Styles
Because you want to prepare and serve the healthiest food possible, you monitor the fat
and calorie content of items on your menu. Some of the menu items are included in the
graph below

Answer:

Since the slope of KM and ST are different, they are not parallel

Step-by-step explanation:

Slope of line KM = [tex]\frac{5}{8}[/tex]

 Slope of ST = [tex]-\frac{8}{5}[/tex]

Determine whether the lines are perpendicular;

Solution:

We can use the slope of a line to determine whether they are perpendicular or parallel to one another.

Parallel lines do not meet one another

Perpendicular lines cross one another at an angle of 90°

Two lines are parallel if their slopes are the same;

  Since the slope of KM and ST are different, they are not parallel

Answer:

13 pages : 1/2 hour Multiply both sides by 2

26 pages : 1 hour ------>> 26 pages/hr

Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages

Split up the fraction: (1/26) hr / page

Answer:

26

Step-by-step explanation:

13 in 1/2 hour

13:1/2

26:1

Answer:

1) dividend

2) divisor

3) quotient

Answer:

common ratio is 2/5

First term is  125/2

The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]

The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]

Step-by-step explanation:

The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:

[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]

Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:

[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]

So, the common ratio is 2/5

we can now determine the first term:

[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]

The sum of the first n terms is given by the formula:

[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]

and therefore, the infinite sum is:

[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]

Answer:

The angles are: 50.3 and 129.7

Step-by-step explanation:

The sum of supplementary angles is 180°.

Let x be one angle then the other angle will be x+79.4

Using the supplementary angle sum

[tex]x+x+79.4 = 180\\2x+79.4 = 180\\2x = 180-79.4\\2x = 100.6\\\frac{2x}{2} = \frac{100.6}{2}\\x = 50.3[/tex]

For the measurement of 2nd angle

x+79.4 => 50.3+79.4 => 129.7

Hence,

The angles are: 50.3 and 129.7

Answer:

Step-by-step explanation:

5.23x+3.76-3.67x+6.39

x(5.23-3.67) +(3.76+6.39)

1.56x + 10.15

Answer:

1.56x + 10.15

Step-by-step explanation:

(5.23x + 3.76) – (3.67x – 6.39)

(a + b) – (c – d) = a + b – c + d

Remove the parentheses and change the signs as needed:

5.23x + 3.76 – 3.67x + 6.39.

Group the like terms and simplify:

5.23x – 3.67x + 3.76 + 6.39

1.56x +10.15.

Answer:

I think its 15600..

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

2(30-7x)

Step-by-step explanation:

=14+14x-65-9

=14+14x-79

=60+14x

=2(30-7x)

Answer:

Length of rectangle = 36 yd and width of rectangle = 9 yd

Step-by-step explanation:

Let width of rectangle = w

Length of rectangle = 4w (four times the width)

Perimeter of rectangle = 90 yd

We need to find length and width of rectangle.

The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]

Where l is length and w is width

Putting values and finding length and width of rectangle

[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]

So,width (w) of rectangle is w= 9 yd

Finding length of rectangle = 4w = 4*9 = 36 yd

So, length of rectangle = 36 yd and width of rectangle = 9 yd

Answer:

100/35 = 2

35 goes into 100 2 times

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Using the triangle formula: a+b>c , b+c>a , and c+a>b, we can conclude that these values can form a triangle because 14+18>19 , 14+19>18 , and 18+19>14.

Answer:

To confirm if this can form it, we take the lower of the two numbers , square them, and equal it to the biggest number squared. (AKA The Pythagorean Theorem).

Step-by-step explanation:

[tex]14^{2} +18^{2} = 19^{2}[/tex]

Now solve to see if it equates to be true.

196 + 324 = 361

520 [tex]\neq[/tex] 361

That means 14, 18, and 19 can't form a triangle.

Answer:

Step-by-step explanation:

Step 1             f(x) = [tex]\frac{3x+4}{8}[/tex]                 Given

Step 2            y = [tex]\frac{3x+4}{8}[/tex]                    Change f(x) to y

Step 3            x = [tex]\frac{3y+4}{8}[/tex]                    Switch x and y

Step 4            8x = 3y + 4              multiply each side by 8

Step 5            8x - 4 = 3y               Subtract 4 from each side

Step 6            [tex]\frac{8x-4}{3}=y[/tex]                   Divide by 3 on each side

Step 7            [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]           Replace y by [tex]f^{-1}(x)[/tex]

Therefore, inverse of the function will be,

[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]

Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.

Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].

It is required to calculate the inverse of the function.

So, the steps involved in finding the inverse of the function will be,

Step 1:

Write the given function as,

[tex]f(x)=\dfrac{3x+4}{8}[/tex]

Step 2:

Change the function f(x) to y as,

[tex]y=\dfrac{3x+4}{8}[/tex]

Step 3:

Switch x and y as,

[tex]x=\dfrac{3y+4}{8}[/tex]

Step 4:

Multiply each side of the equation by 8 as,

[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]

Step 5:

Now, subtract 4 from each side of the equation as,

[tex]8x-4=3y+4-4\\8x-4=3y[/tex]

Step 6:

Now, it is required to divide each side by 3.

[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]

Step 7:

Now, replace y with [tex]f^{-1}(x)[/tex] as,

[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]

So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].

Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

For more details, refer to the link:

https://brainly.com/question/19606498

Answer:

The Trench or The Mariana Trench is the deepest part of the ocean.

Answer:

B) trench

Step-by-step explanation:

The deepest part of the ocean is called the Challenger Deep and is located beneath the western Pacific Ocean in the southern end of the Mariana Trench

I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)

Answer:

r=0

Step-by-step explanation:

the line passes through the origin which means there is no y-intercept

This should be what you're looking for.

Answer:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.

I hope this might help you

Mark it as brainliest answer and follow me

Answer:

250 centimeters

Step-by-step explanation:

2 meters into centimeters is 200 so 200+50=250

Answer:

100cm

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given that the measure of segment BC must equal the addition of the measure of segment BA plus the measure of segment AC, we can write this in equation form:

BC = BA + AC

then we replace them with the measure information they provide:

12 x + 4 = 7 x - 4 + 8 x + 2

and we solve for x in the equation:

12 x + 4 = 15 x - 2

subtract 12 x from both sides:

4 = 15 x - 12 x - 2

4 = 3 x - 2

add 2 on both sides

4 + 2 = 3 x

6 = 3 x

x = 6/3

x = 2

Answer:

im gonna go with yes

Step-by-step explanation:

Answer:

is what a perfect square?

Step-by-step explanation:

there is no pic attached

Answer:

its b

Step-by-step explanation:

i took the test

y = - 0.5x + 5.5 is the equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).

The slope-intercept form of a straight line is y = mx + c.

Here, x and y are coordinates, m is the slope and c is the y-intercept of the line.

Given, two points are C(1, 1) and (3, 5).

Therefore, equation of the line CD is:

[tex]\frac{x - x_{1} }{y-y_{1} }[/tex] = [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]

⇒ [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{1-3}{1-5}}[/tex]

⇒  [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{-2}{-4}}[/tex]

⇒2(x - 1) = (y - 1)

⇒ y = 2x - 1

Let, line AB is perpendicular to the line CD and passes through the point (-1, 6).

Therefore, slope of the line CD is = 2.

We know, slope of CD × slope of AB = -1

Therefore, slope of AB = -1 / slope of CD = [tex]-\frac{1}{2}[/tex].

Now, line AB has a slope of [tex]-\frac{1}{2}[/tex] and passes through the point (-1, 6).

Therefore, equation of the line AB is:

(y - y₁) = m(x - x₁)

⇒ [y - (6)] = [tex]-\frac{1}{2}[/tex][x - (- 1)]

⇒ 2(y - 6) = (-x - 1)

⇒ 2y - 12 + x + 1 = 0

⇒ x + 2y = 11

⇒ y = - 0.5x + 5.5

Learn more about slope-intercept form of a straight line here: https://brainly.com/question/12763756

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Answer: The 2 answers are inequality form and interval notation: n>200, and (200, ∞).

Step-by-step explanation: To solve for n, you’ll need to simplify the both sides of the inequality, and then isolating the variable.

Answer:

2) 8x^2 -6x-7 hope this helps

Answer:

It"s the second answer, "An 8-foot ramp leans....".

Step-by-step explanation:

Answer:

Step-by-step explanation:

⊕ An 8-foot ramp leans against a building 5 feet away.  

cos x = [tex]\frac{5}{8}[/tex] ⇒ x ≈ 51.3178°

Answer:

Never applies

Step-by-step explanation:

Given

Argument: The sum of a number and its opposite is always 1

Assume a positive number x

The opposite of the number is negative x (i.e. -x)

The sum of both numbers is:

[tex]Sum = x + (-x)[/tex]

Open Bracket

[tex]Sum = x -x[/tex]

[tex]Sum = 0[/tex]

Now, take for instance.

[tex]Number = 5[/tex]

Opposite would be

[tex]Opposite = -5[/tex]

Their sum is:

[tex]Sum = 5 + (-5)[/tex]

[tex]Sum = 5 -5[/tex]

[tex]Sum = 0[/tex]

Another instance is:

[tex]Number = -8[/tex]

Opposite would be

[tex]Opposite = 8[/tex]

Their sum is;

[tex]Sum = -8 + 8[/tex]

[tex]Sum = -0[/tex]

Hence, the argument never applies because the sum is never 1

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm