Solve (x + 2 < 5) ∩ (x - 7 > -6).

1. {x | 1 < x < 3}
2. {x | x < 3 or x > 1}
3. {all real numbers}

Answer:

B

Step-by-step explanation:

Just multiply it, which multiplies up to -126.

Answer:

Positive 126

Step-by-step explanation:

  Because if you multiply a positive with a negative it becomes positive. So -18*7 would equal positive 126

When purchasing a car, consider using libraries, newspaper advertisements, and various websites to determine the manufacturer's invoice.

When purchasing a car, three sources for determining the manufacturer's invoice for the basic vehicle include:

Libraries

Newspaper advertisements

Various websites

Utilizing these sources can help buyers obtain accurate pricing information before making a purchase decision.

The sources for determining the manufacturer's invoice for the basic vehicle include:

- Libraries

- Various websites

When purchasing a car, determining the manufacturer's invoice price for the basic vehicle can be crucial for negotiating a fair deal. Libraries offer access to automotive reference materials and pricing guides, providing reliable information on invoice prices. Similarly, various websites dedicated to car pricing, such as manufacturer websites, automotive research sites, and online marketplaces, offer up-to-date invoice pricing data. These sources compile information from manufacturers and dealerships, ensuring accuracy and comprehensiveness. Newspaper advertisements and bookstore resources, however, typically focus more on retail prices and promotions rather than invoice pricing. Therefore, while they may provide some insight into car pricing trends, they are not typically the primary sources for determining the manufacturer's invoice price. Utilizing libraries and online resources ensures consumers have access to accurate and detailed invoice pricing information, empowering them to make informed decisions when purchasing a car.

Answer:

infinite solutions

Step-by-step explanation:

Distribute the left side and simplify

- 8x - 17 = - 8x + 4 - 21

- 8x - 17 = - 8x - 17

Since both sides are equal the equation has infinite solutions

In the finding of m<FOE, I think it would be 70°.

Answer:

∠FOE = 90°

Step-by-step explanation:

In this question given is m∠AOC = 120°, m∠BOD = 150°.

We have to calculate ∠FOE.

Since ∠AOB + ∠COD + ∠BOC = 180°  [ Angle at a point on a straight line ]

∠AOB + ∠COD = 180° - ∠BOC ---(1)

It is given ∠AOC = 120° = ∠AOB + ∠BOC -----(2)

and ∠BOD = 150° = ∠BOC + ∠COD ------(3)

By adding equation (2) and (3)

150 + 120 = ∠ BOC + ∠COD + ∠AOB + BOC

270 = 2∠BOC + ∠COD + ∠ AOB

Now from equation (1)

270 = 2∠BOC + (180 - ∠BOC)

270 = 180 + ∠BOC

270 -180 = ∠BOC

∠BOC = 90°

Since ∠ BOC ≅ ∠FOE   (opposite angles)

Therefore, ∠FOE = 90° is the answer.

Answer:

C

Step-by-step explanation:

The area (A) of the triangle is calculated using

A = [tex]\frac{1}{2}[/tex] ab sinC

where a, b are the 2 sides and C is the angle between them

here a = 9, b = 15 and C = 70°, hence

A = 0.5 × 9 × 15 × sin70° = 63.4 cm² → C

Answer:

C.[tex]63.4cm^2[/tex]

Step-by-step explanation:

I love trigonometry

the area of a triangle is equal to [tex]\frac{1}{2}*a*b*sinC[/tex]

we have a b and Angle C so just put that in the formula :)

[tex]\frac{1}{2}*9*15*sin70\\[/tex]

[tex]63.4cm^2[/tex]

ANSWER

D) 20

EXPLANATION

The given expression is

13 − 2(1 − 15) ÷ 4

Use PEDMAS,

Deal with the parenthesis first.

[tex]13 - 2( - 14) \div 4[/tex]

This gives us,

[tex]13 + 28 \div 4[/tex]

Next Divide :

[tex]13 + 7[/tex]

Next add to obtain,

[tex]20[/tex]

The correct choice is D.

12

mean is adding all the terms and dividing by number of terms so once you add them all you be 108 and then divide by 9 giving you the mean, 12

Answer:

The mean should be 12.

Step-by-step explanation:

To find the mean of a range of numbers, you must simply add all of the numbers together and divide by how many numbers there are in the group.

In this case, I did 15+11+10+11+14+10+15+10+12, which came to be 108. I divided that by 9, since there are nine numbers, which gave me 12.

Hopefully this helps!

$10.0000000000000000000

10.00

Answer:   294.4 m²

Step-by-step explanation:

Separate the shaded region into two parts:

[tex]1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3[/tex]

[tex]2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1[/tex]

Area of shaded region = Area of (1) + Area of (2)

                                      =    247.3     +      47.1

                                      =               294.4

Answer:

294.36

Step-by-step explanation:

Find the area of the entire circle.

Subtract out the area of a sector with 130 degrees for the central angle.

Add the area of the isosceles triangle with an apex angle of 130 degrees.

Area of The entire circle

Area = pi * r^2

Area = 3.14 * 11.1^2

Area = 386.88 m^2

Area of the sector with 130 degrees for a central angle

Area_130 = (130/360) * pi * r^2

Area_130 = (130/360) * 3.14* 11.1^2

Area_130 = 139.71

Area of the triangle

1/2 central angle = 130/2 = 65

Bisect the apex angle so that each half = 65 degrees.

Sin(65) = opposite / hypotenuse

Sin(65) = Opposite / 11.1

11.1 * sin(65) = opposite

opposite = 10.06

This is 1/2 the base so the base = 2*10.06 = 20.12

The height of the triangle is found by cos(65) = adjacent/hypotenuse

hypotenuse = 11.1

Cos(65) = adjacent / hypotenuse

adjacent = hypotenuse * cos(65)

adjacent = 4.69 This is the height of the triangle.

Area of the triangle = 1/2 * 20.12 * 4.69

Area of the triangle = 47.19 m^2

Area of the Shaded Area

Area of entire circle - area of sector + area of triangle

=386.88 - 139.71 + 47.19

=294.36

Note

The area of the triangle could be done using Area = 1/2 * 11.1^2 * (2*sin(65)*cos(65) = 1/2 * 11.1^2 * sin(130) = 47.2 but you may not know all the math to do the area this way.

Answer:

27 is correct.

Step-by-step explanation:

Answer:   a) 27

Step-by-step explanation:

[tex]81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}}=3^{\frac{12}{4}}=3^3=3\cdot 3\cdot 3=\boxed{27}[/tex]

The values of x and y are x = 375 square feet and y = 6,300 pounds

To find the values of x and y, we need to determine the ratio of lifting force to area and use it to fill in the missing values in the table.

Given:

- The ratio of lifting force to area is equivalent for all pairs in the table.

Let's calculate the ratio for the given pairs:

1. [tex]\( \frac{125}{1875} = \frac{150}{2250} = \frac{175}{2625} = \frac{250}{3750} \)[/tex]

2. [tex]\( \frac{250}{3750} = \frac{x}{5625} \)[/tex]

3. [tex]\( \frac{250}{3750} = \frac{420}{y} \)[/tex]

From the given pairs, we can observe that the ratio is [tex]\( \frac{250}{3750} \)[/tex] for all of them.

Now, using this ratio, we can find the missing values:

2. [tex]\( \frac{250}{3750} = \frac{x}{5625} \)[/tex]

[tex]\[ x = \frac{250 \times 5625}{3750} = 375 \, \text{square feet} \][/tex]

3. [tex]\( \frac{250}{3750} = \frac{420}{y} \)[/tex]

[tex]\[ y = \frac{3750 \times 420}{250} = 6300 \, \text{pounds} \][/tex]

Therefore, the correct values are:

[tex]\[ x = 375 \, \text{square feet} \][/tex]

[tex]\[ y = 6300 \, \text{pounds} \][/tex]

So, the correct answer is: [tex]\[ \text{Option D: } x = 375 \, \text{square feet} \, \text{and} \, y = 6300 \, \text{pounds} \][/tex]

Complete question:

The area of an airplane's wings is related to the airplane's lifting force, which holds the airplane in the air. The table below lists several wing areas and the corresponding lifting forces. The ratio of lifting force to area is equivalent for all pairs in the table. What are the values of x and y?

AIRPLANE LIFTING FORCE  Area of Wings Lifting Force

125                                           1,875

150                                           2250

175                                           2625

250                                          3750

   x                                          5625

420                                             y

x = 375 square feet and y = 7,500 pounds

x= 335 square feet and y = 6,300 pounds

x= 335 square feet and y = 7,500 pounds

x = 375 square feet and y = 6,300 pounds

Answer:

40°

Step-by-step explanation:

arc AB has twice the measure of the inscribed angle BCA that intercepts it, so we have the relation ...

(6x-50)° = 2(2x)°

2x -50 = 0

2x = 50

So, angle BCA has measure 50°. Since AC is a diameter, angles BCA and BAC are complementary. Thus ...

m∠BAC = 90° - m∠BCA = 90° - 50°

m∠BAC = 40°

Answer:

7

Step-by-step explanation:

Replace both instances of x in f(x) = 2x + 9 with -1:

f(-1) = 2(-1) + 9 = 7

Thus, f(-1) = 7

The value of the function f(x) = 2x + 9 at x = - 1 Or f(-1) is 7.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 2x + 9.

We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.

Therefore, f(-1) = 2(-1) + 9.

f(-1) = - 2 + 9.

f(-1) = 7.

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What are the other equations to compare it to ?

Answer:

here x =6

which gives equivalent equation

[tex]log_{6} 36 = 2[/tex]

Step-by-step explanation:

[tex]log_{x} 36 = 2[/tex]

      36 = [tex]x^{2}[/tex]

solving it we get ,

x =+6 and x =-6

since x is the base of log so it cannot be negative

therefore x =6

therefore this equation can be

[tex]log_{6} 36 = 2[/tex]

Answer:

[tex]x= -7[/tex]

Step-by-step explanation:

We need to solve the following root equation:

[tex]\sqrt[3]{x-1} + 2 = 0[/tex]

1. First, we need to add minus two to both sides of the equation:

[tex]\sqrt[3]{x-1}= -2[/tex]

2. Elevate each side of the equation to the power of 3:

[tex]x-1= -8[/tex]

3. Solve for 'x':

[tex]x= -8 + 1[/tex]

[tex]x= -7[/tex]

Therefore, the result is:

[tex]x= -7[/tex]✔️

Answer:

The function increase between 0 and 1, and from 2 to infinity.

Step-by-step explanation:

Any one variable function f(x) increases when f(x2) is greater than f(x1), where x2 is greater than x1. For example, in the plot it can be seen that for x2 = 1, f(x2) = 1 and for x1 = 0, f(x1) = 0. So, between points 0 and 1, the function increase. Also, from 2 onwards, the function increase their values.

Answer:

vertex = (2, - 16)

Step-by-step explanation:

given

f(x) = (x - 6)(x + 2) ← equate to zero to find the zeros

(x - 6)(x + 2) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros, hence

[tex]x_{vertex}[/tex] = [tex]\frac{6-2}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Substitute x = 2 into f(x) for corresponding y- coordinate of vertex

f(2) = (2 - 6)(2 + 2) = - 4 × 4 = - 16

vertex = (2, - 16)

Does it have any ANSWER CHOISES!

Answer:

c = 36.87

Step-by-step explanation:

arcsin(3/5)=36.87

Answer:

The equation represents an even function

Step-by-step explanation:

For the function above, the value of f(x) is fixed at 3 for positive or negative values of x.

For the absolute value function below, the value of f(x) will always be positive due to the absolute symbol.

In general, a function f(x) is said to be even if;

f(-x) = f(x) such that the function is symmetrical with respect to the y-axis.

[tex]cos\ u=-\dfrac{15}{15}\implies sin\ u=\dfrac{\sqrt{210}}{15}\\\\sin\ v=-\dfrac{5}{13}\implies cos\ v=-\dfrac{12}{13}[/tex]

6.Answer: [tex]\bold{\dfrac{12\sqrt{15}+5\sqrt{210}}{195}}[/tex]

Step-by-step explanation:

[tex]cos(u+v)=cosu\cdot cosv-sinu\cdot sinv\\\\.\qquad\qquad=\dfrac{-\sqrt{15}}{15}\cdot \dfrac{-12}{13}-\dfrac{\sqrt{210}}{15}\cdot \dfrac{-5}{13}\\\\\\.\qquad\qquad=\dfrac{12\sqrt{15}}{195}+\dfrac{5\sqrt{210}}{195}\\\\\\.\qquad\qquad=\boxed{\dfrac{12\sqrt{15}+5\sqrt{210}}{195}}[/tex]

7.[tex]\bold{\dfrac{-12\sqrt{210}-5\sqrt{15}}{195}}[/tex]

Step-by-step explanation:

[tex]sin(u-v)=sinu\cdot cosv-cosu\cdot sinv\\\\.\qquad\qquad=\dfrac{\sqrt{210}}{15}\cdot \dfrac{-12}{13}-\dfrac{-\sqrt{15}}{15}\cdot \dfrac{-5}{13}\\\\\\.\qquad\qquad=\dfrac{-12\sqrt{210}}{195}-\dfrac{5\sqrt{15}}{195}\\\\\\.\qquad\qquad=\boxed{\dfrac{-12\sqrt{210}-5\sqrt{15}}{195}}[/tex]

8.Answer: [tex]\bold{-\dfrac{19}{67}}[/tex]

Step-by-step explanation:

[tex]tan\ u=-\dfrac{3}{4}\\\\cos\ v=-\dfrac{12}{13}\implies tan\ v=\dfrac{5}{13}\\\\\\\\tan(u+v)=\dfrac{tan\ u+tan\ v}{1-tan\ u\cdot tan\ v}\\\\\\.\qquad\qquad=\dfrac{\frac{-3}{4}+\frac{5}{13}}{1-(\frac{-3}{4}\cdot \frac{5}{13})}\\\\\\.\qquad\qquad=\dfrac{\frac{-39}{52}+\frac{20}{52}}{\frac{52}{52}+\frac{15}{52}}\\\\\\.\qquad\qquad=\boxed{-\dfrac{19}{67}}[/tex]

The median {Q2} is 10

Q1 is 7+7/2 which is 7

Q3 is 15+12/2 which is 13.5

Final answer:

The quartiles for the data set (5, 7, 7, 8, 10, 11, 12, 15, 17) are found by arranging the data in order and then finding the medians of the lower and upper halves. The first quartile (Q1) is 7, the median (Q2) is 10, and the third quartile (Q3) is 13.5.

Explanation:

To find the quartiles for the data set (5, 7, 7, 8, 10, 11, 12, 15, 17), you first arrange the data in ascending order, which is already done. The median (Q2) is the middle value when the data set is in order, so since there are 9 data points, the median is the fifth value, which is 10.

The first quartile (Q1) is the median of the lower half of the data. For our data set, the lower half is (5, 7, 7, 8), so the median of this set is the average of the middle two values because we have an even number of data points in the lower half. Thus, Q1 is (7 + 7)/2 = 7.

The third quartile (Q3) is the median of the upper half of the data. For our dataset, the upper half is (11, 12, 15, 17). Similarly, since this is an even set, Q3 is the average of the middle two values, (12 + 15)/2 = 13.5.

Therefore, the quartiles for this data set are:

the 4 in the tens place is 10 times the 4 in the ones place

The 4 in the tenth place is the product of 10 and the 4 to its right

The number is given as:

Number = 4,444,444

The 4 in the tenth place is:

40

The 4 to its right is:

4

Divide both numbers

40/4 = 10

Hence, the 4 in the tenth place is the product of 10 and the 4 to its right

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[tex]x^{2} (2xy^3)^5\\x^2(32x^5y^15)\\32x^7y^15[/tex]

your answer is B

Answer:

the answer is 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

add the the numbers and divide the sum by how many numbers are given

Answer:

11 is -1 `0 is c

Step-by-step explanation:

11 you subtract 1 from each 10 look for points on griid

Answer:

true

Step-by-step explanation:

Answer:7

Step-by-step explanation:

There are 15 sleeping and only 8 snoring you subtract 8 from 15 which leave you with 7 and that's how many people

By subtracting the number of travelers snoring (8) from the total number of travelers (15), we determine that there are 7 travelers not snoring.

To find out how many travelers in the hostel are not snoring, we will subtract the number of travelers who are snoring from the total number of travelers. The problem states that 8 travelers are snoring, and there are 15 travelers in total. So, we perform the following calculation:

Total travelers - Travelers snoring = Travelers not snoring

15 - 8 = 7

Thus, there are 7 travelers who are not snoring.

Answer:

B) irrational

Step-by-step explanation:

It can not be imaginary, because imaginary numbers are √(negative number).

It can not be rational, because the cube root of 11 can not be displayed as a repeating or ending number (it's 2.22398009... by the way).

The only option is irrational.

Answer:   irrational

Step-by-step explanation:

[tex]\sqrt[3]{11} = 2.2239800905693152........\\\\\text{It has a decimal that never terminates (ends) or r e p e a t s, so it is an}\\\text{irrational number.}[/tex]