What is the image of the point (4,0) after a rotation of 90 counterclockwise about the origin ?

Answer:

3.5 hours

Step-by-step explanation:

74-32=42

42/12=3.5

Step-by-step explanation:

(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷

(1 + i)² = 1 + 2i - 1 = 2i

((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =

= 128×-1×-1×-1×i = -128i

In a case whereby Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long the lenght of the remaining piece of rope is 9.84 metres.

Distance can be described as the space that exist between two or more point, the concept that willbe used in the question is the concept of distance.

The total distance of the rope is 18 meters long , and she cut 8.16 meters long awya which implies that the remaining lenght of the rope will be ( 18 - 8.16)= 9.84 metres

Learn more about distance here: https://brainly.com/question/4931057

#SPJ1

The factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)

The expression is

16 - [tex](5y-2)^2[/tex]

The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators

The expression is

The expression is

16 - [tex](5y-2)^2[/tex]

We know the identity

[tex](a+b)^2= a^2+2ab+b^2[/tex]

Apply this identity on the expression

= 16 -( [tex]25y^2[/tex]- 20y + 4)

Apply the distributive property

= 16 - [tex]25y^2[/tex]+ 20y - 4

Subtract the like terms

= - [tex]25y^2[/tex]+ 20y + 12

Take common term outside

= -1([tex]25y^2[/tex]- 20y - 12)

Split the middle term and apply factorization

= -1 ([tex]25y^2[/tex]+ 10y -30y - 12)

Take common term outside

= -1 ( 5y(5y+ 2) -6(5y +2)

Take common term outside

= -1(5y+2)(5y-6)

Hence, the factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)

Learn more about factorization here

brainly.com/question/20293447

#SPJ1

Answer:

slope: 6

y-intercept: -4

easy: y = 6x -4

Answer:

5.37/3 = 1.79

Step-by-step explanation:

Given statement,

→ 5.37 divided by 3 equals?

Forming the problem,

→ 5.37/3

Let's solve the problem,

→ 5.37/3

→ (5.37 ÷ 3)

→ 1.79

Hence, the answer is 1.79.

The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,

Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:

0.75 x 1.15 = X

0.8625 = X

0.8625 - 0.1125 = 0.75

Therefore, the amount of fabric that Chloe cut is correct.

To learn more about proportions, click here https://brainly.com/question/870035

#SPJ4

1).  0 + (-3) = = -3 is Additive Inverse

2).2(3-5) = 2(3)3) - 2(5) is Associative Property

3). (-6) + (-7) = (-7) + (-6) is Commutative Property

4).1(-9) = = -9 is Multiplicative Identity

5).(-4) (-1/4) = 1 is Commutative Property

6). 2 (3 x 7) = (2 X 3) x 7 is  Associative Property

7). 10 + (-10) = 0 is Additive Inverse

8). 2(5) 5(2) is Commutative Property

9).1(-1/4)= -1/4 is  Multiplicative Identity

10).  (-3)(4 + 9) = (-3)(4) + (-3)(9) ​ is Distributive Property

What is Additive inverse ?

To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

What is Commutative Property ?

This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution. Division and subtraction do not work interchangeably.

A+B=B+A

What is Multiplicative Identity ?

An element of a set that remains intact after being multiplied by any other element of the set. In the set of real numbers, 1 is a multiplicative identity.

What is  Distributive Property?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

What is  Associative Property?

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

Learn more about Property of opertion on integers click here;

https://brainly.com/question/15273113

#SPJ1

Using proportion, if 94 kilometres is 6 hours, 47 kilometres is 3 hours.

Proportion is a mathematical comparison between two numbers

Proportion says that two ratios (or fractions) are equal.

Therefore, let's solve the proportion.

94 kilometres  = 6 hours

47 kilometres = ?

cross multiply

time = 47 × 6 / 94

time = 282 / 94

time = 3 hours

Therefore, if 94 km is 6 hours, 47 km is 3 hours.

learn more on proportion here: https://brainly.com/question/12181329

#SPJ1

The rounded value of x² = 521/73 is ± 2.67 and already rounded to the nearest hundred.

A perfect square number when taken the square root of it results in an integer.

Numbers that are not perfect squares when taken the square root of it are irrational numbers.

One method of obtaining square roots for perfect squares is prime factorization.

Given, x² = 521/73.

∴ x² = 7.13.

x = ± √7.13.

x = ± 2.67.

learn more about perfect squares here :

https://brainly.com/question/385286

#SPJ1

Matthew will need 222 feet of fabric to make 74 curtains.

According to the question,

We have the following information:

Required length of each curtain = 36 inches

Total number of curtains to be made = 74

Now, the total length of the fabric needed to make 4 curtains can be found by multiplying length of one curtain by total number of curtains.

