1. Henry wants to go on a vacation. He knows it will cost $300 per
day that he's on vacation plus $650 for miscellaneous activities. He
has $2750 dollars in his savings account. How many days can he go
on vacation?

FOR PERPENDICULAR LINES WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE -1

BUT IF WE ARE TO CHECK IN THE LJNE y=1 the gradient is 0

there is no number when multiplied with 0 that will give us -1 it means that the gradient of the line perpendicular to the given one will also be 0

when we substitute in the general equation y=mx+c together with the points

[tex] - 9 = (0)(4) + c \\ c = - 9[/tex]

IT MEANS THE EQUATION OF THE NEW EQUATION WILL BE

[tex]y = - 9[/tex]

HOPE THIS HELPS

The correct answer is:  [D]:  " [tex]m = \frac{-5}{2}[/tex]  ".

______
Step-by-step explanation:
We are given:
" 5x  +  2y  =  -10 " ; Find the slope of the equation.
______
Rewrite this equation in slope-intercept format ;

that is:  " y =  mx  + b " ;

      in which:  
        y  remains as single value, as an 'output' ; or 'dependent  
variable', on the 'y-axis' (if graphed);
         isolated on the 'left-hand side' of the equation.
      m  is the coefficient of x in the equation; and represents the slope; for which we shall solve.
           {If there is no slope, then "m = 0" ; and "[0 * x = 0]." };
And the "slope-intercept format" is:  "y = b" }.
       b  represents the "y-intercept" ; i.e. when the line crosses the
"y-axis" when graphed;  that is, the "y-value" of the "coordinate" of the "y-intercept" ; [i.e. the value of "y" when "x = 0" ;  so;  " (0, b) ".

{ Note:  b  can equal "0" ; in those cases:  y = mx + 0 ; write as " y = mx "}.

{ If there is no slope, [i.e. "m = 0" ; and no "y-intercept" ;  [i.e. "b = 0"];
 Then:  write the equation accordingly—e.g. " y = [whatever number the graph represents]." }.

 Also, note that b can be a "negative number"; as well.
  In that case,  write an equation in "slope-intercept format" ; that is;  
   →" y = mx + b " ;   as:   " y = mx " .     
______
Given:  " 5x  +  2y  =  -10 " ;  
 Let's rewrite:    ↔  " 2y + 5x  =  -10 " ;  to get the "y-value" a bit closer to the 'left-hand side' of the equation.

  Then: Let's subtract 5x from Each Side of the equation;
      2y + 5x − 5x  = -10 − 5x  ;

 to get:  " 2y =  -10 − 5x " ;

______
Method 1):
  We have: " 2y = -10 − 5x " ;

 Divide Each Side by 2 ; to isolate y on the 'left-hand side' of the equation, and to rewrite as an equation in the slope-intercept format :

  2y / 2 = (-10 − 5x)/2 ;

   →  [tex]y =\frac{-10-5x}{2}= \frac{-10}{2}-\frac{5x}{2}[/tex] ;
              →    [tex]\frac{-10}{2} =[/tex] -10 ÷ 2  = -5 ;

                   Rewrite the equation by replacing " [tex]\frac{-10}{2}[/tex] " ;  with:  -5 ;
              →  [tex]y = -5 - \frac{5x}{2}[/tex] ;

             Then, rewrite to get the equation in "slope-intercept format"

              →  [tex]y = -5 - \frac{5x}{2}[/tex] ;
                     [tex]= -5 + (-\frac{5x}{2})[/tex] ;  ↔ Rewrite:
                     [tex]= \frac{-5x}{2} + (-5)[/tex] ;   ↔ Rewrite again:
                     [tex]=\frac{-5x}{2} -5[/tex] ;

             →   [tex]y = \frac{-5x}{2} -5[/tex] .

Note:  " [tex]\frac{-5x}{2} = \frac{-5}{2} x[/tex] " ;

            →   [tex]y = \frac{-5}{2}x-5[/tex] ;

 This is the equation written in "slope-intercept format" ;

 that is:  " y = mx + b " ;

  in which:
 y is isolated as a single variable on the 'left-hand side' of the equation;

 m = [tex]\frac{-5}{2}[/tex] ; which is the slope; which is also the "coefficient" of x ;

 b = -5 ; which is the 'y-coordinate' of the "y-intercept" of the graph;
So, the slope; "m = -5/2" ; is the correct answer; which corresponds to:
Answer choice:  [D]: " m = [tex]\frac{-5}{2}[/tex]  " .
______

Method 2):

Given:  " 5x + 2y = -10" ; Find the slope of the line.

We want to rewrite the equation in the "slope-intercept format" ;

" y = mx + b " ; as explained above;

  to get the correct answer for m, the slope of the line.

" 5x + 2y = -10 " ↔ Rewrite as:
  2y + 5x =  -10 ;  since we want to isolate y as a single variable on the 'left-hand side' of the equation;  and by rearranging & rewriting this equation, the 2y is closer to the 'left' of the equation.

Now, subtract 5x from Each Side of the equation:
  2y + 5x − 5x = -10 − 5x ;
  to get:  2y = -10 − 5x ;

Now, Let's multiply the entire equation (i.e. "Each Side") by  -1 ;

to make the equation easier to handle;
    -1(2y) = -1 (-10 − 5x) ;
For the 'left-hand side' of the equation:
 -1*2y = -2y
For the 'right-hand side' of the equation:

Note the 'distributive property of multiplication'; as follows:
    a(b + c) = ab + ac ;
Likewise:  
-1(-10 − 5x) = (-1 *-10) + (-1 *-5x) ;

                 =  (10) + (5x) = 10 + 5x ;

Now, rewrite the entire equation:

-2y = 10 + 5x ;  ↔ Rewrite as;
   -2y = 5x + 10 ;  
Then, we divide Each Side of the equation by -2 ;
  to isolate y as a "single variable" on the 'left-hand side' of the equation;

   and to rewrite the equation in "slope-intercept format" ;

    -2y / -2 = (5x + 10) /-2 ;

    →  [tex]y=\frac{5x+10}{-2} =\frac{5x}{-2} +\frac{10}{-2} =\frac{5x}{-2}+(-5) =\frac{5x}{-2}-5[/tex] ;
    → [tex]y=\frac{5x}{-2} - 5[/tex] ;
which is written in "slope-intercept format" ; that is:
 " y = mx + b " ;

in which:  

y is isolated as a single variable on the 'left-hand side' of the equation;

m = [tex]\frac{5}{-2}[/tex] ; which does equal  " [tex]-\frac{5}{2}[/tex] " ;  which does equal " [tex]\frac{-5}{2}[/tex] " ;

which is the slope of the equation, as well as the 'coefficent of x' ;

b = -5 ; which is the 'y-coordinate' of the "y-intercept".
______
As such:  
The correct answer choice is:  [D]: " m = [tex]\frac{-5}{2}[/tex] " .
{Note: This is consistent with the answer choice from Method 1  above.}

______
Hope this answer and explanation is helpful.
Best of luck to you!
______

In order to calculate after how many days all three food items will be eaten in the same day, we need to calculate the least common multiple (LCM) between the periods of 6 days, 8 days and 10 days.

First, let's factorize each number:

Then, let's multiply the factors using the maximum number of time they appear in a number, that is, number 2 three times, number 3 one time and number 5 one time:

So after 120 days all three food items will be eaten on the same day.

Answer: B: 10

Step-by-step explanation:

complementary angles are two angles that add up to 90 degrees

The value of x after solving the equation 3sinx+3 = 1 for 0° is -46.455.

First, take the equation 3sinx+3 = 1. This is a first order linear equation with a single variable, x. To solve this equation find the value of x.

First subtract three from both LHS and RHS part. The equation becomes

3sinx+3-3 = 1-3,

which is equal to,

3sinx = -2. now divide both LHS and RHS by 3 and the equation becomes, (3sinx)÷3 = -2÷3 solving this we get the equation as sinx = -2÷3.

now take the sine to the LHS we get the equation as,

x = [tex]sin^{-1}[/tex](-2÷3)

so by solving this, the final answer for x is,

x = -46.455

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Answer:

50+((10n) =

so 50 is how much it cost to walk in the park and 10 is how much each ride (n) cost soif you know how many rides your ride you times that by 10 the add 10 to 50 and you get how much it will cost you for the day

The slope of the line in the graph is undefined.

The line in the graph is a straight vertical line whose slope can be found.

The characteristics of a vertical line can be used to find the slope of the vertical line given.

A vertical line has same x-co-ordinate but will have different y-co-ordinates.

Slope of a line is the change in y-co-ordinates divided by change in x-co-ordinates.

That is, slope = change in y-co-ordinates/ change in y-co-ordinates

But here, change in x-co-ordinates is zero since the x-co-ordinates are same for the vertical line given in the graph.

So slope = change in y-co-ordinates/ 0

This is undefined.

So the slope of the line in the graph is undefined.

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Answer:

stuff and more stuff

Step-by-step explanation:

Let's first write both numbers in their fraction form:

then, we can write the division like this:

Now, given the general rule for the division of fractions, we have:

also notice that we are dividing two negative numbers, then our final result will be positive according to the law of signs. Then, we have in this case:

therefore the final result is 360

Answer:

v=60

Step-by-step explanation:

3v=180

v=60

:]

Answer:

175.259 cm

Step-by-step explanation:

The maximum area that the farmer can enclose for the rectangular garden is 488 sq ft and the dimensions of the rectangular garden are 24ft and 12 ft respectively.

It is given that a farmer decided to enclose a rectangular garden with one side using the barn of a tree and other 3 sides with 48 ft of fencing.

Let the length of the rectangle be y and the breadth of the rectangle be u.

So perimeter of the fencing needed = y + 2u (as one side is barn)

∴ y + 2u = 48

⇒ y = 48 - 2u (equation 1)

Area = yu (equation 2)

Putting the value of variable y from equation 1 in equation 2 we have,

Area = (48-2u)u

∴ Area = 48u - 2[tex]u^{2}[/tex]

⇒ Area = -2[tex]u^{2}[/tex] + 48u

⇒ Area = -2([tex]u^{2}[/tex] - 24u)

⇒ Area = -2([tex]u^{2}[/tex] - 24u + 144) + 288   (using completing the square method)

⇒ Area = -2[tex](u-12)^{2}[/tex] + 288

So the maximum area is 288 sq units as for any value of u the area value will decrease as seen from the above equation.

So if Area = 288

Then yu = 288

⇒ u = 288/y equation 3

Putting this value in Perimeter equation 1 we have,

y = 48 - 2u

⇒ y = 48 - 2 x [tex]\frac{288}{y}[/tex]

⇒ [tex]y^{2} = 48y - 576[/tex]

⇒ [tex]y^{2} - 48y + 576 = 0[/tex]

⇒ [tex](y-24)^{2}[/tex] = 0

Solving we get y = 24 ft

Hence the value of u is calculated as follows:

⇒ u = 288 / y

⇒ u = 288/ 24 = 12 ft

The maximum area that the farmer can enclose is 488 sq ft and the dimensions of the rectangle are 24ft and 12 ft respectively.

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The study of the correlations between triangles' side lengths and angles is known as trigonometry. x= 0.11

The study of the correlations between triangles' side lengths and angles is known as trigonometry. The field was created in Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.

Trigonometry has been used historically in the fields like geodesy, surveying, celestial mechanics, and navigation.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰​

x0.7*0.70*1.73 =1*1-0.5*0.5

x = [tex]\frac{0.7*0.70*1.73}{1*1 - 0.5*0.5}[/tex] = 0.11

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The correct option is- Percent = 75, Amount = 45, Base = 60 for the movement of the progress bar.

For the given question,

The movement of the progress bar could be uneven due to questions can be worth more or less (including zero) due-

The amount of something is stated in terms of a fraction of a hundred. The ratio can be expressed as a fraction of 100.

Base = 60 and the Amount is the 45.

Let the % will be x;

x% of 60 =45

60x =45

x=45/60

x=0.75

To obtain the percentage value, multiply it by 100 as follows:

% x = 0.75 × 100

% x = 75

Thus, the percentage of 60 is 45 will become 75%.

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The equation that can be used to express the relationship between total cost and tickets is t = $2.91n.

The first step is to determine the cost of one ticket. The cost of one ticket can be determined by dividing the total cost of the ticket by the total number of tickets. Division is the operation that is used to determine the quotient of two or more numbers.

Cost of one ticket = $34.92 / 12 = $2.91

The equation that can be used to determine the total cost would have this form:

Total cost = cost per ticket x number of tickets

t = $2.91 x n

t = $2.91n

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Answer:

Hopt: 10 Gesplil; 6

Step-by-step explanation:

The four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.

The parallelogram is divided into two congruent triangles by each diagonal. The total of the squares of a parallelogram's sides equals the sum of the squares of its diagonals. It is also known as parallelogram law.

A parallelogram is a two-dimensional geometrical shape with two parallel sides. It is a four-sided polygon (sometimes known as a quadrilateral) with parallel sides that are equal in length. The sum of a parallelogram's neighboring angles equals 180 degrees.

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Answer:

x = 8.3

Step-by-step explanation:

We look at the final place of the decimal to round, in this case the thousandths place (underlined)

8.27

If the final place of the decimal is greater than or equal to 5, we round up the decimal to the left, otherwise we round down.

Because 7 > 5, round 2 up to 3, therefore giving 8.3

Answer:

Your answer is 8.3!

