a 12 ft ladder is leaning against a building. if the base of the ladder is 5 ft from the base of the building, what is the angle of elevation of the ladder in degrees? (round your answer to one decimal place.)

Answer:

2

Step-by-step explanation:

Hey there!

The equation is asking us, c x c = 4

What is c?

Well the only number that is equal to 4 when you square it is 2

Answer:8

Step-by-step explanation: 5 x 3= 15

23-15=8

Answer:

8

Step-by-step explanation:

5 times 3 =15 23 minus 15 is three

The distance between Ibadan and Onitsha is 450km

The distance between Ibadan and Kafanchan is 636. 4km

To determine the distance, we have that;

The distance of Onitsha from Kafanchan is 450km

The distance between Ibadan and Onitsha is x

The distance between Ibadan and Kafanchan is y

Note that the third quadrant is 270 degrees

Then, the value of the angle = 270 - 225 = 45 degrees

Then, using the tangent identity, we have that;

tan 45 = x/450

cross multiply the values

x = 450km

Also, using the sine identity

sin 45 = 450/y

cross multiply the values

y = 636. 4 km

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Answer:

A. The slope is  \(\frac{3}{2}\)

B.  the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point.

Step-by-step explanation:

PART A: Slope

Given tangent line;

\(y = \frac{3x}{2} + \frac{9}{2}\)

The slope of the tangent line is equal to the derivative of the function;

\(\frac{dy}{dx} =\frac{3}{2}\)

the slope = \(\frac{3}{2}\)

PART B: Correct statement that describe the slope of a tangent line:

A secant line is a straight line joining two points on a function and the slope of the function is equal to average rate of change of the function between the two points.

A tangent line is a straight line that touches a function at only one point, and the slope of the function is equal to the instantaneous rate of change of the function at that one point.

Thus, the correct statement is " the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point".

Answer:

0.71 weeks

Step-by-step explanation:

To convert 5 days to weeks, we can use the conversion factor:

1 week = 7 days

Therefore, we have:

5 days = 5/7 weeks

Rounding to the nearest hundredth, we get:

5 days ≈ 0.71 weeks

Therefore, 5 days is approximately equal to 0.71 weeks.

Answer:

1. Sound

Step-by-step explanation:

Sorry if wrong :> Hope i helped! Have a awesome day!!! You're a great hooman ^_^ Please mark brainliest !! I know the first one and only the first one ><

Answer:

No

Step-by-step explanation:

By the Factor theorem

If (x - h) is a factor of f(x) then f(h) = 0

Here (x - 2) with h = 2 and

f(x) = x³ - 3x² - x + 7 , then

f(2) = 2³ - 3(2)² - 2 + 7 = 8 - 3(4) + 5 = 8 - 12 + 5 = 1

Since f(2) ≠ 0 then (x - 2) is not a factor of f(x)

The points that he average on the last two tests will be 93 points.

A mean is the average of the set of numbers that are given.

On the first five tests that he took, he averaged 86 points. The total points will be:

= 86 × 5

= 430 points

He averaged 88 points on all seven tests. The total will be:

= (88 × 7)

= 616 points

The point average on the last two tests will be:

= (616 - 430)/2

= 186/2

= 93 points

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Answer:

4

Step-by-step explanation:

1+2+2+3+4+5+6+9=32

32/8=4

Answer: 4

Step-by-step explanation:

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

Answer:

64

Step-by-step explanation:

Answer: Your answer is 64 4 times 4 equals 16 then 16 times 4 equals 64 <3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The common ratio of the following sequence is:

If the common ratio is less than 1 or greater than -1 but not 0, we can use the following expression to determine the sum of the infinite geometric series:

Therefore, if we have a common ratio of 3/8 or 0.375 and the first term of the series is 3/2.

The sum would be:

The entire trip to the mall took 5 hours, and it was 24 miles away. Cameron biked for 2 hours and walked for 3 hours.

Cameron started biking to the mall at a speed of 9 mph. After some time, the bike got a flat so Cameron walked the rest of the way, traveling at a speed of 2 mph. The distance that Cameron biked to the mall was x, and the distance he walked to the mall was 24 - x.

Cameron traveled at two different speeds, 9 mph and 2 mph, and traveled a total of 24 miles. So the time he spent biking plus the time he spent walking was 5 hours, and we can create an equation:

Time biking + time walking = 5 hours x/9 + (24 - x)/2 = 5 hours

Multiply everything by 18 to remove the denominators:
2x + 9(24 - x) = 90
2x + 216 - 9x = 90-7x = -126x = 18
Time biking = x/9 = 18/9 = 2 hours
Time walking = (24 - x)/2 = (24 - 18)/2 = 3 hours

Therefore, Cameron biked for 2 hours and walked for 3 hours.

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The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

\(m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$\)

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

\($$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$\)

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The relationship between numbers divisible by 6, 2, and 3 is that they are all multiples of 6.

The numbers divisible by 6, 2, and 3 are those that can be evenly divided by all three of these numbers.

To understand this relationship, we need to consider the factors of 6. The factors of 6 are 1, 2, 3, and 6. Since a number divisible by 6 must also be divisible by 2 and 3, it means that it must have both 2 and 3 as factors. For example, 12 is divisible by 2 and 3 because it can be divided evenly by both of these numbers. Similarly, 24, 36, 48, and so on, are all divisible by 6, 2, and 3 because they have both 2 and 3 as factors. In other words, any number that is divisible by 6 is also divisible by 2 and 3 because these numbers are factors of 6.

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What is the nature of the relationship between the numbers that are divisible by both 2 and 3, specifically those that are also divisible by 6?

keeping in mind that 6¼ is just 6 + ¼ or 6 + 0.25 or just 6.25

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.25\% of 3872}}{\left( \cfrac{6.25}{100} \right)3872}\implies 242\)

Answer: 36

Step-by-step explanation: I used a calculator to multiply 9 by 9 & 1 1/2 by 1 1/2. For 9 by 9 you get 81, for 1 1/2 by 1 1/2 you get 2 1/4. 81 divided by 2 1/4 is 36. You’re welcome sorry if I’m late!

(a) The product of two rational numbers, the quotient of a rational number and a non-zero rational number, 3x + 2y and 3x² + 2y are all rational numbers.

b) The quotient of a rational number and a non-zero rational number is a rational number.

c) If x and y are rational numbers, then 3x + 2y is also a rational number.

d) If x and y are rational numbers, then 3x² + 2y is also a rational number.

(a) Statement: The product of two rational numbers is a rational number.

Proof:

Let x and y be rational numbers, where x = a/b and y = c/d, where a, b, c, and d are integers and b, d are non-zero.

The product of x and y is given by xy = (a/b) * (c/d) = (ac)/(bd).

Since ac and bd are both integers (as the product of integers is an integer) and bd is non-zero (as the product of non-zero numbers is non-zero), xy = (ac)/(bd) is a rational number.

Therefore, the product of two rational numbers is a rational number.

(b) Statement: The quotient of a rational number and a non-zero rational number is a rational number.

Proof:

Let x be a rational number and y be a non-zero rational number, where x = a/b and y = c/d, where a, b, c, and d are integers and b, d are non-zero.

The quotient of x and y is given by x/y = (a/b) / (c/d) = (a/b) * (d/c) = (ad)/(bc).

Since ad and bc are both integers (as the product of integers is an integer) and bc is non-zero (as the product of non-zero numbers is non-zero), x/y = (ad)/(bc) is a rational number.

Therefore, the quotient of a rational number and a non-zero rational number is a rational number.

(c) Statement: If x and y are rational numbers, then 3x + 2y is also a rational number.

Proof:

Let x and y be rational numbers, where x = a/b and y = c/d, where a, b, c, and d are integers and b, d are non-zero.

The expression 3x + 2y can be written as 3(a/b) + 2(c/d) = (3a/b) + (2c/d) = (3ad + 2bc)/(b*d).

Since 3ad + 2bc and bd are both integers (as the sum and product of integers is an integer) and bd is non-zero (as the product of non-zero numbers is non-zero), (3ad + 2bc)/(b*d) is a rational number.

Therefore, if x and y are rational numbers, then 3x + 2y is also a rational number.

(d) Statement: If x and y are rational numbers, then 3x² + 2y is also a rational number.

Proof:

Let x and y be rational numbers, where x = a/b and y = c/d, where a, b, c, and d are integers and b, d are non-zero.

The expression 3x² + 2y can be written as 3(a/b)² + 2(c/d) = (3a²/b²) + (2c/d) = (3a²d + 2b²c)/(b²d).

Since 3a²d + 2b²c and b²d are both integers (as the sum and product of integers is an integer) and b²d is non-zero (as the product of non-zero numbers is non-zero), (3a²d + 2b²c)/(b²d) is a rational number.

Therefore, if x and y are rational numbers, then 3x² + 2y is also a rational number.

Therefore, the product of two rational numbers, the quotient of a rational number and a non-zero rational number, 3x + 2y (where x and y are rational numbers), and 3x² + 2y (where x and y are rational numbers) are all rational numbers.

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Answer:

Umm this is like 2 grade stuff? Ummm well difference means to subtract soo just use a calutour the answer is 1.69

Step-by-step explanation:

Danielle earned $951.25

Step-by-step explanation:

Multiply her commission by her sales and add her base rate

x=7.25%($4500)+625 or x=0.0725(4500)+625

distribute

x=326.25+625

simplify

x=951.25

Answer:

The pizza parlors cost the same when delivering 4 pizzas.

Step-by-step explanation:

For each store, the total price is

cost of pizzas + cost of delivery

The cost of delivery is just a fixed number for each store, $20 or $12.

The cost of the pizzas is the price of a pizza multiplied by the number of pizzas.

Let x = number of pizzas

The cost of the pizzas is

Jacob's: 10x

Ashley's: 12x

Jacob's total cost (pizzas + delivery):

10x + 20

Ashley's total cost (pizzas + delivery):

12x + 12

We want the total costs to be the same, so we set our two total cost expressions equal and solve for x.

12x + 12 = 10x + 20

Subtract 10 from both sides.

2x + 12 = 20

Subtract 12 from both sides.

2x = 8

Divide both sides by 2.

x = 4

Answer: The pizza parlors cost the same when delivering 4 pizzas.

The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

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Answer:

-3

Step-by-step explanation:

6x - 4 = -22 6x = -18 x = -3

Answer:

x=-3

Step-by-step explanation:

the given system of differential equations is: provide:

\(x = (6/4) * e^{(2t)} + C * e^{(5t)}\)

To solve the given system of differential equations by systematic elimination, we'll eliminate one variable at a time until we obtain a single equation in one variable.

The given system of differential equations is:

(1) \(2(dx/dt) - 6x + (dy/dt) = e^t\)

(2)\((dx/dt) - x + (dy/dt) = 7e^t\)

To eliminate dx/dt from the equations, we'll subtract equation (2) from equation (1):

\(2(dx/dt) - (dx/dt) - 6x + x + (dy/dt) - (dy/dt) = e^t - 7e^t\)

Simplifying, we have:

\((dx/dt) - 5x = -6e^t\)

Now, we have a single equation in one variable (x):

\((dx/dt) - 5x = -6e^t\)

To solve this linear first-order ordinary differential equation, we'll use an integrating factor. Let's denote the integrating factor as μ(t):

μ(t) = \(e^{\int ( -5dt)} = e^{(-5t)}\\\)

Multiplying the entire equation by μ(t), we have:

\(e^{(-5t)} * (dx/dt) - 5e^{(-5t)} * x = -6e^{(-5t)} * e^t\)

Applying the product rule, we can rewrite the left side of the equation as:

\((d/dt)[e^{(-5t)} * x] = -6e^{(-4t)}\)

Integrating both sides with respect to t, we obtain:

\(e^{(-5t)} * x = 6/4 * e^{(-4t)} + C\)

where C is the constant of integration.

Finally, solving for x, we have:

\(x = (6/4) * e^{(t)} * e^t + C * e^{(5t)}\)

Therefore, the solution to the given system of differential equations is:

\(x = (6/4) * e^{(2t)} + C * e^{(5t)}\)

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Answer:

Ricardo spends $14 on the backpack and $11 o the binder.

Step-by-step explanation:

First, you have to calculate 56% of the amount Ricardo has to spend on school supplies to find the money he spends on the backpack:

$25*56%=$14

Now, you have to subtract 56% from 100% to find the percentage that he spent on a large binder:

100%-56%=44%

Finally, you have to calculate the 44% of the amount Ricardo has to spend on school supplies to find the money he spends on a large binder:

$25*44%=11

According to this, the answer is that Ricardo spends $14 on the backpack and $11 o the binder.

Answer:

$6.39/3=x

x=2.13

Each sister will earn 2 dollars and 13 cents.

Step-by-step explanation:

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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