*****HELP ASAP WILL MARK BRAINLIEST****** Ignore if you don't know!!!! Geometry problem: Point D is the incenter of triangleABC, if DE=x^2 and DF= 20-8x, find each of the following

Answer:

Approximately [tex]101\; \rm ft[/tex] (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Angles:

Let the length of segment [tex]\rm BR[/tex] (vertical distance between the base of the tree and the base of the hill) be [tex]x\; \rm ft[/tex].

The question is asking for the length of segment [tex]\rm AB[/tex]. Notice that the length of this segment is [tex]\mathrm{AB} = (x + 20)\; \rm ft[/tex].

The length of segment [tex]\rm OB[/tex] could be represented in two ways:

For example, in right triangle [tex]\rm \triangle OBR[/tex], the length of the side opposite to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex] is segment [tex]\rm BR[/tex]. The length of that segment is [tex]x\; \rm ft[/tex].

[tex]\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}[/tex].

Rearrange to find an expression for the length of [tex]\rm OB[/tex] (in [tex]\rm ft[/tex]) in terms of [tex]x[/tex]:

[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}[/tex].

Similarly, in right triangle [tex]\rm \triangle OBA[/tex]:

[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}[/tex].

Equate the right-hand side of these two equations:

[tex]0.810\, x \approx 0.649\, (x + 20)[/tex].

Solve for [tex]x[/tex]:

[tex]x \approx 81\; \rm ft[/tex].

Hence, the height of the top of this tree relative to the base of the hill would be [tex](x + 20)\; {\rm ft}\approx 101\; \rm ft[/tex].

Answer:

A

Step-by-step explanation:

16 x 100 = 1600

1600 / 40 = 40.0

Answer:

A. 40.0

Step-by-step explanation:

Answer:

-25 + 75 = 50

Step-by-step explanation:

Since we don't know the value of the bar, we will call it x.

-25 + x = 50

Add 25 to both sides to find the value of x.

x = 75

You can also double check this answer by doing simple math.

-25 + 75 = 50

Answer:

3)   (4, 2)

Step-by-step explanation:

The point of intersection of the lines is the solution. That point is (4, 2).

Answer: 3)   (4, 2)

Answer:

the answer is the third one (4, 2)

Step-by-step explanation:

the solution to a system of equations is always where they intersect. in this case, the two lines intersect at (4, 2), which means that the solution is (4, 2).

hope this helped!! :D

Answer:

2.4 kg/week

Step-by-step explanation:

(48 kg)/(20 weeks) = 2.4 kg/week

Answer:

y=2/5x + 2

Step-by-step explanation:

find slope by using formula between these two points: (0,2) and (-5,0); then put into slope-intercept form (y=mx+b)

Answer:

Step 1

Step-by-step explanation:

His first error occurred in step 1.

The common denominator of [tex] \frac{2}{9} [/tex] and [tex] \frac{1}{5} [/tex] is 45, and not 14.

Common denominator of both fractions, is a number of which both 9 and 5 are its factor. That is, it is a common multiple of 9 and 5.

45 can be divided by 9 without remainder. Also 45 can be divide by 5 without a remainder.

45 would make both fractions common not 14.

Answer:

9425912.111

Step-by-step explanation:

Answer:

9425912.111

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf 74}}[/tex]

Step-by-step explanation:

The nth term of an arithmetic sequence can be found using the following formula.

[tex]a_n=a_1+(n-1)d[/tex]

Where n is the term, a₁ is the first term, and d is the common difference.

We want to find the 21st term, we know the first term is -6, and the common difference is 4.

[tex]n= 21\\a_1= -6 \\d=4[/tex]

Substitute the values into the formula.

[tex]a_{21}=-6+(21-1)4[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve inside the parentheses.

[tex]a_{21}=-6+(20)4[/tex]

Multiply 20 and 4.

[tex]a_{21}= -6+80 \\[/tex]

Add -6 and 80.

