A boat is 2000m from a cliff. If the angle of depression from the top of the cliff to the boat is 10 degrees, how tall is the cliff.

Answer:Perimeter of a quarter circle with radius

To find the perimeter of the quarter circle, find the circumference of the whole circle, divide by 4, and then add the radius twice. To find the radius when you are given the area of the quarter circle, multiply the given area by 4, then plug this number in for A into the formula A = pi * r^2 and then solve for r.

I HOPE THIS HELPS

The principal amount was £1260, and the annual interest rate is 5.5%.

Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.

SI = principal × rate × time / 100

So,

P + 5pr = £1606.50

P = £1606.50 - 5pr............(i)

P + 6pr = £1675.80

P = £1675.80 - 6pr.........(ii)

Therefore,

£1606.50 - 5pr = £1675.80 - 6pr

Pr = 69.3

Put the value of pr in eq(i)

P + 5(69.3) = 1606.50

P = 1606.5 - 346.5

P = 1260

Now,

(1260)r = 69.3

r = 0.055

The annual interest is 5.5%

Hence, the principal amount was £1260, and the annual interest rate is 5.5%.

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(a) f(x) =  \(log_2(x)\) is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2

(e) v(t) = \(5^t\)is an exponential function

(f) w(θ) = sin θ \(cos^{2}\theta\) is a trigonometric function.

(a) f(x) = \(log_2(x)\) is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = \(5^t\) is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ \(cos^{2}\theta\) is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  \(log_2(x)\)    

(b) g(x) = ∜x    

(c) h(x) = \(2x^3/(1 - x^2)\)    

(d) u(t) = 1 - 1.1t + \(2.54t^2\)                    

(e) v(t) = \(5^t\)    

(f) w(θ) = sin θ \(cos^{2}\theta\)

Answer:

7.80 ounces can be bought for $1.95

Step-by-step explanation:

Step 1:  Determine how many ounces is in a pound:

Thus, 16 ounces cost $4.

Step 2:  Create a proportion to determine how many ounces can be bought for $1.95.

Since you can get 16 ounces for $4, we can create a proportion to determine how many ounces can be bought for $1.95:

16 ounces / $4 = x ounces / $1.95

Step 3:  Simplify on the left-hand side of the equation:

16/4 = x/1.95

4 = x/1.95

Step 4: multiply both sides by 1.95 to determine how many ounces can be bought for $1.95:

(4 = x/1.95) * 1.95

7.80 = x

Thus, 7.80 ounces can be bought for $1.95.

The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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4x-4=20

or, 4x=20+4

or,4x=24

or,x=20/4

tgerefore,x=5

Answer:

honesty i don't know fam

subtract 2 from both sides

3a - 3y =  15 - 2x

factor out the common term 3

3 (a-y) = 15 - 2x

divide both sides by 3

a - y = 15 - 2x/3

add y to both sides

a = 15-2x/3 + y

then solve put the value for a =

15-2x/3 + y + 7 ÷10​

simplify using the common denominator

10(15-2x)+7*3/30

simplify 7 * 3 to 21

10(15-2x)+21/30

expand

150-20x+21/30

simplify 150-20x+21 to -20x + 171

-20x+171/30

Answer: -20x+171/30

\(\huge\bf Question:– \)

\(\sf \longmapsto \: 3a+2x−3y=15\)

\( \bf \huge \: To \: Find:–\)

\( \boxed{\bf \: Value\: of \: A}\)

\(\huge\bf Solution:–\)

\(\sf \longmapsto \: 3a+2x−3y=15\)

\(\boxed{ \bf \: Add -2x \: to \: both \: sides}\)

\(\sf \longmapsto \: 3a+2x−3y+−2x=15+−2x\)

\(\sf \longmapsto \: 3a−3y=−2x+15\)

\(\boxed{ \bf \: Add \: 3y \: to \: both \: sides}\)

\(\sf \longmapsto \: 3a−3y+3y=−2x+15+3y\)

\(\sf \longmapsto \: 3a=−2x+3y+15\)

\( \boxed{\bf \: \: Divide \: both \: sides \: by \: 3}\)

\(\sf \longmapsto \: \dfrac{3a}{3} = \dfrac{−2x+3y+15}{3} \)

\( \boxed{\bf \: Cross \: Multiply}\)

\(\boxed{\sf \longmapsto \: a = \dfrac{ - 2}{3} x + y + 5}\)

______________________________________

\(\bf \: Put\:The\: Value\)

\( \sf \longmapsto \: \dfrac{−2x+3y+15}{3} +7÷10\)

\( \boxed{\bf \: Distribute}\)

\(\sf \longmapsto \: \dfrac{ - 2}{3} x+y+5+ \dfrac{7}{10} \)

\( \boxed{\bf \: Combine \: Like \: terms}\)

\(\sf \longmapsto \: \bigg( \dfrac{ - 2}{3} x\bigg) + y +\bigg( 5 + \dfrac{7}{10} \bigg)\)

\(\sf \longmapsto \: \dfrac{ - 2}{3} x + y + \dfrac{57}{10} \)

______________________________________

\(\boxed{\bf The Answer\: is:–}\)

\(\boxed{{\underline{\bf\dfrac{ - 2}{3} x + y + \dfrac{57}{10}} }}\)

Answer:

24 feet wide

Step-by-step explanation:

72/18 = 4

80/20 = 4

88/22 = 4

Since there is one common answer between all sizes, you can make a ratio to help or you can use inverse operations.

Inverse operations is easier, so you would divide 96 by 4, and that will equal 24.

Answer:

18 lawns

Step-by-step explanation:

Lets take the number of lands that would be mow(ed) in 36 hours as x

Hence,

\(Thriugh\ the\ proportion\ method\ , we\ get\ \\\\3 : 6::x:36\\36*3=6x\\\frac{36*3}{6} =x\\\frac{108}{6}=x\\x=18\)

The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Answer:

\( - 4\)

Step-by-step explanation:

1) Simplify 5 - 10 to -5.

\(3 - ( - 5) - 7 + 1 - 6\)

2) Remove parentheses.

\(3 + 5 - 7 + 1 - 6\)

3) Simplify 3 + 5 to 8.

\(8 - 7 + 1 - 6\)

4) Simplify 8 - 7 to 1.

\(1 + 1 - 6\)

5) Simplify 1 + 2 to 2.

\(2 - 6\)

6) Simplify.

\( - 4\)

Therefor, the answer is -4.

Answer:

The number of units that must be produced and sold to maximize the profit is 30 units

The maximum profit is;

Explanation:

Given that the profit P(x) obtained by manufacturing and selling x units of a certain product is given by;

The maximum point is at;

Differentiating P(x);

The number of units that must be produced and sold to maximize the profit is 30 units

Substituting x into p(x);

The maximum profit is;

Answer:

Hi! The correct answer is 15x^2 + 36x + 12!

Step-by-step explanation:

~Expand the polynominal using the FOIL method~

Answer:

1 5 \(x^{2}\) + 3 6 + 1 2

Step-by-step explanation:

Answer:

\(x^3y^{12}\)

Step-by-step explanation:

\(\left(xy^4\right)^3\\\left(xy^4\right)^3=x^3\left(y^4\right)^3\\=x^3\left(y^4\right)^3\\=(y^4)^3\\=(y)^{4\times 3}\\= y^{12}\\= x^3y^{12}\)

\(\textsf{Hi Brainy User, I'm Here to Help you!}\)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

\(\textsf{By using the \textbf{Exponent Property}, we can simplify this.}\)

\(\textsf{This is what it states:}\)

\(\sf{(x^m)^n=x^{(m*n)}}\)

\(\textsf{Multiply:}\)

\(\sf{(xy^4)^3=x^3y^{3*4}=x^3y^{12}}\)

\(\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star\)

There can be one valid triangle created from the given conditions of side a being 5 and angles b and c being 30 and 50 degrees respectively.

To calculate how many triangles can be created from two angles and a side, the user must click the “calculator” tab. Once this is done, it is important to click the “clear” button to begin a new calculation. After this, the user must enter the side (a) under the “sides” section, and the angles (b and c) under the “angles” section. This example used 5 for the side, 30 for angle b, and 50 for angle c. Once the information is entered, the user must click “calculate”. This will result in a valid triangle being created from the given conditions. It is important to note that if the user entered different values, a different result may be obtained. Therefore it is important to ensure that the values entered are the desired ones. Additionally, if the sum of the angles entered are not equal to 180 degrees, then no valid triangle can be created.

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Answer:

1500+

Step-by-step explanation:

The angles are 28° and 62°.

It should be noted that perpendicular angles equal to 90°.

Therefore, that value of x will be calculated thus:

(x + 5) + (3x - 7) = 90°

4x - 2 = 90°

4x = 90° + 2°

4x = 92°

x = 92/4

x = 23°

(x + 5) = 23° + 5 = 28°

(3x - 7) = 3(23) - 7 = 62°

Therefore, the angles are 28° and 62°.

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Answer:

=−2x+4y−8

Step-by-step explanation:

Let's simplify step-by-step.

2x+4y−8−4x

Answer:

Option 3

Step-by-step explanation:

The  statement be rewritten as a conditional statement in if-then form as If a rectangle has 4 congruent sides, then it is a square.

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.

Given:

The conditional statement is  A rectangle with 4 congruent sides is a square.

According to given question we have

The conditional statement is given as A rectangle with 4 congruent sides is a square.

The counterexample must satisfy the hypothesis of the conditional statement.

So, '' If a rectangle has 4 congruent sides, then it is a square.''

Therefore, the  statement be rewritten as a conditional statement in if-then form as If a rectangle has 4 congruent sides, then it is a square.

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Answer: A

Step-by-step explanation:

i took it

Answer:

Not perpendicular

Step-by-step explanation:

Convert it to y-intercept form first:

5x - 4y = -1

-4y = -5x - 1

y = 5/4x + 1/4

4x - y = -9

-y = -4x - 9

y = 4x + 9

y = 5/4x + 1/4

y = 4x + 9

From the slopes, they are not considered perpendicular because one of the line slope is not a negative reciprocal of the other line slope.

Answer:

The lines are not perpendicular.

Step-by-step explanation:

If the lines are perpendicular, the product of the slopes should be -1.

These equations are in standard form (Ax + By = C), so we can easily find the slopes through using equation: slope= - A / B

For line 5x−4y=−1,

slope = -A / B

= - 5 /- 4

= 5/4

For line 4x−y=−9

slope = -A / B

= - 4 / -1

= 4

Now multiply the slopes to find the product:

5 /4 x 4

= 5

Since 5 ≠ -1, the lines are not perpendicular.

Answer:

8 students per group

Step-by-step explanation:

Since it says divided in the problem you use division.

Out of 72 students, we must divide them equally into 9 groups.

This means our equation will look like:

72 ÷ 9

After using a calculator or long division, your answer should be 8.

Answer:

Option B

Step-by-step explanation:

704 cubic centimeters

Answer:

20 cm^2

Step-by-step explanation:

A = 1/2 * d1 * d2 = 1/2 * 8 * 5 = 1/2 * 40 = 20cm^2

Answer:

.65

Step-by-step explanation:

Expressions are mathematical statements without the equation sign

The possible integer values of q, r, and z are 1, -5 and 8

The expressions are given as:

\(2x^{2} + zx - 10\)  (say eq. 1)

(x + q)(x + r)  

Both expressions are equal.

So, we have:

\(2x^{2} + z x - 10 = (x+q)(x+r)\)

we know that , roots of a quadratic equation (\(ax^{2} + bx + c = 0\)) are ,

\(m = \frac{-b + \sqrt{b^{2} - 4ac } }{2a} , n = \frac{-b - \sqrt{b^{2} - 4ac } }{2a}\)

on comparing \(ax^{2} + bx + c = 0\) with eq . 1 , we get

a = 2 , b = z , c = -10

Therefore , \(m = \frac{(-z) + \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z + \sqrt{}z^{2} + 80 }{4}\),

                   \(n = \frac{(-z) - \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z - \sqrt{}z^{2} + 80 }{4}\)

Now , we can express eq. 1 as ,

(x-m)(x-n)

By comparison, we have:

q = -m

r = -n

or

\(q = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\r = \frac{-z - \sqrt{}z^{2} + 80 }{4}\)

Assume that q = 1.

So, we have:

\(1 = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\or\\4 = -z + \sqrt{z^{2} + 80 } \\\)

Rearranging and Squaring both sides ,

\((z+4)^{2} = (\sqrt{z^{2} + 80 }) ^{2} \\z^{2} + 16 + 8z = z^{2} + 80\\8z = 64\)

This gives , z = 8

Substitute , z= 8 in r

So, we have:

\(r = \frac{-8 - \sqrt{8^{2} + 80 } }{4} = \frac{-8 - \sqrt{144} }{4} = \frac{-8 - 12}{4} = -5\)

Hence, the possible integer values of q, r, and z are 1, -5 and 8.

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Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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Answer:

The temperature is -5F

Step-by-step explanation:

You start at -3 then add 5 to get 2 degrees Fahrenheit then you subtract 7 to get -5 degrees Fahrenheit