17 gallons = ? liters

The equation that has no real roots is 3x² + 4√3x + 4.

Option D is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

If the discriminant of the equation is less than zero the equation has no real roots.

Discriminant < 0

D < 0

D = b² - 4ac

Now,

The equation is in the form of ax² + bx + c

x² - 4x + 3√2 = 0

D = (-4)² - 4 x 1 x 3√2 = 16 - 12√2 > 0

x² + 4x - 3√2 = 0

D = 16 + 12√2 > 0

x² - 4x - 3√2 = 0

D = 16 + 12√2 > 0

3x² + 4√3x + 4 = 0

D = 16 - 48 = 32 < 0

Thus,

The equation 3x² + 4√3x + 4 has no real roots.

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The complete question is:

Which of the following equations has no real roots

a. x² - 4x + 3√2 = 0

b. x² + 4x - 3√2 = 0

c. x² - 4x - 3√2 = 0

d. 3x² + 4√3x + 4 = 0

You must be aware that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles in order to utilize the AAS Theorem to verify congruence.

Triangles are said to be congruent if two of their matching angles and one of their excluded sides are congruent with those of two other triangles. Because it can be demonstrated, this is a theorem.

The AAS Theorem uses two angles and a side to demonstrate triangle congruence, just as the ASA Postulate. The letters are arranged differently from the angles and sides they represent.

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Answer:

2x^3 - 2x^2 - 9x + 3

Step-by-step explanation:

(2x^3 − 3x + 2) - (2x^2 + 6x − 1) =

2x^3 − 3x + 2 - 2x^2 + (-6x) − (-1) =  ==> distribute the negative sign to 2x^2,

                                                               6x, and -1 in (2x^2 + 6x − 1)

Adding a negative number is equivalent to subtracting by a positive number.

Subtracting a negative number is equivalent to adding by a positive number.

Hence:

2x^3 − 3x + 2 - 2x^2 - 6x + 1 =  

2x^3 - 2x^2 - 3x - 6x + 2 + 1 =  ==> rearrange the expression in which like

                                                      terms are matching

2x^3 - 2x^2 - 9x + 3 ==> simplify

A function is increasing if the function value increases on increasing the input value and the function is decreasing if the function value decreases on increasing the input value.

We know that a function is a relation between input and output values where each input has exactly one output.

Consider a function y = f(x)

For a given function if the value of y increases on increasing the value of x, then the function is called as an increasing function

If the y-value decreases on increasing the value of x, then the function is called as a decreasing function.

Another method is that if a function f(x) is differentiable on an open interval, we calculate the derivative of function f(x)

If the derivative f′(x) > 0 on an open interval, then function f(x) is increasing on that interval.

If the derivative f′(x) < 0 on an open interval, then function f(x) is decreasing on that interval.

Therefore, if the output value of function increases on increasing the input value then the function is an increasing function and if the output value of function decreases on increasing the input value then the function is an decreasing function.

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Answer:

Congruence in two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

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Step-by-step explanation:

The statements that are true are the volume of the box is v = lwh = 864 in³ and the volume can be expressed in an equation as v = 6x² = 864in³

The volume of a square box is equal to the cube of the length of the side of the square box. The formula for the volume is V = l³, where "l" is the length of the side of the square box.

In the given problem, the volume of the box is 864 cubic inches.

However, we have to remember that the box isn't a square, but rather the base has a square shape.

The volume of the figure is

v = l * w * h

If we divide the volume by the height, we will have the area of the figure

Area = volume / height

Area = 864 / 6

Area = 144 square inches

Since the base has a square shape;

A = l²

144 = l²

l = √144

l = 12 in

The side length is 12 inches.

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The present age of the Son will be 10 years and Father's present age will be 40 years.

We will solve this problem with the concept of age.

Age is referred to as the length of time that a person or item has been alive. Problems based on age generally consist of information about the ages of two or more people and a relation between their ages in the present or future or past. Using this information it is asked to calculate the ages of one or more people in the present past or future.

The important thing to keep in mind while solving problems of ages.

If the present age is y, then n times the present age = ny.

If the present age is x, then age n years later/hence = x + n.

