Find the distance between a point (–7, –19) and a horizontal line at y = 3. Choices are in the attachment...

Answer:

16.59

Step-by-step explanation:

Given:

[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]

Expanding the left hand side, we have:

[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]

Therefore:

[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]

To find the minimum value, we take the derivative and solve for its critical point.

[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]

Recall that:

[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]

The minimum possible value of the coefficient of x is 16.59.

Answer:

173

Step-by-step explanation:

For sympliciy let the box equal y.

Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that  (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].

Answer:

I hope it will help you :)

Let us take the 2nd equation.

x + 2z = 4

x = 4 - 2z

Let us substitute this value of x in equation 1.

5x + 2y + z = 4

5(4-2z) + 2y + z = 4

20 - 10z + 2y + z = 4

2y - 9z + 20 = 4

2y = 9z - 16

y = (9z - 16)/2

Let us substitute this value of y, as well as that of x that we used earlier, in the third equation.

2x + y - z = -1

2(4-2z) + (9z-16)/2 + z = -1

8 - 4z + (9z/2) - 8 + z = -1

Let us multiply both sides of this equation by 2.

16 - 8z + 9z - 16 + 2z = -2

3z = -2

z = [tex]\frac{-2}{3}[/tex]

x = 4 - 2z

  = 4 + [tex]\frac{4}{3}[/tex]

  = [tex]\frac{16}{3}[/tex]

y = (9z-16)/2

  = ([tex]\frac{-18}{3}[/tex] - 16)/2

  = ( [tex]\frac{-66}{3}[/tex])/2

  = -22/2

  = -11

Therefore, x = [tex]\frac{16}{3}[/tex], y = -11, and z = [tex]\frac{-2}{3}[/tex].

Answer:

hope it will help uh.....

Same number of rows to chairs in a row would form a square.

Use the total number of students as the area

Find the number or rows by taking the square root of student:

The square root of 7033 is 83.86

Round up to 84

Total seats would be rows x seats per row:

84 x 84 = 7,056 total seats

7056 seats - 7033 students = 23 empty seats

Answer:

115/5 23 so 20% =23 23x4 =92

Answer:

700 AUD ⇒ 430.72 euros

Hope this helps.

Answer:

y is equal to 50 degrees.

Step-by-step explanation:

The sum of the angles of a triangle is always 180 degrees.  To find what y is, subtract 80 from 180 and divide the difference by 2.  This will give you 50 degrees.

Answer:

y= 50°

Step-by-step explanation:

∠A =∠B = y. So, ΔABC is an isosceles triangle.

Sum of angles of triangle = 180

∠A + ∠B + ∠C = 180

y + y + 80 = 180   {add like terms}

2y + 80 = 180  {Subtract 80 from both sides}

2y + 80 - 80 = 180 - 80

2y = 100   {divide both sides by 2}

2y/2 = 100/2

y= 50°

Answer:

150 degrees

Step-by-step explanation:

You can figure this out by looking at the degrees below d, and you see it is thirty, and that it is equal to the degree above the x, so then you subtract 30 from 180 to get 150. Hopefully that makes sence, I forgot what some of the terms are called.

Answer:

144 cm^2

Step-by-step explanation:

8x6+4x10+4x8+4x6

48+40+32+24

80+40+24

120+24

144

Answer:

22.467

Step-by-step explanation:

Hello,

You just have to do the computation in XL or using a calculator, and round each number to the nearest hundred

x sqrt(x)

1 1

2 1.414

3 1.732

4 2

5 2.236

6 2.449

7 2.646

8 2.828

9 3

10 3.162

and do the sum which is 22.467

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

300

Step-by-step explanation:

First let's square all the integers from 1 to 10 inclusive. We get:

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100.

Rounding to the nearest hundred, we get that 1, 4, 9, 16, 36, and 49 all round to 0 and 64, 81, and 100 round to 100.

Therefore, we obtain 

0+0+0+0+0+0+0+100+100+100,

or 300.

Answer: B. rectangular pyramid

Answer: 6 or 9

Step-by-step explanation:

Given the following :

Let the number of green pens = x

Number of red pens = x + 3

Probability of picking same color = 17/35

Taking two pens at random; probability of picking two pens of same color.

Probability of picking red on first pick then red on second pick ; or picking blue on first pick then blue on second pick

Probability = (Required outcome / Total possible outcomes)

Total number of pens = x + x + 3 = 2x + 3

Probability of picking red then red:

P(red first) = (x+3)/2x+3

P(red second) = x+3-1 / 2x+3-1 = (x+2)/2x+2)

Therefore, probability of red then red =

(x+3)/(2x+3) × (x+2)/2x+2)

= (x+3)(x+2) / (2x+3)(2x+2)

Probability of green then green:

P(first green) = x/(2x+3)

P(second green) = (x-1) / (2x+3-1) = (x-1) / (2x+2)

P(green then green) = x(x-1)/(2x+3)(2x+2)

Therefore,

[(x+3)(x+2) / (2x+3)(2x+2)] + [x(x-1)/(2x+3)(2x+2)] = 17/35

(x+3)(x+2)+x(x-1) / (2x+3)(2x+2) = 17/35

Cross multiply :

35(x+3)(x+2)+x(x-1) = 17(2x+3)(2x+2)

35(2x^2 + 4x + 6) = 17(4x^2 + 10x + 6)

70x^2 + 140x + 210 = 68x^2 + 170x + 102

70x^2 - 68x^2 + 140x - 170x + 210 - 102 = 0

2x^2 - 30x + 108 = 0

Now we have a quadratic equation which can be factoeized used using any known factorization method.

Factorizing this, we get

(x-6) = 0 or (x-9) = 0

x = 6 or x = 9

Answer:

4 AND 2

Step-by-step explanation:

Answer:

Hello!

______________________

This question is very easy.

2 + 2 = 4

1 + 1 = 2

Step-by-step explanation: Add.

Hope this helped you!

Answer:

Step-by-step explanation:

Part A:

We have two lines: y = 2 - x and y = 4x + 3 . Given two equations that are both required to be true. The answer is the points where the lines cross, this means we have to make the equations equal to each other. It will look like this:

                                                       2 - x = 4x + 3

Part B:

In order to solve the equation we need to put the like terms together. So we will add x on each side.

                                                       2 - x = 4x + 3

                                                           +x   +x

So now we get:

                                                           2 = 5x + 3

Now that x is on one side and is positive we will move 3 on the left side by subtracting it from each side.

                                                           2 = 5x + 3

                                                           -3         -3

So now we get:

                                                           -1 = 5x

Now that the like terms have been combined we need to find out what x alone is so we divide 5 on each side:

                                                           [tex]\frac{-1}{5}[/tex] = [tex]\frac{5x}{5}[/tex]

No we see that:

                                                           x = [tex]-\frac{1}{5}[/tex]

Answer:

Los números son 6 y 9

Step-by-step explanation:

Este problema se puede resolver por medio de un sistema de ecuaciones.

El primer número será x y el segundo número será y.

Sabemos que los dos números suman 15, por lo tanto esto se puede escribir como:

[tex]x+y=15[/tex]

Por otro lado sabemos que el doble de uno de ellos es igual al otro más 3 unidades, esto lo podemos escribir de la siguiente manera:

[tex]2x=y+3[/tex] (el doble del primero es igual al segundo más 3)

Reescribiendo esta segunda ecuación tenemos:

[tex]2x-y=3[/tex]

Por lo tanto, nuestras dos ecuaciones son:

[tex]x+y=15\\2x-y=3[/tex]

Resolviendo el sistema por el método de reducción observamos que, si sumamos ambas ecuaciones, las y se cancelan y quedamos con:

[tex]3x=18\\x=6[/tex]

Ahora, sustituimos este valor en la primera ecuación para obtener el valor de y:

[tex]x+y=15\\6+y=15\\y=15-6\\y=9[/tex]

Por lo tanto, los números son 6 y 9

Por medio de un sistema de ecuaciones, hay qué los números son 6 y 9.

Los números sumados den 15, o sea:

[tex]x + y = 15[/tex]

El doble de uno de ellos sea igual al otro más 3 unidades, o sea:

[tex]2x = y + 3[/tex]

[tex]y = 2x - 3[/tex]

Reemplazando en la primera ecuación:

[tex]x + y = 15[/tex]

[tex]x + 2x - 3 = 15[/tex]

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3}[/tex]

[tex]x = 6[/tex]

[tex]y = 2x - 3 = 2(6) - 3 = 12 - 3 = 9[/tex]

Los números son 6 y 9.

Un problema similar es dado en https://brainly.com/question/24646137

Answer: AI:EF

Step-by-step explanation:

Answer:

D. ) AI:EF

Step-by-step explanation:

PLATO

Answer: C) 5

Step-by-step explanation:

First let's distribute the left side of the equation.

2/3a - 9 1/3 = -3(a-3)

Then let's distribute the right side of the equation.

2/3a - 9 1/3 = -3a + 9

Then let's move all the a's to one side, and all the constants to the other.

3 2/3a = 18 1/3

Then divide both sides of the equation by 3 2/3.

a = 5

Hope it helps <3

Answer:

1200 bacteria

Step-by-step explanation:

20 hours divided by 10 hours = 2, so it will be doubled two times.

300 times 2 for the first doubling = 600

600 times 2 for the second doubling = 1200

Answer:

The absolute value function that models the path of the ball is

[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]

The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]

Step-by-step explanation:

Given that the ball rolls without other external influences, we have;

(y - 0) = (x - 15)

The slope, m is give by the relation;

m = (y₂ - y₁)/(x₂ - x₁)

m = (15 - 0)/(0-20) = -3/4

The equation of the path of the ball in slope and intercept form is presented as follows;

y = m·x + c

15 = -3/4 ×0 + c = 15

c = 15

The absolute value function that models the path of the ball is then;

[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]

The vale of the function when x = 3 is given by the relation

[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]

Therefore, we have the coordinates as  [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].

The scale factor of the dilation shown in the diagram 2.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The image and pre image are shown in figure.

Now, We know that;

The basic formula to find the scale factor of a dilated figure is,

⇒ Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Substitute the given values, we get;

⇒ Scale factor = 6 / 3

⇒ Scale factor = 2

Thus, The scale factor of the dilation shown in the diagram 2.

Learn more about the divide visit:

https://brainly.com/question/28119824

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Answer:1/2

Step-by-step explanation:

got it right on edge

Answer:

507x223 is greater than 530 x 200

914x385 is less than 900 x 400

Answer:

1) [tex]7 \frac{11}{16} [/tex]

2) [tex] \frac{7}{15} [/tex]

Step-by-step explanation:

1) Let's convert the mixed fraction into a improper fraction.

[tex]5\frac{1}{8} \\ = \frac{5(8) + 1}{8} \\ = \frac{41}{8} [/tex]

Let the number be x.

[tex] \frac{2}{3} x = \frac{41}{8} \\ x = \frac{41}{8} \div \frac{2}{3} \\ x = \frac{41}{8} \times \frac{3}{2} \\ x = \frac{123}{6} \\ x = 7 \frac{11}{16} [/tex]

2)[tex]4 \frac{3}{8} = \frac{35}{8} [/tex]

[tex]9 \frac{3}{8} = \frac{75}{8} [/tex]

[tex]4 \frac{3}{8} \div 9 \frac{3}{8} \\ = \frac{35}{8} \div \frac{75}{8} \\ = \frac{35}{8} \times \frac{8}{75} \\ = \frac{7}{15} [/tex]

Answer:

24 cm

Step-by-step explanation:

Let the length of other base be x cm

Therefore, by mid segment formula of a trapezoid, we have:

[tex]23 = \frac{1}{2} (x + 22) \\ \\ 23 \times 2 = x + 22 \\ 46 = x + 22 \\ 46 - 22 = x \\ x = 24 \: cm[/tex]

Answer:

children take 3 pieces of candy are 6

Step-by-step explanation:

x+y=19-1          x+y=18

3x+5y=85-7    3x+5y=78

eliminate x by multiplying the first equation by 3:

3x+3y=54

3x+5y=85   subtract

(3x+3y)-(3x+6y)=54-78

3x-3y-3x-5y=-24

-2y=-24         y=-24/-2=12

y=12 , substitute for y:

x+y=18

x=18-12

x=6

check: 3x+5y=78

3(6)+5(12)=78

18+60=78 correct

Answer:

44%

Step-by-step explanation:

For these types of problems, look at the totals. We know that there are 0.44 out of 1 eighth graders. Since it doesn't specify how the 8th grader is dropped off, we take 0.44 and divide it by 1 (the total). We get 0.44, but since it's most likely asking for percentages, multiply that by 100.

Answer:

average speed = 8y/s

Step-by-step explanation:

Formula

s = d/t

d = 40 yards

t = 5 seconds

s = 40y/5s

= 8y/s