Given triangle ABC with vertices A(−3, 0), B(0, 6), and C(4, 6).
c
Find the equations of the three altitudes of the same triangle

Answer:

Step-by-step explanation:

Option 3 is the correct answer

Answer: x = {1 , 5 , 7}

Step-by-step explanation:

We have x^3 - 13x^2 + 47x - 35 = 0.

Taking -13x^2, we can split it up into -x^2 - 12x^2

Taking 47x, we can split it up into 12x + 35x

Putting these into the original equation, we have:

x^3 - x^2 - 12x^2 + 12x + 35x - 35 = 0

From this you can see that we have 3 pairs of terms that we can easily factor. From the first pair we can factor x^2, from the second we can factor -12x, and from the third one we can factor 35.

1. (x^3 - x^2)  = x^2 (x - 1)

2. (- 12x^2 + 12x) = -12x (x - 1)

3. (35x - 35) = 35 (x - 1)

Putting them back into the equation we have:

x^2 (x - 1) - 12x (x - 1) + 35 (x - 1) = 0

               (x^2 - 12x + 35) (x - 1) = 0

To find the roots, we can set (x - 1) = 0 and  (x^2 - 12x + 35) = 0.

x - 1 = 0

    x = 1 (First root)

x^2 - 12x + 35 = 0

Factoring using the Sum-Product Rule:

Sum of -12, Product of 35 --> -7 and -5

x^2 - 12x + 35 = 0

  (x - 7) (x - 5) = 0

We can see that x = 7 and x = 5.

So the solution set it x = {1 , 5 , 7}

The solution set will be {1,5,7}

Zero of a function is the root of the function for which the function value of that root will be zero.

If a is the zero of function f(x)=0 then f(a)=0.

So according to question,

the equation is

x³-13x²+47x-35=0

spilting -13x² as -x²-12x² and 47x as 12x+35x

⇒x³-x²-12x²+12x+35x-35=0

⇒x²(x-1)-12x(x-1)+35(x-1)=0

taking (x-1) common from each term

⇒(x-1)(x²-12x+35)=0

In another way, as 1 is zero of x³-13x²+47x-35=0

then (x-1) is one factor of x³-13x²+47x-35=0

another factor will be x³-13x²+47x-35/(x-1)=x²-12x+35

for which we can write the equation x³-13x²+47x-35=(x-1)(x²-12x+35).

⇒(x-1)(x²-5x-7x-35)=0

⇒(x-1)(x(x-5)-7(x-5))=0

⇒(x-1)(x-5)(x-7)=0

⇒x-1=0  or  x-5=0  or  x-7=0

⇒x=1   or   x=5   or   x=7

Therefore The solution set will be {1,5,7}

Learn more about the zero of the function

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Answer:

4/8

Step-by-step explanation:

You add 3 and 1 thats 4 then you add 5 and 3 and thats 8

please mark brainliest

Answer:

4/8

Step-by-step explanation:

pretty sure because I'm pretty sure that's the correct answer

Answer:

Wait

Step-by-step explanation:

Is a equation or polynomial

Answer:

0, +/- 1. +/- 2

Step-by-step explanation:

[tex]x^{5} -5x^{3} +4x=0[/tex] Write the equation in the form of P(x) = 0.

[tex]x(x^{4} - 5x^{2} + 4) = 0[/tex] Factor out the GCF, x.

[tex]x(x^{2})^{2} - 5x^{2} + 4 = 0[/tex] Factor [tex](x^{2})^{2}- 5x^{2} + 4 = 0[/tex].

[tex]x = 0,[/tex] [tex](x^{2})^{2} - 5x^{2} + 4 = 0[/tex] Let a = [tex]x^{2}[/tex] and substitute.

[tex]a^{2} - 5a + 4 = 0[/tex] Factor.

[tex](a - 4)(a - 1) = 0[/tex] Replace a with [tex]x^{2}[/tex].

[tex](x^{2} - 4)(x^{2} -1) = 0[/tex] Factor [tex](x^{2} - 4)[/tex] as a difference of squares.

[tex](x -2)(x+2)(x^{2} -1) = 0[/tex] Use the Zero Product Property

[tex]x = 2, x = -2, x^{2} = -1[/tex]

[tex]x = 0, 1, -1, 2, -2[/tex]

Answer:-3.5

Step-by-step explanation:

Answer:

wdd

Step-by-step explanation:

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Answer:

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vv

Step-by-step explanation:

Answer:

[tex] - \frac{6}{7}p + \frac{1}{7} [/tex]

Step-by-step explanation:

Get rid of the parenthesis then combine like terms

Answer:

Step-by-step explanation:

Answer:

1.96 * 10^9 (1,960,000,000)

Step-by-step explanation:

This is basically 1,200,000,000 + 760,000,000

Answer:

(-infinity, 6] U [-6, infinity)

Answer:

Coin a is 33 and coin b is 11

Step-by-step explanation:

Answer:

B = 11

A =33

Step-by-step explanation:

A = 3B

A+B = 44

Substitute the first equation into the second equation

3B + B = 44

Combine like terms

4B = 44

Divide by 4

4B /4 = 44/4

B = 11

A = 3B

A = 3*11

A =33

Answer:

Step-by-step explanation:

answer is x=1/4y+3/4

Let's call it [tex]k[/tex].

We have,

[tex]-\frac{1}{5}(kx+15)=2x-3[/tex]

[tex]kx+15=-10x+15[/tex]

[tex]\boxed{k=-10}[/tex]

Hope this helps.

Answer:

there are two answers, whether the tax is applied AFTER you get the discount or BEFORE you get the discount, the two answers are: $61.60 or $59.92

Step-by-step explanation:

80-24+5.60

(Jacket-sale)+tax

or

80+3.92-24

(Jacket+tax)-sale

Answer: 59.92

Step-by-step explanation:

Answer:

1.5 ft remaining

$30 per ft of sheet

Sheet metal costs $30 per square foot.

Step-by-step explanation:

6.4x - 4.9x = 45

           1.5x = 45

                x = 30

6.4 - 4.9 = 1.5 ft remaining

$45 : 1.5 = $30 per ft of sheet

Answer (the system of equations input doesn't work, so there is no brace):

x = 1.5y

x + y =800

Step-by-step explanation:

First, identify the vital information:

- 800 total students

- 1.5 times as many boys as girls

So, if x = number of boys and y = number of girls, we can agree that:

x = 1.5y

And because there are 800 kids in total, we can agree that:

x + y = 800

There are 320 girls and 480 boys. (see below)

Since you have the value of x, 1.5y, you can plug-in the value:

x + y = 800

1.5 + y = 800

2.5y = 800

y = 320 girls

Plug-in the y-value into the equation for the number of boys:

x = 1.5y

x = 1.5(320)

x = 480 boys

To double-check:

320 + 480 = 800 ☺

Answer:

[tex]\huge\boxed{No \ solutions}[/tex]

Step-by-step explanation:

Our first goal is to transform these words into numbers for an expression.

Let's break it down.

-7 times a number

We'll assume that the number is [tex]n[/tex]. -7 times a number can be represented as [tex]-7n[/tex].

8 times the sum of the number and 1

We can break this complex statement down.

8 times the sum of the number and 1

The sum of the number and 1 will be [tex]n+1[/tex]. 8 times that will be [tex]8(n+1)[/tex]. Since it says at the beginning the sum of, we add [tex]8(n+1)[/tex] to [tex]-7n[/tex].

[tex]-7n + 8(n+1)[/tex]

Is the same as the number minus 7.

"Is the same" means we use an equal sign. The number minus 7 will be [tex]n-7[/tex]. So we get [tex]-7n + 8(n+1)=n-7[/tex]

Now we can solve for n by reversing the equation until we have n isolated on one side.

[tex]-7n + 8n + 8 = n-7[/tex]

[tex]n + 8 = n-7[/tex]

[tex]8 = -7[/tex]

We end up with 8 = -7. This is not possible. Therefore, there are no real values of x that satisfy this equation.

Hope this helped!

Answer:

4.5 > 4.05

Step-by-step explanation:

Simplifying then comparing both terms  4.5  and  4.05 ,  4.5  is greater than  4.05 , which means that the first term is greater than the second term.

Answer:

4.5 > 4.05

Step-by-step explanation:

This is the answer because:

1) 4.5 means 4 and 5 tenths

2) 4.05 means 4 and 5 hundredths

3) We know tenths is greater than hundredths in decimal numbers

Therefore, the answer is 4.5 > 4.05

Hope this helps! :D

Answer:

45

Step-by-step explanation:

my brain told me

Chris can lift 54 kilograms above his head.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here, 4 rocks with 12 kg each and a box weighing 6 kilograms

therefore the total weight = 4 ×12 + 6

                                           = 54 kg

Hence Chris can carry 54 kg above his head

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following annual growth rates:

land/food = - 1%

food/kcal = 0.5%

kcal/person = 0.1%

population = 1.5%

Σ annual growth rates = (-1 + 0.5 + 0.1 + 1.5)% = 1.1% = 0.011

Exponential growth in Land :

L = Lo * e^(rt)

Where Lo = Initial ; L = increase after t years ; r = growth rate

Time for amount of cultivated land to double

L = 2 * initial

L = 2Lo

2Lo = Lo * e^(rt)

2 = e^(0.011t)

Take the In of both sides

In(2) = 0.011t

0.6931471 = 0.011t

t = 0.6931471 / 0.011

t = 63.01 years

Land per unit of food at t = 63.01 years

L = Fo * e^(rt)

r = growth rate of land required to grow a unit of food = 1% = 0.01

L/Fo = e^(-0.01* 63.01)

L/Fo = e^(−0.6301)

= 0.5325385 = 0.53253 * 100% = 53.25%

Land per unit now takes (100% - 53.25%) = 46.75%

Answer:

wheres the question

Step-by-step explanation:

Answer:

1 /7 is .1428571429

Good Luck!!!

Answer:

i love myself

Step-by-step explanation:

Answer:

The average cost of a dog's annual visit is about $76.10 more......

Step-by-step explanation:

Mean is the average of a dataset.

The question gives you the mean (average) of the cost of a dog's annual visit. As you can see at A New Leash of Life, the mean (average) is $300.75, whereas at No Ruff Stuff, the mean (average) is $224.65.

Since the question is only asking for a statement that matches the info above, the only option that matches is the first option.

Answer:

First one!!!

hope it help you

Answer: y = 1/4x + 1.25 ?? OR y = -4x + 23

Step-by-step explanation:

y = mx + c

3 = 1/4 (5) + c

3 = 1.25 + c

-1.25 from both sides  

c = 1.75

y = 1/4x + 1.75

----------------------------------

perpendicular gradient = -4

y = -4x + c

3 = -4(5) + c

3 = -20 + c

+20 to both sides

c = 23

y = -4x + 23

Answer:

3⁴

Step-by-step explanation:

Exponent Rule: [tex](b^m)(b^n) = b^{m+n}[/tex]

Apply the Exponent Rule.

3² · 3² = 3²⁺² = 3⁴

Answer:

I think its 81

Step-by-step explanation:

3^2=3x3=9

3^2=3x3=9

9x9=81

Answer:

B

Step-by-step explanation:

traditional notation states h:g

which is h/g

Answer:

I think you multiply because it is asking you how much money he earns in 5 hour, 6 hour and 8 hours .It also said that he gets paid $1 and 10 cent each hour.

Step-by-step explanation:

1.10 * 5=5.5

1.10 * 6=6.6

1.10 * 8=8.8

So, he earns $8.8

Sorry it doesn't let me make a table but use the equation

As per linear equation, the amount of money Harry will earn by working 5, 6, and hours are $50, $60, and $80, respectively.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

Given, the ratio of the number of hours Harry works in the yard to the money he earns in dollars is 1:10.

Let, Harry works for x hours.

Then the money he will earn is $10x.

Work(in hours)                Earned money (in dollars)

         5                                                 50

         6                                                 60

         8                                                 80

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Answer:

The change should be -24 points

Answer:

x= - 0.6

Step-by-step explanation: