2/5 (1/3x - 15/8) - 1/3(1/2 - 2/3x)

The equation that represent the eclipse in the image attached is option A.

We were given:

The center of an ellipse  (0, 0).

One focus is located at (12, 0),

One directrix is at x = 14 1/12.

To Find the equation of the ellipse will be:

The standard equation of an ellipse is :  [tex]\frac{(x- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]

Note that c = 12

One need to compare the equation of directrix with the above equation:

a^2/c = 14[tex]\frac{1}{12}[/tex]

a^2/c = 169/12

Then Substitute the value c=12 and solve for a.

a^2/12 = 169/12

a² = 169

a = 13

Use the equation of  c² = a² - b² to find b.

= (12)² = (13/12)² - b²

b²= 169-144

b²= 25

b = 5

Then substitute the value of a and b into the standard equation of the ellipse.

[tex]\frac{(a- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]

[tex]\frac{(x- 0 )^ 2}{13^2} + \frac{(y - 0)^2}{5^2}[/tex]

Therefore: [tex]\frac{(x)^ 2}{13^2} + \frac{(y)^2}{5^2}[/tex]

Hence, The equation that represent the eclipse in the image attached is option A.

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Answer:

1,338,750$

Step-by-step explanation:

1990 price was 850,000

in 2000

850,000 + 125% = 1,062,500

850,000 + 1,062,500 = 1,912,500

in 2013

1,912,500 - 30% = 573,750

1,912,500 - 573,750 = 1,338,750

Answer:

x = 100 degrees

Step-by-step explanation:

Angle AEG is vertical to angle BEF. Vertical angles are congruent angles. The measure of angle BEF is 100 degrees (80 + 20 = 100), so angle AEG is 100 degrees which makes the measure of x 100 degrees.

Answer:

24 and 25

Step-by-step explanation:

Angle a will be 20° because angle a+angle b=90°

angle c is 90°(right angle)

now to find the sides we will have to do a Pythagoras theorem for this indirectly therefore:

7²=49/2 sides

=24.5

therefore one side will be 24 the other side will be 25

if I am right mark as brainliest

Answer:

(x+5)(x+1)(2x+3) cubic feet

Step-by-step explanation:

The location of the fountain as described in the task content is; (-1, -0.5).

According to the task content, the locations of Fernando and Maria are given as; (-4, -2) and (4,2) respectively and the ratio of division is expected to be; 5: 3.

Hence, the coordinates of the fountain can be evaluated as;

x = (4) - (4-(-4)) × (5/8) = -1.

y = 2 - (2-(-2)) × (5/8) = -0.5

Hence, it follows that the coordinates of the fountain location is; (-1, -0.5) since the fountain is closer to Fernando than Maria.

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Answer:

-1 AND -0.5

Step-by-step explanation:

The value of y is 116 degrees

To solve for y, we make use of the following angle theorem.

The angle at the center is twice the angle at the circumference.

So, we have:

y = 2 * 58

Evaluate the product

y = 116

Hence, the value of y is 116 degrees

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The table for the complete ratios between distance and time is shown below.

The ratio of distance to time, given that 280 miles will be covered in 4 hours is: 280/4 = 70 miles per hour.

Thus, for 2 hours: 2(70) = 140 miles distance.

For 350 miles, we would have: 350/70 = 5 hours time.

For 6 hours: 6(70) = 420 miles distance.

For 8 hours: 8(70) = 560 miles distance.

For 700 miles, we would have: 700/70 = 7 hours time.

The complete table is shown in the image below.

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Answer:

[tex]\sqrt{-3}[/tex]

Step-by-step explanation:

Since each of these answers contain a radical, you want to find the one that has a negative value, because technically sqrt(some negative number) isn't defined, or rather it has no real solution. This is because you can rewrite a radical as [tex]\sqrt{a * b} = \sqrt{a} * \sqrt{b}[/tex]. And since [tex]i = \sqrt{-1}[/tex] you can rewrite [tex]\sqrt{-3}[/tex] as [tex]\sqrt{-1} * \sqrt{3}[/tex] which becomes [tex]i\sqrt{3}[/tex]

The y-intercept of the function (g/f)(x) is [tex]\mathbf{-\dfrac{3}{2} }[/tex]

The y-intercept of a given function f(x) is those values of y when x is equal to zero.

From the information given:

The division of the function (g/f)(x) can be computed as:

[tex]\mathbf{y= \dfrac{x^{12}-x -12}{x^2-6x+8}}[/tex]

The division of the y-intercept is:

[tex]\mathbf{=-\dfrac{12}{8} }[/tex]

[tex]\mathbf{=-\dfrac{3}{2} }[/tex]

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The ray that is opposite FH in the image given is: FE.

A ray is a straight line that starts from one end and extends infinitely towards the opposite end.

