I need help this is so confusing

Answer:

x² + y² - 12x - 6y + 29 = 0

Step-by-step explanation:

Simplifying the equation using (a + b)² = a² + 2ab + b²:

(x - 6)² + (y - 3)² = 16

⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16

⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

General form of a circle = x² + y² + Cx + Dy + E = 0

Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.

Subtract 16 both sides:

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

Reorganizing the equation in general form:

x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x - 6y + 20 + 9 = 0

⇒ x² + y² - 12x - 6y + 29 = 0

Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.

Solving the system of equations, it is found that a viable time that the trains are side by side is given by:

B. 15 sec

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

[tex]y = 14t^2[/tex]

[tex]y = 130t + 1200[/tex]

They will be side by side when:

[tex]14t^2 = 130t + 1200[/tex]

[tex]14t^2 - 130t - 1200 = 0[/tex]

It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:

[tex]\Delta = (-130)^2 - 4(14)(-1200) = 84100[/tex]

[tex]x_1 = \frac{130 + \sqrt{84100}}{28} = 15[/tex]

[tex]x_2 = \frac{130 - \sqrt{84100}}{28} = -5.71[/tex]

Time is a non-negative measure, hence option B is correct.

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Answer:

B: 15 sec

Step-by-step explanation:

I took the algebra exam

Answer:

D

Step-by-step explanation:

The quotient is the result of dividing one number by another.

[tex]\frac{10}{\frac{1}{7} } = ?[/tex]

is how you would represent the quotient of 10 and 1/7.

The opposite of division is multiplication, and those we can rearrange that and get:

[tex]? * \frac{1}{7} = 10, or, ?/7 = 10[/tex]

or in other words, "what number divided by 7 is 10"

The answer becomes clearer, 70 is that number.

D represents this idea.

The value which shows the true solution to the given logarithmic equation is 1.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The given logarithmic equation is,

[tex]\rm log_{2} (x) + log_{2} (x +7) = 3.[/tex]

Use the addition property of log in the above expression.

[tex]\rm log_{2} (x \times (x +7) )= 3.\\ (x \times (x +7) ) = 2^{3} \\x \times (x +7) = 8\\x^{2} +7x-8=0[/tex]

Solve the quadratic equation we get,

[tex](x+8)(x-1)=0[/tex]

x = -8, 1

Here, the logarithmic function is defined only for positive real numbers as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

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Answer:X=1

Step-by-step explanation:b on edge

Answer:

5a + ab = 40

Step-by-step explanation:

Sub in 10 for a, making the equation 5 x 10 + 10 x b

Then sub in - 1 for b making it 5 x 10 + 10 x - 1

Then multiply making it 50 + - 10

Then subtract since adding negative is actually subtracting and you get 40

Hey there!

In order to evaluate this expression, all we should do is plug in the values of the variables and simplify.

We are given that

a=10

b=-1

Plug in the values:

5(10)+(10)(-1)

multiply 5 times 10 and 10 times (-1) and add the products:

50+(-10)

or... actually subtract.

50-10

40

Hence, the answer is

[tex]\boxed{\boxed{\bold{40}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

Answer:

A. (-4,-13)

Step-by-step explanation:

y = 2x - 5

y = 4x + 3

-2(y = 2x - 5) ==> -2y = -4x + 10

y = 4x + 3     ==>     y = 4x + 3

-2y = -4x + 10

y = 4x + 3

___________

-y = 13

/-1    /-1

y = -13

Now we find x, by substituting -13 for y

y = 2x - 5

-13 = 2x - 5

+ 5        +5

-8 = 2x

/2    /2

-4 = x

(x, y) ==> (-4, -13)

Check your answer:

y = 2x - 5

-13 = 2(-4) - 5

-13 = -8 -5

-13 = -13

This statement is correct

Hope this helps!

Answer:

4 1/14

Step-by-step explanation:

1 5/14 x 3 = 4 1/14

Answer:

4 1/14 pages

Step-by-step explanation:

multiply 1 5/14 by 3

start by multiplying 1 by 3 which is 3

then multiply 5/14 by 3, you just have to multiply the 5 and you get 15/14 which is 1 1/14

add 3 and 1 1/14 and you get 4 1/14

Answer:

$8.75

8.75x3=26.25

Step-by-step explanation:

Answer:

$8.75

Step-by-step explanation:

To find out the unit price, take the whole and divide it by the number of units. In this case the whole cost is $26.25. There are 3 scarves in a whole. Divide $26.25 by 3 to find out the cost of the unit price. It is $8.75. Knowing how to figure out a unit price for something is very useful. For example, if you wanted to buy some Pepsi but didn't know if the 24-pack, 12-pack or 36-pack was a better deal, you can find out the unit price to see which is cheaper. For example, if the 24-pack of Pepsi cost $5, the unit price per can would be .21. A 12-pack at$ 2.75 would be .22 per can. A 36-pack at $6.50 is .18 per can. This tells you that you'd save more money per can if you bought the 36-pack of Pepsi.

Answer:

Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.

Step-by-step explanation:

So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:

m = 28.8 g

The Hypotheses are; Null Hypothesis; H₀: μ = 76.4 and Alternative Hypothesis; Hₐ: μ > 76.4 where μ is the true mean height of all trucks.

We are given;

Population Mean; μ = 76.4 inches

Sample Mean; x' = 77.1 inches

Sample standard deviation; s = 5.2 inches

Sample size; n = 100 trucks

Now we can thus define the hypotheses as;

Null Hypothesis; H₀: μ = 76.4

Alternative Hypothesis; Hₐ: μ > 76.4

where μ is the true mean height of all trucks

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Answer:

1 pound of potatoes costs $0.87

Hello!

The first step is to subtract 1 from both sides.

[tex]\bf{3x+1=38}[/tex]

[tex]\bf{3x=37}[/tex]

Now, divide both sides by 3:

[tex]\bf{\displaystyle\frac{37}{3} }[/tex]

Can this fraction be simplified? Nope.

Why? Because 37 and 3 do not have any common factors, except 1 (and what's the point of dividing by 1?)

Hence, the answer is

[tex]\huge\boxed{\text{Answer:{\boxed{\circ\star{\frac{37}{3} }}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepOnLearning

[tex]\boxed{An~Emotional~Helper!}[/tex]

Answer:

5, 6, 7

Step-by-step explanation:

5 + 6 + 7 = 18

Answer:

15,16,17

Step-by-step explanation:

The question states, The sum of three consecutive, positive, even integers is 18 more than twice the smallest.

Let a,b,c be positive integers

Let a be the smallest integer.

Because the answer says the sum of the integers has to be 18 more than   2 x  the smallest integer. It means the situation can be represented as:

a + b + c = 2a + 18

Because these numbers are consecutive, meaning they are right besides each other. Every variable can be written in terms of a.

a = a

b = a + 1

c = a + 2

Now we can solve for a:

a + (a+1) + (a+2) = 2a + 18

a + a + 1 + a + 2 = 2a + 18

3a + 3 = 2a + 18

a + 3 = 18

a = 15

then we can fill in the rest.

b = (15) + 1 = 16

c = (15) + 2 = 17

Now we verify.

15 + 16 + 17 = 2(15) + 18 ?

15 + 16 + 17 = 48

2(15) + 18 = 48

We now have the solution. The consecutive numbers, are, and can only be

15,16,17

Answer:

Step-by-step explanation:

The value of measurement of the closest to the height of the mountain cliff in feet is,

⇒ Mountain Height = 360 feet

Given that;

When Donetle stands at point R, he is 1000 feet from point S at the base of a cliff.

And, When he looks up at an angle of 20 degrees, he sees a friend at the top of the mountain cliff at point T

Hence, By graph we get;

⇒ tan 20° = Mountain Height / 1000

⇒ 0.36 = Mountain Height / 1000

⇒ 0.36 × 1000 = Mountain Height

⇒ Mountain Height = 360 feet

Thus, The value of measurement of the closest to the height of the mountain cliff in feet is,

⇒ Mountain Height = 360 feet

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Answer:

  $12,463

Step-by-step explanation:

The amount owed after one month is the sum of the original amount and the interest fee, less the amount paid.

__

The interest fee is 0.5% of $12,600, so is ...

  0.005 × $12,600 = $63

After her $200 payment, the amount Didi owes is ...

  $12,600 +63 -200 = $12,463 . . . owed after 1 month

Answer:

x = 3, y = 1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}x+4y=7\\ 4x-3y=9\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=7-4y[/tex]

[tex]\begin{bmatrix}4\left(7-4y\right)-3y=9\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}28-19y=9\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=7-4y[/tex]

[tex]\mathrm{Substitute\:}y=1[/tex]

[tex]x=7-4\cdot \:1[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=3[/tex]

[tex]\mathrm{The\:Answer\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=3,y=1[/tex]

Check Answer:

3 + 4(1)

7 (1) = 7

True

4(3) - 3(1)

12 - 3 = 9

True

Hence, x = 3 , y =1

~lenvy~

Answer:

30 fish

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

5 tanks with 30 fish each so 5x30

5x30=150

The conclusion based on the mean of the ball and the distance traveled is D. Inferences cannot be made about all the golf balls produced on that day.

From the information given, a golf pro randomly selects a ball, not knowing the type of ball, hits it and end of the session, the mean distance traveled for the new type of golf ball was found to be greater than the mean distance for the original-style golf ball.

In this case, inferences cannot be made about all the golf balls produced on that day; however, the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.

Learn more about mean on:

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Answer:

should be A. Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.

Step-by-step explanation:

correct for edge, nov. 2022

Answer:

0.7

Step-by-step explanation:

you have a slope of 6 and it goes through 4,22 so slope = rise over run so you would divide them

The number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.

Given numbers are:

1)[tex]4.5*10^{-3}[/tex]

2)[tex]14.5*10^{2}[/tex]

3)[tex]0.78*10^{-6}[/tex]

4)[tex]5.7*4^8[/tex]

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

In the first number [tex]1 < 4.5 < 10[/tex] multiplied by [tex]10^{-3}[/tex]

As per the definition [tex]4.5*10^{-3}[/tex] is written in scientific notation.

The Rest of the numbers do not follow the definition of scientific notation so they are not in scientific notation.

Hence, the number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.

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Answer:

21

Step-by-step explanation:

-9=9

9+12=21

Answer:

144

Step-by-step explanation:

The equation to find c is:

[tex](\frac{b}{2} )^{2}[/tex]

So put -24 into b:

[tex](\frac{-24}{2} )^{2}[/tex]

Which simplifies to:

144

So if you want to test this:

x^2 - 24x + 144

is

(x-12)^2

Answer:

 (x3 - 2x2 - 4) • (x + 2)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (((x4) -  22x2) -  4x) -  8

STEP

2

:

Checking for a perfect cube

2.1    x4-4x2-4x-8  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x4-4x2-4x-8

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x4-8

Group 2:  -4x2-4x

Pull out from each group separately :

Group 1:   (x4-8) • (1)

Group 2:   (x+1) • (-4x)

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x4-4x2-4x-8

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -8.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,8

The object attached to a string illustrates a sinusoidal trigonometric function

The trigonometric function is H(t) = 5sin(π/2(t-0.2))-20, and the object's height after 0.6 seconds is  -17.06 cm

The trigonometry model of the object is a sine function represented by:

H(t) = Asin(B(t - c)) + D

The maximum height is 5 cm.

So, we have:

Amplitude, A = 5

The average height is - 20 cm.

So, we have

Vertical shift, D = -20

Its first average height is at t = 0.2.

So, we have:

Horizontal shift, C = 0.2

The period B is then calculated as:

B = π/t

The object reaches the maximum height every 2 seconds.

So, we have:

B = π/2

Substitute these values in H(t) = Asin(B(t - c)) + D

H(t) = 5sin(π/2(t-0.2))-20

Hence, the trigonometric function is H(t) = 5sin(π/2(t-0.2))-20

Substitute 0.6 for t in H(t)

H(0.6) = 5sin(π/2(0.6-0.2))-20

Evaluate

H(0.6) = -17.06

Hence, the object's height after 0.6 seconds is  -17.06 cm

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Answer:

What is the importance of biology laboratory?

Biological Science Laboratory Apparatus is essential for meeting our basic needs of food, clothing, shelter, health, energy, clean air, water and soil. Biological Science Laboratory Apparatus enrich the quality of life in numerous ways by providing new solutions to problems in health and materials and energy usage.

Answer:

Step-by-step explanation:

57 of them were cinnamon.

Explanation:

100-40 = 60 and 3 of those were glazed so that leaves us with 57

The answer is: Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

Step-by-step explanation:

(x - 1)×3

a random number minus 1, and the result is multiplied by 3.

bingo !

Answer:

3(x - 1).

Step-by-step explanation:

Taken away 1 is x - 1

Multiply this by 3 is 3(x - 1).

Answer:

$4440 for all performances

Step-by-step explanation:

11 × ¢120 for short performances

12 × $260 for long performances

$1320 for short performances

$3120 for long performances

To get the totel you add them up

( $1320 + $3120)

The total is $4440

The probability of winning when there is only one prize, is:

P = 1/2,790,720

Each ticket has 6 different numbers, in order, from 1 to 20.

The total number of possible combinations is given by the product between the numbers of options, so there are:

C = 20*19*18*17*16*15 = 27,907,200 possible tickets.

So, if Trina purchases 10 tickets, she has a probability of 10 out of 27,907,200 winning (when we assume that there is only one prize)

Then the probability is:

P = 10/27,907,200 = 1/2,790,720

If you want to learn more about probability, you can read:

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Let's see

[tex]\\ \rm\rightarrowtail x^2+12x+36=0[/tex]

[tex]\\ \rm\rightarrowtail x^2+6x+6x+36=0[/tex]

[tex]\\ \rm\rightarrowtail x(x+6)+6(x+6)=0[/tex]

[tex]\\ \rm\rightarrowtail (x+6)(x+6)=0[/tex]

[tex]\\ \rm\rightarrowtail x=-6[/tex]