Determine the equation of the altitude from A.

Determine The Equation Of The Altitude From A.

Answers

Answer 1

Answer:

y = - 3x + 11

Step-by-step explanation:

the altitude is a line from the vertex A drawn perpendicular to the opposite side BC

calculate the slope of BC using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )

[tex]m_{BC}[/tex] = [tex]\frac{5-3}{-1-(-7)}[/tex] = [tex]\frac{2}{-1+7}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = - 3x + c ← is the partial equation

to find c substitute A (4, - 1 ) into the partial equation

- 1 = - 12 + c ⇒ c = - 1 + 12 = 11

y = - 3x + 11 ← equation of altitude from A


Related Questions

helllppppppppppp please

Answers

Answer:

h = 5t

Step-by-step explanation:

So basically, its a slope problem again. You are trying to find the equation that equals hits. So you can cross off t = 5h and t = h + 5. So now, you need to find the most reasonable answer by calculating the slope.

If you try h = t + 5,

Put in 3 - you get 8

Put in 7 - you get 12

But on the table you get 15, 36 respectively.

If you try h = 5t,

Put in 3 - you get 15

Put in 7 - you get 35

Which is much closer to the numbers in the table, therefore it is the answer.

y + 3x ≤7

solve it…… …

Answers

Answer:

[tex]x \leq \frac{7 - x}{3}[/tex]

Step-by-step explanation:

This expression is an inequality which is a relation that makes a non-equal comparison between two numbers/expressions

we want x to be alone in one side, y + 3x ≤ 7

Subtract y from both sides,

y + - y + 3x ≤ 7 - y

3x ≤ 7 - y

divided both sides by 3 to get x alone

3x / 3 ≤ 7 - y / 3

x ≤ 7 - y / 3

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The graph shows a vertical translation of y=√x
4
3-
2
1+
-10-8-6-4-2₁- 2
What is the range of the translated function?
O {vly < 0)
O {vly 20}
Oyly is a natural number)
Oyly is a real number)
4

Answers


The range of the cubed root of x is all real numbers.

Graphically
The height of this function will start at - infinity and continue to infinity.
(look at the vertical growth of the graph. It will keep going down and will also keep growing forever)

Algebraically
Nothing will "break" this function as it is a cubed root. Thus the output (range) could be anything

Select the value that completes the perfect square trinomial: x^ 2 +22x+_____

Answers

Answer:

121 i.e. 11²

Step-by-step explanation:

(a+b)² = a² + 2ab + b²

x² + 2 × x × 11 + 11² = (x + 11)²

can you help me i give you brainly

Answers

Answer:

Step-by-step explanation:

it should be sth like green graph

Triangle ABC is isosceles.

Triangle A B C. Angle A is x degrees, angle B is 118 degrees, angle C is x degrees. Sides A B and B C are equal.

Which equation can be used to find the degree measure of Angle A?
118 = x + x
x + x + 118 = 180
118 + 180 = x + x
(x + x) minus 118 = 180

Answers

Step-by-step explanation:

118+2×=180

180-118=62

62÷2(×)=31

×=31

Answer:

x + x + 118 = 180

Step-by-step explanation:

...........

Graph the image of this figure after a dilation with a scale factor of 12centered at the point (−3, 0)

Answers

Answer:

bro tbh just use like or

Step-by-step explanation:

its not that deep

What is the constant rate of change of the table below? Please help

Answers

Answer:

4 m/s

Step-by-step explanation:

Well the constant rate of change can be defined as the slope or rise/run. This can be calculated using any two points. So I'll use (10, 40) and (20, 80). the seconds increased by 10 (run) and the meters increased by 40 (rise) This gives you the equation 40/10 which simplifies to 4. That is the constant rate of change

If a coin is tossed, a die is rolled, and a candy is taken from a dish of 20 candies, 7 of which are red, what is the probability of getting a red candy, a heads, and a 2 on a 6-sided die?


ANSWER OPTIONS:

0.0167


0.29167


1.0167


0.029167

Answers

Answer:

B

Step-by-step explanation:

7/20 x 1/2 x 1/6

Y<2/3x+2

A. (0,3)
B. (-3,1)
C. (3,5)
D. (1,2)

Answers

The ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

How to determine the ordered pair?

The inequality is given as:

y < 2/3x + 2

Next, we test the options:

A. (0,3)

3 < 2/3 * 0 + 2

3 < 2 --- false

B. (-3,1)

1 < 2/3 * -3 + 2

1 < 0 --- false

C. (3,5)

5 < 2/3 * 3 + 2

5 < 4 --- false

D. (1,2)

2 < 2/3 * 1 + 2

2 < 2.67 --- true

Hence, the ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

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PLEASE HELPP I NEED ASAP

Answers

Answer:

[-6, -2](-2, 1](1, 5]

Step-by-step explanation:

The question is asking you to identify the domain for each of the parts of the piecewise-defined function. This means you need to identify the corresponding part on the graph, and determine its horizontal extent.

Observation

The first step in solving a problem is to look at the given information. The graph is shown as three (3) non-overlapping horizontal line segments. The open- or filled-circle end points tell you whether that x-value is part of the line segment.

The blanks in the function definition are where the domain descriptions go for the piecewise-defined function. This means you have to match the function description to the left of "if x ∈" with the set of x-values it corresponds to. The "x ∈" notation suggests you want to specify the domain in "interval notation," rather than as an inequality.

Bottom piece

The first part of the function definition is ...

  f(x) = -4

This matches the horizontal line segment at the bottom of the graph. The closed dots at its ends mean it is defined for ...

  -6 ≤ x ≤ -2

In interval notation, a square bracket is used when the end point is included in the interval.

  f(x) = -4  if x ∈ [-6, -2]

Middle piece

The second part of the function definition is ...

  f(x) = -3

This matches the horizontal line segment in the middle of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  -2 < x ≤ 1

We use a round bracket (parenthesis) when an end point is not included in the interval.

  f(x) = -3  if x ∈ (-2, 1]

Top piece

The third part of the function definition is ...

  f(x) = 4

This matches the horizontal line segment at the top of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  1 < x ≤ 5

In interval notation, this is ...

  f(x) = 4  if x ∈ (1, 5]

. 40% of students passed 90% students attended class 30% both passed and attended class martin was selected at random he attend class daily determine the probability that he passed the exam

Answers

Probability that Martin passed the exam when he attend the class daily is given by 1/3.

Probability is the possibility to occurrence of an event.

In other words, Probability is the ratio of number of favorable cases under an event to total number of cases under that event.

Let P be the event that Martin passed the exam and A be the event that he attend the class daily.

Given that,

40% of students passed tbe exam.

The probability to pass the exam is given by,

[tex]P(P)=40%=\frac{40}{100}=\frac{4}{10}[/tex]

90% students attend the class daily

probability to attend the class daily is given by,

[tex]P(A)=90%=\frac{90}{100}=\frac{9}{10}[/tex]

30% student both passed the exam and attended class

So probability to both passed the exam and attend the class is given by,

[tex]P(P\cap A)=30%=\frac{30}{100}=\frac{3}{10}[/tex]

Now conditional probability that Martin will passed the exam if he attend class daily is given by,

[tex]P(P|A)=\frac{P(P\cap A)}{P(A)}=\frac{\frac{3}{10}}{\frac{9}{10}}=\frac{3}{9}=\frac{1}{3}[/tex]

Hence the required pobability that Martin passed the exam when he attend the class daily is given by 1/3.

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A spherical ball is inflated so that it’s radius increases in the ratio 4:3. Find the ratio in which it’s volume is increased

Answers

Answer:

64:27

Step-by-step explanation:

If the ratio between the old and new radius is described with the ratio: 4:3, then if the first radius was 3, then the new radius is 4.

Also if you multiply 3 by (4/3) it also equals 4

The volume of a sphere is described as:  [tex]\frac{4}{3} \pi r^{3}[/tex]

So let's plug in 3 and 4 and see their ratio.

[tex]\frac{\frac{4}{3}\pi 4^{3} }{ \frac{4}{3}\pi 3^{3} }} = \frac{4^{3} }{3^{3} } = \frac{64}{27}[/tex]

The answer is 64/27 or (4/3)^3

 

Answer:

by a factor of 64/27   or   64:27

Step-by-step explanation:

Volume of a sphere = 4/3  pi  r^3    

    now increase the radius  by 4/3      ( this is  4:3)

               new volume = 4/3 pi  (4/3 r)^3  

                                     = 64/27  *  4/3 pi r^3

so the original volume is increased by  64/27

Insurance protects you from liability and allows you to provide for your own and others' long-term needs. But what if you never need the insurance? You wind up putting out a lot of money and you get nothing out of it. Which kinds of insurance do you think are worth the cost? Which are not?

Answers

Life , Health , Car are considered to be very important insurance ,  Rental Car Damage , Travel Insurance has no usage.

What is Insurance ?

Insurance is safe guarding any thing which has some monetary or emotional value to it , It can be life , health , car , house , your gold etc.

Insurance protects you against something you can never predict .The life is unpredictable and Insurance is a cover to that .

As given in the question , a person can be lucky enough that he never gets to use the money that he invested in the Insurance , but not investing due to this is wrong.

This is not difference of opinion but lack of prediction of future and lack of understanding the needs of life.

Life , Health , Car , Home , Fire etc . insurance that protects the basic amenities of life are considered to be very important ,

while nowadays insurance of Rental Car Damage , Travel Insurance , these are some which has no usage beyond the fact that they cover nothing.

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(x + 1 < 4) ∩ (x - 8 > -7).

Answers

The correct answer is x = 2

Inequality

(x + 1 < 4) ∩ (x-8>-7)

Make x the subject in each case:

(x<4-1)(x>-7+8)

        (x<3)∩(x>1)

If x<3, then x could be 2, 1, -1, etc.

If x>1, then x could be 2, 3, 4, etc.

Thus (x<3)∩(x>1) = 2

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Answer:

x = 2

Step-by-step explanation:

Hello!

We are looking at the intersection of two sets, or common values found between two sets of data.

We can solve for x on each side and find any common values between.

Find the Intersection[tex](x + 1 < 4) \cap(x - 8 > -7)[/tex][tex](x < 3)\cap(x > 1)[/tex][tex](x = 2, 1, 0, -1, -2...)\cap(x = 2, 3, 4, 5, 6...)[/tex][tex]x = 2[/tex]

As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.

Therefore, the intersection of these sets is 2.

Please help ill give whoever answers the best the brainliest answer :)))

Answers

Answer:

w(w-5)

Step-by-step explanation:

Given Width of rectangle = w

Length of rectangle is 5 less than width of rectangle = w - 5

Area of Rectangle = Length x Width = w * w-5 = w(w-5)

Answer:

the second answer option

Step-by-step explanation:

the area of a rectangle is

length × width

or

l × w

l = w - 5

so, when we use the second in the first equation, we get

(w - 5)×w

or

w(w - 5)

What is the slope of the line shown below??

Answers

Answer:

1

Step-by-step explanation:

We can find the slope using the slope formula, which is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

The order of the points doesn't matter, but the points that are farthest right (8, 8) can be our y2 and x2 and the points that are farthest left (5, 5) can be our y1 and x1.

Thus, we have [tex]\frac{8-5}{8-5}=\frac{3}{3}=1[/tex]

What is the tangent
ratio of angle C₂ ?

Answers

Answer:Tangent ratio of an angle

Step-by-step explanation:

Tangent ratio of an angle  the ratio of the length of the opposite side of an angle divided by the length of the adjacent side.

Solve for this trig identity step by step.

Answers

Using trigonometric identities, and equality is reached, hence the equality is proved.

Which trigonometric identity are used to solve this question?

These three identities are used:

[tex]\sin^2{x} + \cos^2{x} = 1 \rightarrow \cos^2{x} = 1 - \sin^2{x}[/tex].[tex]\sec^2{x} = 1 + \tan^2{x}[/tex].[tex]\sec^2{x} = \frac{1}{\cos^2{x}}[/tex]

Hence:

[tex]\sec^4{x} = \frac{1 + \tan^2{x}}{1 - \sin^2{x}}[/tex]

[tex]\sec^4{x} = \frac{\sec^2{x}}{\cos^2{x}}[/tex]

[tex]\sec^4{x} = \sec^2{x} \times \sec^2{x}[/tex]

[tex]\sec^4{x} = \sec^4{x}[/tex]

Equality is reached, hence the equality is proved.

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Suppose $n$ is a positive integer such that $6n$ has exactly 9 positive divisors. How many prime numbers are divisors of $6n$

Answers

The number of prime divisors of "6n" is 2 numbers 2 and 3

Given

"n"  = 6    

thus 6n  = 6(6) = 36

The positive divisors are   1, 2, 3, 4, 6, 9, 12, 18 and 36

So, the number of prime divisors of "6n" is 2 numbers 2 and 3.

The prime factors of a positive integer are the top numbers that divide that integer exactly. The technique of finding those numbers is known as integer factorization or prime factorization.

The fundamental theorem of mathematics says that every positive integer has a completely unique prime factorization.

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Pls helppppppppppppppp

Answers

Answer:

y = 4/5x + 2

Step-by-step explanation:

Standard equation given slope and y-intercept -> y = mx + b

After substituting variables m and b, you get y = 4/5x + 2.

What is the value of x?

Answers

Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]

Jorge wants to determine the enlarged dimensions of a digital photo was 800 pixels high. The new photo will be 1,260 pixels wide .what will the new height be

Answers

The height of the new photo must be 945 pixels (option B).

How to calculate the width of the new photograph?

To calculate the height of the photograph, we must first know what proportion the sides of the previous photo have, for this we do the following operation:

600 × 100 = 60,00060,000 ÷ 800 = 75

According to the above, the height of the photo is equal to 75% of the width. So to find the height of the new photograph we must do the following operation:

1.260 ÷ 100 = 12.612.6 × 75 = 945

So the height of the new photo should be 945 pixels.

Note: This question is incomplete. Here is the missing part:

Question

Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?

Options

460 pixels

945 pixels

1,680 pixels

1,860 pixels

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Given:
\overleftrightarrow{BD}
BD
B, D, with, \overleftrightarrow, on top is the perpendicular bisector of segment \overline{AC}
AC
start overline, A, C, end overline.
\overline{BD}
BD
start overline, B, D, end overline is 333 units long.
\overline{AC}
AC
start overline, A, C, end overline is 888 units long.
Naomi was asked to show that point DDD is equidistant from points AAA and CCC.

Answers

A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points  A and C.

BD ⊥ AC (given)

BD = 3 units, and AC = 8 units.

BD is the perpendicular bisector of segment AC (given)

Thus,

<BDA  ≅ <BDC (right angles formed by a perpendicular bisector)

AD ≅ DC (equal parts of a bisected line)

AD ≅ DC = 4 units

Thus joining points B to A, and B to C,

BA ≅ BC.

So that applying Pythagoras theorem to ΔABD, we have:

[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]

[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]

       = [tex]\sqrt{25}[/tex]

 AB      = 5 units

So that,

BA ≅ BC = 5 units

Therefore, it can be concluded that point D is equidistant from points A and C.

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Which explicit formula is equivalent to a1 = 1, an = -6an-1

Answers

The explicit formula that is equivalent to aₙ = -6aₙ₋₁  is; aₙ = 1(-6)ⁿ⁻¹

What is the explicit formula?

We are given;

a₁ = 1

aₙ = -6aₙ₋₁

Thus, for second term;

a₂ = -6a₁

a₂ = -6

For the third term;

a₃ =  -6a₂

a₃ = 36

The resulting sequence is 1, -6, 36,......

The sequence is a geometric sequence with;

a = 1

r = -6

The explicit rule will be aₙ = 1(-6)ⁿ⁻¹

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(-1,8) and (8,5). this is a coordinate distance wuestion that i rly need help on

Answers

Answer:

3[tex]\sqrt{10}[/tex] ≈ 9.45

Step-by-step explanation:

calculate the distance d between the points using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (8, 5 )

d = [tex]\sqrt{(8-(-1))^2+(5-8)^2}[/tex]

   = [tex]\sqrt{(8+1)^2+(-3)^2}[/tex]

   = [tex]\sqrt{9^2+9}[/tex]

   = [tex]\sqrt{81+9}[/tex]

   = [tex]\sqrt{90}[/tex]

   = [tex]\sqrt{9(10)}[/tex]

   = [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]

   = 3[tex]\sqrt{10}[/tex] ← exact value

   ≈ 9.49 ( to 2 dec. places )

what does 4r-8=6r+14 equal to?

Answers

Answer:

r is -11

Step-by-step explanation:

Move the like terms to the same side. 4r-6r is -2r

14 + 8 is 22

22/-2 is -11

How do you simplify 6 by the power of negative 2 multiplied by 6 by the power of 3

Answers

Answer:

Keep in mind the rules.

When we multiply terms with same bases we keep one base and add the exponents.

Step-by-step explanation:

[tex] = {6}^{ - 2} \times {6}^{3} \\ = { 6}^{ - 2 + 3} \\ = {6}^{1} \\ = 6[/tex]Hope this helps.




A rectangular quilt is to be made so that the length is 1.2 times the width. The quilt must be between 72ft^2 and 96ft^2 to cover
the bed. Determine the restrictions on the width so that the dimensions of the quilt will meet the required area.

Answers

W is the width of the quilt, the restrictions are given by the inequality:

7.7ft ≤  W ≤  8.9 ft

How to determine the restrictions on the width?

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case, we know that:

L = 1.2*W

Replacing that we get:

A = 1.2*W²

And we know that the area must be between 72 square feet and 96 square feet, then:

72ft² ≤  1.2W² ≤ 96ft²

Now we can divide all by 1.2:

(72ft²)/1.2 ≤  W² ≤ (96ft²)/1.2

60ft² ≤  W² ≤ 80ft²

If we apply the square root in the 3 sides of the inequality, we get:

√60ft² ≤  √W² ≤ √80ft²

7.7ft ≤  W ≤  8.9 ft

These are the restrictions on the width such that the quilt will meet the required area.

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vincent ordered pizza for him and his wife for dinner. when they had finished, they realized that 5/8 of the pizza was gone. for lunch the next day, vincent decided to eat 1/4 of what was left. how much was left after lunch?

Answers

Answer:

1/8 of the pizza

Step-by-step explanation:

whole pizza=1

5/8 is gone so 1-5/8=8/8-5/8=3/8

3/8-1/4 = 3/8-2/8=1/8

hope this helps

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