So, we have the following expression:

36*74

2664 inches

Now, we will convert this into feet:

1 inch = 1/12 foot

2664 inches = 2664/12 feet

2664 inches = 222 feet

Hence, Matthew will need 222 feet of fabric to make 74 curtains.

To know more about feet of fabric here

https://brainly.com/question/17269103

#SPJ4

Answer:

the answer is 1/27

Step-by-step explanation:

so firstly

10/30 has 20 tickets left

3 tickets are winning so

1/27

The new coordinates for point S are (84,24), for a dilation centered around the origin,  

Dk (x,y) = (kx, ky) ,

K is the dilated scale factor that is multiplied by points vertices of a rectangle,

then rectangle QPRS where vertices were,

P = (1,1)

Q = (1,3)

R = (5,2)

S = (7,2)  

To get the dilation of this QPRS to Q'P'R'S' with a scale factor of 12 you have to multiply each and every coordinate of its vertices by 12.  

Q' = (12,12)

P' = (12,36)

R' = (60,24)

S' = (84,24)

Hence, The new coordinates for point S are (84,24)

To know more about dilated scale factor:

https://brainly.com/question/8765466

#SPJ4

Answer:

x=2

y=-4

Step-by-step explanation:

a) we isolate y

18=7x-y

+y.     +y

y+18=7x

-18.  -18

y=7x-18

b) now fill this in

3x+(7x-18)=2

10x-18=2

    +18. +18

10x=20

/10.  /10

x=2

Now fill in X to find y

3(2)+y=2

6+y=2

-6.  -6

y=-4

Hopes this helps

The following equation is not proportional.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

Main Body:

we now that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=y/x  or y= kx.

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

y= 1/(3x+5)

This is the equation of the line in slope intercept form

where

m= 3

b= 5

The given equation not represent a proportional relationship, because the line not pass through the origin

In a proportional relationship the value of b (y-intercept) is equal to zero

Hence , equation is not proportional.

To learn more about equation click on the link below

https://brainly.com/question/25896797

#SPJ9

The 3rd degree equation that is divisible by x, (x − 3), (x+1) is x³ - 2x² - 3x.

A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3. An algebraic statement having variables, constants, and exponents that are whole integers is called a polynomial.

The given factors are x, (x - 3), (x + 1)

To find the 3rd-degree polynomial divisible by x, (x - 3), (x + 1) multiply the three expressions.

First multiply x, (x - 3)

x × (x - 3)

= x × x - 3 × x

= x² - 3x

Now multiply x² - 3x and (x +1)

(x² - 3x) × (x + 1)

= x²(x) - 3x(x) + x²(1)  - 3x(1)

= x³ - 3x² + x² - 3x
= x³ - 2x² - 3x

So, this is the 3rd-degree equation that is divisible by x, (x − 3), (x+1).

To know more about the degree of polynomials, visit:

https://brainly.com/question/3778572

#SPJ13

The equations in quadratic will be:

a) x⁴ – 6x² – 27 = 0

d) 6(2x + 4)² = (2x + 4) + 2

e) 6x⁴ = -x² + 5.

The quadratic equation au² +bu + c=0 can be written as a formula. where u is an algebraic expression. In each of these examples, doubling the exponent of the middle term equals doubling the exponent of the leading term.

The quadratic function f(x) = a(x - h)² + k is said to be in standard form if an is not equal to zero. If an is positive, the graph will open upward; if an is negative, it will open downward. The vertical line x = h is the line of symmetry, and the point is the vertex (h,k)

Learn more about equations on:

https://brainly.com/question/16923993

#SPJ1

Answer:

55 cars

Step-by-step explanation:

x + (x-14) = 96

The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

Read more about compound interest at:

brainly.com/question/2455673

#SPJ1

The division of the fraction 27/22 will result to 1.22 rounded to the nearest hundredth.

To divide the fraction using long division, we first divide the dividend with the divisor, write the whole number result, and then multiply it by the divisor, subtract the result from the dividend to get a new dividend. Repeat the process for the new dividend until you arrive at a remainder of zero, or continue to a given place value.

27/22 = 1 whole number and a remainder of 5

1 × 22 = 22

27 - 22 = 5

drop the value for the tenth digit of 27.00 which is 0 to yeild 50{ new dividend}

50/22 = 2 whole number and a remainder of 6

2 × 22 = 44

50 - 44 = 6

drop the value for the hundredth digit of 27.00 which is 0 to yeild 60{ new dividend}

60/22 = 2 whole number and a remainder of 16

2 × 22 = 44

69 - 44 = 16

we are rounding up to the nearest hundredth, we stop with the quotient of 1.222.

Hence, the fraction 27/22 is equal 1.22 rounded up to the nearest hundredth using the long division process.

Learn more about division here:https://brainly.com/question/1622425

#SPJ1

The name of the function that matches each equation on the blank is,

-|x-7|= h(x)

0.5|x-3|= g(x)

|x-3|-2= f(x)

-5|x-7|=j(x)

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

The name of the function that matches each equation on the blank is,

-|x-7|= h(x)

0.5|x-3|= g(x)

|x-3|-2= f(x)

-5|x-7|=j(x)

To know more about function, visit:

https://brainly.com/question/12976942

#SPJ1

Answer:

The correct answer is 1 pitcher.

Step-by-step explanation:

Oscar sold 2 pitchers of lemon are from his lemonade stand on Friday.

On Saturday, he sold as much lemonade as on Friday.

The number of pitchers of lemon from the lemonade stand which Oscar sold on Saturday is given by × 2 = 1 pitcher.

Thus Oscar sold 1 pitcher on Saturday which is half of the number of pitchers of lemon he could sell on Friday.

Answer:

c

Step-by-step explanation:

There is no proportional relationship between the given equations.

What is proportional relationship?

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".

The given equations are,

7x - 2 = y

y = 2x + 4

y = 5x

y + 1 = 3x

These equations can be written as,

y = 7x - 2

y = 2x + 4

y = 5x

y = 3x - 1

Now consider the following table,

               x          y         y/x

             7           1          1/7

              2          1          1/2

               5          1          1/5

               3          1          1/3      

From above we can see that none of the ratio are equal, all ratios are different.

Hence, none of the given equations having proportional relationship.

To know more about proportional relationship, click on the link

https://brainly.com/question/2143065

#SPJ1

The best line fit go through to represent the data is (3,8) and (5,12)

The correct option is Option c)

What is best fit line?

A straight line that minimises the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

We are given some points we will plot the graph on the points

From that if we plot the line through the point (3,8) and (5,12)

That will leave 2 points above the line and 2 point below the line

Hence it is the best fit line

The correct option is option C)

To learn more about best fit line please refer the following link

https://brainly.com/question/17013321

#SPJ1

From the given set of statements, the conjecture which represent the inductive reasoning are given by :

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

As given in the question,

Inductive reasoning is the conclusion which is based on the process of observed pattern.

Given set of statements represents the inductive reasoning or not:

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

From observing pattern based on Friday dressing we conclude all Fridays are casual days.

Represent inductive reasoning.

b. Given : 3a² = 48

Conjecture : a = 6

Here we cannot observe the process , we have to show the calculation.

Not representing inductive reasoning.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

From observing pattern based on property of rectangle it is concluded that WX = YZ and WZ = XY.

Represent inductive reasoning.

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

From observing pattern based on all donuts property it is concluded that   chocolate donuts is also unhealthy.

Represent inductive reasoning.

Therefore, from the given set of statements, the conjecture which represent the inductive reasoning are given by :

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

Learn more about inductive reasoning here

brainly.com/question/13445962

#SPJ9

The expression 2x + 1 = y and y = 2x + 1 has no solution.

Expression:

The expression means a mathematical statements that have two terms at least that contain variables, numbers, or both connected by the arithmetic operators.

Given,

Here we have the expressions 2x + 1 = y and y = 2x + 1.

Now, we have to find the number of solution for this expression.

When we try to find the solution(s) graphically, you would plot both of the equations as straight lines. The solution(s) lies where the lines intersect.

But here we looking into the given equation both are equal.

And if we plot these on the graph then it will simply present the straight line. And there is no intersection in it.

Which also states that there is no solution for this expression.

To know more about Expression here.

https://brainly.com/question/14083225

#SPJ9

The measure of the exterior angle to ∠G is 138.9°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, In triangle EFG, m∠E = 95.2° and m∠F = 43.7°.

We know the sum of all the interior angles in a triangle is 180°.

We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.

∴ The measure of the exterior angle to m∠G is = m∠E + m∠F.

= 95.2° + 43.7°.

= 138.9°.

learn more about triangles here :

https://brainly.com/question/2773823

#SPJ2

Hercules got 300 cattle from the King for cleaning out his stable

Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.

To find how many cattle Hercules got for his work, we can simply multiply 3000 by 1/10 and get the value.

3000 * 1/10 = 300.

He got 300 cattle for his work.

Learn more on fractions here;

https://brainly.com/question/21967367
#SPJ1

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6.

x=4.25 is the GPA highest 2.5% of the students.

We have to find the GPA of the highest 2.5% of the students.

Mean = μ = 2.9

Standard deviation = σ = 0.6

Finding the z value for corresponding area 0.9750

For 95% confidence interval ,

z = 1.96

For 97.5% confidence interval,

We get z = 2.25

From

Z = ( x - μ ) / σ

For 2.5% of the students

To solve for x

x = Z*σ + μ

x = 2.25*0.6 + 2.9

x = 1.35 + 2.9

x = 4.25   GPA of highest 2.5% of students

Hence the answer is, x=4.25 is the GPA highest 2.5% of the students.

To learn more about distribution click here https://brainly.com/question/4079902

#SPJ4

Answer: 18/20

Step-by-step explanation: