Triangle ABC is defined by the points A(2,9), B(8,4), and ((-3,-2).
Complete the following equation for a line passing through point C and perpendicular AB.

Answer:

31°

Step-by-step explanation:

As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.

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Solving :

⇒ tan x° = 9/15

⇒ tan x° = 3/5

⇒ x = tan⁻¹ (0.6)

⇒ x = 31°

The size of the unknown angle "x"

We'll have to check which is the appropriate one from SOHCAHTOA.

In this question we'll have to use tan because opposite and adjacent is given.

[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]

Substitute according to the formula.

[tex]tan \: x= \frac{9}{15}[/tex]

We'll have to use tan inverse.

[tex]x={tan}^{-1}(\frac{9}{15})[/tex]

[tex]x=30.96375653[/tex]

[tex]\large\boxed{x=31° }[/tex]

Hence, the size of the unknown angle "x" is 31°

Answer:

:

Step-by-step explanation:

Answer:gotchu g there it is

Step-by-step explanation:

Answer:sike gtf

Step-by-step explanation:

Answer:

50.13

Step-by-step explanation:

We can easily find the area of our square, so to get that over with, 6*6=36. Now, for our circle, a full circle would be A=pi*r^2, but we only have half a circle. That means our equation will be A= 1/2(pi*r^2). We have our diameter, but we need our radius. Radius is just half the diameter, so 6/2=3. Now, we multiply. 3^3 is 9, and 9*3.14 is 28.26. All we have to do now is divide that by 2. If we do that, we get 14.13. The area of the semi-circle is 14.13. But we still have to add it to the area of the square, which will be our final step. 36+14.13=50.13, which is your area.

Hope this helps!

The type of variation between the speed and time is inverse.

The equation is r = d / t

The number of miles travelled is 102 miles.

When the speed a person is driving at increases, the time it takes to travel would decrease. On the hand,  speed a person is driving at decreases, the time it takes to travel would increase. This means that there is an inverse relationship.

The equation that represents an inverse relationship is

r = d / t

Where d is the distance

Distance = t x r

51 x 2 = 102 miles

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Answer:

49 ÷ 66 × 100= x

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

8-2 (i+1) < 12 − 7i + 4i

Left side of the inequality:

8 - 2(i + 1)        distribute

8 - 2i - 2        simplify

(8 - 2) - 2i

6 - 2i

Right side of the inequality:

12 − 7i + 4i        simplify

12 − 3i

Combine:

6 - 2i < 12 − 3i

6 is less than 12

3i is less than 2i

leads to the assumption that the statement is true

For 95% of all randomly selected samples of n = 130 students, the

amount of sleep will be between [tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex].

According to the empirical rule, also known as the 68-95-99.7 rule.

The percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

For 95% of all randomly selected samples of n = 130 students, the

amount of sleep will be between can be

[tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex]

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Answer:

55

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ordered pairs

( 1 , -1 )

( 2 , -3 )

( 3 , -5 )

( 4 , -7 )

( 0 , 1 )

( -1 , 3)

( -2 , 5)

( -3 , 7)

Answer:

x-intercept = (0.5, 0)

y-intercept = (0, 1)

Step-by-step explanation:

x-intercept : where the line intersects the x-axis

y-intercept : where the line intersects the y-axis

Step-by-step explanation:

♡ #jennifer ♡

A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets is mathematically given as

Generally, the equation for a sold tickets is mathematically given as

S=x+72

Therefore

x+x+72=772

2x+72=772

2x=772-72

x=350

In conclusion, tickets sold was

x=350

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The domain of the function will be (-∞, ∞) and the range of the function will be (-∞, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The set of ordered pairs is given below.

{(-3, 2), (-2, 1), (-1,0), (0, -1)}

Then the line function will be

    y – 0 = [(– 1 – 0)/(0 + 1)] (x + 1)

          y = – x – 1

x + y + 1 = 0

Then the domain of the function will be (-∞, ∞) and the range of the function will be (-∞, ∞).

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Answer:

B

Step-by-step explanation:

6% of her salary is  .06 * 50000 = 3000  <===== matched 100%

   from 6- 12% is another 3000 <=====matched 50% =  1500

3000 + 1500 = 4500 dollars matched

(she put in 6000 and her employer put in 4500 = 10500 total)

answer 7344012

percent *612000 =

(12:100)*612000 =

(12*612000):100 =

7344000:100 = 73440

Now we have: 12 percent of 612000 = 73440

Question: What is 12 percent of 612000?

Percentage solution with steps:

Step 1: Our output value is 612000.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$612000=100\%$.

Step 4: Similarly, $x=12\%$.

Step 5: This results in a pair of simple equations:

$612000=100\%(1)$.

$x=12\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{612000}{x}=\frac{100\%}{12\%}$

Step 7: Again, the reciprocal of both sides gives

$\frac{x}{612000}=\frac{12}{100}$

$\Rightarrow x=73440$

Therefore, $12\%$ of $612000$ is $73440$

The number of feet of fencing that is needed to go around the pool path is D. 201 ft.

We have a pool with a radius of 28 feet. The radius of the outer edge of the pool path would be equal to the radius of the pool plus the width of the path.

= (28 + 4) feet

= 32 feet

The circumference of the outer edge of the pool path would be equal to the perimeter.

p = 2 * pi * r

p = 2 * 3.14 * 32

p = 200.96 feet

p = 201 feet

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Answer:

1. Reflection

2. G` will coincide with A, because having a reflection along with BC would mean G` directly goes on A.

3. GBC is congruent to triangle ABC because triangle GBC and triangle ABC have the same exact line measurements, and angles, and share a line.

Step-by-step explanation:

I don't know your notes on 6/3 so number 3 might not be 100% correct.

Answer:

Step-by-step explanation:

We want to identify a rigid transformation that maps congruent triangles to one-another, to explain the coincidence of corresponding parts, and to identify the theorems that show congruence.

__

Triangles GBC and ABC share side BC. Whatever rigid transformation we use will leave segment BC invariant. Translation and rotation do not do that. The only possible transformation that will leave BC invariant is reflection across line BC.

__

In part 3, we show ∆GBC ≅ ∆ABC. That means vertices A and G are corresponding vertices. When we map the congruent figures onto each other, corresponding parts are coincident. That is, vertex G' (the image of vertex G) will coincide with vertex A.

__

The markings on the figure show the corresponding parts to be ...

And the reflexive property of congruence tells us BC corresponds to itself:

There are four available congruence theorems applicable to triangles that are not right triangles

We don't know which of these are in your notes, but we do know that all of them can be used. AAS can be used with two different sides. SAS can be used with two different angles.

SSS

  Corresponding sides are listed above. Here, we list them again:

  AB and GB; AC and GC; BC and BC

SAS

  One use is with AB, BC, and angle ABC corresponding to GB, BC, and angle GBC.

  Another use is with BA, AC, and angle BAC corresponding to BG, GC, and angle BGC.

ASA

  Angles CAB and CBA, side AB corresponding to angles CGB and CBG, side GB.

AAS

  One use is with angles CBA and CAB, side CB corresponding to angles CBG and CGB, side CB.

  Another use is with angles CBA and CAB, side CA corresponding to angles CBG and CGB, side CG.

Answer:

 B. 8.56

Explanation:

Given:

So using cosine rule:

[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]

[tex]\rightarrow \sf cos(50) = \dfrac{5.5}{x}[/tex]

[tex]\rightarrow \sf x= \dfrac{5.5}{cos(50) }[/tex]

[tex]\rightarrow \sf x= 8.56[/tex]

Answer:

hi the answer is c

Step-by-step explanation:

Answer:

Check the attached image

let's firstly convert the mixed fractions to improper fractions and then get their difference.

[tex]\stackrel{mixed}{5\frac{3}{4}}\implies \cfrac{5\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{23}{4}} ~\hfill \stackrel{mixed}{1\frac{5}{8}}\implies \cfrac{1\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Saturday and Sunday}}{\cfrac{23}{4}}~~ - ~~\stackrel{Saturday~only}{\cfrac{13}{8}}\implies \cfrac{(2)23~~ - ~~(1)13}{\underset{\textit{using this LCD}}{8}}\implies \underset{Sunday~only}{\cfrac{33}{8}\implies 4\frac{1}{8}}[/tex]

Answer:

Step-by-step explanation:

Answer: it suggests that this equation has no remainder and that the value of x is the factor.

Answer:

(10, 14)

Step-by-step explanation:

Hello there!

Given such a problem, we have been told to use substitution method to solve it.

To cut it short, substitution refers to replacing a variable with a value.

Here is a way to solve this problem even in future:

Back to our problem,

y = 2x - 6, x = 10

Substitute x into equation y = 2x - 6

y = 2(10) - 6

= 20 - 6

= 14

. ° . x = 10, y = 14

Variables in terms of x and y

(x, y) = (10,14) ✓

This is our answer.

I hope this helps.

Have a nice studies.

Answer:

61

Step-by-step explanation:

aₙ = a₁ + (n - 1)d

aₙ = 4 + (20 - 1)3

aₙ = 4 + (19)3

aₙ = 4 + 57

aₙ = 61

Answer:

  no

Step-by-step explanation:

The prices are inconsistent, so there is no unique price that can be set for either an apple or an orange that will give the total prices indicated.

__

The first relation can be written as ...

  $10 = 4A +4O

  $10 = 4(A +O) . . . . factor out 4

  $2.50 = A +O . . . . divide by 4

The second relation can be written as ...

  $12 = 6A +6O

  $12 = 6(A +O) . . . . factor out 6

  $2 = A +O . . . . . . . divide by 6

These two relations give different prices for 1 apple and 1 orange. There is no price that can be set for either fruit that will give this result.

No unique prices can be assigned.

Answer: 9

Step-by-step explanation:

By the geometric mean theorem, [tex]\frac{x}[6} =\frac{6}{4} \longrightarrow x=\left(\frac{6}{4} \right)(6)=\boxed{9}[/tex]

Answer:

Yes and the answer is 16/5

Step-by-step explanation:

Find the reciprocal of the divisor

Reciprocal of 1/6 : 6/1

Now, multiply it with the dividend

8/15 ÷ 1/6 = 8/15 × 6/1

And after that you get 48/15 but after reducing the fraction, the answer is 16/5. ( In mixed form, 3 1/5 )

I hope this helps and I am a middle school student answering this question.

Answer:

Step-by-step explanation:

can you simplify 8/15+1/6

8/15 + 1/6 =

(16 + 5)/30 =

21/30 =

semplify (21:3 and 30:3)

7/10

Answer:

Maria

Step-by-step explanation:

Marias suitcase is heavier as 1600 grams to kg is 1.6kg which is less than Marias suitcase which weighs 14kg hope this helps:)