Use the x-intercept method to find all real solutions of the equation.
x^3-7x^2+4x+12=0

the falcon flew 56 miles more than the eagle

Answer:

the eagle flew 56 miles less than the falcon

Step-by-step explanation:

112-56=56

Answer:

(a) 0.48

(b) 0.20

(c) it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the​ casino.

Step-by-step explanation:

​(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino. ​

The probability that a radomly selected resident opposes the casino and strongly opposes the cassino is the product of the two probabilities, that a resident opposes the casino and that it strongly opposes the casino (once it is in the first group) as it is shown below.

Use this notation:

i) Determine the probability that a radomly selected resident opposes the casino, P(A)

Probability = number of favorable outcomes / number of possible outcomes

ii) Next, determine,the probability that a resident who opposes the casino strongly opposes it, P(B/A):

iii) You want the probability of both events, which is the joint probability or  intersection: P(A∩B).

So, you can use the definition of conditional probability:

iv) From which you can solve for P(A∩B)

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

In this case, you just want the complement of the probability that a radomly selected resident who opposes the casino does strongly oppose the casino, which is 1 - P(B/A) = 1 - 8/10 = 1 - 0.8 = 0.2.

​(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the​ casino?

You are being asked about the joint probability (PA∩B), which you found in the part (a) and it is 0.48.

That is almost 0.50 or half of the population, so you conclude it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the​ casino.

For a system of 2 equations in 2 unknowns, there are 3 cases:

When slopes are different, the two lines intersect at one point, the solution.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence no solutions. If the lines are the same line, they intersect at all points, so there are infinitely many solutions.

I am considering the point you have given is point on a circumference of a circle and center of circle is (0,0) and we have to calculate radius

so radius = root((x-h)^2 + (y-k)^2)

where (h,k) is center of circle

so r = root((5-0)^2+(10-0)^2)

= √(100+25) = √125 = 5√5

so answer is option c

The distance r from the point (5, 10) to the origin is calculated using the distance formula, resulting in r = 5√5. So, the correct answer is option (c) 5√5.

The student's question involves finding the distance r from a point to the origin in a coordinate system, given a point (x, y). Given the point (5, 10), we can calculate r using the distance formula [tex]r = \( \sqrt{(x - x_1)^2 + (y - y_1)^2} \).[/tex]

We want to find the distance r from the origin [tex](x_1,y_1)[/tex] = (0, 0) to this point (x, y) = (5, 10).

Substituting x = 5 and y = 10 into the equation, we get:

[tex]r = \( \sqrt{(5 - 0)^2 + (10 - 0)^2} \)\\ = \( \sqrt{5^2 + 10^2} \)\\ = \( \sqrt{25 + 100} \)\\ = \( \sqrt{125} \)\\ r = 5\sqrt{5}.[/tex]

Therefore, the correct answer is option (c) [tex]5\sqrt{5}[/tex].

Answer:

A = 25π ft² or A = 78.5398 ft²

Step-by-step explanation:

The formula for area of a circle is

A = πr² where r is the radius

We are given a diameter of 10, the radius is half of the diameter, so for our problem r = 5.  Plug that in and evaluate

A = π(5²)

 A = 25π

or

A = 78.5398 if you multiply out pi

Answer:

Part 1) Greta's right, the triangle is incorrect.

Part 2) [tex]34,203\ ft[/tex]

Part 3) The height of the tree is [tex]23.3\ ft[/tex], Trey’s house is not at risk

Step-by-step explanation:

Part 1) we know that

In the right triangle of the figure

[tex]sin(30\°)=\frac{1}{2}[/tex]

[tex]sin(30\°)=\frac{6\sqrt{3}}{12}=\frac{\sqrt{3}}{2}[/tex]

Compare

[tex]\frac{1}{2}\neq\frac{\sqrt{3}}{2}[/tex]

therefore

The triangle is not correct

Because

The side adjacent to the 30 degree angle should be [tex]6\sqrt{3}[/tex] and the side opposite the 30 degree angle should be [tex]6[/tex]

Part 2)

Let

x--------> the distance from the airplane to the SCCA (hypotenuse of the right triangle)

we know that

[tex]sin(17\°)=\frac{10,000}{x}[/tex]

[tex]x=\frac{10,000}{sin(17\°)}[/tex]

[tex]x=34,203\ ft[/tex]

Part 3)

Let

x-------->  the height of the tree

we know that

[tex]tan(43\°)=\frac{h}{25}[/tex]

[tex]h=tan(43\°)(25)=23.3\ ft[/tex]

[tex]23.3\ ft< 25\ ft[/tex]

therefore

Trey’s house is not at risk

Answer:

It's B.   f(x) = (x + 3(^2 + 1.

Step-by-step explanation:

f(x) ---- > f(x + 3)   is a translation of 3 units to the left.

The correct function that includes a 3 unit leftward translation is f(x) = [tex](x-3)^2+1.[/tex]

The correct function that includes a translation of 3 units to the left is option D, f(x) = [tex](x-3)^2+1.[/tex]

When we translate a function to the left by a certain number of units, we subtract that number from the x-values. In this case, subtracting 3 units from x would result in a translation to the left. The function f(x) = [tex](x-3)^2+1.[/tex] represents this translation. The x-3 part shifts the graph horizontally to the left by 3 units.

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Answer:

She bought .9 ton of compost.

Step-by-step explanation:

Take the amount of bags she bought and multiply it by the weight of each bag.

40*50=2,000

Then divide it by the amount a ton is.

2,000/2,204=0.90718474

Round it to the nearest tenth.

=.9

Then that's you're answer.

Answer:

There are 162 students in the school.

Step-by-step explanation:

10% do not like purple.   x is the number of students in the school.  We have 162 students that do not like purple.

x*.10 = 162

Divide each side by .10

x = 162/.10

x =1620

There are 162 students in the school.

Answer:

262,440

Step-by-step explanation:

Multiply the population (243000) times 8% (0.08)

   243000*0.08 = 19,440

Add the 8% to the total population

   19,440 + 243,000 = 262,440

The new population of City A after one year with an 8% of the increasing rate will be 262,440.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The number of inhabitants in City A was roughly 243000 individuals, and it expanded by 8% in one year.

The new population of City A after one year with an 8% of the increasing rate is given as,

⇒ (1 + 0.08) x 243,000

⇒ 1.08 x 243,000

⇒ 262,440

The new population of City A after one year with an 8% of the increasing rate will be 262,440.

More about the percentage link is given below.

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A full circle is 360 degrees.

The circle is separated into 8 parts, so each arc is 1/8 of a circle, which equals: 360/8 = 45 degrees.

There are 2 45 degree arcs between B and C, so the arc from B to C = 45 x 2 = 90 degrees.

The answer is B.

Answer:

$89340

Step-by-step explanation:

Answer:

$386794

Step-by-step explanation:

To find how much we're going to make in total after working for 5 years in the company, we can solve it by calculating for the total amount after each year.

So in the first year we get.

$70,000

To get how much we get in the 2nd year we add the extra 5%.

2nd year salary = (70000 x 0.05) + 70000

2nd year salary = 73500

Now we continue to do that until the 5th year

3rd = (73500 x 0.05) + 73500

3rd = 77175

4th = (77175 x 0.05) + 77175

4th = 81033.75

5th = (81033.75 x 0.05) + 81033.75

5th = 85085.44

Now we add them all up to get the total.

70000 + 73500 + 77175 + 81033.75 + 85085.44

We get:

$386794.19 or $386794

Answer:

-5

Step-by-step explanation:

Point P represents -5. You can see that the line counts up in increments of 2. P is in between -6 and -4. It must be -5.

The correct answer is -5

As we can see from the picture, we have the number -4 before P and -6 after P. Which would mean -5 is the correct answer.

I hope this helps! :)

Have a wonderful day!

-LizzyIsTheQueen

To calculate the volume of the triangular prism, first find the area of the right triangle that forms the base and then multiply it by the height of the prism.

The question involves finding the volume of a triangular prism whose base is a right triangle with sides measuring 7 inches, 24 inches, and 25 inches, where 25 inches is the hypotenuse. The height of the prism is given as 3 inches. To find the volume of the prism, we use the formula for the volume of a triangular prism, which is the area of the triangular base times the height of the prism.

First, we find the area of the triangular base using the formula for the area of a right triangle, which is (1/2) × base × height. For this triangle, the base and height are the perpendicular sides, which are 7 inches and 24 inches respectively. Thus, the area of the base triangle is (1/2) × 7 × 24 square inches.

Next, we multiply the area of the base by the height of the prism to get the volume. The height of the prism is 3 inches, so the volume will be the area of the base triangle times 3 inches.

Answer:

Step-by-step explanation:

(4x + 3) + (-2x + 4)

= 4x + 3 - 2x + 4         combine like terms

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

= 2x + 7

Answer:

addition, subtraction, and multiplication only

Step-by-step explanation:

There are a couple of reasons why polynomials are not closed under division:

1. the set of polynomials includes zero, and division by zero is undefined.

2. division by a polynomial can give rise to terms that are not non-negative powers of the variable, 1/x, for example. These terms are not included in the set of polynomials.

Answer:

Addition, Subtraction, and Multiplication

Step-by-step explanation:

Answer:

E, B, A,

Step-by-step explanation:

C is wrong because it isn't decreasing

D is wrong because if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning y goes lower than 5

F is wrong because  if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning the y intercept is 2 not 5

Answer:

[tex]\Large \boxed{\mathrm{A , \ B, \ and \ E}}[/tex]

Step-by-step explanation:

[tex]F(x)=2 \cdot 5^x[/tex]

There are no restrictions on x. The domain is all real numbers.

To find the y-intercept, we set the x value to 0. The y-intercept of the function is (0, 2).

The function is increasing, because as the value of the input increases, the value of the output increases as well.

Answer:

The perimeter would also be multiplied by 6.

Step-by-step explanation:

The perimeter would also be multiplied by 6. Suppose the sides are 5 and 10. The perimeter would be the sum of the side lengths or 5 + 5 + 10 + 10 = 30.

Multiply each side length so 5*6 = 30 and 10*6 = 60. Find the perimeter by finding their sum, 30 + 30 + 60 + 60 = 180.

Divide the new perimeter by the old perimeter to find a scale factor.

180/30 = 6.

The new perimeter is exactly 6 times bigger since 6*30 = 180.

Answer:

The perimeter is multiplied by 6.

Step-by-step explanation:

Answer:

c. 1

Step-by-step explanation:

The given expression is

[tex]\cos(x) \csc(x) \tan(x)[/tex]

We express everything in terms of sine and cosine to obtain;

[tex]\cos(x) \times \frac{1}{\sin(x)} \times \frac{\sin(x)}{\cos(x)}[/tex]

We cancel out the common factors to obtain;

[tex]\frac{1}{1} =1[/tex]

Answer:

cos(x)csc(x)tan(x)  =  1

Step-by-step explanation:

We have given a trigonometric expression.

cos(x)csc(x)tan(x)

We have to simplify the above expression.

Since, we know that

Tan(x) is ratio of sin(x) and cos(x).

Tan(x)   =  sin(x)/cos(x)

csc(x) is reciprocal of sin(x).

csc(x)   =   1/sin(x)

Putting above values in given expression,we have

cos(x)csc(x)tan(x)  =  cos(x) × 1/sin(x) × sin(x)/cos(x)

cos(x)csc(x)tan(x)  =  1 which is the answer.

Answer:

D

Step-by-step explanation:

If there is a 2x2 matrix as  [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

The determinant is given by  [tex]\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]

Now, if we calculate the value of "ad - bc", we see that:

[tex](-4)(-12)-(8)(6)=0[/tex]

We can't calculate the inverse, the inverse doesn't exist. The answer is D.

Answer:

The increase as a percentage is (2.60)(100%) = 260%

Step-by-step explanation:

The premium increase from last year is ($883 - $245), or $638.

The increase as a ratio is then $638/$245, or 2.60.

The increase as a percentage is (2.60)(100%) = 260%

This is the answer to your mathematical question !!

The other angel is also equal to x and the sum of all angels need to be 360:

2x+90+26=360

2x=244

X=122

Answer:

The answer is 112

Step-by-step explanation:

Because seven ate nine :D but seriously 90+26+2x=360 so thats

116+2x=360 and 360-116 is 244 and you divide that by the remaining 2

and that gives you your answer of 112

Answer:

$96.93

Step-by-step explanation:

1. multipy the cost of the item (89.75) times the 8% tax.

    89.75 * 0.08 = 7.18 in tax

2. add the item cost plus tax

    89.75 + 7.18 = $96.93

Max will have to pay $ 96.93  in total for the DVD player.

An extra amount of money to be paid to the seller as tax on sales or on the receipt of sales is called sales tax.

According to the problem,

So, Max will have to pay $ { 89.75 + [tex](\frac{8}{100}) 89.75[/tex]}

                                   = $ 96.93

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☆ ☆

Answer:

m∠A = 9.1°

m∠B = 10.9°

c = 54.2

The answer is (d)

Step-by-step explanation:

∵ a = 25

∵ b = 30

∵ m∠C = 160°

∴ c² = a² + b² - 2 × ab × cos(C)

∴ c² = 25² + 30² - 2(25)(30) × cos(160) = 2934.5389

∴ c = 54.2

∵ a/sin(A) = b/sin(B) = c/sin(C)

∵ 25/sin(A) = 54.2/sin(160)

∴ sin(A) = (25 × sin(160)) ÷ 54.2 = 0.1577584

∴ m∠A = 9.1°

∵ 30/sin(B) = 54.2/sin(160)

∴ sin(B) = (30 × sin(160)) ÷ 54.2 = 0.18931

∴ m∠B = 10.9°

[tex]Domain: x\in\mathbb{R}[/tex]

Answer:

$42.09

Step-by-step explanation:

1. multiply the cost per gallon (3.45) by the gallons purchased (12.2)

    3.45*12.2 = 42.09

Answer:

42.09

Step-by-step explanation:

12.2×3.45

x= twin 1 and 2

x=5x-60

x-5x=-60

-4x=-60

x=15

check 15=5(15)-60

15=75-60

15=15

Answer:

4.66667

Step-by-step explanation: