I confused on how to solve these trigonometric ratios.

We have to find the missing value to the nearest whole number of tan x° =0.9.

Since, tan x° =0.9

To evaluate the missing value of 'x', we will take [tex] \arctan (0.9) [/tex]

So, [tex] x^{\circ}=\arctan (0.9) [/tex]

Now, we will find the value of [tex] \arctan (0.9) [/tex]using the calculator, we get,

[tex] x^{\circ}=\arctan (0.9)=41.9^{\circ}=42^{\circ} [/tex]

So, the missing value of 'x' to the nearest whole number is [tex] 42^{\circ} [/tex].

Answer:  The required equation of line BC is [tex] x=4.[/tex]

Step-by-step explanation:  As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).

We are to find the equation of line BC.

We know that the slope of a line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of the line AB will be

[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]

Therefore, the equation of the line AB is

[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]

Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.

So, its equation will be of the form

x = constant.

Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have

[tex]x=4.[/tex]

Thus, the required equation of line BC is [tex] x=4.[/tex]

Final answer:

The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.

Explanation:

To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.

The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.

we can re-write our expression as:

-3a^2+27a+1200=0

-3(a^2-9a-400)=0

a^2-9a-400=0

factorizing the above we have:

a^2+16a-25a-400=0

a(a+16)-25(a+16)=0

(a+16)(a-25)

thus replacing back x^2 we have:

(x^2+16)(x^2-25)

=(x^2+16)(x-5)(x+5)

factorizing (x^2+16) we get

x^2=+/-√-16

x=+/-4i

thus the zeros of the expression are:

x=-5, x=5 , x=-4i, x=4i

The length of AD is 18 units.

To find the length of AD, we can use the fact that the altitude from the right angle of a right triangle divides the triangle into two smaller similar triangles.

Let's denote the length of AD as x.

Since triangle ADC and triangle CDB are similar to triangle ACB, we can set up the following proportions:

For triangle ADC:

AD / AC = CD / AB

For triangle CDB:

BD / AC = CD / AB

We already know that AC = 12, AB = 36, and CD = x. So, let's substitute these values into the proportions:

For triangle ADC:

x / 12 = CD / 36

For triangle CDB:

(36 - x) / 12 = CD / 36

Now, let's solve these equations:

From the first equation:

x / 12 = CD / 36

x = (12 * CD) / 36

x = CD / 3

From the second equation:

(36 - x) / 12 = CD / 36

36 - x = (12 * CD) / 36

36 - x = CD / 3

Now, let's solve for CD using the second equation:

36 - x = CD / 3

36 - (CD / 3) = CD / 3

36 = (2 * CD) / 3

CD = (36 * 3) / 2

CD = 54

Now that we have found CD, we can substitute it into the first equation to find x:

x = CD / 3

x = 54 / 3

x = 18

So, the length of AD is 18 units.

Answer:

B. False.

Step-by-step explanation:

We have been given an image of a quadrilateral. We are asked to determine whether a circle could be circumscribed about the given quadrilateral.

We know that opposite angles of a cyclic quadrilateral are supplementary.

Let us check is this true for our given quadrilateral or not.

[tex]m\angle B+m\angle D=180^{\circ}[/tex]

[tex]80^{\circ}+60^{\circ}=180^{\circ}[/tex]

[tex]140^{\circ}\neq 180^{\circ}[/tex]

Now let us check other pair of angles.

[tex]m\angle A+m\angle C=180^{\circ}[/tex]

[tex]110^{\circ}+110^{\circ}=180^{\circ}[/tex]

[tex]220^{\circ}\neq 180^{\circ}[/tex]

Since opposite angles of our given quadrilateral are not supplementary, therefore, a circle could not be circumscribed about the given quadrilateral.

Answer is -2x^2+8-10 hope this helps!!!!

The length of the diagonal of a square with side lengths 7√2 is approximately 14.1 units.

The length of the diagonal of a square can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides. Since a square has all sides equal, the length of each side can be represented as 7√2. Substituting this value into the Pythagorean theorem, we get:

Diagonal² = (7√2)² + (7√2)²

Diagonal² = 98 + 98 = 196

Taking the square root of 196, we find the length of the diagonal to be approximately 14 units. Rounding to the nearest tenth gives us 14.1 units.

Given is the borrowed amount = 380 dollars.

Repayment period = 6 months.

Monthly installments = 67 dollars.

After six months, total repaid amount would be sum of all six monthly installments i.e. 6 x 67 = 402 dollars.

The interest to be paid on this loan would be difference of total repaid amount and borrowed amount.

Interest paid = Repaid amount - Borrowed amount

Interest = 402 dollars - 380 dollars

Interest = 22 dollars.

So, he would pay 22 dollars as interest on this loan.

Answer:

[tex]^{10}C_5(2a)^{5}(-3b)^5[/tex]

Option 1 is correct.

Step-by-step explanation:

Given: [tex](2a-3b)^{10}[/tex]

We need to find 6th term of binomial expansion.

Formula:

[tex]T_{r+1}=^nC_rx^{n-r}y^{r}[/tex]

We need to find 6th term, [tex]T_6[/tex]

[tex]T_6=T_{r+1}[/tex]

So, r=5

Put r=5 into formula

[tex]n=10, x=2a \text{ and }y=-3b[/tex]

[tex]T_6=^{10}C_5(2a)^{10-5}(-3b)^5[/tex]

Now we will simplify it to calculate 6th term

[tex]T_6=^{10}C_5(2a)^{5}(-3b)^5[/tex]

Hence, The 6th term of binomial is [tex]^{10}C_5(2a)^{5}(-3b)^5[/tex]

The expression that represents the sixth term in the binomial expansion of (2a - 3b)¹⁰ is expressed as  ¹⁰C₆(2a)⁴(-3b)⁶.

To find the sixth term in the binomial expansion of (2a - 3b)¹⁰, we can use the binomial theorem,

which states that the k-th term in the expansion of (a + b)ⁿ can be calculated using the following formula:

T(x) = C(n, x) × (aⁿ⁻ˣ) × (bˣ)

Where:

T(x) is the x-th term in the expansion.

C(n, x) is the binomial coefficient, also denoted as "n choose x," and it is equal to n! / (x! × (n-x)!), where "!" denotes factorial.

a is the first term in the binomial (2a in this case).

b is the second term in the binomial (-3b in this case).

n is the exponent of the binomial (10 in this case).

x is the term we want to find (the sixth term in this case).

Now, let's calculate the sixth term:

x = 6

n = 10

a = 2a

b = -3b

First, calculate the binomial coefficient:

C(10, 6) = 10! / (6! × (10-6)!)

C(10, 6) = 210

Now, plug these values into the formula:

T(6) = 210 × (2a)¹⁰⁻⁶ × (-3b)⁶

Simplify the exponents:

T(6) = 210 × (2a)⁴ × (-3b)⁶

T(6) = 210 × 16a⁴× 729b⁶

Now, multiply the constants:

T(6) = 30,240a⁴b⁶

Therefore, the sixth term in the binomial expansion of (2a - 3b)¹⁰ is 30,240a⁴b⁶ which is written as ¹⁰C₆(2a)⁴(-3b)⁶.

learn more about binomial expansion here

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Answer:

The number of steps in a stairway is discrete.

Step-by-step explanation:

A discrete data is that, which can take only integer values like number of apples in a basket.

But the continuous data is that, which can take on any value like a decimal. For example, the weight of patients in a hospital.

So, the number of steps in a stairway will be a discrete data. As stairs are counted in whole numbers and not decimals.

Answer:

[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]

Step-by-step explanation:

Given that a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

we have to find the area of pentagon.

Apothem=a=3 cm

Perimeter=s=21.8 cm

[tex]\text{Area of regular pentagon=}\frac{1}{2}\times apothem\times perimeter[/tex]

[tex]\frac{1}{2}\times s \times a[/tex]

[tex]=\frac{1}{2}\times 21.8\times 3[/tex]

[tex]=\frac{65.4}{2}=32.7 cm^2[/tex]

[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]

Option 3 is correct.

Answer:

To estimate 179% of 41 by rounding, use the expression

✔ 180%(40)

.

Using the distributive property, the expression is equivalent to

✔ (100%)(40) + (80%)(40)

.

179% of 41 is about

✔ 72

.

Step-by-step explanation:

Answer:

The answer is 5.

Step-by-step explanation:

Answer:

The correct option is:

Option: C

C valid; There is no bias in the survey.

Step-by-step explanation:

It is given that:

An organisation president  uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey.

So, the sample used by her is a valid sample.

Since, she sets a random rule to choose the members  to participate in the survey.

The sample used by her is unbiased.

( Since, the aim of our survey questions are to capture an unbiased opinion to capture the true sentiments of the survey taker )

Hence, the correct statement regarding her survey is:

C. valid; There is no bias in the survey

Answer:

B. the y -intercept is (0,3)

Step-by-step explanation:

Answer:

greatest common factor the largest factor that any given numbers have in common

Step-by-step explanation:

so the answer is greatest common factor

Final answer:

Knowledge of prime and common factors is essential for finding the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers, a key element in simplifying fractions and understanding ratios.

Explanation:

Understanding prime and common factors is instrumental in finding the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers. The GCD is the highest number that divides evenly into each of the numbers in question. For example, the GCD of 48 and 60 is 12 since 12 is the largest number that can divide both 48 and 60 without leaving a remainder. Finding the GCD is crucial in simplifying fractions, solving problems involving ratios, and is also a fundamental concept in more advanced mathematics including algebra and number theory.

The process often involves factoring the numbers down to their prime factors, identifying the common primes, and then multiplying these common prime factors together to find the GCD. This method not only highlights the importance of prime numbers in the mathematical hierarchy but also underlines the indelible role of factorization in simplifying and solving numerical problems.