The problem number is 2-32. The question is: Graph the rectangle with vertices at (2, 1),(2, 5), (7, 1), and (7, 5)

Sum of APs 2+5+8+........ as far as the 18th term is 495.

Sum of n terms of A.P.

[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex]

where,

[tex]S_{n}[/tex] = sum of n terms of A.P.

a = first term of A.P.

d = Common difference.

Given,

d=5−2=3

a=2

[tex]S_{11}[/tex]=[tex]\frac{18}{2}[/tex][4+(18-1)×3]

=[tex]\frac{18}{2}\\[/tex][4+51]

=[tex]\frac{18}{2}[/tex]×55

=495

An arithmetic progression, or arithmetic sequence, is a sequence of numbers in which the difference between successive members is constant. Here is the AP formula for AP a, a + d, a + 2d, a + 3d, . . . a + (n - 1) d. The formula for finding the nth term is [tex]a_{n}[/tex] = a + (n – 1) × d.

Then the formula for finding the sum of the arithmetic progressions is:[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex] where a = first term in arithmetic progression, n = number of terms in arithmetic progression, and d = total difference.

Learn more about Arithmetic Progression at

https://brainly.com/question/16947807?referrer=searchResults

The sale price of the magazine subscription is $11.55

From the question, the given parameters are:

Subscription = $35

Discount = 67% off

The sale price of the magazine subscription is then calculated as

Sales price = Subscription x (1 - Discount)

Substitute the known values in the above equation

So, we have the following equation

Sales price = 35 x (1 - 67%)

Evaluate the product

Sales price = 11.55

Hence, the sales price is $11.55

Read more about discounts at

https://brainly.com/question/7459025

#SPJ1

All of the translations describes the same inclination for a straight line because the they all have a pitch (slope) of 2/5.

Mathematically, the pitch (slope) of a geometric figure or straight line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the information provided, the pitch (slope) of this line is given by:

Pitch (slope) = Up 2/Right 5 = 2/5

Pitch (slope) = Up 4/Right 10 = 2/5

Pitch (slope) = Down 42/Left 5 = 2/5

Pitch (slope) = Up 1/Right 5/2 = 2/5

Pitch (slope) = Down 2/5/Left 1 = 2/5

Read more on pitch here: brainly.com/question/6781555

#SPJ1

1) The relationship between ∠2 and ∠6 is that they are alternate angles.

2) The relationship between ∠1 and ∠3 is that they are corresponding angles.

Corresponding angles are defined as the angles that are formed in  corresponding corners with the transversal when two parallel lines are intersected by any other line.

Alternate angles are defined as the angles that are formed by the intersection of a transversal and two parallel lines.

This alternate angle could either be interior alternate or exterior alternate.

1) Since we are told that Line 1 is parallel to Line 2, then it means that from definition of alternate angles that ∠2 and ∠6 are alternate angles.

2) Since we are told that Line 1 is parallel to Line 2, then it means that from definition of corresponding angles that ∠1 and ∠3 are corresponding angles.

Read more about Congruent Angles at; https://brainly.com/question/2938476

#SPJ1

Answer:

0%

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 10*9 ways of selecting two biscuits (in order 1,2)

Of these 90 possible orders

2 digestives can be picked in 5*4 ways =20

2 chocolate can be picked in 2*1 ways = 2

2 ginger can be picked in 3*2 ways =6

Digestive then chocolate can be selected 5*2 ways =10

Chocolate then Digestive can be selected 2*5 ways = 10

Digestive then ginger can be selected 5*3 ways ways = 15

Ginger then digestive can be selected 3*5 ways ways = 15

Chocolate then Ginger can be selected 2*3 ways =6

Ginger then chocolate can be selected 3*2 ways = 6

I have done this the ‘long’ way to demonstrate that all 90 possible outcomes are covered. (Double check)

Probability of taking two different is then the total of the last 6 options divided by the total number of options = 2*(10+15+6)/90 = 31/45 = 68.89% (Approx.)

The range of the function  f(x) = |x| − 5 is −5 ≤ y < ∞.

Given the function is  f(x) = |x| − 5

we know the domain is (−∞,∞)

therefore from the domain we calculate the range as:

−5 ≤ y < ∞.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

All real numbers are defined by the function y=|ax+b|. Consequently, the set of all real numbers is the domain of the absolute value function. Every time a number has an absolute value, it has a positive value. The range of an absolute value function with the form y= |ax+b| is hence y R | y 0.

Hence we get the required range if the function.

Learn more about Range and domain here:

brainly.com/question/10197594

#SPJ1

Answer:

hello Your answer is down below

Step-by-step explanation:

The Question given "What is the range of f(x) = |x| − 5?"

The answer choices:

−∞ < y ≤ −5

−5 ≤ y < ∞

0 ≤ y < ∞

5 ≤ y < ∞

So what do we know? hmm: The definition of Function range is: "The set of values of the dependent variable for which a function is defined".

So the range of: [tex]\mathrm{Range\:of\:}\left|x\right|-5\\[/tex]  is f(x) ≥ -5.

Which would mean the Interval Notation                Oh yeah btw the answer is −5 ≤ y < ∞

is [-5, [tex]\:\infty[/tex])

So based of that we can infer the answer is gonna have -5 in it.

As a graph it would look like this

SO from the graph we can see the answer is −5 ≤ y < ∞

On average, the bear's weight change per month was 8.6 pounds.

The average is the mean value in a data set.

We compute the average by adding the data values and dividing by the number of items in the data set.

In this scenario, the average weight loss per month offers an idea of the weight change the bear experienced during the 7¹/₂ months.

The number of months during hibernation = 7¹/₂ or 7.5 months

The total weight loss = 64.5 pounds

The average weight change per month = 8.6 pounds (64.5/7.5)

Thus, we can conclude that, on average, the bear experienced a weight loss of 8.6 pounds per month and reduced by a total of 64.5 pounds in 7¹/₂ months.

Learn more about average at https://brainly.com/question/1136789

#SPJ1

During 7 1/2months of hibernation, a black bear experienced a weight loss of 64.5 pounds.

$7.99 is the constant of proportionality in this relationship.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

Given Data

The cost for 6 months is $47.94.

x = number of months

x = 6

y =  total amount of money they have paid for the subscription

y = 47.94

Constant of proportionality = [tex]\frac{47.94}{6}[/tex]

Constant of proportionality = 7.99

$7.99 is the constant of proportionality in this relationship.

To learn more about proportional relationship, visit:

https://brainly.com/question/18366151

#SPJ9

The value of x is 4 , the correct option is (C)4 .

In the question ,

it is given that AD and BE are diameters , hence they are straight lines .

From the figure shown below , we can see that

∠AOE and ∠BOD are vertically opposite angles ,

the property of vertically opposite angle states that " the vertically opposite angles are equal in measure ."

So,

substituting the values of ∠AOE and ∠BOD from the figure , we get

36x-4 = 92+(11x+4)

36x-11x = 92+4+4

25x = 100

x=4

Therefore , the value of x = 4, the correct option is (C)4 .

Learn more about Angles here

https://brainly.com/question/20293543

#SPJ1

When a scale factor of 1 inch to 6 feet is used, the length is 9 inches.

From the information illustrated, a scale factor of 1 inch to 6 feet is used. In this situation, an object in real life is 55 feet long.

The number of inches that should be in the scale drawing will be:

= Number of feet / Scale used

= 55 / 6

= 9.17 inches

The length that should be in the scale is 9 inches.

Learn more about scale on:

brainly.com/question/25722260

#SPJ1

A scale factor of 1 inch to 6 feet is used. An object in real life is 55 feet long. How many inches long should it be in the scale drawing?

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

By using the method of trigonometry,

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry. The unit circle is the most straight forward way to define the trigonometric functions. Let theta represent an angle that is calculated along a circle's arc counterclockwise from the x-axis.

Given that,

[tex]AD^{2}= AB^{2}- BD^{2}= 13^{2}- 5^{2}= 169-25= 144[/tex]

=>AD=12cm

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

[tex]AC^{2}= AD^{2}+ DC^{2}= 12^{2}+ 16^{2}= 144+ 256= 400[/tex]

=>AC=20cm

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

note: P=perpendicular

B=base

H=hypotenuse

To know more about trigonometry visit:

https://brainly.com/question/22986150

#SPJ9

The equation of the line that contains the point P(-4,6) and has slope 4 is  y=4x+22 .

The equation of line passing through the point (x₁,y₁) with slope (m) is given by the formula

(y-y₁)=m(x-x₁)

In the question ,

it is given that

the required line passes through the point P(-4,6) and has slope 4

So, x₁= -4 , y₁=6 and m = 4

Substituting the values of x₁, y₁ and m in the equation of line formula , we get

y-6=4(x-(-4))

y-6=4(x+4)

y-6=4x+16

y=4x+16+6

y=4x+22

Therefore , the equation of the line that contains the point P(-4,6) and has slope 4 is  y=4x+22 .

Learn more about Equation Of Line here

https://brainly.com/question/15169364

#SPJ1

We will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.

What is integer?

What is fraction?

- [tex]1\frac{2}{3}[/tex]  = _ + (2/3)

we will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.

Learn more about integer

brainly.com/question/15276410

#SPJ13

Answer: Corresponding angles

Step-by-step explanation:

True by the definition of corresponding angles.

Answer:

92 men

Step-by-step explanation:

First, since they give you the total employees, you need to add the ratios together to get a total.

4 + 7 = 11

Next, setup a proportion using men to total employees.

[tex]\frac{4}{11}=\frac{m}{253}[/tex]

The left side is the ratio and the right side is the actual. m will represent the total number of men employed.

Cross multiply then divide.

4 x 253 = 1012

11 x m = 11m

11m = 1012

11m/11 = 1012/11

m = 92

The value of the equation illustrated as 2(x + 3) is 2x + 6.

In Mathematics, an equation simply illustrates the relationship that the variables have. This can be replaced with letters to express the information.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same values.

In this case, it should be noted that the expression for 2(x + 3) will be:

= 2(x + 3)

Open the bracket

= 2x + 6

The value of the expression is 2x + 6.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

We can identify vertical lines by seeing if two points that fall on the line have the same x-coordinate.

If they do, then it is a vertical line.

The slope of vertical lines are always undefined.

We're given the following points:

These points have the same x-coordinate, revealing that this is a vertical line. Therefore, it has an undefined slope.

Undefined

Yes, a triangle that has sides with lengths of 9 feet, 12 feet, and 15 feet is a right-angled triangle

A right-angled triangle can be defined as a type of triangle, having one of its interior angles equivalent to 90 degrees.

The properties of right angled triangles include;

From the information given, we have;

Hypotenuse side = 15 feet

Opposite side = 12 feet

Adjacent side = 9 feet

We can see that the properties of a right-angles triangle submits to the parameters given.

Hence, it is a right-angled triangle

Learn more about right-angled triangle here:

https://brainly.com/question/64787

#SPJ1

Answer:

We will get that the distance is 3.22.

Answer: move the base and exponent to the other side of the fraction line and change the exponent to positive: 1/(24)

There are 10 students in a class, 6 of them wear glasses. If a student is chosen at random from the class, then the probability that they do not wear glass is 2/5

Total number of Students = 10

Students who wear glasses = 6

Students who don't wear glasses = 4

Probability is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

P(E) = (Number of favorable outcomes) ÷ (Total favorable outcomes).

The probability of a student not wearing glasses is,

Probability = Students who don't wear glasses/Total number of Students

Probability = 4/10 i.e., 2/5

Learn more about Probability here:
https://www.cuemath.com/data/probability/

If QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units.

The length of the line QR = 6x

The length of the line RS = 10

The length of the line QS = 5x+13

We know

The length of the line QS = The length of the line QR + The length of the line RS

Substitute the values in the equation

5x+13 = 6x + 10

Move the 6x to the left hand side of the equation and move 13 to the right hand side of the equation

5x-6x = 10-13

Subtract the terms

(5-6)x = 10-13

-1x = -3

x = 3

Then the length of the QS = 5x+13

Substitute the value of x in the equation

The length of the line QS = 5×3+13

= 15+13

= 28 units

Hence, if QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units

Learn more about length of the line here

brainly.com/question/17281779

#SPJ1

The ratio of consonants to vowels is 21:5.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4), while the ratio of oranges to overall fruit is 8:14. (or 4:7).

No. of consonants = 21

No. of vowels = 5

(A) Ratio of consonant to vowels = 21/5 = 21:5

(B) Fraction of vowels = 5/26

To know more about ratios, click on the link

https://brainly.com/question/23036013

#SPJ9

Answer:

9

Step-by-step explanation:

So we'll need to add both angles to make it equal to the total angle. Then we can find X by solving an equation.

(4x + 12) + (12x - 8) = 148

16x + 4 = 148

16x = 144

x = 9

1; basically the therom states that 90 + 36 = 126 = 5n + 1;

126 = 5n + 1;

125 = 5n

25 = n

Answer:

y=-3x-2

Step-by-step explanation:

y=mx+b; adjust b value --> y=-3x-2

There are thing we must already know:

From this, we must know that:

The scientis needs 0.25kilograms. From this we calculate:

Answer:If 104 items were sold and 32 if these are cookies, to get number of brownies sold subtract 32 from 104.  This gives 72 brownies sold.  

A ratio is a fraction.  If we want the ratio of brownies to cookies it would look like

    brownies            72

   ________     =  _____

     cookies             32

This ratio could be reduced by dividing both parts of the fraction by the greatest common factor of 8.

This gives a reduced ratio of     9

                                             _____

                                                4

Step-by-step explanation:

Answer:I think 82 or 56

Step-by-step explanation: