<5 is a complement of <6 and m<5 = 59 degrees. Find m<6.

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer:

The total  cost of sales  department is  \(a =   \$ 84,000\)

The total cost of services department  is \(b  =  \$ 21,000\)  

Step-by-step explanation:

From the question we are told that

  The  direct  for sales cost is  \(SC  =  \$88,200\)

  The direct cost for service department is  \( SV =  \$29,400\)

Given that the  sales department charges 10% of its total monthly costs to the service department

   The indirect cost of  service department is  10% of  a =  0.10 a

Here a is the total cost of sales

Given that the  service  department charges 20% of its total monthly costs to the sales department

    The indirect cost of  sales department is  20% of  b =  0.20 b

Here b is the total  cost for service department  

Generally the direct cost of sales can be mathematically represented as

       \(SC  = a + 0.20b \)

=>     \(88200  =  a + 0.20b\)

=>    \(a = 88200-0.20b\)

Generally the direct cost of services can be mathematically represented as

       \(SV  = b + 0.10a \)

=>     \(29400  =  b + 0.10a\)  

substituting for a  in the above equation

=>     \(29400  =  b + 0.10 [88200-0.20b]\)      

=>    \(b  =  \$ 21,000\)  

substituting this value into the equation for a

     \(a = 88200-0.20 (21000)\)

=>  \(a =   \$ 84000\)

The solution to the inequality expression is -8/9 ≤ x ≥ 4/9

From the question, we have the following parameters that can be used in our computation:

|3x + 6/9| ≥ 2

Expand the inequality expression

So, we have

-2 ≤ 3x + 6/9 ≥ 2

Subtract 6/9 from both sides

So, we have

-24/9 ≤ 3x ≥ 12/9

Divide through the equation by 3

-8/9 ≤ x ≥ 4/9

Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9

The graph is attached

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Answer:

The best buy is the 16-ounce drink

Step-by-step explanation:

here, we see that,

12 ounce = 3/4 (16 ounce)

So, the price should reflect that,

i.e,

price of 12 ounce drink = 3/4 (price of 16 ounce drink)

By this metric,

Price of 12 ounce drink = 3/4 ( 1.19)

Price of 12 ounce drink = $0.8925

So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,

So, it is more expensive than it should be,

So, the best buy is the 16-ounce drink

Matt takes 157 seconds to run 1 lap.

Ratio basically compares quantities, that means it shows value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Time taken to run 8 laps = 1,256 seconds

To find time taken to run 1 lap, use the ratio property,

8 laps = 1256 seconds

1 lap = 1256/8 seconds

1 lap =  157 seconds

Matt takes 157 seconds to run 1 lap.

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Answer:

1. This is an observational study.

2. The explanatory variable is A. red meat consumption

3. The response variable is B. Whether or not a subject dies.

Step-by-step explanation:

1. An observational study is a type of study where the researcher would observe the effects and he would also make no attempt to change the outcome

2. The explanatory variable is also called the independent variable and in this case it is red meat consumption because it is what would be used to predict the dependent variable

3. The response variable is known as the dependent variable it is our variable of interest. It is what the researcher is trying to find out. In this case the answer is whether or not the subject dies

Answers:

==========================================

Explanations:

Answer:

multiply the length value by 3

so its 3 foot

Answer:

the parabola opens down

Step-by-step explanation:

The quadratic equation is

ax^2 + bx + c

When a < 0 the parabola opens down

          a > 0 it opens up

since a  = -2 the parabola opens down

Answer:

x=5/8

Step-by-step explanation:

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

8+2x-2 = 5

2x+6 =5

2x = -1

Step-by-step explanation:

8+2(x-1)=5

Distribute

8+2x-2 = 5

Combine like terms

2x+6 =5

Subtract 6

2x+6-6=5-6

2x = -1

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.

Subjects are the different sets of information which is studied.

9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.

The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.

Thus, the correct option is C, 9th graders in her school.

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Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.

To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.

For Brett:

APR = 12.6%

MPR = 12.6% / 12 = 1.05%

For Andy:

APR = 16.2%

MPR = 16.2% / 12 = 1.35%

Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.

For Brett:

Finance charge = $7,980 * 1.05% = $83.79

For Andy:

Finance charge = $7,980 * 1.35% = $107.73

To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:

Difference = $107.73 - $83.79 = $23.94

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The ratio shows how many times one value is contained in another value.

The number of top dogs is 192.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of top dogs to fat cats was 24 to 19.

if they were 152 fat cats.

This means,

Number of top dogs = 24x

Number of fat cats = 19x

Now,

Number of fat cats = 152

This means,

152 = 19x

x = 8

Now,

Number of top dogs = 24x

= 24x

= 24 x 8

= 192

Thus,

The number of top dogs is 192.

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Answer:

21.161

Step-by-step explanation:

use Pythagoras theorem ti find your slant height

then you use your formula which

\(1 \3\pi {r }^{2} h\)

estimated Volume of tennis ball by given data = 38.808 .

estimated Volume of golf ball by given data = 33.523 .

In terms of geometry, a sphere is described as a collection of points that are spaced apart by a specific amount. The supplied point is referred to as the sphere's center, and the given distance from the sphere's center to the collection of points that make up the sphere is referred to as the sphere's radius.

Many everyday things, including balls and globes, are spheres. Finding a sphere's radius and entering it into the straightforward formula V = \(\frac{4}{3}\)π \(r^{3}\) will allow you to determine its volume.

Given: The radius of the tennis ball is 2.1cm and the radius of the golf ball is 2.0cm. the formula is V=4πr(to the 3rd power) /3 .

To find: Volume of tennis ball and golf ball .

Formula used: V = \(\frac{4}{3}\)π \(r^{3}\) .

pi(π) =\(\frac{22}{7}\) .

We are given that

Radius of the tennis ball = 2.1 cm

radius  of the golf ball =2.0 cm.

We need to find the volume of each ball

So , plugging the given values of radius in above formula

Volume of the tennis = \(\frac{4 * 22 * (2.1)^{3} }{3 * 7}\) = 38.808 \(cm^{3}\)

On simplification we get, volume of tennis ball = 38.808 \(cm^{3}\)

Volume of the golf ball= \(\frac{4 * 22 * (2.0)^{3} }{ 3*7}\) = 33.523\(cm^{3}\)

On simplification we get, volume of golf ball = 33.523\(cm^{3}\)

∴ The volume of tennis ball = 38.808\(cm^{3}\)

Volume of golf ball = 33.523\(cm^{3}\)

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\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

Step-by-step explanation:

Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Asymptotes f(x)=(2x^2)/(x^2-1)

f

(

x

)

=

2

x

2

x

2

−

1

Find where the expression

2

x

2

x

2

−

1

is undefined.

x

=

−

1

,

x

=

1

The vertical asymptotes occur at areas of infinite discontinuity.

x

=

−

1

,

1

Consider the rational function

R

(

x

)

=

a

x

n

b

x

m

where

n

is the degree of the numerator and

m

is the degree of the denominator.

1. If

n

<

m

, then the x-axis,

y

=

0

, is the horizontal asymptote.

2. If

n

=

m

, then the horizontal asymptote is the line

y

=

a

b

.

3. If

n

>

m

, then there is no horizontal asymptote (there is an oblique asymptote).

Find

n

and

m

.

n

=

2

m

=

2

Since

n

=

m

, the horizontal asymptote is the line

y

=

a

b

where

a

=

2

and

b

=

1

.

y

=

2

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

x

=

−

1

,

1

Horizontal Asymptotes:

y

=

2

No Oblique Asymptotes

Answer:

The difference between 77 and 38 is 39. According to this paragraph it is better to study topics mixed together

Step-by-step explanation:

Answer: sorry no

Step-by-step explanation: sorry i dont want to explain it.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

From the question, we have the following parameters that can be used in our computation:

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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Therefore , the solution of the given problem of triangle comes out to be perimeter is 11.8v + 5.7w - 0.9 centimetres.

Because a triangular has two or more additional sections, it is a polygon. Its form is a simple rectangular one. A triangle is a rectangle with only edges A, B, and C. A single plane as opposed to a cube is produced by Euclidean geometry when the sides aren't perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here,

The total length of the edges makes up a triangle's perimeter. Consequently, the following formula is the triangle's perimeter:

=> (4.9v - 2.4) centimetre + (5.7w + 7.2) cm + (6.9v - 5.7) cm

We can condense this statement by combining similar terms:

=>  6.9v+4.9v+5.7w-5.7-2.4+7.2cm=11.8v+5.7-0.9cm

As a result, the triangle's perimeter is 11.8v + 5.7w - 0.9 centimetres.

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Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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