Simplify the expression
using only positive exponents.

Answer:

Where is the triangle?

Step-by-step explanation:

The measure of Supplementary angles is ∠1 is 59° and ∠2 is 121°.

The word "supplementary" refers to two angles coming together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles complement one another.

It has an acute angle on one side and an obtuse angle on the other.

The angles are both right angles.

Given ∠1 and ∠2 are supplementary angles,

let ∠ 1 = x°

∠1 + ∠2 = 180°

so ∠2 = 180 - x

angle 2 is 3° more than twice the measure of angle 1,

and ∠2 = 3 + 2x

substitute the values

∠2 = 180 - x

3 + 2x = 180 - x

2x  + x = 180 - 3

3x = 177

x = 177/3

x = 59°

∠2 = 180 - x

∠2 = 180 - 59

∠2 = 121°

Hence the value of ∠1 is 59° and ∠2 is 121°.

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An example of Equivalent Expressions in math is

2(x² -1 ) - 1 and 2x² - 3 , because the value both remains same for any value of x.

Equivalent expressions are defined as the expressions that work the same even though they look different. Two expressions are equivalent when they can be simplified to the same third expression or if one of the expressions can be written like the other. In other words we can say that two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(p) for the variable(x). Let's consider an example for better understanding, let 2( x² - 1) - 1 be an algebraic expression and we want to determine its equivalent expression.

Simplify, the expression, 2( x² - 1) - 1 --(1)

=> 2x² - 2 -1

=> 2x² - 3 --(2)

if x= 1 , 2( x² - 1) - 1 = 2( 1² - 1) - 1 = -1 and 2x² - 3 = 2(1)² - 3 = -1

Now, expression (1) and (2) looks different but we get same value when substitute the same value of variable(x). By using definition, both expressions are equivalent.

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Answer:

Obtuse

Step-by-step explanation:

An angle that is measured more than 90 degrees is an obtuse angle. Although an angle that measures 180 degrees is a straight angle or a half angle, and an angle that measures 360 degrees is a straight angle or a complete angle. However, when it's 360 degrees it's a full circle because a circle measures 360 degrees. If you want to measure an angle to determine which one it is, you must use a protractor.

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Answer:

Step-by-step solution:

Let's first familiarize ourselves with the basic types of angles out there.

The simplest angles are:

In a nutshell, acute angles are angles whose measure is less than 90 degrees, right angles are the ones whose measure is exactly 90 degrees, and obtuse angles are the ones whose measure is greater than 90 degrees.

Here's what an obtuse angle looks like.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{.4mm}\qbezier(1,1)(1,1)(5.5,1)\qbezier(1,1)(1,1)( -1,4)\qbezier(0.65,1.55)(1.5,1.8)(2,1)\put(3,3){\rm Obtuse Angle :}\put(3,2.5){\it measures more than}\put(3,2){\sf 90 degrees}\end{picture}[/tex]

--

Now, since 140 measures more than 90 degrees, it's an obtuse angle.

[tex]\therefore\quad\underline{\boxed{\sf{The~angle~is~obtuse}}}[/tex]

Answer: 8.46 years

Step-by-step explanation:

To find out how long it will take for the account value to reach $25,300, you would need to use the formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount (25,300)

P is the initial amount (3,100)

r is the annual interest rate (7.25%)

n is the number of times the interest is compounded per year

t is the number of years

In this case, we can assume that the interest is compounded annually, so n=1.

We can then plug in the values and solve for t:

25,300 = 3,100(1 + 0.0725)^t

t = (ln(25,300/3,100)) / (ln(1 + 0.0725))

t ≈ 8.46 years

So it would take approximately 8.46 years, rounded to the nearest year.

Answer:

The correct answer would be 30

Step-by-step explanation:

Answer:

1296

Step-by-step explanation:

(6+30)²=36²=1296

Answer:

1296

Step-by-step explanation:

(6+30)^2

(36)^2

1296

The expression that represents the total cost of buying and shipping the baseball cards,

= 6(1.75) + 5(9.5) + 2(20.5) + 4

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Jake is buying baseball cards for his brother in college.

The price of a card is based on its condition.

The table shows the total cost of x number of cards for each condition.

He buys 6 that are in fair condition, 5 that are in good condition, and 2 that are in excellent condition.

The shipping cost for the baseball cards is $4.00.

The expression that represents the total cost of buying and shipping the baseball cards,

= 6(1.75) + 5(9.5) + 2(20.5) + 4

= 10.5 + 47.5 + 41 + 4

= 103

Therefore, the total cost is $103.

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A. Rachel have the amount of money left in her account after 9 trips, $112

B. Rachel can take a number of trips until her account is empty, 16 trips

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Rachel spends amount of money in each trip = $16

Rachel has total money in beginning of a month = $256

Equation for a relation between number of trips and amount of money in account,

A(t)=256-16t

A.   Amount of money left in account after 9 trips

    A(9) = 256-16×9

    A(9) =  256 - 144

    A(9) =    112

B.   Number of trips she can do till her account becomes empty

      0 = 256 - 16t

      16t = 256

       t =  256/16

       t = 16

Hence, the results are respectively,   $112 and 16    

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Answer:

Hope it will help you...

If this help you then please mark my answer brainliest....

Any three equations do not have any solution if all the determinants associated with the system of equations are equal to 0.

For a system of 3 linear equations

a₁x + b₁y + c₁z + d₁ = 0

a₂x + b₂y + c₂z + d₂ = 0

a₃x + b₃y + c₃z + d₃ = 0

We need to find some determinants that will help us determine the no. of solutions it can have.

We have,

 [tex]\Delta = \left[\begin{array}{ccc}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{array}\right][/tex]

[tex]\Delta_1 = \left[\begin{array}{ccc}d_1&b_1&c_1\\d_2&b_2&c_2\\d_3&b_3&c_3\end{array}\right][/tex]

[tex]\Delta_2 = \left[\begin{array}{ccc}a_1&d_1&c_1\\a_2&d_2&c_2\\a_3&d_3&c_3\end{array}\right][/tex]

[tex]\Delta_3 = \left[\begin{array}{ccc}a_1&b_1&d_1\\a_2&b_2&d_2\\a_3&b_3&d_3\end{array}\right][/tex]

Now first we need to check the value of Δ

If, Δ ≠ 0, then we can say that the system of equations is consistent and will give us a unique solution.

However, we are concerned with the case when Δ = 0.

If Δ = 0, then we need to find the values of Δ₁, Δ₂, and Δ₃.

If at least one of the three Δ₁, Δ₂, and Δ₃ is not equal to 0 then we say that the equation is consistent.

Now if,

Δ₁ = Δ₂ = Δ₃ = 0, then we need to do the following:-

We need to take any 2 equations and get the values of x and y in terms of z.

Now we need to substitute the value of x and y for these values in the third equation.

If the third equation is satisfied, we can say that they will have infinite solutions but if they don't, then we can say the given system of equations will have no solutions.

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The equation of the circle in the form of x^2 + y^2 + Px + qy + c = 0

The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.

Given the center of the circle is (-2,3) and the radius is 3cm.

Substituting the given values we get (x + 2)^2 + (y - 3)^2 = 3^2

Expanding and simplifying we get x^2 + 4x + 4 + y^2 - 6y + 9 = 9

x^2 + 4x + y^2 - 6y + 5 = 0 is the equation of the circle in the form of x^2 + y^2 + Px + qy + c = 0

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Answer:

88 yards

Step-by-step explanation:

because the park is 11 inches wide in the drawling, and the scale of it is 1:8

so the actual width of the park is

[tex]11/1/8=11*8=88 yards[/tex]

11 divided by 1/8

The speed of a point on the wheel rim is 35000π cm/s (2500 rev/min and 14cm diameter).

what is circumference ?

Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

To express the speed of a point on the rim of the wheel in centimeters per second, we first need to find the circumference of the wheel using the diameter. The circumference can be found using the formula: C = 2πr, where C is the circumference and r is the radius of the wheel.

Since the diameter is 14cm, the radius of the wheel is 14/2 = 7cm.

Therefore, the circumference of the wheel is: C = 2π(7) = 14π cm

Next, we need to find the distance traveled by a point on the rim of the wheel in one revolution. This distance is equal to the circumference of the wheel.

So, the distance traveled by a point on the rim of the wheel in one revolution is: 14π cm

To find the speed in centimeters per second, we need to multiply the distance traveled in one revolution by the number of revolutions per minute.

The wheel rotate 2500 revolution per minute.

The speed of a point on the wheel rim is 35000π cm/s (2500 rev/min and 14cm diameter).

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Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

We must first determine the circumference of the wheel using the diameter in order to describe the speed of a point on the rim of the wheel in centimeters per second. The formula C = 2r, where C is the circle and r is the radius of the wheel, can be used to determine the circumference.

Since the diameter is 14cm, the radius of the wheel is 14/2 = 7cm.

Therefore, the circumference of the wheel is: C = 2π(7) = 14π cm

36 feet of fencing will be needed

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m2).

Area of a Square = Side × Side

Therefore, the area of square = Side2  square units

and the perimeter of a square = 4 ×  side units

Area of square field = 81 hectare

1 hectare = 10000 sq.m.

So, 81 hectare = 810000 sq.m.

So, Area of square field = 810000 sq.m.

Area of square=Side²

side²=810000

side =√810000

side=900

So,

Perimeter of square = 4×  side

Perimeter of square field = 4 × 900 =3600m

Therefore 36 feet of fencing will be needed

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Trigonometric ratios depend only on angles as they remain constant no matter what.

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides relate to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trigonometric ratios, cosec, sec, and cot.

Even if the sides of the triangle increases or decreases in a specific ratio, the angles of the triangle will always remain the same no matter what.

Trigonometric ratios in right triangles are therefore independent of the side lengths  and solely depend on the magnitude of the angles.

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The area of an isosceles triangle with an equal side of 8 cm and each equal side of 5cm is 12cm².

[tex]Altitude =\sqrt{5^{2} -4^{2} }=3[/tex]

[tex]Area = 1/2(base)(height)[/tex]

[tex]Area = 1/2*8*3 = 12cm^{2}[/tex]

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Answer:

A line plot is the most appropriate way to visualize these data. The scale should be labeled starting at 14 and going up to 19, with increments of 1/8 pound. For example, the x-axis labels could be 14, 14⅛, 14¼, 14⅜, 14½, 14⅝, 14¾, 14⅞, 15, 15⅛ and so on up to 19.

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Answer :

Domain: Domain of a functions is defined as set of all values of x taken by the function, Which means all the values of x taken by the graph.

From the figure, we can see that all values of x taken from [-1, - 4]. So domain is [-1, - 4].

Range: Set of all values produce of by function, Which means all y's values taken by the graph.

From the graph, we can see that between - 2 to - 4 all values are taken by graph Hence, Range is given as [-2,-4].

The German mark appreciated by 1.3% against the US dollar between 1970 and 1976.

This was due to strong economic growth in Germany and a decrease in inflation, which increased the purchasing power of the mark against the dollar. The appreciation of the mark against the dollar also helped to stimulate exports from Germany and reduce imports, creating a more balanced trade balance between the two countries.

The German mark appreciated by 1.3% against the US dollar due to strong economic growth and reduced inflation.

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The one example of absolute value function is x =|y| , and the graph is sketched below .

What is Absolut value Function ?

The absolute value function is defined as a function in algebra that consists of the variable in the absolute value bars. The general form of absolute value function is written as f(y) = a |y - h| + k .

let the absolute value function be : x = |y|  ;

we put y = -1 , we get ⇒ x = 1  ;

we put y = 1 , we get ⇒ x = 1 ;

we put y = 0 , we get ⇒ x = 0 ;

from the above points we observe that , what ever we put in the function , the result "x" is always positive .

Therefore , the graph of the function x = |y| , is a V shaped graph that faces Right .

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Answer:74 blue beads and 90 purple beads

Step-by-step explanation:

first you need to take the total number of beads 164 divide by the 2 colors so 164÷2=86 then you subtract the 8 more purple from 1/2 of 86 and you get 74 then you add 8 more to the other half of 82 and get 90 purple and 74 blue.

The solution for the logarithm, log2 x 2 is x=2log(2) or x=6.6438561

Given,

In an exponential equation, the variable is expressed as an exponent.

A logarithmic equation is one that uses the logarithm of an expression involving a variable.

Check to check if you can write both sides of an exponential equation as powers of the same number before you attempt to solve it.

Here,

Divide each term in

log(2)x=2

by log(2).

That is,

log(2) x log(2)=2log(2)

Simplify the left side.

log(2).

x=2log(2)

The result can be shown in multiple forms.

Exact Form:

x=2log(2)

Decimal Form:

x=6.6438561

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$12034 is the worth of the car after 4 years.

Percentage, a relative value indicating hundredth parts of any quantity.

Given that we purchased a  car for $22,000

Every year your car depreciates by 14%

We have to find the worth of the car after 4 years.

[tex]A=P(1-r)^{t}[/tex]

P is the principal amount=$12000

r is rate of interest =14%=0.14

t is time =4 years

A=22000(1-0.14)⁴

A=22000(0.86)⁴

A=22000×0.547

A=$12034

Hence, $12034 is the worth of the car after 4 years.

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Answer:

1/9880

Step-by-step explanation:

Number of Combinations

[tex]\displaystyle C(40,3)=\frac{40!}{3!(40-3)!}=\frac{40!}{3!\cdot37!}=\frac{40*39*38}{3*2*1}=40*13*19=9880[/tex]

Thus, the probability of guessing that exact combination on the first try is 1/9880.

The sentence that correctly places the slash between the subject and the predicate of the stated sentence is, Four groups / of four soldiers guarded / Pedro in jail. Correct answer: letter B.

Is important to consider the context in which the sentence is used. Depending on the situation, the answer may vary. For example, if the sentence is part of a larger dialogue about the strength of a prison guard, then more information about the security measures taken and the number of soldiers deployed to guard Peter would be relevant.

Alternatively, if the sentence is part of a discussion about the importance of loyalty and friendship, then information about the relationship between Peter and the soldiers would be important.

Which sentence correctly places the slash mark between the subject and predicate of the sentence? Four groups of four soldiers watched over Peter in jail.

A) Four groups / of four soldiers watched over Peter in jail.

B) Four groups of four soldiers / watched over Peter in jail.

C) Four groups of four soldiers watched / over Peter in jail.

D) Four groups of four soldiers watched over Peter/in jail.

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The axis of symmetry for a parabola in the form of f(x) = a(x - h)^2 + k is x = h.

For f(x) = 4x^2 - 1, the axis of symmetry is x = 0.

For g(x) = x^2 - 8x + 5, the axis of symmetry is x = 4.

For h(x) = -3x^2 - 12x + 1, the axis of symmetry is x = -4/3

So, the ranking from least to greatest based on their axis of symmetry would be:

h(x) = -3x^2 - 12x + 1 with x = -4/3

g(x) = x^2 - 8x + 5 with x = 4

f(x) = 4x^2 - 1 with x = 0

The results for X = -5 and y = 2 yield one solution.

An equation is an expression that states the equality of two values using mathematical operators. It is a mathematical statement consisting of an expression involving variables and constants, connected by an equal sign. Equations are used to solve problems in a wide range of fields, such as science, engineering, and economics.

This is because a system of equations will always have either one solution, no solutions, or infinitely many solutions. Since the equations are equal to a single value, the solution is unique, yielding one solution.

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Answer:

24 children

Step-by-step explanation:

Given ratios:

Multiply the first ratio by 2 and the second ratio by 3 so that the ratios of children are the same:

Therefore the combined ratio is:

So the ratio of Adult Males to Adult Females is 22 : 15.

If the difference between the number of Adult Males and Adult Females is 28 then:

[tex]\implies \dfrac{22}{22+15}x-\dfrac{15}{22+15}x=28[/tex]

[tex]\implies \dfrac{22}{37}x-\dfrac{15}{37}x=28[/tex]

[tex]\implies \dfrac{7}{37}x=28[/tex]

[tex]\implies 7x=1036[/tex]

[tex]\implies x=148[/tex]

Therefore:

[tex]\implies \textsf{Adult Males}=\dfrac{22}{37} \times 148=88[/tex]

[tex]\implies \textsf{Adult Females}=\dfrac{15}{37} \times 148=60[/tex]

If the original ratio of Adult Males to Children is 11 : 3, and the number of Adult Males is 88:

[tex]\implies 11:3=88:c[/tex]

[tex]\implies \dfrac{11}{3}=\dfrac{88}{c}[/tex]

[tex]\implies 11c=264[/tex]

[tex]\implies c=24[/tex]

Therefore, the number of children in the village is 24.

Emilia and her brother used the computer for 1.5 hours.

When Emilia and her brother need to use the family computer for their homework, they have agreed to share the computer equally. On this particular evening, they both needed the computer for 3 hours. To understand how much time each of them used the computer, we need to divide the total time by the number of users.

Dividing the total time of 3 hours by the number of users which is 2, we get 3 hours / 2 = 1.5 hours. This means each person, Emilia, and her brother, use the computer for 1.5 hours each.

It's important to note that this is possible because they both agreed to share the computer equally. If one of them needed more time than the other, they might have to work out a different arrangement.

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Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.

A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.

In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.

On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.

In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.

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