Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. A. C. B. D. Please select the best answer from the choices provided a b c d.

The range of integer value in C is: -2,147,483,647 to 2,147,483,647

We know that the range  of data types means the maximum and minimum value that can be stored inside the variable of a given type.

In C programming, the primitive data types are:

char – this data type hold a single character

float –  this data type hold single-precision types of floating-point.

int –  this data type hold integers

double  - this data type hold double-precision types of floating-point

The int i.e., integer data type holds whole numbers that range from -2,147,483,647 to 2,147,483,647.

The number 2,147,483,648 cannot be used.

The integer value is stored as a signed binary integer.

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Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.

In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.

The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.

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On Solving the given quadratic equation , we get the zeros of the equation is x = 3 .

A quadratic equation is an algebraic equation of second degree in x. The standard form of a quadratic is written as ax² + bx + c = 0  , where "a" and "b" are coefficients, x is variable, and c is constant term.

The given equation is : p(x) = x² - 6x + 9 ;

to find the zero , we equate the given quadratic function to zero(0) .

On equating ,

we have ;  x² - 6x + 9 = 0;

⇒ x² - 3x -3x + 9 .....by split middle term method ;

⇒ x(x - 3) -3(x - 3) = 0;

⇒ (x - 3)(x - 3) = 0;

which means that x - 3 = 0 ,and x = 3 .

Therefore , the zero of the given quadratic function is x = 3 .

The given question is incomplete , the complete question is

What is the zero of p(x) = x² - 6x + 9 ?

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The cannonball will be at a height of 640 feet for the first time after 6.5 seconds.

Acceleration, is a rate at which velocity changes with time, in terms of both speed and direction.

The time it will take for the cannonball to reach a height of 640 feet for the first time can be found using the equation:

t = (vf - vi) / a

where:

t = time (in seconds)

vf = final velocity (in feet per second) = 0 (at the top)

vi = initial velocity (in feet per second) = 208

a = acceleration (in feet per second squared) = -32 (upwards)

Plugging in the values:

t = (0 - 208) / (-32) = 6.5 seconds.

So, the cannonball will be at a height of 640 feet for the first time after 6.5 seconds.

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Based on the information provided, the length of the rope for the goat to graze over half of the field is 0.5 units.

The radius of a circle can be defined as a straight line that goes from any of the borders of the circle to its center of it.

The radius and the proportion of the field that the goat can graze is proportional. In this case if the length is 1 unit the goat can graze all the field; therefore, if we cut the graze to 0.5 the goat will graze only half of the field.

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The polynomial, so d can be any value less than b.

A polynomial is an expression made up of multiple terms, each of which is a number, a variable, or the product of a number and one or more variables. Polynomials are typically used to model real-world scenarios including, but not limited to, population growth, force and acceleration, and angles of elevation. Each term of the polynomial is separated from the others by an addition or subtraction sign.

Given the polynomial 4x^3 + ax^2 + bx + c,
a = 4, b = -3, c = 5, d = -2.
To find the values of a, b, c, and d, we need to compare the coefficients of the polynomial to the given values.
The coefficient of the term with the highest degree (x^3) is 4, so a = 4.
The coefficient of the next degree (x^2) is a, so a = -3.
The coefficient of the next degree (x) is b, so b = 5. The coefficient of the constant term is c, so c = -2. Finally, d is not given in the polynomial, so d can be any value less than b.

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To find the greatest common factor (GCF) of a sum, list the prime factors of each term in the sum. The GCF is the product of the common prime factors raised to the lowest exponent.

To find the greatest common factor (GCF) of a sum, you can first list the prime factors of each term in the sum. The GCF is the product of the common prime factors raised to the lowest exponent.

For example, to find the GCF of 36x² + 18x² + 12x², you would list the prime factors of each term:

36x² = 2² × 3² × x²

18x² = 2 ×  3² ×  x²

12x² = 2² ×3 × x²

The GCF is 2 × 3 ×  x² = 6x²

To rewrite the sum using the GCF and the distributive property, you divide each term in the sum by the GCF, and then multiply the GCF by the sum of the quotients:

(36x² + 18x²  + 12x²) / (6x² ) = 6 + 3 + 2

6x² × (6 + 3 + 2) = 6x² ×  11

So the sum can be rewritten as 6x² × 11

You can also use the same method to find GCF of numbers as well.

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No, it is not. X square 22 X square is not a polynomial because it does not have the standard form of a polynomial which is ax^n + bx^n-1 + cx^n-2 + ... + z.

A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power.

Leading term and leading coefficient are terms used to describe the first term and its coefficient, respectively, in the polynomial's standard form.

A polynomial's standard form is denoted by the formula f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

According to the definition of a polynomial in standard form, exponents must be written in decreasing order.

The standard form of polynomials is used to facilitate calculations.

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Answer:

Growth

Growth

Decay

Decay

Answer: [tex]y=\frac{1}{3} x+6[/tex]

Step-by-step explanation:

To find the perpendicular line, we have to change the slope of the original, equation.

The slope of the perpendicular line is 1/3. We can plug in the new point. To find the equation.

[tex]8=\frac{1}{3}(6)+b[/tex]          [multiply]
[tex]8=2+b[/tex]               [subtract both sides by 2]
b=6

Final equation is [tex]y=\frac{1}{3} x+6[/tex]

Answer:

y = 1/3x + 6

Step-by-step explanation:

Because perpendicular lines have opposite and reciprocal slopes, we have to change our slope into a positive and flip it into it's reciprocal.

Now its: y = 1/3x + b

Next, we find b using slope intercept form.

8 = 1/3(6) + b

8 = 2 + b

6 = b

Place b into the equation.

y = 1/3x + 6

Answer:

3. (-4/5, -3) 6. (4, 12/-5)

Step-by-step explanation:

3. so first we have

-5x - 10y = 20

-5x - 8y = 14

so first we have to have the x's be opposite so we multiply the top one by -1 which gets us

5x + 10y = -20

-5x - 8y = 14

then we cancel out the x's and subtract 10 by 8 and -20 by 14 so it's now

2y = -6

then we divide by 2 on both sides so it's

y = -3

but now we have to solve for x so we substitute y in on the bottom equation so now it is

-5x - 8(-3) = 20

now we multiply

-5x + 24 = 20

subtract 24 from both sides

-5x = -4

divide by -5

x = -4/5

then put it in coordinates

(-4/5, -3)

6. so we have

x = 4

-4x - 5y = 4

so first we have to substitute the top in for the bottom so now we have

-4(4) - 5y = 4

distribute

-8 - 5y = 4

add 8 to both sides

-5y = 12

divide

y = 12/-5

coordinates

(4, 12/-5)

The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.

In mathematics, an identity is a statement or equation that is true for all values of the variables involved. For example, the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, is an identity.

In summary, identities in mathematics are statement that are true for all values of variables, they are used to simplify expressions, solve equations and prove theorems, and they play an important role in the study of mathematical structures.

The 12 algebraic identities in mathematics are:

Commutative property of addition: a + b = b + a

Commutative property of multiplication: a x b = b x a

Associative property of addition: (a + b) + c = a + (b + c)

Associative property of multiplication: (a x b) x c = a x (b x c)

Distributive property: a x (b + c) = (a x b) + (a x c)

Identity property of addition: a + 0 = a

Identity property of multiplication: a x 1 = a

Additive inverse property: a + (-a) = 0

Multiplicative inverse property: a x (1/a) = 1

Transitive property: a = b and b = c then a = c

Substitution property: a + b = b + a

Reflexive property: a = a

It's worth noting that these are some of the algebraic identities which are frequently used in algebra and other related mathematical branches.

The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.

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The area of the triangle is 27.9 sq.cm.

What is meant by area of triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area.

We have the lengths of two sides and the measure of the included angle. So, you can use the formula R = [tex]\frac{1}{2}[/tex]pr sin(Q), where p and r are the lengths of the sides opposite to the vertices P and R respectively.

Using the formula, the area, R= [tex]\frac{1}{2}[/tex] (9) (8.4) sin (132°).

R = 37.8 sin (132°)

R = 37.8 (0.74)

R = 27.9 (approx)

Hence, the area of the triangle is 27.9 sq.cm.

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Answer:

x = 131

y = 131

Step-by-step explanation:

x = 180 - 49 (sum of angles on a straight line)

x = 131

y = x (corresponding angles)

y = 131

Answer:

82+54=136°

Step-by-step explanation:

the value of the extreior angle in a tringle equals to the sum of the further two angles in the tringle

Answer: The least number of bottles the trader can obtain is the greatest common divisor (GCD) of the number of liters in the two buckets.

We can use the Euclidean algorithm to find the GCD:

First find the remainder of 24 divided by 27, which is 24 % 27 = 0.

Since the remainder is 0, we know that the GCD of 24 and 27 is 27.

Therefore, the trader can obtain at least 27 bottles from the two buckets of beverages A and B.

Note that the GCD represents the size of the bottle and this is the least number of bottles that the trader can obtain.

Step-by-step explanation:

The value of the length of side UX for the right triangle formed by sides tangent to the circle is equal to 3.4 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The side XV is perpendicular to the side UV tangent to the circle, which makes the triangle a right triangle.

so by evaluation we derive the value for the hypotenuse UX as follows;

UX = √(3² + 1.6²)

UX = √(9 + 2.56)

UX = √11.56

UX = 3.4

Therefore, the length of side UX for the right triangle is equal to 3.4 using the Pythagoras rule.

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[tex]( \frac{3}{5} ){}^{2} + 4 \times 3 - 2[/tex]

[tex] \frac{9}{25} {}^{} + 12- 2[/tex]

[tex] \frac{9}{25} {}^{} + 10[/tex]

[tex] \frac{9 + 10(25)}{25} [/tex]

[tex] \frac{9 + 250}{25} [/tex]

[tex] \frac{259}{25} [/tex]

The value of {p} is equivalent to 1.68.

Given is the expression -

43p = 72

The given equation is -

43p = 72

{p} = 72/43

{p} = 1.68

Therefore, the value of {p} is equivalent to 1.68.

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The distance remained to be covered by amrita to attend a function is 2950 meters or 2.95 kilometers.

Given,

  Total distance to be covered by Amrita = 20 KM = 20000 m

  Distance covered by her car before broken = 17 Km 50 meter = 17050m

We know that,

                        1 Kilometer = 1000 meter

Remaining Distance = (20000 - 17050)m

                                  = 2950 m

                                  = 2.95 KM

Therefore, the distance remaining to be covered by amrita is 2950 meters or 2.95 Kilometers.

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Answer: The friends who shared 2 chocolate chip cookies.

Step-by-step explanation: 3/2= 1.5  and 4/3= 1.3

1.5>1.3

Answer:

49.5°

Step-by-step explanation:

Draw a line b/w B and D, this will "cut" the angles of both down the exact middle making it much easier to work with now that you have 2 separate triangles

For example, angle A remains 36° but angle B becomes 54° and angle D becomes 76.5°. Now that you have B and D, just subtract 180 from both to get your C value. 180° - 54° - 76.5° = 49.5°

Answer: (A) 16

must be less than 19

and more than 5

Step-by-step explanation:

The missing value for x is 7.

The inverse variation relationship between two variables x and y is described by the equation y = k/x,

where k is a constant.

We can use this equation to find the missing value, using the information given.

First, we'll use the first set of points to find the constant k:

y = k/x

16 = k/3.5

16 * 3.5 = k

56 = k

Next, we'll use the constant k and the second set of points to find the missing x value:

y = k/x

8 = 56/x

8 * x = 56

x = 56/8

x = 7

hence x is 7

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An average mean of 1.72 children can be found on every house

One method for making data more comprehensible is to put it in a frequency distribution table. Consider having a list of IQ results for a talented class at a certain elementary school. The frequency of a value in a set of data is how frequently it appears.

Victor, for instance, made nine attempts to obtain a red gumball. The quantity of gumballs in each hue that were produced would be the frequency in this situation. The distribution of observations based on a variable's possible values is displayed in a frequency table.

frequency = 10 + 4 + 2 + 3 + 4 + 2

= 25

Sum of children

= (10 × 0)+(4 ×1)+(2 × 2)+(3 × 3)+(4 × 4)+(2 × 5)

= 43

Mean =  43/25

= 1.72

Thus, An average mean of 1.72 children can be found on every house.

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The length of the third side is 14.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case since it is opposite the angle of 90°.

Given that,

a = 8

b = 12

Let the length of the third side be c,

Applying the Pythagorean theorem:

a² + b² = c²

8²+ 12² = c²

c² = 64+144

c² = 208

c = √208 = 14.42

Thus, the length of the third side is 14.

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If a circular mulch bed has a radius of 1.6 feet. A bag of mulch contains 2 cubic feet of mulch. The mulch's depth to an appropriate number of significant digits is: C. 0.25 foot.

The volume of the mulch bed is given by the formula for the volume of a cylinder:

V = π * r^2 * h

Where:

r = radius (1.6 feet)

h=  the height (the depth of the mulch).

Since we have 2 cubic feet of mulch, and want to spread it evenly over the bed, we can set 2 = π * r^2 * h and solve for h:

h = 2 / (π * r^2) = 2 / (π * 1.6^2)

h ≈ 0.25 feet

Therefore the depth of the mulch is approximately 0.25 feet.

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