PRACTICING SKILLS & CONCEPTS
1. Solve the shape equation puzzle.
+
+
=
= 10
6=
8 =

Step-by-step explanation:

Assume the number of double matches is x (matches)

the number of single matches is y (matches)

(Condition: x > 0 and y > 0)

Because there are 13 matches in progress, so:

x + y = 13 (1)

Because there are 38 people playing (4 people on each double match and 2 people on each single match), so:

4x + 2y = 38 (2)

A system of equation is made by combining (1) and (2):

x + y = 13 (1)

4x + 2y = 38 (2)

Take (2) - 2×(1):

=> 2x = 12

=> x = 6

Substitute the result on (1)

=> y = 7

So there are 6 double matches and 7 single matches being played

Answer:

2/3

Step-by-step explanation:

Compute the slope of the line through the following points:

p_1 = (1, -1) and p_2 = (-8, -7)

The slope of the line through (x_1, y_1) and (x_2, y_2) is:

(y_2 - y_1)/(x_2 - x_1)

Substitute (x_1, y_1) = (1, -1) and (x_2, y_2) = (-8, -7):

= (-7 - -1)/(-8 - 1)

-8 - 1 = -(8 + 1):

= (-7 - -1)/(-(8 + 1))

8 + 1 = 9:

= (-7 - -1)/(-9)

(-1)^2 = 1:

= (-7 + 1)/(-9)

-7 + 1 = -6:

= (-6)/(-9)

The gcd of -6 and -9 is -3, so (-6)/(-9) = (-3×2)/(-3×3) = (-3)/(-3)×2/3 = 2/3:

Answer: = 2/3

The correct option is A which is Yixing should clean out the kennels, and Olivia should move the food bags.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

All the parts will be solved below:-

a. Olivia has an absolute advantage as she takes less time for completing both the tasks

b. Olivia's opportunity cost of cleaning a kennel is

= 6 ÷ 6

= 1 bag of food moved.

c. Olivia's opportunity cost of moving one bag of food is

= 6 ÷ 6

= 1 kennel cleaned

d. Yixing's opportunity cost of cleaning a kennel is

= 10 ÷ 12

= 0.83 bags of food moved.

e. Yixing's opportunity cost of moving one bag of food is

= 12 ÷ 10

= 1.2 kennels cleaned

f. From the above calculations, we can see that the opportunity cost of kennel cleaning would be less sin Yixing so here Yixing should have a comparative advantage and Olivia should have moved the food bags

The complete question is given below:-

Olivia and Yixing are volunteering at a cat rescue shelter. The shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. It takes Olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. It takes Yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food.

A. ____has an absolute advantage in completing both tasks.

B. Olivia's opportunity cost of cleaning a kennel:___bags of food moved.

C. Olivia's opportunity cost of moving one bag of food:_____kennels cleaned.

D. Yixing's opportunity cost of cleaning a kennel:____bags of food moved.

E. Yixing's opportunity cost of moving one bag of food:____kennels cleaned.

F. Yixing says it does not matter which task each of them performs because Olivia is faster at both tasks. Is she correct?

A) No, Yixing should clean out the kennels, and Olivia should move the food bags.

B) No, Olivia should clean out the kennels, and Yixing should move the food bags.

C) Yes, Olivia should do both tasks because she is faster at both.

D) No, Yixing should do both tasks so that she can practice and become more efficient.

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By definition of vertical angles, the value of the variable x behind the geometric system is equal to 12. The measure of the labeled angle is 48°.

The image shows a geometric system generated by two non-parallel lines that intersect each other and consequently two pairs of vertical angles are therefore created. In geometry, two vertical angles are opposite to each other and have the same measure. Then, the following mathematical relationship is found:

4 · x = 48

In addition, we must clear the variable x within the equation:

4 · x = 48                                   Given

x = 48 / 4                                   Compatibility with multiplication / Commutative, associative and modulative properties / Existence of multiplication

x = 12                                         Definition of division / Result

The value of the variable x behind the geometric system is equal to 12.

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By using Pythagorean theorem, the shortest distance between planet Q and planet R is 1.25 × 10⁷ kilometers (12.5 million kilometers).

The picture shows the geometry between three planets, which represents the three vertices of a right triangle, the straight line distance between the points Q and R represents the hypotenuse of the right triangle. The hypotenuse can be found by using the Pythagorean theorem:

QR = √(PQ² + PR²)

Where QR is the hypotenuse of the right triangle, in kilometers.

If we know that PQ = 3.5 × 10⁶ km and PR = 1.2 × 10⁷ km, then the distance between planet Q and planet R is:

QR = √[(3.5 × 10⁶ km)² + (1.2 × 10⁷ km)²]

QR = 1.25 × 10⁷ km

The shortest distance between planet Q and planet R is 1.25 × 10⁷ kilometers (12.5 million kilometers).

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Answer:

answer is ((1 × 2) + 3) × 4 × 5 + 6 - 7 - 8 + 9 = 100

Answer:

27

Step-by-step explanation:

27

Explanation:

"Percent" or "%" means "out of 100" or "per 100", Therefore 18% can be written as  

18 /100 .

When dealing with percentage, the word "of" means "times" or "to multiply".

Finally, lets call the number we are looking for "n".

Putting this altogether we can write this equation and solve for  "n "

while keeping the equation balanced:

n  =  18 /100  ×  150

n  =  2700 /100

n  =  27

27 is 18% of 150

Answer:

second is obtuse angle .

Step-by-step explanation:

5. 160°

6. 120°

[im not sure what they're asking for but if its degree then this is the answer]

The product, in scientific notation, can be rewritten as:

3.4196*10²⁵

We want to find the product between the two numbers:

(4.12*10⁹)*(8.3*10¹⁵)

To take it, we can rewrite the product as:

(4.12*8.3)*(10⁹*10¹⁵)

(34.196)*(10⁹⁺¹⁵)

(34.196)*10²⁴

Now, to get this in scientific notation, we need to have only one digit in the left side of the decimal point, then we can rewrite:

(34.196)*10²⁴ = 3.4196*10²⁵

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The measure of the angles ( 15y - 48 )°, ( 8x - 1 )°, and ( 11x - 25 )° are 165°, 15°, and 63° respectively.

The lines j and k are parallel and lines l and m are parallel.

Consider the figure,

( 8x - 1 )° ≅ 1, corresponding angles

1 ≅ 9, corresponding angles

9 ≅ ( 11x - 25 )°, vertical angles

Therefore,

m∠ 1 = m∠ 9

m∠9 = ( 8x - 1 )°

So,

( 8x - 1 )° = ( 11x - 25 )°

Subtracting 8x from both sides of the equation.

11x - 25 - 8x = 8x - 1 - 8x

3x - 25 = - 1

Adding 25 on both sides of the equation.

3x - 25 + 25 = - 1 + 25

3x = 24

Dividing each side of the equation by 3

( 3x/3 ) = ( 24/3 )

x = 8

Now, the angle made by a straight line is 180°.

Therefore,

( 8x - 1 )° + ( 15y  - 48 )° = 180°

( 8 × 8 - 1 )° + ( 15y - 48 )° = 180°

15° + 15y - 48° = 180°

15y - 33° = 180°

Adding each side of the equation by 33°.

15y - 33° + 33° = 180° + 33°

15y = 213°

Dividing each side of the equation by 15

( 15y/15 ) = ( 213/15 )°

y = 14.2°

So, the measure of the angles are:

( 15y  - 48 )° = ( 15 × 14.2 - 48 )° = ( 213 - 48 )° = 165°

( 8x - 1 )° = ( 8 × 8 - 1 )° = 15°

( 11x - 25 )° = ( 11 × 8 - 25 )° = ( 88 - 25 )° = 63°

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Answer: Height = 5m

Step-by-step explanation: To solve the height of the triangle we can use the Area formula and substitute the values given to solve for heigh.

A = ( b * h ) / 2

17.5 = (7 * h) / 2

17.5 (*2) = 7 * h

(Remember that everything done to one side has to be done to both. We can multiply by 2 on both sides to eliminate the 2.)

35 = 7 * h

35/7 = h

5 = h

The height of the triangle equals 5.

The value of j from the equation h-10/j=k is equal to 10/(h-k).

Given that the equation is h-10/j=k.

We are required to find the value of j from the given equation.

Equation is a relationship between two or more variables that are expressed in equal to form. It may be a linear equation,quadratic equation, cubic equation and many more depending on the power of the variables present in that equation.

The equation is h-10/j=k.

-10/j=k-h

1/j=(k-h)/-10

j=-10/(k-h)

j=10/(h-k)  

(We can eliminate the negative sign by taking negative out from the denominator.)

Hence the value of j from the equation h-10/j=k is equal to 10/(h-k).

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The coffee reaches t ≈ 12 minutes a temperature of 150◦F.

(t) = Ts + (T0 - Ts)e-kt, according to Newton's Law of Cooling.

T(t) = temperature of the coffee cup t minutes after being placed in the roomTs is the ambient temperature.T0 indicates the coffee cup's beginning temperature.

(a).  Using the given information, we have T(t) = 70 + (160 - 70)e-kt

= 70 + 90e-kt

T(5) = 70 + 90e-k(5) = 112.5

So, 90e-5k = 42.5

e-5k = 0.47222222

-5k = ln(0.47222222)

 k = 0.15      Temperature after 10 minutes = T(10) = 70 + 90e-0.15(10)

 ≈ 90.1

-------------------------------------------------------------------------------------

(b). When will the temperature of the coffee reach 85°?

     Find t so that T(t) = 85:   70 + 90e-0.15t = 85

90e-0.15t = 15

e-0.15t = 0.16666666

-0.15t = ln(0.166666666)      

t ≈ 12 minutes

According to Newton's law of cooling, a body's rate of heat loss is inversely related to the temperature difference between it and its surroundings. The law is frequently qualified to state that the tiny temperature differential and the consistency of the heat transmission mechanism must exist. As a result, it is the same as asserting that the heat transfer coefficient, which mediates between heat losses and temperature variations, is constant. Due to the fact that the thermal conductivity of the majority of materials very slightly depends on temperature, this requirement is typically satisfied in heat conduction (where it is guaranteed by Fourier's law). Newton's Law is applied in convective heat transfer for forced air or pumped fluid cooling.

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It depend on the repeating part.

If x = 0.393939… (the repeating part is underlined), then 100x = 39.393939…, and

100x - x = 39.393939… - 0.393939…

99x = 39

x = 39/99 = 13/33

On the other hand, if you mean x = 0.3999…, then 10x = 3.999… and 100x = 39.999…, so that

100x - 10x = 39.999… - 3.999…

90x = 36

x = 36/90 = 2/5

Using a linear function, it is found that:

A linear function is modeled by the following rule:

y = mx + b

In which:

From the table, we have that:

Hence, we have that when x = 0, y = 45, meaning that:

The y-intercept is of 45.

When x increases by 5, y decays by 8, hence the slope is given as follows:

m = -8/5 = -1.6.

Then the function is:

y = -1.6x + 45.

The x-intercept is found as follows:

-1.6x + 45 = 0

1.6x = 45

x = 45/1.6

x = 28.125.

The x-intercept is of 28.125.

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The fastest vehicle is: the all terrain that can travel at a speed of 72 mi/h

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the velocity of the all terrain vehicle we get:

v(all terrain vehicle) =  6 * 12mi/h

v(all terrain vehicle) =  72 mi/h

By ordering the velocities from highest to lowest we have:

(all terrain vehicle)72 mi/h >(go kart)67 mi/h >(scooter)12mi/h

Due to the all terrain vehicle has the highest velocity it is the faster vehicle.

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

Step-by-step explanation:

Comment

2 angles are complementary means together they = 90 Degrees.

Let the smaller angle be x

The complement = 3*x - 14  It is the larger angle.

Givens

<1 = x

<2 = 3x - 14

<1 + <2 = 90

Solution

x + 3x -14 = 90              Combine the left

4x - 14 = 90                  Add 14 to both sides

4x - 14+14 = 90 + 14     Combine

4x = 104                       Divide both sides by 4

4x/4 = 104/4

x = 26

Answer

<1 = 26

<2 = 3*26 - 14

<2 = 78 - 14

<2 = 64

Answer:

.549 (all under bar/repeted)

Step-by-step explanation:

Answer:

Randall and the most money. she earned 50 cents more than Stephano did.

Step-by-step explanation:

so it's Randall makes $27.50 on his first day and $25 on a second date and and 32.50 on his third day you would add those up to get $85 in all. now Stefano gets 7.50 22.50 12.50 15.00 and 17.00 dollars , and when you add all those together he gets 84.50 and all. meaning that random made more money by .50 cents.

number = x

2/3x + 18 = 23

2/3x = 5

x = 15/2 = 7.5

An unreliable study can occur if the test administration is inconsistent

Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.

Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.

For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.

Therefore, a proper set schedule must be followed for the tests with consistency.

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Answer:

2(x+y)=98 is the answer.

Answer:

-4-9=-13

Step-by-step explanation:

The dimensions of expensive television is 32 inches through 64 inches.

This trouble may be solved if we understand the idea of fraction and a way to calculate the part of a fragment.

right here it is for the reason that the inexpensive tv is 12 inches by means of 24 inches.

Also it is given that the expensive television is [tex]\frac{8}{3}[/tex] of the cheaper one.

Now taking the length into consideration the length of the television is

  =[tex]\frac{8}{3}*12[/tex]

  = 32 inches

Now taking the width into consideration the width of the television is

 =[tex]\frac{8}{3}*24[/tex]

 = 64 inches

So, the dimension of the expensive television is 32 inches by 64 inches.

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Both cyclist are moving apart at a speed of 9.434 mi/hr.

Velocity is the direction at which an item is moving and serves as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a basic idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system).

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Answer:

-11x + 30

Step-by-step explanation:

distribute the 5 into the parenthesis

= 4x -15x + 30

combine like terms

= -11x + 30

Answer:

-11x + 30

Step-by-step explanation:

4x + 5(-3x + 6)  Distribute the 5

4x + (5)-3x + (5)6

4x -15x + 30 Combine the x's

-11x + 30

Answer: 24

Step-by-step explanation: first we can rewrite the expression as 170%*x=40.8 (x is your answer). By solving and simplifying it, you should get 24.

Answer:

EQ = 47

Step-by-step explanation:

Since Q is midpoint, EQ = QF

or EQ = EF/2

5x + 2 = (9x + 13)/2

10x + 4 = 9x + 13

10x - 9x = 13 - 4

x = 9

EQ = 5x + 2 = 5(9) + 2 = 45 + 2 = 47