Step-by-step explanation:

Step 1: Locate and underline the tenths place (2) then look at the digit to the right (7):

8.27

Step 2: In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tenth place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 8.3 as the answer.

In short: 8.27 rounded to the nearest tenth is 8.3.

On simplifying the proportion 18:54:12, we get answer as 3:9:2.

The following are crucial proportional characteristics:

If a: b = c: d, then a + c: b + d. Addendum

A - c: b - d if a: b = c: d. Subtrahendo

Dividendo states that if a: b = c: d, then a- b: b = c- d: d.

If a: b = c: d, then a Plus b: b Equals c+d: d. This is known as combining.

To put it another way, if a: b = c: d, then a: c = b: d.

On simplifying,

18:54:12

Firstly, dividing the all numbers by 3

= 6:18:4

Now dividing by 2

= 3:9:2

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[tex]{\Large \begin{array}{llll} i^4=1 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ -i^{32}\implies -i^{4\cdot 8}\implies -(i^4)^8\implies -(1)^8\implies \text{\LARGE -1}[/tex]

Conversion factor [tex]= \frac{final serving}{initialserving}[/tex][tex]=\frac{5}{2} =2.5[/tex]

The recipe conversion factor is 2.5

Answer:

Ray

Step-by-step explanation:

A ray has a starting point and then continues in one direction.

Answer:

Kirsten owes $3240 more on the car.

Step-by-step explanation:

$3600 - $360 = $3240

Answer:

y=1x-5

Step-by-step explanation:

Use rise/run

Answer:

[tex]y=x-5[/tex]

Step-by-step explanation:

Just look at the slope and the y-intercept.

The y-intercept is b, and it's -5. The slope is 1, so it is x.

Volume of the rectangular prism = 1,728 in³

Volume of the rectangular prism = width × height × length

width = 12 in

length = 18 in

height = 8 in

Volume of the rectangular prism = 12 in × 8 in × 18 in

Volume of the rectangular prism = 1,728 in³

The value of the expression given as (9x-26) (4x+43) (2x-12) is 72x³ + 134x²  -5642x + 13416

From the question, the expression is given as

(9x-26) (4x+43) (2x-12)

Next, we evaluate the expression in pairs

So, we have

(9x-26) (4x+43) (2x-12) = (9x-26) (4x+43) (2x-12)

Evaluate the first two factors

So, we have

(9x-26) (4x+43) (2x-12) = (36x² + 387x - 104x  - 1118) (2x-12)

Evaluate the like terms in the expression

So, we have

(9x-26) (4x+43) (2x-12) = (36x² + 283x  - 1118) (2x-12)

Evaluate the first two factors

So, we have

(9x-26) (4x+43) (2x-12) = (72x³ - 432x² + 566x² - 3396x  - 2246x + 13416)

Evaluate the like terms

So, we have

(9x-26) (4x+43) (2x-12) = (72x³ + 134x²  -5642x + 13416)

Remove the bracket

(9x-26) (4x+43) (2x-12) = 72x³ + 134x²  -5642x + 13416

Hence, the solution is 72x³ + 134x²  -5642x + 13416

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Answer:

3rd answer option (1.6, 1.4)

Step-by-step explanation:

the slope of the lines is different.

to see we transform the equations to the regular slope-intercept form

y = ax + b

with "a" being the slope and "b" being the y-intercept (the y value when x = 0).

1.5x + 0.2y = 2.68

0.2y = -1.5x + 2.68

y = -1.5x/0.2 + 2.68/0.2 = -7.5x + 13.4

1.6x + 0.3y = 2.98

0.3y = -1.6x + 2.98

y = -1.6x/0.3 + 2.98/0.3 = -5.33333...x + 9.93333...

-7.5 is not -5.3333...

so, the lines are not parallel nor overlap at all points.

therefore, they intersect at a point.

(1.6, 1.4) ?

the equations must remain true when using the coordinates :

1.5×1.6 + 0.2×1.4 = 2.68

1.6×1.6 + 0.3×1.4 = 2.98

2.4 + 0.28 = 2.68

2.68 = 2.68 correct

2.56 + 0.42 = 2.98

2.98 = 2.98 correct

yes, they intersect at (1.6, 1.4).

for (3.1, 0.5) already the x coordinate is way too large.

1.5×3.1 or 1.6×3.1 are already by themselves much larger than 2.68 or 2.98.

Explanation:

Let's replace p with something like 0.72

Pick any number between 0 and 1.

This says he has a 72% chance to win

1-p = 1-0.72 = 0.28

and he has a 28% chance of not winning.

For more information, check out "probability complement".

Answer:

8x-40=200

Step-by-step explanation: