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2 years ago

Consider isosceles ΔXYZ.

Mathematics

2 answers:

kompoz [17]2 years ago

8 0

The value of n : 3 . ( 9x3+12 = 39 ) so leg XY equals 39
( 15x3-6 = 39 ) so that makes leg XZ equal 39 as well.

julia-pushkina [17]2 years ago

5 0

1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.

In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:

XY=XZ

(9n+12)ft=(15n-6)ft

From this equation we have to find n:

9n-15n=-6-12

-6n=-18

$n=\frac{-18}{-6}$

n=3

2) The measure of the leg XY in ft

XY=(9n+12)ft

Substitute the value of n calculated in the first question:

XY=(9(3)+12)ft

XY=39 ft

3) The measure of the leg XZ in ft

XZ=(15n-6)ft

Substitute the value of n calculated in the first question:

XZ=(15(3)-6)ft

XZ=39ft

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The length of a rectangle is 3 inches more than three times the width. the perimeter is 94 inches. find the length and width.

Zina [86]

Let length be (l) and width be (w).

According to the question, l=3w+3......equation1
And perimeter that is 2(l+w) =94........equation2

Solve these two equations, you get your answer.
l=36
w=11

3 0

2 years ago

T= 300 (d−15) 2 +20space, T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, start superscript, 2,

stealth61 [152]

As can be read from your statement written "T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, strt superscript, 2, end superscript, divided by, 300, end fraction, plus, 20", I hope your model equation is this :

$T = \frac{(d-15)^{2}}{300} + 20$

Hope this is your question, if not I think you will, still be able to find an answer of your question based on this solution

As we have to find lowest average temperature, So for minimum of a function its derivative is equal to 0 there.

So lets find derivative of T function first

So first expand $(d-15)^{2}$ as (d-15)(d-15)

we will use FOIL to multiply these

so $(d-15)(d-15) = d^{2} -15d -15d +225$

$= d^{2} -30d +225$

so we have $T = \frac{d^{2} -30d +225}{300} +20$

Now we will derivate each term here,300 in denominator is constant so that will come as it in in denominator.

To derivate terms in $dx^{2} -30d +225$ we will use power rule formula:

$(x^{n} )'= nx^{n-1}$

so derivative of $(d^{2} )'= 2d^{2-1} = 2d^{1} = 2d$

Then derivative of d will be 1

so that of -30d will be -30

then derivate of constant -225 will be 0

so we will have derivative as $\frac{2d-30}{300}$ for the fraction part and then derivative of +20 is again 0 as its constant term

$T' = \frac{2d-30}{300}$

For minimum we will put this derivative =0

$0 = \frac{2d-30}{300}$

Now solve for d

times both sides by 300

$0 \times 300 = \frac{2d-30}{300} \times 300$

$0 = 2d-30$

$0 +30 = 2d -30 +30$

$30 = 2d$

$\frac{30}{2} = \frac{2d}{2}$

$15 = d$

So now we have to find value of lowest temperature.

For that simply plug 15 in d place in original T function equation

$T = \frac{(d-15)^{2}}{300} + 20$

$T = \frac{(15-15)^{2}}{300} + 20$

$T = 20$

So T = 20 °C is the lowest average temperature and the answer.

6 0

2 years ago

Read 2 more answers

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

ollegr [7]

Answer: a. A point estimate for p is 0.597 .

b. The 95% confidence interval for p.

Lower limit = 0.48

Upper limit = 0.71

Step-by-step explanation:

Given : Sample size of professional actors : n= 67

Number of extroverts : x= 40

Let p represent the proportion of all actors who are extroverts.

a. The point estimate for p = sample proportion = $\hat{p}=\dfrac{x}{n}$

$=\dfrac{40}{67}=0.597$

b. Confidence interval for population proportion :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Since the critical value for 95% confidence interval is 1.96 , so the 95% confidence interval for p would be

$0.597\pm (1.96)\sqrt{\dfrac{0.597(1-0.597)}{67}}$

$0.597\pm (1.96)\sqrt{0.0036}$

$0.597\pm (1.96)(0.06)$

$0.597\pm 0.1176$

$(0.597-0.1176,\ 0.597+0.1176)\\\\=(0.4794,\ 0.7146)\\\\\approx(0.48,\ 0.71)$

In the 95% confidence interval for p.

Lower limit = 0.48

Upper limit = 0.71

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2 years ago

Read 2 more answers

Which part of the proof does the fourth statement and reason represent?

denis-greek [22]

Answer:

Option B is correct.

Reason:It is an argument

Step-by-step explanation:

Given: $AB \cong BC$ and $BC \cong EF$

By transitive property: a = b and b = c then, a =c

⇒ $AB \cong EF$

AB = EF [def of $\cong$ segment]

By Segment Addition Postulate states that given two points A and C, and a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation

AB + BC = AC.

Since, the line segment EG , F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG hence proved!

Since, in the fourth statement reason is: It is an argument

3 0

2 years ago

What is the product of (8.8 × 106)(5 × 102)?

Serhud [2]

(8.8 × 106)(5 × 102)

= (932.8)(510)

= 475,728

7 0

2 years ago