MATHEMATICS COLLEGE

Order the Angel's from least to greatest with numbers 21, 24, 17

Answers

Answer 1

Answer:

17,21,24

is the answer form least to greatest

Answer 2

Answer: 17,21,24 is the answer

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A(2,9), B(4,k), and C(9, -12) are 3 collinear points.
Find the value of k.

Answers

Answer is 3

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Explanation:

We're going to be using the slope formula a bunch of times.

Find the slope of the line through points A and C

m = (y2 - y1)/(x2 - x1)

m = (-12-9)/(9-2)

m = -21/7

m = -3

The slope of line AC is -3. The slopes of line AB and line BC must also be the same for points A,B,C to be collinear. The term collinear means all three points fall on the same straight line.

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Let's find the expression for the slope of line AB in terms of k

m = (y2 - y1)/(x2 - x1)

m = (k-9)/(4-2)

m = (k-9)/2

Set this equal to the desired slope -3 and solve for k

(k-9)/2 = -3

k-9 = 2*(-3) ..... multiply both sides by 2

k-9 = -6

k = -6+9 .... add 9 to both sides

k = 3

If k = 3, then B(4,k) updates to B(4,3)

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Let's find the slope of the line through A(2,9) and B(4,3)

m = (y2 - y1)/(x2 - x1)

m = (3-9)/(4-2)

m = -6/2

m = -3 we get the proper slope value

Finally let's check to see if line BC also has slope -3

m = (y2 - y1)/(x2 - x1)

m = (-12-3)/(9-4)

m = -15/5

m = -3 we get the same value as well

Since we have found lines AB, BC and AC all have slope -3, we have proven that A,B,C fall on the same straight line. Therefore, this shows A,B,C are collinear.

An investment company advertised that last year its clients, on average, made a profit of 8% . Assuming that average refers to the mean, which of the following claims must be true based on this information?a. This year some of their clients will make a profit of at least 8%.
b. Last year some of their clients made a profit of at least 8%.
c. Last year more than half of their clients made a profit of at least 8%.
d. Last year at least one of their clients made a profit of more than 11%.
e. Last year at least one of their clients made a profit of exactly 8%.
f. None of the above statements is true.

Answers

Answer:

The answer is "Option 2".

Step-by-step explanation:

Please find the complete question in the attached file.

When there is a mean value k in a set of data. Otherwise, we will assert with certainty that at least one of the values is k. They can't say anything at all about the maximum or even the minimum using knowledge only. Nevertheless, we know that certain numbers cannot be over and that all numbers cannot be below than mean. Mean also no value throughout the data set must be equal.

Final answer:

None of the claims must necessarily be true based on the 8% average profit data provided. The information supplied does not specify individual profits, future profits, or the distribution of profits.

Explanation:

Based on the statement that the investment company's clients on average, made a profit of 8% last year, none of the claims must necessarily be true. The key phrase here is that the average profit was 8% - this does not provide specific information about any individual client's profit.

Option a is not necessarily true because this statement makes assumptions about future profits, which cannot be ascertained from last year’s average profit. For option b: even if the average profit was 8%, it's possible that no single client made exactly 8%. Similar logic applies to option c. The average doesn't tell us the distribution of the data, so we cannot deduce that more than half the clients made a profit of at least 8%. For option d: we cannot confirm if at least one client made a profit of more than 11% purely based on the average profit figure of 8%. Lastly, for option e: it's possible, but not guaranteed, that at least one client made a profit of exactly 8%. Hence, the answer is option f: None of the above statements is true.

Learn more about Statistics here:

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tommy has a car with a 22-gallon gas tank that yields 16 miles per gallon. How far can he drive on a full tank of gas?

Answers

Answer:

On a full tank of gas, Tommy can drive a distance:

D = 22 x 16 = 352 miles

Hope this helps!

Answer:352 miles

Step-by-step explanation:

1 gallons for 16 miles

22 gallons for ______

For 22 gallons 22x16=352 miles

Solve the following quadratic equation. (x+12)^2=1 A. x = 11 and x = 13 B. x = -11 and x = -13 C. x = -11 and x = 13 D. x = 11 and x = -13Will make brainiest!!!

Answers

Answer:

Step-by-step explanation:

(x+12)^2=1

(x+12)= +or - 1

when

x+12=1

x=1-12 =-11

when

x+12=-1

x=-1-12 =-13

then

x=-11 and x= -13

Answer:

Step-by-step explanation:

Plato

Use the following steps to prove that log b(xy)- log bx+ log by. a. Letx-bp and y= bq. Solve these expressions for p and q, respectively
b. Use the property b*b b to express xy in terms of b, p, and q
c. Compute log b(xy) and simplify

Answers

Answer with Step-by-step explanation:

a. $x=b^p$

$y=b^q$

Taking both sides log

$log x=plog b$

Using identity: $logx^y=ylogx$

$p=(logx)/(log b)=log_b x$

Using identity: $log_x y=(log y)/(log x)$

$log y=qlog b$

$q=(log y)/(log b)=log_b y$

b. $xy=b^pb^q$

We know that

$x^a\cdot x^b=x^(a+b)$

Using identity

$xy=b^(p+q)$

c. $log_b(xy)=log_b(b^(p+q))$

$log_b(xy)=(p+q)log_b b$

Substitute the values then we get

$log_b(xy)=(log_b x+log_b y)$

By using $log_b b=1$

Hence, $log_b(xy)=log_b x+log_b y$

Final answer:

To prove the property log b(xy) = log bx + log by, we let x = $b^p$ and y = $b^q$ , express xy in terms of the base b and the exponents p and q, and then use the properties of logarithms to show the equality.

Explanation:

The student is asking to prove the logarithmic property − log b(xy) = log bx + log by. Here's a step-by-step explanation:

Let x = bp and y = bq. To solve for p and q, take the logarithm base b of both sides. Thus, p = logbx and q = logby.

Using the property of exponents, xy = bp*bq = bp+q.

Now compute logb(xy). According to the logarithmic property, logb(bp+q) = p + q. Since p = logbx and q = logby, then logb(xy) = logbx + logby.

Therefore, we have proven the given logarithmic property using the steps provided in the question.

Learn more about Logarithmic Properties here:

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Solve the equation for x 2x+y=5x-6

Answers

Answer:

x = 2+ $(y)/(3)$

Step-by-step explanation:

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