100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.

In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.

AB = AC - BC = (80√3 - 80) meters

= 80(√3 - 1) meters

= about 58.56 meters

The distance between points A and B is approximately 138.6 meters.

To find the distance between points A and B, we can use the concept of trigonometry and the given information.

Let's denote the distance between points A and B as x.

From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:

tan(30°) = opposite/adjacent

tan(30°) = 80.0/x

Simplifying the equation, we have:

x = 80.0 / tan(30°)

Using a calculator, we can find the value of tan(30°) ≈ 0.5774.

Substituting the value, we get:

x = 80.0 / 0.5774

Calculating the value, we find:

x ≈ 138.6 meters

In light of this, the separation between positions A and B is roughly 138.6 metres.

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The data points form a straight line, suggesting a negative linear association.

Based on the given scatter plot, the association can be described as a negative linear association. A linear association refers to a relationship between two variables where the data points tend to cluster around a straight line. In this case, as the x-values increase, the corresponding y-values consistently decrease.

The scatter plot displays a clear negative slope, indicating that as the x-values increase, the y-values decrease in a linear fashion. This pattern suggests an inverse relationship between the two variables: as one variable increases, the other decreases proportionally.

The dots are arranged in a downward trend, with a clear linear pattern. This is characteristic of a negative linear association. The relationship between the variables can be described by a negative slope or a negative correlation coefficient.

It's worth noting that the scatter plot does not exhibit any curvature or nonlinear patterns. If there were a curvature present, indicating a non-linear relationship, it could be further classified as either positive or negative based on the direction of the curve.

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To convert the vertex form back to standard form, simply square the binomial, distribute a, and add the constants.

Example :

[tex]y=3(x+1)^2+5[/tex]

[tex]y=3(x^2+2x+1)+5[/tex]

[tex]y=3x^2+6x+3+5[/tex]

[tex]y=3x^2+6x+8[/tex] , This is the original standard form of the equation.

The vertex form of a quadratic equation is written as [tex]y = a(x - h)^2 + k[/tex] , where (h, k) represents the coordinates of the vertex.

To convert from vertex form to standard form, expand the equation using the distributive property:

[tex]y = a(x - h)^2 + k[/tex]

[tex]y = a(x^2 - 2hx + h^2) + k[/tex]

[tex]y = ax^2 - 2ahx + ah^2 + k[/tex]

Next, combine like terms by grouping the x^2 and x terms:

[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]

[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]

Finally, rearrange the terms in standard form:

[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]

[tex]y = ax^2 - 2ahx + ah^2 + k[/tex]

The resulting equation is in standard form, which is written as y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = a, b = -2ah, and c = ah^2 + k.

By converting from vertex form to standard form, we express the quadratic equation in a different but equivalent format, allowing for different types of analysis and calculations.

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Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

25,

-7

Step-by-step explanation:

r ° q= r(q(x))= (-x+2) ^2

So, using perfect square trinomial,

[tex](-x+2)^{2} =x^{2} -4x+4[/tex]

Thus q(-3)=25

q(r(x))= (-x^2)+2=-7

Answer:

a) r = .1880

b) a = .1186

c) r² = .0353

d) b = 3.6780

Answer:

a)  Commutative Property of Multiplication

b)  Associative Property of Multiplication

c)  Distributive Property of Multiplication over Addition

d)  Inverse Property of Multiplication

e)  Zero Property of Multiplication

Step-by-step explanation:

The Commutative Property of Multiplication states that the order of factors in a multiplication operation can be rearranged without changing the end result.

The Associative Property of Multiplication states that the grouping of factors in a multiplication operation by parentheses in a different way does not affect their product.

The Distributive Property of Multiplication over Addition states that multiplying a number by the sum of two other numbers is equivalent to multiplying the number separately by each of the two numbers and then adding the results.

The Inverse Property of Multiplication states that if a number is multiplied by its reciprocal (multiplicative inverse), the product is always equal to 1.

The Zero Property of Multiplication states that the product of any number and zero is always zero.

The point (2, 7π / 2) does not belong to the implicit curve 8 · x · y + π · sin y = 55π and tangent and normal lines cannot be determined.

In this question we find the definition of an implicit curve, in which we must determine if point (2, 7π / 2) belongs to the curve. First, we check that point:

8 · x · y + π · sin y = 55π

8 · 2 · (7π / 2) + π · sin (7π / 2) = 55π

56π + 0.191π = 55π

56.191π = 55π

56.191 = 55 (CRASH!)

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0.225 can be expressed as the fraction  1/200.

To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).

Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.

Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).

Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).

Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).

Therefore, 0.225 can be expressed as the fraction 1/200.

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Answer:

thousandths place value

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine which option will yield the most money after three years, let's calculate the final amount for each option.

Option #1 - CD for 3 years:

Principal (initial investment) = $1000

Interest rate = 3% per year (compounded monthly)

No additional money can be added

To calculate the final amount, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Final amount

P = Principal (initial investment)

r = Interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

For Option #1:

P = $1000

r = 3% = 0.03 (as a decimal)

n = 12 (compounded monthly)

t = 3 years

A = $1000 * (1 + 0.03/12)^(12*3)

Calculating the final amount for Option #1, we get:

A = $1000 * (1 + 0.0025)^(36)

A ≈ $1000 * (1.0025)^(36)

A ≈ $1000 * 1.0916768

A ≈ $1091.68

Option #2 - CD for 1 year:

Principal (initial investment) = $1000

Interest rate = 2% per year (compounded quarterly)

Money can be added at the end of each year

To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.

First Year:

P = $1000

r = 2% = 0.02 (as a decimal)

n = 4 (compounded quarterly)

t = 1 year

A = $1000 * (1 + 0.02/4)^(4*1)

A ≈ $1000 * (1.005)^(4)

A ≈ $1000 * 1.0202

A ≈ $1020.20

At the end of the first year, the total amount is $1020.20.

Second Year:

Now we add an additional $60 to the previous amount:

P = $1020.20 + $60 = $1080.20

r = 2% = 0.02 (as a decimal)

n = 4 (compounded quarterly)

t = 1 year

A = $1080.20 * (1 + 0.02/4)^(4*1)

A ≈ $1080.20 * (1.005)^(4)

A ≈ $1080.20 * 1.0202

A ≈ $1101.59

At the end of the second year, the total amount is $1101.59.

Third Year:

Again, we add $60 to the previous amount:

P = $1101.59 + $60 = $1161.59

r = 2% = 0.02 (as a decimal)

n = 4 (compounded quarterly)

t = 1 year

A = $1161.59 * (1 + 0.02/4)^(4*1)

A ≈ $1161.59 * (1.005)^(4)

A ≈ $1161.59 * 1.0202

A ≈ $1185.39

At the end of the third year, the total amount is $1185.39.

Comparing the final amounts:

Option #1: $1091.68

Option #2: $1185.39

Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.

The solution to the given equation is x = -1/4.To solve the equation, let's break down the steps as outlined by Deepak:

Combine like terms: Starting with the left side of the equation, combine the x terms and the constant terms separately. On the left side, we have -3x and 4x, which can be combined to give x. Similarly, we have -5 and 5, which cancel each other out, leaving us with zero.

Simplify both sides: Now, the equation becomes x = -7/4 - 3x.

Move all the x terms to one side: To isolate the x term on one side, we can add 3x to both sides of the equation. This gives us 4x + 3x = -7/4.

Combine like terms: On the left side, we have 4x and 3x, which can be added to give 7x. The equation now becomes 7x = -7/4.

Solve for x: To solve for x, we divide both sides of the equation by 7. This yields x = -1/4.

Therefore, the solution to the given equation is x = -1/4.

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a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.

b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.

a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:

h(t) = [tex]-16(t^2 - 10t)[/tex]

Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:

h(t) = -16t(t - 10)

Therefore, the factored expression for h(t) is -16t(t - 10).

b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.

Using the original expression:

h(1) = [tex]-16(1)^2 + 160(1)[/tex]

h(1) = -16 + 160

h(1) = 144

Using the factored expression:

h(1) = -16(1)(1 - 10)

h(1) = -16(1)(-9)

h(1) = 144

Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.

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Answer:

31

Step-by-step explanation:

you add the hats to get the total number of hats then divide the answer by

No, it is much too high. Then the correct option is B.

An equation is a statement of equality between two expressions consisting of variables and/or numbers.

Given the question above, we need to find if the hats is to high or low.

Calculating the total numbers of hats made, we have

[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]

If Edna wants to split 62 hats evenly between two hospital, then each hospital will get

[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]

Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available

Hence, the correct option is B.

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Edna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?

A. Yes

B. No, it is much too high

C. No, it is much too low

[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]

Sum up ;

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]

So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years

Answer:

Sydney= 20, Devaughn= 60

Step-by-step explanation:

Let Sydney's age be 'x'

Devaughn's age = 3 times x = 3x

We Know That

The sum of their ages is 80.

So,

3x + x = 80

4x = 80

If we shift the 4 to the 80 side

x = 80/4

x = 20

So, Sydney's age is 20

Therefore, Devaughn's age =

3x = 3 times x

= 3 times 20

= 60

Answer:

Here's an example:

convert 2.5 into a mixed number.

Make the denominator less than the original.

The easy way for this is to do 25/10

when you put it through a calculator it ends up being 2.5

(essentially the mixed number and the decimal are the SAME numbers.)

Hope this clarified. :)

To convert a decimal to a mixed number, follow these steps:

Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.

Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.

Step 3: Express the decimal part as a fraction by using the place value of the last digit.

Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Step 5: Combine the whole number part, the fraction, and simplify if necessary.

Here's an example:

Let's say we have the decimal 2.75.

Step 1: The whole number part is 2.

Step 2: The decimal part is 0.75.

Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.

Step 4: The fraction 3/4 is already in its simplest form.

Step 5: Combining the whole number part and the fraction, we have 2 3/4.

So, the decimal 2.75 can be written as the mixed number 2 3/4.

Remember to always simplify the fraction part if possible.

Vinay buys "two thousand seven" fruits.

To find the number of fruits that Vinay buys, we need to determine the place value of 2 in the number 37,523 and add 7 to it.

In the number 37,523, the digit 2 is in the thousands place.

The place value of 2 in the thousands place is 2,000.

Adding 7 to the place value of 2, we get:

2,000 + 7 = 2,007.

Therefore, Vinay buys 2,007 fruits.

In number names, we can write 2,007 as "two thousand seven."

So, Vinay buys "two thousand seven" fruits.

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Answer:

bob

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.

We have,

The monthly basic salary of the married Chief Secretary of Nepal Government is given as Rs 74,000.

This is the fixed amount he receives as his base salary every month, before any additional allowances or deductions are considered.

Now,

In this case, the dearness allowance of Rs 2,000 is added to the basic salary.

This allowance is provided to compensate for the rising cost of living and is a fixed amount added to the basic salary.

Additionally, he receives 1 month's basic salary as a festival allowance. Since his monthly basic salary is Rs 74,000, his festival allowance would also be Rs 74,000.

Therefore, his total monthly salary can be calculated as follows:

Basic salary + Dearness allowance + Festival allowance

= Rs 74,000 + Rs 2,000 + Rs 74,000

= Rs 1,50,000

Thus,

The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.

Answer:

m = undefined

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-4,7) (-4,1)

We see the y decrease by 6 and the x stay the same, so the slope is

m = undefined

[tex]\pmb{Question}[/tex]

Find the slope of a line passing through (-4,7) (-4,1).

[tex]\pmb{Answer}[/tex]

Not Defined

[tex]\pmb{Formula}[/tex]

[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\pmb{Where}[/tex]

[tex]\pmb{Plug\:in\:the\:data}[/tex]

[tex]\sf{m=\dfrac{1-7}{-4-(-4)}}[/tex]

[tex]\sf{m=\dfrac{-6}{-4+4}}[/tex]

[tex]\sf{m=-\dfrac{6}{0}}[/tex]

[tex]\sf{Slope=Not\;De fined}[/tex]

∴ the slope is undefined

[tex]\rule{350}{3}[/tex]

[tex]\frak{-star-}[/tex]

Solution:

Formula: Total = Group 1 + Group 2 - Both + Neither

where:

- Total = total number of girls in the class (34)

- Group 1 = number of girls playing tennis (21)

- Group 2 = number of girls playing netball (18)

- Both = number of girls playing both games (what we want to find)

- Neither = number of girls playing neither game (0, since all the girls play at least one game)

Plugging in the values, we get:

34 = 21 + 18 - Both + 0

Simplifying:

34 = 39 - Both

Both = 39 - 34

Both = 5

The sentence that contains no errors in subject-verb agreement is: "Those people whose long lives are about to end feel reassured by this belief."

This sentence correctly matches the plural subject "Those people whose long lives are about to end" with the plural verb "feel." The verb "feel" agrees in number with the subject "people."

The other sentences have subject-verb agreement errors:

"Those people whose long lives are about to end feels reassured by this belief."

The verb "feels" does not agree with the plural subject "Those people." It should be "feel."

"A person whose long life is about to end feel reassured by this belief."

The verb "feel" does not agree with the singular subject "A person." It should be "feels."

"A person whose long life are about to end feels reassured by this belief."

The verb "are" does not agree with the singular subject "A person." It should be "is."

Therefore, the sentence with no errors in subject-verb agreement is: "Those people whose long lives are about to end feel reassured by this belief."

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Answer:

Step-by-step explanation:

A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres

20 * 10 * 10 = 2000cm^3

1000 cm^3 = 1 Litres

​2000 cm^3 = 2 Litres

Answer:

x=-24

Step-by-step explanation:

2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)

Hello,

Answer:

[tex]30+((-2\times(25- (13-3)))[/tex]

[tex]=30+((-2\times(25- 10))[/tex]

[tex]=30+(-2\times 15)[/tex]

[tex]=30+(-30)[/tex]

[tex]=30-30[/tex]

[tex]=\boxed{0}[/tex]

The shape is represented as below

The figure is of three shapes, the firs two are whole numbers then the last is a fraction.

Adding them results to

shape 1 + shape 2 + shape 3

1 + 1 + 1/4

As one fraction

= 9/4

as a mixed number

= 2 1/4

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Answer:

B. 7

Step-by-step explanation:

3/KL = 12/28

KL = 3/(12/28) = (28 x 3)/12 = 7