translate triangle P using the vector (2 -7)

The coordinates of Z are (2,7).

What is coordinates in math?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

The formula to calculate the midpoint between two points is equal to

[tex]Y = ( \frac{(x_{1} + x_{2}) }{2} , (\frac{y_{1} + y{2} }{2} )[/tex]

we have

X(-10,9),Y(-4,8)

Let

(x2,y2) ----> the coordinates of Z

substitute the values

( -4.8) = ( -10 + x₂ /2 , 9 + y₂/2)

Solve for x2

-4 = ( -10 + x₂/2

-8 = -10 + x₂

x₂ = -8 + 10

x₂ = 2

Solve for y2

8 = (9 + y₂)/2

16 = 9 + y₂

y₂ = 16 - 9

y₂ = 7

therefore, The coordinates of Z are (2,7)

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Answer:

A. $93.28

Step-by-step explanation:

The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get $93.28

The Cookie Shop's profit at the end of January due to the decrease was $12000

An equation is an expression that shows the relationship between two or more numbers and variables.

The Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Hence:

Decrease in profit = 20% of $15000 = 0.2 * 15000 = $3000

Profit at end of January = $15000 - $3000 = $12000

The Cookie Shop's profit at the end of January due to the decrease was $12000

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The given sentence about polygon is true.

A statement is given in the question.

We have to tell whether the statement is true or false.

What is a polygon ?

A polygon is a two-dimensional geometric figure that has a finite number of sides i.e., triangle has three sides.

As per the question ;

The statement given is , "An included side is the side located between two consecutive angles of a polygon."

Let's check whether it is true or false ;

We know that ,

Included side is one which links two angles together.

For example in a right angle triangle ABC ;

Side (base) AC links two angles one a right angle at A and other angle at C.

So ,

We can conclude that the given statement is true i.e., an included side is located between two consecutive angles of a polygon.

Thus , the given statement about polygon is true.

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True, The sequence an = 8, 13, 18, 23, ...is the same as the sequence a₁ = 8,

an = an-1 +5.

An arithmetic sequence is a set of integers which follow a specific pattern. It is an arithmetic sequence if you pick any number in the sequence and subtract it from the preceding one, and the result is always the same or constant.

The common difference, indicated by the letter d, is the constant difference between all pairs of consecutive or succeeding numbers in a sequence. To transition from one phrase to another, we use the common difference. How? To get to the following term, take the current term and add the common difference, and so on. That is how the sequence's terms are formed.

The first equation is as follows: a(sub n) = 8, 13, 18, 23.

The second equation is: a(sub 1)=8; a(sub n)= a(sub n-1)+5

To obtain the second term, enter two into the equation for n 8+5=13. To find the third, enter the second term, 13, into the equation for n 13+5=18.

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The truth value of the statement "If you have a f e v e r, then you are s i c k." can be classified as T because it is true.

The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as Fa l s e.

The definition of a truth value is the a t t r i b u t e of a p r o p o s i t i o n as to whether the p r o position is true or false.

For example, the truth value for "3 is odd" is true, which can be denoted as T. The truth value of "2 + 2 = 5" is false.

Now, it is well known that fever is a symptom of a s i c k n e s s. Thus, if you have f e v e r, then you are classified as being s i c k. Thus;

The truth value of the statement "If you have a fever, then you are s i c k." can be classified as T because it is true.

The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as False

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Answer:

See attached image.

Step-by-step explanation:

Substitute 1,2,3, or 4 for [tex]x[/tex]. Then calculate using the order described by PEMDAS.

Answer:

6 1/3

Step-by-step explanation:

Well 5 goes into 15 3 times because 5 * 3 = 15.

So the answer would be 1/3 for the fraction and 6 1/3 for the answer.

Answer:

6 1/3

Step-by-step explanation:

6 is already in its simplest form.

5/15 = 1/3

^ 5/15 is equivalent to 1/3

Answer:

Between -3 and -2, but closer to -2

Step-by-step explanation:

The square root of 45 is approximately 6.708.

Subtract 9 from that and you get -2.292.

-2.292 is between -3 and -2, but is closer to -2.

The domain of the function that models Salvatore's price scale is;  {x 0 < x < 8}.

The domain of a graph is defined as the set of possible input values of a function.

Now, we are told that he charges $100  for all work that is completed in less than 2 hours and also that he charges $400 for work that takes between 5 and 8 hours.

This means that the number of hours will be less than 2 but cannot be zero but it is less than or equal to 8

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Answer:

12 inches = 1 foot

Step-by-step explanation:

Really?

The quotient of 6/8 divided by 1/4 is 3.

It should be noted that the information is to find the quotient of 6/8 divided by 1/4.

This will be:

= 6/8 ÷ 1/4

= 6/8 × 4/1

= 3

Therefore, the quotient is 3.

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Answer: 0.75

Step-by-step explanation:

Step-by-step explanation:

2x - 11 = 3

2x = 3 + 11

2x = 14 (divide both sides by 2 to get x)

2x/2 = 14/2

x = 7

Answer:      x= neagtive 4

Step-by-step explanation:

Answer:

f(0) = 1

Step-by-step explanation:

f(0) means what is the value of y when x = 0

locate x = 0 on the number line, at the origin, go vertically up to meet the graph at (0, 1 ) , then

f(0) = 1

a. The probability that a first number is 4 is 1/10

b. The probability that the second number is less than 8/10.

c. The probability that there will not be any zero's is 81/100

Given, a number generator produces two digits in a box, each of it is generated randomly from 0 to 9.

a. The probability that the first number is 4 = ?

probability of an event = favourable number of outcomes/ Total number of outcomes.

Total number of outcomes = 10

P(n) = 1/10

b. The probability that the second number is less than 8 = ?

probability of an event = favourable number of outcomes/ Total number of outcomes.

Total number of outcomes = 10

P(n) = 8/10

c. The probability that there are no zero's = ?

since there are two boxes, there is possibility of getting two zero's.

probability of an event = favourable number of outcomes/ Total number of outcomes.

9/10 × 9/10

= 81/100

Hence we get the required results.

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The total fencing material needed for the triangular plot is 537.03 feet.

A trigonometric law: the square of a plane triangle's side equals the sum of the squares of a remaining sides minus double the the product of such sides as well as the cosine of a angle between them.

If the triangle ABC is having the sides a, b and c.

Then, the formula for law of cosine is;

c² = a² + b² - 2abcosC

Now, as per the given question;

The first step is to compute the length of the fence's third side. The following formula can be used to calculate the length of a third side:

c² = a² + b² - 2abcosC

Where a,b and c are the three sides and C is the angle forming between sides a and b.

The sides are a = 160 feet, b = 160 feet.

The angle between the sides a and b is 85 degrees.

Now, estimate for c by substituting all the value in the formula.

c² = 160² + 160² - (2 x 160 x 160)cos85

c² = 51,200 - 51200 x0.087

c = √47104

c = 217.03 feet

Now, the total length of the perimeter = 160 + 160 + 217.03

                                                               = 537.03 feet                

Therefore, the total length of the perimeter of the fencing material is found to be 537.03 feet.

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Answer:

-8

Step-by-step explanation:

8d-3=5+9d

8d-9d=5+3

-d=8

d=-8

Answer:

d = -8

Step-by-step explanation:

Hello!

Solve for d by isolating the variable.

The value of d is -8.

Answer - 9,369 divided 53 = 176.773584906

y = x - 4 is an equation of the line in slope-intercept form passing through points (4 , 0) and (-3 , -7)

An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.

Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.

1. Find the slope of the line using the two given points.

let Point 1(4 , 0) and Point 2(-3 , -7)

slope = m = (y2 - y1) / (x2 -x1)

m = (-7 - 0) / (-3 - 4)

m = -7/-7

m = 1

2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.

y = mx+ b

y = 1x + b

Using Point 1,

0 = 1(4) + b

b = -4

3. Write the equation of the line in slope-intercept form.

y = mx+ b

where m = 1 and b = -4

y = x - 4

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The amount deposited by Shilpi is 8850

The final answer if I have this same question would be 8850

We are to use simple interest to find out the initial amount deposited

The formula for getting Simple Interest is

SI = (P × R ×T) / 100

Thus,

8850= P * 0.06 * 3

8850= 0.18P

P= 8850 * 0.18

P= 1593

Therefore, the amount deposited by Shilpi is 1593

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If the total charge on 8 particles is -56 units and all the particles have the same charge, then the charge on each particle is equal to -7 units.

The charge on each particle can be determined by division.

Division is a part of the basic operations of arithmetic which are four in number, the rest being addition, subtraction, and multiplication. It can be considered the opposite of multiplication and involves separating into equal parts or groups.

The change on each particle can be calculated by dividing the total charge units by the total number of particles. Hence,

charge on each particle = total charge units ÷ total number of particles

charge on each particle = -56 / 8

charge on each particle = -7

Therefore, the charge on each particle is equal to -7 units if all the particles have the same charge.

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Based on the total budget of Mr. Bell for the incentive and the cost of a pizza box, the equation that matches the word problem is 60 ≥ 9.25x

The amount that Mr. Bell will spend at the most is the budget for the incentive of $60.

He will not spend more than this amount but will spend a maximum of it. This amount of $60 is therefore equal to or greater than the cost of the pizzas:

60 ≥ cost of the pizza

The cost of the pizza is:

= Cost per pizza box x number of boxes

= 9 × x

= 9x

The equation is therefore:

60 ≥ 9.25x

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After simplifying the expression we get the answer as ₋3x²/8¹³.

Given the expression is (₋8)³ 6x (1/2)²2x(₋8)⁻¹⁶

expand the powers.

(₋8×₋8×₋8) 6x (1/2 × 1/2)2x × 1/8¹⁶

we get:

(₋512) 6x (1/4) 2x × 1/8¹⁶

(₋8)³ 6x (1/4) × 2x × 1/8¹⁶

cancel 8 from numerator and denominator.

₋6x × 1/4 × 2x × 1/8¹³

divide the numbers.

₋3x² × 1/8¹³

₋3x²/8¹³

Hence we get the simplified answer as ₋3x²/8¹³.

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Required coordinate proof of distance formula between two points in 3 dimension is:

[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]

As given,

Let points  A(x₁, y₁, z₁) and  B(x₂, y₂, z₂) be referred to a system of rectangular axes OX , OY, OZ.

Through the points A and B, we draw planes parallel to rectangular coordinate plane as rectangular parallelepiped with AB as diagonal.

Pythagoras Theorem

[tex]AB^2 = AC^2 + CB^2....(1)[/tex]

[tex]AB^2=CD^2+DB^2...(2)[/tex]

From equation (1) and (2) we have,

[tex]AB^2=AC^2+DB^2+CD^2[/tex]

As coordinates of the points, A and B as known,

[tex]AC =y_{2}-y_{1}, CD = x_{2} -x_{1} and DB= z_{2}-z_{1}[/tex]

Distance formula :

[tex]AB^2=(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2[/tex]

Therefore, required coordinate proof of distance formula between two points in 3 dimension is  ,

[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]

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The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .

The given expression is 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y.

We have x = 2 and y = -2 as per the question.

To evaluate the expression, first we need to simplify the given expression and then we can substitute the given value of  x and y in simplified expression.

The given expression can be simplified as,

   12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y

⇒ 9x - (1/2)y - 3x - (3/4)y

⇒ 6x - ((1/2)+(3/4))y

On taking LCM of coefficient of y, we will get

6x - (5/4)y

Now on substituting x = 2 and y = -2, we get

6(2) - (5/4)(-2)

= 12 + (5/2)

= 29/2 = 14.5

The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .

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$59 increase in her bank account during that week.

Any of the basic arithmetic operations—addition, subtraction, multiplication, division, raising to the power of a whole number, and taking roots (fractional power)—is considered an algebraic operation. These procedures could be applied to numerical data, in which case they are frequently referred to as arithmetic operations. Similar operations can be carried out on variables, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of a set to the same set.

Given that : Sheila made four withdrawals of each from an ATM. . She also made a $156 purchase with her check card. She then deposited her $375 salary.

It's difficult to determine the solution because we don't know how much money she had in her bank account before making 4 withdrawals, thus a like and rating would be really appreciated. We know she took out $40 four times, which is $160. She also used her card to make a $156 purchase, so when we sum the two amounts, we get $316. She then placed a check for $375 into the bank account, therefore we must deduct $316 from that sum to get at $59; but, since we deducted, Given that we end up with $59 rather than the money we wasted at the beginning, the fact that the price is higher than $316 indicates that there has been an increase.

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Answer: 4

Step-by-step explanation: We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.

The value for  x = -2,0,1 , and 4 will be -9, -8, -15/2 and -6 respectively.

For x = -2

The value will be -

(1/2)x-8

(1/2)(-2) - 8

= -9

For x = 0

The value will be -

(1/2)x - 8

(1/2)(0) - 8

= -8

For x = 1

The value will be -

1/2(1) - 8

= -15/2

For x = 4

The value will be -

1/2(4) - 8

= -6

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