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3 years ago

What is the LCM of 72 and 75

Mathematics

1 answer:

Ganezh [65]3 years ago

7 0

Lcm (72; 75) = 1,800: least common multiple, calculated. The numbers have common prime factors.

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Please help, the question below

Licemer1 [7]

Answer:

$\sf R=\left(3, -\dfrac{5}{4}\right)$

Step-by-step explanation:

Given:

P = (1, 5)
Q = (-2, 3)
R = (a, b)
R lies on line x = 3
PR = QR

If point R lies on the line x = 3, then the x-value of point R is 3.

⇒ a = 3

Distance between two points

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

(where (x₁, y₁) and (x₂, y₂) are the two points)

Use the distance formula to derive equations for PR and QR.

Let (x₁, y₁) = P = (1, 5)

Let (x₂, y₂) = R = (3, b)

$\begin{aligned} \sf PR & =\sf \sqrt{(3-1)^2+(b-5)^2}\\ & = \sf \sqrt{4+(b-5)^2} \end{aligned}$

Let (x₁, y₁) = Q = (-2, 3)

Let (x₂, y₂) = R = (3, b)

$\begin{aligned} \sf QR & =\sf \sqrt{(3-(-2))^2+(b-3)^2}\\ & = \sf \sqrt{25+(b-3)^2} \end{aligned}$

As PR = QR, equate the derived equations and solve for b:

$\begin{aligned} \sf PR & = \sf QR \\\sf \sqrt{4+(b-5)^2} & = \sf \sqrt{25+(b-3)^2}\\\sf 4+(b-5)^2 & = \sf 25+(b-3)^2\\\sf 4+b^2-10b+25 & = \sf 25 + b^2-6b+9\\\sf b^2-10b+29 & = \sf b^2 -6b +34\\\sf -10b+29 & = \sf -6b + 34\\\sf -4b & = \sf 5\\\sf b & = -\dfrac{5}{4}\end{aligned}$

Substitute the found values of a and b to find the coordinates of R:

$\sf R=(a,b)=\left(3, -\dfrac{5}{4}\right)$

Learn more about the distance formula here:

brainly.com/question/28144723

8 0

2 years ago

Read 2 more answers

1. The national mean (μ) IQ score from an IQ test is 100 with a standard deviation (s) of 15. The dean of a college wants to kno

Nat2105 [25]

Answer:

We conclude that the mean IQ of her students is different from the national average.

Step-by-step explanation:

We are given that the national mean (μ) IQ score from an IQ test is 100 with a standard deviation (s) of 15.

The dean of a college want to test whether the mean IQ of her students is different from the national average. For this, she administers IQ tests to her 144 students and calculates a mean score of 113

Let, Null Hypothesis, $H_0$ : $\mu$ = 100 {means that the mean IQ of her students is same as of national average}

Alternate Hypothesis, $H_1$ : $\mu\neq$ 100 {means that the mean IQ of her students is different from the national average}

(a) The test statistics that will be used here is One sample z-test statistics;

T.S. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} } }$ ~ N(0,1)

where, Xbar = sample mean score = 113

s = population standard deviation = 15

n = sample of students = 144

So, test statistics = $\frac{113-100}{\frac{15}{\sqrt{144} } }$

= 10.4

Now, at 0.05 significance level, the z table gives critical value of 1.96. Since our test statistics is more than the critical value of z which means our test statistics will fall in the rejection region and we have sufficient evidence to reject our null hypothesis.

Therefore, we conclude that the mean IQ of her students is different from the national average.

3 0

4 years ago

Why are the triangles congruent? (Need ASAP 15points)

MAVERICK [17]

Answer:

Same sides

Step-by-step explanation:

When the sides are the same then the triangles are congruent. because they all have exactly the same sides. because the two triangles do not have exactly the same sides.

8 0

3 years ago

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0.326

Ksivusya [100]

Answer:

three hundred twenty six thousandths

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3 years ago

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What type of insurance can be waived (refused) if a driver feels that his/her car is not worth insuring? A. collision B. compreh

Mars2501 [29]