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2 years ago

In the diagram, −→− bisects ∠ .

Mathematics

1 answer:

11111nata11111 [884]2 years ago

4 0

Answer:

x = 9 and ∠ JKM = 59°.

Step-by-step explanation:

See the attached diagram with this question.

∠ JKL is bisected by line KM.

Therefore, angle JKM = angle MKL

Now, ∠ JKM is given to be ( x² - 22 ) and ∠ LKM = ( 6x + 5 ).

So, x² - 22 = 6x + 5

⇒ x² - 6x -27 = 0

⇒ ( x - 9 ) ( x + 3 ) = 0

Therefore, x = 9 or - 3.

∠ JKM = x² - 22 = 59° for x = 9 and ∠ JKM = x² - 22 = - 13° for x = - 3

Since angle JKM can not be negative, so, x = 9 and ∠ JKM = 59°. (Answer)

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rewona [7]

Answer:

8.5 feet

Explanation:

The function that can determine the distance from a point on the bottom edge of the banner to the floor is:

$f(x)=0.25x^2-x+9.5$

That function is a quadratic function which means that it is a parabola. Given that the coefficient of the quadratic term (0.25) is positive, the parabola open upwards, and the vertex is the lowest point of the parabola and it represents how high above the floor is the lowest point on the bottom edge of the banner.

So, you need to find the vertex of the parabola.

I will complete squares to find the form A(x -h)² + k, where h and k are the coordinates of the vertex (h, k).

$f(x)=0.25x^2-x+9.5\\ \\ 4(f(x))=4(0.25x^2-x+9.5)\\ \\ 4f(x)=x^2-4x+38\\ \\ 4f(x)-38=x^2-4x\\ \\ 4f(x)-38+4=x^2-4x+4\\ \\ 4f(x)-34=(x-2)^2\\ \\ 4f(x)=(x-2)^2+34\\ \\ f(x)=(1/4)(x-2)^2+8.5$

Hence, the vertex (h,k) is (2, 8.5), meaning that the lowest point on the bottom edge of the banner is at 2 feet from the left edge of the banner and 8.5 feet above the floor.

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2 years ago

You currently have a balance of $712.35 in your bank account. To avoid paying a monthly fee, you must maintain a minimum balance

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Answer:

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Step-by-step explanation:

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2 years ago

Suppose that 1 month before the election a random sample of 500 registered voters are surveyed. From this sample 270 indicate th

Aleonysh [2.5K]

Answer:

[ 0.4964, 0.5836 ]

Step-by-step explanation:

Data provided in the question:

Total sample size = 500

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thus,

P( person voting for smith ), p = $\frac{270}{500}$ = 0.54

Confidence level = 95%

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standard error, SE = $\sqrt{\frac{p(1-p)}{n}$

SE = $\sqrt{\frac{0.54(1-0.54)}{500}$

SE = 0.0223

now,

Confidence interval = p ± ( z × SE )

here,

z value for 95% confidence interval is 1.96

Confidence interval = [ 0.54 - ( 1.96 × 0.0223 ), 0.54 + ( 1.96 × 0.0223 ) ]

= [ 0.54 - 0.0436 , 0.54 + 0.0436 ]

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2 years ago

What is the slope of a line perpendicular to a line that's passes through (3,8) and (1,-4)?

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Answer:

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First find the slope of the line through the points

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Now we need to find the slope of the line that is perpendicular

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3 years ago

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algol [13]

5 People can be chosen in 1287 ways if the order in which they are chosen is not important.

Step-by-step explanation:

Given:

Total number of students= 13

Number of Students to be selected= 5

To Find :

The number of ways in which the 5 people can be selected=?

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Let us use the permutation and combination to solve this problem

$nCr=\frac{(n)!}{(n-r)!(r)!}$

So here , n =13 and r=5 ,

So after putting the value of n and r , the equation will be

$13C_5=\frac{(13)!}{(13-5)!(5)!}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 \times8\times7 \times6 \times5 \times4 \times3 \times2 \times1)}{(8 \times7 \times6 \times5 \times4 \times3 \times2 \times1)(5 \times4 \times3 \times2 \times1)}$

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3 years ago