Given the function f(x) = x3 + 2x2 − 3x − 5, what is resulting function when f(x) is shifted to the right 1 unit?

Answer:

D. (5x + 4)(5x – 4)

Step-by-step explanation:

This is the difference of two squares

[tex]a^{2} - b^{2}  = (a-b)(a+b)\\[/tex]

Following from above,

25[tex]25x^{2} -16[/tex]

Taking the elements of the expression

[tex]25x^{2} = 5^{2}x^{2}[/tex]

Using the law of indices,

[tex]a^{2} b^{2} = (ab)^{2}[/tex]

[tex]25x^{2} = (5x)^{2}[/tex]

[tex]16 = 4^{2}[/tex]

Therefore,

[tex]25x^{2} -16[/tex] =  [tex](5x)^{2}  - 4^{2}[/tex]

=[tex](5x-4)(5x+4)[/tex]

Hence the correct answer is Option D.

Final answer:

To calculate the total cost of the coat with a 7% sales tax, multiply the cost of the coat by 0.07 to get the sales tax amount of $7.98, then add it to the original cost for a total of $121.98.

Explanation:

To find the total cost of a coat that costs $114 with a 7% sales tax, you first need to calculate the amount of sales tax by converting the percentage to a decimal. Then multiply the decimail by the price of the coat to get the sales tax amount.

Here is the calculation for sales tax:

$114 × 0.07 = $7.98

Next, add the sales tax to the original price to find the total cost:

$114 + $7.98 = $121.98

So, the total cost of the coat, including sales tax, is $121.98.

The given equation, cos 65° + cos 55° = cos θ doesn't follow normal trigonometric relationships. Therefore, a value for θ can't easily be computed without further transformations using a cosine formula. Converting θ from degrees to radians also wouldn't directly work due to the equation's specifics.

This question pertains to the field of trigonometry. We have the equation cos 65° + cos 55° = cos θ and we need to find the value of θ in radians. Unfortunately, we cannot resolve this equation directly as the addition of cosines does not equal another cosine. However, one can use cosine formula to transform this equation and solve analytically with a lot of work.

To convert degrees to radians, you would use the formula: θ(radians) = θ(degrees) * π / 180. However, as noted, this task won't work directly for this problem due to the nature of the equation.

This is a particular challenge problem that might not have an easy solution that would fall into the regular high school curriculum.

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Answer:

the answer is 8

Step-by-step explanation:

the answer is :

1332113

a. The value of x ≈ 60°

b. The value of y ≈ 93°

The relevant relations are ...

external angle A is half the difference of intercepted arcs BC and BD

inscribed angle y° is half the measure of intercepted arc CD

the sum of arcs of a circle is 360°

Using these relations, we have ...

(a) A = (BC -x°)/2

x° = BC -2A = 112° -2(27°)

x° = 58°

(b) y° = CD/2 = (360° -BC -BD)/2 = (360° -112° -60°)/2

y° = 91°

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Answer:

Option (c) is correct.

The interest gained by Gini in 6 years is $ 866.34

Step-by-step explanation:

Given: Gina invests $1,677 in an account paying 8.61% simple interest annually for 6 years.

We have to calculate the interest gained by Gina in 6 years.

Using formula for simple interest

[tex]S.I.=\frac{P\times I\times T}{100}[/tex]

Where,

S.I = simple interest

P is principal

R is interest rate

T is time  

Given : P = $ 1677

R = 8.61%

T = 6 years

Substitute, we get,

[tex]S.I.=\frac{1677\times 8.61\times 6}{100}[/tex]

Simplify, we get,

S.I. = $ 866.3382

Rounding off to nearest hundred  we get, Interest is $866.34

Thus, the interest gained by Gini in 6 years is $ 866.34

Gina has gained $866.34 in interest after six years.

To find the interest gained, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $1,677, the rate is 8.61%, and the time is 6 years. Plugging these values into the formula, we get: Interest = $1,677 * 0.0861 * 6 = $866.34. Therefore, Gina has gained $866.34 in interest after six years.

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Answer: A. 4

Step-by-step explanation:

The characteristic equation of a circle is

[tex]x^2+y^2=r^2[/tex]

The characteristic equation of a hyperbola is

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

The intersection points will be obtained as the solution of the both characteristic equations.

[tex]x^2+y^2=r^2[/tex].......(1)

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].............(2)

⇒[tex]y^2=r^2-x^2[/tex].....(from 1)

put this in (2)

[tex]\frac{x^2}{a^2}-\frac{r^2-x^2}{b^2}=1[/tex]

⇒[tex]y^2=r^2-x^2\\\frac{x^2}{a^2}+\frac{-x^2}{b^2}=1+\frac{r^2}{b^2}[/tex]

⇒[tex]y^2=r^2-x^2\\x^2(\frac{1}{a^2}+\frac{1}{b^2})=1+\frac{r^2}{b^2}[/tex]

⇒[tex]y^2=r^2-x^2\\x^2(\frac{a^2+b^2}{a^2b^2})=\frac{b^2+r^2}{b^2}[/tex]

[tex]\Rightarrow\ x^2=\frac{a^2(b^2+r^2)}{a^2+b^2}\\y^2=\frac{b^2(r^2-a^2)}{a^2+b^2}[/tex]

So there are 2 different values of x and two different values of y, thus the maximum number of intersection points  is 4.

Answer:

statement is true

Step-by-step explanation:

Given  : If triangle RST is congruent to triangle WXY and  area of triangle WXY is 20 square inches, then the area of triangle RST is 20 in.

To find : Statement is true or false .

Explanation :

Yes,if two triangles are congruent then you can place one above the other perfectly and  both cover the same region.

So,we can say that both have the same area.

But the conversion is not true .

Therefore, statement is true .

The student buying water and a sports drink to avoid dehydration during soccer practice based on their coach's advice is an example of deductive reasoning, as it applies a general principle to a specific situation.

The scenario described involves a student purchasing fluids to prevent dehydration during soccer practice based on the advice from a coach. This example of reasoning is deductive reasoning. The coach has provided a general principle that drinking a lot of fluids prevents dehydration. The student applies this general principle to a specific situation (soccer practice) and takes action (buying water and a sports drink) to avoid dehydration. This reasoning starts from a general rule and applies it to a particular case, characteristic of deductive reasoning.

Answer:

$4

Step-by-step explanation:

In order to solve this problem you just have to create an equation, and it´s very simple, each kid ticket will be represented by the letter "x", and as we know a kid´s ticket is worth half what is worth an adult ticket, so the adult ticket = 2 kids tickets=2x

So we know that there are 2 adults and three kids, and the totla was $14, we create our equation:

[tex]2 adults+3kids=14\\2(2x)+3x=14\\4x+3x=14\\7x=14\\x=\frac{14}{7}\\ x=2[/tex]

Now we know that the kids ticket is $2, so the adult ticket would be twice that, $4 is the price of the adult ticket.

Answer:

The solution is (–6, 2, 1). (Option A)

Step-by-step explanation:

Given three equations

2x + 4y - 3z = -7  →   (1)

3x + y + 4z = -12  →   (2)

x + 3y + 4z = 4    →   (3)

we have to find the solution of above equations.

By elimination method

Multiply equation (2) by 4 and then subtracting from (1), we get

(2x + 4y - 3z+7)-4(3x + y + 4z + 12)=0

  ⇒  -10x-19z=41 → (4)

Multiply equation (2) by 3 and then subtracting from (3), we get

(x + 3y + 4z - 4)-3(3x + y + 4z + 12)=0

  ⇒ -8x-8z=40 ⇒ x+z=-5 → (5)

Solving (4) and (5), we get

-10x-19z-41+10(x+z+5)=0

 ⇒ -9z=-9 ⇒ z=1

⇒ x+1=-5 ⇒ x=-6

and (3) implies -6 + 3y + 4 = 4 ⇒ y=2

Hence, the solution of above 3 equations will be (x,y,z)=(-6,2,1)

Hence, option (1) is correct.

Answer:

D. Conditional

Step-by-step explanation:

The statement is a conditional statement.

Answer:

Remainder is 24.

Step-by-step explanation:

Given dividend = 3x² + 10x - 8

and divisor = x - 2

To find: Remainder using Remainder theorem.

Remainder Theorem states that let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).

Let p(x) = 3x² + 10x - 8

using remainder theorem,

Remainder = p(2) = 3 × 2² + 10 × 2 - 8

                  = 3 × 4 + 20 - 8

                  = 12 + 12

                  = 24

Therefore, Remainder is 24.

The equestrian's father will catch up to her at 2:00 pm by using the concept of relative speed and calculating the time it will take for him to close the gap between them.

The student's father will catch up to the equestrian at 2:00 pm. To solve this problem, we can use the concept of relative speed. The equestrian starts riding away from the house at 10 miles per hour (mph) at 10:00 am. By noon, when the father starts chasing her on his scooter at 15 mph, the equestrian is already 20 miles away (2 hours × 10 mph).

Since the father's speed is 15 mph and the equestrian's speed is 10 mph, the father is closing the gap at a speed of 15 mph - 10 mph = 5 mph. To cover the 20 miles gap, the father will need 20 miles / 5 mph = 4 hours. Therefore, if the father starts at noon, he will catch up to her at 4 hours later, which is 2:00 pm.

∠Z ≅ ∠X and ∠W ≅ ∠Y is the correct answer

D