Find the measures of numbered angle.

b. ∠3

Answer:

x = 2

y = 17

Step-by-step explanation:

Rule that applies to this question: Opposite sides of a parallelogram are equal.

Therefore:

x+2 = 4

x = 4 - 2

x = 2

y-5 = 12

y = 12 + 5

y = 17

Luna already had,

→ consumed 900 cal

→ burned 500 cal

She wants to keep her daily calorie,

→ 1,500 cal/day

Calories she have left to consume,

→ 1500 - (900 - 500)

→ 1500 - 400

→ 1100 cal

Therefore, 1,200 cal will cause her to exceed 1,500 cal/day.

9.27  rounded to 2 decimal places is 9.27

The important thing to remember is that you should round 9.270 to two digits or places after the decimal point. As a result, we wish to do rid of the final digit in 9.270. We utilize the following Two Decimal Places Rules to find the answer by removing the final digit in 9.270:

Rule #1 for two decimal places: If the final digit in 9.27 is less than 5, it should be removed.

Two Decimal Places Rule #2: If the second-to-last digit in 9.27 is less than 9 and the previous digit is 5 or greater, the last digit must be removed and one added to the second-to-last digit.

Three Decimal Places Rule #3: If the final digit in a number, such as 9.27, is five or more, the second to last digit is nine, and the third to last digit is less than nine, the last digit is eliminated, the second to last digit is changed to zero, and the third to last digit is increased by one.

Fourth Rule of Two Decimal Places: Add 1 to the value on the left side of the decimal point and change the right side of the decimal point to 00 if the final digit in 9.270 is 5 or more, the next-to-last digit is 9, and the next-to-last digit is 9.

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The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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The two inequalities are:

y = 20x when x ≤ 6  and y = 15x when x > 6

The scenario given here is of a chicken that is being roasted. To solve this problem, we will take y as the time required to roast the chicken and x as the lbs of the chicken. (weight)

Now two different conditions are applied depending upon the lbs of the chicken the taken to roast the chicken will vary,

20min/lb for a chicken weighs as much as 6lb.

y = 20x when x ≤ 6

15 min/lb for a chicken weighs more than 6lb.

y = 15x when x > 6

The above two equations are the two inequalities that represent time needed to roast both the chicken.

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The cost of the pizzas that Christina bought will be $4.30.

From the information, The cost of a large pizza is $0.90 and the cost of a small pizza is $0.70. Christina bought 4 large pizzas and 1 small pizza.

The number of pizzas will be:

= 4 + 1

= 5 pizzas

The cost will be:

= 4($0.90) + 1($0.70)

= $3.60 + $0.70

= $4.30

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The cost of a large pizza is $0.90 and the cost of a small pizza is $0.70. Christina bought 4 large pizzas and 1 small pizza. How much pizza did Christina buy how much did she pay?

The number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.

We are given that:

For Company A:

Fixed cost = $ 110

Variable cost = $ 0.20 per mile

For Company B:

Fixed cost = $ 70

Variables cost = $ 0.40 per mile

Let the number of miles in a day be x.

So, the equation for rental cost for company A will be:

Rental cost = 110 + 0.20 x

The equation for rental cost for company B will be:

rental cost = 70 + 0.40 x

Now, put both rental cost equal.

110 + 0.20 x = 70 + 0.40 x

0.40 x - 0.20 x = 110 - 70

0.20 x = 40

x = 40 / 0.20

x = 200 miles.

Therefore, the number of miles in a day at which the rental costs for Company A and Company B are the same will be 200 miles.

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The recursive formula for sequence 1,4,9,16, . . .  is a(n) = 2 a(n-1) - a(n-2) + 2

The recursive formula of a sequence is a formula that relates the nth term of the sequence with the preceding term(s), (n-1)th, (n-2)th, and so on.

The given sequence is: 1,4,9,16, . . .

So, we must ask ourselves:

How can we get 4 from 1?

How  can we get 9 from 4 and 1?

and so on.

Notice that:

4 = 1 + 3

9 = 4 + 5

16 = 9 + 7

Notice that the differences (3, 5, 7) increase by 2.

