If 3x - 4y = 15 and -2x + 3y = 10, then x - y = ?

Answer:

-6 and -1

Step-by-step explanation:

The excluded values are the values of x that satisfy [tex]2x^{2} + 14x + 12 = 0[/tex]

Let us solve the equation [tex]2x^{2} + 14x + 12 = 0[/tex]

It's a quadratic equation

Thus, let us calculate the discriminant Δ

Δ [tex]= 14^{2} - 4 .2.12 = 100[/tex]

the discriminant is greater than 0, so the equation has two solutions

[tex]x = \frac{-14 - 10}{4} = \frac{-24}{4} = -6[/tex]  or  [tex]x = \frac{-14+10}{4} = \frac{-4}{4} = -1[/tex]

the excluded values are -6 and -1

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]

[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex]              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]

[tex]3=k\dfrac{1}{0.4}[/tex]

[tex]3\times 0.4=k[/tex]

[tex]1.2=k[/tex]

Therefore, the constant of proportionality is [tex]k=1.2[/tex].

b) From part (a), we have [tex]k=1.2[/tex].

Substituting [tex]k=1.2[/tex] in (i), we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]

[tex]z=\dfrac{1.2}{0.5}[/tex]

[tex]z=2.4[/tex]

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n}[/tex]

or

[tex]n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]

Let the constant of proportionality be k, then we have:

[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]

Putting value y = 0.0125, we get:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]

Thus, for the given relation between y and z, we have:

Learn more about proportionality here:

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Answer:

20

Step-by-step explanation:

a²+b²=c²

25²-15²=b²

625-225=b²

400=b²

√400=√b²

20=b

Answer:

3x

Step-by-step explanation:

You multiply the pervious number with 3 to get the next number

For example 2 times 3 = 6

6 times 3 = 18

18 times 3 =54

54 times 3= 162

So on and so forth

Answer:

a) (4,7/2)

Step-by-step explanation:

Midpoint Formula:

[(-1+9)/2], [(2+5)/2]

(8/2, 7/2) = (4, 7/2)

Answer:

option  C

Step-by-step explanation:

We will take 2 coordinates from the graph and Find the equation of the line.

Let the coordinates be : ( 0, 1) and (1, 3)

step 1 : find slope

[tex]slope , m = \frac{y_2 - y_ 1}{x_2 - x_1} = \frac{3-1}{1-0} = 2[/tex]

Step 2 : equation of the line :

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

[tex](y -1) = 2 ( x -0)\\y - 1 = 2x \\y = 2x + 1[/tex]

Therefore, y = 2x + 1 represent the equation of the line.

Answer:

C

Step-by-step explanation:

You need to solve for y = mx + b

You can solve for b right away. It is clear that the line crosses the y axis at (0,1) so you have

y = mx + 1 so far.

Normally you would need two clear points to solve for m, but since you know the y intercept, you need only 1 point.

The clearest point I can see is (-2,-3) which means that

x = -2

y = - 3

Put that into the equation and solve for m.

-3 = m(-2) + 1          Subtract 1 from both sides

-3-1 = m(-2)             Combine

-4 = -2 m                 Divide both sides by - 2

-4/-2 = m

m = 2

Answer

only a and c are real choices. That's because m = 2 in both cases.

The equation we got is y = 2x + 1 which is c

Answer:

15, 9, 3n

Step-by-step explanation:

Just multiply the number of red balls by 3 to get total number, and divide the total number by three to get the number of red balls

Answer:

What math game is this?

Oh and this guy is correct.

Step-by-step explanation:

Answer:

-8 X 3 = -24 + 9 = -15 or you could do    -24+9=-15

Step-by-step explanation:

Answer:

242/48

Step-by-step explanation:

Answer:

90 students.

Step-by-step explanation:

279-9=270, and 270 divided by 9 is 90.

16

Step-by-step explanation:

10x+2=9x+18

-2 -2

10x=9x+16

-9x -9x

x=16

Hope this helps! :)

Answer:

x = 16°

Step-by-step explanation:

(10x + 2)° = (9x + 18)°

10x + 2 = 9x + 18

10x + 2 - 2 = 9x + 18 - 2

10x = 9x + 16

10x - 9x = 9x - 9x + 16

x = 16°

Using the z-distribution, as we have the standard deviation for the population, it is found that the 99.7% confidence interval is given by:

[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

99.7% confidence level, hence[tex]\alpha = 0.997[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.997}{2} = 0.9985[/tex], so [tex]z = 3[/tex].

The other parameters are:

[tex]\mu = 112.5, \sigma = 37.5, n = 96[/tex]

Hence, the interval is:

[tex]112.5 \pm 3\frac{37.5}{\sqrt{96}}[/tex]

To learn more about the z-distribution, you can check https://brainly.com/question/25890103

Answer:

Number of additional inches= x

Number of additional topping= y

Total cost= 8+1.5(x)+0.75(y)

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

hope it helps...

have a great day!!

The length of the leg is 9.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

From the triangle,

S = length of the leg.

Now,

Applying the Pythagorean theorem.

√18² = 3² + s²

18 = 9 + s²

s² = 18 - 9

s² = 9

s = 9

Thus,

The length of the leg is 9.

Learn more about the Pythagorean theorem here:

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Answer:

1:26

Step-by-step explanation:

You can divide both sides by 2.

Answer:

To find the area, you have to multiply the length times the width

Step-by-step explanation:

Answer:

The area of this rectangle is 6 square units.

Step-by-step explanation:

Multiply the width (8/3 inches) by the height (9/4 inches) to get the rectangle area:

 8       9

----- * -----

  3      4

                        8 * 9

This results in ----------    which itself reduces to 6.  

                          4 * 3

The area of this rectangle is 6.

Answer:

Expression B: 0.8p

Expression D: p - 0.2p

Step-by-step explanation:

The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.

Expression A: 0.2p

Expression B: 0.8p

Expression C:1 - 0.2p

Expression D: p - 0.2p

Expression E: p - 0.8p

Which two expressions each represent the sale price of the item?

Regular price of the item = $p

Sale price = 20% off regular price

Sale price = $p - 20% of p

= p - 20/100 * p

= p - 0.2 * p

= p - 0.2p

= p(1 - 0.2)

= p(0.8)

= 0.8p

The sale price is represented by the following expressions

Expression B: 0.8p

Expression D: p - 0.2p

Answer:

Slope of line B: 1/3

Step-by-step explanation:

To find a slope perpendicular to another slope, you take its negative reciprocal.

Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3

Answer:

1695.6 cubic feet

Step-by-step explanation:

Given that,

The corn fills 25% of the height of the silo.

The diameter of silo, d = 12 feet

Radius, r = 6 feet

Height, h = 60 feet

The volume of the part of the silo that is filled with corn is given by :

[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]

So, the required volume is equal to 1695.6 cubic feet.

Answer:

ANSWER IS B

Step-by-step explanation:

5x - 3 = 3x + 1

5x - 3x = 1 + 3

2x = 4

x = 4/2

x = 2

Answer:

B. 2

Step-by-step explanation:

The sides 5x - 3 and 3x + 1 are the same length, so you can put an equal sign: 5x - 3 = 3x + 1, x = 2:

5(2) - 3 = 3(2) + 1

10 - 3 = 6 + 1

7 = 7

So x is 2

Answer:

Ten thousands

Step-by-step explanation:

Replace all other digits with zero

This gives 40,000

Ten thousand (10,000) has the same amount of digits

Answer:

diagonal, congruent triangles

Step-by-step explanation:

Answer:

[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]

Answer:

D(12) = 2,600 miles

It means a distance of 2,600 miles is already traveled from home after 12 hours

Step-by-step explanation:

To find D(12); all we have to do is to substitute the value of 12 for D

We have this as;

D(12) = 3260-55(12)

D(12) = 2,600

In the context of this problem, what this mean is that the distance away from home is 2,600 miles after traveling 12 hours

Answer:

306 square inches.

Step-by-step explanation:

All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).

6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.

Each face of one cube = 3*3 = 9 in^2.

Therefore the surface area =  9 * 34 = 306 in^2.

Answer:

0.76

or

-0.76

hope this helps

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²

                      = x(x  - 3y) - 2y(x - 3y)

                      = (x - 3y)(x -2y)

x² - 4xy + 3y² = x² -xy - 3xy + 3y²

                      = x(x - y) - 3y(x - y)

                      = (x - y)(x - 3y)

x² - 3xy + 2y² = x² - xy - 2xy + 2y²

                      = x(x - y) - 2y(x - y)

                     = (x - y)(x - 2y)

Least common denominator = (x-y)(x - 2y)(x - 3y)

[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]