What is the solution to the system of equations Y equals -1/4 X +2 and 3Y equals -3/4 X -6

Answer:

a ≠ 2b

Step-by-step explanation:

The given expression is

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}}[/tex]

[tex]=\frac{8ab^{2}x}{4ab(a-2b)}[/tex]

Simplifying it, we have

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}} = \frac{bx}{a-2b}[/tex]

For the above fraction to exist, the denominator must not be equal to zero.

i.e, a-2b ≠ 0

=> a≠2b

∴ The algebraic fraction exists when a≠2b.

Answer:

A valid exclusion for the algebraic fraction is when a=2b

Step-by-step explanation:

You have:

[tex]8ab^2x/4a^2b-8ab^2[/tex]

First you must to simplify:

Taking out common factor 4ab

[tex]4ab(2bx)/4ab(a-2b)[/tex]

[tex]2bx/a-2b[/tex]

The fraction can be written only if  the denominator is different to zero, then

a-2b[tex]\neq[/tex]0

the excluded values are where  

a-2b=0

this expression is equal to 0 when a=2b

Answer:

Intercept form  y=-5/64 (x) (x-160)

Vertex form  y =  -5/64 (x-80)^2 + 500

Step-by-step explanation:

The equation for a parabola in intercept form is y =a(x-p) (x-q)

where p and q are the intercepts.  We know that it intersects the x axis at 0 and 160, so we can substitute these in

y = a(x-0) (x-160)

y = a(x) (x-160)

We have to calculate the value of a.

Using the point (80, 500)

500 = a(80) (80-160)

500 = a (80) *(-80)

500 = a *-6400

Divide each side by -6400

a = -500/6400

a = -5/64

So the equation in intercept form is

y = -5/64 (x) (x-160)

The equation for a parabola in vertex  form is

y = a(x-h)^2 +k    

We know the vertex is (80,500)

y = a(x-80)^2 + 500

We need to pick a point to solve for a.  (0,0)

0 = a(0-80)^2 + 500

Subtract 500 from each side.

-500 = a(-80)^2

-500 = a (6400)

Divide by 6400

-500/6400 = a

-5/64 = a   ( Does this look familiar?)

y = -5/64 (x-80)^2 + 500

To find the proportional relationship of 15 mL to 3.75 L, we first convert 3.75 L to milliliters, which is 3,750 mL. Then, we set up a proportion and solve for the unknown liter value. The proportional relationship of 15 mL to 3.75 L is 0.05625 L.

The student is asking about the proportional relationship between two different units of liquid volume: milliliters (mL) and liters (L). To establish this relationship, a conversion is needed, since 1 liter is equivalent to 1,000 milliliters.

First, we need to convert 3.75 liters to milliliters:

Now, let's express the proportion:

Answer:

6-y

Step-by-step explanation:

Six less than y means you take away y from six.

Hope this helps

Final answer:

The equation of the line with an x-intercept of -4 and a y-intercept of 2 is y = 0.5x + 2. We found this by calculating the slope using the two given points and then using the slope-intercept form to construct the equation.

Explanation:

To write the equation of the line with an x-intercept of -4 and a y-intercept of 2, we can use the two intercepts as points on the line: (-4,0) and (0,2). We can find the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. For our points this would be:

m = (2 - 0) / (0 - (-4)) = 2 / 4 = 0.5

Once we have the slope, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept is given as 2, we can write:

y = 0.5x + 2

This is the equation of the line with the given intercepts.

Answer:

2(4x - 3)

Step-by-step explanation:

Factor 3(x-2) + 5x

8x - 6

= 2(4x - 3)

Answer:

#5: 80mm, #6: 50yd, #7: 36m, #8: 32ft

Step-by-step explanation:

For #5:

The ratio between the two shapes is 24/15 = 8/5, based on the corresponding sides.

So, multiplying 8/5 with the smaller shape's perimeter of 50 would give you 80mm, which is the bigger shape's perimeter.

For #6:

The ratio between the two shapes is 15/9 = 5/3, based on the corresponding sides.

So, multiplying 5/3 with the smaller shape's perimeter of 30 would give you 50yd, which is the bigger shape's perimeter.

For #7:

The ratio between the two shapes is 12/4 = 3, based on the corresponding sides (You can also check this with 15/5).

So, multiplying 3 with the smaller shape's perimeter of 12 would give you 36m, which is the bigger shape's perimeter.

For #8:

The ratio between the two shapes is 12/21 = 4/7, based on the corresponding sides.

So, multiplying 4/7 with the bigger shape's perimeter of 56 would give you 32ft, which is the smaller shape's perimeter.

Hope this helps! Have a nice day!

Answer:

X^2 y

Step-by-step explanation:

So now you can make this x^2 y because the ^3 cancels it out

Answer:

x^6/27y

Step-by-step explanation:

(x^2/3y^1/3)^3

x^2 ^3/  (3^3 y^1/3 ^3)

Using the power of power rule, when a power is raised to a power, we multiply the powers.

x^ (2*3)/ (3^3 y^(1/3*3))

x^6/(27 y^1)

x^6/27y

Answer:

B. 585

Step-by-step explanation:

A graph of the scatter plot and line of best fit is attached.

The temperature in this problem will be the independent variable, or x.  This is because we are assuming that the number of ice cream cones sold depends on the temperature; this means the number of ice cream cones will be the dependent variable, or y.

This means in our graphing calculator, we will enter temperature in the first list and the number of cones in the second.

After drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax+b:

a = 5.08

b = 46.59

This gives us the equation y = 5.08x + 46.59.

Entering our temperature, 106, in for x gives us

y = 5.08(106) + 46.59 = 585.07 ≈ 585

Answer:

B

Step-by-step explanation:

585 Just took the test. Reference above to see explanation.

Answer:

[tex]A=8.2 cm^2[/tex] or [tex]A=\frac{81}{\pi }[/tex]

Step-by-step explanation:

Since the the formula for the circumference of a circle is [tex]C=2\pi r[/tex] and C is 18, we can substitute and solve for r. After we solve for r, we substitute it into the area formula.

[tex]18=2\pi r\\\frac{18}{2\pi } =\frac{2\pi r}{2\pi }\\2.866=r[/tex]

The formula for the area is [tex]A=\pi r^{2} \\A=\pi 2.866^{2} \\A=8.2 cm^2[/tex]

As a fraction, we would not simplify to a decimal and the solution would be:

[tex]A=\pi r^{2} \\A=\pi (\frac{9}{\pi }) ^{2} \\A=\frac{81}{\pi }[/tex]

Answer:

[tex]\frac{C}{2\pi } =r[/tex]

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. Since we need r, we will use the second formula for circumference.

We start by solving for r in the Circumference formula. using inverse operations. We divide both sides (as the inverse of multiply) by 2pi.

[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex].

Answer: C

Step-by-step explanation:

Answer:

976 421; 124 679

Step-by-step explanation:

Part A. Largest number

Leslie's number was 976 421.

This is because the largest numbers are in the positions of largest value.

For example, 9 in the hundred thousands place, the next largest number in the ten thousands place, and so on.

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

Part B. Smallest number

The smallest possible number is 124 679.

The value of the 4 is greater than the value of the 6 because the 4 is in the thousands place and the 6 is only in the hundreds place.

4000 > 600.

Answer:

f(x) = 2/3 x +3

Step-by-step explanation:

We know the y intercept ( where it crosses the y axis)  is 3

We can calculate the slope from 2 points (-3,1) and (0,3)

Slope = (y2-y1)/(x2-x1)

         = (3-1)/(0--3)

          = (3-1)/(0+3)

          = (2/3)

The slope is 2/3

Since we know the slope and the y intercept, we can use the slope intercept form

y= mx+b

y = 2/3 x+3

f(x) = 2/3 x +3

Answer:

Greece had a larger difference ($7.07)

Step-by-step explanation:

Brazil -

18.33 - 12.25 = 6.08

Greece-

16.55 - 9.48 = 7.07

Answer:

Greece has the larger difference between categories

Step-by-step explanation:

Difference in categories of Brazil

[tex]= 18.33 - 12.25\\= 6.08\\[/tex]

Difference in categories of Greece

[tex]= 16.55 - 9.48\\= 7.07\\[/tex]

Thus, Greece has the larger difference between categories

Answer:

Linear

Step-by-step explanation:

This can be written in slope intercept form (y=-5x+7) and there are no exponents.

Answer:

24 total students

Step-by-step explanation:

multiply 25 times 18 to get 450 then divide 450 by 75 then you get 6, which is the total amount of girls, so 6 + 18 = 24

x = number of students

75% of x = number of boys

(75/100)*x = 18

0.75x = 18

x = 18/0.75 <--- divide both sides by 0.75 to isolate x

x = 24

So there are 24 students in the class

Note how 18/24 = 3/4 = 0.75 = 75% represents the percentage of boys

Answer: D) y = - 1 /2 x + 1

Step-by-step explanation:

Got this right on USA test prep

The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = 2x + 8

Then the slope of the line is 2, then the slope of the perpendicular line will be - 1/2. Then the equation is given as,

y = - (1/2)x + c

The equation of the line is passing through (6, -2). Then we have

- 2 = - (1/2)6 + c

- 2 = - 3 + c

c = 1

Then the equation of the line is given as,

y = - (1/2)x + 1

The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.

More about the equation of a perpendicular line link is given below.

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(1) is correct. [tex]\mathbf u\cdot\mathbf v=(-14)(0)+(8)(11)=0+88=88[/tex]

(2) is correct. I assume you just computed the dot product as above, but another way to do it is to notice that [tex]\mathbf v\cdot\mathbf v=\|\mathbf v\|^2[/tex] (that is, the dot product of a vector with itself is the square of its magnitude). Then since [tex]\|\mathbf v\|=\sqrt{1^2+2^2}=\sqrt5[/tex], we have [tex]\mathbf v\cdot\mathbf v=\|\mathbf v\|^2=5[/tex].

(3) is not correct. Since [tex]\mathbf u\cdot\mathbf u=\|\mathbf u\|^2=\sqrt{45}[/tex], we have [tex]\|\mathbf u\|=\sqrt{\sqrt{45}}[/tex].

(4) is correct.

[tex]2\mathbf u\cdot\mathbf v=2(\mathbf u\cdot\mathbf v)=2((-3)(1)+(6)(2))=2(-3+12)=2(9)=18[/tex]

Answer:

30.50 = 8p +2d

49= 7p +6d

The price of a bag of popcorn is $2.50

Step-by-step explanation:

p = price of popcorn

d = price of drinks

Luke costs:

30.50 = 8p +2d

Aiden

49= 7p +6d

I will multiply  Lukes equation by -3 so I can use elimination on the d variable

-3 (30.50) =-3( 8p +2d)

-91.50 = -24p -6d

Now add the modified equation to Aidens equation

49       = 7p +6d

-91.50 = -24p -6d

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

-42.5 = -17p

Divide each side by -17

-42.50/-17 = -17p/-17

2.5 = p

Each popcorn costs 2.5

Answer:

30 divided by 2+3 is 6.

Step-by-step explanation:

The first thing you need to do is add 2 and 3, which is five, and then divide 30/5. The quotient is 6.

The quotient of 30 and the sum of 2 and 3 is 6.

The quotient of 30 and the sum of 2 and 3 can be found by dividing 30 by the sum of 2 and 3.

Step 1: Calculate the sum of 2 and 3. 2 + 3 = 5.

Step 2: Divide 30 by 5. 30 ÷ 5 = 6.

Therefore, the quotient of 30 and the sum of 2 and 3 is 6.

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Answer: (B) a=3, b=3

Step-by-step explanation:

   [tex]\dfrac{(2xy)^4}{4xy}[/tex]

[tex]=\dfrac{2^4x^4y^4}{4xy}[/tex]

[tex]=\dfrac{16x^4y^4}{4xy}[/tex]

[tex]=4x^{4-1}y^{4-1}[/tex]

[tex]=4x^3y^3[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Ca^(2+) or the charge is 2 plus or just 2

Step-by-step explanation:

Charge on the calcium ion = 20*(+1) + 18*(-1) = 20 - 18 = 2

The charge on the calcium ion is +2

Answer:

c. y = 1.25

Step-by-step explanation:

The equation for direct variation is

y = kx,

where k is the constant of proportionality.

We can use the given values of x and y to find k for this case.

y = kx

-10 = k * 40

k = -10/40

k = -0.25

The equation for this case is

y = -0.25x

Now we let x = -5 and solve for y.

y = -0.25x

y = -0.25(-5)

y = 1.25

Answer: c. y = 1.25

Answer:

c    y = 1.25

Step-by-step explanation:

The equation for direct variation is y= kx

If we know y and x we can solve for k

-10 = k*40

Divide each side by 40

-10/40 =k

-1/4 =k

The equation for this direct variation is

y =-1/4 x

Given that x =-5

y = -1/4 *-5

y = 5/4

y = 1.25

Answer:

I didn’t know you could have more than 2 answers that’s pretty cool

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(2x^2 + 3x - 4) (x + 4)

FOIL.

2x^2 times x = 2x^3

3x times x is 3x^2

-4 times x = -4x

2x^2 times 4 = 8x^2

3x times 4 = 12 x

-4 times 4 = -16

Combine like terms to get 2x^3 + 11x^2 + 8x - 16.

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = 4 and the point (-1, -3). Substitute:

[tex]y-(-3)=4(x-(-1))\\\\\boxed{y+3=4(x+1)}[/tex]

Answer:

Step-by-step explanation:

About Point Slope Form:

Y - 3 = 4 (x - -1)

First find the difference

160-40=120

Take the difference and divide it by the original number

120/160=0.75

Multiply by 100

75

Answer:$5.1

Step-by-step explanation: so since theres the 1 in 1.2 we know we have $3.40 right?, yeah so, half of $3.40 is 1.7 so jus add $1.7 to $3.40 wich is $5.1

Answer:

The answer is 8 1/3.

The answer will be 8 1/3

Answer: After about years 27 Account B will have more money than Account A  

Step-by-step explanation:  

Account A: 27(50) + 500 = $1850

Account B: 500(1.05^27) = $1866.73  

Hope this help

PS. If it did Mark me Brainliest