"For each of the following, two sides and an angle of a triangle
are given. Determine whether the given information results in two
triangles, one triangle, or no triangles. Show your thinking using
the"

Answer: end balance: $8,496.95

total interest: $1,496.95

Step-by-step explanation: total interest = $7000 × 8.554% × 30 ÷ 12 = $1,496.95

end balance = $7000 + $1,496.95 = $8,496.95

So, the answer to the question is:

i = 0.051
n = 6

The annuity in question is an ordinary annuity, which means that the deposits are made at the end of each period. In this case, the period is one year, so the rate per period (i) is simply the annual interest rate of 5.1%. Therefore, i = 0.051.

The number of periods (n) is the number of years that the deposits are made, which is 6. Therefore, n = 6.

So, the answer to the question is:

i = 0.051
n = 6

It is important to note that the terms "period" and "annuity" are used in the context of this question to refer to the time frame and the type of investment, respectively. The term "pays" is used to describe the interest rate that the annuity pays on the deposits.

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Answer:

I AINT SOLVING ALL THAT

The measure of the vertex angle of triangle ACE is 50°. The solution has been obtained by using properties of angles.

What is an angle?

An angle is a figure in plane geometry that is created when two rays or lines share an endpoint.

We are given an isosceles triangle ACE which means that AC = CE.

We are given ∠BDE = 115°

Since, angles on a straight line form a linear pair, therefore

⇒∠BDE + ∠BDC = 180°

⇒115° + ∠BDC = 180°

⇒∠BDC = 65°

Since, BD║AE so,

∠BDC = ∠AEC

So, ∠AEC = 65°

Since, AC = CE so,

∠AEC = ∠CAE

So, ∠CAE = 65°

Now, using angle sum property, we get

⇒∠AEC + ∠CAE + ∠ACE = 180°

⇒65° + 65° + ∠ACE = 180°

⇒130° + ∠ACE = 180°

⇒∠ACE = 50°

Hence, the measure of the vertex angle of triangle ACE is 50°.

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The set G = Zp × is a group under modular multiplication. This is because the set contains all the non-zero elements of Zp, and modular multiplication satisfies the four group properties:

Using Lagrange's Theorem, we can prove Fermat's Little Theorem: that for any integer a not divisible by p, ap-1 ≡ 1 (mod p). Let n be the smallest positive integer such that an ≡ 1 (mod p).

Since a is not divisible by p, the order of a (the smallest value of n) must divide p - 1, or in other words, n | (p - 1). By Lagrange's Theorem, this implies n = p - 1, which in turn implies that ap - 1 ≡ 1 (mod p). This proves Fermat's Little Theorem.

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The part of the mural that Trevor has completed is 6/20 square meter.

The correct answer choice is option C.

Area of a rectangle is the measure of the extent of a surface. it is measured in square units.

Total area of the mural = 1 square meter

Rectangular part of the mural:

Length = 2/5 meter

Width = 3/4 meter

Area of the rectangular part of the mural = length × width

= 2/5 × 3/4

= 6/20 square meter

Ultimately, Trevor has completed 6/20 of the mural.

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150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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The scale factor using in that dilation of the dashed triangle would be = 3:1

A scale factor is defined as the ratio that exists between an original size of an object and the new formed size of the same object.

The formula that can be used to calculate the scale factor ;

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Using the base of the triangle from the centre of origin in the graph;

The dimension of the new shape = 18

The dimension of the original shape = 6

scale factor = 18/6 =3

That is, the scale factor = 3:1

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The least positive angle is 180 - θ.

To sketch the least positive angle and find the values of the six trigonometric functions for the given equation 3x + 5y = 0, x ≥ 0, we need to first find the slope and y-intercept of the equation.

The slope of the equation is -3/5 and the y-intercept is 0. This means that the line passes through the origin and has a negative slope.

To sketch the least positive angle, we need to find the angle between the x-axis and the line. Since the slope is negative, the angle will be in the second quadrant. The least positive angle is the reference angle in the second quadrant, which is 180 - θ.

To find the values of the six trigonometric functions, we can use the slope and y-intercept to find the coordinates of a point on the line. One such point is (5, -3).

Using these coordinates, we can find the values of the trigonometric functions:
sin θ = -3/√(5^2 + (-3)^2) = -3/√34
cos θ = 5/√(5^2 + (-3)^2) = 5/√34
tan θ = -3/5
csc θ = √34/-3
sec θ = √34/5
cot θ = -5/3

Therefore, the least positive angle is 180 - θ and the values of the six trigonometric functions are as follows:
sin θ = -3/√34
cos θ = 5/√34
tan θ = -3/5
csc θ = √34/-3
sec θ = √34/5
cot θ = -5/3

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Liam opened the savings account 4 years ago based on the given condition of a $400 deposit.

The formula for simple interest is I = Prt, where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time in years.

We are given that Liam deposited $400 and the interest rate is 7.5%. Let's first calculate the interest earned:

I = Prt = 4000.075t = 30t

After some time t, the balance of the account is $760, which means the total amount in the account is the principal plus the interest earned:

400 + 30t = 760

Simplifying this equation, we get:

30t = 360

t = 12

Therefore, Liam opened the savings account 12/3 = 4 years ago.

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Answer: split it into smaller solids and calculate their separate volumes.

Step-by-step explanation:

The difference in price of both the shops is £0.25.  

What is price?

Price is the amount of money one pays for a good or service. It is determined by a variety of factors, such as supply and demand, the cost of production, and the availability of resources. Prices are also affected by government regulations, taxes, inflation, and other economic and market forces. The price of a product or service is an important factor in determining whether consumers will purchase it or not.

Shop A  | Shop B

200 cm | £0.50 | 300 cm | £0.75

The difference in the price of 300cm of ribbon between shop A and shop B is £0.25. Eloise spent £0.50 on 200cm of ribbon at shop A, and £0.75 on 300cm of ribbon at shop B. Therefore, the difference in price is £0.25.

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The total amount of money two friends had is $3430.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here the ratio of the money of friends = 4:3.

Let us take shares of money as 4x and 3x.

Here larger amount  4x=R1960

=> 4x=1960

=> x= 1960/4= $490

Then Total amount = 4x+3x=7x

=> Total amount = 7*490=$3430

Hence the total amount of money two friends had is $3430.

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a) A drawn model to illustrate the number of rows that will be needed is as follows:

b) An estimated number of rows is 30, which will seat about 720 students.

c) The information organization is as follows:

d) The pattern shows that each row will seat no more 24 students.

e) Working backwards indicates that only between 27 and 28 rows are required.

f) Using an equation, the number of rows that will be needed to seat all students is 28 rows.

An equation is a mathematical statement depicting the equality of two or more algebraic expressions.

An equation is more than an algebraic or mathematical expression because it uses all the elements in an expression, and includes the equal symbol (=).

The total number of students at Fairview Elementary = 657

The number of students per row of auditorium = 24

Let the number of rows required = x

x = 657/24

= 27.375

≈ 28 rows.

Thus, 28 rows must be arranged to accommodate 24 students per row.

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This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I.

A principle ideal is an ideal that is generated by a single element. This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I. This is an important concept in the study of rings and algebraic structures, as it allows us to understand how ideals are generated and how they relate to other ideals in the same ring.

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A. we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.

B. We have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.

A. To prove that 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous only at x = kπ, where k is an integer without using L'Hospital's Rule, we can use the concept of limits.Let's consider the left limit of the function at x = kπ+ (where ε > 0 is a small value).

Here, we can observe that:

lim x → kπ+ 1(x) = lim x → kπ+ sin(x)/x > 0 since sin(x) > 0 when x is in (kπ, kπ + ε/2) and x is in (kπ - ε/2, kπ)

So, 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous at x = kπ+ for any integer k.

Similarly, we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.

B. To prove that limx → 2 f(x) = 3, we can use the following definition of a limit:

For any ε > 0, there exists a δ > 0 such that |f(x) - 3| < ε for all 0 < |x - 2| < δ.

Here, f(x) = x2 - 1, and we need to prove that limx → 2 (x2 - 1) = 3.

Using algebraic manipulation, we can write x2 - 1 - 3 = (x + 2)(x - 2).Now, |(x + 2)(x - 2)| = |x + 2||x - 2|.

Therefore, we need to find δ such that |(x + 2)(x - 2)| < ε whenever 0 < |x - 2| < δ.

In order to ensure this, we can put an upper bound on |x + 2| and |x - 2|:|x + 2| < 4 (since x is close to 2)|x - 2| < δ

From the above inequalities, we can say that |(x + 2)(x - 2)| < 4δ.

Then, we can say that |(x2 - 1) - 3| = |(x + 2)(x - 2)| < 4δ < ε.

So, we can choose δ = ε/4.

Hence, we have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.

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If Angela used 1/5 of her beads and gave 78 to Santiago, she would have 130 beads left.

To find out how many beads Angela had left, we need to first find out how many beads she started with. We can do this by using the information given in the question and setting up an equation. Let's let x represent the number of beads Angela started with.

According to the question, Angela used (1)/(5) of her beads to make bracelets, so she had (4)/(5) of her beads left. She then gave 78 beads to Santiago, which left her with (1)/(2) of her original number of beads. We can write this as an equation:

(4)/(5)x - 78 = (1)/(2)x

To solve for x, we can first multiply both sides of the equation by 10 to get rid of the fractions:

8x - 780 = 5x

Next, we can subtract 5x from both sides of the equation to isolate the variable:

3x = 780

Finally, we can divide both sides of the equation by 3 to find the value of x:

x = 260

So Angela started with 260 beads. We proceed to find out how many you have left:

P = (1/2)(260)

P = 130

So Angela had 130 beads left after giving 78 beads to Santiago.

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Nick is 36 years old now.

To solve the problem, we can use the following steps:

Step 1: Let Nick's age be x and Madelyn's age be y.

Step 2: We are given that Nick is 64 years younger than Madelyn, so we can write an equation: x = y - 64

Step 3: We are also given that 4 years ago, Madelyn's age was 3 times Nick's age, so we can write another equation: y - 4 = 3(x - 4)

Step 4: Substitute the first equation into the second equation to get: y - 4 = 3(y - 64 - 4)

Step 5: Simplify the equation to get: y - 4 = 3y - 204

Step 6: Solve for y to get: y = 100

Step 7: Substitute the value of y back into the first equation to get: x = 100 - 64 = 36

Therefore, Nick is 36 years old now.

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Answer:

1/2

Step-by-step explanation:

because 5 times 1/2 and you get 2 1/2

the value of the expression is 0.

To solve this expression, we can use the PEMDAS order of operations:

since there are no Parentheses and Exponents we move to multiplication and division

-2(-3) + 27 ÷ (-3) + 3 = 6 + (-9) + 3

6 + (-9) + 3 = 0

As a result, the equation has a value of 0.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Here,

5 and 13 are expressions for 2x.

These two expressions are joined together by the sign "=".

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality. The two most well-known groups of equations in algebra are linear equations and polynomial equations. P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations. Here, are the parameters a and b.

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Answer:

1/4

Step-by-step explanation:

you can plug it into a calculator

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × [tex]r^{2}[/tex].

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is [tex]118.7[/tex] [tex]in^{2}[/tex].

The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)

An expressiοn in mathematics is made up οf different numbers, variables, and mathematical prοcesses, such as expοnents, lοgarithms, trigοnοmetric functiοns, and arithmetic. It can symbοlise a number οr a fοrmula, but it lacks an equals sign (=) and cannοt be evaluated οr sοlved withοut being cοmbined οr simplified. Expressiοns can be straightfοrward, like 3x + 4, οr they can be cοmplicated, like (2x - 1)/(x + 3).

given:

(a) We must multiply each term in the first expressiοn by each term in the secοnd expressiοn befοre cοmbining like terms tο determine the prοduct οf (-3x³ + 2x - 5) and (2x4 - 4x² - 3). The distributive principle allοws us tο write:

= (-3x³ + 2x - 5) * (2x⁴ - 4x² - 3) * (3x³ + 2x - 5) * = 3x³ * 2x⁴ + (-3x³) * (-4x²)  * (-3)

= 2x * 2x⁴  + 2x * (-4x²) + 2x * (-3)

= -6x⁷ + 12x⁵ + 9x³ + 4x⁵ - 8x³ - 6x - 10x⁴  + 20x² + 15 = 5 * 2x⁴  - 5 * (-4x²) - 5 * (-3)

The result οf the οperatiοns (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3) is as fοllοws: -6x⁷ + 10x⁴  + 16x⁵ - 17x³ - 6x + 15

(b) The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3). Due tο the fact that multiplicatiοn is cοmmutative, changing the οrder οf the variables has nο effect οn the οutcοme οf the prοduct. Cοnsequently, we can write:

(2x⁴  - 4x² - 3) * (-3x³ + 2x - 5) = (-3x³ + 2x - 5) * (2x⁴  - 4x² - 3)

The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)

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[tex]f(n) = f(n - 1) * (- 3)[/tex]

[tex]f(2) = f(2 - 1) * (- 3) = \boxed{f(1) * (- 3)} = (-1)*(-3) = \bf 3\\[/tex]

[tex]f(3) = f(3 - 1) * (- 3) = f(2) * (- 3) = f(1) * (-3) * (- 3) = \boxed{f(1) * (-3)^{2}} = (-1)*3^{2} =-3^{2} = \bf -9\\[/tex]

[tex]f(4) = f(4 - 1) * (- 3) = f(3) * (- 3) = f(1) * (-3)^{2} * (- 3) = \boxed{f(1) * (-3)^{3}} = (-1)*(-3^{3}) = 3^{3} = \bf 27\\[/tex]

[tex]f(5) = f(5 - 1) * (- 3) = f(4) * (- 3) = f(1) * (-3)^{3} * (- 3) = \boxed{f(1) * (-3)^{4}} = (-1)*3^{4} =-3^{4} = \bf -64\\[/tex]

[tex]f(12) = f(12 - 1) * (- 3) = f(1) * (-3)^{10} * (- 3) = \boxed{f(1) * (-3)^{11}} = (-1)* (-3)^{11} = -(-3^{11}) = 3^{11} \\[/tex]

⇒

[tex]\boxed{f(n) = (-1)^{n} * 3^{n - 1}}[/tex]

The only possible rational zero of the polynomial is 0

The possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v can be found by using the Rational Root Theorem. This theorem states that if a polynomial has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is 0 and the leading coefficient is 14. The factors of 0 are just 0, and the factors of 14 are 1, 2, 7, and 14. Therefore, the possible rational zeros of the polynomial are 0/1, 0/2, 0/7, and 0/14, which all simplify to just 0.

This means that the only possible rational zero of the polynomial is 0. However, there may also be irrational or complex zeros. To find these, we would need to use other methods, such as synthetic division or the quadratic formula.

In conclusion, the possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v are 0 and any irrational or complex numbers that satisfy the equation.

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Answer:

y-intercept: 3

equation: y = -x + 3

Step-by-step explanation:

For problem #6: (-2,5) and (2,1)

Slope m = (y2 - y1)/(x2 - x1)

=>m = (1 - 5)/(2 - -2) = -4/4 = -1

Slope-intercept form is y = mx + b

Given m = -1, y = 1, x = 2

=> 1 = -1(2) + b

=> 1 = -2 + b

=> b = 1 + 2  = 3

equation: y = -x + 3

since b is the y-intercept => 3

Answer:

x= 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The right rectangle prism contains 48 cubes, which results in a volume of 131,712 cubic inches.

A prism is a solid geometric form with two parallel bases that are congruent and typically shaped like polygons, as well as parallelogram-shaped sides that connect the bases. Prisms come in different shapes, such as hexagonal, triangular, and rectangle.

given

The 48 blocks that make up the right rectangular prism each have an edge length of 14 inches. By dividing the quantity of cubes by the sum of their individual volumes, one can determine the volume of the prism.

Each cube has a volume of (14 in.)3 = 2744 cubic inches.

Cube count is 48.

48 squares at 2744 cubic inches each equals 131,712 cubic inches of volume for the prism.

The right rectangle prism contains 48 cubes, which results in a volume of 131,712 cubic inches.

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Answer:

Step-by-step explanation:

ypi ,tfr

Equation A = (P ÷ 4)*(P ÷ 4) can be used to find area of a square.

A square is a geometrical shape that has four equal sides and four equal angles (90-degree angles or right angles). It is a type of rectangle where all sides have the same length. A square is a two-dimensional shape, meaning it only has length and width, and all of its sides are parallel to each other. The opposite sides of a square are parallel and equal in length, and its diagonals bisect each other at 90-degree angles. Squares are used in mathematics, geometry, and various other fields.

Now,

As Area =a² where a=side of square

and perimeter=4a⇒a=p/4

then area=(p/4)²

Hence, The equation that can be used to find A, the area of a square that has a perimeter of P units is:

A = (P ÷ 4)*(P ÷ 4)

Therefore, the correct option is A.

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