the complement of an angle is 57 degrees, what is the size of the angle?

The data represents the linear equation.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

We have the table:

x → y

-9 →  -71

-8 → -63

-7 → -55

-6 →  -47

-5 →  -39

To prove that the data represents in the tables are from the linear equation:

If a first difference of the table of values shows a constant rate of change,

then the function is a linear equation.

So,

y₂-y₁ = -63 + 71 = 8

y₃ - y₂ = -55 + 63 = 8

y₄ - y₃ = -47 + 55 = 8

y₅ - y₄ = -39 + 47 = 8

Here, 8 is the constant rate of change.

So, the data represents the linear equation.

Therefore, the data represents the linear equation.

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The digit which the letter A represents as required in the task content so that the given problem is true is; 5.

As evident in the task content; it follows that the digit which the letter A represents in the given task content is to be determined.

On this note, first, 47 can be subtracted from 137 so that we have;

137 - 47 = 90.

On this note, it can be inferred that;

A A + 3 A = 90

Therefore, by using the place value concept, it follows that we have;

( 10 × A ) + ( 1 × A ) + ( 3 × 10 ) + ( 1 × A ) = 90

10A + A + 30 + A = 90

12A = 90 - 30

12A = 60

A = 5.

On this note, the letter A as represented in the task content represents the digit; 5.

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the orginal price is really "x", which oddly enough is the 100%, but we also know that 260 is 35% off that, so 260 is really 100% - 35% = 65% of the original price, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 260& 65 \end{array} \implies \cfrac{x}{260}~~=~~\cfrac{100}{65} \\\\\\ \cfrac{ x }{ 260 } ~~=~~ \cfrac{ 20 }{ 13 }\implies 13x=5200\implies x=\cfrac{5200}{13}\implies x=400[/tex]

1. Michael is a better grader.

2. Catherine received the better grader.

3. Sam received the better grader.

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The graph is attached in the solution.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Given that, a function f(x) = 3√x

Let x = 0,

f(0) = 3√0 = 0

Let x = 1,

f(1) = 3√1 = 3

Let x = 2

f(2) = 3√2 = 4.24

Plotting the graph, we get, (attached)

Hence, the answer is the graph attached to the solution.

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Answer:

Below

Step-by-step explanation:

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Answer:

80.456 is a 9.6% decrease of 89.

Step-by-step explanation:

Answer:

Step-by-step explanation:

 89×(1-9.6%)

=89×(1-0.096)

=89×0.904

=80.456

≈80

the answer is 80 if you have to round it.

The horizontal asymptote is y = 0 because m = n. A function's graph has a line known as a horizontal asymptote.

A horizontal asymptote is a line that the graph of a function approaches as x tends to either positive or negative infinity. If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote of the function is the line y = a/b, whereThe leading coefficients in the denominator and numerator, respectively, are a and b. Therefore, if m = n, then the horizontal asymptote is y = a/b, which reduces to y = 0.

The statement that defines the horizontal asymptote is that if m = n, then the horizontal asymptote is y = 0.

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The probability that both cards will be red cards is P(A⋅B) = 25/102

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The first event, random drawing of a red card (event A), has a sample space of an entire deck with 52 different elementary events occurring with equal probabilities of 1/52. Out of them only 26 events are "good" (that is, the card we randomly pick is red). Therefore, the probability of picking a red card equals to

P(A) = 26/52

P(A) = 1/2.

The second event, random drawing of a red card from a deck of only 51 remaining cards (event B), is dependent on the results of the first event. If the first event (event A) occurs (red card is drawn), the deck for the second drawing contains 25 red and 26 black cards and the conditional probability of picking red card is

P(B/A) = 25/51.

Now we can use the concept of conditional probability and a formula that describes the probability of a combined event through the probability of one and conditional probability of another:

P(A⋅B) = P(A) * P(B/A)

In our case P(A) = 1/2 and P(B/A) = 25/51

Therefore,

P(A⋅B) = (1/2) * (25/51)

P(A⋅B) =25/102

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Answer: 12...12...12...57

The length should be x ≥ 3 inch and 4x ≥ 12 square inches.

What is linear inequality?

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠), can take the place of the equal sign "=" in this expression. Polynomial inequality, rational inequality, and absolute value inequality are the various kinds of mathematical inequalities.