If the present age is x, then the age n years ago = x – n.

The ages in a ratio a: b will be ax and bx.

If the current age is y, then 1/n of the age is y/n.

According to our problem:

Let the present age of the son = x

The present age of the father = 4x

After 5 years

Son age = x+5.

Father age = 4x+5

According to the condition =

4x+5 = 3(x+5)

4x+5 = 3x + 15

x = 10

Therefore the present age of the son will be x = 10 years and the father will be 4x= 40 years.

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the root is zero when the graph crosses the X-axis.

The word root used in mathematics to express a solution of equation.

The root is written in a number or algebraic form.

When graph crosses the x axis the root of an equation become zero.

hence, we get zero value while crossing the X-axis

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Answer:

The square root of 20 is 4.472.

Step-by-step explanation:

In the case of the two lines you described, the y-intercepts are 1 and 2, meaning that the lines cross the y-axis at the points (0,1) and (0,2), respectively.

To find the equations of the lines, you can use the slope-intercept form of a line, which is written as y = mx + b, where m is the slope of the line and b is the y-intercept. Since the lines intersect at the point (1,3), you can use this point and the y-intercept of each line to find the slope of each line.

For the first line, with y-intercept 1, the slope is given by the formula m = (y2 - y1) / (x2 - x1), where (x1,y1) is the given point (1,3) and (x2,y2) is the y-intercept (0,1). Plugging in these values, we get m = (1 - 3) / (0 - 1) = -2. So the equation of this line is y = -2x + 1.

For the second line, with y-intercept 2, the slope is given by the same formula, using the point (1,3) and the y-intercept (0,2). This gives us m = (2 - 3) / (0 - 1) = -1. So the equation of this line is y = -1x + 2.

Therefore, the equations of the two lines are y = -2x + 1 and y = -1x + 2.

Temperature is typically represented on a graph by plotting points along the vertical (y-axis) to represent the temperature. The horizontal (x-axis) is typically used to represent time or location.

Temperature is typically represented on a graph by plotting points along the vertical (y-axis) to represent the temperature. The horizontal (x-axis) is typically used to represent either time or location. Each point on the graph is a measurement of temperature at a specific moment in time or location. The data points can be connected with a line to create a line graph, which can show temperature trends over time or in different locations. If two sets of data are being compared, such as indoor and outdoor temperatures, two lines can be drawn on the same graph to compare the two. By looking at the graph, one can easily identify the highest and lowest temperatures, as well as any trends over time. Additionally, the graph can be used to identify when temperatures are above or below a certain threshold. Graphs can be used to quickly and easily represent data, making them a powerful tool in understanding temperature.

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Answer:

Step-by-step explanation:

The formula of Volume of the Cone, V = 1/3πr^2h

Now, r^2 = 3v/πh

         r = √(3v/ πh)

Answer: 6 ft by 3 ft by 1 ft

Step-by-step explanation:

it already shows the outer dimension in the world problem just need to put it into numbers

The equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone is 5(8) + 5r = 1.

Simplify surely approach to make it simple. In mathematics, surely or simplification is lowering the expression/fraction/trouble in a less difficult form. It makes the trouble clean with calculations and solving.

Let r be the rate in parts per minute at which the lawn sprinkler would fill the pool if use alone then. If the handheld hose and the lawn sprinkler are used together, we have this equation:

5/r + 5/8 = 1

Simplifying this expression,

5(8) + 5r = 1

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To tell if a limit is coming from the right or left, you need to look at the sign of the x-value in the limit equation. If the x-value is positive, the limit is coming from the right. If the x-value is negative, the limit is coming from the left.

To determine which side a limit is coming from, you must first examine the x-value in the limit equation. If the x-value is positive, then the limit is coming from the right side. This is because when the x-value is positive, it is approaching from the positive side of the number line. On the other hand, if the x-value in the limit equation is negative, then the limit is coming from the left side. This is because when the x-value is negative, it is approaching from the negative side of the number line. It is important to note that the sign of the x-value in the limit equation indicates which side the limit is coming from.

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The nature of root equation is depends of their types.

(1) When D=0, the roots in this situation are x = -b/2a.

(2) When D>0, the roots are real and unequal.

(3) When D<0, the roots are imaginary and unequal.

The type of roots depends on the discriminator:

We will talk about the following scenarios involving the nature of roots in accordance with the discriminates value.

Case: D=0

The roots of the quadratic equation ax^2 + bx + c = 0 are real and equivalent if the discriminate is equal to zero (b^2 - 4ac = 0), a, b, and c are real values, and a(0) . The roots in this situation are x = -b/2a. The X axis is the only location at which the equation's graph meets it.

Case: D>0

The roots of the quadratic equation ax2 + bx + c = 0 are real and unequal if the discriminate is bigger than zero (b2 - 4ac > 0), a, b, and c are real integers, and a0. The X-axis is intersected by the equation's graph twice.

Case: D<0

When a, b, and c are real numbers and the discriminate is smaller than zero (b2 - 4ac 0), the roots of the quadratic equation ax2 + bx + c = 0 are imaginary and unequal. There are conjugate pairings of roots. The equation's graph does not extend to the X-axis.

Case: D > 0 and perfect square

The roots of the quadratic equation are real, unequal, and rational if D > 0 and a perfect square.

Case: D < 0 and perfect square

The roots of the quadratic equation are real, unequal, and irrational if D > 0 and not a perfect square.

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The slope is 3 and the y-intercept is −5 of the equation y = 3x - 5.

The line with m as the slope, m, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope.

Slope-intercept form,

y = mx + c

Given equation,

y = 3x-5

Slope, m = 3

y-intercept, c = -5

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The value of expression lim x→1 g(x) is 4.

In mathematics, a limit is a point at which a function becomes close to producing the desired result for the given input values. Limits are necessary for calculus and mathematical analysis and are also needed to establish integrals, derivatives, and continuity. It is used during the analysis process and continually thinks about how the function will act in a particular situation. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category.

Given expression,

[tex]4x\leq g(x)\leq2x^{4}-2x^{2} +4[/tex]

For x → 1

4x = 4(1)

    = 4

[tex]2x^{4}-2x^{2} +4[/tex] = 2(1)-2(1)+4

                     = 4

Hence, the value of lim x→1 g(x) is 4.

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Answer:

40 inches

Step-by-step explanation:

Similar Triangles

In similar triangles, corresponding sides are always in the same ratio.

Let x be the length of the missing side.

Therefore:

[tex]\implies \sf x:16=30:12[/tex]

[tex]\implies \sf \dfrac{x}{16}=\dfrac{30}{12}[/tex]

[tex]\implies \sf 16 \cdot \dfrac{x}{16}=16 \cdot \dfrac{30}{12}[/tex]

[tex]\implies \sf x=\dfrac{480}{12}[/tex]

[tex]\implies \sf x=\dfrac{40 \cdot 12}{12}[/tex]

[tex]\implies \sf x=40[/tex]

Therefore, the length of the missing side is 40 inches.

The width of the doll house's front door is  2400 cm.

The area of the rectangle is

(240 cm x 100 cm) / 2

= 2400 cm

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By distributing the division, we will get the simplified expression:

(3/2)*x² + 2

Here we have the following quadratic expression:

(9x² + 12)/6

Remember that the division is distributive, then we can rewrite:

(9x² + 12)/6 = 9x²/6 + 12/6

Now we can just simplify the two fractions.

 (9x² + 12)/6 = (9/6)*x² + 2

                   = (3/2)*x² + 2

This is the most we can simplify the given expression.

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A system of equations with an infinity number of solutions, along with y = x - 4, is formed with the following equation:

y - x = -4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients of the function are given as follows:

The combination of two linear functions results in a system of equations.

Each intersection point of the linear functions is a solution to the system of equations, then a system with infinity solutions will only happen when the two lines are the same, that is, they have the same slope and the same intercept.

Hence the desired equation in this problem is given as follows:

y - x = -4.

Which in slope-intercept form is given by:

y = x - 4.

Which is equals to the graphed equation, hence they intersect infinite times.

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Answer:

A) y - x = -4

Step-by-step explanation:

Linear regression is used to model the linear relationship between two variables and r2 measures the strength of this relationship. It is calculated by squaring the correlation coefficient, which is a measure of the strength and direction of the relationship.

To determine the value of r2, you can use technology to perform a linear regression analysis on the given data. Linear regression is a statistical method used to model the linear relationship between two variables, x and y. The value of r2, also known as the coefficient of determination, measures the strength of the relationship between x and y and indicates how well the model fits the data.

The value of r2 is calculated using the following formula:

r2 = (Correlation coefficient)2

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the relationship between two variables. It is calculated using the following formula:

r = ∑(x - x')(y - y') / √[∑(x - x')2 ∑(y - y')2]

where x' and y' are the means of the x and y variables, respectively, and ∑ indicates the sum of the values.

To determine the value of r2, you would first need to calculate the correlation coefficient using the given data. Once you have calculated the correlation coefficient, you can then square it to get the value of r2.

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You can use technology to do a linear regression analysis on the supplied data to find the value of r2. A statistical technique called linear regression is used to simulate the linear relationship between two variables, x and y. The strength of the link between x and y is measured by the coefficient of determination, or r2, which also serves as a measure of how well the model fits the data.

The value of r2 is calculated using the following formula:

r2 = (Correlation coefficient)2

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the relationship between two variables. It is calculated using the following formula:

r = ∑(x - x')(y - y') / √[∑(x - x')2 ∑(y - y')2]

where x' and y' are the means of the x and y variables, respectively, and ∑ indicates the sum of the values.

You must first compute the correlation coefficient using the provided data in order to obtain the value of r2. Once the correlation coefficient has been determined, you can square it to obtain the value of r2.

An example of distributive property is 3 × (4 + 7) = (3 × 4) + (3 ×  7).

Distributive Property is a property of multiplication and it is related with the distribution of numbers.

It states that the product of three numbers do not change even if the distribution of numbers are changed.

The distributive property of multiplication states that:

a × (b + c) = (a × b) + (a ×  c).

Let us verify it with help of an example.

3 × (4 + 7) = (3 × 4) + (3 ×  7)

Taking L.H.S

3 × (4 + 7) = 3 × 11 = 33

Taking R.H.S

(3 × 4) + (3 ×  7) = 12 + 21 = 33

Therefore, L.H.S = R.H.S

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Answer:

Step-by-step explanation:

answer:

Mel was descending at a faster rate

Mel's rate of change is negative. That means that your height in the air decreases 5 feet every second.

Victor's rate of change is negative. That means that his height in the air decreases 3.33 feet every second.

Answer:

Mel (2, 50) and (5, 35)Victor (1, 60) and (4, 50)

Step-by-step explanation:

Edge 2020.

Answer:

-20

Step-by-step explanation:

if y varies jointly as x and z, then y = k * x * z

where k is the variation constant.

-40 = k * -2 * -1

-40 =2k

k = -20

Answer:

An expression is a group of terms with an operation performed on them.

TL;DR:

An expression is an equation without an equal sign (=).

Examples:

[tex]\frac{(4x+2y)}{10}[/tex]

[tex]2y-5[/tex]

[tex]3x+2y+z[/tex]

The roots of the quadratic equation 4x² + 4√3x - 3 = 0 are two distinct imaginary roots.

To find the roots of a quadratic equation, we have to use the quadratic formula. The formula is x = [-b ± √(b² - 4ac)]/2a. In this case, a = 4, b = 4√3, and c = -3. Plugging in the values, we get x = [-4√3 ± √(4√3² - 4*4*(-3))]/8. Simplifying and solving, we get x = [-2i ± √12]/4. Since both solutions contain an imaginary component, this means that the roots of the equation are two distinct imaginary roots.

x = [-4√3 ± √(4√3² - 4*4*(-3))]/8

x = [-4√3 ± √(48)]/8

x = [-2i ± √12]/4

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The slope of the line that passes through the points (2,8) and (12, 20) is 6/5.

given :

points  (2,8) and (12, 20)

slope = m=(y2-y1)/(x2-x1).

= 20-8 / 12-2

= 12/10 =6/5

the slope of the line that passes through the points (2,8) and (12, 20) is 6/5.

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Answer:

6/5

Step-by-step explanation: