6. Critical Thinking
Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the
point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.

The inequality will be written as 40x + 20 < 280.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that a group of friends wants to go to the amusement park. They have no more than $280 to spend on parking and admission. Parking is $20, and tickets cost $40 per person, including tax.

The inequality will be written as:-

40x + 20 < 280.

Here, x is the number of persons.

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Answer:

20

Step-by-step explanation:

I took the test and passed I hope this helps.

The ordering of the weight from the least to greatest will be 1 1/8, 1.6, 1.625 and 1 5/6.

From the information, Orlando uses 1 5/6 pounds of cashews, 1.6 pounds of sunflower seeds, 1 1/8 pounds of raisins, and 1.625 pounds of pecans..

It should be noted that 1 5/6 will be 1.833.

It should be noted that 1 1/8 will be 1.125

Therefore, it van be seen that the least of the pounds of raisins and the greatest is pounds of cashew.

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Answer:

a percent greater than 100 could be 150%.

Lets say part is 15

15 is 150% of what?

is/of=%/100

fill in that and cross multiply to find "of"

15/x=150/100

x should equal 10.

I'm not sure exactly what your asking but if you are supposed to just make up numbers?  And solve for it?  That should be what you're looking for. Good luck I guess!

Step-by-step explanation:

y =3x^2+2

In the function notation we write f(x) instead of y.

So, for this case:

f(x)=3x^2+2

The equation of line perpendicular to the given line is 5x - y = - 18 OR y = 5x + 18

Given: The line y = 5x + 6 and it passes through the point ( -3, 3)

And we know the general equation of line is y = mx+c

On comparing the above mentioned two equations we get;

m = 5 that is slope is 5.

Also to find a equation of line perpendicular to the given line

we know the general equation

that is y - y₁ = m ( x - x₁ )

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

y - 3 = 5 ( x + 3 )

On further calculating we get

y - 3 = 5x + 15

5x - y = - 18 Or y = 5x + 18

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Answer: -3

Step-by-step explanation:

The slope can be calculated by the equation

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

So choosing any two points, we can find the slope.

I'll chose (0,3) and (2,-3).

-3 - 3 = -6

2 - 0 = 2

So, the slope is -6/2 which simplifies to -3.

The perimeter of a square having area of 36[tex]cm^{2}[/tex] is equal to 24cm

Square of area A= 36[tex]cm^{2}[/tex]

We know that a square is a quadrilateral( a closed figure with four sides) with all 4 sides equal in length. Let the measure of one side of a square be x. from the formula to find out the area of a square we know that

Area of a square A = [tex]x^{2}[/tex]

∴From the data given in the problem

[tex]x^{2}[/tex] = 36

⇒x = √36

⇒x = 6

∴The measure of one side of a square = x cm = 6 cm

We know that the perimeter of a square = x+x+x+x = 4x

∴The perimeter of the given square = 4x = 4 × 6 = 24cm

Hence we get by solving as done above that for a square of area 36cm^2

the perimeter of the square is 24cm

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The two figures are not the same size because 6/3 twice less than 8/4.

A scale factor is defined as the factor that shows how much a figure is greater or smaller than the original size that it's been compared to.

From the square diagram that is given the smaller square is double the larger square.

This can be calculated by dividing the bigger sides by the smaller sides.

That is ;

6/3 =2

8/4 = 2

It can therefore be concluded that the two square shapes are not of the same size as the smaller square is two time smaller that the bigger square.

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To find the set of a quadratic inequation, we first need to find the roots of the quatradic equation. The roots can be found by using the same inequality but changing the inequality sign the euqal sign:

Let's use the Bharkara Equation to find the roots:

So we get the roots x = 3 and x = -5. This are the point at which the graph changes its sign.

The quadratic term (the one multiplying x²) is 1, which is positive. Because of that, the parabola of the quadratic expression has a minimum vertex:

For the drawing, it can be seen that when x is between -5 and 3, the equation has a negative sign, while when x is lower than -5 or greater than 3 the expression has positive sign. We want the expression:

So, when it is greater than 0, meaning positive. Then, the set that solves the quadratic inequation is:

Explanation:

Think of a set of dominoes. If domino A pushes over B, which pushes over C, then ultimately A caused C to fall over. So that's how we combine both A=B and B=C to end up with A = C.

You could also think of it using this kind of arrow notation

[tex]\text{If }A \to B \text{ and } B \to C, \ \text{then }A \to C[/tex]

Or you can think of it like going from city A to city B, then to city C. Ultimately you have gone from city A to city C.

The required equation that is perpendicular to the line y = -¾ x - 14 and goes through the point (0, 13) is 3x + 4y = 52 .

Given equation is y = - 3/4 - 14

this is of the form y = mx + c

on comparing, m= - 3/4

And the points given are x = 0 and y =13

thus as we know that the equation of the line is

y - y₁ = m ( x- x₁ )

On substituting the values mentioned above we see that

y - 13 = - 3/ 4 ( x - 0 )

4 y - 52 = - 3 x

and on rearranging we get :

3x + 4y = 52

Thus the required equation that is perpendicular to the line y = -¾ x - 14 and goes through the point (0, 13) is 3x + 4y = 52 .

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Answer:

there are 60 slices of ham

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

34-15 goes into paratheses because it goes first.

Then multiply by 4.

(34 - 15) x 4

Hope this helps!

If you get this right, giving me brainliest would mean a lot! Thanks!

Answer:

The feasible region is bounded by the corner points:

Step-by-step explanation:

Given constraints:

[tex]\begin{cases}x \geq 0\\y \geq 0\\4x+2y \leq 40\\2x+4y \leq 32\end{cases}[/tex]

Rewrite the third and fourth inequalities to isolate y:

[tex]\begin{aligned}\implies 4x+2y & \leq 40\\2y & \leq -4x+40\\y & \leq -2x+20\end{aligned}[/tex]

[tex]\begin{aligned}\implies 2x+4y & \leq 32\\4y & \leq -2x+32\\y & \leq -\dfrac{1}{2}x+8\end{aligned}[/tex]

When graphing inequalities:

Therefore:

The feasible region is the set of all possible values of the variables which satisfy the constraints.  

Therefore, the feasible region is bounded by the corner points:

Answer:

2,3,5

Step-by-step explanation:

First, 10^3 is 1000 and 3.6 x 1000 = 3600.

So, the factors of 3600 are 2,3,5

Through this photo if this helps:

3.6 x 10³ as a product of the powers of its prime factors is

[tex]2^4[/tex] x 3² x 5²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3.6 x 10³

This can be written as,

= 3.6 x 1000

= 36/10 x 1000

= 3600

Now,

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

2, 3, and 5 are prime numbers.

This means,

[tex]2^4[/tex] x 3² x 5²

Thus,

The powers of prime factors are

[tex]2^4[/tex] x 3² x 5²

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The ratio of pens Meredith has to ratio of pens Brody has is 2 : 1

The of pencils Meredith has to ratio of pencils Brody has is 1 : 2

Ratio refers to the number representing a comparison between two named quantities.

Comparison of their ratios of pens to pencils:

Ratio of pens Meredith has to ratio of pens Brody has = 8 pens : 4 pens

= 8 / 4

= 2 / 1

= 2 : 1

Ratio of pencils Meredith has to ratio of pencils Brody has = 9 pencils : 9 pencils

= 1 / 1

= 1 : 1

So therefore, their ratio of pens is 2 : 1 and their ratio of pencils is 1 : 1

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Answer:

c = 6

Step-by-step explanation:

7c + 12 = -4c + 78

subtract 12 from both sides:

7c + 12 - 12 = -4c + 78 - 12

7c = -4c + 66

add 4c to both sides:

7c+  4c = -4c + 66 + 4c

11c = 66

divide both sides by 11:

11c/11 = 66/11

c = 6

Some of the math sums in which the result is under 13 are (5+2), (6+3), (7+5), etc.

According to the question,

We have the following information:

Math sums under 13

Now, we have to find mathematical expressions involving addition but the condition is that the result should be under 13.

Now, we know that we can have 2 or more than 2 numbers in sums but to make it easy we will have only two numbers.

Now, we will take some first numbers in some math sums to be 5, 6 and 7.

Now, the second digit can be found easily by subtracting the numbers from 13.

So, the digits should be less than the result we get.

13-5 = 8

So, it can be less than 8.

13-6 = 7

So, it can be less than 7.

In this way, we can take any digit less than these numbers.

Hence, some of the math sums in which the result is under 13 are (5+2), (6+3), (7+5), etc.

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Ana is traveling North America, she can exchange for 150 Canadian dollars, 2500 pesos.

Canada's official currency is the Canadian dollar. There is no standard disambiguating form, nevertheless, prominent style guides frequently recommend abbreviation Can$ to distinguish it from other dollar-denominated currencies. It is abbreviated with dollar sign $. There are 100 cents (¢) in it.

Due to the common loon depicted on its reverse, the dollar coin and occasionally the money itself are referred to as "loonies" by English-speaking Canadians, currency dealers, and analysts.

The Canadian dollar ranks behind the U.S. dollar, the euro, the yen, and sterling as the fifth most widely held reserve currency in the world, making up around 2% of all reserves. Because of Canada's relatively stable economy, strong sovereign position, and stability of its judicial and political systems, the Canadian dollar is favored by central banks.

5 pesos = 0.3 Canadian dollars

5\0.3 pesos = 1 Canadian dollars

[tex]150 Canadian dollars= \frac{5}{0.3} * 150 pesos = 2500 pesos[/tex]

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[tex]=\sqrt{10*8} \\=\sqrt{80} \\=\sqrt{16*5} \\=\sqrt{16} *\sqrt{5} \\=4\sqrt{5}[/tex]

⇒The SECOND option is The BEST answer .

Δ...BUT also the THIRD OPTION CAN be the answer but it is not simplified completely. IT IS SAFE TO CHOOSE THE SECOND OPTION because it is completely simplified.

Answer:

168=18·x+12·2x

Step-by-step explanation:

try and split the shape into 2 rectangles to picture it .

There are 32 natural numbers less than 200 that are divisible by 4 but not 3.

Natural numbers are those positive numbers which start from one and goes to infinity.

Here, we have to find the natural numbers divisible by 4 but they should not be divisible by 3.

First, we will find all the natural numbers that are less than 200 and divisble by 4.

We will find all those numbers which can be divided by 4 starting from 4 till 200.

Such numbers ae 4,8,12,16,20,24,28,32,36,40,44,48,52,54,56,60,64,68,72,76,80,84,88,92,94,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,154,156,160,164, 168, 172,176,180,184,188,192,194,196, 200

There are total 50 numbers which are divisible by 4 which are less than 200

Now we will find among these which are divisible by 3

We will find all those numbers which are divisible by 3 starting from 4 till 200 because 4 is the first number which is divisible by 4.

These are 12,24,36,48,54,60,72,84,96,108,120,124,132,144,156,168,180,192

These are in total 18

Now, we will subtract them

Answer is 50-18 = 32

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By solving the system of equations, and seeing in which quadrant is each solution, we conclude that:

Here we get the following system of equations:

x^2 - y = 7

y - 5x = -11

If we isolate the same variable in both of the equations, then we can equate them, so I will isolate "y" in both of the equations of the system.

y = x^2 - 7

y = -11 + 5x

Now we can write:

x^2 - 7 = -11 + 5x

So we have the quadratic equation, this can be rewritten as:

x^2 - 7 + 11 - 5x = 0

x^2 - 5x + 4 = 0

Using the Baskhara's formula (or the quadratic formula), we will get the two solutions for x.

[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*(4)} }{2*1}[/tex]

The solutions are:

[tex]x = \frac{5 \pm \sqrt{(9} }{2} \\\\x = \frac{5 \pm 3}{2}[/tex]

So we get:

x = (5 + 3)/2 = 4

x = (5 - 3)/2 = 1

Evaluating the linear equation in these values of x:

y = -11 + 5*4 = -11 + 20 = 9

y = -11 + 5*1 = -6

So we get the coordinate pairs (4, 9) which is on the first quadrant because both values are positive, and (1, -6) which is on the fourth quadrant because the x-value is positive and the y-value is negative.

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1) Let's find the slope plugging those points into that formula:

Since we have a linear equation, with its linear coefficient "b" = 0, then we can write this function as y=15x

m=15

So the money earned increases by $ 15 for each hour worked

Total change to Dracula account balance will be the account balance is $40.

What is mean by subtraction?

The operation of taking the difference of two number is called Subtraction.

Given that;

Dracula made a deposit of $220 into his checking account.

Dracula made two withdrawals of $80 each.

Now, Total change to his account after transaction will be calculated as;

Total amount in Dracula account = $220

And, Total withdrawals amount = 2 x $80

                                                = $160

Thus, Money in account after transaction = $220 - $160

                                                               = $40

Therefore, Total change to Dracula account balance will be the account balance is $40.

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According to the solution of the fractions. Hiroko cuts her string into 6 equal-size pieces.

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces.​The numerator and denominator of positive common fractions are both natural integers. The denominator shows how many of the numerator's equal parts make up a unit or whole, while the numerator reflects the number of equal parts.

When a fraction is divided, it reciprocated i.e, denominator and numerator change their places. So, in given fraction-

4÷4/6=4×6/4

     =6

Therefore, Hiroko cuts her string into 6 equal pieces.

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Answer: Volume = 192

Step-by-step explanation:

Volume of Rectangular Prism = Length x Width x Height

Volume = 8x3x8

Volume = 192

Using the concept of unit rate we calculate the cost of mowing 6 laws as $150 .

Rates and ratios frequently vary with regard to time, geography, a particular object (or group of objects), etc. They are typically mathematical functions as a result.

The charge to mow one lawn is $25 . This is the unite rate of the lawn.

Therefore the charge for 6 lawns is  = $25 × 6 = $150

Hence the cost to mow 5 lawns is $150.

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Answer:

77.2

Step-by-step explanation: