MATHEMATICS HIGH SCHOOL

What is the slope of side AC?

Answers

Answer 1

Answer:

Answer:

The slope is ( d-b)/ ( c-a)

Step-by-step explanation:

To find the slope we can use the slope formula

m = ( y2-y1_/(x2-x1)

= ( d-b)/ ( c-a)

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Find the mean, median, and mode of the data set. Round to the nearest tenth.15, 1, 4, 4, 8, 7, 15, 4, 15, 4, 5
Choose one answer.
a. mean = 6.8, median = 5, mode = 4
b. mean = 7.5, median = 5, mode = 4
c. mean = 7.5, median = 8, mode =4
d. mean = 6.8, median = 5, mode = 8

Answers

First im gonna organize the numbers from smallest to biggest:
1, 4, 4, 4, 4, 5, 7, 8, 15, 15, 15 ( These are 11 numbers)

For mean, you have to add all the numbers then divide it by 11.
The answer is about 7.5

For median, you have to find the "middle number, but you have to organize the numbers from smallest to largest like I did.
1, 4, 4, 4, 4, 5, 7, 8, 15, 15, 15 . 5 is the middle number, well because its in the middle

For mode you have to find the number that is most repeated.
1, 4, 4, 4, 4, 5, 7, 8, 15, 15, 15 (there are three 15's)
There are four 4's so the answer is 4

The answer, then is B

The mean is the average, add up the numbers and divide by how many numbers there are.

$\sf~Mean=(15+1+4+4+8+7+15+4+15+4+5)/(11)$

Add:

$\sf~Mean=(82)/(11)$

Divide:

$\sf~Mean\approx7.5$

The median is the middle number. First, line up the numbers in order of least to greatest.

1, 4, 4, 4, 4, 5, 7, 8, 15, 15, 15

Now find the number in the middle:

That number is 5, so that's our median.

The mode is the most repeated number.

As you can see, 4 is repeated the most, so it's the mode.

What additional information do you need to prove that ∆LMO ≅ ∆LNO by the HL Theorem? ∠NLO ≅ ∠MLO ∠MOL ≅ ∠NOL

Answers

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The triangles ΔLNO and ΔLMO have the same leg Lo, therefore you need the equality of hypotenuses LM=LN.

For a better understanding of the solution given here please find the diagram in the file attached.

We know from the Hypotenuse Leg Theorem (the HL theorem) that "if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent."

Thus, as can be seen from the diagram, Side LO (also called leg LO) is common to both the triangles LMO and LNO. Therefore, the additional information that will be required to prove the congruence is that the respective hypotenuses, MO and NO are equal.

A right Triangle is shown. if m angle H= 68°, What is GI? show work if you can and explain to me I don't understand

Answers

Ok, so we've been told that the angle H=68 degrees.

Let's now flip the right angled triangle 90 degrees clockwise.

If we do so, it turns out we'd have to find the opposite length of the right angled triangle (Opp) which is GI. We know that we have the adjacent (Adj) length of this triangle which is in fact 2cm. What we also know is that:

tan(β)=Opp/Adj *Whereby "β" is an angle.

As β=68 degrees, Opp=GI and Adj=2:

tan(68)=GI/2

Therefore:

GI = 2 * tan(68)

GI = 4.95 cm (to 2 decimal places)

I am confused on this , I’ve tried twice and got it wrong.

Answers

Answer:

$f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$

Step-by-step explanation:

Consider the function $f(x)=√(4-x)+3$ for the domain $(- \infty, 4]$ .

Find $f^-^1(x)$ , where f^(-1) is the inverse of f.

Also state the domain of f^(-1) in interval notation.

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We can start solving this problem by finding the inverse of f(x). This is done by switching the x- and y- variables, and solving for y.

$y=√(4-x)+3 \rightarrow x=√(4-y)+3$
$x=√(4-y)+3$

We can start solving for y by subtracting 3 from both sides of the equation.

$x-3=√(4-y)$

Get rid of the radical by squaring both sides of the equation.

$(x-3)^2=(√(4-y))^2$
$(x-3)(x-3)=4-y$

Use FOIL to multiply the binomial (x-3) together.

$x^2-3x-3x+9=4-y$

Combine like terms.

$x^2-6x+9=4-y$

Subtract 4 from both sides of the equation.

$x^2-6x+5=-y$

Divide both sides of the equation by -1.

$-x^2+6x-5=y$
$f^-^1(x)=-x^2+6x-5$

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The domain and range of a function are flipped for its inverse, meaning that to find the domain of the inverse function, you can find the range of the original function f(x), and that will be your inverse function's domain.

The range of $f(x)=√(4-x) +3$ is $y \geq 3$ , since the vertical shift of the graph is at k = 3. You can also graph this function on a calculator to see that the graph does indeed start at y = 3.

Now that we know the domain and range of the original function, we know that these are flipped for the inverse function.

Original function:

Domain: $x\leq 4$
Range: $y\geq 3$

Inverse function:

Domain: $x\geq 3$
Range: $y\leq 4$

The final answer is:

The inverse $f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$ .

You can also write the domain as: $x\geq 3$ .

Gary bought an MP3 player at a 20% discount sale for $40. What was the original price of the MP3 player?

Answers

40*.20=8.00
40 - 8=32
answer32
hope you understand.
explain:]
40*.20=8
and second time i do ( - ) becouse they said 20% discount discount main is ( - )
so i do ( - ) i think now you understand.

A rectangular lot that measures 125 feet by 185 feet is completely fenced. What is the length, in feet, of the fence?Can you please explain with some details?

Answers

620, because 125+125+185+185=620, and that would be the perimeter of the rectangle.

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