Vega set up a coordinate
system with units of feet to locate the
position of the vegetables she planted
in her garden. She has a tomato plant
at (1, 3) and a pepper plant at (5, 6).
How far apart are the two plants?
Round to the nearest tenth if
necessary.

Answer:

[tex]y = f(x) = \frac{1}{5}x + 1[/tex]

Step-by-step explanation:

The function notation of a linear function is given by y = f(x) = ax + b.

Now, the given equation is - x + 5y = 5

So, we have to arrange it for the function notation.

Now, - x + 5y = 5

⇒ 5y = x + 5

⇒ [tex]y = \frac{1}{5}(x + 5)[/tex]

⇒ [tex]y = \frac{1}{5}x + 1[/tex]

Therefore, the function notation of the given equation will be

[tex]y = f(x) = \frac{1}{5}x + 1[/tex] (Answer)

Answer:

answer is c i did the test

Step-by-step explanation:

Answer:

i) the value of a = 0 is non-permissible

ii) the value of b = 0 is non-permissible

Step-by-step explanation:

i) the given expression is [tex]\frac{5a^{2} + 80a }{50ab^{2} }[/tex]

ii) if a = 0 then the expression will become infinity hence the value of a = 0 cannot be used

iii) if b = 0 then the expression will become infinity, hence the value of b = 0 also cannot be used.

iv) In the numerator of the expression if it is factorized we get 5a[tex]\times[/tex] ( a + 16)

    if a = -16 then the value of the expression becomes zero.

Answer:

14

Step-by-step explanation:

12+b=26

b=26-12

b=14

Answer:14

Step-by-step explanation:You first want to do 12+12 because that =24 and then keep on adding until u get 26

Answer:

I believe the answer to this question is: 1 x 10^21 equal to 1000000000000000000000.

Answer:

d) 1998 to 2000

Step-by-step explanation:

Consumer price index (CPI) is an economic indicator that shows the average change in prices of items, goods and services. Basically, if CPI is increasing over a period of time that means that there is inflation, and if it decreases that means that there is deflation (lowering of prices).

Now, looking at our table, we see that:

- 1992-1994: CPI increased from 44.3 to 58.2 -> inflation

- 1994-1996: CPI increased from 58.2 to 65.9 -> inflation

- 1996-1998: CPI increased from 65.9 to 70.4 -> inflation

- 1998-2000: CPI decreased from 70.4 to 69.1 -> deflation

Answer:

The correct answer is D. 1998 to 2000

Step-by-step explanation:

Answer:

Total cost of painting the pyramid including the base = 19,200

Total cost of painting the pyramid excluding the base = 12,000

Step-by-step explanation:

Data provided in the question:

Height of the doll = 8 cm

Slant height of the pyramid, s = 5 cm

Base dimensions = 6 × 6

Cost of painting = 200 per cm²

Now,

Area of the base = 6 × 6 = 36 cm²

Area of the Pyramid = Area of the base + [tex]\frac{1}{2} \times P\times s[/tex]

here,

P is the perimeter of the base = 4 × side

= 4 × 6

= 24 cm

Thus,

Area of the Pyramid = 36 + [tex]\frac{1}{2} \times24\times 5[/tex]

or

Area of the Pyramid = 36 + 60 = 96 cm²

Total cost of painting the pyramid including the base = 96 cm² × 200

= 19,200

Total cost of painting the pyramid excluding the base = 60 cm² × 200

= 12,000

Answer:

The slope of the line passing through the given points (-2,-7) and (9,-7) is m=0

Step-by-step explanation:

Given that the line passing through the points (-2,-7) and (9,-7)

To find the slope of the line passing through the points :

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-2,-7) and (9,-7) respectively

Substitute the points in the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7-(-7)}{9-(-2)}[/tex]

[tex]=\frac{-7+7}{9+2}[/tex]

[tex]=\frac{0}{11}[/tex]

Therefore m=0

Therefore Slope m is 0

Therefore the slope of the line passing through the given points (-2,-7) and (9,-7) is m=0

Answer:

B

Step-by-step explanation:

Substitute the value of (2,1) into the equations, and you find that only B works.

Answer: 18cm

Step-by-step explanation:

Let original drawing's base be b.

We are using scale factor of 0.4, so

0.4 of b = 7.2cm

0.4 × b = 7.2cm

b = (7.2/0.4)cm

b = 18cm

The base of the original drawing must be 18 cm.

Option B is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Scale factor = 0.4.

From the figure,

Original height = 25.6 cm

Original base = b cm

Scale height.

= 25.6 x 0.4

= 10.24 cm

Scale base = 7.2 cm

Now,

Original base.

b x 0.4 = 7.2

b = 7.2 / 0.4

b = 18 cm

Thus,

The base of the original drawing must be 18 cm.

Learn more about scale factors here:

https://brainly.com/question/20759556

#SPJ6

Answer:

B is the answer to the equation

The probability that John will practice his trombone is 34%.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

If it rains ​tomorrow, the probability is 0.9. If it does not rain ​tomorrow, there is only a 0.5 chance. And, the chance of rain tomorrow is 70​%.

Calculation of probability:

= 0.9 (0.1) + 0.5 (0.5)

= 0.34

= 34%

Learn more about the probability here:

brainly.com/question/3974756

#SPJ3

The probability that John will practice his trombone is 0.7 or 70%, calculated using the law of total probability considering the two scenarios of snow and no snow.

To calculate the probability that John will practice his trombone, we need to consider two scenarios: one where it snows and one where it does not. We can solve this by using the law of total probability.

Let's denote the probabilities as follows:
P(Snow) is the probability it will snow, which is given as 0.5.
P(Practice|Snow) is the probability John will practice given that it snows, which is 0.9.
P(Practice|No Snow) is the probability John will practice given that it does not snow, which is 0.5.

The total probability that John will practice is:

P(Practice) = P(Snow) * P(Practice|Snow) + P(No Snow) * P(Practice|No Snow)
          = 0.5 * 0.9 + 0.5 * 0.5
          = 0.45 + 0.25
          = 0.7

Therefore, the probability that John will practice his trombone is 0.7 or 70%.

Answer:

A function and its inverse

Step-by-step explanation:

The property (fg)(x)= x holds for a function and its inverse.

For instance:

Let

[tex]f(x) = 2x[/tex]

and

[tex]g(x) = \frac{x}{2} [/tex]

These two functions are inverse of each other.

[tex]f(g(x)) = 2( \frac{x}{2} ) = x[/tex]

The correct pair is B: [tex]\(f(x)=\frac{2}{x}\) and \(g(x)=\frac{2}{c}\)[/tex], satisfying [tex]\((f \circ g)(x)=x\).[/tex]

To find which pairs of functions satisfy the condition [tex]\((f \circ g)(x) = x\),[/tex] let's compute [tex]\(f(g(x))\)[/tex] for each pair of functions and see if it equals [tex]\(x\).[/tex]

A. [tex]\(f(x) = x^2\) and \(g(x) = \frac{1}{x}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2}\][/tex]

[tex]\(f(g(x)) \neq x\),[/tex] so option A is not correct.

B. [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{2}{c}\right) = \frac{2}{\frac{2}{c}} = c\][/tex]

[tex]\(f(g(x)) = x\)[/tex] if [tex]\(c = x\).[/tex] So, option B is correct.

C. [tex]\(f(x) = \frac{x - 2}{3}\) and \(g(x) = 2 - 3x\):[/tex]

[tex]\[f(g(x)) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x\][/tex]

[tex]\(f(g(x)) \neq x\)[/tex], so option C is not correct.

D. [tex]\(f(x) = \frac{1}{2x - 2}\) and \(g(x) = \frac{1}{2x + 2}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{2x + 2}\right) = \frac{1}{2\left(\frac{1}{2x + 2}\right) - 2}\][/tex]

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

[tex]\[= \frac{1}{\frac{1 - 2(x + 1)}{x + 1}}\][/tex]

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

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

[tex]\(f(g(x))\)[/tex] does not simplify to [tex]\(x\)[/tex], so option D is not correct.

Thus, the correct answer is option B: [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\).[/tex]

Complete Question:

For which pairs of functions is (fg)(x)=x?

A. f(x)=x^2 and g(x)=1/x

B.f(x)=2/x and g(x)=2/c

C. f(x)=x-2/3 and g(x)=2-3x

D. f(x)=1/2x-2 and g(x)=1/2x+2

Answer:

16.75

Step-by-step explanation:

7.5+9.25=16.75

Line up the digits and use traditional algorithm.

Answer:

x ≈ 745.5 ft

Step-by-step explanation:

The angle at the lower right of the triangle is 28° ( alternate angle )

Using the sine ratio in the right triangle

sin28° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{350}{x}[/tex]

Multiply both sides by x

x × sin28° = 350 ( divide both sides by sin28° )

x = [tex]\frac{350}{sin28}[/tex] ≈ 745.5 ft ( to the nearest tenth )

Answer:

Last one is your answer

Step-by-step explanation:

Answer:

48.5 gal/min

Step-by-step explanation:

I used a ratio to solve this problem.

If 97 gallons flow in 2 minutes, the ratio is 97/2

To find the flow per one minute, the ratio is x/1

You can then cross multiply to get 97=2x

When solved, this gives you 48.5 gal/min.

To check, you can multiply x2.

Answer:

The value of given expression is 3.8.

Step-by-step explanation:

Given:

[tex]1.8+0.5(y+6)-2^3[/tex]

We need to find the simplified value of given expression using y =14

Solution:

Now we will substitute y =14 we get;

[tex]1.8+0.5(y+6)-2^3\\\\1.8+0.5(14+6)-2^3[/tex]

Now using PEDMAS we will first solve the parenthesis we get;

[tex]1.8+0.5\times20-2^3[/tex]

Now we will solve the exponent function we get;

we know that;

[tex]2^3=8[/tex]

So we can say that;

[tex]1.8+0.5\times20-8[/tex]

Now we will solve the multiplication operation.

[tex]1.8+10-8[/tex]

Now we will perform addition operation.

[tex]11.8-8[/tex]

And finally we will perform subtraction operation.

3.8

Hence The value of given expression is 3.8.

Answer:

(-2,5) and (7,23)

Step-by-step explanation:

we have

[tex]y=x^{2} -3x-5[/tex] ---> equation A

[tex]y=2x+9[/tex] ---> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

Using a graphing tool

The intersection points are (-2,5) and (7,23)

see the attached figure

therefore

The solutions are (-2,5) and (7,23)

The solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].

It is given equations are,

Explanation:

From the given graph it is clear that the curve and line intersect each other at two points. These points are the solutions for the given system of equations.

The graph of line and curve intersect each other at [tex](-2,5)[/tex] and [tex](7,23)[/tex].

Thus, the solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].

Learn more:

https://brainly.com/question/14300335

Final answer:

To find the difference between 83456 and 728.88, subtract the second number from the first, resulting in the answer 82727.12.

Explanation:

To find the difference between the two numbers 83456 and 728.88, we simply subtract the second number from the first:

Write the numbers in a vertical column, aligning the digits by place value.

Perform the subtraction, starting from the rightmost digits (the ones place) and moving to the left, borrowing as needed.

Subtract each digit in the smaller number from the corresponding digit in the larger number.

83456
-  728.88
_______
82727.12

The difference is 82727.12.

Answer:5y+5

Step-by-step explanation:

2+y+y+y+y+y+3

Collect like terms

y+y+y+y+y+3+2

5y+5

Answer:

Step-by-step explanation:

The amount of simple interest is ...

  I = Prt = $218·0.06·7 = $91.56

The total account balance is this amount added to the original deposit:

  $218.00 + 91.56 = $309.56

Step-by-step explanation:

Given that , the scale on map is 1 : 320000.

Its means that if the scale shows 1 unit  then actual length is 320000 units

So If the  shows 1  cm then the actual distance = 320000 cm

                                                                              =[tex]\frac{320000}{100000}[/tex] km = 3. 2 km

The wheel covered 785 feet in one complete turn

Solution:

Given that, The first Ferris wheel was built in 1893 in Chicago

Diameter of wheel = 250 feet

Let us find the radius of wheel

[tex]Radius = \frac{diameter}{2}\\\\Radius = \frac{250}{2}\\\\Radius = 125[/tex]

Thus radius of wheel is 125 feet

We have to find the distance covered in one complete turn

The number of feet the wheel rotated in one turn is equal to its circumference

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14

Substituting the values we get,

[tex]C = 2 \times 3.14 \times 125\\\\C = 785[/tex]

Thus the wheel covered 785 feet in one complete turn

Answer:

The points (12,3), (-2,-5) and (1,15) through which the line can pass.

Step-by-step explanation:

A line passes through the point (0, –1) and has a positive slope.

(i) The slope of the line passing through the points (0,-1) and (12,3) will be

[tex]\frac{- 1 - 3}{0 - 12} = \frac{1}{3} > 0[/tex]

(ii) The slope of the line passing through the points (0,-1) and (-2,-5) will be

[tex]\frac{- 1 + 5}{0 + 2} = 2 > 0[/tex]

(iii) The slope of the line passing through the points (0,-1) and (- 3,1) will be

[tex]\frac{- 1 - 1}{0 + 3} = - \frac{2}{3} < 0[/tex]

(iv) The slope of the line passing through the points (0,-1) and (1,15) will be

[tex]\frac{- 1 - 15}{0 - 1} = 16 > 0[/tex]

(v) The slope of the line passing through the points (0,-1) and (5,-2) will be

[tex]\frac{- 1 + 2}{0 - 5} = - \frac{1}{5} < 0[/tex]

Therefore, the points (12,3), (-2,-5) and (1,15) through which the line can pass. (Answer)

Answer:

A, B, D

Step-by-step explanation:

just took it on edg

Answer:

D(-6,-4)

Step-by-step explanation:

-5x + y = 26

2x - 7y = 16

-5x/-5 = 26-y/-5

x = -26/5 + y/5

2(-26/5 + y/5) = 7y = 16

-52/5 + 2y/5 = 16 + 52/5

-33y/5 = 80/5 + 52/5

-33y/5 = 132/5

-33y = 132

y = -4

2x - 7(-4) = 16

2x + 28 = 16

2x = -12

x = -6

The number of batches of cookies made is [tex]7\frac{1}{2}[/tex]

Solution:

Given that, baker has 10 cups of sugar to make cookies

Each batch calls for [tex]1\frac{1}{3}[/tex] cups of sugar

To find: Number of batches of cookies can be made

From given information,

Total number of cups of sugar = 10

Cups of sugar for 1 batch = [tex]1\frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}[/tex]

Therefore, number of batches of cookies can be made is found by dividing the total number of cups of sugar by cups of sugar for 1 batch

Thus we get,

[tex]\text{Number of batches of cookies can be made} = \frac{\text{Total number of cups of sugar}}{\text{Cups of sugar for 1 batch}}[/tex]

Substituting the values, we get

[tex]\text{Number of batches of cookies can be made} = \frac{10}{\frac{4}{3}}\\\\\text{Number of batches of cookies can be made} = 10 \times \frac{3}{4}\\\\\text{Number of batches of cookies can be made} = \frac{15}{2}\\\\\text{In mixed form, we get }\\\\\rightarrow \frac{15}{2} = 7\frac{1}{2}[/tex]

Thus number of batches of cookies made is [tex]7\frac{1}{2}[/tex]

The expression 1/4x + 19/4 can be factored by taking out the common factor of 1/4, resulting in the completely factored form (1/4)(x + 19).

The student has asked to factor the expression 1/4x + 19/4 completely. To begin with, we note that both terms in the expression share a common factor of 1/4. Thus, we can factor out this common factor. The expression becomes:

(1/4)(x + 19)

The 1/4 is factored out, and we are left with the binomial x + 19 inside the parentheses. This is the completely factored form of the expression. Remember that factoring is essentially reversing the distribution process. In this case, we took out the common factor of 1/4 that was distributed across the x and 19.