[tex]a_{21}=74[/tex]

The 21st term of the sequence is 74

Answer:

Here we will use the formula

[tex] \tt \: a_n \: = a_1 +( n - 1)\: \times d[/tex]

[tex] \tt\: a_{21} = −6+(21−1)4[/tex]

By using PEMDAS

[tex] \tt \: a_{21} = - 6 + (20)4[/tex]

[tex] \tt \: a_{21} \: = - 6 + 80 = 74[/tex]

[tex] \huge \tt \bigodot \: \: 74[/tex]

Answer:

1) intersection of both lines is the solution: (-3, 1)

2) y = -1/6x + 1 will produce a perpendicular line and intersect at only one point  (slopes of 6 and -1/6 are opposite and reciprocal, thereby producing perpendicular lines)

3) 'b' can be any value except 1

Step-by-step explanation:

Answer:

translation

W(-10, 0)

X(-10, -8)

Y(-18, -4)

Z(-14, 8)

dilation

W(-8, 16)

X(-8, 0)

Y(-24, 8)

Z(-16, 32)

Step-by-step explanation:

In translation, all you are doing is taking each point and subtracting 6 from the x, and subtracting 8 from the y. The point of W is (-4, 8). Thus you do (-4 - 6 , 8-8) and you get the new point (-10,0). Repeat this for all the others.

In dilation you are multiply both x and y by 2. For point W you do (-4*2, 8*2) to get the new point (-8, 16). You repeat this for the remaining points.

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Answer:

a) 9 inches

is correct answer for you

Answer:

C, 25

Step-by-step explanation:

3 x 5 = 15

5 x 5 = 25

Answer:

c is the correct answer

Step-by-step explanation:

Answer:

Correct Answer is B

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (−3,−10)

Focus: (−3,−[tex]\frac{39}{4}[/tex])

Axis of Symmetry: x = −3

Directrix: y = −[tex]\frac{41}{4}[/tex]

x               y

-5             -6

-4             -9

-3            -10

-2             -9

-1              -6

Answer:

A

Step-by-step explanation:

Answer:

120/2 = x/5....120 miles to 2 hrs = x miles to 5 hrs

cross multiply

(2)(x) = (120)(5)

2x = 600

x = 600/2

x = 300....the motorcyclist would travel 300 miles in 5 hrs

or u could do it this way..

120/2 = 60 miles per hr

60 * 5 = 300 miles

Step-by-step explanation:

Answer:

SSS

Step-by-step explanation:

The SSS theorem is the side-side-side theorem. Basically, since all three sides from one triangle is congruent to the corresponding sides of the other triangle, then the triangles have to be congruent. There are other theorems such as the SAS theorem (side-angle-side), but since the question only give us the fact that the sides are congruent, its SSS. Sorry, I hope this is good enough. XD

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The calculation can be done by any method that adds 6% of the original salary to the original salary. That's equivalent to multiplying the original salary by 1.06 or 106%. The attachment shows some possibilities.

Answer:

_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_

Step-by-step explanation:

Answer: Pedro tiene 2 años.

Step-by-step explanation:

Definamos la variable P como la edad de Pedro.

Sabemos que " El triple de la edad de pedro, más 2, es igual a la edad actual de pedro más 6"

Esto se escribe como:

3*P + 2 = P + 6.

Para encontrar la edad de Pedro, tenemos que resolver esa ecuación.

Para hacerlo, el primer paso es llevar todos los términos con "P" al lado izquierdo, y los términos sin "P" al lado derecho.

3*P - P = 6 - 2

2*P = 4

Ahora podemos dividir por 2 en ambos lados:

2*P/2 = 4/2

P = 2

Entonces podemos concluir que Pedro tiene 2 años.

Answer: There are 20 years in a score. The year he is talking about is 1776

Step-by-step explanation:

Answer:

0.75 - 0.8

Step-by-step explanation:

4.5/6 = 0.75

The closest number to round 0.75 to is 0.8

We are given the expression:

4.5 / 6

Simplifying the given expression:

We can rewrite 4.5 as 4/10:

[tex]\frac{45}{10}*\frac{1}{6}[/tex]

Since 45 and 6 have a common factor: 3

[tex]\frac{3*15}{10}*\frac{1}{3*2}[/tex]

The 3 in the numerator and the denominator will cancel out:

[tex]\frac{15}{10}* \frac{1}{2}[/tex]

We know that 15/2 is 7.5

[tex]\frac{7.5}{10}[/tex]

0.75

Hence, the quotient of the expression: 4.5/6 is 0.75

Answer:

4(x + 15)

Step-by-step explanation:

1/2x - 1/2x = 0

You're then left with 4x + 60

Factor out the 4 and you get 4(x + 15)

Answer: ITS C.

Step-by-step explanation: It’s not B I took the test and put C and got it right

Answer:

150 in

Step-by-step explanation:

Answer:

the answer is the third option (C)

Answer:

I think that answer is 5 or 35

9514 1404 393

Answer:

  24

Step-by-step explanation:

The product of lengths from the point where the secants meet to the near and far circle intersection points is the same for both secants.

  RQ·RC = RS·RT

  8(27) = (3x)(8x)

  9 = x^2 . . . . . . . . . divide by 24

  3 = x

Then the length of interest is ...

  TR = 8x = 8·3

  TR = 24

Answer:

mLNM=63

Step-by-step explanation:

triangle JKL is isocelese so mKJL and KLJ are the same

180-72=108

108/2=54

so both mKLJ and mMLN are equal

and since triangle LMN is an isoceles then mLNM and mLMN are equal to each other

so 180-54=126

126/2=63

mLNM=63

Answer:

Step-by-step explanation:

The nth term of a geometric sequence is expressed as;

Sn = a(r^n - 1)/r - 1

a is the first term of the sequence

r is the common ratio

n is the number of terms

From the sequence;

a = 3

r = -6/3 = 12/-6 = -2

n = 5 (since are looking for the sum of first five terms)

Substitute into the formula;

S5 = 3((-2)^5 - 1)/-2 - 1

S5 = 3(-32-1)/-3

S5 = 3(-33)/-3

S5 = -(-33)

S5 = 33

Hence the sum of the first five terms of the sequence is 33

Answer:

Explained below.

Step-by-step explanation:

The scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida are,

Season 1: {75, 79, 80, 78, 76, 74, 76, 78}

Season 2: {72, 71, 76, 78, 86, 81, 72, 80}

(a)

Compute the mean and standard deviation of the golfer's scores as follows:

Season 1:

[tex]\bar x_{1}=\frac{1}{n_{1}}\sum x_{1}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]

[tex]s_{1}=\sqrt{\frac{1}{n-1}\sum(x_{1}-\bar x_{1})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 30}\\\\=2.0702\\\\\approx 2.07[/tex]

Season 2:

[tex]\bar x_{2}=\frac{1}{n_{2}}\sum x_{2}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]

[tex]s_{2}=\sqrt{\frac{1}{n_{2}-1}\sum(x_{2}-\bar x_{2})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 194}\\\\=5.26444\\\\\approx 5.26[/tex]

(b)

The primary difference in performance between the two seasons is:

[tex]\text{Diff} = \bar x_{2}-\bar x_{1}\\\\=5.26-2.07\\\\=3.19[/tex]

Complete question is;

A shareholders’ group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least seven years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x¯ = 7.27 years for CEOs with a standard deviation of s = 6.38 years (The Wall Street Journal, January 2, 2007).

a. Formulate hypotheses that can be used to challenge the validity of the claim made by

the shareholders’ group.

b. Assume 85 companies were included in the sample. What is the p-value for your hypothesis

test?

Answer:

A) Null hypothesis: H0: μ ≥ 7

Alternative hypothesis: μ < 7

B) p-value = 0.3488

Step-by-step explanation:

A) We are told that the shareholders group claimed that the mean tenure for a chief executive office (CEO) was at least seven years.

Thus, defining the hypothesis, we have;

Null hypothesis: H0: μ ≥ 7

Alternative hypothesis: μ < 7

B) Sample mean: x¯ = 7.27 years standard deviation: s = 6.38 years

Sample size = 85

Formula for the test static is;

t = (x¯ - μ)/(s/√n)

t = (7.27 - 7)/(6.38/√85)

t = 0.39

From online p-value from t score calculator attached using: t = 0.39, DF= 85 - 1 = 84, significance value = 0.05, one tail, we have;

p-value = 0.3488