Given a rectangle, length  = 4 inches

area is at least 12 square inches

inequality equation for area

A ≥ 12

area  = l x b

where l = length = 4 inches and b = breadth = x

A ≥ 12

4x ≥ 12

x ≥ 3 inches

Hence the breadth should be x ≥ 3 inches and equation of area is

4x ≥ 12 square inches.

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The maximum number of comparisons in a bubble sort if there are 5 elements in the array = 10

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity is quite high.

Due to its simplicity, bubble sort is often used to introduce the concept of a sorting algorithm.

In computer graphics, it is popular for its capability to detect a tiny error (like a swap of just two elements) in almost-sorted arrays and fix it with just linear

complexity (2n).

Example: It is used in a polygon filling algorithm, where bounding lines are sorted by their x coordinate at a specific scan line (a line parallel to the x-axis), and with incrementing y their order changes (two elements are swapped) only at intersections of two lines

Calculating total number of comparison required to sort the array

= (n-1) + (n-2) +  (n-3) + . . . 2 + 1

= (n-1)*(n-1+1)/2  { by using sum of N natural Number formula }

= n (n-1)/2    

= 5(4)/2

=20/2

=10

The maximum number of comparisons in a bubble sort if there are 5 elements in the array = 10

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The Indian rupees do you receive when you exchange $13 will be 601.2 rupees.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The expression 62.4d-210 gives the number of Indian rupees you receive when you exchange dollar d at the local currency exchange.

The Indian rupees do you receive when you exchange $13 will be:

= 62.4d - 210

= 62.4(13) - 210

= 601.2 rupees

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The solution for the give differential equation is y = c1e⁻ˣ+c2e⁻²ˣ·e⁻ˣsineˣ-[e⁻ˣ+e⁻²ˣ]coseˣ

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable

Given that, solve the differential equation by variation of parameters. y'' + 3y' + 2y = sineˣ

AE = m²+3m+2 = 0

Where, m1 = -1, m2 = -2

CF = y = c1e⁻ˣ+c2e⁻²ˣ

PI = y1 = eˣ and y2 = e⁻²ˣ

W = -e⁻³ˣ

W1 = -e⁻²ˣsineˣ

W2 = e⁻ˣsineˣ

u'1 = W1/W = eˣsineˣ;

u1 = ∫eˣsineˣ dx = ∫sint dt [put t = eˣ]

= -cost = -coseˣ

Similary,

u'2 = W2/W =  -e²ˣsineˣ;

u2 = -∫e²ˣcoseˣ dx = -∫tcost dt [put t = eˣ]

= -(tsint+cost) = -(eˣsineˣ+coseˣ)

PI: y = u1y1 + u2y2 = e⁻ˣ[-coseˣ] + e²ˣ[-(eˣsineˣ+coseˣ)]

= -e⁻ˣsineˣ-[e⁻ˣ+e⁻²ˣ]cose²ˣ

Hence, the complete solution is y = c1e⁻ˣ+c2e⁻²ˣ·e⁻ˣsineˣ-[e⁻ˣ+e⁻²ˣ]coseˣ

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The amount in quarts of liquid soap that Charlie use to make the cleaning solution is 3/4 quarts

From the problem we have the following information

Charlie makes 6 quarts of a cleaning solution

The solution is 3/4 water and 1/4 soap mixture

The soap mixture is 1/2 liquid soap and 1/2 vinegar

The soap mixture is 1/4 of the solution, and the solution is 6 quarts

= 1/4 * 6

= 3/2 quarts

The liquid soap is 1/2 soap mixture which is solved to be 3/2 quarts

= 1/2 * 3*2

= 3/4 quarts

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Therefore , the value of the given problem of linear equation comes out to be  x = -250.

In algebra, a mathematical model is just one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since x and y are variables, the previous sentence is frequently referred to as a "mathematical expression with 2 variables." Bivariate linear equations are linear equations with two variables. Linear equations can be found in many different situations. Once an issue has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.

Here,

Given : 70.50 - 45.50 + 0.15x - 0.09x =0

To find the value of x,

Thus,

We do : 70.50 - 45.50 + 0.15x - 0.09x =0

=> 15 + 0.06x =0

=> 6/100 *x = -15

=> 6x = -1500

=> x = -1500/6

=> x = -250

Therefore , the value of the given problem of linear equation comes out to be  x = -250.

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Answer:

140 feet.

Step-by-step explanation:

Hope its correct and it helps!

The fundamental theorem of algebra states that every polynomial equation of degree n, where n is a positive integer, has at least one root in the complex number system.

The Fundamental Theorem of Algebra states that any polynomial equation of degree n, with real or complex coefficients, has at least one root (real or complex).

In the case of the equation 2x^2 - 4x + 16 = 0, the Fundamental Theorem of Algebra implies that there is at least one real or complex root. In fact, this equation has two real roots: x=4 and x=-2.

This theorem provides an important foundation for many branches of mathematics, as it proves that solutions to equations exist.

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1. The value of -5.1m + 2.3m is -2.8m.

2. The value of 3/5y + (-6/5y) is -3/5y

3. The value of 3.1n + 1.5 - 1.1n - 2.9 is 2n - 1.4

4. The value of -2.6c - 0.8 - 2.8c + 3.4 is 5.4c + 2.6.

5. The value of -3x - 2.6y + 1.2 + 1.2x - 4.7 is -1.8x - 2.6y - 3.5

6. The value of -4/22t - 5/22t + 15 + (-5) is -9/22t + 10.

7. The expression equivalent to -2.3v + (-4.2) + 8.8 + (-3.2v) is -5.5v + 4.6.

8. The expression equivalent to 3/14x + (-1) + (-4) - 2/7x is -1/14x - 5.

It should be noted that expression is used to show the relationship that the variables have in a data or based on the question given.

Here, the value of -5.1m + 2.3m is will be:

= -5.1m + 2.3m

= -2.8m.

The value of 3/5y + (-6/5y) is:

= 3/5y + (-6/5y) is:

= 3/5y - 6/5y) is:

= -3/5y

The value of 3.1n + 1.5 - 1.1n - 2.9 is:

= 2n - 1.4

The value of -2.6c - 0.8 - 2.8c + 3.4 is:

= -2.6c - 0.8 - 2.8c + 3.4

= -5.4c + 2.6

The value of -3x - 2.6y + 1.2 + 1.2x - 4.7 is:

= -3x - 2.6y + 1.2 + 1.2x - 4.7

= -1.8x - 2.6y - 3.5

The value of -4/22t - 5/22t + 15 + (-5) is:

= -4/22t - 5/22t + 15 + (-5)

= - 9/22t + 10

The expression equivalent to -2.3v + (-4.2) + 8.8 + (-3.2v) is:

= -2.3v + (-4.2) + 8.8 + (-3.2v)

= -5.5v + 4.6

The expression equivalent to 3/14x + (-1) + (-4) - 2/7x is:

= 3/14x + (-1) + (-4) - 2/7x:

= - 1/14x - 5

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sorry bro i don't know the answer

After solving, the exact value of tan5π/8 = -2.425

In the given question we have to find the exact value of tan5π/8.

The angles and sides of a right-angle triangle are measured using these trigonometric values. Cotangent, secant, and cosecant are the other three significant values in addition to sine, cosine, and tangent.

To find the value of tan5π/8 we simplify the values.

Rephrase 5π/8 as the angle divided by two where the values of the six trigonometric functions are known.

tan5π/8 = tan[(5π/4)/2]

Now applying the tangent half-angle identity.

tan5π/8 = ±√[{1-cos(5π/4)}/{1+cos(5π/4)}]

The tangent is negative in the second quadrant, so change the ± to -.

tan5π/8 = -√[{1-cos(5π/4)}/{1+cos(5π/4)}]

We know the value of cos(5π/4) = -1/√2

Now putting the value

tan5π/8 = -√[{1-(-1/√2)}/{1+(-1/√2)}]

tan5π/8 = -√[{1+1/√2}/{1-1/√2}]

tan5π/8 = -√[{√2+1}/√2/{√2-1}/√2]

tan5π/8 = -√(√2+1)/(√2-1)

As we know that, √2 = 1.41. So

tan5π/8 = -√(1.41+1)/(1.41-1)

tan5π/8 = -√(2.41)/(0.41)

tan5π/8 = -√5.88

tan5π/8 = -2.425

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The exact value of tan (5π/8) is 1.7320508076.

The exact value of tan (5π/8) can be calculated using the tangent of a sum formula. The formula states that tangent of (A+B) can be calculated by the formula:

tan(A+B) = (tan A + tan B) / (1 - tan A tan B).

Therefore, we can calculate the tan (5π/8) as follows:

tan (5π/8) = tan (3π/4 + π/8)

           = (tan (3π/4) + tan (π/8)) / (1 - tan (3π/4) tan (π/8))

           = (√2 + 0.3826834) / (1 - √2 * 0.3826834)

           = 1.7320508076

Therefore, the exact value of tan (5π/8) is 1.7320508076.

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Answer:

y - 1 = -6( x - 2)

Step-by-step explanation:

(2,1)  The x is 2 and the y is 1.

Answer: x > 3

Step-by-step explanation:

Step 1: Subtract 5x from both sides.

−2x+9−5x<5x−12−5x

−7x+9<−12

Step 2: Subtract 9 from both sides.

−7x+9−9<−12−9

−7x<−21

Step 3: Divide both sides by -7.

−7x/−7 < −21/−7

x > 3

On a line graph it would look like this:

Answer:

Step-by-step explanation:

Answer:

63 students

Step-by-step explanation:

The length, width, and height of the box is 23 inches, 24 inches, and 25 inches.

The desired length of the diagonal of the box d ≥ 41.5 inches

The length of the box = l

The width of the box = w

The height of the box = h

The formula for the diagonal of the box, obtained using the  Pythagorean Theorem is:

                                     d = [tex]\sqrt[]{l^{2}+w^{2}+h^{2} }[/tex]

So, the square of the diagonal of the box, d² ≥ 41.5² = 1722.25

                                     [tex]d^{2} = l^{2} + w^{2} + h^{2}[/tex]

                                   l² + w² + h² ≥ 1722.25

Since,20² = 400

21² = 441

22² = 484

23² = 529

24² = 576

25² = 625

26² = 676

27² = 729

Hence, 23² + 24² + 25² = 1730 > 1722.25

20² + 20² + 27² = 1529 < 1722.25

21² + 24² + 26² = 1693 < 1722.25

20² + 21² + 26² = 1517 < 1722.25

So, the box's possible length is 23 inches.

                                      width is 24 inches.

                             and height is 25 inches.

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The data in a table indicate the exponential function f(x) = 3(2)x.The formula for an exponential function is: y = abx, where y and x are variables .

A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. If your function has the formula y = a b x, where and are constants, a 0 and b > 0 and b 1, then it must be exponential. Your functions in quadratic equations were always to the second power. The exponent of exponential functions is a variable.

given

From the table, at point (0, 3):

3 = ab°  , a = 3

At point (2, 12):

12 = ab²

12 = 3b²

b² = 4

b = 2

f(x) = 3(2)ˣ

The data in a table indicate the exponential function f(x) = 3(2)x.

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According to the word problem states that they must string at least 31 beads per day.

Math word problems require students to apply their arithmetic abilities in a "real-life" setting and are mathematical questions that are described in one or more sentences. Kids must therefore be familiar with the vocabulary associated with the mathematical symbols they are used to in order to comprehend the word problem.

given the string's existing 70 beads They intend to string 1000 beads by both the start of class in just 30 more days.

The minimal number of beads that must be strung each day is calculated by dividing the remaining beads by the number of days:

The quantity of beads needed to reach 1000 = 1000 - 70 = 930

Now, putting the values,

= (1000 - 70)/30

= 930/30

= 31

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Answer:

y = 11

Step-by-step explanation:

It is just an equation with one variable ( 'y') which you can solve

-7y + 2 = - 75     subtract 2 from both sides of the equation

-7y = -77             divide both sides by -7

y = 11  

Answer:

-7y+2=-75

-7y=-75-2

-7y=-77

y=11

The number 1/10 is not equal to the 0.01.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equivalent number is,

⇒ 0.01

Now, We will check all the expression as;

1) 10⁻²

⇒ 1/10²

⇒ 1/100

⇒ 0.01

2) 1%

⇒ 1/100

⇒ 0.01

3) 1/10

⇒ 0.1

4) One hundredth

⇒ 1/100

⇒ 0.01

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