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

Answer:

3 18/19

Step-by-step explanation:

7 1/2 ÷ 1 9/10 =

= 15/2 × 10/19

= 150/38

= 75/19

= 3 18/19

Answer:

$972                

36 × 27 = 972                      

Natalie will be paid $656.61 every week in addition to $10505.76 for the summer.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that Natalie works as a playground supervisor for 8 weeks over the summer and makes $15.27 per hour. She works a 40-hour work week, although she usually works 3 hours of overtime.

For a week = ( 40 + 3 ) x 15.27 = $656.61

For a summer = 4 x 4 = 16 weeks

For a summer = 16 x $656.61 = $10505.76

Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.

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The value of x in the equilateral triangle is 10

The equilateral triangle's three characteristics are: Equal on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure. Additionally, each inside angle is identical (60 degrees).

A unique isosceles triangle with three equal sides is called an equilateral triangle. The formulas that we take into account most frequently for a triangle are: Dimensions of an equilateral triangle , the equilateral triangle's circumference, Equilateral triangle's height

An equiangular triangle's area can be calculated using the following formula:

If A=√3a2/4, then ABC's perimeter 3a

where a is the triangle's side length.

In equilateral triangle, the sum of the 3 angles are 180°.then the angle of each side is 60°

From the given data,

(7x-10)°=60°

7x=60+10

7x=70, x=10

Hence the value of x is 10

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Answer:

Step-by-step explanation:

You are asked to identify the real number properties that justify various changes in the way an expression is written.

In general, there are associative, commutative, identity, and inverse properties of addition and multiplication. You can use these properties to simplify and rewrite expressions, and to help perform arithmetic.

This is basically a vocabulary question, to see if you know the names associated with the behaviors these properties describe.

When an operation (such as addition or multiplication) has the commutative property, it means the order of its operands does not matter

  addition: a + b = b + a

  multiplication: a × b = b × a

When an operation has the associative property, it means that grouping of operands does not matter.

  addition: (a + b) + c = a + (b + c)

  multiplication: (ab)c = a(bc)

When an operation is performed using its identity element, the value of the other operand is not changed:

  addition: a + 0 = a

  multiplication: a × 1 = a

When an operation has an inverse, performing the operation with the inverse produces the identity element.

  addition: a + (-a) = 0

  multiplication: a × (1/a) = 1

Note: these last two properties are used to simplify and solve algebraic expressions. They let you "undo" operations done to variables or expressions.

You can match the given expressions to the example expressions shown above. The "multiplication property of zero" is also known as the "zero product rule": a product is zero if and only if a factor is zero.

  [tex]\begin{aligned}d\cdot4=4\cdot d\quad&\text{commutative property, multiplication}\\(2+a)+8=2+(a+8)\quad&\text{associative property, addition}\\m+(-m)=0\quad&\text{additive inverse property}\\0\cdot b=0\quad&\text{multiplication property of 0}\end{aligned}[/tex]

Answer:

.................................................................................................................................

From the given table, the relationship that is an inverse variation is the fourth relationship with (1, -2) and (3, -6).

An inverse variation refers to when the values of x and y move in opposite directions.

For instance, when x increases, y decreases. The decrease will have to be constant however which is why the fourth relationship is an inverse variation.

When x increases by 1, the value of y decreases by 2.

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Considering the circumference of a circle, it is found that Eric has walked 151.68 km.

The missing information is that the lake is a circle of radius 5 miles.

The circumference of a circle of radius r is given by:

C = 2πr.

Hence the circumference in miles of the circle is:

C = 2π x 5 = 10π miles.

This is the length of one lap, hence the length of 3 laps is:

3 x 10π = 30π miles.

In kilometers, the distance is:

30π x 1.60934 = 151.68 km.

Hence Eric has walked 151.68 km.

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Answer:

The least common multiple of 40, 36 and 32 is 1440.

Step-by-step explanation:

Greetings !

The LCM of a, b

Is the smallest positive number that is divisible by both a and b.

prime factorization of 32:

[tex]2.2.2.2.2[/tex]

prime factorization of 40:

[tex]2.2.2.5[/tex]

prime factorization of 36:

[tex]2.2.3.3[/tex]

Compute a number comprised of factors that appear in at least one of the following

32,40,36

[tex] = 2.2.2.2.2.5.3.3[/tex]

Multiply the numbers 2.2.2.2.2.5.3.3 = 1440

[tex] = 1440[/tex]

Hope it helps !!!

Answer:

Grayson's party will cost $516.

Step-by-step explanation:

Start with putting a unit rate for money per person

60/10

Divide by 10

6/1 (6$ per person)

Then multiply by 86 (# of guests attending)

86 x 6 = 516

If a, b, c, and d are four different numbers and the proportion. The given statement is true.

We take one example,

When you split them, they will all equal the same thing.

A = 5 ,B = 20 20 divided by 5 equals 4

C = 28 ,D = 7 28 divided by 7 equals 4

The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.

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Answer:

x=−44

Step-by-step explanation:

Rewrite the equation as

−x11+43=47.−x11+43=47

Move all terms not containing

x

to the right side of the equation.