Therefore, we can write:

4 = 1 + 3

  = 1 + (1 - 0) + 2

9 = 4 + (4 - 1) + 2       (9 is a(3), and 4 is a(2))

a(3) = a(2) + a(2) - a(1) + 2

       = 2 a(2) - a(1) + 2

16 = 9 + (9 - 4) + 2

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

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

Continue this process, we get:

a(n) = 2 a(n-1) - a(n-2) + 2

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Using integer numbers, we have that:

1. The integer -5 would represent traveling west at -5 miles per hour, while the integer 5 would represent traveling east at 5 miles per hour.

2. The positions are given as follows:

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

For the number line, we have that:

Hence, for item 1, we have that:

The integer -5 would represent traveling west at -5 miles per hour, while the integer 5 would represent traveling east at 5 miles per hour.

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For item b, to find the distance, we apply the proportion, multiplying the velocity by 5, hence the positions would be given by:

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Answer:

She bought 8.625 wings

Step-by-step explanation:

We can use a ratio to solve

3               x

-------   = ----------

8.80        25.30

Using cross products

3 * 25.30 = 8.80x

75.9 = 8.80x

Divide each side by 8.8

75.9/8.8 = 8.8x/8.8

8.625 = x

She bought 8.625 wings

Pseudocode algorithms are used as prototypes of an actual program.

The required pseudocode algorithm is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The pseudocode that prints the first n odd numbers starting from 1 is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The above pseudocodes would print the first n odd numbers starting from 1, given that n is the input

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The value of the expression given as negative one sixth times the quantity 3 minus 15 times the quantity one third squared is 2/9

The expression is given as:

negative one sixth times the quantity 3 minus 15 times the quantity one third squared

Rewrite the above expression properly as

-1/6(3 - 15) * (1/3)^2

Evaluate the square in the above expression

-1/6(3 - 15) * 1/9

Evaluate the difference in the above expression

-1/6 * - 12 * 1/9

Evaluate the product in the above expression

2/9

Hence, the value of the expression given as negative one sixth times the quantity 3 minus 15 times the quantity one third squared is 2/9

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Answer:

The value of the expression given as negative one sixth times the quantity 3 minus 15 times the quantity one third squared is 2/9

According to the question, the given parameters of a triangle Δ IJK is given below:

j = 960 inches, i = 200 inches and ∠I = 68 degree.

As we know, the sum of the angle of a triangle is 180 degree.

Therefore, ∠I + ∠J + ∠K = 180 degree

Substituting above values in the given expression, we get:

∠J + ∠K = 180 - 68 = 112 degree

For isosceles triangle, two sides are equal. Therefore, ∠J = 56 degree

Hence, the calculated value for the ∠J is 56 degree.

What is triangle?

In the geometry of mathematics, the triangle can be defined as a polygon shape which has three edges as well as three vertices. There are three different forms of triangle which are known as scalene, isosceles and equilateral triangle.

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(-4x2-3x+6) + (6x2 - 2x + 1) = 2x2-5x + 7, the opposite of 2x2 + x-7 is -2x2 - X+ 7 and (-4x2+2x-1) - (-2x2 + 3x+6) = -2x-x - 7

1. (-4x2-3x+6) + (6x2 - 2x + 1)

= -4x2+ 6x2- 3x- 2x + 1+ 6

= 2x2- 5x + 7

Thus, adding gives us 2x2- 5x + 7 and thus (-4x2-3x+6) + (6x2 - 2x + 1) will be matched with the 5th equation.

2. opposite of: 2x2 + x-7

The opposite of 2x2 + x-7 can be found if we just reverse the signs of each of the term. This means that + becomes - and - becomes -

Thus the opposite is: -2x2 - X+ 7

Thus, it will be matched with the second option.

3. (-4x2+2x-1) - (-2x2 + 3x+6)

= -4x2+2x-1 + 2x2 - 3x - 6

= -4x2+ 2x2 +2x - 3x - 6-1 = -2x-x - 7

Thus, this equation will be matched with the 1st option.

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The slope of the line that contains the given points R(-2,1) and, S(10,6) is 5/12 .

It is given in the question that the line contains the points R(-2,1) and S(10,6).

We know that:-

The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-

m = (d-b)/(c-a)

Here, we have

m = slope of the line

(a,b) = (-2,1)

(c,d) = (10,6)

Hence, putting the values of (a,b) and (c,d) , we get

Slope of the line that contains the given points R(-2,1) and, S(10,6) is given by:-

(6-1)/(10-(-2)) = 5/12=

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Answer: B

Step-by-step explanation:

The found value are-

A straight line's general equation is y = mx + c, in which m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.

Now, as per the given question;

The general equation of the line is given as;

y = mx + b

Each point (x,y) of the line is moved to the point (x+a, y+b) by the translation:

(x,y) ---> (x+a, y+b)

We find the original line's x and y intercepts:

Put y=0 in general equation of the line

⇒mx+b = 0

⇒x = −b/m

When, x=0

⇒y = m⋅0 + b

⇒ y = b

A, (0,b) and B( -b/m, 0)

We find the translational coordinates of the points A,B:

A(0,b) ---> A′ (0+a,b+b)

A(0,b) ---> A′ (a,2b)

And,

B( -b/m, 0) ----> B'( -b/m + a, 0 + b)

B( -b/m, 0) ----> B'( -b/m + a, b)

To find the equation of the line's translation, we use the points A and B ′:

m' = (2b - b)/[a  - (-b/m +a)]

m' = b/(b/m)

m'  =m

And,

y−yA' = m' (x−xA')

y−2b=m(x−a)

y=mx−am+2b

The translation of the line's x and y intercepts are:

Put x=0

⇒y = m⋅0−am+2b

⇒y = 2b−am

And, put y=0

⇒0 = mx−am+2b

⇒x = a - (2b/m)

Therefore, the equation of the translate line is found to be  y = mx − am + 2b.

And, the value of the y-intercept is found to be 2b−am.

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The inequality  [tex]5.5+37.93d\leq300[/tex] should be used to calculate the number of days.

What is an inequality?

The relationship between two non-equal expressions, denoted by a symbol such as 'not equal to, 'greater than' or 'less than' is known as inequality.

She drives 50 miles and per mile it costs $0.11.

So, for 50 miles, cost = 50 x $0.11 = $5.5

and per day cost = $37.93

Thus, the inequality that must be used to calculate number of days is

  [tex]5.5+37.93d\leq300[/tex]

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The image seen in the compact mirror is not of the same size as seen in the plane mirror. This compact mirror is concave on one side and convex on the other side.

The size of the image as compared to the object is related to the magnification. The size of an object’s image is larger (or smaller) than the object itself by its magnification,  The level of magnification is proportional to the ratio of  and  An image that appears to be double the size of the actual object would have magnification

The radius of curvature of a mirror is twice its focal length.

All distances measured to the right of the origin (along the positive x-axis) are taken as positive while those measured to the left of the origin (along the negative x-axis) are taken as negative.

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3/5w - 1/5w +10 = 4

First, simplify 3/5w - 1/5w

2/5w + 10 = 4

Then, subtract each side by 10

2/5w = -6

Multiply each side by the denominator

2w = -30

Then divide each side by 2

w = -15

Hey there!

(3^2 * 5^4)^3

= (3 * 3 * 5 * 5 * 5 * 5)^3

= (9 * 25 * 25)^3

= (9 * 625)^3

= (5,625)^3

= 5,625 * 5,625 * 5,625

= 31,640,625 * 5,625

= 177,978,515,625

= 3^6 * 5^12

Therefore, your answer should be:

Option C. 3^6 * 5^12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

-5a+8a=-20+10.4

-3a=-10.4a

Answer:[tex]x= \frac{f (x) - 5}{4}[/tex]

Step-by-step explanation:

f(x) = 4x+5

- 5 for both

f(x) - 5  = 4x+5 -5

4x = f (x) - 5

divided 4 for both

(4x)/4 = (f (x) - 5) / 4

[tex]x= \frac{f (x) - 5}{4}[/tex]

Answer:

2x+y

Step-by-step explanation:

They have 2 bags containing "x" counters and 1 containing "y" counters. So 2 multiply the number of x since there are 2 bags + y because y also contains counters we need to add. (I'm pretty sure)

The percent increase from 200 to 460 is 130% increase

The numbers are given as

200 and 460.

460 is greater than 200

So, the percentage is an increment

The percentage increment is then calculated as

Percentage = (Final value - Initial value)/Initial value * 100%

Substitute the known values in the above equation

Percentage = (460 - 200)/200 * 100%

Evaluate the difference

So, we have

Percentage = 260/200 * 100%

Evaluate the quotient

So, we have

Percentage = 1.3 * 100%

Evaluate the product

So, we have

Percentage = 130%

Hence, the percent increase from 200 to 460 is 130% increase

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Answer:

2 6 9 7 4 7 66 46 66 74 89 84 653 88