Word Problems
1) Sandy has 22 books in her library. She bought several books at a yard
over the weekend. She now has 61 books in her library. How many be
did she buy at the yard sale?
) How many ink cartridges can you buy with 143 dollars if
one cartridge costs 11 dollars ?
) Melanie is baking a cake. The recipe calls for 6 cups of flour. She alre
4 cups. How many more cups does she need to add ?

The equation that will make a system with infinite solutions is the third option.

y = 2x + 6

A system of linear equations will have infinite solutions only if the two equations represent the same line.

Here we know that one of the linear equations of the system is:

2y - 4x = 12

If we now divide the whole equation by 2, we will get:

(2y - 4x)/2 = 12/2

y - 2x = 6

Now we can move the "2x" term to the right side, then we will get.

y = 2x + 6

So the equations:

y = 2x + 6

2y - 4x = 12

Represent the same line, then that system will have infinite solutions.

Finally, the correct option is the third one.

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Slope Sales will be $-159.474 at 0 degrees Celsius, which is nonsensical to understand.

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

given information,

Temperature=20 egression equation,

[tex]sales= 442.284\\ Slope=$ 30.0879[/tex]

temperature increases by 1 degree

$30.0879, on average.

[tex]y-intercept= -159.474[/tex]

At 0 degree celsius of temperature, Sales will be [tex]$-159.474[/tex]which is meaningless to interpret.

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Autumn and Terry can talk because the distance between them is 2 miles

Polly and terry can not talk because the distance between them is 2.27 miles.

Polly and Autumn's distance can talk because the distance between them is 1.56 miles.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Autumn and Terry distance = 2 mile

Polly and Autumn's distance = x miles

Polly and terry's distance = y miles

Now,

Applying the Sin rule of a triangle.

2 / sin 59° = x / sin 42° = y / sin 79°

2 / 0.86 = x / 0.67 = y / 0.98

Find x.

2 / 0.86 = x / 0.67

x = 1.56

Find y.

2/0.86 = y / 0.98

y = 2.27

Now,

Polly and Autumn's distance is 1.56 miles.

This means they can talk.

Polly and terry's distance is 2.27 miles.

This means they can not talk.

Thus,

Polly and Autumn can talk.

Polly and terry can not talk.

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The value of h is 6.

Now, According to the question:

In right triangle, ABC

Given data:

AD = 12 and DB = 3

The equivalent ratio of the triangles is:

h : 12 = 3 : h

Express as fractions

[tex]\frac{h}{12} =\frac{3}{h}[/tex]

Cross Multiply:

[tex]h^2[/tex] = 36

Take positive square roots of both sides

h = 6

Hence, the value of h is 6.

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Answer:

10

Step-by-step explanation:

5²+10÷2

10+10÷2

20÷2

10

Answer:17.5

Step-by-step explanation:

5^2 is 25

25+10=35

35/2 is 17.5

Answer:

Given, two numbers 56 and 57 we need to find out the numbers lie between the squares of the given numbers.

Now, we have numbers lying between the square of n and (n + 1) is 2n

⇒ Numbers between squares of 56 and (56 + 1) = 2 × 56 = 112

Hence, 112 numbers lies between the square of the given numbers.

112

Given, two numbers 56 and 57 we need to find out the numbers lie between the squares of the given numbers. Now, we have numbers lying between the square of n and (n + 1) is 2n. ⇒ Numbers between squares of 56 and (56 + 1) = 2 × 56 = 112. Hence, 112 numbers lies between the square of the given numbers.

The distance between the school and the house is 1.6 miles.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Let the distance between the school and the house be x miles.

Given that:

Lisa:

Rate = 10mph

Time = t hours

Distance= x

According to distance formula we have:

x = 10 *t  [ equation 1]

Jen:

Rate = 4mph

Time = t hours

Distance= x-1 miles

According to the distance formula we have:

x-1 = 4*t [equation 2]

Substitute the value of equation 1 in equation 2 we have:

10t -1 = 4t

6t =1

t = [tex]\frac{1}{6}[/tex]

Now substitute the value of t in equation 1.

[tex]x = 10 * \frac{1}{6}[/tex]

x= 1.6 miles.

Hence the distance between the school and the house is 1.6 miles.

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The probability that Sabreena is going to lose is given as 0.5833

Probability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.

A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.

If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7

In this case, the odds of Sabreena winning are 5:7,

so the probability of winning is 5/(5+7)

the probability of not winning is 1 -  5/12

The probability of not winning is approximately 0.5833

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Answer:5.7ft

Step-by-step explanation:

sin = opposite/adjacent

sin 35 = x/10

10 * sin 35 = x

x=5.7

The answer of 2/7 + 3/5 is a fraction. The answer is 31/ 35.

To add two fractions, the denominators must be the same, in this case, the denominators are different, so we need to find a common denominator to add these two fractions.

A common denominator for 2/7 and 3/5 is 35.

So we can convert both fractions to have 35 as the denominator,

2/7 becomes (2×5)/(7×5) = 10/35

3/5 becomes (3×7)/(5×7) = 21/35

then we can add the numerators:

10/35 + 21/35 = 31/35

so the final answer is 31/35

This is also the simplest form of this fraction which would be 31/35.

--The question is not clear, answering to the question below--

"What is the answer of 2/7 + 3/5?"

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The length of piece of wood now will be;

⇒ 0.72 meters

What is Addition?

A process of combining or adding two or more numbers is called addition.

Given that;

A carpenter bought a piece of wood that was 0.42 meters long.

And, She sawed 0.3 meters off the end.

Here,

A carpenter bought a piece of wood that was 0.42 meters long.

And, She sawed 0.3 meters off the end.

Hence, The length of piece of wood now = 0.42 + 0.3 meter

                                                                = 0.72 meters

Thus, The length of piece of wood now = 0.72 meters

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Answer: a) 35% b) 39

Step-by-step explanation:

Answer:

A) 35% B) 39

Step-by-step explanation:

do 14÷40=35% and you already know that have of 60 is 30 so you do 40 ÷60 and see if it is close then you go down one to 39÷60=65%

The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Place the arithmetic symbol between the 6 times 6 to become one. Then we have

⇒ 6 + 6 - 6 - 6 + 6 / 6

⇒ 1

The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.

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Answer:

Below

Step-by-step explanation:

Slope - intercept form is    y = mx + b    you just need to manipulate the given equation to this form

-x +3y = 6         add 'x' to both sides of the equation

3y = x + 6         divide by 3

y = 1/3 x + 2      Done !

Answer:

In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line.

Step-by-step explanation:

In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line. A linear function is defined as a function of the form y = mx + b, where m and b are constants. The graph of a linear function is a straight line with a constant slope, and so any graph that is not a straight line is not a linear function.

Without the actual graph it's hard to say for sure, but based on the provided information, "The graph does not contain the point (20, –8)" indicates that the graph does not pass through this point (20, -8), and it could be indicating that it's not a straight line, So, The graph does not represent a linear function.

Answer:

Step-by-step explanation:

DE and FG are of equal length.

Answer:

The answer is A and D

Step-by-step explanation:

DE and FG are parallel to each other. They don't intersect, touch, or meet each other. Also they are equal length since they both are the same. Perpendicular is when the intersect or crossover each other, which they don't. Proportional is something completely different from this topic. I hope this is helpful!

Answer:

No radicands have perfect square factors other than 1.

No radicand contains a fraction.

No radicals appear in the denominator of a fraction.

Simplified Radical Form. All exponents in the radicand must be less than the index. Any exponents in the radicand can have no factors in common with the index. No fractions appear under a radical

Answer:

when it is multiplyed by its conjugate

The value of y, given the equation, can be found to be - 8 .6

To find the value of y, first convert the mixed fraction to a decimal for easier calculation :

2 ² / ₅ = 2 + 2 / 5

= 2 + 0. 4

= 2. 4

The equation then becomes :

0. 5 - 2.4 = 1 / 2 y + 2. 4

This can be rewritten as :

0. 5 - 2.4 = 1 / 2 y + 2. 4

0. 5 - 2 . 4 - 2. 4 = 1 / 2 y

1 / 2 y = - 4. 3

y = - 4. 3 / 1 / 2

y = - 8 .6

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A polynomial of degree 4 is called bi-quadratic polynomial.

Bi-quadratic polynomial

A biquadratic equation is a polynomial equation with degree 4, and it strictly does not consist of any term with degrees 3 and 1.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

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Answer:

24 WEEKS

BECAUSE IF U MULTIPLY 24X25.50 U WILL GET 612 ADD 42.50 AND U WILL GET 654.50

Answer:

A is the answer ...........

Answer: 7 hours

Step-by-step explanation: blake is gains 10 more miles then Jake each hour so if you divide 70 by 10 you get 7.

Answer:

D

Step-by-step explanation:

Answer:

D. 12x = 72

Step-by-step explanation:

If 'x' represents the unknown number, then only option D fits this statement.

12x is basically 12 times x, the unknown number.

Hope this helps!

Answer:

8

Step-by-step explanation:

Because when you add them you get 2m+8/2m

Which is equal to 8/1 or 8

Answer:

8

or

[tex]\frac{2m(m+4)}{(m+1)(m-1)}[/tex]

Depends what the question is asking for...

According to question, we can say that there are 128 quarters in the machine.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

N  = the  number of dollars  2N  the  number of  quaters.....so  we  have

25(2N)  + 1N   =   96

1.50N  =  96

so, by fraction we have -

N  =  96  / 1,50   =  64   dollars

2(64)   =    128  quarters

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Answer:

quadratic

Step-by-step explanation:

The system of linear equations has no solution for any value of a.

The equations Ax + 3y = a and 3x + 3y = a can be written in matrix form as

[A  3]   [x]   [a]

[3  3] * [y] = [a]

By using the Gaussian elimination method, the reduced form of the matrix is

[A  3]   [x]   [a]

[0  0] * [y] = [0]

This implies that the system has no solution for any value of a.

The system of linear equation

Ax + 3y = a and 3x + 3y = a can be written in matrix form as

[A  3]   [x]   [a]

[3  3] * [y] = [a]

We can use the gaussian method to solve this system. First, we subtract 3 times the first equation from the second equation to get

[A  3]   [x]   [a]

[0  0] * [y] = [0]

This implies that the system has no solution for any value of a.

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Answer:

y= -9x+5

Step-by-step explanation:

i hope this helps :)