How do you know if 3 equations have no solution?.

b.  a = two-thirds, b = 0, c = 3 c is correct

We have to find the values of a, b, and c of the equation:

y = 2/3 x square + 3  (Given)

y = 2/3 x square + 3  which is in the form of y = ax square + bx +c

y = 2/3 x square + (0)b + 3

therefore, a = 2/3 , b = 0, c= 3

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The given number lies between 64 and 81

A value that, when multiplied by itself, equals the original number is said to be the square root of a number. The character "√" stands for it. For instance, since 4 × 4 is 16, the square root of 16 is 4. Although a number's square root can be positive or negative, the positive value is more frequently utilized. To determine a distance or length, it is also used in mathematics.

given that square root is approximately 8.1066

let the value of the number be x

so √x>8 and √x<9

=>     8 < √x < 9

squaring on the both side we get

64 < x < 81

so the number lies between 64 and 81

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The results of this question are listed below:

Herein we find a quadratic function that relates doll production and production cost, of which we must determine what quantity minimizes production costs. This can be done by transforming the equation into vertex form.  First, write the equation in standard form:

PC = 0.2 · t² - 8 · t + 500

Second, use algebra properties until vertex form is obtained:

PC = 0.2 · (t² - 40 · t + 2500)

PC = 0.2 · (t² - 40 · t + 400) + 0.2 · 2100

PC - 420 = 0.2 · (t - 20)²

Third, determine the critical point:

(t, PC) = (20, 420)

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Answer:

Step-by-step explanation:

y=5x(dollars per hour)+3(flat fee)

y=5x+3

Answer:500

Step-by-step explanation:

take y + 2

x-3

The angle between the ladder and the ground is decreasing at the rate of 1 ft/sec.

According to the question,

A sliding ladder of length let L=13ft.

Let the ladder touches the house at height h and touches the ground

x ft from the house. This is shown in the figure.

In ΔABC,

 θ = [tex]cos^{-1} \frac{AB}{BC}[/tex]

⇒ θ  = [tex]cos^{-1} \frac{x}{BC}[/tex]

⇒ dθ/dt= [tex]\frac{d}{dt} cos^{-1} \frac{x}{BC}[/tex]

⇒ dθ/dt=  [tex]\frac{-1}{\sqrt{1 - (\frac{x}{13} )^{2} } } \frac{1}{13} \frac{dx}{dt}[/tex]

substituting the value of x=12ft and [tex]\frac{dh}{dt} = 5ft/sec[/tex] , we have

⇒ dθ/dt= [tex]\frac{-1}{\sqrt{1 - (\frac{12}{13} )^{2} } } \frac{1}{13} (5)[/tex]

⇒ dθ/dt=  [tex]\frac{-1}{\frac{5}{13} } \frac{1}{13} (5)[/tex]

dθ/dt= -1

so the angle between the ladder and the ground is decreasing at the rate of 1 ft/sec.

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The complete question is:

A 13 ft. ladder is leaning against a wall when its base starts to slide away At the instant when the base is 12 ft. away from the wall, the base is moving away from the wall at the rate of 5 ft/sec. The rate at which the angle θ between the ladder and the ground is changing is -

A polynomial function that has zeros,

5 and -2+2i, is x² -x(3 +2i) +10(i - 1).

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial function has zeros,

5 and -2+2i.

Firstly, we will write the zeros as factors of the polynomial,

(x-5) and (x +2 - 2i).

Now, multiply the factors,

⇒ x²+2x -2ix -5x -10 + 10i

⇒ x² -x(3 +2i) +10(i - 1)

Therefore, x² -x(3 +2i) +10(i - 1) is the required polynomial.

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Answer:

  (x, y) = (2, 4)

Step-by-step explanation:

You want to solve the system of equations ...

There are numerous ways to solve this system of equations. One of the simplest is to use a graphing calculator. (See the attachment)

  (x, y) = (2, 4)

The second equation gives an expression for x that can be substituted into the first equation:

  y = -2(y -2) +8

  3y = 12 . . . . . . . . add 2y and simplify

  y = 4

  4-2 = x = 2

The solution is (x, y) = (2, 4).

The y-variable has a coefficient of 1 on the left side of the equal sign, so we can eliminate the y-variable by subtracting the second equation from the first.

  (y) -(y -2) = (-2x+8) -(x)

  2 = -3x +8 . . . . . . . . . . . simplify

  3x = 6 . . . . . . . . . . add 3x-2

  x = 2 . . . . . . . . divide by 3

  y = -2(2) +8 = 4 . . . . . substitute for x in the first equation

The solution is (x, y) = (2, 4).

The total salary of Saul is given by the equation A = $ 1,740

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total salary of Saul be represented as A

Now , the equation will be

The basic monthly salary of Saul = $ 1,500

The total commission percentage of Saul = 4 %

The minimum amount of items to sell = $ 20,000

The amount of items worth sold = $ 26,000

So , the extra amount of items sold by Saul = 26,000 - 20,000 = $ 6,000

Now ,

The total salary of Saul A = basic monthly salary of Saul + ( commission percentage x extra amount of items sold by Saul )

Substituting the values in the equation , we get

The total salary of Saul A = 1,500 + ( 4 % x 6,000 )

On simplifying the equation , we get

The total salary of Saul A = 1500 + ( 4/100 ) x 6,000

The total salary of Saul A = 1500 + 240

The total salary of Saul A = 1,740

Hence , the total salary including the commission is $ 1,740

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A product of mixed numbers is a fraction or a natural number.

We know that a mixed number is a number consisting of a natural number and a proper fraction.

It is a combination of a natural number and fraction

We can say that a mixed number can be written as [tex]a\frac{b}{c}[/tex]

where a, b and c are non-zero real numbers with c > b

When we need to multiply two mixed numbers, first we change each mixed number to an improper fraction. Then multiply the numerators.

Then we multiply the denominators. And simplfy the resultant fraction if needed.

Consider two mixed numbers [tex]2\frac{1}{4} , 3\frac{2}{5}[/tex]

After converting given mixed numbers into an improper fractions we get,

[tex]2\frac{1}{4} =\frac{9}{4} , 3\frac{2}{5}=\frac{17}{5}[/tex]

So the product of given mixed numbers would be,

[tex]2\frac{1}{4} \times 3\frac{2}{5}[/tex]

[tex]=\frac{9}{4} \times \frac{17}{5} \\\\=\frac{153}{20}[/tex]

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Yes, it is possible to order a list of numbers by their number of words. To do this, you will need to count the number of words in each number, then order them in ascending or descending order based on this number.

Here is an example of how to do this:

1. Count the number of words in each number. For example, the number “twenty-nine” has two words (“twenty” and “nine”).

2. Order the numbers from least to greatest or greatest to least based on the number of words. For example, “nine” has one word, so it would come before “twenty-nine” which has two words.

3. Place the numbers in order from least to greatest or greatest to least.

This method can also be used to order numbers that are written in words or numbers that are written in numerals. However, if the numbers are written in numerals, you will need to convert them to words before you can count the number of words.

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The quotient of 3 and 15 is 0.2.

The division is breaking something up into equal parts. The Dividend is the whole we start with, the Divisor is what you use to divide up the whole, and the Quotient is the answer like this:

Dividend ÷ Divisor = Quotient

So if asked that, "What is the quotient of 3 and 15?" it means sense that 3 is the Dividend, 15 is the Divisor, and you want to know the Quotient. Thus, the answer is:

3 ÷ 15 = 0.2

Therefore, the quotient of the given question, 3 and 15, that is, 3 ÷ 15 is equal to 0.2.

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Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

Congruence, in mathematics, a term employed in several senses, each connoting harmonious relation, agreement, or correspondence .Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout. Thus two triangles are congruent if two sides and their included angle in the one are equal to two sides and their included angle in the other.

This idea of congruence seems to be founded on that of a "rigid body," which may be moved from place to place without change in the internal relations of its parts. The position of a straight line (of infinite extent) in space may be specified by assigning four suitably chosen coordinates. A congruence of lines in space is the set of lines obtained when the four coordinates of each line satisfy two given conditions. For example, all the lines cutting each of two given curves form a congruence.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 8x + 3}\\\mathsf{f(x) = 8x + 3}\\\mathsf{f(x) = 8(3) + 3}\\\mathsf{f(x) = 24 + 3}\\\mathsf{f(x) = 27}\\\\\huge\text{Therefore, your answer could possibly be: }\\\huge\boxed{\mathsf{f(x) = 27}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex] \sf \: f(3) = 27[/tex]

Step-by-step explanation:

Given function,

→ f(x) = 8x + 3

Now the value of f(3) will be,

→ f(x) = 8x + 3

→ f(3) = 8(3) + 3

→ f(3) = 24 + 3

→ [ f(3) = 27 ]

Hence, the value of f(3) is 27.

The length of TS  in ΔTRS using Similarity of triange is 12 cm .

If two items have the same shape or have the same shape as their mirror images, they are said to be Similar. One can be produced from the other more accurately by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.

If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be comparable (corresponding sides). Similar triangles may have varying individual side lengths, but they must have equal angles and the same scale factor or matching ratio of the side lengths. If two triangles resemble one another, then

In ΔTPQ and ΔTPS

∠T is common in both triangle

PQ ║ RS

∴∠TPQ = ∠TRS (Corresponding Angles)

similarly ,

∠TQP = ∠TSR

∴ Δ TPQ ~ ΔTRS

So,

PQ/ RS = TQ/ TS

⇒ 2/ 6 = 4 / TS

⇒TS = (4*6)/2  = 12

The length of TS  in ΔTRS using Similarity of triange is 12 cm .

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The length of TS  in ΔTRS using Similarity of triangel is 12 cm .

What is meant by length ?

In ΔTPQ and ΔTPS

∠T is common in both triangle

PQ ║ RS

∴∠TPQ = ∠TRS (Corresponding Angles)

similarly ,

∠TQP = ∠TSR

∴ Δ TPQ ~ ΔTRS

So,

PQ/ RS = TQ/ TS

⇒ 2/ 6 = 4 / TS

⇒TS = (4*6)/2  = 12

The length of TS  in ΔTRS using Similarity of triange is 12 cm.

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To calculate the mode in math is to place all the given set in order and calculate the number of times the number appears in the order, the number that appears for most of the time is the Mode.

A value or number that appears most frequently in a dataset is referred to as the mode. We might occasionally need to identify the value that appears more frequently in the dataset. In these situations, we determine the mode for the given collection of data. For a certain set of data, a modal value might or might not exist. There might not be any mode at all for data without any repeated values.

Mode = L+h [tex]\frac{(fm - f1)}{(fm - f1)+(fm - f2)}[/tex]

where,

L is the lower limit of the modal class

h is the size of the class interval

fm is the frequency of the modal class

f1 is the frequency of the class preceding the modal class

f2 is the frequency of the class succeeding the modal class

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Answer: Circle 3

Step-by-step explanation:

There are p plates, and 4 are unable to be used, so the expression is p - 4 = Circle 3

Answer:

c

Step-by-step explanation:

Because the number of plates on the table minus 4 saved for dessert mean p-4

Answer:

[tex]\boxed{41\;meters}[/tex]

Step-by-step explanation:

The flagpole, the shadow and the line connecting the tip of the shadow to the top of the flagpole construe a right-angle triangle with the flagpole and shadow being the legs of the triangle and the other the hypotenuse

Given flagpole height is 24 meters and shadow is 33 meters we can compute the third side using the Pythagorean Theorem for the hypotenuse:

[tex]c = \sqrt{a^{2} + b^{2}}[/tex]

Substituting known values we get
[tex]c = \sqrt{24^{2} + 33^{2}}\\\\c = \sqrt{576 + 1089}\\\\c = \sqrt{1665}\\\\c=40.804 \;meters[/tex]

Rounded to the nearest meter this would be 41 meters

The slope and y-intercept of the linear function y = -10x + 1 are -10 and (0,1) respectively.

The given linear function is y = -10x + 1.

The slope of a linear function is the coefficient of the x-term. In this case, the slope is -10.

The y-intercept of a linear function is the point at which the line crosses the y-axis. To find the y-intercept, we can substitute x = 0 into the equation and solve for y.

y = -10(0) + 1

y = 1

So, the y-intercept is (0,1).

Therefore, the slope and y-intercept of the linear function y = -10x + 1 are -10 and (0,1) respectively.

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4(6x³ -2x² + 1) is the  polynomial expression  with GCF 4.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The polynomial expression is 24x³ - 8x² + 4

We have to write this polynomial expression in the factored from by taking GCF.

Rewrite 24 as 4×6

8 as 4×2

24x³ - 8x² + 4

4(6x³ -2x² + 1)

Hence, 4(6x³ -2x² + 1) is the  polynomial expression  with GCF 4.

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The slope of line 3x-7y=9 is 3/7.

The equation for the slope of a line and the points also called a point-slope form of the equation of a straight line is given by:

y − y₁ = m(x − x₁)

If P(x₁,y₁) and Q(x₂,y₂) are the two points on a straight line, then the slope formula is given by:

Slope,m = Change in y-coordinates/Change in x-coordinates

m=(y₂–y₁)/(x₂– x₁)

First, rewrite this to isolate y.

7y = 3x - 9

y = (3/7)x - (9/7)

In this form, the slope is given by the number multiplying the x, so the slope is 3/7

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The given expression is not an equivalent expression.

What is an equivalent expression?

An equivalent expression is a mathematical expression that has the same value as another expression, even though they may appear to be different. Equivalent expressions are obtained by using the same operations or by making substitutions that preserve the value of the expression.

The expressions -6z + (-5.5) and 3.5z - 5y - 2.5 are not equivalent. They have different coefficients for the variables z and y, and different constants. To determine if two expressions are equivalent, you need to check that they have the same value for all possible values of the variables. If the values are the same for all inputs, then the expressions are equivalent. If the values are not the same for all inputs, then the expressions are not equivalent.

Hence, the given expression is not an equivalent expression.

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The inverse of a square root function looks like a half parabola when we plot it on the graph.

Curved graphs of square root functions are typical. In actuality, the curve above is a parabola's half that is lying on its side. On a graph of the equation y² = x, it represents one half of the parabola.

A quadratic function is defined as f(x) = ax² + bx + c, where a, b, and c are all integers and an is not equal to zero. The graph of a quadratic function has the form of a parabola.

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Circle M has a center (h+d, k+e) and the radius is rs. Therefore, option C is the correct answer.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, circle B has a center (h, k) and a raius of r. Circle B is translated d units to the right and e units up. Then it is dilated about its new center by a scale factor s resulting in a new circle

Translation rules:

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

Now, (h, k)→(h+d, k+e) and the radius is rs.

Therefore, option C is the correct answer.

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Step 1: Think about this as four separate division questions:

     [tex]\dfrac{10c^3de^2}{2cde} =\dfrac{10}{2} \cdot \dfrac{c^3}{c} \cdot\dfrac{d}{d}\cdot \dfrac{e^2}{e}[/tex]

Step 2: Simplify each of the four, one at a time:

     [tex]\begin{aligned}\dfrac{10c^3de^2}{2cde} &=\dfrac{10}{2} \cdot \dfrac{c^3}{c} \cdot\dfrac{d}{d}\cdot \dfrac{e^2}{e}\\[0.5em]&=5 \cdot c^{3-1} \cdot1\cdot e^{2-1}\\[0.5em]&=5 c^{2} e\end{aligned}[/tex]

Answer: The graph that could be the graph of f(x) is a parabola that opens upwards, with a vertex at (2,-4) and x-intercepts at x = -1 and x = 4. Since the degree of the polynomial function f(x) is 3 and the roots are -1, 0, and 4, the polynomial function is a cubic function and its graph is a parabola.

The roots of a polynomial function are the x-coordinates of the x-intercepts of the graph of the function. Therefore, since the roots of the equation f(x) = 0 are -1, 0, and 4, the graph of f(x) will have x-intercepts at x = -1 and x = 4.

The fact that the vertex is at (2, -4) mean that the parabola will open upwards and pass through the point (2, -4)

It's important to note that, if the polynomial function has a degree greater than 3, there may be multiple graphs that could represent the polynomial function, as long as they have the same roots.

Step-by-step explanation:

The total number of ceiling tiles required is 78

Measurement in the ceiling =  24 feet by 26 feet.

Measurement of the tiles =  2 feet by 4 feet

Mathematicians use units of measurement, rules, and formulas to calculate various measurement parameters, including area, volume, length, perimeter, surface area, time, etc. The process of comparing a physical quantity with a recognised standard quantity of the same kind is called comparison.

Calculating the total number of tiles required -

= Measurement in the ceiling / Measurement of the tiles

= 24 x 26 / 2 x 4

= 624 / 8

= 78

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Answer:

Step-by-step explanation:From the issue, we may deduce that:

x + y = 50 She desires to produce 50 ounces of the combination (because to this).

(0.35x) + (0.60y) = 0.55(x+y) (because we're calculating the amount of salt in each solution and the combination contains 55% salt)

We may take the first equation and replace it in the second equation:

(0.35x) + (0.60y) = 0.55(50) (50)

0.35x + 0.60y = 27.5 when x is substituted.

A system of two equations with two variables is now available:

x + y = 50\s0.35x + 0.60y = 27.5

To determine one of the variables in terms of the other, we may utilize the first equation. Let's figure out y:

y = 50 - x

We now change y in the second equation to the following expression:

0.35x + 0.60(50-x) = 27.5

Finding the value of x:

0.35x + 30 - 0.6x = 27.5

0.25x= -2.5

x= -10

Since the number of ounces cannot be negative, the answer is illogical. As a result, you should double-check your calculations or determine if the issue statement contains a mistake.

To get the answer, you can also try an alternative approach like substitution or elimination. Then, double-check your calculations.