Frank makes $320 a week. If he works more than 8 hours in a day, he gets paid $10 for each hour of overtime. What did Frank earn if he worked 9 hours on 3 days last week?

Step-by-step explanation:

what is the problem to solve ?

I assume we need to calculate the area of the whole figure ?

in any case, we have a problem :

a rhombus is a tilted square, a special parallelogram, as it has 4 equal sides.

that would mean all 4 sides of that central rhombus are 5 in.

that would make both triangles equilateral triangles (all 3 sides are equally long : 5 in).

but in order for a right-angled triangle to have the Hypotenuse = 5 in and the height (= left leg) = 4 in, that must make the right leg

5² = 4² + leg²

25 = 16 + leg²

9 = leg²

leg = 3 in

and so, the baseline of the large triangle 2×3 = 6 in.

and not 5 in, which must be the top and base line of the rhombus.

so, the whole problem definition is wrong.

the only solution when accepting the given lengths, is that the triangle sides are NOT a straight extension of the rhombus sides.

the triangle side is the Hypotenuse of the smaller internal right-angled triangle

side² = 4² + (5/2)² = 16 + 6.25 = 22.25

side = 4.716990566... in

anyway, the area of each of the large triangles is

baseline×height / 2 = 5×4/2 = 10 in²

we have 2 triangles = 2×10 = 20 in²

the area of the rhombus is

baseline×height = 5×4 = 20 in²

please note that the area of a rhombus is also

diagonal1 × diagonal2 / 2

but that applies only, when we have the lengths of the diagonals. both approaches give the same result, of course.

so, the whole area is

20 + 20 = 40 in²

Answer: y-9 = 17(x+7)

Step-by-step explanation:

We will use the second coordinate point to use in the equation and the first coordinate (-8, -8) to figure out the slope of this line.

Answer:

y-9=17x+119

Step-by-step explanation:

given points (-8,-8) & (-7,9)

let's take (-7,9) as (x1,y1) and (-8,-8) as (x2,y2)  

now for finding out equation through two points, we use

[tex] \frac{x-x_{1} }{x_{1}-x_{2}  } =\frac{y-y_{1} }{y_{1}-y_{2}  } [/tex]

So accordingly, we input the values

[tex] \frac{x-(-7) }{-7-(-8)}  } =\frac{y-9 }{9-(-8)  } [/tex]

[tex] \frac{x+7 }{-7+8}  } =\frac{y-9 }{9+8  } [/tex]

[tex] \frac{x+7 }{1}  } =\frac{y-9 }{17 } [/tex]

[tex] 17(x+7) = y-9 [/tex]

[tex] 17x+119 = y-9 [/tex]

Each pair of angles should be matched with the correct property (theorem) as follows:

e. Vertical Angles: Angles 7 and 6.

a. Alternate Exterior Angles: Angles 1 and 8.

g. Alternate Interior Angles: Angles 4 and 5.

h. Corresponding Angles: Angles 2 and 6.

d. Supplementary Angles: Angles 6 and 8.

Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude such as Angles 1 and 8.

The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent such as Angles 4 and 5.

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The required rotation of the 180° is given by, (X,y) -> (-X,-y), option A is correct and the required translation is given by (x + 6, y - 2), option D is correct.

Given that,
To determine which option shows the rotation of 180°, and translation of right 6 units and down 2 units.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
For the rotation of the 180°, the given coordinate undergoes the change in direction so the required coordinate after 180° rotation is given as (-x, -y).
Now, for the translation of 6 units right we must add x with 6 and for 2 units down we must subtract y by 2, the required translation is given as(x + 6, y -2).

Thus, the required rotation of the 180° is given by, (X,y) -> (-X,-y), and the required translation is given by (x + 6, y - 2).

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THE LENGTH AND WIDTH WILL BE = length: 5.7 yd

width: 1.7 yd.

According to our question-

 w(w +4) = 10

 w² +4w = 10 . . . . . eliminate parentheses

 w² +4w +4 = 14 . . . . . . add the square of half the w-coefficient to complete the square

 (w +2)² = 14 . . . . . . . . . rewrite as a square

 w +2 = √14 . . . . . . . . . take the square root

 2 = -2 +√14 ≈ 1.7 . . . . yards (width)

Then the length is 4 more yards than this, so is ...

 length = 1.7 +4 = 5.7 . . . yards

The length and width are 5.7 and 1.7 yards, respectively.

In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.

HENCE,THE LENGTH AND WIDTH WILL BE = length: 5.7 yd width: 1.7 yd.

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The new price of the car is $25441.

Given that the $26,000 car is on sale for 5% off with 3% tax.

The discount will be:

= 5% × $26000

= $1300

The tax will be:

= 3% × ($26000 - $1300)

= 3% × $24700

= $741

The new price will be:

= Amount - Discount + Tax

= $26000 - $1300 + $741

= $25441

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The value of (CnD)'= {3,5} and the valueof C' U D = { 2,3,5,7}

The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).

if U = { 2,3,4,5,7}

C= { 2,4}

D= { 2,7}

therefore (CnD)= { 2,4,7}

the complement of set (CnD) that is, (CnD)' = {3,5}

complement of set C (C')= { 3,5,7}

Therefore the union of C' and D(C' U D) = { 2,3,5,7}

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Answer:

y = 4 sin(2x/3)

Step-by-step explanation:

The parent function for sine functions is:   y = a sin b(x - c) + d

"a" defines amplitude/vertical dilation

"b" defines the change to the period/horizontal dilation

"c" defines the phase shift/horizontal translation

"d" defines the midline/vertical translation  

We can already set "a = 4" because 4 is the amplitude.

However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.

This means: 2π/b = period

                    2π/period = b

                    2π/3π = b

                    2/3 = b

Knowing the "a" and "b" values, we can set up the equation:

y = 4 sin(2x/3)

No horizontal/vertical translations were applied, so "c" and "d" are both zero.

{3, 4} are the values which make up the solution set of the inequality

2b ≥ 6.

Given, an inequality

2b ≥ 6.

Now, we have to find the solution set of the given inequality,

2b ≥ 6

On dividing both the sides by 2, we get

2b/2 ≥ 6/2

b ≥ 3

So, the solution set of the given inequality, be

the values of b must be greater than or equal to 3.

So, Option (3) i.e. {3 , 4} is the solution set of the inequality.

Hence, {3, 4} are the values which make up the solution set of the inequality 2b ≥ 6.

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The simplified form of the expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] after evaluating is equal to [tex]\sqrt[3]{2}[/tex]

What are Powers?

Steps to Combine and Simplify Exponents

The three basic rules of exponents used to combine the exponents and simplify the expression are as follows:

Here, we have to simplify and evaluate the given expression using the rules of exponents.

We have the given expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex]  -------(4)

Using the exponents rules, [tex](a^{m})^{n} =a^{m \times n}[/tex] and [tex](a \times b)^{m}=a^{m} \times b^{m}[/tex] in the above expression, we get

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3} } \times 3^{\frac{2}{3} } \times 2^{3 \times \frac{1}{3} } }{2^{\frac{2}{3} } \times 2^{\frac{2}{3} } \times 3^{\frac{2}{3} }}[/tex]

Simplifying further using (1) and (2), we get (4) as,

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3}}}{2^{\frac{2}{3}+\frac{2}{3} }} \times \frac{3^{\frac{2}{3} } }{3^{\frac{2}{3} }} \times 2^{1} \\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =\frac{2^{\frac{2}{3}}}{2^{\frac{4}{3} }} \times 2^{\frac{2}{3}-\frac{2}{3} } \times 2\\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{\frac{2}{3}-\frac{4}{3} } \times 2^{0} \times 2[/tex]

We know that, [tex]a^{0} =1[/tex]

So, further simplifying we get

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{-\frac{2}{3} } \times 1 \times 2\\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = 2^{-\frac{2}{3}+1 } \\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=2^{\frac{1}{3}}\\ \imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=\sqrt[3]{2}[/tex]

Therefore, the simplied form of the given expression is [tex]\sqrt[3]{2}[/tex]

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Answer:

136 cm

Step-by-step explanation:

area of rectangle-- width x length--- 112

area of triangle-- base x height divided by 2--- 24

please mark brainiest

Answer: Yes

Step-by-step explanation:   Most month have 4 weeks so your right.

Answer:

value of stock =1.5% × 420?= 6.3

Answer:

ft HD st he do it to we if do ks do just bc

Booker's father amount of commission earned is 668.31 dollars.

Sophia needs to make sells of 16744 dollars in order to earn at least 1800 dollars in commission.

Booker's father sells computer software and earns a 4.25% commission on every software package he sells.

The amount of commission he will earn after selling a software package of $15, 725 can be calculated as follows:

amount of commission earned = 4.25% of 15725

amount of commission earned =  4.25 / 100 × 15725

amount of commission earned = 66831.25 / 100

Therefore,

amount of commission earned = 668.3125

amount of commission earned = 668.31 dollars

Sophia needs to earn at least 1800 dollars each month to cover her living expenses.

The minimum she needs to sell in order to earn at least 1800 dollars if she earns 10.75% commission can be calculated as follows:

let

x = amount she needs to sell

Therefore,

10.75% of x ≥ 1800

10.75 / 100 x ≥  1800

multiply both sides by 100

10.75x ≥ 180000

divide both sides by 10.75

x ≥ 16744.1860465

x ≥ 16744

Therefore, she needs to sell 16744 dollars worth of goods.

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Answer:

No solution.  The lines are parallel

Step-by-step explanation:

I graphed with Desmos.  It is a free.

A 32% mark up means that the price goes up by 32 percent. The way to find this is by finding 132% of $400.

1.32 x 400 = $528.

I hope this helps!

The price of the microscope after the markup of 32% at the store will be equal to $528.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the given data in the question,

Price of microscope = $400

Markup percentage = 32%

Increase in price = 400 × 32/100

= $128.

Price after markup will be,

$400 + $128 = $528.

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Check the picture below.

Answer:

Step-by-step explanation:

Ok:

Area of circle:

A=πr^2

1. Apply to question!

5^2π=

25π/4: Since it is a 1/4 of the circle

6.25π

Answer: 6.25π or 6.25 pie

Answer:

about 19.63496 m^2

Step-by-step explanation:

this is 1/4 of a circle so we find the are of the full circle

pi(r)^2

pi(5)^2

pi25

78.53982

Divide by 4

78.53982/4

19.63496

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The number is 17

Let the number = x

From the question, we have

(x*100)/10*1000 = 170000

x = 17

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

53 1/3

Step-by-step explanation:

[tex]1\frac{2}{3} =\frac{3+2}{3} =\frac{5}{3}[/tex]

[tex](32)(\frac{5}{3} )=\frac{(32)(5)}{3} =\frac{160}{3}[/tex]

[tex]\frac{160}{3} =53 +\frac{1}{3} =53\frac{1}{3}[/tex]

Hope this helps

The value of the expression is [tex]\frac{160}{3}[/tex].

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

[tex]1\frac{2}{3}[/tex] of 32

= [tex]\frac{5}{3}[/tex] x 32

[ 5 x 32 = 160 ]

= [tex]\frac{160}{3}[/tex]

Thus,

The value of the expression is [tex]\frac{160}{3}[/tex].

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The inequality that relates [tex]LN[/tex] and [tex]OQ[/tex] is [tex]LN>OQ[/tex].

Answer:

Step-by-step explanation:

OK:

I won't be able to draw this but if I can I will

1. Find 2/3 of the 12 pieces

2/3*12=

24/3=

8

2. Answer: Shade 8 out of 12 pieces

Answer:

The answer to this problem is 1401.

