2x + 5y=-7 7x+ y =-8 yousing systems of equations Substituition

The sum of the roots of 2x² − 6x + 1 = 0 is 3 and the product is 0.5076.

The values of variables that satisfy the given quadratic equation are known as its roots. In other words, x = α is a root of the quadratic equation f(x) if f(α ) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersects the x-axis.

To find  sum and the product we first need to find roots/zeroes of the quadratic equation 2x² − 6x + 1 = 0, i.e.

⇒ 2x² − 6x + 1

⇒ 2x²−6x + 1

Putting them in quadratic equation

[tex]$ \Rightarrow x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}[/tex]

[tex]$ \Rightarrow x={\frac {-(-6)\pm {\sqrt {(-6)^{2}-4(2)(1)}}}{2(2)}}[/tex]

[tex]$ \Rightarrow x = \frac{3 -\sqrt{7} }{2}[/tex], [tex]$ \Rightarrow x_2 = \frac{3 +\sqrt{7} }{2}[/tex]

⇒ x = 0.177124,  x₂ = 2.822876

⇒ x = 0.18,  x₂ = 2.82

The sum of the equation roots of 2x² − 6x + 1 = 0 is

0.18 + 2.82 = 3

The Product of the equation roots of 2x² − 6x + 1 = 0 is

0.18 × 2.82 = 0.5076

Thus, The sum of the roots of 2x² − 6x + 1 = 0 is 3 and the product is 0.5076.

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The Pythagorean theorem and the above information can be used to deduce that the diagonal SU has a length of 13.

Given :

It is known that RS=12 and ST=5 in the rectangle RSTU.

The steps listed below can be used to calculate the diagonal SU's length:

The Pythagorean theorem can be used to calculate the diagonal SU's length in step 1.

Step 2 - The following is the Pythagorean theorem:

H² = B² + P²

Where B is the base, P is the perpendicular, and H is the hypotenuse.

Step 3: Replace the known terms' values in the aforementioned expression.

SU² = 12² + 5²

Step 4: Condense the previous expression.

SU = √144 + 25

SU = 13

So, the length of the diagonal SU is 13.

The complete question is:

In rectangle RSTU it is known that RS=12 and ST=5. What is the length of diagonal SU?

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Yes, 4x is an exponential function. An exponential function is one where there is a constant being raised to a variable.

Exponential functions involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round. if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function. The exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price that are growing or decay exponentially. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. it can be extended to the complex numbers or generalized to other mathematical objects like matrices.

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The distance between Afia's school and her babysitter's house is 16 units.

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

The distance between two points in a coordinate plane can be found using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

In this case, the coordinates of Afia's school are (-8, -3) and the coordinates of her babysitter's house are (8, -3).

Plugging these values into the distance formula:

d = √((8 - (-8))^2 + (-3 - (-3))^2)

d = √((8 + 8)^2 + (0)^2)

d = √(16^2)

d = √(256)

d = 16 units

Therefore, the distance between Afia's school and her babysitter's house is 16 units.

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Amber and Jeica go out for lunch. Amber’ lunch cot $11. 70, and he tip 18%. Jeica’ lunch cot $12. 30, and he tip 15%, then the percentage of tip is = 33.9%

Define Percentage :

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

Given that the Amber’ lunch cot is $11.70.

There is a 18% tax.

Therefore the tax on $11.70 is,

= $11.70×18%

= $2.106

The Amber’ lunch cot with tax is $(11.70 + 2.106)

= $13.806.

The Jeica’ lunch cot is $12.30.

There is a 15% tax.

Therefore the tax on $12.30 is,

= $12.30×15%

= $1.845

The Amber’ lunch cot with tax is $(12.30 + 1.845)

= $14.145.

The tip that is given is $(14.145 - 13.806)

= $0.339

The percentage of tip is

= $0.339 * 100

= 33.9%

Therefore,

Amber and Jeica go out for lunch. Amber’ lunch cot $11. 70, and he tip 18%. Jeica’ lunch cot $12. 30, and he tip 15%, then the percentage of tip is = 33.9%

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amber - $13.81

jeica - $1.85

so, jeica paid $11.96 less than amber

The intersection of a triangle's three medians is known as the centroid, and the point at which the perpendicular bisectors of its three sides meet is known as the circumcenter.

The object's centre is represented by its centroid. The centroid of a triangle is where the triangle's three medians connect. The junction of all three medians is another way to describe it. The middle point of a side and the opposing vertex of a triangle are connected by a line known as the median.

The circumcenter of a triangle is the point where three perpendicular bisectors of its sides meet. A triangle's circumcenter is defined as the point at which the perpendicular bisectors of its own sides cross.  In all other senses, the circumcenter is the point at which a triangle's sides intersect to form a bisector.

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The given statement "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)" is true.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

The given statement is "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)".

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Therefore, the given statement is true.

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Answer:

m∠1 = 32

Step-by-step explanation:

∠WXZ = 115

m∠2 = m∠1 + 51

x + x + 51 = 115

2x + 51 = 115

2x = 64

x = 32

After integrating the expression  [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex] we will get the value as: [tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]

Integration by parts, also known as partial integration, is a technique used in calculus and more widely in mathematical analysis to determine the integral of a function's product in terms of the integral of the product of the function's derivative and antiderivative.

The integration of the result of two functions is the integration by parts. Typically, the two functions are shown as f(x) and g. (x). The first function, f(x), is chosen from the two functions in such a way that its derivative formula exists, while the second function, g(x), is chosen in such a way that its integral formula exists.

∫ f(x).g(x).dx = f(x) ∫ g(x).dx - ∫(f'(x) ∫g(x).dx).dx + C

We have, [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]

We know that

[tex]\frac{1}{x}=arccot(x) \\I=5 \int_1^{\sqrt{3}} arccot(x) dx[/tex]

Integrating by parts

[tex]$$\int f g^{\prime}=f g-\int f^{\prime} g$$[/tex]

let  us assume that,

[tex]$\quad f=\cot ^{-1}(x) \quad g^{\prime}=1$[/tex]

[tex]$I=5 \int_1^{\sqrt{3}} \cot ^{-1}(x) d x$[/tex]

[tex]$I=5\left[x \cot ^{-1}(x)-\int \frac{-x}{x^2+1} d x\right]$[/tex]

[tex]$I=5\left[x \cot ^{-1}(x)+\frac{1}{2} \ln \left|x^2+1\right|\right]_1^{\sqrt{3}}$[/tex]

[tex]$I=5\left[\left(\sqrt{3} \cot ^{-1}(\sqrt{3})+\frac{1}{2} \ln |4|\right)-\left(\cot ^{-1}(1)+\frac{1}{2} \ln |2|\right)\right]$[/tex]

[tex]$I=5\left[\frac{\sqrt{3} \pi}{6}+\ln 2-\frac{\pi}{4}-\frac{1}{2} \ln |2|\right]$[/tex]

[tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]

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The correct question should be:

Evaluate the integral [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]

Answer: that realy saadddddddddd

Step-by-step explanation:  4xx 6y 9x

Answer: The slope is -1/5

The mean of Evelyn’s scores based on the information will be 138.

From the information, Robin and Evelyn are playing a target game, the object of the game is to get an object as close to the center as possible and each player’s score is the number of centimeters away from the center.

It should be noted that Robin and Evelyn’s results from five rounds are shown. The mean simply means the average of the numbers.

The mean of Evelyn’s scores based on the information will be:

= (125 + 137 + 138 + 145 + 145) / 5

= 690/5

= 138

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The midline theorem claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long.

The condition for the midline theorem is that the two triangles must have the same size and shape, so all three sides have the same length, and all three angles have the same measure.

For the theorem, we draw a line through two points on either side of the triangle and then we prove that the line divides the sides into equal halves. Once proven that the sides are in two equal halves using congruency it is proved that the base and midline are parallel.

Since the base and midline are parallel to each other using the SAS rule of congruency therefore according to the theorem the segment is half as long as the base.

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Answer:

8, 3

Step-by-step explanation:

28, 23, 18, 13

Subtract each term from the next term.

23 - 28 = -5

18 - 23 = -5

13 - 18 = -5

All differences are equal. When all differences are equal, you have an arithmetic sequence. The equal differences are called the "common difference." To find a new term, add the common difference to the previous term.

13 + (-5) = 13 - 5 = 8

8 + (-5) = 8 - 5 = 3

Answer: 8, 3

The exponential of 16, also known as [tex]e^{16[/tex], is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 16.

To calculate e^16, we would use the following formula:

[tex]e^{16[/tex] = e x e x e x e x e x e x e x e x e x e x e x e x e = 8.222838 x [tex]10^6[/tex]

So, the exponential of 16 is approximately 8.222838 x [tex]10^6[/tex].

It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.

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The equation parallel to the given line is y=-1/4 x+5.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y =-1/4 x+7 and the coordinate point is (8, 3).

Here, slope is -1/4

We know that, the slope of parallel lines are equal.

Now, substitute m=-1/4 and (x, y)=(8, 3) in y=mx+c, we get

3=-1/4 (8)+c

c=5

Substitute m=-1/4 and c=5 in y=mx+c, we get

y=-1/4 x+5

Therefore, the equation parallel to the given line is y=-1/4 x+5.

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So on solving the provided question we cans ay that by unitary method earns 47 hours = 15.34375 * 47 = $721.15625

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

so here,

She earns a fixed salary for the first  = 40hours.

he worked  and earned $613.75

earns per hour = 613.75/40 = 15.34375

earns 47 hours = 15.34375 * 47 = $721.15625

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=> n-4<5

=> n-4+4<5+4

=> n<9

Answer:

Below

Step-by-step explanation:

Point -4, 6    slope = - 3

Point slope form of the line :      ( y-y1) = m (x - x1)

(y-6) = -3 (x - -4)

y - 6 = -3 (x+4)

Using the law of cosines we know that the outfielder throws the ball 169.26 feet away.

The law of cosines in trigonometry establishes a relationship between a triangle's side lengths and the cosine of one of its angles.

According to the Law of Cosines, c2=a2+b22ab cosC.

With the exception of the third component, which equals zero if C is a straight angle and the Pythagorean Theorem results, this is similar to the Pythagorean Theorem.

So, here, the pitcher's mound is 60.5 feet away from home plate.

Additionally, the ball traveled 216 feet when it was struck by the bat.

Allow the outfielder to toss the ball x feet away.

According to the diagram below:

x² = 216² + 60.5² - 2 * 216 * 60.5 * cos34°

x = 169.258748677 ⇒ 169.26 feet

Therefore, using the law of cosines we know that the outfielder throws the ball 169.26 feet away.

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Correct question:

Use the law of cosines to solve the problem. On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. an outfielder catches the ball and throws it to the pitcher. how far does the outfielder throw the ball?

We can see that:

Part A: 3 appointments

Part B: 5 appointments

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Part A

Let x = number of dog grooming appointments Macy had in one day.

Given information:

Charge per appointment = $60

Total amount earned = $220

Total amount of tips earned = $40

Create an equation with the given information:

⇒ 60x + 40 = 220

Solving the equation:

Subtracting 40 from bothsides, we have:

⇒ 60x + 40 - 40 = 220 - 40

⇒ 60x = 180

⇒ 60x ÷ 60 = 180 ÷ 60

⇒ x = 3 appointments.

Part B

Let x = number of dog grooming appointments Logan had.

Given information:

Charge per appointment = $70

Total amount earned = $300

Total amount of tips earned = $50

Rental fee per appointment = $20

Create an equation with the given information:

⇒ 70x - 20x + 50 = 300

Solve the equation:

⇒ 50x + 50 = 300

⇒ 50x + 50 - 50 = 300 - 50

⇒ 50x = 250

⇒ 50x ÷ 50 = 250 ÷ 50

⇒ x = 5 appointments.

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The height of the tree is 5 times of the castle. Then the height of tree is 70 m.

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.

The castle tower has a height of 14 m. The height of the tree is 5 times of the castle.

The height of the tree is calculated as,

⇒ 14 x 5

⇒ 70 m

The height of the tree is 70 m.

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The complete question is given below.

The castle tower has a height of 14 m. The height of the tree is 5 times of the castle. Work out the height of the tree.

Part A:

We want to see how often the number 4 comes up when we roll a fair dice 100 times. We will use a dice with numbers 1,2,3,4,5,6. We will keep track of how many times 4 comes up and we think it should be around 16 times because there are 6 numbers on the dice.

Part B:

We rolled the dice 100 times and got 4 32 times.

-We want to know if that is normal or if something is wrong with the dice.

-We use special numbers to check if this is normal, it's called the confidence interval

-The confidence interval tells us if 32 times is normal or not.

Part C:

The confidence interval tells us that 32 times is not normal, it's unlikely that it happened by chance. So, the dice might not be fair.

The order of rotational symmetry is the number of times a shape can be rotated and still look the same.

Generally, The amount of times that a form may be rotated through 360 degrees with maintaining its appearance is referred to as its rotational symmetry.

For instance, a circle has an order of rotational symmetry of infinity, which means that it can be rotated any number of times and still look the same.

On the other hand, a square has an order of rotational symmetry of 4, which means that it can be rotated by 90 degrees four times while maintaining its original appearance.

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Answer:

x = 50

Step-by-step explanation:

These two angles are supplementary angles which means their sum is equal to 180°.

We can write the following equation based on this information:

3x+5+x-25 = 180

4x - 20 = 180

4x = 200

x = 50

So on solving the provided question we can say that here, coefficient of x² in 3x³+ 2x² -x+ 1 is 2

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of x² in 3x³+ 2x² -x+ 1 is 2

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The Exponential form of the given expression "2 into 2 into a" is represented as [tex]2^{2} \times a[/tex] , and the value is 4a .

The Expression is given as :  " 2 into 2 into a" ;

mathematically the given expression can be written as : ⇒ [tex]2\times 2\times a[/tex] ;

By using the Law Of Exponents , which states that : when the base of the exponents are same the power gets added ;

we see that , the base number 2 is same , So , we add the power of 2 ;

So , on adding the power ,

we get ;

⇒ [tex]2^{2} \times a[/tex] ;

So, the exponential form is [tex]2^{2} \times a[/tex] ;

and the value of this exponential expression is 4a .

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Answer:

  a.  x²

  b.  144 cm²

Step-by-step explanation:

You want to know an expression for the area of the four white triangles in the given figure, and you want to know that area when x = 12 cm.

If you draw horizontal and vertical lines through the middle of the figure, you can see that for each white triangle there is a matching shaded triangle. That is, the shaded area is equal to the white area.

The shaded area is the square of the length of the side of the shaded square, so is ...

  shaded area = x²

The white area is the same, so is ...

  white area = x²

Using x = 12 cm, the formula from part (a) tells us ...

  white area = (12 cm)² = 144 cm²

The total area of the four white triangles is 144 cm².

__

Additional comment

The relation between the side lengths of the shaded area and the side length of the total area is ...

  2x/√2 = x+6

This has one solution: x = 6/(√2 -1) ≈ 14.485281 (cm).

The figure cannot be drawn to scale for any other value of x, so it is impossible for x=12 cm, unless the outside length is (x+4.97056...)

If you take the white triangles to be isosceles right triangles, each will have an area of A = 1/2bh = 1/2(x/√2)(x/√2) = x²/4. The four of them will have an area of 4(x²/4) = x². If you take the white area to be the overall area less the area of a square of side length x, then the area of the four triangles will be (x+6)² -x² = 12x+36. You will notice that these expressions give different values of the area of the white triangles when x=12. (See the previous comment about the value of x.)

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Analyzing the question, Tony must deliver them 35 pieces to make at least $70 an hour.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is used to study mathematical structures that include numbers, as well as variables and other abstract concepts. Algebraic concepts include operations such as addition, subtraction, multiplication, and division, as well as the properties of operations such as distributivity and associativity. Algebraic concepts also include equations, inequalities, and functions.

According the question,

tony make 2 dollars for each delivery,

so, he need to do 70/2 = 35 delivery

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The coordinates of point B of the line AB with M as a midpoint are; (-11, 2)

The formula for the midpoint between two coordinates is;

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

For the line AB, we are told that M is the point and that we have the coordinates as;

A(-7, 2) and M(-2, 2). Thus, plugging in the relevant values gives;

(-2, 2) = (7 + x₂)/2, (2 + y₂)/2

Thus;

(7 + x₂)/2 = -2

(7 + x₂) = -4

x₂ = -11

Similarly, we have;

(2 + y₂)/2 = 2

2 + y₂ = 4

y₂ = 2

B coordinate is (-11, 2)

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The rectangle has a length of 222 feet and a width of 150 feet.

A quadrilateral with parallel sides equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms since their opposite sides are equal and parallel.

We know that the perimeter of a rectangle is the sum of all four sides. So in this case:

Perimeter = 2(length) + 2(width)

Given that the perimeter is 446 feet, we can set up the equation:

446 = 2(13x-1) + 2(9x+4)

On Simplifying, we get:

446 = 44x + 6

Now we can solve for x by subtracting 6 from both sides:

440 = 44x

Finally, dividing both sides by 44:

x = 10 feet

Now that we know the value of x, we can substitute it back into the expressions for the length and width:

Length = (13x-1) = (13(10)-1) = 129 feet

Width = (9x+4) = (9(10)+4) = 94 feet

Therefore, the rectangle has a length of 129 feet and a width of 94 feet.

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