Solve. x² + 20x + 100 = 50
A)x=−10±52√
​B)x=50±252√ ​
​C) x=10±52√ ​ ​
​D)x=50±52√ ​

To transport particles that are 15 times as massive as usual in a river, the speed of the river would need to increase to about 4.14 miles per hour, calculated based on a proportionality relationship to the sixth power.

Given the mass of the particles that a river can transport is proportional to the sixth power of the speed of the river, we can express this relationship as m ∝ v6, where m is the mass of the particles and v is the speed of the river. Then, m1/v16 = m2/v26 which is a statement of the proportionality. If a river, with a normal speed of 2 miles per hour (v1), can transport particles of a certain mass (m1), in order to transport particles that are 15 times as massive as usual (m2 = 15m1), we want to find the required speed (v2).

Substituting the known quantities into the proportionality, we get m1/26 = 15m1/v26. Simplifying this equation gives 1/26 = 15/v26.

To solve for v2, you can perform a sixth root operation on both sides of the equation, resulting in v2 = 6√(15*26). By calculating this, the required speed is nearly 4.14 miles per hour.

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Answer:

The measure of MN is 21 inches.

Step-by-step explanation:

It is given that △ABC∼△LMN.

The corresponding sides of two similar triangles are proportional.

[tex]\frac{AB}{LM}=\frac{BC}{MN}[/tex]

[tex]\frac{8}{12}=\frac{14}{MN}[/tex]

[tex]8\times MN=14\times 12[/tex]

Divide both sides by 8.

[tex]MN=\frac{168}{8}[/tex]

[tex]MN=21[/tex]

Therefore we can say that if △ABC∼△LMN, then the measure of MN is 21 inches.

Answer:

i just want to say that the answer above is correct 15 ft by 30 ft is the write answer

Step-by-step explanation:

i just took my test and got it right

Answer:

A)29 and B) 21,

Step-by-step explanation:

First,in the sequence[tex]a_n=4n-7[/tex] , the parameter [tex]n[/tex] must to be a integer.

Second, we need to solve the equations by  [tex]n[/tex].

[tex]n=(a_n+7)/4[/tex]

All the option in the problem represent an [tex]a_n[/tex]

Then, we need to prove all number in the options, if the result is a integer number, this option can be part of the sequence.

For A)

[tex]n=(29+7)/4=9\\[/tex]

For B)

[tex]n=(21+7)/4=7\\[/tex]

For C)

[tex]n=(20+7)/4=6.75\\[/tex]

For D)

[tex]n=(28+7)/4=8.75\\[/tex]

Only A) and B)  only A and B meet the requirement

The first step Patrick will take in the construction of a circumscribed circle for △RST is: Construct the perpendicular bisector of line segment ST.

A circumscribed circle for a triangle can be defined as a circle is placed inside a polygon or triangle such that it touches all the sides of the triangle.

An example of a circumscribed circle of a triangle is shown in the image attached below.

Therefore, the first step Patrick will take in the construction of a circumscribed circle for △RST is: Construct the perpendicular bisector of line segment ST.

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Answer: Quotient rule of division

Explanation:

In this question, a & b are the exponent of the x.

We know that division is the opposite operation of the multiplication.

Quotient rule division: We subtract the exponent (power) when we dividing the numbers with same base..

Here same base means numerator (top) and denominator (bottom) contain same number and exponent (power) of both numerator and denominator are same or different.

For example: [tex] \frac{5x^{8}}{5x^{6}} [/tex]

Here base 5 is same and exponent are different.

It is same as 5⁸⁻⁶ = 5³ = 125

Now given that,

[tex] \frac{x^{a}}{x^{b}} [/tex] = [tex] x^{a-b} [/tex]

The  correct ordered pairs are (-2, 6)

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

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.

An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables.

Given:

x + 1/2 y = 1

Now, we will take the ordered pairs (-2, 6)

So, substitute x= -2 and y= 6 in the given equation we get

x+ 1/2y

=-2 + 1/2(6)

=-2 + 3

=+1

Hence, the correct ordered pairs are (-2, 6)

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Final answer:

The correct equation to find the length of each of Liam's rectangular plots is x³ + 15x² - 100x - 2,688=0. This cubic equation must be solved to determine the actual length of each plot.

Explanation:

To solve the problem involving Liam's rectangular plots of land, you need to find the length x of each plot. Since the width is 5 yards less than the length, the width is x - 5 yards. With the number of plots being 20 + x, and the total area given as 2,688 square yards, you can set up an equation using the area of a rectangle (length times width) multiplied by the number of plots equal to the total area

The correct equation to determine the length of each plot is as follows:

X (width) × X (length) × (number of plots) = total area

(x) (x - 5) (20 + x) = 2,688

x(x - 5)(x + 20) = 2,688

x³ + 15x² - 100x = 2,688

This simplifies to the equation x³ + 15x² - 100x - 2,688 = 0, which corresponds to option three. Upon solving this cubic equation, you would find the length of each plot. However, the last options are not supported by the given information and should be solved for using the derived equation.

Answer:

If your on edu the simple answer is A

Step-by-step explanation:

Answer: The selling price of a pair of shoes  is $26.46.

Step-by-step explanation:

Given : The wholesale price of a pair of shoes = $24.50

i.e. C.P. = $24.50

Mark up percent = 8% = 0.08 ( To convert a percentage into decimal we divide it by 100)

Formula : S.P. = (Mark up percentage ( in decimal)) x  (C.P.)+ (C.P.)

i.e.

[tex]S.P.=(0.08) \times (24.50)+24.50\\\\\Rightarrow\ S.P.=(0.08+1)(24.50)\\\\\Rightarrow\ S.P.=(1.08)(24.50)\\\\\Rightarrow\ S.P.=26.46[/tex]

Hence, the selling price of a pair of shoes  is $26.46.

Answer: D.    693.55 yd3

Step-by-step explanation:

Given: The diameter of the composite solid = 8.7 yards

Then , the radius of the composite solid = [tex]\dfrac{8.7}{2}=4.35\ \text{yards}[/tex]

Height of cylinder = 9 yards

Height of cone = 8 yards

The volume of cylinder is given by :-

[tex]V_1=\pi r^2h\\\\\Rightarrow V_1=(3.14159265359)(4.35)^2(9)\\\\\Rightarrow V_1=535.021082888{ yards}^3[/tex]

The volume of cone is given by :-

[tex]V_2=\dfrac{1}{3}\pi r^2h\\\\\Rightarrow V=\dfrac{1}{3}(3.14159265359)(4.35)^2(8)\\\\\Rightarrow V=158.5247653\text{ yards}^3[/tex]

Now, Volume of the composite figure will be :

[tex]V=V_1+V_2\\\\\Rightarrow\ V=535.021082888+158.5247653\\\\\Rightarrow\ V=693.545848188\approx693.55\text{ yards}^3[/tex]

Final answer:

The acute base angles of the isosceles trapezoid are each 71 degrees, and the obtuse base angles of the trapezoid are each 109 degrees.

Explanation:

The task is to determine the measure of the acute and obtuse base angles of an isosceles trapezoid that is part of an isosceles triangle with a vertex angle of 38 degrees.

By the isosceles triangle theorem, the angles opposite the equal sides are equal. Since the vertex angle of the isosceles triangle is given as 38 degrees, the base angles of this triangle must be equal. Since the sum of the angles in any triangle must be 180 degrees, we could set up the equation:

38 + 2B = 180

where B represents the base angle of the isosceles triangle. Solving for B gives us:

B = (180 - 38) / 2

B = 71 degre

Each base angle of the isosceles triangle is 71 degrees.

The acute base angles of the trapezoid are also the base angles of the isosceles triangle, so they are 71 degrees each. To find the obtuse base angles of the trapezoid, we note that they are supplementary to the acute base angles. Hence:

Obtuse base angle of trapezoid = 180 - 71

= 109 degrees

Final answer:

To determine the angle of elevation of the road, we use the tangent ratio of rise (400m) to run (1600m), resulting in an angle of approximately 14 degrees.

Explanation:

To calculate the angle of elevation of the road, we can use trigonometry. Specifically, we'll use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. In this context, the opposite side is the rise, which is 400 meters (the vertical height the road climbs), and the adjacent side is the run, which is the horizontal distance of the road, 1.6 km or 1600 meters.

We can calculate the angle of elevation, ϴ (theta), using the formula:

tangent(ϴ) = opposite/adjacent

tangent(ϴ) = 400/1600

ϴ = arctangent(400/1600)

ϴ = arctangent(0.25)

After calculating arctangent(0.25), we find the angle of elevation is approximately 14 degrees.

Answer:

A

Step-by-step explanation:

A function composition is where one function is substituted within another function and is written g(f(x)). Here we will substitute f(x) into g(x). For g(f(-7)), we substitute -7 for x.

[tex] \frac{x^2+6+8}{x^2+6}[/tex]

Now substitute -7 for x.

[tex]\frac{x^2+6+8}{x^2+6} = \frac{(-7)^2+6+8}{(-7)^2+6}=\frac{49+6+8}{49+6}=\frac{63}{55}[/tex]