2 cos^2 x - 3 cos x +1 =0

Answer:  62 ft

Step-by-step explanation:

The scale shows that for every 1/4 inches on the paper, the distance of the actual house is 1 ft.

If the floor plan lists the length as 15 ¹/₂ inches therefore, the length in inches feet is:

= 15 ¹/₂ ÷ 1/4

= 31/2 ÷ 1/4

= 31/2 * 4/1

= 62 ft

When dividing by a fraction, you can multiply its inverse.

mhorn seems to be correct

Step-by-step explanation:

yshahaa

Before graphing a given rational function, it is occasionally necessary to simplify it. If, other than at asymptotes, there are any excluded values then graphing the function requires an additional step.

The function y=f(x), where f(x) is a rational expression, is the formula for a rational function.

Drawing the graphs of the rational functions might be challenging. Finding the asymptotes and intercepts is a good place to start when attempting to sketch a graph of a rational function.

The steps in graphing rational functions are as follows:

Find the rational function's asymptotes, if any exist.

Create dotted lines for the asymptotes.

Find the rational function's x-intercept (s) and y-intercept, if any.

For various x values, determine the values of y.

Plot the spots and then create a straight line to connect them and check to see if the graph crosses the vertical asymptotes.

Make sure the function is not a continuous smooth curve at the excluded value if you want to portray an undefined function. Typically referred to as the "hole in the rational function," this excluded value

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Answer:

7.4 mins

Step-by-step explanation:

135 -----> 1 min

1000 ----> x

1000/135 mins = x

= 7.4 mins

Answer:

To determine how long it will take to fill 1000 containers at a rate of 135 containers per minute, you can use the formula: time = number of containers / filling rate. In this case, the filling rate is 135 containers per minute, and the number of containers you want to fill is 1000. Plugging these values into the formula, we get: time = 1000 / 135 = 7.41 minutes.

The surface area of the triangular prism is 152 sq, ft.

A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.

The surface area of the triangular prism is given as:

SA = bh + (b1 + b2 + b3)l

Here, b = 6, h = 4, b1 = b2 = 5, b3 = 6 and l = 8.

Substituting the values we have:

SA = (6)(4) + (5 + 5 + 6) (8)

SA = 24 + (16)(8)

SA = 152 sq. ft.

Hence, the surface area of the triangular prism is 152 sq, ft.

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Answer:

-5x - 24

Step-by-step explanation:

3(2x − 8) – 11x =

Distribute the 3.

= 6x - 24 - 11x

Combine like terms.

= -5x - 24

Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

The account will have a balance of $820 after approximately 72 years. Hence, the correct answer is H. 72 years.

The equation \(\[A(x) = 500e^{0.015x}\]\) represents the balance in the account after x years, where e is the base of the natural logarithm and approximately equal to 2.71828.

To obtain how many years the account will have a balance of $820, we can set up the equation:
\(\(820 = 500e^{0.015x}\)\)
To solve for x, we need to isolate the exponential term. Divide both sides of the equation by 500:

\(\[ e^{0.015x} = \frac{820}{500} = 1.64 \]\)

Now, take the natural logarithm (ln) of both sides to remove the exponent:
\(\[ 0.015x = \ln(1.64) \]\)

Dividing both sides by 0.015:

\(\[ x = \frac{\ln(1.64)}{0.015} \approx 72.24 \]\)

Therefore, it will take approximately 72 years for the account to have a balance of $820. Therefore, the correct answer is option H: 72 years.

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The most appropriate technique for the researcher to make this prediction would be multiple regression analysis, which would allow her to examine the relationship between the two predictor variables (high school grade-point averages and SAT scores) and the outcome variable (first semester college grade-point averages) while controlling for their effects on each other. This technique would help the researcher to determine the most accurate way to combine these two predictors in order to make the most accurate prediction possible.

A researcher aiming to predict first semester college grade-point averages (GPAs) using high school GPAs and SAT scores as predictor variables should use the Multiple Linear Regression technique. This technique allows the researcher to analyze the relationship between multiple predictor variables (high school GPAs and SAT scores) and a single continuous outcome variable (college GPAs), which can lead to more accurate predictions.

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The spacecraft takes approximately 199.43 days to travel from Earth to Mars.

To calculate the number of days the spacecraft takes to travel from Earth to Mars, we need to first convert the given distance from miles to kilometers, and then find the time it takes by dividing the distance by the average speed.

Given:
Distance = 1.4 × 10^8 miles
Average speed = 13 km/s

Step 1: Convert distance from miles to kilometers:
1 mile = 1.6 km
1.4 × 10^8 miles × 1.6 km/mile = 2.24 × 10^8 km

Step 2: Convert average speed from km/s to miles per hour:
13 km/s × 2250 miles/hour per km/s = 29,250 miles/hour

Step 3: Convert average speed from miles per hour to km per hour:
1 mile = 1.6 km
29,250 miles/hour × 1.6 km/mile = 46,800 km/hour

Step 4: Calculate the time it takes to travel the distance:
Time = Distance ÷ Speed
Time = (2.24 × 10^8 km) ÷ (46,800 km/hour) = 4,786.32 hours

Step 5: Convert time from hours to days:
1 day = 24 hours
4,786.32 hours ÷ 24 hours/day = 199.43 days

The spacecraft takes approximately 199.43 days to travel from Earth to Mars.

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Answer:

\(17.2 {m}^{2} \)

Step-by-step explanation:

\((m + m)(8.6m) = (2m)(8.6m) = (2 \times 8.6) {m}^{2} = 17.2 {m}^{2} \)

Answer:

hold up this will take a min to work out

Step-by-step explanation:

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?

Answer:

84.82275

Step-by-step explanation:

The formula for Area of a circle is

\(A=\pi r^{2} \\A=\pi 6^{2} \\A=113.097\)

That would be for the entire circle, now divide that number by .75 to get 3/4 of the circle.

84.82275

Answer:

3. alternative interior angle

4. consecutive exterior angle

5. corresponding angle

6. consecutive interior angle

7. corresponding angle

8. alternative exterior angle

Step-by-step explanation:

since the braindead jacka** above was no help

The Answer would be 18

Answer:

f(-3) = -360

Step-by-step explanation:

f(x) = 2x^3 + 4x^2 = f(-3)

x = -3

(2 * -3)^3 + (4 * -3)^2

2 * -3 = -6

-6^3 = -6 * -6 * -6 = -216

4 * -3 = -12

-12^2 = -12 * -12 = -144

-216 + (-144) = -360

1/64 fraction is equal to 0.015625 in decimal form.

To change the fraction 1/64 to a decimal, we need to perform division.

1 divided by 64 can be written as:

0.015625

----------

64 | 1.000000

   0

  10

   0

The result of the division is 0.015625. This means that 1/64 is equal to 0.015625 in decimal form.

Note that in this case, we carried the division out to six decimal places, but the question specified that we should carry it out to three decimal places. In that case, we would round the answer to 0.016.

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Answer:

It decreases by 5 each time. -5 would be another way to state it

Step-by-step explanation:

Answer:

d = - 5

Step-by-step explanation:

The common difference d is the difference between consecutive terms, so

d = a₂ - a₁ = 40 - 45 = = 5

Answer:

104°

Step-by-step explanation:

Angles in a triangle add up to 180.

so 180-51-25=104

Hope this helps!:)

Answer: 104°

Step-by-step explanation:

In a triangle, the total or the interior angles will always be 180°

51° + 25° = 76°

180° - 76° = 104°

Therefore, the answer is 104°

I hope this helps!

Step-by-step explanation:

move the parent function to the right 2 times.

Answer:

see image

Step-by-step explanation:

An absolute value graph is a V-shaped graph(in yellow, see image) You can use "transformations of parent functions" to graph it (high school/college) OR use a table of values (middleschool/hs). The - 2 that's in the parenthesis with the x causes the graph to slide to the RIGHT 2 units. (shown in green) The green graph is what you are asking for.

If you aren't learning about translations (which means shift or slide and is a type of transformation) then you can just make a table of values. Pick several x's and put them in the equation and find out what y's go with them. Plot the points on the graph and connect. See image.

Answer:

7

Step-by-step explanation:

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Answer:

I am sorry I want points

Step-by-step explanation:

thanks for your help

To integrate the function f(x) = (\(x^3\) - 2\(x^2\) + 2x + 1) / (\(x^2\) - 2x + 1), we can divide the numerator by the denominator using polynomial long division. The final answer to the integral is ∫ f(x) dx = (1/2)\(x^2\)+ x + C.

Let's start by performing polynomial long division to divide the numerator (\(x^3\) - 2\(x^2\) + 2x + 1) by the denominator (\(x^2\) - 2x + 1). The division yields x + 1 as the quotient and a remainder of 0. Therefore, we can rewrite the original function as f(x) = x + 1.

Now, we can integrate f(x) = x + 1 term by term. The integral of x with respect to x is (1/2)\(x^2\), and the integral of 1 with respect to x is x. Therefore, the integral of f(x) is given by:

∫ f(x) dx = ∫ (x + 1) dx = (1/2)x^2 + x + C,

where C is the constant of integration.

So, the final answer to the integral of f(x) = (\(x^3\) - 2\(x^2\) + 2x + 1) / (\(x^2\) - 2x + 1) is:

∫ f(x) dx = (1/2)\(x^2\) + x + C.

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To find (dw/dy)x and (dw/dy)z at the point (w, x, y, z) if w=x^2y^2 yz-z^3 and x^2 y^2 z^2=12, we will start by finding the partial derivatives. We will use the chain rule of differentiation to calculate the partial derivative of w with respect to y, holding x and z constant.

We will also use the chain rule of differentiation to calculate the partial derivative of w with respect to z, holding x and y constant. We will find the partial derivatives at the point (w, x, y, z) using the given equations.Using the product rule of differentiation, we can find that;dw/dy = 2xy²yz + x²y²z.  (eqn 1)And, using the product rule of differentiation again, we can find that;dw/dz = y²z² - 3z².   (eqn 2)Using the equation, x² y² z² = 12, we can substitute for z² in eqn 2 to get;dw/dz = y²(12/(x²y²))-3(12/(x²y²)).          (eqn 3)

Using the equation, w = x²y² yz-z³, we can substitute for z³ as (xyz)²/3. Hence, w = x²y² yz - (xyz)²/3. Since x²y² z² = 12, y = (12/(x²z²))^(1/2).We can now substitute these values into eqn 1 to obtain;(dw/dy)x = 2xy²z(12/(x²z²)^(1/2)) + x²y²z.(12/(x²z²)^(1/2))Dividing through by y gives;(dw/dy)x = 2xz(12/(x²z²))^(1/2) + 12/x^(3/2)z^(1/2).Hence, (dw/dy)x = 2√3 + 2√3 = 4√3.The value of (dw/dy)x is 4√3. Similarly, substituting for y and z in eqn 4 gives;(dw/dz) = (12/4) - (36/48) = 3 - (3/4) = 9/4.The value of (dw/dy)z is 9/4.Answers: (dw/dy)x = 4√3 and (dw/dy)z = 9/4.

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Answer:

x=5, y=41

Step-by-step explanation:

Because both equations are equal to Y, you can set them equal to each other like this:

8x+1=3x+26

From here, solve for x:

1. 5x+1=26

2. 5x=25

3. x=5

Once you have x, plug it back in to one of the original equations:

y=8(5)+1

y=41 and then you have your answer

If this answer was particularly helpful, please feel free to give it brainliest!! I would greatly appreciate it.

Answer:

(x, y) = (5, 41)

Step-by-step explanation:

y = 8x + 1

y = 3x + 26

Substituting the value of y (first equation) into the second equation, we get:

8x + 1 = 3x + 26

5x = 25

x = 5.

So, to get y, all we have to do is to substitute the value of x into the second equation.

y = 3 * 5 + 26

y = 15 + 26

y = 41