MULTIPLE CHOICE QUESTIONWhat do you get when you combinethese equations

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The results of the expression 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45

9 and 1/9 subtracted by 1 and 4/5

= 9 1/9 - 1 4/5

= 82/9 - 9/5

= (410-81) / 45

= 329/45

= 7 14/45

Therefore, 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45

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I don't know the answer so help

Answer:

x = 4√2

Step-by-step explanation:

Identifying the triangle in the diagram:

45-45-90 triangle rules:

Finding x:

Since the hypotenuse is 8 units long and, we can find x by setting 8 equal to x√2:

(8 =  x√2) / √2

8/√2 = x

Rationalize the denominator to simplify:

(8/√2) * (√2/√2)

8√2 / 2

4√2

Thus, x = 4√2

Answer:

2.25 yards per quilt

Step-by-step explanation:

if you add up all the numbers u get 58.5. then divide this by 26 to get 2.25

The number of yards that are used for each quilt will be 2.25 yards.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Dan is making quilts for the sewing class. He will utilize 22 yards of yellow texture, 11.2 yards of green texture, and 25.3 yards of blue texture. This sum makes 26 blankets.

The number of yards that are used for each quilt will be given as,

⇒ (22 / 26) + (11.2 / 26) + (25.3 / 26)

⇒ (22 + 11.2 + 25.3) / 26

⇒ 58.5 / 26

⇒ 2.25 yards

The number of yards that are used for each quilt will be 2.25 yards.

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Answer:

y intercept when x is 0, so the answer is 3

Answer:

The temperature farthest from zero is 5

Step-by-step explanation:

the reason for this is because it doesn't matter whether that temperature is negative or positive because all the question is asking is...."how far from zero"....and would -4 be farther from zero....or would 5 be farther from zero.  How I know this is absolute value is always positive.  And absolute value of -4....is 4.....and absolute value of 5....is 5.

And 5 is 1 temperature more away from zero than -4.

Answer:

5 is the farthest from 0

-4 is the coldest temperature

5 is the warmest temperature

Step-by-step explanation:

The farthest from 0 could be negative or positive. It's just whichever one has the greatest absalute value (if you know that term, if not...), whichever one you would put up more fingers to count to.

In this case, according to the number line, the farthest from 0 into the nagatives is -4, but the farthest from 0 in the positives is 5. This means that 5 is the farthest from 5 because 5 takes 5 of your fingers to count to, whule -4 (yes, even though it's negative) takes just 4 fingers. This is a good way to visualize it until you can wrap your head around it!

The coldest is the lowest number. In this case, it's below zero. Below zero means negatives. In this case, -4 is the lowest number.

The warmest is the highest number. In this case, it's above zero. That means it's a positive number. 5 is the highest number here.

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Answer:

198 1/3

Step-by-step explanation:

arithmetic sequence formula for the nth term:

aₙ = a₁ + (n-1)d

d = the common difference between each term

a₇ = a₁ + (7-1)d

34 = 5 + 6d

subtract 5 from both sides to isolate d and its coefficient

29 = 6d

divide both sides by 6 to isolate d

d = 29/6

a₄₁ = a₁ + (n-1)d

    = 5 + (41-1)d

    = 5 + 40d

    = 5 + 40(29/6)

    = 198 1/3

Answer:

4

Step-by-step explanation:

T(n) = n² + 3

T(1) = 1² + 3 = 1 + 3 = 4

Answer: 5/2

Step-by-step explanation:

slope equation: (y2-y1)/(x2-x1)

13-3/5-1 = 10/4 or 5/2

Answer:

2.5

Step-by-step explanation:

Gradient (slope) =

\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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The percentage of young adults who exercised four or five days a week is 36%

Out of the 25 young adults surveyed, a total of 4 people exercised four days a week and 5 people exercised five days a week. To calculate the percentage of young adults who exercised four or five days a week, we add the number of people who exercised four days a week to the number of people who exercised five days a week, which gives us a total of 9.

We then divide this by the total number of people surveyed (25) and multiply by 100 to get the percentage.

So the percentage of young adults who exercised four or five days a week is

(9/25) x 100 = 36%

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The sample space consists of 8 possible outcomes, each with an equal probability of 1/8. The outcomes are the combinations of heads (h) and tails (t) when flipping 3 coins.

1. Determine how many possible outcomes there are in the sample space.

There are 8 possible outcomes in the sample space: hhh, hht, hth, htt, thh, tht, tth, and ttt.

2. Determine the likelihood of each result.

Since all outcomes have equal probability, the probability of each outcome is 1/8.

In this experiment, we are flipping three coins, and each one lands either heads (h) or tails (t). Our sample space consists of all the possible combinations of heads and tails that can occur when flipping the coins. Therefore, our sample space is {hhh, hht, hth, htt, thh, tht, tth, ttt}. Since all outcomes have equal probability, the probability of each outcome is 1/8. This means that the probability of each combination of heads and tails is the same. For example, the probability of getting 3 heads is 1/8 and the probability of getting 2 heads and 1 tail is also 1/8.

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Answer:

(0,any number from 0 to ten)

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

i don't know

Answer:

-25x-45y, because if we have got + and -, so we will write minus.

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The polynomial function  p(x) = x³ - 7x + 6 divided by x - 2 =  x² + 2x - 3

Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.

We can represent the division of two polynomials in the form:

p(x)/q(x) = Q(x) + R/(q(x))

where,

The polynomial function p(x) = x³ - 7x + 6 is divided by x - 2

x³ - 7x + 6 ÷ x - 2 = (x - 1)(x + 3)

x² + 3x - x - 3 = x² + 2x - 3

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Answer:

Step-by-step explanation:

Since RQT=155

4x-20+3x+14=155

7x-6=155

7x=161

x=23

The domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function as -

f(x) = (x - 3)²

{ 1 } -

The domain of the function f(x) = (x - 3)².

The function has no undefined points. So, we can write the domain as -

Domain → (- ∞ , + ∞)

{ 2 } -

The inverse of the function f(x) = (x - 3)².

We have -

f(x) = (x - 3)²

y = (x - 3)²

x = (y - 3)²

y - 3 = √x

y = 3 + √x

Therefore, the domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

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Answer:

\(q\le \:12\)

Step-by-step explanation:

Solving

\(\mathrm{Switch\:sides}\)  (Not a required step)

\(q+3\le \:15\)

\(\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\)

\(q+3-3\le \:15-3\\=q\le \:12\)

\(\bold{q\le \:12}\)

Graphing

Check the picture below.

Answer:

Step-by-step explanation:

To find the number of ways the letters of the word AFFECTION can be arranged while keeping the vowels in their natural order and ensuring that the two F's do not come together, we can break down the problem into separate steps.

Step 1: Determine the arrangement of the vowels (AEIO). Since the vowels need to be in their natural order, we can consider them as one unit. So, the vowels can be arranged in 1 way.

Step 2: Determine the arrangement of the remaining consonants (FFCTN). Again, since the two F's cannot come together, we need to consider the F's as separate entities. The remaining consonants can be arranged in 5! (5 factorial) ways.

Step 3: Combine the arrangements from Steps 1 and 2. The vowels can be arranged in 1 way, and the consonants can be arranged in 5! ways.

Therefore, the total number of arrangements is 1 × 5! = 1 × 120 = 120.

Hence, there are 120 ways to arrange the letters of the word AFFECTION while keeping the vowels in their natural order and ensuring that the two F's do not come together.

Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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29 years from now, the father will be 49 years old.

Let's start by setting up the given information:

Currently, the father is 20 years old, and the son is 5 years old.

In 10 years, the father will be twice as old as the son.

The father is currently four times as old as the son.

Determine the age of the father and son in 10 years:

In 10 years, the father's age will be 20 + 10 = 30 years.

In 10 years, the son's age will be 5 + 10 = 15 years.

Write equations based on the given information:

The father's age in 10 years will be twice the son's age in 10 years: 30 = 2 × 15.

The father's current age is four times the son's current age: 20 = 4 × 5.

Solve the equations:

From the second equation, we find that the son's current age is 5 years.

Plugging this value into the first equation, we get: 30 = 2 × (5 + 10).

Simplifying further, we have: 30 = 2 × 15, which is true.

Determine the current age of the son in 29 years:

The son's current age is 5 years.

Adding 29 years to the son's current age, we find that the son will be 5 + 29 = 34 years old.

Determine the current age of the father in 29 years:

The father's current age is 20 years.

Adding 29 years to the father's current age, we find that the father will be 20 + 29 = 49 years old.

Therefore, 29 years from now, the father will be 49 years old.

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The required probability of selecting red candy from a bag is 2/7.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

Number of red candies in bag = 4,

Number of green candies in bag = 3,

And number of yellow candies in bag = 7.

Total number of candies in bag = 4 + 3 + 7 = 14

The probability of selecting red candy = \(\frac{^4 C_1}{^{14}C_1}\) = = 4 / 14 = 2 / 7.

The probability of selecting red candy is 2/7.                                                                

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