The product of a + 3 and –2a2 + 15a + 6 is –2a3 + xa2 + 51a + 18. What is the value of x?A=3
B=9
C=12
D=15

Answers

Answer 1

Answer: (A+3) x ( -2A2+15A+6) = (-2A3+XA2+51A+18)
(3+3) x ( -2*3*2+15*3+6) = (-2*3*3+X *3*2+51*3+18)
(6) x (-2*3*2=-12 + 15*3=45 +6 = 51
(6) x (-12 +51=39)
6 x 39 =( -2*3*3= -18)+ x *3*2+(51*3+18=171)
6 x 39 -18 + x*3*2+ 171
6 x 39 =234
234 -171=63
-18 + 5x=63
X = 13.5

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Benjamin & Associates, a real estate developer, recently built 198 condominiums in McCall, Idaho. The condos were either three-bedroom units or four-bedroom units. If the total number of rooms in the entire complex is 711, how many three-bedroom units are there? How many four-bedroom units are there?

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Use system of equations to solve this problem. set up x and y =198 and 3x +4y =711. solve for x and y

Please someone help me to prove this.

Answers

Answer: see proof below

Step-by-step explanation:

Use the Power Reducing Identity: sin² Ф = (1 - cos 2Ф)/2

Use the Double Angle Identity: sin 2Ф = 2 sin Ф · cos Ф

Use the following Sum to Product Identities:

$\sin x - \sin y = 2\cos \bigg((x+y)/(2)\bigg)\sin \bigg((x-y)/(2)\bigg)\n\n\n\cos x - \cos y = -2\sin \bigg((x+y)/(2)\bigg)\sin \bigg((x-y)/(2)\bigg)$

Proof LHS → RHS

$\text{LHS:}\qquad \qquad \qquad (\sin^2A-\sin^2B)/(\sin A\cos A-\sin B \cos B)$

$\text{Power Reducing:}\qquad (\bigg((1-\cos 2A)/(2)\bigg)-\bigg((1-\cos 2B)/(2)\bigg))/(\sin A \cos A-\sin B\cos B)$

$\text{Half-Angle:}\qquad \qquad (\bigg((1-\cos 2A)/(2)\bigg)-\bigg((1-\cos 2B)/(2)\bigg))/((1)/(2)\bigg(\sin 2A-\sin 2B\bigg))$

$\text{Simplify:}\qquad \qquad (1-\cos 2A-1+\cos 2B)/(\sin 2A-\sin 2B)\n\n\n.\qquad \qquad \qquad =(-\cos 2A+\cos 2B)/(\sin 2A - \sin 2B)\n\n\n.\qquad \qquad \qquad =(\cos 2B-\cos 2A)/(\sin 2A-\sin 2B)$

$\text{Sum to Product:}\qquad \qquad (-2\sin \bigg((2B+2A)/(2)\bigg)\sin \bigg((2B-2A)/(2)\bigg))/(2\cos \bigg((2A+2B)/(2)\bigg)\sin \bigg((2A-2B)/(2)\bigg))$

$\text{Simplify:}\qquad \qquad (-2\sin (A + B)\cdot \sin (-[A - B]))/(2\cos (A + B) \cdot \sin (A - B))$

$\text{Co-function:}\qquad \qquad (2\sin (A + B)\cdot \sin (A - B))/(2\cos (A + B) \cdot \sin (A - B))$

$\text{Simplify:}\qquad \qquad \quad (\cos (A+B))/(\sin (A+B))\n\n\n.\qquad \qquad \qquad \quad =\tan (A+B)$

LHS = RHS: tan (A + B) = tan (A + B) $\checkmark$

Answer:

We know that,

$\dag\bf\:sin^2A=(1-cos2A)/(2)$

$\dag\bf\:sin2A=2sinA\:cosA$

___________________________________

Now, Let's solve !

$\leadsto\:\bf(sin^2A-sin^2B)/(sinA\:cosA-sinB\:cosB)$

$\leadsto\:\sf((1-cos2A)/(2)-(1-cos2B)/(2))/((2sinA\:cosA)/(2)-(2sinB\:cosB)/(2))$

$\leadsto\:\sf(1-cos2A-1+cos2B)/(sin2A-sin2B)$

$\leadsto\:\sf(2sin(2A+2B)/(2)\:sin(2A-2B)/(2))/(2sin(2A-2B)/(2)\:cos(2A+2B)/(2))$

$\leadsto\:\sf(sin(A+B))/(cos(A+B))$

$\leadsto\:\bf{tan(A+B)}$

Smither thinks that a special juice will increase the productivity of workers. He creates two groups of 50 workers and assigns each group the same task (in this case, they’re supposed to staple a set of papers). Group A is given the special juice to drink while they work. Group B is not given the special juice. After an hour, Smither counts how many stacks of papers each group has made. The above experiment could be made more valid by _____. Choose the best answer • running a pretrial or using existing data from a time when nobody drinks the juice as a baseline. • increasing the number of groups to 4 with 25 people in each group. • using coconut water instead of juice. • testing the subjects for longer periods of time

Answers

Answer:

The experiment could be made more valid by:

• Running a pretrial or using existing data from a time when nobody drinks the juice as a baseline.

This option would help establish a baseline productivity level for the workers before introducing the special juice. By comparing the performance of Group A (given the special juice) with the baseline performance, it would be easier to determine whether the special juice indeed had an impact on productivity. This approach helps control for any external factors that may affect productivity, making the experiment more valid and the results more reliable.

The best answer is: running a pretrial or using existing data from a time when nobody drinks the juice as a baseline.
This would make the experiment more valid because it establishes a baseline for comparison. By comparing the productivity of both groups with no juice consumption, any differences observed in productivity between Group A (given the special juice) and Group B (not given the special juice) can be more confidently attributed to the juice itself rather than other factors. This helps to ensure that any observed effects are indeed caused by the special juice and not due to other variables or random chance.

why did the united states push for control of the oregon country? increased american settlement in the pacific northwest increased threat of british attacks on the louisiana territory discovery of gold in the rocky mountains need for more territory north of the missouri compromise

Answers

The United States pushed for control of Oregon county to increase American settlement in the Pacific Northwest.

A four-sided shape with the top side labeled as 10.2 cm. The height is labeled 5 cm. A portion of the base from the perpendicular to a vertex is labeled 4 cm. The portion of the base from the perpendicular to the right vertex is 6.2 cm.What is the area of the figure?

25.5 cm2
45.5 cm2
51 cm2
56.1 cm2

Answers

The area of the figure is 51 cm².

Given that,

A four-sided figure with the top side labeled as 10.2 cm.

The height is labeled 5 cm.

This shape is a trapezium.

Total length of the base = 6.2 + 4 = 10.2 cm

Area of the figure = 10.2 × 5 = 51 cm²

Hence the required area of the figure is 51 cm².

Learn more about Area here :

brainly.com/question/29266824

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Suppose that you have a $2,000 balance on a credit card with a 7.99% annual interest rate, and you can afford to pay $150 per month toward this debt. a. Find the amount of time it takes to pay off this debt. Give your answer in months and years.
b. Calculate the total amount paid over the life of the debt.