Determine the set of all real numbers 푥 such that

2푥 + 1 ≤ 5푥,
3푥 + 5 > 4푥 − 2.
Note that 푥 must satisfy both inequalities. Graph the result on the number
line.

Solving the provided question we can say that the  quadratic equation is  [tex]x^2+4x-21[/tex] answer is x = -5 and 1

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the  quadratic equation is

[tex]x^2+4x-21[/tex]

answer is x = -5 and 1

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The incorrect statement is that You can solve for the unknown side in any triangle, if you know the lengths of the other two sides, by using the Pythagorean theorem.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Pythagoras theorem is only applied for right angled triangles.

There is hypotenuse which is the longest side for only right angled triangles. So we cannot find the length of the third side of any triangle using the Pythagorean theorem.

Hence the statement that you can solve for any triangle's unknown side using the Pythagorean theorem is incorrect.

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The exponential model that’s the point shown in the table is 8.00 * 0.10ˣ.

An exponential model is a mathematical function that describes the growth or decay of a quantity over time, where the rate of change is proportional to the current value of the quantity. It takes the form y = ab^x, where a is the initial value, b is the growth factor (b > 1 for growth, 0 < b < 1 for decay), and x is the time or independent variable.

To find the exponential model that fits the points shown in the table, we can use the least-squares method. This method involves finding the line of best fit that minimizes the sum of the squares of the differences between the observed y values and the estimated y values from the model.

For an exponential model of the form y = abˣ, the least-squares method requires taking the natural logarithm of both sides to obtain the equation ln(y) = ln(a) + xln(b). This equation has the form of a linear equation, y = mx + b, where m = ln(b) and b = ln(a). We can then use the least-squares method to find the line of best fit for this equation and solve for m and b.

Given the points (0,8) and (3,1), we can use the following calculations to find m and b:

ln(8) = m0 + b

ln(1) = m3 + b

Solving the system of equations, we obtain:

m = -2.3026

b = 2.3026

Therefore, the exponential model that fits the points is:

y = [tex]e^{b} *e^{m * x}[/tex]

y = [tex]e^{2.3026} *e^{-2.3026 * x}[/tex]

Rounding the exponent to four decimal places, we get:

y = 8.00 * 0.10ˣ

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Answer:

5 5/8

Step-by-step explanation:

2 2/3=8/3

8/3x=15

x=15*3/8

x=5 5/8

Answer:

Step-by-step explanation:

67267642qwu62we2q[tex]x^{2} \alpha we2qe\pi qeqe\beta \beta \left \{ {{y=2} \atop {x=2}} \right. \int\limits^a_b {x} \, dx x_{123} \alpha \pi \\ \\ \\ \\ \neq x^{2} \alpha \sqrt[n]{x} \sqrt[n]{x} x^{2}[/tex]e5427856418548248e654815

The triangle that is produced is a right-angled triangle, as can be seen in the diagram. ∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height

The triangle that is produced is a right-angled triangle, as can be seen in the diagram.

∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height

Additionally, the right-angled triangle's area ($) (0,0),

[tex](\mathrm{x}, 0),(0, \mathrm{y})=$ $\frac{1}{2}|x y|$ sq.units[/tex]

⇒ Area of the right-angled triangle formed by the points

(0,0),(4,0),(0,3) =  [tex]$\frac{1}{2}|4 \times 3|$[/tex]  sq.units

[tex]$=\frac{1}{2} \times(12)[/tex]

= 6 sq.units

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Using the ALEKS calculator , 13.1 would roughly equal 172, rounded to the closest hundredth.

When necessary, ALEKS offers a calculator so that users may determine the difference. Instead of using your own calculator, just utilize ALEKS'. For the calculator to produce most accurate assessment results, it must only be used in the manner specified by ALEKS.

Reviewers believed that Khan Academy and ALEKS better satisfy their needs as a business. Reviewers believed that Open Courseware is the best choice when considering the level of continuing product support. Our evaluators liked the approach of Online Courses over ALEKS for feature releases and roadmaps.

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The statements that are true are:

1. f(2) = 0 , therefore (x-2) is a factor

2. (x+3) is a factor of f (x) because f (x) divided by (x+3) has a remainder of 0.

3. x-7) is a factor of f(x).

Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying. To factor polynomials, we generally make use of the following properties or identities; along with other more techniques.

The polynomial x³- 6x2 - 13x + 42 has three factors.

The first factor is found by by representing x by 2 i.e f(2) = 2³-6(2)²-13(2)+42

this will give 0

therefore if x= 2

then x-2 =0

when x-2 is used to divide the polynomial it gives a quadratic equation x²-4x-21. This will give a factor (x+3) and (x-7)

Therefore the factors of the polynomial are( x-2)(x+3) and( x-7)

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As per the standard deviation, the probability of 8≤ X < 11 is 0.1429.

A random variable X is a mathematical representation of the possible values that a random process or experiment can take on. X has a normal distribution, meaning that its distribution follows a bell-shaped curve.

The standard deviation measures how spread out the values of X are around the mean.

If X has a mean of μ and a standard deviation of 2, then 68% of the values of X will fall within one standard deviation of the mean.

This means that about 68% of the values of X will fall between μ-2 and μ+2.

To find the probability that X falls between 8 and 11, we need to use the cumulative distribution function (CDF).  

Using the standard normal distribution table, we find that P(X < 8) = 0.8413 and P(X < 11) = 0.9842.

Thus, the probability that 8≤ X < 11 is

=> 0.9842 - 0.8413 = 0.1429,

which rounded off to the 4th decimal place is 0.1429.

Complete Question:

Random variable X has a normal distribution with mean μ and standard deviation 2. The pdf f(x) of X satisfies the following conditions: (A) f(6) > f(16), (B) f(1) < f(17). When u is an integer, what is P(8≤ X < 11) (round off to the 4th decimal place)?

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Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]

Check attached images 1 and 2.

[tex]\frac{d}{dx} =y'\\ \\y'=(3*\frac{1}{3})x^{3-1} +2*x^{2-1} -(1*3)x^{1-1} \\ \\y'=x^{2} +2x-3[/tex]

Use the quadratic formula.

Check attached image 3.

a = 1

b = 2

c = -3

[tex]x_{1} =\frac{-(2)+\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =1\\ \\x_{2} =\frac{-(2)-\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =-3[/tex]

Quick analysis. This results tell us that the minimun and maximum points different that infinity of the original function ([tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]) are located in points x = 1 and x = -3. Now, we need to discover who's the maximum point and who's the minimum. For this, evaluate both point in the original function.

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(x)=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(1)=\frac{1}{3}(1)^{3} +(1)^{2} -3(1)\\\\ =\frac{1}{3}+1-3 \\\\ =\frac{1}{3} +\frac{3}{3}-\frac{9}{3} \\ \\=\frac{1+3-9}{3} \\ \\=-\frac{5}{3}[/tex]

[tex]f(-3)=\frac{1}{3}(-3)^{3} +(-3)^{2} -3(-3)\\ \\=\frac{1}{3}(-27) +(9)-(-9)\\ \\=\frac{-27}{3} +9+9\\ \\=-9+9+9\\ \\=9[/tex]

Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

Check out the graph (attached image 4) to better understand the method used for this solution.

Note. See that the "x" coordinates where the function has maximum and minimum points are the exact same "x" coordinates where the derivative touches the "y" axis, that's why we calculated the roots of the derivative and then evaluated in the original function.

Given the L-shaped line

where p 1 = ( 0, 2, 2 )

L → Р = Ро + tυwhere p = ( x, y, z ) and p 0 = ( 1, 1, 0 ) and v = ( 1, 2, 2 )

The components p 1 and L constitute a plane with the normal vector n given by

→ \sn \s= \sλ \s1 \s( \sp \s0 \s− \sp \s1 \s)

when R = 1

L 1 is the desired line and is orthogonal to L, so

L 1 p = p 1 + t 1 v 1 = p 1 + t 1 v 1 where

2 v n with 2 R v 1 = 2 v n with 2 R

It is more advantageous to parameterize relations or implicit equations since they become explicit functions once parameterized.

A circle, for example, may be defined as x 2 + y 2 = r 2. When a relation passes the vertical line test, you know it is a function; a circle does not.

When you try to define the circle directly, you get: y = r 2 x 2. Again, this is not a function; it is the combination of two functions.

When we parameterize a circle, we get: x = r cos t

y \s= \sr \ssin \st

t \s∈ \sR

Both x and y are explicit functions that may be plotted, integrated, or differentiated as needed.

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The parametric equation of the plane is x = 11/6 t, y = -5/2t, z = 1 1/2 t.

(x, y, z) = (0, 2, 2) + t(i - j +2 k)

A plane that is parallel to this line will have the general equation:

x - y + 2z = c

We make it contain the point by substituting in the point and solving for c:

0 + 2 +2(2) = 4

c = 4

The plane x - y + 2z = 4 contains the point (0, 1, 2) and is perpendicular to the line.

To find the point where the line intersects the plane, substitute the parametric equations of the line into the equation of the plane:

x - y + 2z = 4

(1 + t) − (2 − t) + 2(2t) = 4

1+t-2+t+ 4t = 4

6t = 5

t = 5/6

x = 11/6, y = 7/6, z=5/3

The line intersects the plane at the point (11/6, 7/6, 5/3)

The vector, v, from the given point to the intersection point

v = (11/6 - 0)i + (7/6 - 2)j + (5/3 - 2)k

v = 11/6 i -5/2 j - 1/2 k

The vector equation of the line is:

(x, y, z) = (0, 2, 2) + t (11/6 i -5/2 j - 1/2 k)

The parametric equations are:

x = 11/6 t,

y = -5/2t,

z = 1 1/2 t

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The fourth term a₄ of the sequence is 15

The definition of the function is given as

a₁= 6

aₙ = aₙ₋₁ + 3

The above definitions imply that we simply add 3 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = 6 + 3

a₂ = 9

Also, we have

a₃ = 9 + 3

a₃ = 12

Lastly, we have

a₄ = 12 + 3

Evaluate the equation

a₄ = 15

Hence, the value of a₄ is 15

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Complete question

Sequence and series:

If a_1=6 and a_n=a_{n-1}+3, then find the value of a_4

The new length of the longer side after application of a scale factor of 1/4 is; 7.125 ft

A scale factor is defined as the ratio between the scale of a given original object and a new object. This will be indicative of its' representation but of a different size. Thus, it could represent an enlargement or a reduction.

Now, we are given that the length of the sides are;

Length of longer sides = 28.5 cm

Length of shorter side = 16.5 cm

Thus, if the scale factor is 1/4, then it means that;

New length of longer side = 1/4 * 28.5

New length = 7.125 ft

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Step-by-step explanation:

A whole can be divided into many parts and the number of parts will depend on the unit of measurement we use to divide it.

A whole can be divided into fifty equal parts, each of which is called a "fiftieth." So, one whole would be equal to 50 fiftieths.

1 whole = 50 fiftieths

Alternatively, we can say that one fiftieth is equal to 1/50th of a whole. This can be represented as a decimal or a fraction.

1 fiftieth = 1/50th of a whole = 0.02 (decimal)

Answer:

30.39 and 10.26 pounds.

Step-by-step explanation:

Step 1 of 2: if the variables x (for 41% alloy) and y (for 54% alloy), then

Step 1 of 2: it is possible to make up the system of two equations:

[tex]\left \{ {{x+y=0.45*40} \atop {0.41x+0.54y=0.45(x+y)}} \right. < = > \ \left \{ {{y=\frac{72}{13} } \atop {x=\frac{162}{13}}} \right.[/tex]

then the mass of the alloy containing 41% of coper is 162/13:0.41≈30.39

the mass of the alloy containing 54% of copper is 72/13:0.54=10.26.

Answer:

A train traveling at a constant speed of 105 miles per hour covers a distance of 315 miles in 3 hours. To find the distance in feet, we need to convert miles to feet:

315 miles * 5,280 feet/mile = 1,654,400 feet

So, in 3 seconds, the train travels approximately:

1,654,400 feet / (60 seconds/minute * 60 minutes/hour) = 9,072 feet

Therefore, in 3 seconds, the train traveling at a constant speed of 105 miles per hour travels approximately 9,072 feet.

Answer:

To convert miles per hour to feet per second, multiply the speed in mph by 5280/3600 = 1.46667.

105 mph * 1.46667 ft/s = 153.333 ft/s

To find the distance travelled in 3 seconds, multiply the speed by time:

153.333 ft/s * 3 s = 315 ft

Answer: Here are the evaluations of the expression 46 + (-2k) for the given values of k:

For k = 3: 46 + (-2 * 3) = 46 - 6 = 40

For k = 23: 46 + (-2 * 23) = 46 - 46 = 0

For k = -2: 46 + (-2 * -2) = 46 + 4 = 50

So, the evaluated expressions are 40, 0, and 50 respectively.

Step-by-step explanation:

The point slope form of the equation is y-5=4(x-3).

What is point slope form of the equation?

The slope of a straight line and a point on the line are both components of the point-slope form. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line. In order to calculate the equation of a straight line in the point-slope form, only the line's slope and a point on it are needed.

Here the given point [tex](x_1,y_1)=(3,5)[/tex] and slope m=4 then using equation of line formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-5 =4(x-3)

Hence the point slope form of the equation is y-5=4(x-3).

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The order of the quadrants in a Cartesian plane goes in a counterclockwise direction. The correct option is C

Quadrants is the axes of a two-dimensional Cartesian system divide the plane into four infinite regions, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I coordinates are I, II , III and IV .

Therefore, Quadrant is an instrument used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings such as longitude and latitude.

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The required number word that is one more than fourteen is "fifteen."

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
In the number system when we add 1 to the number 14, what we get is 15 in words it is fifteen
So,
one + fourteen = fifteen

Thus, the required number word that is one more than fourteen is "fifteen."

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Answer:

4.2 yrs hope this helped. :)

Step-by-step explanation:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

Answer:

Inverse

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

1 is FIRST degree

degree of 2 would be a second degree

The expected value of each warranty sold is the amount of $15.

A written guarantee of a product's integrity and the maker's duty for the repair or replacement of damaged parts.

As per the question, the required solution would be as:

The expected cost of a failed product without a warranty is :

= $100 x (6/100)

= $100 x 0.006

Apply the multiplication operation,

= $0.6.

The expected cost of a failed product with a warranty is :

= $100 x 0.006 + $15 = $15.6.

So the expected value of each warranty sold is :

= $15.6 - $0.6

Apply the subtraction operation, we get

= $15.

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The required cost of the extended warranty is given as $115, as pe the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
The original warranty period but within 2 years of the purchase, with a replacement cost of $100.  They offer a 2-year extended warranty for $15,
Expected value = 100 + 15 = $115

Thus, the required cost of the extended warranty is given as $115, as per the given condition.

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Answer:

Step-by-step explanation:

P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.5 - 0.3 = 0.8.

Answer:

129

Step-by-step explanation:

516/4 = 129

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Therefore , the solution of the given problem of angles comes out to be 41.92 angles is the correct option.

In Euclidean space, an angle is indeed a construction comprised of two beams that split at the apex & vertex, which are located in the middle of the angle. The side of loops are the name given to these rays. A combination of two rays may result in an angle that is within the planes in that they are located. Two planes can be combined to form an angle as well. They are referred to as dihedral angles. Two line rays with end points can be arranged in a variety of ways to create styles in two dimensions.

Here,

Given :

=>  speed = 35 feet per second

=> time = 0.8 second

=> height = 9 feet

Distance covered slantly = 0.8 * 35 = 28 feet

=> Sin x = 9/28

=> x =  Sin⁻¹(9/28)

=> x = 41.92

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Answer:

The demand curve is shown below, with the equation P = 50 - 1Qp. The supply curve is shown below, with the equation P = 40 + 1Qs. The point at the market equilibrium is shown with an asterisk, where the two curves intersect.

Demand Curve: 60- 50- * 40- 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON

Supply Curve: 60- 50- 40- * 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON