Find an expression which represents the sum of (6x + 9y) and (7x – 4y) in
simplest terms.
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Answer:

x1 = 0.64575

x2 = -4.64574

Step-by-step explanation:

Step 1: We want to rearrange the equation so all the variables are on one side

0 = -x² - 4x + 3

Step 2: We take out -1 in the first 2 terms so a = 1

0 = -(x² + 4x) + 3

Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets

b = 4

4/2 = 2

2² = 4

0 = -(x² + 4x + 4 - 4) + 3

Step 4: Move the -4 out remembering to apply the -

= -(x² + 4x + 4) + 4 + 3

Step 5: We notice is inside the brackets is a perfect square

0 = -(x + 2)² + 7

Therefore the vertex form of the equation is

y = -(x + 2)² + 7

Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x

0 = -(x + 2)² + 7

-7 = -(x + 2)²

7 = (x + 2)²

[tex] \sqrt{7 } = x + 2 [/tex]

[tex]x = \sqrt{7} - 2[/tex]

1st Solution:

x = +2.64575 - 2

x = 0.64575

2nd Solution:

x = -2.64575 - 2

x = -4.64574

Answer:  see proof below

Step-by-step explanation:

The standard equation of a circle is (x - h)² + (y - k)² = r² where (h. k) is the center of the circle and r is the radius.  It is given that A (h, k) = (1, 3) and point B (x, y) = (-2,4) is on the circle.  Substitute the center (h, k) and point B(x, y) = (-2,4) into the standard equation of a circle to get r² = 10.  To prove that C(x, y) = (4, 2) is also a point on the circle, substitute the center (h, k) and the point C(x, y) = (4, 2) into the standard equation of a circle to get r² = 10.  Since the radius is the same for both point B and point C and it is given that point B is on the circle, then we must conclude that point C is also on the circle.

Answer:

I am given that the center of a circle is at A(1, 3) and that point B(-2, 4) lies on the circle. Applying the distance formula to A and B, I get the following:

AB=Square Root ( (-2 - 1 )^2 + (4 - 3 )^2 ) = Square root ( 9 + 1 )

AB = Square root (10)

Since B lies on the circle, this length is the length of the radius of the circle. Applying the distance formula to A and C(4, 2), I get the following:

AC = Square Root ( ( 4 - 1 )^2 + (2 - 3 )^2 ) = Square root ( 9 + 1 )

AC = Square root (10)

Thus, the distance to C from the center A is equal to the length of the radius of the circle. Any point whose distance from the center is equal to the length of the radius lies on the circle. Therefore, point C lies on the circle.

Step-by-step explanation:

Answer:

Step-by-step explanation:

|x-a|≤b

-b≤x-a≤b

add a

a-b≤x≤a+b

put a-b=-8

a+b=-4

add

2a=-12

a=-12/2=-6

-6+b=-4

b=-4+6=2

so |x+6|≤2

Answer:

4360

Step-by-step explanation:

MXC is 1090 and a IV is 4 so 1090 x 4 is 4360

Answer:

a. 126 pie cm^3

Step-by-step explanation:

Area of a circle = pi*r²

Volume = area*height

(pi*r²)*14

Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³

Answer:

A. 126pi cm^3

Step-by-step explanation:

The volume of a cylinder can be found using the following formula.

[tex]v=\pi r^2 h[/tex]

First, we must find the radius. The radius is half of the diameter.

[tex]r=\frac{d}{2}[/tex]

The diameter of the cylinder is 6 cm.

[tex]r=\frac{6cm}{2}[/tex]

[tex]r= 3cm[/tex]

The radius is 3 cm.

Now, we can substitute values into the formula.

[tex]v=\pi r^2 h[/tex]

[tex]r= 3cm\\h=14 cm[/tex]

[tex]v=\pi (3cm)^2*14 cm[/tex]

Evaluate the exponent.

[tex](3cm)^2=3cm*3cm=9cm^2[/tex]

[tex]v=\pi*9cm^2*14cm[/tex]

Multiply 9 cm^2 and 14 cm

[tex]9 cm^2*14cm=126cm^3[/tex]

[tex]v=\pi*126cm^3[/tex]

The answer choices are in terms of pi, so we can simply rearrange our answer:

[tex]v=126\pi cm^3[/tex]

The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.

Answer:

12

Step-by-step explanation:

Hello, as the coefficient of the leading term is negative we know that the vertex of the parabola is a maximum. So we need to find the vertex.

This expression is maximum for

[tex]t=-\dfrac{b}{2a} \text{ where the parabola equation is}\\\\ax^2+bx+c=0[/tex]

So, here, it gives t = 8/2=4, and then, the maximum is

[tex]-4^2+8*4-4=-16+32-4=32-20=12[/tex]

So the answer is 12.

Thanks

Answer:

23,29,31,37,41,43,47,53,59,61 and 67.

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

23, 29, 31, 37, 41, 43, 47, 53, 61, 67

Step-by-step explanation:

Im not entirely sure but I believe I'm correct here.

Answer:

Step-by-step explanation:

4 4 4

4 4 6

4 6 6

4 6 4

6 6 6

6 6 4

6 4 4

6 4 6

Answer:

The length of Segment GF is 120

Step-by-step explanation:

Given that EH = 80, and AB, GF, RH, and DI are  parallel lines, we have;

DC ≅ DE ≅ EF ≅ FA Given

Therefore, CI ≅ HI ≅HG ≅ GB (Triangle proportionality theorem)

From where we have;

EH/GF =CH/CG (Intercept theorem otherwise known as Thales' theorem )

CH = 2 × CI (Transitive property of equality)

Also CG = 3 × CI (Transitive property of equality)

EH/GF = 2×CI/(3×CI) = 2/3

EH/GF = 2/3

80/GF = 2/3

Therefore we have;

Segment GF = 80 × 3/2 = 120

The length of Segment GF = 120.

120 U-U

Mostly cuz i looked it up and i am not explaining it cuz i dont wanna

Answer:

-15 then -10   = -25 we can only take one sign that accompanies the -10 and put in front of the brackets.

Step-by-step explanation:

-10 + (-15) = -25

just like (-15) -10 = 25

This is because ( ) is order of parenthesis Brackets first.

Answer:

-10 + (-15) is -25 and you do subtraction first.

Step-by-step explanation:

Since negative + negative is negative, you ignore the plus sign and continue with the equation. So -10 minus -15 is -25.

Answer:

Value of the function will be 2742.06

Step-by-step explanation:

Given function is,

f(x) = 1500(1.09)ˣ

By substituting the value of x we can find the value of the given function.

For x = 7,

f(7) = 1500(1.09)⁷

     = 1500(1.828)

     = 2742.0587

     ≈ 2742.06

Value of the function will be 2742.06

Answer: it would be 40/2 or 20, but im not sure.

Step-by-step explanation: so what I did was: 100 1/4 - 60 1/2: 100 - 60 = 40 and then I subtracted 1-1 which is 0 then 4-2 which is 2, and got 40/2 or just simplify which will be equal to 20

Answer:

108 children and 115 adults were admitted

Step-by-step explanation:

Create a system of equations where c is the number of children admitted and a is the number of adults admitted:

c + a = 223

3.5c + 6.8a = 1160

Solve by elimination by multiplying the top equation by -3.5:

-3.5c - 3.5a = -780.5

3.5c + 6.8a = 1160

Add the equations together and solve for a:

3.3a = 379.5

a = 115

So, 115 adults were admitted.

Find how many children were admitted by subtracting 115 from 223, the total number of people admitted:

223 - 115

= 108

108 children and 115 adults were admitted.

Answer:

-2.45

Step-by-step explanation:

I used a calculator to find this so I hope it helps :)

Answer:

10 mns later

Step-by-step explanation:

Answer:

5/2=20/8=35/14=125/50

Answer:

8, 14, 50

Step-by-step explanation:

5 x 4 = 20

2 x 4 = 8

5 x 7 = 35

2 x 7 = 14

5 x 25 = 125

2 x 25 = 50

Answer:

15x+6=10x+21

15x-10x=21-6

5x=15

divide by 5

5x/5=15/5

x=3

Answer:

x=3

Step-by-step explanation:

15x+6=10x+21

-10x

5x+6=21

-6

5x=15

divided by 5

x=3

Answer:

15

Step-by-step explanation:

1.8 over 0.4 multiply 0.3

Answer: 15

Step-by-step explanation:

 1.8/(0.4×0.3)

=1.8/0.12

=15

Hope this helps!! :)

Answer:

9

Step-by-step explanation:

Consider the polygon to consist of 2 rectangles, rectangle X (The bigger rectangular) and Y(the smaller rectangle), as shown in the diagram attached below.

To find DE + EF, let's find each lengths as follows:

DE = BC - FA

DE = 9 - 5 = 4

EF = AB - DC

EF = 8 - DC (we don't know DC)

Let's find out DC by considering the area of the entire polygon to derive an equation that will enable us to find DC.

Area of a rectangle = L*B

Therefore:

Area of the polygon = Area of rectangle X + Area of rectangle Y

Area of Polygon = (AB*FA) + (DE*DC)

52 = (8*5) + (4*DC)

52 = 40 + (4*DC)

Subtract 40 from both sides

52 - 40 = 4*DC

12 = 4*DC

Divide both sides by 4 to make DC the subject.

12/4 = DC

3 = DC

DC = 3

Thus,

DE + EF = (BC - FA) + (AB - DC)

= (9 - 5) + (8 - 3)

= 4 + 5

= 9

Answer:

Step-by-step explanation:

Cos^-1(1/2) = 60

To get from a degree to radian, simply multiply by pi then divide by 180. So the final answer is 1/3pi or approximately 1.0472

I hope this helped! :D

Answer:

The price of each CD is:

$14.70

Step-by-step explanation:

(61.6 - 2.8) /4

=  58.8/4

= $14.7

Answer:

$14.70

Step-by-step explanation:

We want to find the price of each CD before tax. Therefore, we must first subtract the tax from the total.

total -tax

The total cost was $61.60 and the tax was $2.80

$61.60 - $2.80

$58.80

The price for the 4 CDs (without tax) was $58.50.

We know that each CD costs the same price and Rita bought four CDs. Therefore, we can divide the cost without tax by 4.

cost without tax / 4

The cost without tax is $58.80

$58.80 /4

$14.70

Each CD before tax costs $14.70

Answer:

For it to be parallel the answer is B (3)

Answer:

B) 3

Explanation:

If two lines are parallel that means that their equations have the same value of slope.

3*sqrt(7)

3 times the square root of 7

====================================================

Explanation:

I'm assuming the V stands for square root. You can write sqrt(63).

[tex]\sqrt{63} = \sqrt{9*7}\\\\\sqrt{63} = \sqrt{9}*\sqrt{7}\\\\\sqrt{63} = 3\sqrt{7}[/tex]

The idea is to factor 63 in such a way that one factor is the largest perfect square possible, that way we can pull the root apart to simplify as shown above. The rule I used for the second step is [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex]

Answer:

Step-by-step explanation:

a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...

  m = -1/(5/6) = -6/5

Then the point-slope form of the desired line through (-3, 6) can be written as ...

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

  y = (-6/5)(x +3) +6

  y = -6/5x +12/5 . . . equation of line B

__

b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.

When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...

  d = |ax +by +c|/√(a² +b²)

The equation of line A can be written in general form as ...

  y = 5/6x -5/2

  6y = 5x -15

  5x -6y -15 = 0

Then the distance from P to the line is ...

  d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61

The length of segment PX is (66√61)/61.

__

c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...

  y = 5/6x -5/2

  y = -6/5x +12/5

Equating y-values gives ...

  5/6x -5/2 = -6/5x +12/5

Adding 6/5x +5/2 gives ...

  x(5/6+6/5) = 12/5 +5/2

  x(61/30) = 49/10

  x = (49/10)(30/61) = 147/61

  y = 5/6(147/61) -5/2 = -30/61

Then the point of intersection of the lines is X = (147/61, -30/61).

So, the midpoint of PX is ...

  M = (P +X)/2

  M = ((-3, 6) +(147/61, -30/61))/2

  M = (-18/61, 168/61)

Answer:

not exactly sure what the question is but

if it is "what is the max that 15 - x^2 - x can be

then 2x-1 = 0 solves that

x = 1/2

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

From the question

[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as

where k is the constant of proportionality

When

Substituting the values into the formula

we have

[tex]4 = \frac{k}{9} [/tex]

cross multiply

k = 4 × 9

k = 36

So the formula for the variation is

[tex] \alpha = \frac{36}{ \beta } [/tex]

when

[tex]\beta[/tex] = - 72

That's

[tex] \alpha = \frac{36}{ - 72} [/tex]

Simplify

We have the final answer as

Hope this helps you

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{pq+1}{9}[/tex]

= [tex]\frac{(3x+1)(3x-1)+1}{9}[/tex]

= [tex]\frac{9x^2- 1+1}{9}[/tex]

= [tex]\frac{9x^2}{9}[/tex]

= x²

Answer:

Hello,

Step-by-step explanation:

[tex]Using\ the\ formula\ (a+b)(a-b)=a^2-b^2\\p=3x+1\\q=3x-1\\\\p*q=(3x+1)*(3x-1)=9x²-1\\\\p*q+1=9x^2\\\\x^2=\dfrac{p*q+1}{9} \\[/tex]

It depends really. If you stay close to the present, then predicting future results isn't too bad. The further you go out, the more unpredictable things get. This is because the points may deviate from the line of best fit (aka regression line) as time wears on. Of course, it also depends on what kind of data we're working with. Some pairs of variables are naturally going to correlate very strongly together. An example would be temperature versus ice cream sales.

A best-fit line shows an association between two variables and can therefore be used to make predictions.

An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.

(see attachment below).

Recall:

Therefore, a best-fit line shows an association between two variables and can therefore be used to make predictions.

An example is a scatterplot attached below showing a best-fit line that depicts the association between the number of people that bath in a pool and daily temperature.

(see attachment below).

Learn more here:

https://brainly.com/question/2396661