−x11=4

Multiply both sides of the equation by

−11.−11(−x11)=−11⋅4

Answer:104,500

Step-by-step explanation:

Area = l × w= 475 × 220= 104500 feet2

Answer: A. (g•f)(x)= log(5x) ( 5x + 4)=5x log(5x) + 4log(5x)

Step-by-step explanation:

Hope this helps :)

Answer:

  t - s

------------

  t + s

Step-by-step explanation:

To solve a problem like this you need to flip the denominator and multiply

Step 1: Write the equation

      s

1 - ------

      t

--------------  

        s

1 +  -------

         t

Step 2: Flip it and multiply

      s                 t

1 - ------  ×  1 + -------

      t                 s

Step 3: Multiply Across

      s                 t             -s + t               t - s

1 - ------  ×  1 + -------  =  -------------- or ---------------

      t                 s              t + s               t + s

I hope this helps!

Answer:

h(-4) = 72

Step-by-step explanation:

Given:

h(x) = 5x² +2x

Evaluate the function h(x) = 5x²+2x for x=-4 means to

find h(-4) by substituting x with -4:

h(-4) = 5·(-4)² +2·(-4)

h(-4) = 5·16 -2·4

h(-4) = 5·16 -2·4

h(-4) = 80 -8

h(-4) = 72

The length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.

The perimeter of rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

Let 'x' represent the width of the rectangle.

Plug these values into the equation above.

P = 2( l + w )

94 = 2( (x+5) + x )

94 = 2x + 10 + 2x

94 = 4x + 10

4x = 94 - 10

4x = 84

x = 84/4

x = 21

Hence;

Width of the rectangle = x = 21ft

Length of the rectangle = x+5 = 21+5 = 26ft

Therefore the length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.

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Answer:

y = -1/4x + 7/4

Step-by-step explanation:

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

m = (3 - 0)/(-5 - 7) = 3/(-12) = -1/4

using m = -1/4, y = 0 , x = 7

y = mx + b

0 = -1/4(7) + b

0 = -7/4 + b

b = 7/4

y = -1/4x + 7/4

Answer:

13

Step-by-step explanation:

Hypotenuse is c

so c^2 = a^2 + b^2

c^2 = 5^2 + 12^2

c^2 = 25 + 144 = 169

c^2 = 13^2

c = 13

Answer: 59.5

Step-by-step explanation:

U(t) = 5.1t^2 − 1.7t

U'(t)=2*5.1t-1.7

U'(t)=10.2t-1.7

U'(6)=10.2(6)-1.7

U'(6)=61.2-1.7

U'(6)=59.5

Answer:

24

Step-by-step explanation:

The extrema is halfway between the roots, so for f(x), it has coordinates (1, f(1)) = (1, -4).

For g(x), we can rewrite it as -2(x²-2x-3) = -2(x-3)(x+1). We can see that the extrema has coordinates (1, 8).

Finding the intersection,

[tex](x-3)(x+1)=-2(x-3)(x+1) \\ \\ 3(x-3)(x+1)=0 \\ \\ x=-1, 3 \\ \\ x=-1 \implies f(x)=g(x)=0 \\ \\ x=3 \implies f(x)=g(x)=0[/tex]

So, we need to find the quadrilateral with vertices (1,-4), (1,8), (-1,0), and (3,0).

We observe this is a kite with diagonals of lengths 4 and 12. So, using the formula for the area of a kite, the area is 24.

Length of the missing side. Leave your answer in the simplest radical form b= root of 69 feet

Pythagorean theorem:

Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2

The Pythagorean Theorem is tremendously useful. In many realistic scenarios it is possible to measure a and b with ease, but it is often difficult to measure c. For instance, c might pass through a lake or private property or might be up in the air! We'll do a few example puzzles in class together to show you how this works.

Nonetheless, the Pythagorean Theorem still presents a substantial limitation to utility. Specifically, it requires that the angle between a and b is 90 degrees. If the angle is not 90 degrees, the Pythagorean Theorem doesn't help.

This is where the Law of Cosines comes in. The Law of Cosines allows us to find c even when the angle between a and b is not 90 degrees. Check out this applet which illustrates the relationship between a2 and b2 and c2 that also takes into account the angle C (note the angle is capital C to distinguish it from lower case c, the side opposite angle C) between the legs a and b.

Adjust the blue dots in the triangle on the right right side of the screen to see the relationship. At the outset, when angle C is 90 degrees, a2+b2 is exactly equal to c2. However, when you move any of the three vertices of the triangle, note that the equality is not maintained. The problem is that angle C becomes not 90 degrees.

Now ,

a= 10

c= 13

b=?

a2 + b2 = c2

[tex]10^{2} +b^{2} = 13^{2} \\\\100+ b^{2} = 169\\\\b^{2} = 169-100\\\\b=\sqrt{69}[/tex]

Length of the missing side. Leave your answer in the simplest radical form

b= root of 69 feet

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Answer:

 ≥ 50 sets

Step-by-step explanation:

Mayerlin wants to know how many sets of 8 forks she needs to buy to increase her supply of forks from 223 to at least 623.

The number of additional forks will be the number of sets (s) times 8 forks each. Mayerlin wants at least 623.

  223 +8s ≥ 623 . . . . . . the inequality

Subtract 223:

  8s ≥ 400

  s ≥ 50 . . . . . . divide by 8

Mayerlin could by at least 50 sets of forks to have enough.

Answer:

$6

Step-by-step explanation

$32 is the total(100%)

in order to find what she needs to tip, you have to divide by 5 because 100% / 5=20%

now, to find 20% of 32, you divide 32 by 5.

32 you can just round to 30, so that you can divide it by 5.

30/5=$6

you could've rounded the total up to 35, but 30 was closer, therefore $6 was the closest whole number tip rosita could've left.

hope this helps