In the right-angled triangle ABC, cos C = 4/5 and BC = 16 cm, find the following:

i) AC
ii) AB​

Answer:

the radius

Step-by-step explanation:

Answer:

radius

Step-by-step explanation:

Answer:

Yup!

Step-by-step explanation:

I can confirm these answers are all correct!

Answer:

The answer is B

Step-by-step explanation:

Since -2/3 multiplied by 3 equals -2, all you need to do is -2+1 which equals -1 which is the same number y is supposed to be.  

Hope this helps

Answer:

The answer is B.

Step-by-step explanation:

You have to substitute x values into the equation to see if it matches y values in the table :

\(y = - \frac{2}{3}x + 1\)

\(sub \: \: x = 3\)

\(y = - \frac{2}{3} (3) + 1 = - 1\)

\(sub \: \: x = 6\)

\(y = - \frac{2}{3} (6) + 1 = - 3\)

\(sub \: \: x = 9\)

\(y = - \frac{2}{3} (9) + 1 = - 5\)

Answer:

The area is 112.

Step-by-step explanation:

14 x 16 = 224

224/2 = 112

Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

Answer:

Every number in decimal form, in which either decimals terminate or certain numbers after decimal point continue to repeat endlessly, can be written as a fraction. As the given number 4.5 terminates after first deciimal it can be written as fraction. Here we have 4.5=4510=92 a fraction.

Step-by-step explanation:

hope i could help

Answer:

−5 ⋅ 2 − 12

Step-by-step explanation:

Answer:

C 2b3 + b2 - 2b - 380

Step-by-step explanation:

Given:

Factory A: 2b^3 – 3b^2 + b - 120

Factory B: 4b^2 – 3b – 260

The company's total output = factory A + factory B

= (2b^3 – 3b^2 + b - 120) + (4b^2 – 3b – 260)

= 2b^3 – 3b^2 + b - 120 + 4b^2 – 3b – 260

Collect like terms

= 2b^3 – 3b^2 + 4b^2 – 3b + b - 120 - 260

= 2b^3 + b^2 - 2b - 380

C. 2b^3 + b^2 - 2b - 380

Option C is the correct answer

Answer: C) 2b^3+b^2-2b-380

Step-by-step explanation:

I had this question on a recent test and got it right

Hope this helps! :)

Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

\(a=\pi r^{2}\)

\(a=\pi (19)^{2} =361\pi\)

\(a=1134.11cm^{2}\)

Hope this helps

Answer:

Shift 4 units down: \(g(x) = 2x - 10\)

Stretching f(x) by 4 : \(g(x) =8x - 24\)

Shift 4 units left:  \(g(x) = 2x - 14\)

Compress by 1/4 units : \(g(x) = 8x - 6\)

Step-by-step explanation:

Given

\(f(x) = 2x - 6\)

Required

Match the transformations (See attachment)

Shift 4 units down

Shifting down a function is represented as:

\(g(x) = f(x) - b\)

In this case:

\(b = 4\)

Substitute expression for f(x) and 4 for b in \(g(x) = f(x) - b\)

\(g(x) = 2x - 6 - 4\)

\(g(x) = 2x - 10\)

Stretching f(x) by 4

Stretching a function by some units is represented as:

\(g(x) =b.f(x)\)

In this case:

\(b = 4\)

Substitute expression for f(x) and 4 for b in \(g(x) =b.f(x)\)

\(g(x) =4 * (2x - 6)\)

\(g(x) =8x - 24\)

Shift 4 units left

Shifting a function to the left is represented as:

\(g(x) = f(x - b)\)

In this case:

\(b = 4\)

Substitute expression for f(x) and 4 for b in \(g(x) = f(x - b)\)

\(g(x) = f(x-4)\)

Calculating f(x - 4)

\(f(x) = 2x - 6\)

\(f(x - 4) = 2(x - 4) - 6\)

\(f(x - 4) = 2x - 8 - 6\)

\(f(x - 4) = 2x - 14\)

Hence:

\(g(x) = 2x - 14\)

Compress by 1/4 units

This means that the function is stretched by \(1/\frac{1}{4}\)

Compressing a function is represented as:

\(g(x) =f(bx)\)

In this case:

\(b = 1/\frac{1}{4}\)

\(b = 1 * \frac{4}{1}\)

\(b = 4\)

Substitute expression for f(x) and 4 for b in \(g(x) =f(bx)\)

\(g(x) =f(4x)\)

Calculating f(4x)

\(f(4x) = 2(4x) - 6\)

\(f(4x) = 8x - 6\)

Hence:

\(g(x) = 8x - 6\)

Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

Answer:

D. t < -4 or t > 5

Step-by-step explanation:

Inequality 1

Inequality 2

⇒ t < -4 or t > 5

⇒ Option D

Graph

Answer:

\(\sf D. \quad t < -4, t > 5\)

Step-by-step explanation:

Given system of inequalities:

\(\begin{cases}5t-1 < -21\\4t+2 > 22\end{cases}\)

Solve the inequalities by isolating t.

Inequality 1

\(\sf \implies 5t-1 < -21\)

\(\implies \sf 5t-1+1 < -21+1\)

\(\sf \implies 5t < -20\)

\(\sf \implies 5t \div 5 < -20 \div 5\)

\(\sf \implies t < -4\)

Inequality 2

\(\sf \implies 4t+2 > 22\)

\(\sf \implies 4t+2-2 > 22-2\)

\(\sf \implies 4t > 20\)

\(\sf \implies 4t \div 4 > 20 \div 4\)

\(\sf \implies t > 5\)

Therefore, the solution to the system of inequities is:

\(\sf t < -4, t > 5\)

When graphing inequalities:

Therefore, to graph the given system of inequalities:

(Refer to attachment for the graph).

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Answer:

The function g(x) has a greater x- intercept than the function f(x)

Step-by-step explanation:

Answer: Area of Cylinder = 753.982

Step-by-step explanation:

Given:

h = 7 cm

r = 8cm

Formula for cylinder:

A = (Perimeter of base) x height + 2 (Area of Base)

Breakdown:

Perimeter of base = 2\(\pi r\)

Perimeter of base = 2 \(\pi\) (8)

Perimeter of base = 50.2655

Area of Base = \(\pi r^{2}\)

Area of Base = \(\pi 8^{2}\)

Area of Base = 201.0619

Area of Cylinder = (Perimeter of base) x height + 2 (Area of Base)

Area of Cylinder = (50.2655)(7) +2(201.0619)

Area of Cylinder = 753.982

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

C and E

Step-by-step explanation:

The change in elevation was 44 + 20 = 64 m

the rate of fall was 64 m / 32 s = 2 m/s

The anchor reached the surface in 44 / 2 = 22 s so C is valid

E is correct as the ocean surface is origin and Up is the positive direction.

The anchor starts at 44 m above the surface and position is lower by 2 meters every second

From the question, the two correct options about the speed with which the anchor was released are:

First we have to calculate the change that occurred in the elevation. Initially it was 44 meters but dropped 20 m below water.

44 + 20 = 64 meters

Next we calculate the rate with which the fall occurred

The time with which it fell was 32 seconds. = 64/32 = 2 meters pers second

44/2 = 22 hence it can be concluded that C is right.

Option E is also correct given that the water surface is above the ground and it is positive

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Answer:

Step-by-step explanation:

To solve this equation, use the distributive property. Isolate the difference between the numbers from one side of the equation.

Distributive property:

A(B+C)=AB+AC

-1.9 = 0.5(p +1.7)

First, switch sides.

0.5(p+1.7)=-1.9

Divide by 0.5 from both sides.

\(\sf{\dfrac{0.5\left(p+1.7\right)}{0.5}=\dfrac{-1.9}{0.5}}\)

Solve.

-1.9/0.5=-3.8

p+1.7=-3.8

Then, you subtract by 1.7 from both sides.

p+1.7-1.7=-3.8-1.7

Solve.

Add or subtract the numbers from left to right.

-3.8-1.7=-5.5

\(\rightarrow \boxed{\sf{p=-5.5}}\)

Therefore, the correct answer is p=-5.5.

I hope this helps, let me know if you have any questions.

The value of p on the equation - 1.9 = 0.5(p +1.7) is - 5.5.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, we have to solve for p in the equation - 1.9 = 0.5(p +1.7).

0.5(p + 1.7) = - 1.9

First, we'll distribute the terms.

0.5p + 0.85 = - 1.9.

0.5p = - 1.9 - 0.85.

0.5p = - 2.75.

p = - 2.75/0.5.

p = - 5.5

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Answer:

$128.10

Step-by-step explanation:

(8 * 16.95) - 7.50

(135.6) - 7.50

128.1

Therefore, your answer would be $128.10

$128.10 is the answer

Answer:

im not smart

Step-by-step explanation:

Part A: The function is nonlinear.

Part B: We determined the function to be nonlinear because the corresponding y-values do not change by a constant rate as the x-values increase, indicating a lack of a linear relationship.

Part A: The given function is nonlinear.

Part B: To determine whether the function is linear or nonlinear, we need to examine the relationship between the x-values and the corresponding y-values in the table.

In a linear function, there is a constant rate of change between the x and y values.

This means that for every increase in x by a fixed amount, the corresponding y value will change by a constant amount.

If we look at the x-values in the given table (2, 3, 4), we can see that they are increasing by a fixed amount of 1 each time.

However, when we examine the corresponding y-values (20, 10, 40), we don't see a constant rate of change.

The y-values are not changing by the same amount for each increase in x.

For instance, when x increases from 2 to 3, the y-value decreases from 20 to 10.

This indicates a non-linear relationship as the change in y is not constant for each unit increase in x.

Additionally, when x increases from 3 to 4, the y-value jumps significantly from 10 to 40, which further confirms the nonlinear nature of the function.

Based on these observations, we can conclude that the given function is nonlinear.

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Answer:

5x^2 + x + 7.

Step-by-step explanation:

6x^2 + 7 + x - x^2

= (6x^2 - x^2) + (x + 7) // Rearranging the terms

= 5x^2 + x + 7

So, 6x^2 + 7 + x - x^2 simplifies to 5x^2 + x + 7.

The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The measure of the frame is 8.5 inches and 11 inches

a) if the frame is 4 papers long then we  have the length of the frame as

11×4=44 inches (since he lays the paper along the edge of frame)

We know 1 inch= 0.0833 foot

Thus      44 inches= 3.66667 foot

b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches

∴25.5 inches= 2.125 feet

Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

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Answer:

AC = 13.3

Make proportional relationship:

\(\dfrac{\text{AB}}{\text{AC}} =\dfrac{\text{AM}}{\text{AN}}\)

Insert values

\(\rightarrow\dfrac{10}{\text{AC}} =\dfrac{6}{8}\)

Cross multiply

\(\rightarrow \text{AC}=\dfrac{10(8)}{6}\)

Simplify

\(\rightarrow \text{AC}=13.3\)

The inverse function:  \(f^{-1} (x) =\) \((\frac{x -5}{5} )^{2} -13\)

The inverse is defined on the domain x < 5 and x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5.

A function is a relationship that exists between two sets of numbers, with each input from the first set, known as the domain, corresponding to only one output from the second set, known as the range.

Given function is;   \(f(x) = 5\sqrt{(x + 13)} + 5\)

To find the inverse of the given function, we first replace f(x) with y:

⇒  \(y = 5\sqrt{(x + 13)} + 5\)

Subtract 5 from both sides:

⇒ \(y -5 = 5\sqrt{(x + 13)}\)

⇒ \(\frac{(y -5)}{5} = \sqrt{(x + 13)}\)

⇒ \((\frac{y -5}{5} )^{2} = x + 13\)

⇒ \((\frac{y -5}{5} )^{2} -13 = x\)

Now we have x in terms of y, so we can replace x with f⁻¹(x) and y with x to get the inverse function:

f⁻¹(x) = \((\frac{x -5}{5} )^{2} -13\)

The domain of the inverse function is x ≥ 5, because this is the range of the original function, and we were given that the inverse is defined on the domain x < 5. However, we must also exclude the value x = 5, because the denominator of the fraction \((\frac{x -5}{5} )^{2}\) becomes zero at this value. Therefore, the domain of f⁻¹(x) is x > 5.

We were given that x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5. Therefore, the domain of the inverse function becomes the range of the original function, and the range of the inverse function becomes the domain of the original function.

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9514 1404 393

Answer:

  B.  470 miles

Step-by-step explanation:

Using numbers rounded to the nearest 10, the remaining distance is ...

  1270 -420 -380 = 470 . . . . miles

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

7b+5w=$225

I think so.

C

The answer to the question is C

Answer:

D is the answer cuz 2x-1=5

2x=5-1

2x=4

X=2

We divide both side by two

To determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle, we can compare the given information with the formulas for each law.

The Law of Sines states:

a / sin(A) = b / sin(B) = c / sin(C)

The Law of Cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are given the lengths of all three sides of the triangle (a = 6.0, b = 7.7, c = 13.6). Therefore, we have enough information to use the Law of Cosines to solve the triangle.

Using the Law of Cosines, we can find the measures of the angles:

c^2 = a^2 + b^2 - 2ab * cos(C)

(13.6)^2 = (6.0)^2 + (7.7)^2 - 2 * 6.0 * 7.7 * cos(C)

184.96 = 36 + 59.29 - 92.4 * cos(C)

184.96 = 95.29 - 92.4 * cos(C)

92.67 = -92.4 * cos(C)

cos(C) ≈ -1

Since the cosine of an angle cannot be greater than 1 or less than -1, it is not possible for the given triangle to have an angle with a cosine of -1. Therefore, the triangle is not solvable with the given side lengths.

In this case, the Law of Cosines is needed, but the triangle cannot be solved with the given information.