We are asked to find the ray that is opposite to FH. This means the ray opposite to FH will definitely start from point B and extends to the opposite direction.

Ray FE is opposite FH.

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The equation of the line will be y = -3.9, and the height after rounding off will be -4.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The horizontal line can be defined as:

y = a

Where a is the constant.

Here a = -3.9

y = -3.9

The height = -3.9 ≈ -4

Thus, the equation of the line will be y = -3.9, and the height after rounding off will be -4.

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Answer:

Each pipe is 24m

Step-by-step explanation:

Given:

Algebraic Expression:

3 pipes times length equals 72m (the total length)

3x = 72, we want x to be alone so divided both sides by 3

3x / 3 = 72 / 3

x = 24

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Answer:

A

Step-by-step explanation:

given 2 secants drawn from an external point to the circle , then

the product of the measures of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is

9(9 + 2 + 3x) = 10(10 + 2x + 2)

9(11 + 3x) = 10(12 + 2x) ← distribute parenthesis on both sides

99 + 27x = 120 + 20x ( subtract 20x from both sides )

99 + 7x = 120 ( subtract 99 from both sides )

7x = 21 ( divide both sides by 7 )

x = 3

Answer:

(A). 3

Step-by-step explanation:

[ 9 + ( 2 + 3x )] × 9 = [ 10 + ( 2x + 2 )] × 10

27x + 99 = 20x + 120

7x = 21

x = 3

[tex]\large\boxed{\frac{1}{1369}}[/tex]

We'll assume that there is an equal probability of any position on the wheel, so a [tex]\frac{1}{37}[/tex] chance for any given number.

We must take the probability of getting a 27, then the probability of getting a 15, and multiply them together to find the chances that they both happen in a row.

[tex]\frac{1}{37}\cdot\frac{1}{37}=\boxed{\frac{1}{1369}}[/tex]

The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.

A numerical assessment of a line's angle relative to the ground is known as the slope.

Given data;

m₁ is the slope of line AB

m₂ is the slope of a line perpendicular to AB

The coordinate points are,

A,(x₁,y₁)= (0, 6)

B,(x₂,y₂)=(3, 0).

The gradient of line AB;

[tex]\rm m_{{1} }= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm m_{{1} }= \frac{0-6}{3-0} \\\\ m_{{1} }=-2[/tex]

The slope of the lines has a perpendicular relation is -1;

m₁ × m₂ = -1

(-2) × m₂ = -1

m₂ = 1/2

m₂ = 0.5

The equation of the line passing through point A and perpendicular to AB;

(y - y₁) = m₂(x-x₁)

(y-6)=0.5(x-0)

y-6 = 0.5 x

y-0.5x=6

Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.

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Answer:

1) y = 2/3x - 2

2) y = -1/2x + 3

Step-by-step explanation:

1) Parallel lines have the same slopes. Write it in standard form (y = mx + c), then substitute the values of the coordinates into the equation.

y = 2/3x + c

0 = 2/3(3) + c

0 = 2 + c

0 - 2 = c

- 2 = c

Therefore, the slope-intercept form for the first part is y = 2/3x - 2.

2) Parallel lines have the same slopes. Write it in standard form (y = mx + c), then substitute the values of the coordinates into the equation.

y = -1/2x + c

1 = -1/2(4) + c

1 = -2 + c

1 + 2 = c

3 = c

Therefore, the slope-intercept form for the second part is y = -1/2x + 3.

Answer: [tex]-11\sqrt{7}[/tex]

Step-by-step explanation:

To find the expression equal to the given, we will simplify the original.

   Given:

[tex]\displaystyle 2\sqrt{28} -5\sqrt{63}[/tex]

   Simplify:

[tex]-11\sqrt{7}[/tex]

           Answer:  [tex]-11\sqrt{7}[/tex]

Answer:  [tex]-11\sqrt{7}[/tex]

Step-by-step explanation:

[tex]2\sqrt{28}-5\sqrt{63}[/tex]

= [tex]2\sqrt{4*7}-5\sqrt{7*9}[/tex]

= [tex]2*\sqrt{4}*\sqrt{7} - 5*\sqrt{7} *\sqrt{9}[/tex]

= [tex]2*2*\sqrt{7} - 5*\sqrt{7}*3[/tex]

= [tex]4\sqrt{7} - 15\sqrt{7}[/tex]

= [tex]-11\sqrt{7}[/tex]

Step-by-step explanation:

Answer:

2a^2 + 3a - 1 ,

Step-by-step explanation:

I am assuming you mean

2a^3-a^2-7a+2

By long division:

a - 2 ) 2a^3 -   a^2 - 7a +  2 ( 2a^2 + 3a - 1 <------- Quotient

          2a^3 - 4a^2

                     3a^2 - 7a

                     3a^2 - 6a

                                -a + 2

                                -a + 2

                                 . . . . .

The missing statement are:

4.  ∠B ≅ ∠B; Reflexive Property of Equality.

5.   ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate.

The missing statement are number 4 and 5.

If we say that  4. ∠B ≅ ∠B; Reflexive Property of Equality then:

∠B ≅ ∠B,

Note that  there are two triangles, which are ΔABC and ΔDBE and we also have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B +  ∠BCA = 180°

Hence, ∠BED = ∠BCA Substitution property of equality

That  birth ΔABC ~ ΔDBE,which is Angle Angle Similarity Postulate

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Answer: 4.∠B ≅ ∠B; Reflexive Property of Equality

5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

Step-by-step explanation:

I just took the test; this exact order should be correct. :D

Answer:

120 degrees

Step-by-step explanation:

Angle 1 is congruent to angle 5 by the corresponding angles theorem.

The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm

An equation is an expression that shows the relationship between two or more numbers and variables.

The length (L) is inversely proportional to the width (W), hence:

L = k/W

18 = k/6

k = 108

When L = 27:

27 = 108/W

W = 4

The constant of variation, k, is equal to 108. This is an inverse proportion and when L is 27 cm, W is 4 cm

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No

Let the groups be x and 2x

Its decimal not natual so can't be divided

Answer:

y = (1/4)x + 2

Step-by-step explanation:

y - 4 = 1/4 (x-8)

y - 4 = 1/4(x) - 2

y = (1/4)x + 2

Answer:

40.9

Step-by-step explanation:

Law Of Cosines:

   [tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]

   This can generally be understand as the cosine(angle) = the sum of squares of the two other sides - the opposite side squares divided by 2 times the other two sides

   If this is to confusing to understand I'll just provide the formula for the other two angles which is essentially the same thing just different variables

   [tex]cos(B)=\frac{a^2+c^2-b^2}{2ac}\\\\cos(C)=\frac{a^2+b^2-c^2}{2ab}[/tex]

Anyways for the law of cosines we need all three sides, but since we're given the two other sides, we can also rearrange the equation to solve for the other missing side.

Original Equation

[tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}\\[/tex]

Multiply both sides by 2bc

[tex]cos(A)*2bc=b^2+c^2-a^2[/tex]

Add a^2 to both sides

[tex]cos(A)*2bc+a^2=b^2+c^2[/tex]

Subtract 2bc * cosA from both sides

[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]

So this can be applied for any side, and it can be generally seen as: side ^2 = sum of squares of other two sides - 2 times the other two sides * cos(opposite angle of the original side). If that's to confusing you can also just look at the other formulas which are essentially the same just different variables

[tex]b^2=a^2+c^2-2ac * cos(B)\\c^2=a^2+b^2-2ab*cos(C)[/tex]

anyways, applying this formula we get the equation:

[tex]a^2=20^2+30^2-2(20)(30)*cos(60)[/tex]

Square and multiply values you get

[tex]a^2=400+900-1200*cos(60)[/tex]

Now add the values and you can calculator cos(60) using a calculator or using the unit circle, both should give the same value

[tex]a^2=1300-1200(0.5)[/tex]

Multiply

[tex]a^2=1300-600[/tex]

Simplify

[tex]a^2=700[/tex]

Take the square root of both sides

[tex]a\approx 26.4575[/tex]

So now use this to solve for B using the original law of cosines equation. Plugging in all the sides you get the equation:

[tex]cos(B)=\frac{26.4575^2+30^2-20^2}{2(26.4575)(30)}[/tex]

Square values and simplify denominator

[tex]cos(B)=\frac{700+900-400}{1,587.451}[/tex]

Simplify numerator

[tex]cos(B)=\frac{1200}{1,587.451}[/tex]

Convert to decimal

[tex]cos(B)\approx 0.755[/tex]

Take the inverse cosine of both sides

[tex]B \approx cos^{-1}(0.755)[/tex]

Approximate this using a calculator

[tex]B\approx 40.8934[/tex]

Round to the nearest tenth

[tex]B\approx40.9[/tex]

Answer:

5

Step-by-step explanation:

a number and its additive inverse sum to zero , then

the additive inverse is the opposite of the number

the opposite of - 5 is + 5

and - 5 + 5 = 0

The system of inequality that the graph represents is E. 2x + 3y is less than or equal to 4 and 2x + 2y is less than or equal to 3

In the graph, when 2x + 3y = 4

3y = 4 - 2x

y = -2/3x + 4/3

When 2x + 2y = 3

2y = -2x + 3

y = -x + 3/2

On the graph, -2/3x + 4/3 is illustrated on the first line while -x + 3/2 is illustrated on the second line.

Therefore, the correct option is E.

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Answer:Multiply using the FOIL method, then combine the real and imaginary parts of the expression.

−

28+3i

Step-by-step explanation: