|x+1| + |x-2| = 3 i need help with this pls

The value of the expression:  [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex] will be: [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]

We have to determine the value of the expression:  [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex]

First solving the expression without using the values of Limits:

As we can write the above as:

[tex]\int {( x^2 + 9)^{0.5}} \, dx \\\frac{1}{0.5+1}[( x^2 + 9)^{0.5+1}] \times \frac{x^3}{3} +9x[/tex]

As we know, [tex]\int{x^n} \, dx =\frac{1}{n+1}x^{n+1}[/tex], where, n is any number.

So we can write the above as:

[tex]\\\frac{1}{1.5}[( x^2 + 9)^{1.5} \times \frac{x^3}{3} +9x][/tex]

Now we will put the value of limits in the above expression:

First putting the lower limit, i.e. the value of x = 3

We will get it as:

[tex]\frac{1}{1.5}[( 3^2 + 9)^{1.5} \times (\frac{3^3}{3} +9\times 3)]\\\frac{1}{1.5} [18^{1.5}\times (9+27)]\\\frac{1}{1.5} [18^{1.5}\times 36][/tex]

Now putting the value of lower limit, i.e the value of x = 3,

We will get it as:

[tex]\frac{1}{1.5}[( 0^2 + 9)^{1.5} \times ({\frac{0^3}{3} +9\times 0)}]\\\frac{1}{1.5} [9^{1.5}\times ({0+0})]\\\frac{1}{1.5} [9^{1.5}\times 0]=0[/tex]

Now, for detemining the value of the expression,

We will subtract the value of lower limit from upper limit

We will get it as; [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]

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Answer:

----------------------------------

Simplify each product and compare with the right side:

A)

B)

C)

D)

E)

Answer:

3 and 4

Step-by-step explanation:

Evaluate each given expression.

Expression 1

[tex]\begin{aligned} \implies \dfrac{3}{8} \times 54 & =\dfrac{3\times54}{8}\\\\&=\dfrac{162}{8}\\\\&=\dfrac{162 \div 2}{8 \div2}\\\\&=\dfrac{81}{4}\\\\&=20\; \rm r\;1\\\\&=20\frac{1}{4}\end{aligned}[/tex]

Therefore, as 20⁵/₆ ≠ 20¹/₄ the equation is not true.

Expression 2

[tex]\begin{aligned} \implies \dfrac{5}{12} \times 26 & =\dfrac{5 \times 26}{12}\\\\&=\dfrac{130}{12}\\\\&=\dfrac{130\div2}{12\div2}\\\\&=\dfrac{65}{6}\\\\&=10\;\rm r\;5\\\\&=10\dfrac{5}{6}\end{aligned}[/tex]

Therefore, as 9³/₄ ≠ 10⁵/₆ the equation is not true.

Expression 3

[tex]\begin{aligned}\implies \dfrac{11}{15} \times 20 & =\dfrac{11 \times 20}{15}\\\\&=\dfrac{220}{15}\\\\&=\dfrac{220\div5}{15\div5}\\\\&=\dfrac{44}{3}\\\\&=14\; \rm r \;2\\\\&=14\dfrac{2}{3}\end{aligned}[/tex]

Therefore, as 14²/₃ = 14²/₃ the equation is true.

Expression 4

[tex]\begin{aligned} \implies\dfrac{3}{8} \times 48 & =\dfrac{3\times 48 }{8} \\\\& =\dfrac{144}{8} \\\\& =\dfrac{18 \times \diagup\!\!\!\!8}{\diagup\!\!\!\!8}\\\\&=18\end{aligned}[/tex]

Therefore, as 18 = 18 the equation is true.

Expression 5

[tex]\begin{aligned} \implies\dfrac{7}{12} \times 48 & =\dfrac{7\times 48 }{12} \\\\&=\dfrac{336}{12}\\\\&=\dfrac{28 \times 12}{12}\\\\&=28\end{aligned}[/tex]

Therefore, as 21 ≠ 28 the equation is not true.

Yes, the sides 5 cm, 12 cm, and 13 cm form a right-angled triangle.

This is because of the Pythagorean Theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, 13 cm is the hypotenuse, and 5 cm and 12 cm are the other two sides.

5^2 + 12^2 = 25 + 144 = 169

13^2 = 169

Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, this means that the triangle is indeed a right-angled triangle.

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The perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.

The complete length of a semicircle's boundary is referred to as the circumference of a semicircle, which is another name for its perimeter. The diameter's length and one-half of the original circle's circumference are added to determine it. Linear units such as "inches," "feet," "metres," or "centimetres," etc. are used to indicate the circle's circumference.

Given that the radius of the semicircle is 3cm.

The formula for the perimeter of a semicircle is:

P = pi(r) + 2r

Substituting the value of r = 3 we have:

P = pi(3) + 2(3)

P = 6 + 3pi

Hence, the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.

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The rocket’s height to the nearest hundredth when the distance between you and the rocket is 100 feet is equal to 96.83 feet.

Based on the information provided, the height h (in feet), of this rocket during its launching with respect to distance d between you and the rocket can be modeled by this quadratic function:

d(h) = √(625 + h²)

Substituting the given parameters into the quadratic function d(h), we have the following;

d(h) = √(625 + h²)

100 = √(625 + h²)

Taking the square of both sides of the quadratic function, we have the following:

100² = [√(625 + h²)]²

10,000 = 625 + h²

Rocket’s height, h² = 10,000 - 625

Rocket’s height, h² = 9,375

Rocket’s height, h = √9,375

Rocket’s height, h = 96.83 feet.

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Yes, The ordered pair (-1,- 3) is a solution to the inequality y > -5x⁴ + 7x³ + 8.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ y > -5x⁴ + 7x³ + 8.

And, The point is (- 1, - 3).

Now, We can substitute the value of (x, y) = (- 1, - 3) in given inequality and check as;

⇒ y > -5x⁴ + 7x³ + 8.

⇒ -3 > -5(-1)⁴ + 7(-1)³ + 8

⇒ -3 > -5 + 7 × - 1 + 8

⇒ - 3 > - 5 - 7 + 8

⇒ - 3 > - 4

This is true.

Thus, The ordered pair (-1,- 3) is a solution to the inequality

y > -5x⁴ + 7x³+ 8.

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The complete question is this,

The ordered pair (-1,- 3) is a solution to the inequality y >-5x⁴ + 7x³ + 8.

1) True

2) False

The dimensions of the rectangle are y - 4y−4 for the length and 3y3y for the width

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Answer:

(1)...  x1 = -14, x2 = -3

(2)... t1 = -2, t2 = 28

(3)... y1 = -7, y2 = 12

(4)... r1 = -13, r2 = -4  

Step-by-step explanation:

Answer:

1.

[tex] {x}^{2} + 17x + 42 = 0 \\ using \: quadratic \: equation \: formula \\ x = \frac{ - 17± \sqrt{ {17}^{2} - 4 \times 1 \times 42 } }{2 \times 1} \\ x = \frac{ - 17±11}{2} \\ for \: x = \frac{ - 17 + 11}{2} \\ x = - 3 \\ for \: x = \frac{ - 17 - 11}{2} \\ x = - 14[/tex]

Answer for 1 : x=-3, x=-14

2.

[tex]t^2-26t=56 \\ also \: using \: quadratic \: equation \\ t = 28 \: or \: t = - 2[/tex]

Answer for 2: t=28, x=-2

3.

[tex]y^2-84=5y \\ {y}^{2} - 5y - 84 = 0 \\ applying \: quadratic \: equation \\ y = 12 \: or \: y = - 7[/tex]

Answer for 3: y=12, y=-7

4.

[tex]17r+r^2=-52 \\ {r}^{2} + 17r + 52 = 0 \\ r = - 4 \: or \: r = - 13[/tex]

Answer for 4: r=-4, r=-13

The number is 14. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.

20 = 4 × (number + 6)

20 = 4 × number + 24

20 - 24 = 4 × number

-4 = 4 × number

number = -4 ÷ 4

number = -1

The equation provided is 20 = 4 × (number + 6). Rearranging this equation gives 20 = 4 × number + 24. Subtracting 24 from both sides gives 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number. Dividing both sides by 4 once again gives number = -4 ÷ 4. Therefore, the number is 14.

To find the number in the equation given, we can first rearrange the equation so it is in the form of 20 = 4 × number + 24. Then, subtracting 24 from both sides gives us 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.

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So on solving the provided question we can say that here, coefficient of 3x² is 3

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 3x² is 3

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The other possible length for the third side of the triangle is 15 cm.

What is an Angle Bisector Theorem?

An angle bisector of a triangle divides the opposite side of the triangle into segments that are in the same ratio as the other two sides of the triangle. This is called the Angle Bisector Theorem.

Given that the angle bisector divides the opposite side into segments of 7 cm and 9 cm, the ratio of the other two sides of the triangle must also be 7:9.

Since the second side of the triangle is 22.5 cm, the third side must be:

x = (22.5 * 9) / 7 = 27 cm

So, the third side of the triangle is 27 cm.

The other side can be calculated by using the Pythagorean theorem.

c^2 = a² + b²

b = √(c² - a²)

b = √((27)² - (22.5)²)

b = √(729 - 506.25)

b = √222.75 = 15cm

Hence, The other possible length for the third side of the triangle is 15 cm.

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Yes, a coordinate plane 2 dimensional

A coordinated plane is an area formed by the intersection of two lines and so is called 2-Dimensional. The horizontal line is called X-axis and the vertical line is called Y-axis. The intersection point of these two lines is called origin.

Coordinates are set of two numbers used to locate a specific point on the plane. They are represented in form of (x,y). The points can be positive zero or negative. They are used to plot graphs pin points draw lines etc.

A coordinated plane has 4 quadrants. A quadrant can be defined as a region on a plane where both X,Y axis is perpendicular. They are:

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Answer:

-5 and -2

Step-by-step explanation:

Answer: x = 2

Step-by-step explanation:

8 = 2x + 4

2x = 8-4

    = 4

x = 4 ÷ 2

  = 2

x = 2

What it would look like if it was an actual equation :

8 = 2₂ + 4

Answer:

x = 2

Terminology

Variable: Any letter than stands for a value than can be solved and change value.

Coefficient: The number right before a variable (without being separated by an operator). It is a multiplication factor for a variable. Basically, it's just a way to express what you are multiplying a variable by,

If the coefficient is 1, it means [variable] * 1. 1[variable]

If the coefficient is 3, it means [variable]  * x.  3[variable]

etc.

Constant: A fixed value (i.e. 3, 8, 1928). A variable is not a constant because if you were to add a coefficient (not including 0) to the start of a variable, the result would change depending on the value of the variable.

How to Solve

To solve, you must isolate the variable. It means moving the variable and it's coefficient to the other side of the equation with only the same variable on the same side with all the constants on the other side.

Do this with this rule that is extremely important in ALL of math beyond per-algebra and algebra.

Rule

If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same. That is how you solve for it.

Subtract 4 on both sides to isolate the variable.

8 - 4 = 2x + 4 - 4

Simplify by combining like terms.

4 = 2x

Divide 2 on both sides to solve for x as the coefficient is currently 2.

[tex]\frac{4}{2} =\frac{2x}{2}[/tex]

Simplify.

x = 2

The cost of fencing the triangular park  at the rate of  ₹18.50 per meter is ₹4903.65

To find the cost of fencing a triangular park with sides measuring 115m, 81.63m, and 69.27m, we first need to calculate the perimeter of the triangle. The perimeter of any two-dimensional figure is defined as the distance around the figure. We can calculate the perimeter of any closed shape just adding up the length of each of the sides.

Perimeter of triangle= Sum of the three sides

To do this, we add up the lengths of all three sides: 115m + 81.63m + 69.27m = 265.9m.

We can then multiply the perimeter by the cost per meter of fencing to find the total cost: 265.9m * ₹18.50/m = ₹4903.65.

So the cost of fencing the triangular park at the rate of ₹18.50 per meter is ₹4903.65

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Answer:

n>10

Step-by-step explanation:

2n>20

n>20/2

n>10

Answer:

your answer is 561,072,052

It is possible to construct a triangle whose sides are 2.5 cm 6.5 cm and 6 cm because the sum of two sides are greater than three sides. 6.5 is the hypotenuse of the triangle because it is the largest length.

In the given question, we have to check that it is possible to construct a triangle whose sides are 2.5 cm 6.5 cm and 6 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 2.5 and 6.5

2.5 + 6.5 > 6

9 > 6

Now we add 2.5 and 6

2.5 + 6 > 6.5

8.5 > 6.5

Now we add 6.5 and 6

6.5 + 6 > 2.5

12.5 > 2.5

It is possible to construct a triangle whose sides are 2.5 cm 6.5 cm and 6 cm because the sum of two sides are greater than third sides.

As we know that the largest length is the hypotenuse of the triangle. So 6.5 is the hypotenuse of the triangle because it is the largest length.

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Answer:

Please see attached.

Step-by-step explanation:

answer: hello

Step-by-step explanation:

If you get the answer then tell me

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Ratio of side of bigger rectangle to that to corresponding side of smaller rectangle (as they are similar) is :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{15}{6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2.5[/tex]

So, the bigger rectangle is a scaled up version of the smaller version with a scale factor of 2.5

So, our required answer will be :

Enlargement with scale factor of 2.5

The table shows a proportional relationship between the cups of milk used and number of tablespoons of chocolate syrup used. The scale factor shown is 3/2. The constant of proportionality for this relationship is 3/2. The units for the constant of proportionality are teaspoons of chocolate syrup used per cups of milk used.

When it comes to ratios and fractions, the concept of proportion is very connected. When two amounts with the same unit are compared, they form a ratio. When comparing two quantities, a ratio enables us to determine whether one is larger or smaller.

Two ratios or two fractions are equivalent when they are compared according to the proportional rule. To put it another way, two ratios are said to be proportional when they are equal. Performing arithmetic operations on both sides of the ratio taught us that a ratio can be expressed in a variety of ways.

Both the 3: 5 and 6: 10 are equivalent ratios. This indicates that these ratios are proportional. This proportionality can be expressed mathematically as follows:

                                                 [tex]$ \frac{3}{5} = \frac{6}{10}[/tex]

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The perimeter of a square with an area of 100 square meters is calculated to be 40 m

The perimeter of a square is calculated using the formula 4 * length

Some necessary properties of a square

A square is a four sided polygon otherwise known as quadrilateral

All the sides are equal hence Length =  width or breadth

The angles at which each side intersect is at 90 degrees

The area of a square is Length² hence

Length² = 100

Length = √100

Length = 10

plugging in Length = 10 to the perimeter

P = 4 * length

P = 4 *10

P = 40 m

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The location of the point k after dilation and reflection over the x-axis is (3,-1).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis.

Dilation of the point will be,

J(2,4) = j'(1,2

K(6,2) = k'(3,1)

The reflection over the x-axis of point k is,

k'(3,1) = ( 3,-1)

Hence, the point k will be (3,-1)

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Answer:

32

Please mark brainliest if this is correct! :)

Answer:

1024/32= 32.

Step-by-step explanation:

i call it a calculator

The probability of P(26 < X < 30) is 0.48.

In this case, the given parameters are:

Mean μ = 26

Standard deviation σ = 2

So, the probability P(26 < X < 30) will be represented as:

P(26 < X < 30)

= P(z1 < z < z2)

where:

z = (X – μ) / σ

Thus, now we have:

P(26 < X < 30)

= P((26 – 26) / 2 < z < (30 – 26) / 2)

= P(0 / 2 < z < 4 / 2)

= P(0 < z < 2)

= P(z < 2) – P(z < 0)

For z-score of probabilities, we have:

P(26 < X < 30)

= P(z < 2) – P(z < 0)

= 0.97725 – 0.5

= 0.47725

= 0.48

Hence, the probability of P(26 < X < 30) is 0.48.

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Although part of your question is missing, you might be referring to this full question: Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively. Suppose we select one of these cars at random. Let X represent the sale price (in thousands of dollars) for the selected car. Find P(26< X<30).

one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.

An obtuse triangle is a triangle that has one angle which measures greater than 90 degrees. In order to determine if a triangle is an obtuse triangle, we need to calculate its angles.

To calculate the angles of the triangle, we can use the following formula:

Angle 1 = arccos ( (b2 + c2 - a2) / 2bc )

Angle 2 = arccos ( (a2 + c2 - b2) / 2ac )

Angle 3 = arccos ( (a2 + b2 - c2) / 2ab )

In this case, a = 6cm, b = 10cm, and c = 13cm. Substituting these values into the formula, we get:

Angle 1 = arccos ( (102 + 132 - 62) / 2 x 10 x 13 ) = 89.99 degrees

Angle 2 = arccos ( (62 + 132 - 102) / 2 x 6 x 13 ) = 110.01 degrees

Angle 3 = arccos ( (62 + 102 - 132) / 2 x 6 x 10 ) = 89.99 degrees

Since one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.

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For weeks before labor starts, the cervix can dilate to 1 centimeter. The cervix is only beginning to prepare for labor at this stage of dilatation.

Every woman experiences a different amount of time between dilation to 1 cm and delivery. While another woman maybe 1-2 cm dilated for days or weeks, one woman may move from having a closed cervix to giving birth in a matter of hours.

Some women don't start dilating until they start laboring actively. This indicates that the cervix is initially fully closed, but as labor goes on, it opens to a diameter of 10 cm. First pregnancies are where it occurs most frequently. Other women, particularly those who have already given birth, may begin dilating days or weeks before the commencement of labor.

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Chord of a circle is a straight line segment whose endpoints both lie on the circle.

A chord is a line segment that connects any two locations on the circle’s circumference.A straight line segment that connects and includes two points on a circle. A straight line connecting two points on a curve. 3.: an unique mood or temperament. I hit a responsive chord.

A chord is a line segment that connects two points on a curve in plane geometry. The word is frequently used to denote a line segment with endpoints on a circle. A chord is a line segment that connects two points on any curve, such as an ellipse. The diameter of a circle is defined as a chord that goes through its center point. The word chord is derived from the Latin chorda, which means bowstring.

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The complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

What is the congruent triangle?

The triangles are congruent regardless of how they are rotated or flipped. The symbol “≅” is frequently used to express the congruence of two items. In the diagram given, ΔABC ≅  ΔXYZ.

The corresponding angles and the sides of the triangles are also congruent with each other.

We have given,

all the corresponding congruent angles and sides. Then the triangle congruence statement.

a)

∠A ≅ ∠Y

∠B ≅ ∠Z

∠C ≅ ∠X

b)

AB ≅ YZ

AC ≅ XY

BC ≅ XZ

c)

ΔABC ≅  ΔXYZ.

Therefore, the complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

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