The compliment of an angle is three times the measurement of the angle. Find the measurement of the larger angle

Evander's principal at the beginning of July was approximately $16,533. Rounded to the nearest whole dollar, this is $16,533.

Applying  the formula for simple interest:

Interest = Principal x Rate x Time

Here, we know the interest ($248), the rate (18%), and the time (1/12 of a year for one month, since we're using a 360-day year).

Let the principal = "P":

$248 = P x 0.18 x (1/12)

$248 = P x 0.015

P = $248 / 0.015

P ≈ $16,533.33

Simple interest is described as an interest charge that borrowers pay lenders for a loan.

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The expression that is equivalent to 6x2y + 2xy^5 include:

2(3x²y + xy^5).

2xy(3x + y⁴)

xy(6x + 2y⁴)

An expression can refer to a variety of things depending on the context in which it is used.

In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"

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Answer:

-20

Step-by-step explanation:

[tex]\frac{5}{3}x +\frac{1}{3} x=13\frac{1}{3}+\frac{8}{3}x\\\\\frac{6}{3} x = 13 \frac{1}{3} +\frac{8}{3} x\\\\\frac{-40}{3} =\frac{2}{3} x\\\\\frac{3}{2} *(\frac{-40}{3} )\\\\\frac{3}{2} *\frac{2}{3} x\\\\-20 = x[/tex]

Answer:

If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the values given in the problem:

y = kx

12 = k(8)

Solving for k, we get:

k = 12/8 = 3/2

Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:

y = kx

30 = (3/2)x

Solving for x, we get:

x = (30)/(3/2) = 20

Therefore, when y = 30, x = 20

Answer:

A. 60 miles

Step-by-step explanation:

2 in. = 15mi or like 2in+2in+2in+2in = 8in

15mi+15mi+15mi+15mi = 60mi

2×4 =8

/

/

v

4 × 15mi = 60mi

On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Let's use "x" to symbolise box A's weight. Then, we could type:

Given that box B weighs 5 kg more than box A, its weight is "x + 5".

Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".

We can write: Since we are aware that the combined weight of the three boxes is 51 kg:

[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]

Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:

17.67 kg (x + 5) is the estimated weight of Box B.

The approximate weight of Box C is 25.67 kg (x + 8).

Therefore, none of the answers to the question's assertions are true.

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Answer:

Using the FOIL method to multiply (x + 80)(x - 20), we get:

(x + 80)(x - 20) = x^2 - 20x + 80x - 1600

Simplifying the expression, we get:

(x + 80)(x - 20) = x^2 + 60x - 1600

Therefore, the answer is x^2 + 60x - 1600.

The simplified form of the expression is 71/24.

To simplify the expression 4 - 1/3 - 7/8 + 1/6, we can follow the order of operations, which dictates that we perform multiplication and division before addition and subtraction.

Here's the step-by-step solution:

Find a common denominator for the fractions involved. In this case, the least common denominator (LCD) is 24, which is the least common multiple of 3, 8, and 6.

Convert the fractions to have the same denominator, which is 24:

4 - 1/3 - 7/8 + 1/6

= 4 * 24/24 - 1/3 * 8/8 - 7/8 * 3/3 + 1/6 * 4/4 (Multiplying each fraction by the appropriate form of 1 to get the common denominator)

= 96/24 - 8/24 - 21/24 + 4/24 (Performing the multiplication)

Combine the numerators over the common denominator:

= (96 - 8 - 21 + 4)/24 (Combining numerators)

= 71/24 (Performing the subtraction)

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The scatter plots that do not show a linear relationship are B and C

The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.

The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.

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use slope equation -5 - (-3)/(2-1) then solve

hi

4/7  =   8

7/7 =  ?  

so ?  =  7/7 * 8  /4/7 =   8/4/7 =  8 *7/4 = 4*2*7 /4 =   2*7 = 14

so whole thing  is  14

let's check :    14 * 4/7 =   56/7 = 8

Match initial data. answer is correct.

If the radius of smaller-saw is 1.25 in, and radius of larger-saw is 2 inches, then larger-saw is 4.71 inches greater the smaller-saw.

The "Circumference" of a circle is defined as the distance around the boundary of a circle, it is also called perimeter of circle;

The diameter of the smaller saw can be calculated as:

⇒ diameter = 2 × radius = 2 × 1.25 inches = 2.5 inches;

The diameter of the larger saw is 1.5 inches greater than the diameter of the smaller saw, which means,

⇒ diameter of larger saw = diameter of smaller saw + 1.5 inches,

⇒ diameter of larger saw = 2.5 inches + 1.5 inches = 4 inches;

So, Circumference of circle is = 2 × π × radius;

The Circumference of "smaller-saw" = 2 × 3.14 × 1.25 inches,

⇒ circumference of smaller saw = 7.85 inches;

circumference of "larger-saw" = 2 × 3.14 × 2 inches

⇒ circumference of larger saw = 12.56 inches;

The difference in circumference between the two saws is:

⇒ circumference of larger saw - circumference of smaller saw

⇒ 12.56 inches - 7.85 inches = 4.71 inches;

Therefore, the circumference of the larger saw is 4.71 inches greater than the circumference of the smaller saw.

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The given question is incomplete, the complete question is

A carpenter has two different-sized circular saws. The smaller saw has the radius as 1.25 inch. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.

How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π

Answer:

Yes, the figure is line symmetric.

A snowflake has six lines of symmetry. Therefore, the correct answer is: 6.

Answer:

24.6 degrees.

Step-by-step explanation:

To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.

sin(θ) = opposite/hypotenuse

sin(θ) = 3/7

Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.

θ = sin^-1(3/7)

θ ≈ 0.429 radians

To find the degree measure, we must convert radians to degrees by multiplying by 180/π.

θ ≈ 0.429 x 180/π

θ ≈ 24.6 degrees

Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.

Answer:

If the point (1,5) lies on a circle with center (0,0), then the radius of the circle is the distance from the center to the point (1,5), which is:

r = sqrt((1-0)^2 + (5-0)^2) = sqrt(26)

So the equation of the circle is:

x^2 + y^2 = 26

To find a point in quadrant 2 that lies on the circle, we need to find a point with a negative x-coordinate and a positive y-coordinate that satisfies this equation.

Among the given options, only (a) (-5,1) and (e) (-2,3) have a negative x-coordinate. Let's check if they satisfy the equation of the circle:

For point (a) (-5,1):

x^2 + y^2 = 26

(-5)^2 + 1^2 = 26

25 + 1 = 26

This point does not lie on the circle.

For point (e) (-2,3):

x^2 + y^2 = 26

(-2)^2 + 3^2 = 26

4 + 9 = 26

This point also does not lie on the circle.

Therefore, among the given options, there is no point in quadrant 2 that lies on the circle.

Step-by-step explanation:

since the center of the circle is at the origin, that means that the circle is evenly going through all four quadrants - one quarter arc after the other.

the point (1, 5) is in the first quadrant (upper right one, positive x, positive y).

the circle arc in the second quadrant (upper left one, negative x, positive y) is the mirrored image of the arc in the first quadrant across the y-axis.

so, the point on it gets mirrored too.

that means, it's coordinates are then the same y and the x is converted to its negative value :

(-1, 5)

that is the easily identifiable point in the second quadrant that has to be on the circle.

Answer:

If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:

f(x) = (x-1)(ax + b)

where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:

f(x) = (x-1)(ax + b) = 4x² - 4x - K

Expanding the left side of the equation, we get:

ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K

Now we can equate the coefficients of the like terms on both sides of the equation.

The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:

a = 4

The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:

b - a = -4

Substituting a=4, we get:

b - 4 = -4

Solving for b, we get:

b = 0

So the polynomial can be written as:

f(x) = (x-1)(4x + 0) = 4x² - 4x

Therefore, K = 0.

To find the roots of the equation, we need to set f(x) = 0 and solve for x:

4x² - 4x = 0

Factor out 4x:

4x(x - 1) = 0

So the roots of the equation are x = 0 and x = 1.

The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81

To compare the expressions, we can simplify them using the rules of exponents:

a) 3^3 = 27

b) 3^4 = 81

c) 6^2 = 36

d) 6^3 = 216

e) 9^2 = 81

f) 9^3 = 729

Using the above as a guide, we have the following:

Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81

So, options b and e have the same value.

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the cost of day old donuts after the discount is $4.95.

         A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.

       Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.

       The formula to calculate the discount is:

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

the discount is 40% ⇒0.4

customer buys 3 donuts.

price of 1 donut = $2.75

total cost for 3 donuts= $2.75 x 3 = $8.25

discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1

so, for 3 donuts discount = $1.1 x 3 = $3.3

therefore the final price to be paid by customer is

                    =$8.25-$3.3

                    =$4.95

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The difference between 6 5/6 and 5 1/2 is 4/3 .

To subtract these mixed numbers, we need to first convert them into improper fractions:

6 5/6 = (6 x 6 + 5)/6 = 41/6

5 1/2 = (5 x 2 + 1)/2 = 11/2

Now we can subtract:

41/6 - 11/2

To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:

11/2 = (11 x 3)/(2 x 3) = 33/6

Now we can subtract the fractions with the same denominator:

41/6 - 33/6 = 8/6

Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:

8/6 = 4/3

As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..

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The complete question is:

What is the rule for the sequence

5/6, 1 1/2, 2 1/6, 2 5/6.....

Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.

The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where  (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.

To answer this we need to know the equation of a circle.

Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:

(x - a)² + (y - b)² = r²

We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.

We can now substitute these information in the circle equation,

(x - -3)² + (y - 6)² = 2²

(x+3)² + (y - 6)² = 4

That is the equation of the given circle is (x+3)² + (y - 6)² = 4.

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The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).

Looking at the graph, we can see that:

Thus, the correct piecewise function that represents g(x) is:

g(x) = {-2 if x ≤ -1

{ (x-1)^2 if -1 < x ≤ 0

{ -x+1 if x > 0

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The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:

y = 98 - 8x

The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.

Answer:

Step-by-step explanation:

It is -12.

The opposite of a positive number would be its negative.

The resale value of the car after 3 years is $9,984.

Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.

After the first year, the resale value of the car will be 80% of its original value:

Resale value after 1 year = 80/100 * $19,500 = $15,600

After the second year, the resale value of the car will be 80% of its value after the first year:

Resale value after 2 years = 80/100 * $15,600 = $12,480

After the third year, the resale value of the car will be 80% of its value after the second year:

Resale value after 3 years = 80/100 * $12,480 = $9,984

Therefore, the resale value of the car after 3 years will be $9,984.

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Answer:

To find the value of "c" for which the number "a" (-5 in this case) is a solution of the equation, we can substitute "a" into the equation and solve for "c".

Given equation: 4x + 1 + 7c = 8c - 3x + 6

Substituting x with "a": 4(-5) + 1 + 7c = 8c - 3(-5) + 6

Simplifying the equation: -20 + 1 + 7c = 8c + 15 + 6

Combining like terms: -19 + 7c = 8c + 21

Moving all "c" terms to one side: 7c - 8c = 21 + 19

Simplifying: -c = 40

Dividing both sides by -1 to isolate "c": -c/-1 = 40/-1

Flipping the sign when dividing by a negative number: c = -40

So, the value of "c" for which the number "a" (-5) is a solution of the equation is c = -40.

Answer:

[tex]c=-40[/tex]

Step-by-step explanation:

Since a is a Solution to the Equation , then it satisfies the Equation

Substitute by [tex]x=a=-5[/tex] into the Equation [tex]4x+1+7c=8c-3x+6[/tex]

Then [tex]4(-5)+1+7c=8c-3(-5)+6[/tex]

Then [tex]-20+1+7c=8c+15+6[/tex]

By adding like-terms

Then [tex]-19+7c=8c+21[/tex]

Then [tex]8c-7c=-19-21[/tex]

Then [tex]c=-40[/tex]

The equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

We can observe from the table that the number of books collected increases by 10 for each week.

Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:

b = mw + c

where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).

The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):

10 = 10 * 1 + c

c = 0

Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1 10

2 20

3 30

4 40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

Answer: A Map Scale.

Step-by-step explanation:

A Map Scale is the relationship with the ground.

The correct answer is not listed among the options. The correct answer is E. 1/x.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:

f'(x) = d/dx [ln(3x)]

= 1/(3x) * d/dx [3x] (applying the chain rule)

= 1/(3x) * 3

= 1/x

Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.

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