Mrs. Baker drove 450 miles on a trip she took last summer. Her car's gas tank holds 15 gallons of gas and she gets 25 miles to the gallon on long trips. How many tanks of gas did she use on her trip?

The given inequality shows an ellipse with a center at (1,-2)

The major axis will be   [tex]a=\sqrt{\dfrac{26}{9} }[/tex]

The minor axis will be   [tex]b=\sqrt{\dfrac{26}{4} }[/tex]

The equation of an ellipse is written in the form

[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]

The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.

Now the given inequality is

[tex]9x^2+18x+4y^2+16y-11 > 0[/tex]

[tex]9x^2+18x+4y^2+16y > 11[/tex]

[tex]9(x^2-2x)+4(y^2+4y) > 11[/tex]

[tex]9(x^2-2x+1)+4(y^2+4y+4) > 11+9+16[/tex]

[tex]9(x^2-2x+1)+4(y^2+4y+4) > 26[/tex]

On further solving

[tex]9(x-1)^2+4(y+2)^2 > 26[/tex]

[tex]\dfrac{(x-1)^2}{\dfrac{26}{9} } + \dfrac{(y+2)^2}{\dfrac{26}{4} } > 1[/tex]

Thus by comparing the equation with the standard form

[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]

Thus we can see that the center (h,k) is (1,-2)

The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]

The minor axis will be[tex]a=\sqrt{\dfrac{26}{4} }[/tex]

To know more about ellipse follow

https://brainly.com/question/19507943

Answer:

ellipse with a dashed line boundary

(1,-2)

(-2,0)

Step-by-step explanation:

assignment

Answer:

14 ft.

Step-by-step explanation:

First, we will assign variables to each value. If height is h, and base is b, then

1/2bh = 112 and h=b+2.

We will use substitution in this system of equations. first, we will isolate the b in bh/2=112. To do this we will multiply both sides by 2 to isolate the variables, so bh=224. Then, to isolate just one variable, in this case, b, we will divide 224 by h, getting us b=224/h.

Then, we will substitute b for this value in h+2=b, leaving us with h+2=224/h

Then isolate the variable. h will equal either -14 or 16. Because this is a geometric shape, the value of its sides cannot be negative, so it has a height of 16.

Then, plug this into the second equation. If the height is 2 ft more than the base, then the base will be 14 ft.

Answer:

x = 61°

y = 29°

Step-by-step explanation:

Since x°+29° is a right angle (90°), you would have to subtract 29 from 90 to get x.

90 - 29 = x

90 - 29 = 61

x = 61°

For y: You can infer that y°+x°=90° as well because the angles are corresponding angles. So to find y°, you would do the same thing as finding x.

90 - x = y

90 - 61 = 29

y = 29°

Hope this helps :)

Answer:

A factor of 0.2

Step-by-step explanation:

If we multiply 2.5 by 0.2, we get 0.5, the width of the smaller rectangle.

Answer:

7/8 quart

Step-by-step explanation:

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}[/tex]

Answer:

6, 8, 10.

Step-by-step explanation:

Let n be any integer.

Then our first even integer will be [tex]2n[/tex]

And the consecutive integers will be [tex]2n+2[/tex] and [tex]2n+4[/tex]

We want to find the integers such that the sum of twice the smallest number (2n) and three times the largest number (2n+4) is 42. In other words:

[tex]2(2n)+3(2n+4)=42[/tex]

Solve for n. Distribute:

[tex]4n+6n+12=42[/tex]

Combine like terms:

[tex]10n+12=42[/tex]

Subtract 12 from both sides:

[tex]10n=30[/tex]

Divide both sides by 10:

[tex]n=3[/tex]

So, the value of n is 3.

This means that our first even integer is 2(3) or 6.

So, our sequence of integers is: 6, 8, 10.

And we're done!

Notes:

We use 2n because anything integer multiplied by 2 ensures that the resulting number is even. Starting out, n can be either even or odd, but by multiplying it by 2, we will get an even number.

[tex] = \frac{7}{8} \div \frac{1}{4} [/tex]

[tex] = \frac{7}{8} \times \frac{4}{1} [/tex]

[tex] = \frac{(7 \times 8)}{4} [/tex]

[tex] = \frac{56}{4} [/tex]

[tex] = \frac{56 \div 4}{4 \div 4} [/tex]

[tex] = \frac{14}{1} [/tex]

[tex] = 14[/tex]

Therefore :-

[tex] \frac{7}{8} \div \frac{1}{4} = 14[/tex]

Answer:

$110

Step-by-step explanation:

divide 330 by 3

$115 i think..........................

The step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomials.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

The polynomial that Omar is dealing with is:

[tex]3x^3 - 15x^2 -4x + 20[/tex]

We see that 3 times 5 = 15 and 4 times 5 = 20, so trying in that way:

[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5)[/tex]

Taking out a negative factor from second term would make the binomials same, after which we can take that common out, as shown below:

[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5) \\3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) -4(x-5) \\3x^3 - 15x^2 -4x + 20 = (x-5)(3x^2-4)[/tex]

It successfully got factored, thus not a polynomial.

Thus,the step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.

Learn more about prime polynomials here:

https://brainly.com/question/10717989

Answer: Omar should factor out a negative from one of the groups so the binomials will be the same.

Step-by-step explanation: Answer on edge

Answer:

[tex]\frac{13}{12}a\\[/tex]

Step-by-step explanation:

[tex]\frac{a}{3} + \frac{3a}{4}= \frac{13}{12}a[/tex]

Answer:

the answer is 13a/12 simplified

Answer:

x = 9/5 = 1 4/5

Step-by-step explanation:

5x - 6 = 3

    +6   +6

(add positive 6 to the negative 6 = - 6 + 6 = 0, and to the answer = 3 = 3 + 6 = 9)

5x = 9

÷5   ÷5

x = 9/5 (improper fraction)

= 1 4/5 (mixed numeral)

Hello.

First, let's add 6 to both sides:

[tex]\tt{5x-6+6=3+6}[/tex]

[tex]\tt{5x=9}[/tex]

The next step is to divide both sides by 5:

[tex]\tt{x=\displaystyle\frac{9}{5}[/tex] (Improper fraction)

[tex]\tt{x=\displaystyle1\frac{4}{5}[/tex] (Mixed number)

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

We'll need the slope formula which is

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

We subtract the y values together, and divide that over the difference in the x values when subtracted in the same order.

Let's find the slope of line DE

[tex]D = (x_1,y_1) = (6,1) \text{ and } E = (x_2,y_2) = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 1}{2 - 6}\\\\m = \frac{2}{-4}\\\\m = -\frac{1}{2}\\\\[/tex]

The slope of line DE is -1/2.

Next, compute the slope of line EF

[tex]E = (x_1,y_1) = (2,3) \text{ and } F = (x_2,y_2) = (-1,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - 3}{-1 - 2}\\\\m = \frac{-6}{-3}\\\\m = 2\\\\[/tex]

The slope of line EF is 2.

Lastly, compute the slope of line FD

[tex]F = (x_1,y_1) = (-1,-3) \text{ and } D = (x_2,y_2) = (6,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-3)}{6 - (-1)}\\\\m = \frac{1 + 3}{6 + 1}\\\\m = \frac{4}{7}\\\\[/tex]

The slope of line FD is 4/7.

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

To recap everything so far, we found the following:

The product of the first two slopes gets us (-1/2)*(2) = -1 showing that DE is perpendicular to EF.

Perpendicular slopes multiply to -1 as long as neither line is vertical nor horizontal.

Since DE is perpendicular to EF, this proves we have a 90 degree angle at point E.

Therefore triangle DEF is a right triangle.

Answer: 62

Step-by-step explanation:

6840 ÷ 7 = ?

6840  | 7          

63        977          

=54  

  49  

  =50

    49  

    =1

Answer:

1

Step-by-step explanation:

You can find slope by the formula

y2-y1 over x2-x1

In this case, 6-5 over -3-(-3) or -3=3

This is equal to 1 over 0 which is 1

Answer:

65

Step-by-step explanation:

3+5=8

7x8+9

56+9

=65

Please give brainliest!

Answer:

=> 65

Step-by-step explanation:

=> 7(3+5)+9

=> 7(8)+9

=> 56+9

=> 65

Answer:

Reflections, rotations, and translations produce an image that is congruent to the pre-image. Sequences of those transformations produce congruent images.

Answer:

3.2, 3.25, 3 1/2, 3 2/3

Step-by-step explanation:

You can put them on a number line and find out the order. Or, convert to decimals or fractions.

Answer:

Your answer to your question is FALSE!!!!!!

Answer:

True

Step-by-step explanation:

I hope this helps!

Answer:

Ans of a = 18x

Ans of b = 3.111

Answer:

± i [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the result that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-2}[/tex]

= ± [tex]\sqrt{2(-1)}[/tex]

= ± [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex]

= ± [tex]\sqrt{2}[/tex] × i

= ± i [tex]\sqrt{2}[/tex]

1 cm..............2 km               = scale of the map

2,85 cm....... n km              = to be calculated

n x 1 = 2 x 2,85

n = 5,7 km

Step-by-step explanation:

1cm rep 2km

2.85x2

=5.7

=5.7km

Answer:

29568 people cheered for the runners at the start of the race

Step-by-step explanation:

From the question, the crowd lined up 5 feet deep on both sides of the street for the first mile.

This lined up crowd could be related to a rectangle that is 1 mile long and 5 feet wide.

First, Convert 1 mile to feet

1 mile = 5280 feet

Hence, the length of the rectangle is 5280 feet and the width is 5 feet.

Now, we will determine how many 5 feet by 5 feet square we can get from the 5280 feet by 5 feet rectangle. To do that, we will divide 5280 feet by 5 feet

5280 feet ÷ 5 feet = 1056

Hence, from the rectangle, we can get 1056 5 feet by 5 feet square.

From the question, you estimate that 14 people can comfortably fit in a square that measures 5 feet by 5 feet,

∴ 14 × 1056 people will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.

14 × 1056 = 14784 people

This is the amount of people that will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.

Since the crowd lined up on both sides of the street, then

2 × 14784 people will comfortably fit in the crowed lined up 5 feet deep on both sides of the street for the first mile

2 × 14784 = 29568 people

Hence, 29568 people cheered for the runners at the start of the race.

Answer: 30 is the maximum possible value of y

Answer:

A ≈ 62.8 cm²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] ab sinC

where a = 10, b = 13 and C = 105° , then

A = [tex]\frac{1}{2}[/tex] × 10 × 13 × sin105° = 65 × sin105° ≈ 62.8 cm² ( to 1 dec. place )

Answer: x = 2

Steps: x + 3= 8x - 11

Subtract three form both sides: x + 3 - 3 = 8x - 11 - 3

Simplify: x = 8x - 14

Subtract 8x from both sides: x - 8x = 8x - 14 - 8x

Simplify:  -7x = -14

Divide both sides by negative seven: -7x ÷ -7   =   -14 ÷ -7

Simplify:  x = 2

Answer:

22.5 weeks

Step-by-step explanation: