What are the lengths of the major and minor axes of the ellipse?

(x−3)227+(y+4)245=1

Answer:

Step-by-step explanation:

You want the steps to writing the equation of a line parallel or perpendicular to a given line through a given point.

Given line ax+by=c and point (h, k), you can write equations for the desired lines using the forms:

  a(x -h) +b(y -k) = 0 . . . . . . parallel line

  b(x -h) -a(y -k) = 0 . . . . . . . perpendicular line

If you eliminate parentheses and collect terms, you will have the general form equation of the desired line(s). If you solve for y, you will have the slope-intercept form of the equation.

To use these forms, it is helpful to start with the equation of the given line in standard form, as shown. (It could also be in general form ax+by-c=0.)

Using the above solution, the steps are ...

You will note that the same coefficients are used on the same variables for a parallel line. This is because parallel lines have the same slope.

The coefficient of the variables are swapped, and one of them is negated in the equation for the perpendicular line. This is because perpendicular lines have opposite reciprocal slope.

When the given line is in slope-intercept form, y = mx +b, the slope is readily identified as m, the coefficient of x. For the parallel line, this slope can be used directly in the point-slope equation for a line through a given point:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

This can be rearranged to the slope-intercept form:

  y = mx +(k -mh)

The perpendicular line has opposite reciprocal slope. The line perpendicular to the given line with slope m will have slope -1/m. Then the two forms of equation are ...

  y -k = -1/m(x -h) . . . . . . . . . point-slope form

  y = (-1/m)x +(k +h/m) . . . . . slope-intercept form

__

Additional comment

A standard form equation (ax +by = x) has mutually prime integer coefficients, with a positive leading coefficient. When you have written your equation, you may find it necessary to multiply the equation by some value to put it in this form. For example, -2x +4y = -8 must be multiplied by -1/2 to get the standard form equation x -2y = 4.

You need to be aware of the form required by your grader. The wording "the equation" often means slope-intercept form, or the form matching the given equation or the answer box format.

In the making of 22 oz of bread rye flour and whole wheat requirements are 4.4 0z and 17.6 oz.

A ratio is a comparison between two quantities in simplest form.

A ratio of the from a : b can be written as a/(a + b) and b/(a + b).

Given, A recipe for whole grain bread calls for 1 oz of rye flour for every 4 oz of whole wheat flour.

∴ In the making of 22 oz of bread rye flour needed is 1/(1 + 4)×22

= (1/5)×22.

= 4.4 oz.

In the making of 22 oz of bread whole wheat needed is 4/(1 + 4)×22.

= (4/5)×22.

= 17.6 oz.

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Answer:

[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]-3x+9          

Step-by-step explanation:

(x-3)([tex]x^{2}[/tex]-3) = 0

x = -[tex]\sqrt{3}[/tex], [tex]\sqrt{3}[/tex], 3

There is Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x represent Watusi's speed,

y represent Ubangi's speed,

And z represents Pigmy's speed.

According to the given information, we can write the system of equations as

x + y + z = 30  .....(i)

z + 2x/3 = 22 - y  .....(ii)

4x + 3y - z = 12  .....(iii)

The above system of equations gives the values of x, y, and z when solving

x = 6, y = 3, z = 21

This means Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

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Answer:

Step-by-step explanation:

the equation of the cone is given already

r=6 inches

h=7 inches

Substitute in the equation =84pi=263.89

for the sphere substitute the radius r= 6 inches in the equation, and then divide by 2. This is because the spherical shale in top of the cone is half a sphere, as it can be clearly seen.

So It’s 288pi= 904.78 /2 =452.39

add the volume of cone and volume of sphere

The final answer is 716.28 inches^3

Answer:

18243.906

Step-by-step explanation:

Find how much water is used in 1 hour and then multiply that by 3

24325.208/4

6081.302

6081.302x3

18243.906

Answer: Alright, lets get started.

Roberto has already run miles = 16

Total miles for marathon = 26.2

As per percentage formula :

So, percentage completed =

Rounding the answer to whole number 62 %

62 percent of the marathon  he has completed.   :  Answer

Hope it will help :)

Step-by-step explanation:

The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1      .

In the question ,

it is given that ,

the specification of the furniture , is 17.9 ≤ w ≤ 18.1 ,

where w is the width of the desk drawer in inches .

we need to write the given inequality in absolute inequality form ,

we know that the a-b < x < a+b , then the absolute inequality is |x-a|<b ,

On comparing the given inequality with a-b < x < a+b ,

we get

a - b = 17.9 and

a + b = 18.1

adding both the equations , we get

2a = 36

a = 36/2

a = 18

Substituting a = 18 in a + b = 18.1 , we get

18 + b = 18.1

b = 18.1 - 18

b = 0.1

The required inequality is |x-a| ≤ b .

|x - 18| ≤ 0.1

Therefore , The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1   .

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The given descriptions "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.

First, let us understand the logarithmic function:

The inverses of exponential functions are logarithmic functions, and any exponential function could be represented in logarithmic form.

The given description fully stated about the logarithmic function.

Thus, the given description "The domain of f is x > 0. The range of f is all real numbers. The domain of the inverse function is all real numbers. The range of the inverse function is y > 0. The domain of f is the same as the range of the inverse function. The range of f is the same as the domain of the inverse function." is stated about the logarithmic function.

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The value of x in the given triangle is x = 2 .

In the question ,

it is given that ,

a triangle is given ,

let us name the triangle as triangle ABC ,

So , By Basic Proportionality Theorem , which states that ,

The line drawn parallel to one side of triangle and cuts the other two sides divides the other two sides in equal proportion.

So , By Basic Proportionality Theorem

AD/AB = AE/AC

substituting the value from the triangles , we get

4/12 = 6/(6+6x)

1/3 = 1/(1+x)

1 + x = 3

x = 3 - 1

x = 2

Therefore , The value of x in the given triangle is x = 2 .

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The number of laps around the lake that Latrell jogs is 5 1/4 laps.

A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

From the information he jogs 7 miles and each lap is 4/3 miles. The number of laps will be:

= Total laps / Number of miles

= 7 ÷ 4/3

= 7 × 3/4

= 21 / 4.

= 5 1/4 laps.

He jogs 5 1/4 laps.

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Answer:

D: (0,-6)

Step-by-step explanation:

the y intercept in an equation is the "b" value in y=mx+b

Answer:

(0,-6)

Step-by-step explanation:

you can look at the last term in the equation which is -6

Or you can set x to 0

y=4(0)-6

y=-6

Hopes this helps please mark brainliest

The constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.

We know that the constant of proportionality is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given:

The numbers below are what the dots are plotted-

10, 50

20, 100

30, 150

40, 200

50, 250

Take any two points.

Let us choose (20, 100) and (30, 150).

Put the values in the slope formula;

Slope = (150 - 100) / (30 - 20) = 50 / 10 = 5

So, the slope of the line is 5.

Thus, the constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.

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Answer:

its B!!

Step-by-step explanation:

I took the test and got it wrong but the review said it was B

Answer:

30

Step-by-step explanation:

Well I hope this helps Have a good day! :)

The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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Answer:

3^3

Step-by-step explanation:

Exponents

9^3 can be rewritten as

3^2 ^3

Using exponent rules a^b^c = a^ (b*c)

3^2^3 = 3^6

3^6 / 3^3

We know that a^b / a^c = a^(b-c)

3^6 / 3^3  = 3^(6-3) = 3^3

Answer:

2nd answer is correct

Step-by-step explanation:

We know that,

[tex] \rightarrow \sf {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \rightarrow \sf \frac{{x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \rightarrow \sf( {x}^{a} )^{b} = {x}^{ab} [/tex]

Accordingly, let us solve it now.

[tex] \sf \frac{ {9}^{3} }{ {3}^{3} } \\ \\ \sf \frac{ {3}^{2 \times 3} }{ {3}^{3} } \\ \\ \sf\frac{ {3}^{6} }{ {3}^{3} } \\ \\ \sf {3}^{6 - 3} \\ \sf {3}^{3} [/tex]

Answer:

1) Slope: 2 ; y-intercept: (0, -6)

2) Slope: -5; y-intercept: (0, 16)

Step-by-step explanation:

8x-4y=24 is also y=2x-6

Slope: 2

y-intercept: -6

y= -5x+16

Slope: -5

y-intercept: 16

The probability that the spinner will land on grey and then purple is 1/18.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of grey regions = 1

Number of purple regions = 2

Total number of regions = 6

Now,

The probability that the spinner will land on grey.

= Number of grey regions / Total number of regions

= 1 / 6

The probability that the spinner will land on purple.

= Number of purple regions / Total number of regions

= 2 / 6

The probability that the spinner will land on grey and then purple.

= 1/6 x 2/6

= 1/6 x 1/3

= 1/18

Thus,

The probability that the spinner will land on grey and then purple is 1/18.

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[tex]a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}[/tex]

Answer:

Step-by-step explanation:

1. The measured height is the exact value therefore it is to be considered as actual height.

2. The error is the difference between actual and estimated values:

3. Percent error is:

or

The 30 feet by 14 feet by 8 feet, filled in 3.5 hours by two pipes in which one pipe is 1 more than twice the other, indicates;

1. The rational equation from which the time the smaller pipe takes to fill the pool is; [tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]

2. The solution of the equation is t ≈ 10.51 hours

3. The time it takes to fill the pool using only the small pipe is about 10.51 hours

Rational equation are equations that have rational polynomial expressions.

The dimensions of the pool are;

Length = 30 feet

Width = 14 feet

Depth = 8 feet

1. Let x represent the flow rate of the slower pipe

The flow rate of the faster pipe = 2·x + 1

Time it will take both pies to fill the pool = 3.5 hours

The volume of the pool, V = 30 × 14 × 8 = 3360

The volume of the pool is 3360 cubic feet

The rate equation is therefore;

[tex]\dfrac{x}{3360} +\dfrac{2\cdot x+1}{3360} =\dfrac{1}{3.5}[/tex]

[tex]\dfrac{x}{3360} =\dfrac{1}{3.5} - \dfrac{2\cdot x+1}{3360}[/tex]

From the rate equation above, the time it takes the smaller pipe to fill the pool is; t = 3360/x therefore;

[tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]

2. Solving for x from the volume of water in the pool, V, therefore;

The volume of water that fills the pool, V, is found from the equation;

V = 3.5 × (2·x + 1 + x) = 10.5·x + 3.5

V = 10.5·x + 3.5

Therefore;

3360 = 10.5·x + 3.5

[tex]x = \dfrac{3360-3.5}{10.5} =319.\overline 6[/tex]

t = 3360/319.[tex]\overline 6[/tex] ≈ 10.51

The time it takes to fill the pool using only the smaller pipe is approximately 10.51 hours

Aliter;

[tex]\dfrac{3\cdot x}{3360} =\dfrac{1}{3.5}-\dfrac{1}{3360}[/tex]

[tex]t = \dfrac{3360}{x} =\dfrac{3}{\left(\dfrac{1}{3.5}-\dfrac{1}{3360}\right)} \approx 10.51[/tex]

3. The interpretation of the solution is that it takes about 10.51 hours for the smaller pipe working alone to fill the pool

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At this rate 15 more minutes the girls can exchange texts before they are charged extra.

Given that,
Katrina and Becca exchanged 270 text messages in 45 minutes. An equal number of texts was sent each minute. The girls can send 90 more text messages before they are charged additional fees.

Here,
Total message sent = 270
in time = 45 minutes
Rate = 270 / 45 = 6 messages per minute
Time for the exchange of 90 messages = 90 / 6 = 15 minutes

Thus, At this rate 15 more minutes the girls can exchange texts before they are charged extra.

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Answer:

See below

Step-by-step explanation:

First, graph the function to see that the domain ( the values of x the function can have in this context goes from 0 to 4  hours   ( after four hours the concentration goes negative.....can't happen in the real world)

  and the range is 0 to max of  8 mg/L

Here is the graph :

The quantity of violas Kiara collected is 76

From the question, we are to determine the quantity of violas Kiara collected.

From the given information,

"Kiara and Lee are collecting violas in a ratio of 2:5"

First, we will determine the sum of ratios

Sum of ratios = 2 + 5 = 7

Also, from the given information

The total number of violas they collected is 266

Thus,

The quantity of violas Kiara collected will be

2/7 × 266

= 2 × 38

= 76

Hence, the quantity she collected is 76

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The statement if A ⊂ B, then A ∩ B = ∅ is false.

First, let us understand the set:

A set is a mathematical model for a collection of different things; a set contains elements or members that can be any mathematical object: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

We are given;

A ⊂ B

We need to find A ∩ B.

Let us understand the given set;

A ⊂ B means A is a proper subset of B.

All the elements of set A are in set B.

So, A ∩ B = A

But, A ∩ B = ∅ is given.

So, the statement is false.

Thus, the statement if A ⊂ B, then A ∩ B = ∅ is false.

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