Step-by-step explanation:

By using the order of operations listed here, we can solve the problem very easily.

EVALUATE IN PARENTHESES [tex]40-9[/tex]: 40 minus 9 is 31, so now the problem is 15(31) x 3 + 6

MULTIPLY/DIVIDE [tex]15(31)*3[/tex]: X times Y can be [tex]X*Y[/tex] or [tex]X (Y)[/tex]. This evaluates to [tex]15*31*3[/tex] which is 1395.

ADD/SUBTRACT: The problem now is just [tex]1395+6[/tex] which evaluates to a total of [tex]1401[/tex].

The hypotenuse of the right triangle is 7.93 inches.

According to the question,

We have the following information:

A right triangle has a leg that measures 7 in. The angle opposite this side measures 62°.

Now, the hypotenuse can be easily found using the trigonometric function.

(More to know: in a right triangle, we can use the Pythagoras theorem. This theorem can not used in any other triangle.)

We will use sin 62 to find hypotenuse.

Sin 62 = perpendicular/hypotenuse

Hypotenuse = perpendicular/sin 62

Hypotenuse = 7/0.88295

Hypotenuse = 7.93 inches

Hence, the hypotenuse of the right triangle is 7.93 inches.

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The graph of the function g(x) after putting the value in function f(x) is attached with the answer.

What is function?

A relation b/w a collection of inputs and outputs is known as a function. A function is a relationship between inputs in which each input is connected to precisely one output.

Given function:  f(x) = x-1

we have to find: g(x)=f(3/4x)

Putting the value of f(x) in g(x),

g(x) = 3/4x - 1

Now, the graph of the function (3/4)x - 1 is attached in the question.

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To find x, you would do 180-36-63, which would be 81.

Then you would do 180-81 to find z, which is 99.

To find y, would do do 180-99-13, which is 68.

Answer:

x=81

y=68

Z=99

Step-by-step explanation:

to find x we have to remember the rule that all 3 angles sum up to be 180 in a triangle

So we use this to find x

180-(63+36)=x

180-99=x

81=x

Now to find z since it is on a flat plane you just subtract 81 from 180 to find z

180-81=z

99=z

Now to find y we add all the angles of the second triangle and then subtract that sum by 180

180-(13+99)=y

180-112=y

68=y

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Answer:

Part A

[tex](x-r)^2+(y-s)^2=t^2[/tex]

where:

Part B

Domain = [-3, 17]

Range = [-14, 6]

Part C

Point (9, 1) is inside the border of the circle.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute these values into the formula to derive the standard equation of the circle:

[tex]\boxed{ (x-r)^2+(y-s)^2=t^2}[/tex]

where:

Given the center of the circle (r, s) is (7, -4) and the radius (t) is 10.

The domain of the circle is the x-value of the center minus and plus the radius:  

[tex]\begin{aligned}\implies \textsf{Domain}&=[r-t,r+t]\\&= [7-10, 7+10] \\&= [-3, 17]\end{aligned}[/tex]

The range of the circle is the y-value of the center minus and plus the radius:

[tex]\begin{aligned}\implies \textsf{Range}&=[s-t,s+t]\\&=[-4-10, -4+10]\\& = [-14, 6]\end{aligned}[/tex]

Substitute (r, s) = (7, –4) and t = 10 into the derived equation from part A:

[tex]\implies (x-r)^2+(y-s)^2=t^2[/tex]

[tex]\implies (x-7)^2+(y-(-4))^2=10^2[/tex]

[tex]\implies (x-7)^2+(y+4)^2=100[/tex]

Substitute the given point (9, 1) into the equation:

[tex]\begin{aligned}\implies (9-7)^2+(1+4)^2&=2^2+5^2\\&=4+25\\&=29\end{aligned}[/tex]

As 29 < 100, the point (9, 1) is inside the border of the circle.