - 3

LJ = 4x - 8

9x + 7 = (2x - 3) + (4x - 8)

9x + 7 = (2x + 4x) + (-3 - 8)

9x + 7 = 6x + -11

9x + 7 = 6x - 11

9x + 7 - 7 = 6x - 11 - 7

9x = 6x - 18

9x - 6x = 6x - 6x - 18

3x = -18

x = -6

∴ The value of x is -6

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Tatiana [17]

The right answer is Option A.

Step-by-step explanation:

Given,

Amount in Jason's account = $300

Bills paid = \frac{1}{4}

Remaining balance after bills = -$50

Let,

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Amount in account - Bills paid*Amount of bills = Remaining balance

300-\frac{1}{4}x=-50\\-\frac{1}{4}x+300=-50

The equation -\frac{1}{4}x+300=-50 can be used to find x.

The right answer is Option A.

Keywords: equation, subtraction

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5 0
3 years ago
If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95​% confident that the d
katen-ka-za [31]

Answer:

We need a sample size of least 119

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Sample size needed

At least n, in which n is found when M = 0.09

We don't know the proportion, so we use \pi = 0.5, which is when we would need the largest sample size.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.09 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.09\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.09}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.09})^{2}

n = 118.6

Rounding up

We need a sample size of least 119

6 0
3 years ago
Which of the following quadratic equations has the solution set {1/2,5}? select all that apply.
Pie
The answer are B, D and F.

If you solve for x for B, D and F, you'll get (1/2,5)
5 0
3 years ago
You roll a dice twice.<br> Find the probability of getting 3 in first throw and 5 in second throw.
Debora [2.8K]

Answer:

1/6

Step-by-step explanation:

there are 6 faces on a dice so there's a 1 in 6 chance that you would roll a 3 on your second go there is still only a 1 out of 6 chance of getting a 5 because there is still 6 numbers you could roll on.

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8 0
2 years ago
Solve this system using matrices:
sweet [91]

Answer:

Step-by-step explanation:

A system of linear equations is one which may be written in the form

a11x1 + a12x2 + · · · + a1nxn = b1 (1)

a21x1 + a22x2 + · · · + a2nxn = b2 (2)

.

am1x1 + am2x2 + · · · + amnxn = bm (m)

Here, all of the coefficients aij and all of the right hand sides bi are assumed to be known constants. All of the

xi

’s are assumed to be unknowns, that we are to solve for. Note that every left hand side is a sum of terms of

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Solving Linear Systems of Equations

We now introduce, by way of several examples, the systematic procedure for solving systems of linear

equations.

Here is a system of three equations in three unknowns.

x1+ x2 + x3 = 4 (1)

x1+ 2x2 + 3x3 = 9 (2)

2x1+ 3x2 + x3 = 7 (3)

We can reduce the system down to two equations in two unknowns by using the first equation to solve for x1

in terms of x2 and x3

x1 = 4 − x2 − x3 (1’)

1

and substituting this solution into the remaining two equations

(2) (4 − x2 − x3) + 2x2+3x3 = 9 =⇒ x2+2x3 = 5

(3) 2(4 − x2 − x3) + 3x2+ x3 = 7 =⇒ x2− x3 = −1

8 0
3 years ago
Read 2 more answers
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