Needing help with this math question

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:

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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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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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:

3

Step-by-step explanation:

Lets use the slope formula, Which is given as :-

[tex]\sf{ \dfrac{y2-y1}{x2-x1} }[/tex]

Substitute the points we have to the formula :-

[tex]\begin{gathered}\sf \longmapsto {\dfrac{16 - 7}{7-4 }} \\ \sf{ \longmapsto {\dfrac{9}{3}} \\ \sf{\longmapsto 3} \end{gathered}[/tex]

Thus, The correct answer is 3!!

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:

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.

The only graph that correctly shows the given piecewise function is; Graph B

It is pertinent to note that when it comes to piecewise functions and inequalities, a closed, or shaded circle is typically used to represent the inequalities greater than or equal to (≥) or less than or equal to (≤) . However, an open, or unshaded circle is typically used to represent the inequalities greater than or less than.

Now, the first part of the piecewise function states that;

f(x) = x + 1 if x < 1

Thus, it will be an unshaded circle pointing to the left direction indicating less than.

The second inequality says 4 provided that x ≥ 1.

Thus;

The line will be a horizontal line pointing right with a shaded circle. Therefore we conclude that only option B is correct.

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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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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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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

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.

Answer:

x = 16°

Step-by-step explanation:

AOB = 74 · 2 = 148°

triangle AOB is isosceles

2x + 148 = 180

2x = 180 - 148

2x = 32

2/2 x = 32/2

x = 16°

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:

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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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

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 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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2x + 3y is a binomial is a true statement.

A polynomial is of various types like binomial, trinomial and multinomial.

Monomial is said to contain only one term, trinomial is said to contain exactly three terms, multinomial contains n number of terms.

An mathematical expression known as a binomial has exactly two terms.

Examples of binomials are 4x² + 5y², xy² + y, x² + 3, x + y, etc.

Here, the given algebraic expression is 2x + 3y, where 2x is one term and 3y is another term. The coefficient of x is 2 and coefficient of y is 3 where as the exponent of x is 1 and the exponent of y is 1.

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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)

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

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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]

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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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.

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.

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 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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Answer:

The square root of 20 is 4.472.

Step-by-step explanation:

As per the given percentage, the total amount Ms. Clark pays, including tip is $30.1

The term percentage is referred as a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Here we have given that the cost of Ms. Clark's restaurant meal is $25. 50. And as a tip, Ms. Clark gives the waiter 20% of the meal's cost.

Now, we need to find the total amount Ms. Clark pays, including tip.

While we looking into the given question,

The following values are given in the question,

Total amount of bill for Ms. Clark = $25.50

Percentage of tip = 20%

Then the amount of tip is calculated as,

=> 25.50 x 20/100

=> 25.50 x 0.20

=> 5.1

Then the total amount paid by Ms. Clark is

=> 25.50 + 5.1

=> 30.1

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