A student is about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. He can do a
computation problem in 2 minutes and a word problem in 5 minutes. He has 35 minutes to take the test and may answer no more than 10 problems.
Assuming he correctly answers all the problems attempted, how many of each type of problem must he answer to maximize his score? What is the
maximum score?

Isolating x in the second equation, the expression that would be replaced into the first equation to solve the system of equations is given as follows:

b. -3y + 12.

The system of equations for this problem, with variables x and y, is defined as follows:

The second equation of the system is given as follows:

-x - 3y = -12.

The first step to isolate x is move the -3y term to the opposite side of the equality, with an addition symbol, which is the inverse of the negative symbol, hence:

-x = 3y - 12.

As the leading coefficient of x is negative, the entire expression must be multiplied by -1, hence:

x = 12 - 3y.

x = -3y + 12(commutative property).

Meaning that the correct option is given by option b.

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Answer: (b) -3y + 12.

To use the Substitution Method, we would isolate x in the second equation, which gives:

-x = 3y - 12

Multiplying both sides by -1, we get:

x = -3y + 12

We can then substitute this expression for x into the first equation, which gives:

2(-3y + 12) + y = 8

Simplifying this expression, we get:

-5y + 24 = 8

Subtracting 24 from both sides, we get:

-5y = -16

Finally, dividing both sides by -5, we get:

y = 16/5

Therefore, if we isolate x in the second equation, we would substitute x = -3y + 12 into the first equation.

So the expression we would substitute into the first equation is -3y + 12.

Answer:

£145

Step-by-step explanation:

£101.5 divided by 7 gives you £14.5 per each dress then times the £14.5 by 10 and that will give you in total £145 for 10 dresses

The value of 2 ½ is 2.5. As 2 ½ is the same as mixed fraction 2 ½ = 5/2.

2 ½ is a mixed number, it is a whole number combined with a fraction. In this case, 2 is the whole number and ½ is the fraction. The value of 2 ½ is calculated by adding the value of the whole number to the value of the fraction.

The value of the whole number 2 is 2, and the value of the fraction ½ is 0.5. To find the value of 2 ½, we add 2 to 0.5:

2 + 0.5 = 2.5

So, the value of 2 ½ is 2.5.

It's important to note that mixed numbers are used to represent numbers that are between two whole numbers, they consist of a whole number and a proper fraction. This mixed number representation is commonly used in everyday life, and it's easy to understand.

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Answer: The equation is false.

Step-by-step explanation:

2x+3-x-(-1) = 2x-2-x

2x+3-x+1=2x-2-x

x+4=x-2

4 ≠ -2

Answer:

A. 27

Step-by-step explanation:

mG=(180-126)/2=27

(c+1) (c-7) = cc - 7c + c - 7 = c^2 - 7c - 7

So the simplified form of (c+1) (c-7) is c^2 - 7c - 7

Answer:

[tex]c^2-6c-7[/tex]

Step-by-step explanation:

[tex](c+1) (c-7)[/tex]

Apply the FOIL mothed.

[tex]cc+c\left(-7\right)+1\cdot \:c+1\cdot \left(-7\right)[/tex]

[tex]c^2-6c-7[/tex]

Both Aiden's and Natalie's tennis balls can cover the same distance of the catapult length is 40.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

Given:

As, we know the linear intercept form,

y = mx + b

Where m is the rate of change (slope) and b is the initial value of y.

Now, From the graph of both Aiden's and Natalie's data, we can see that the point of intersection is at (-40, 90).

Also, which shows x axis at 40 is the distance.

So, Both of them Aiden's and Natalie's tennis balls can cover the length of 40.

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The ordered pair that is the solution to the linear functions graphed is (b) (5, 25)

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

The lines on the graph

Next, we interpret the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (5, 25)

Hence, the solution is (5, 25)

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The scale factor of two similar circles is equal to the ratio of their radii.

This can be expressed mathematically as a fraction, where the numerator is the radius of the larger circle, and the denominator is the radius of the smaller circle. For example, if the radii of the two circles are 3 cm and 6 cm, then the scale factor is 3/6 or 1/2. To find the scale factor, divide the radius of the larger circle by the radius of the smaller circle. For example, if the radii of the two circles are 10 cm and 4 cm, then the scale factor is 10/4, or 5/2.

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Answer:

B) y = -2/3x -2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (-3,0) (0, -2); we see the y decrease by 2 and the x increase by 3, so the slope is

m = -2/3 = -2/3

The Y-intercept is located at (0, -2)

So, our answer is B) y = -2/3x -2

2.26 pounds equal one kilo of mass and hence, 121 pounds divided by 2.26 equals 53.09 kilograms.

Kg, the metric system's fundamental unit of mass The mass of 1,000 cubic centimeters of water is quite close to one kilogram; originally, it was supposed to be exactly equal. According to definitions, a pound is exactly equivalent to 0.45359237 kg. The kilogram (abbreviated "kg") is the SI Base Unit for calculating mass. One gram (g) is produced when you divide one kilogram by 1000, and one metric ton is produced when you multiply one kilogram by 1000. Consequently, 1000 grams equals 1 kilogram, and 1000 kilograms equal 1 ton.

given

kilogram (kg) weighs 2.2 times more than a pound (represented as lbs).

As a result, 2.26 pounds equal one kilo of mass.

hence, 121 pounds divided by 2.26 equals 53.09 kilograms.

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Answer:

67

Step-by-step explanation:

.__. that it

Answer:

32768

Step-by-step explanation:

8^6 ÷ 8

8^6= 262144

262144 ÷ 8 = 32768

32768

Hope this helps.

Answer:

I think it is 7 as well

Step-by-step explanation:

They look equal and they both have the same degree of angle. I hope this helps!

Therefore , the solution of the given problem of table comes out to be the simplest table is of 1,2,3,4,5,6,7,8,9 and 10.

A statistic list is a group of figures that displays the results of a calculation with several inputs. Data is organized in rows and columns and is composed of descriptions and numbers. It is simple to remember the table and the pattern of 10. The numerals are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50, in that order. Value mapping is a technique for displaying the relationships between various data elements. The values table can be useful in any science class.

Here,

The simple table is easy to remember and

the most simple table is of 1

=>1,2,3,4,5,6,7,8,9 and 10

Therefore , the solution of the given problem of table comes out to be the simplest table is of 1,2,3,4,5,6,7,8,9 and 10.

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Based on the attached boxplot, approximate percentage of the people who entered the amusement park met the height requirement for the attraction is 50%.

A boxplot is a way to present a five number summary in a box chart. The main part of the box shows where the middle portion of the data, the interquartile range. At the ends of the box, we will find the first quartile (Q1 or the 25% mark) and the third quartile (Q3 or the 75% mark). The bottom of the box is the minimum (the smallest number in the set) and the top of the box is the maximum (the largest number in the set). And, the median is represented by a line in the center of the box.

From the boxplot can be seen that:

Minimum = 43

Maximum = 64

Q1 (first quartile) = 46

Q3 (third quartile) = 58

Median = 48

In the passage, given that a person must be at least 48 inches tall to ride the attraction. So, this is the same number as median value, that is 48. Thus, 50% the amusement visitors are eligible for the requirement, and the 50% others are not.

Hence, the percentage of the people who entered the amusement park met the height requirement for the attraction is 50%.

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The price charged depends on the size of the window.

Option (B) is correct.

What is a direct proportion?

Direct proportion is a relationship between two variables, where the ratio of their values is always constant. This means that if one variable increases, the other variable will also increase in the same ratio.

B) The price charged depends on the size of the window.

The statement that is true is that the price charged by David for cleaning windows depends on the size of the windows. It means that the larger the window, the more David charges for cleaning it. The size of the window is a factor in determining the price and not the other way around.

Hence, the correct statement would be "The price charged depends on the size of the window.".

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Answer:

A

Step-by-step explanation:

(x-5)^2 = 3

Take the square root of both sides

You are now left with: x-5 = sqrt(3)

Add 5 to both sides

x= 5 + or - sqrt(3)

Answer: A

Step-by-step explanation:

(x - 5)^2 = 3

take square root of both sides

(x - 5) = +-sqrt 3

you can remove the parentheses

x - 5 = +-sqrt 3

isolate the x variable

x = +-sqrt 3 + 5

The factor of xy 3y − 7x − 21 is x − 3.

xy 3y − 7x − 21 = x(y 3y − 7) − 21 = x(y 3y − 7) − 3(7) = (x − 3)(y 3y − 7)

The expression xy 3y − 7x − 21 can be simplified by factoring out the greatest common factor, which in this case is x. We can factor out an x by dividing the entire expression by x. This gives us y 3y − 7 − 21/x. Now, we can look for a common factor between the two terms. In this case, the factor is -3. We can factor out -3 from both terms to get -3/x and y 3y − 7. This can be rewritten as (x − 3)(y 3y − 7). Therefore, the factor of xy 3y − 7x − 21 is x − 3.

To explain further, factoring is the process of breaking down an expression into its factors. A factor is a number, variable, or expression that can be multiplied to produce the original expression. In this case, we are looking for the factors of xy 3y − 7x − 21. To find these factors, we first simplify the expression by factoring out the greatest common factor, which in this case is x. We then look for a common factor between the two terms, which is -3. We factor out -3 and rewrite the expression as  

(x − 3)(y 3y − 7). This means that the factor of xy 3y − 7x − 21 is x − 3.

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[tex]2v+8v-5v[/tex]

Combine Like Terms:

[tex](2v+8v-5v)[/tex]

[tex]\fbox{5v}[/tex]

The area of the region is between the upper and lower sums, which are 0.5625 and 0.5.

To use upper and lower sums to approximate the area of a region, we need to first divide the region into subintervals of equal width. Once we have the subintervals, we can then use the function values at the upper and lower bounds of each subinterval to calculate the upper and lower sums.

width = (b - a) / n, where a and b are the lower and upper bounds of the region, and n is the number of subintervals.

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i think its 4 x =2x +1

The correct option c. 5/7. The value of cos L is found to be 5 /7.

For the stated right angles triangle:

Cos L = base / hypotenuses

Cos L = 10 / 14

Cos L = 5/7

Thus, the value of cos L is found to be 5/7.

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The factor of 2 is 1 and 2.

What is a factor?

In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.

Factors are also known as divisors. This means they can divide evenly into the number they're a factor of.

Here,

We have to find the possible factors of 2.

We concluded that the factor of 2 is 1 and itself.

Factors of 2 are all the numbers which on multiplying give the result of 2. Factors of 2 are 1 and 2 only.

Hence, the factor of 2 is 1 and 2.

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Answer: r = -3, t = -4

Step-by-step explanation:

6r-6t=6

3r-6t=15

Using the elimination method, you can get

3r=-9

r=-3

Substitute -3 for r, and you get

-9-6t=15

-6t=24

t=-4

r=-3,t=-4

Answer:

r,t=-3,-4

Step-by-step explanation:

[1]    6r - 6t = 6

  [2]    3r - 6t = 15

C. the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible.An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible.

An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible. This means that there may be more than one combination of decision variables that will maximize or minimize the objective, and there may not be exactly one solution that will result in the maximum or minimum objective value.

An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible. This means that the problem has no finite upper or lower limit and is not subject to any specific constraints. As a result, there may be more than one combination of decision variables that will maximize or minimize the objective. In addition, there may not be exactly one solution that will result in the maximum or minimum objective value, as the solution set can be infinite. Thus, it is important to keep in mind that an unbounded problem has no specific solution and that different combinations of decision variables can result in the same objective value.

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The y10 is a linear function, which is a type of function that follows a straight line when graphed.

Linear functions are often written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

The equation y 10 is a linear function with a slope of 0, meaning that the line does not move up or down and a y-intercept of 10, meaning that the line passes through the point (0, 10).

The function y 10 is a mathematical expression that can be used to solve certain equations. It is a linear equation, which means that it follows the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

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A table of equivalent ratios for the number of customers and minutes for customers that entered the store are as follows:

Customers            Hours

1                                4

12                              6

10                              40

In order to have a proportional relationship and equivalent ratios, the number of customers (x) and the number of minutes (y) must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/3

Constant of proportionality (k) = 4.

When minutes y = 4, the number of customers (x) is given by:

x = y/k

x = 4/4

x = 1.

When the number of customers (x) = 10, the number of minutes (y) is given by:

y = kx

y = 4(10)

y = 40.

Next, we would use an online graphing calculator to plot the points on a coordinate axes as shown in the image attached below.

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Therefore , the solution to the given problem of volume comes out to be Volume of the prism =  15x^7 cube unit.

The term "volume" describes the amount of muti space that a thing takes up. Volume, in contrast to mass, varies with the environment. The term "density" describes the mass that a material has in a specific volume. It explains how mass and volume are related.

Here,

Given: The rectangular prism must have a 4.5 inch width.

As follows are the terms for the rectangular prism's volume:

V = l*w*h

where the prism's dimensions are l for length, w for width, and h for height.

Volume of prism equals 5x3 * 3x2 * x2,

or 15x7.

Therefore , the solution to the given problem of volume comes out to be Volume of the prism =  15x^7 cube unit.

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