Which verbal description best matches the equation 876 space equals space 35 x space plus space 421 ?
A.The mechanic’s bill to repair Mr. Pascua’s car was $876. The mechanic charges $421 an hour for labor, and the parts cost $35. How many hours did the mechanic work on the car?
B.The mechanic’s bill to repair Mr. Pascua’s car was $421. The mechanic charges $35 an hour for labor, and the parts cost $876. How many hours did the mechanic work on the car?
C.The mechanic’s bill to repair Mr. Pascua’s car was $421. The mechanic charges $876 an hour for labor, and the parts cost $35. How many hours did the mechanic work on the car?
D.The mechanic’s bill to repair Mr. Pascua’s car was $876. The mechanic charges $35 an hour for labor, and the parts cost $421. How many hours did the mechanic work on the car?

Answer:

sin(a + b) = sinacosb + cosasinb;

tana = 20/21, then cosa = - 1/√1 + (20/21)2 = - 21/29, sina = tanacosa = 20/21·(- 21/29) = - 20/29;

sinb = √1 - (- 4/5)2 = 3/5

sin(a + b) = - 20/29·(-4/5) + (- 21/29)·3/5 = 80/145 - 63/145 = 17/145

Equation of the line

The equation of a line in slope-intercept form is:

y = mx + b

Where m is the slope and b is the y-intercept.

We are required to find the equation of a line that is perpendicular to the line

y = 5x + 4

and passes through the point (-5,2)

The first thing we need to do is to calculate the slope of the required line.

The slope of the given line is m1=5. Two lines are perpendicular if their slopes satisfy the equation:

m1 * m2 = -1

Solving for m2:

The equation of the required line is:

To find the value of b, we substitute the given point (-5,2):

Operating:

Solving for b:

b = 1

Finally, our equation is:

Answer:

PROBABILITY=42/80

=7/20

Answer:

13 tickets

Step-by-step explanation:

Answer:

33 is the answer

Step-by-step explanation:

Answer:

x = 36 km

Step-by-step explanation:

The triangle is a right triangle. To find x, apply Pythagorean theorem which is given as: c² = a² + b²

c = hypotenuse/longest leg = 45 km

a = x

b = 27

Thus:

45² = x² + 27²

2,025 = x² + 729

2,025 - 729 = x²

1,296 = x²

√1,296 = x

36 = x

x = 36 km

The recursive formula of the geometric sequence is given by option D; an = (1) × (5)^(n - 1) for n ≥ 1

Given: 1, 5, 25, 125, 625, ...

= 5

an = a × r^(n - 1)

= 1 × 5^(n - 1)

an = (1) × (5)^(n - 1) for n ≥ 1

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Answer:

I HAVE THE SAME THING

Step-by-step explanation:

Answer:

637.50

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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The solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

(a - b) / (a + b) = 3/5

To solve for a in terms of b, we cross multiply:

5(a - b) = 3(a + b)

Expanding the brackets, we get:

5a - 5b = 3a + 3b

Simplifying the equation by combining like terms, we get:

5a - 3a = 8b

2a = 8b

Dividing both sides of the equation by 2, we get:

a = 4b

Therefore, the solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

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The complete question is:

The equation given is A = 4b. Please write an appropriate question related to this equation.

Answer:

0.564

Step-by-step explanation:

brainliest pls

The surface area of the composite figure is 858 cm².

To find the surface area of a composite figure, we need to break it down into its individual components and then calculate the surface area of each component separately before summing them up.

From the given dimensions, it appears that the composite figure consists of three rectangular prisms. Let's calculate the surface area of each prism and then add them together.

First Prism:

Length = 3 cm

Width = 5 cm

Height = 5 cm

The surface area of the first prism is calculated using the formula: 2lw + 2lh + 2wh. Substituting the values, we get:

2(3)(5) + 2(3)(5) + 2(5)(5) = 30 + 30 + 50 = 110 cm².

Second Prism:

Length = 8 cm

Width = 12 cm

Height = 8 cm

Using the same formula, the surface area of the second prism is:

2(8)(12) + 2(8)(8) + 2(12)(8) = 192 + 128 + 192 = 512 cm².

Third Prism:

Length = 5 cm

Width = 8 cm

Height = 6 cm

Again, applying the surface area formula, the surface area of the third prism is:

2(5)(8) + 2(5)(6) + 2(8)(6) = 80 + 60 + 96 = 236 cm².

Finally, we sum up the surface areas of all three prisms:

110 cm² + 512 cm² + 236 cm² = 858 cm².

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Answer:

94

Step-by-step explanation:

(264+3*6)/3 = e

PEMDAS, so multiplication first.

3*6 = 18

= (264 + 18)/3

= 282/3

= 94

The sum of 18.420 and 28.49, rounded to the correct number of significant figures, is 46.91.

To add the numbers 18.420 and 28.49, we align the decimal points and perform the addition. After adding the numbers, we obtain a sum of 46.910. However, we need to round the answer to the correct number of significant figures.

The rule for determining the number of significant figures in addition is to retain the same number of decimal places as the number with the fewest decimal places being added. In this case, 18.420 has three decimal places, while 28.49 has two decimal places. Therefore, we round the sum to two decimal places: 46.910 rounded to two decimal places is 46.91.

Thus, the sum of 18.420 and 28.49, rounded to the correct number of significant figures, is 46.91.

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The function f(x) = 8 cos(pi x)/sqrt(x) and the series sigma^infinity_n=1 (8 cos(pi n)/sqrt(n)), the correct conclusion is:
The integral test can be used to determine whether the series is convergent since the function is positive and decreasing on (1, infinity).

This is because the function f(x) is positive for x > 0, as cosine has a maximum value of 1 and the square root of x is always positive for x > 0.

Additionally, the function is decreasing on (1, infinity) because the denominator, sqrt(x), increases as x increases, which causes the overall function value to decrease.

Therefore, the integral test can be applied to determine the convergence of the series.

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(-2, -4) and (2, 4) is the solution to the given system of simultaneous equation

Given the system of equation

f(x) = x^2 + 2x - 4

g(x) = -2x^2 + 2x + 8

When solving graphically, the point of intersection of both curves on an xy plane is the solution to the system of equation.

According to the graph attached, the solution to the system of equation is (-2, -4) and (2, 4).

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Answer: B

Step-by-step explanation: I took the test

Answer:

Quadrant III

Step-by-step explanation:

Because both numbers are negative, the point lands in Quadrant III.

If William spends a winter day recording the temperature once every three hours for science class. If  the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F

Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:

Temperature at noon  = -12.2 + 16.2

Temperature at noon  = 3.0°F

Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:

Temperature at 3pm = 3.0 - 9.1

Temperature at 3pm = -6.1°F

Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:

Temperature at 6pm =-6.1 - 5

Temperature at 6pm = -11.1°F

Therefore the temperature at 6pm is  -11.1°F.

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Answer:

Bonjour is the bonjour of qui

Step-by-step explanation:

Points points

The standard deviation of x is 1/√18

Given, f(x) = { 2x if 0 < x < 1

                    { 0 otherwise

The variance of X is given by : Var[X] = E[X²] - (E[X])²

E[X] = ∫₀¹ x f(x) dx

= ∫₀¹ 2x² dx

= 2[x³/3]₀¹

= 2[1/3 - 0]

= 2/3

To find E[X²], we need to integrate x²f(x) from 0 to 1:

E[X²] = ∫₀¹ x² f(x) dx

= ∫₀¹ 2x³ dx

= 2[x⁴/4]₀¹

= 2[1/4 - 0]

= 2[1/4]

= 1/2

So, Var[X] = 1/2 - (2/3)²

= 1/2 - 4/9

= 1/18

Next, the standard deviation of "X" is the square root of variance:

Therefore, SD[X] = √(1/18) = 1/√18.

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In permutation, ³¹C₅  are there to select 5 scoops of ice cream to put into a bowl .

What are some examples of permutation?

Total ice cream flavor n = 31 flavor

selection of (r) = 5 scoop

total number of ways to select 5 scoops of ice cream from 31 flovers

                                                   = ³¹C₅

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The solution is of the form y = tr where r = 5/14 for the given differential equation.

Given differential equation:

t²y''- 10ty' + 28y = 0

Let's assume the solution is of the form y = tr. We need to find the values of r for which this form of the solution holds.Let's differentiate the solution y = tr with respect to t in order to solve for the first and second derivatives of y as follows:

y = tr.....(1)

First derivative of y w.r.t t is given by:

y' = r.....(2)

Second derivative of y w.r.t t is given by:

y'' = 0.....(3)

Substituting equations (1), (2), and (3) in the given differential equation, we get:

(t² * 0) - 10t * r + 28(tr) = 0

Simplifying, we get:

(28r - 10) * t = 0

Since t > 0, then the coefficient of t must be zero. Thus,

28r - 10 = 0

=> 28r = 10

=> r = 10/28 (reduced)

=> r = 5/14

So, the value of r is 5/14 when the given differential equation has solutions of the form y = tr for t > 0.

In summary, the solution is of the form y = tr where r = 5/14 for the given differential equation.

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Answer:

Step-by-step explanation:

3(8n - 1) - 17n

24n - 3 - 17n

   7n - 3

Start by multiplying 3 to both values in the parenthesis.

3(8n - 1) - 17n > 8n(3) - 1(3) - 17n > 24n - 3 - 17n

Next, combine like terms.

24n - 3 - 17n > 24n - 17n - 3 > 24n - 17n - 3 > 7n - 3

Because of the variable, n, you cannot simplify any further. This means your final answer is 7n - 3 :)

Answer:

c

Step-by-step explanation:

volume is the correct answer

Answer:

10 pounds

Step-by-step explanation:

given ratio weight:added weight=10:1

100:x=10:1

100/x=10/1

solving for x

100=10x

x=10