In triangle ABC, AB = 8.9 m, Angle BAC = 90° and Angle ABC = 56°. H lies on BC such that AH
is perpendicular to BC. Find the length of
(i) AH
(ii) HC.

Please help me!! Thank you
​

Answer:

x = 8

Step-by-step explanation:

Two secants drawn from an external point to the circle.

The (outside ) × (whole) of one secant is equal to the (outside) × (whole) of the other secant, that is

(x + 2)(x + 2 + 2x - 8) = (x + 1)(x + 1 + 2x - 5)

(x + 2)(3x - 6) = (x + 1)(3x - 4) ← expand both sides using FOIL

3x² - 12 = 3x² - x - 4  ( subtract 3x² - x - 4 from both sides )

x - 8 = 0 ( add 8 to both sides )

x = 8

The solutions to f(x) = 64 is x = 7 and x = –7.

Solution:

Given data:

[tex]$f(x)=x^{2}+15[/tex] and [tex]f(x)=64[/tex]

To find the solutions when f(x) = 64.

Both are equations of f(x), so equate the given equations, we get

[tex]x^2+15=64[/tex]

Subtract 15 from both sides of the equation.

[tex]x^2+15-15=64-15[/tex]

[tex]x^2=49[/tex]

49 can be written as 7².

[tex]x^2=7^2[/tex]

Taking square root on both sides of the equation, we get

x = ±7

The solutions to f(x) = 64 is x = 7 and x = –7.

Answer:

Step-by-step explanation:

The 21st term of the given geometric sequence can be found by using the formula for the n-th term of a geometric sequence: a_n = a_1 * r^(n-1). In this case, it is 112.5 * 2^(21-1).

In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, 225 divided by 112.5 gives us the common ratio of 2. Therefore, to find the 21st term of the given geometric sequence, we use the formula: a_n = a_1 * r^(n-1). Here, a_n is the n-th term, a_1 is the first term, r is the common ratio and n is the term which we want to find.

So, substituting the given values into the formula, a_21 = 112.5 * 2^(21-1). Calculate this and you'll have the 21st term of the geometric sequence.

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Answer:

see explanation

Step-by-step explanation:

sin M = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{KL}{ML}[/tex] = [tex]\frac{2\sqrt{11} }{12}[/tex] = [tex]\frac{\sqrt{11} }{6}[/tex]

tan M = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{2\sqrt{11} }{10}[/tex] = [tex]\frac{\sqrt{11} }{5}[/tex]

Answer:

Answer:

The answer is C

Step-by-step explanation:

All of the side lengths on the pre-image multiplied by 3 equal out to the side lengths proportional, and the angles are all the same, making them congruent. Please consider giving brainliest.

Answer:

x = 2

Step-by-step explanation:

Start by combining like terms.

Collecting x terms onto the left side results in 8x;

collecting constants onto the right side results in 16.  

Therefore, 8x = 16, and x = 2

Answer:

2 ( 7r - 4 )

Step-by-step explanation:

14r - 8

To factor this expression, you must pull the factor 2 outside the expression by basically reversing the distributive property:

14r - 8  =  2 ( 7r - 4 )

Answer:

Lines that have a slope of -3

Step-by-step explanation:

Take the negative reciprocal of 1/3 and all lines that have that as the slope are perpendicular

Answer:

1. y + 2 = –3(x – 4)

3. y = -3x – 5/3

5. 3x + y = 7

Step-by-step explanation:

because yes

Answer:

Step-by-step explanation:

height of triangle=√(11²-8.6²)=√(11+8.6)(11-8.6)=√(19.6×2.4)

=√(4×4.9×4×0.6)=4√(4.9×0.6)=4√2.94

area of triangle=1/2 bh=1/2×2×8.6×4√2.94

=34.4×√2.94

≈58.984

Answer:

Learning about functions vs. new language

Step-by-step explanation:

Answer:

4x=8y

Step-by-step explanation:

Ok so a number multiplied by 4 equal  a number multiplied by 8.

Both numbers can't have the same variable because if they had the same varable that means they are the same number which in that case means Marcy is wrong but we know she is right because Mr.Kim said so.

let's plug in numbers. If they had the same variable it would be:-4x=8x

                                                                                         let x=2,    4(2)=8(2)

                                                                                                           8=16 not true

if the variables were not the same:-4x=8y

                                   let x=4

                                   let y=2          4(4)=8(2)

                                                          16=16 true                                    

Answer:

a) 675 000

b) 685 000

Step-by-step explanation:

The population of a town is 680 000 correct to the nearest 10 000.

a) To find it lower bound, we level of accuracy by 2 and then subtract from 680 000

The lower bound is:

680 000-5000=675,000

Therefore the least possible population of the town is 675 000

b) We repeat the same process to find the upper bound

680 000+5000=685,000

230 is the  value of the company in 2018.

Option (B) is correct.

To find 230 represent in the function.

science that deals with the addition, subtraction, multiplication, and division of numbers.

It is given that:

The equation of a exponential growth function is equal to

[tex]V(t)=a(1+r)^{t}[/tex]

where,

V(t) is the value of the company

t is the number of years after 2018

a is the initial value or y-intercept

r is the rate of change

Put the value,

a=230

1+r=1.12

r=1.12-1=0.12

r=12%

so 230 is the value of the company when the value of t is equal to zero.

Remember that t is the number of years since 2018

Therefore ,230 is the  value of the company in 2018.

Learn more about arithmetic here:

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Answer: x = -1

Calculation/Explanation:

11x-3 = x-13

11x-3 -x = x-13 -x

10x-3 = -13

10x-3 +3 = -13 +3

10x = -10

10x /10 = -10/10

x = -1

Answer:

Answer is 5

Step-by-step explanation:

if you have any doubts see the image

The Pythagorean Theorem was used on a right triangle with sides of length 4 to find that the hypotenuse has a length approximately equal to 5.7.

Here, your task is to apply the Pythagorean Theorem which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, both a and b are given as 4. We can therefore calculate c as follows:

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Answer:

8:5

Step-by-step explanation:

Given there are 8 male teachers and 5 female teachers,The ratio of number of male teachers to female teachers

= no. Of male teachers/no. Of female teachers

That’s

8/5

8:5

8:5 = 160%

theres not really an explanation to this hope it helps :)

Answer:

(-5)

( 1 )

Step-by-step explanation:

the image is 1 units upper than object and 5 units behind the object therefore

x=-5

y=1

Answer:

$165.50 dollars

Step-by-step explanation:

$993 / 6 = $165.50

Lula will need to pay $165.50 each month for 6 months to pay off her $993 furniture purchase without interest.

Lula purchased furniture on her credit card and plans to make payments over a period of 6 months with no interest charged. To calculate the monthly payment amount, you would divide the total cost of the furniture by the number of months over which she plans to pay.

The formula to find out the monthly payment is:

Monthly Payment = Total Cost / Number of Months

So for Lula, it looks like this:

Monthly Payment = $993 / 6

Monthly Payment = $165.50

Therefore, if Lula pays $165.50 each month, she will have the furniture paid off in 6 months without incurring any interest.

Answer:

w = 30

Step-by-step explanation:

w ÷ 5 = 6

Multiply both sides of the equation by 5

w = 30

Hope this helps :)

Answer:30

Step-by-step explanation:

5 divided by 30 is 6

Answer:

The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8

Step-by-step explanation:

The complete question is

Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and each peach costs $2. She bought  a total of 14 peaches and bananas altogether. Determine the number of peaches and the  number of bananas that Emily bought

Let

x ----> the number of bananas that Emily bought

y ----> the number of peaches that Emily bought

we know that

She bought  a total of 14 bananas and peaches altogether

so

[tex]x+y=14[/tex] -----> equation A

She bought $20.80 worth of bananas and peaches

so

[tex]0.80x+2y=20.80[/tex] -----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (6,8)

see the attached figure

therefore

The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8

Answer:

-30

Step-by-step explanation:

Hope this helps! Brainliest is appriciated.

Answer:

[tex]24x - 12 - 43x - 6 \\ 24x - 43x - 12 - 6 \\ - 19x - 18[/tex]

Answer:

by 2

Step-by-step explanation:

Answer: 2 seconds

Step-by-step explanation:

A computer company is testing a new booster to increase program load times. The box plots show the number of seconds it takes to load a program with and without the booster. Using these plots, how much did the median change?

Answer:

[tex]B) \frac{DE }{EA} =\frac{CB}{AC}[/tex]

Step-by-step explanation:

If ant two given triangles are SIMILAR, then they have equal corresponding angles and their corresponding sides are PROPORTIONAL.

For example: if Δ ABC ≈ Δ PQR, then

∠A  = ∠P  , ∠B  = ∠Q  and ∠C  = ∠R

and [tex]\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}[/tex]

Now, here given:  Δ ADE ≈ Δ ABC

Then by the SIMILAR postulate their corresponding angles are equal and their corresponding sides are Proportional.

[tex]\implies \frac{AD}{AB} = \frac{DE}{BC} = \frac{AE}{AC}[/tex]    ............. (1)

Consider from above:

 [tex]\frac{DE}{BC} = \frac{AE}{AC}\\\implies \frac{DE}{AE} = \frac{BC}{AC}[/tex] ............. (2)

Here, the given options are:

[tex]A) \frac{EA }{DE} =\frac{CB}{AC}[/tex]     FALSE

[tex]B) \frac{DE }{EA} =\frac{CB}{AC}[/tex]   TRUE    (from 2)

[tex]C) \frac{DE }{EA} =\frac{AC}{CB}[/tex]   FALSE

[tex]C) \frac{EA}{DE} =\frac{AC}{CB}[/tex]    FALSE

Answer:

b

Step-by-step explanation:

took test

Answer:

c) 4

Step-by-step explanation:

The sum of two numbers is 14. The larger number minus three times the lesser number is -2

To solve this question, we need to write the statement mathematically;

Let the two numbers be x and y

"The sum of two numbers is 14" can be mathematically written as x+y = 14

and

"The larger number minus three times the lesser number is -2" can be mathematically written as x -  3y  = -2

x + y = 14  ------------------(1)

x - 3y= -2 -------------------(2)

Subtract equation (2) from equation (1)

[x - x = 0          y - (-3y)=4y     14-(-2)=16]

4y  = 16

To get the value of y divide both-side of the equation by 4

4y/4 = 16/4

y  =   4

Substitute y=4 into equation (1)

x + y =14

x +4 =14

Subtract 4 from both-side of the equation

x + 4 -4  = 10]-4

x = 10

x=10 and y =4

Therefore the lesser number is 4

Answer:

120

Step-by-step explanation:

Answer:

sarah has 1 apple left

Answer:

a.

Step-by-step explanation:

A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.

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First question:

The first question involves the test of an hypothesis.

Tests have significance levels, which normally are either 0.01, 0.05 or 0.1. If the p-value is less than the significance level, the results are significant, while if they are more, the results are not significant.

In this question, the p-value is 0.45, which is considerably more than any significance level, meaning that the results are nowhere near to being statistically significant, and the correct option is:

a. The results are nowhere near to being statistically significant.

A similar problem can be found at https://brainly.com/question/22968227

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Second question:

The order in which the people are chosen is important, as the first and second person chosen have different roles, and thus, the permutations formula is used.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, there are 2 people from a set of 10, so:

[tex]P_{10,2} = \frac{10!}{8!} = 10\times9 = 90[/tex]

90 possible combinations, option b.

A similar problem can be found at https://brainly.com/question/24245547

Answer:

3.5

Step-by-step explanation:

30 · 7 = 210

210 ÷ 60 = 3.5