Evaluate the expression [8(2)-4^2]+7(4)

One possible value of ∠U is 80° (to the nearest degree).

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the possible values of ∠U, we can use the Law of Cosines:

c² = a² + b² - 2ab cos(C)

Where c is the side opposite the angle we want to find (∠U), a and b are the other two sides, and C is the angle opposite side c.

In this case, we want to find ∠U, so we'll use side u as c and sides t and s (which we don't know yet) as a and b, respectively:

u² = t² + s² - 2ts cos(U)

Substituting the given values, we get:

340² = 620² + s² - 2(620)(s)cos(U)

Simplifying:

115600 = 384400 + s² - 1240s cos(U)

Subtracting 384400 and rearranging:

s² - 1240s cos(U) + 268800 = 0

Now we can use the quadratic formula to solve for s:

s = [1240 cos(U) ± √(1240² cos²(U) - 4(1)(268800))]/(2)

Simplifying under the square root:

s = [1240 cos(U) ± √(1537600 cos²(U) - 1075200)]/(2)

s = [1240 cos(U) ± √(409600 cos²(U) + 1742400)]/(2)

s = [620 cos(U) ± √(102400 cos²(U) + 435600)]

Since s must be positive, we can discard the negative solution, and we have:

s = 620 cos(U) + √(102400 cos²(U) + 435600)

Now we can use the fact that the sum of angles in a triangle is 180° to find ∠U:

∠U = 180° - ∠T - ∠S

Since we know ∠T = 110°, we just need to find ∠S. We can use the Law of Sines to do this:

sin(S)/s = sin(T)/t

sin(S) = (s/t)sin(T)

Substituting the values we know:

sin(S) = (620 cos(U) + √(102400 cos²(U) + 435600))/620 * sin(110°)

sin(S) ≈ (1.481 cos(U) + 2.225)/6.959

Now we can use a calculator to find the arcsin of both sides to get ∠S:

∠S ≈ arcsin((1.481 cos(U) + 2.225)/6.959)

Finally, we can substitute the values we found for ∠S and ∠T into the equation we found earlier for ∠U:

∠U = 180° - 110° - arcsin((1.481 cos(U) + 2.225)/6.959)

Simplifying:

∠U = 70° - arcsin((1.481 cos(U) + 2.225)/6.959)

Now we can use trial and error or a graphing calculator to find the values of ∠U that satisfy this equation. One possible solution is:

∠U ≈ 80°

Therefore, one possible value of ∠U is 80° (to the nearest degree).

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I think answer is 2.5

HOPE THIS HELPS YOU

The function f(x)=\(x^2\)-2x+3 after putting x=1 then f(1)=2.

What is function?

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). f = (a,b)| for all values of a A and b B. Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.  

Here the given function is ,

=> f(x)=\(x^2\)-2x+3

Now put x= 1 then

=> f(1) = \(1^2\)-2(1)+3

=>f(1) = 1-2+3

=> f(1) = 2

Hence the value of f(1)=2.

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Answer:

1

Step-by-step explanation:

Answer:

0.25

yw have a good day bro

Answer:

(n/4)-1

Step-by-step explanation:

total slices = n

total number of people =4

each people may be eat = n/4 slices

here Harris eats 1 slice fewer

then Harris eats (n/4)-1 slices

hope this helps you

In a set S whic is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, then
the set of integers is infinite, the set of real numbers is infinite and if a set S has a subset A which is infinite, then S must be infinite.

Given that a set S is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, we want to prove the following statements:

(a) The set of integers is infinite.

(b) The set of real numbers is infinite.

(c) If a set S has a subset A which is infinite, then S must be infinite.

(a) Let A be the set of positive integers, i.e., A = {1, 2, 3, 4, 5, ...}. We define a function f: A → Z (the set of integers) by f(n) = n - 1. It can be shown that f is both one-to-one and onto. This means that there is a one-to-one correspondence between A and Z. By repeating the same argument, we can also prove that there is a one-to-one correspondence between the negative integers and A. Hence, Z is infinite.

(b) Suppose, for contradiction, that the set of real numbers, R, is finite. Then there would be a one-to-one correspondence between R and some finite set F. Without loss of generality, let F = {a_1, a_2, ..., a_n} where a_1 < a_2 < ... < a_n. Let ε > 0 be such that ε < min{|a_1|, |a_2| - |a_1|, ..., |a_n| - |a_(n-1)|, |a_n|}. For any x ∈ R, we consider different cases:

- If x < 0, then x < -ε < a_1.

- If 0 ≤ x < a_1, then 0 ≤ x + ε < a_1.

- If a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1, then a_i + ε < x + ε < a_(i+1) - ε < a_(i+1).

- If x > a_n, then x - ε > a_n.

We define a function g: R → F by:

- g(x) = a_1 + ε if x < 0,

- g(x) = x + ε if 0 ≤ x < a_n,

- g(x) = a_(i+1) - ε if a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1,

- g(x) = a_n - ε if x > a_n.

It can be shown that g is both one-to-one and onto. This contradicts the assumption that R is finite. Therefore, R must be infinite.

(c) Let S be a set such that A is a subset of S, and A is infinite. Suppose, for contradiction, that S is finite. Then, there would be a one-to-one correspondence between S and some finite set F. Let F = {a_1, a_2, ..., a_n}. There are finitely many elements in S that are not in A, denoted as {b_1, b_2, ..., b_m}. We choose ε > 0 such that ε < min{|a_1 - b_1|, |a_2 - b_2|, ..., |a_m - b_m|}. We define a function f: A → S as follows: f(a_i) = a_i for 1 ≤ i ≤ n, and f(a_i) = b_i + ε for 1 ≤ i ≤ m. It can be shown that f is both one-to-one and onto. This contradicts the assumption that S is finite. Therefore, S must be infinite.

Hence, we have proved the statements:(a) The set of integers is infinite, (b) The set of real numbers is infinite and (c) If a set S has a subset A which is infinite, then S must be infinite.

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Answer:

-3x³ + 8x² + 7x - 12

Step-by-step explanation:

hope this helps. Could you pls give me brainliest f correct,I   am only 3 away from leveling up!!

Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Answer: a. in the step by step explanation.  b. 20x - 15

Step-by-step explanation:

I think that Denise thought that the 5 only appplied to 4x since they were closer and since she multiplied them both, she thought there would be no use of it.

Example - 2 (3x+2)

                 2 x 3x = 6x

                 6x + 2

Of course this is wrong since the real answer should be 6x + 12 but someoneone like Denise may see it that way, only multiplying the ones closest and not opening it fully.

To find the probability of getting at least 4 fives, we sum up the probabilities of these two cases:

P(at least 4 fives) = P(4 fives and 1 non-five) + P(5 fives)

To calculate the probability of getting at least 4 fives when rolling a fair die 5 times, we need to consider the different possible outcomes.

The probability of rolling a five on a fair die is 1/6, and the probability of not rolling a five is 5/6.

To determine the probability of getting exactly 4 fives and 1 non-five, we use the binomial probability formula:

P(4 fives and 1 non-five) = (5 choose 4) * (1/6)^4 * (5/6)^1

Similarly, for getting exactly 5 fives, we have:

P(5 fives) = (5 choose 5) * (1/6)^5 * (5/6)^0

Rounding the result to the nearest thousandth, we get the probability of getting at least 4 fives when rolling a fair die 5 times.

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The point estimate for the unknown population proportion is approximately 0.5761.

To find the point estimate for the unknown population proportion, we can use the formula:

Point Estimate = x / n

Given that x = 106 and n = 184, we can substitute these values into the formula:

Point Estimate = 106 / 184 ≈ 0.5761

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The resultant moment about a both forces is zero. The statement is true.

A man B exerts a force on the rope, P = 30 lb

To find:

The magnitude of force, F

Consider a statement:

"The resultant moment about A of both forces is Zero."

Diagram attached at the end of the  solution

\($ \theta=\tan ^{-1}\left(\frac{3}{4}\right) \\\)

\(& \theta=36.87^0\)

To prevent the pole from rotating, so that the resultant moment is about A = 0

We will apply the equilibrium Equation \($\sum \mathrm{M}_{\mathbf{A}}=0$\)

Here force \($P \times \sin (45)$\) and \($F \times \sin (\theta)$\) will not produce the moment at A.

Taking clockwise moment as a negative and anticlockwise moment as a positive.

\(& \mathrm{P} \times \cos (45) \times(18)-\mathrm{F} \times \cos (\theta) \times 12=0 \\\)

\(& 30 \times \cos (45) \times(18)=\mathrm{F} \times \cos (\theta) \times 12 \\\)

\($ \mathrm{~F}=\frac{30 \times \cos (45) \times(18)}{\cos (36.87) \times 12} \\\)

F = 39.77 lb

Based on the given parameters,

The magnitude of force, F = 39.77 lb

So there exists the force by considering the resultant moment about an of both forces as zero.

The statement is true.

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Answer:

=−21x2+5x+4

Step-by-step explanation:

Let's simplify step-by-step.

4−3(7x2)+5x

=4+−21x2+5x

Answer:

0.375

Hope this helps....

Have a nice day!!!!

Answer:

3/8

Step-by-step explanation:

Hey there!

\(\frac{3}{8} = \frac{3*8+3}{8} = \frac{24 + 3}{8} = \frac{27}{8}\)

\(\frac{27}{8} = \frac{27 / 9}{8} = \frac{3}{8}\)

= 3/8

Hope this helps :)

The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:

(P/A, i%, n) = (1 - (1 + i)^(-n)) / i

Substituting the values given:

i = 8%

n = 145

(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08

Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:

(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)

Therefore, the correct choice for the value of (P/A,8%,145) is:

C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)

Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:

(F/P, i%, n) = (1 + i)^n

We want the investment to double, so we have:

(1 + i)^9 = 2

Taking the ninth root of both sides:

1 + i = 2^(1/9)

Solving for i:

i ≈ 0.0809 or 8.09% (rounded to two decimal places)

Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

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The number of ways that there are for her to plan her schedule of menus for the 20 school days, with no restrictions, using the Fundamental Counting Theorem, is of:

10^20.

The Fundamental Counting Theorem states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem, we have that:

Then the number of different meals is obtained as follows:

N = 10^20.

As there are 20 trials, each with 10 possible outcomes.

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Step-by-step explanation:

\( \sqrt{7} = {7}^{ \frac{1}{2} } = \sqrt{7} \)

Answer:

D divide both the numerator and denominator by cos(x)cos(y)

Step-by-step explanation:

just took test

The derivation of tangent sum identity taken to the expression in Step 3 to give an expression for Step 4 is option D; divide both the numerator and denominator by cos(x)cos(y).

The trigonometric identities is the relationship between the different trigonometric ratios.

These trigonometric identities are the basic formulae that are true for all the values of the reference angle.

For the given situation, the derivation for the tangent sum identity is given in the table below.

The derivation follows the steps,

\(\dfrac{sin (x+y)}{cos (x +y)}\)

we know that,

sin (x + y) = sin x cos y + cos x sin y

cos (x + y) = cos x cos y - sin x sin y

Substitute;

\(\dfrac{sin x cos y + cos x sin y}{cos x cos y - sin x sin y}\)

Divide each term by cos x cos y

\(\dfrac{\dfrac{sin x cos y}{cos x cos y} + \dfrac{cos x sin y}{cos x cos y} }{\dfrac{cos x cos y}{cos x cos y} - \dfrac{sin x sin y}{cos x cos y} }\)

Now, \(\dfrac{tan x + tan y}{1 - tan x tan y}\)

Hence we can conclude that the derivation of tangent sum identity taken to the expression in Step 3 to give an expression for Step 4 is option D; divide both the numerator and denominator by cos(x)cos(y).

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Answer:

20 + 6L ≤ 60 :)

The exponential function for the new participants is f(x) = 3 * 4^x

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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The weight of train A is 443.5 tons and the weight of train B is 12.4 tons.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that Trains A and B weigh a combined total of 456 tonnes. Train A weighs more than Train B. The weight difference between them is 431 tonnes.

From the given data we can make two linear equations.

A + B = 456

A - B = 431

Solve the above two equations by elimination method,

A + B = 456

A - B = 431

_________

2A = 887

A = 443.5 tons

The weight of train B,

B = A - 443.5

B = 456 - 443.5

B = 12.5 tons

Therefore, train A has a weight of 443.5 tons and the weight of train B is 12.5 tons.

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Step-by-step explanation:

F= G× Mass of sun × Mass of Jupiter

==============================

( distance between them)²

G = 6.67×10^-11

Mass of sun = 1.89×10²⁷

Mass of Jupiter = 2.0×10³⁰

distance between them = 7.73×10¹¹

F= 6.67×10^-11 × 1.89×10²⁷ × 2.0×10³⁰

============================= = 4.219×10^23N

( 7.73×10¹¹ )²