slope of 4 and passes through the point (1, 9) What is its equation in slope-intercept form?

The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let x represent the cost of on kg of mushroom and y represent the cost of one kg of turnips.

The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. Hence:

2x + 2.5y = 8.55  (1)

The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Hence:

3x + 4y = 13.10   (2)

From both equations:

x = 2.9, y = 1.1

The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10

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Motorcycle A  has a greater top speed.

A unit conversion expresses the same property as a different unit of measurement.

given:

Motorcycle A can reach a top speed of 140 miles per hour.

Motorcycle B can reach a top speed of 200 feet per second

Now,

1 miles/h = 1.46667 feet/sec

140 miles/h = 140*

                    = 205.333 feet/sec

So, Motorcycle A can reach a top speed of 205.333 feet/sec.

Hence, Motorcycle A  has a greater top speed

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Check the picture below.

Answer:834$

Step-by-step:150+28.24=834$

Answer: 13

Step-by-step explanation:

Answer:

On the second reduction, she reduced 25% of the original T-Shirt's price. She should have reduced the price of the T-Shirt after one reduction.

Step-by-step explanation:

Answer:

[tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

Slope is the change in y over the change in x.

The ordered pair is in the form (x,y).  The first number is the x value and the second number is the y value.  

for y;

-5 - 1 = -6

for x:

8 - (-4)

8 + 4

12

[tex]\frac{-6}{12}[/tex]  Which is the same as [tex]\frac{-1}{2}[/tex]  if we divide the top and bottom by 6

The midpoint of AB is M(-4, -3). If the coordinates of A are (−1,−2), then B has coordinates of (-2, -7/3)

Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.

Line AB has a midpoint, M.

A is (-1, -2)

B is unknown, M is(−4,−3)

Let's assume straight line of the form y=mx+b, where m is the slope.

Rise = (-3-(-2))= -1

Run = (-4-(-1)) =  -3

Slope = (Rise/Run) = (1/3)

The line becomes y=(1/3)x+b

Calculate b, the y-intercept (the value of y when x is 0)

y=(1/3)x+b

-2 = (1/3)(-1)+b

b = -2 + (1/3)

b = -5/3

The equation becomes:

y=(1/3)x - -5/3

Find the value of y for x=-2:

y=(1/3)x - -5/3

y=(1/3)(-2) - 5/3

y= -7/3

B has coordinates of (-2, -7/3)

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Answer:

2 real different roots

Step-by-step explanation:

Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:

[tex]\displaystyle{D = b^2-4ac}[/tex]

The formula is derived from a quadratic formula which is:

[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]

The expression inside the square root is discriminant. The discriminant says that:

From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:

Therefore, substitute the coefficients’ values in the discriminant:

[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]

Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.

Using the vertical line test, we conclude that the relation that is a function is the bottom right one.

A relation is a function only if all the inputs are mapped into a single output.

If we have the graph of a relation, it only will be a function if it passes the vertical line test.

This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.

With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.

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The temperature that water is increasing per minute is 2 degrees.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.

The first step is to determine what 2/5 of a minute is equivalent to in seconds.

1 minute = 60 seconds

2/5 x 60 = 24 seconds

The formula that can be used to determine the temperature that water is increasing per minute is :

Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute

(4/5 x 60) / 24 = 2 degrees

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According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]

Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]

Using logarithmic definition, we can write:

[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]

The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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Answer:

15-10-11-14

Step-by-step explanation:

15+10= 25

25+11= 36

36+14= 50

Answer:

1/4

Step-by-step explanation:

Get x by itself by dividing both sides by 8

x = 2/8

Reduce

1/4

Answer:

8x=2

/8   /8

Step-by-step explanation:

it is 0.25

8x=2

/8   /8

x=0.25

The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) =  0.5 + √x + 2.25

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = x^2 - x - 2

Start by expressing the above function in vertex form

Using a graphing calculator, we have

f(x) = (x - 0.5)^2 - 2.25

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = (x - 0.5)^2 - 2.25

The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25

The equation becomes

x = (y - 0.5)^2 - 2.25

Add 2.25 to both sides

So, we have

(y - 0.5)^2 = x + 2.25

Take the square root of both sides

y - 0.5 = √x + 2.25

Add 0.5 to both sides

So, we have

y = 0.5 + √x + 2.25

Express as an inverse function

f'1(x) =  0.5 + √x + 2.25

Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) =  0.5 + √x + 2.25

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Answer:

W = 11/8 or 1 3/8

Step-by-step explanation:

The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?

W=(1/4)(L)

width is 1/4 length

if the length is 5 1/2 ft

5 1/2 is equivalent to 11/2

W= (1/4)(11/2)

Multiply across.

W = 11/8 or 1 3/8

Answer:

wait first of all where did they put grandma?

Answer:

-48

Step-by-step explanation:

[tex](-12)4\\(-12) \times 4\\= -48[/tex]

Answer: -48

Step-by-step explanation:

negative x negative x negative x negative = negative

12 x 4 = 48

remember the answer needs to be a negative

(-12)4 = -48

The value of y in the triangle is 7.5

The given parameter is the triangle

On the triangle, we have the following equivalent ratio

y : 8 = y + 15 : 20

Express as fraction

y/8 = y + 15/20

Cross multiply

20y = 8y + 90

Collect the like terms

20y - 8y = 90

Evaluate

12y = 90

Divide by 12

y = 7.5

Hence, the value of y in the triangle is 7.5

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Answer:

11.5307692308

Step-by-step explanation:

Answer:

Around $79.88

Answer: the answer is (6,1)

Step-by-step explanation:

Answer:

(4, 3)

Step-by-step explanation:

If you are moving 2 units left, the x coordinate is shifted to the left by 2 units, the y coordinate remains the same.

A shift to the left means a decrease in the x-coordinate value so new
x-coordinate is 6- 2 = 4 , y coordinate is still 3 so you end up at point (4, 3)

Answer:

-3.78= (-1.2y)+(-4.2y)

y= 0.7

Step-by-step explanation:

-3.78= (-1.2y)+(-4.2y)

-3.78= -5.4y

/-5.4    /-5.4

y=0.7

The value of the expression ( h o g)(0) is 5.

When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.

Consider the two functions,

g(x) = 5x - 2 and h(x) = x² + 1

So,

( h o g)(x) = h(g(x))

( h o g)(x) = ( 5x - 2 )² + 1

( h o g)(x) = 25x² - 20x + 4 + 1

( h o g)(x) = 25x² - 20x + 5

( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1

( h o g)(0) = 0 - 0 + 4 + 1

( h o g)(0) = 5

The value of the expression ( h o g)(0) is 5.

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The correlation coefficient (r) is 0.9168.

The correlation coefficient can be improved by ignoring the bill for the month of July.

The 4th data point on the graph which indicates the month of July is the farthest away from the regression line in comparison to other points, and should not be included in the correlation coefficient improvement calculations for the electricity bill.

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The amount in the account after 40 years will be $5800.

It should be noted that the interest is calculated as:

= (Principal × Rate × Time) / 100

= ($1000 × 12 × 40) / 100

= $480000 / 100

= $4800

Therefore, the amount in the account after 40 years will be:

= Principal + Interest

= $1000 + $4800

= $5800

Therefore, the amount in the account after 40 years will be $5800.

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Answer:

5. 18%

6. 5.25% o 5.3 o 5

7. 33.33%

8. 2005-2010

The simplest form of the expression is 4 x²  .

We have given an expression √8 x² . √2 x²  .   .....(1)

On multiplying , we get

√8 x² . √2 x² = √16 x⁴

On simplifying , we get

√16 x⁴ =  √ 4 × 4 × x² × x²

           = 4 x²

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To cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.

So,

When z "varies jointly" with x and y, the following formula can be used to describe it:

z = kxy

Here, we have mulch bags (n) that vary with the area (a) and depth (d), both in feet.

The information provided allows us to calculate the value of k.

Now we can fill in the blanks with the other values of interest.

Therefore, to cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.

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