Kelly is reading a 1056-page book. During the past 8 days she has read 384 pages. At this rate, how many more days will it take her to complete the book?

Answer:

D

Step-by-step explanation:

∠ PAR is an angle at the centre of the circle subtended by the arc PR

The central angle is equal to the arc that subtends it, thus

∠ PAR = arc PH + arc HR = 80° + 45° = 125° → D

Area of the shaded region is 540 – 65.25π.    

Solution:

Length of the rectangle = 12 + 9 + 6 + 3 = 30 in

Width of the rectangle = 18 in

Radius of the larger circle ([tex]r_1[/tex]) = 12 ÷ 2 = 6 in

Radius of the medium circle ([tex]r_2[/tex]) = 9 ÷ 2 = 4.5 in

Radius of the smaller circle ([tex]r_3[/tex]) = 6 ÷ 2 = 3 in

Area of the shaded region = Area of the rectangle – Area of the larger circle – Area of the medium circle – Area of the smaller circle

                                   [tex]=l\times b-\pi r_1^2-\pi r_2^2-\pi r_3^2[/tex]

                                   [tex]=30\times 18-\pi \times 6^2-\pi \times (4.5)^2-\pi \times 3^2[/tex]

                                   [tex]=540-36\pi-20.25\pi-9\pi[/tex]

                                   [tex]=540-65.25\pi[/tex]

Area of the shaded region is 540 – 65.25π.    

The area of shaded region is,  [tex][540-\pi(65.25)] inch^{2}[/tex]

From given figure, it is observed that unshaded region is sum of  area of three circles.

Diameter of first circle = 12 inch ,  radius = 12/2 = 6 inch

Diameter of second circle = 9 inch ,  radius = 9/2 = 4.5 inch

Diameter of third circle = 6 inch , radius = 6/2 = 3 inch

Area of circle = [tex]\pi r^{2}[/tex] , where r is radius of circle.

Dimension of rectangle is,

 length = 12 + 9 + 6 +3 = 30 inch

width = 18 inch

Shaded area = Area of rectangle  - sum of area of three circles.

                     [tex]=(18*30)-\pi(6^{2} +4.5^{2} +3^{2} )[/tex]

                     [tex]=540-\pi(36+20.25+9)\\\\=540-\pi(65.25)[/tex]

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Suppose the square Lena draws has the following dimensions:

[tex]Side=L \\ \\ A_{s}:Area \\ \\ \\ A_{s}=L^2[/tex]

For the rectangle we have:

[tex]Base=L_{1} \\ \\ Height=L_{2} \\ \\ \\ A_{r}=L_{1}L_{2}[/tex]

Possibility 1. In order for the area of the square to be greater than the area of the rectangle, the following inequality must be true:

[tex]\boxed{\frac{L^2}{L_{1}L_{2}}>1}[/tex]

Possibility 2. If one side of the rectangle equals the side of the square, that is:

[tex]L_{1}=L[/tex]

Then, in order for the area of the square to be greater than the area of the rectangle, the following inequality must be true:

[tex]\frac{L^2}{LL_{2}}>1 \\ \\ \boxed{\frac{L}{L2}>1}[/tex]

The side lengths for Lena's square, with an area greater than rectangle B, must exceed the side lengths of rectangle B if square, or the square root of its area if not. Thus, any side length [tex]\( s \)[/tex] for Lena's square must satisfy [tex]\( s > \sqrt{A_B} \)[/tex], where [tex]\sqrt{A_B}[/tex] is area of rectangle.

Given that the area of the square is greater than the area of rectangle B, we can write the inequality:

[tex]\[ s^2 > l \times w \][/tex]

To find two possible side lengths for the square, we need to find values of [tex]\( s \)[/tex] that satisfy this inequality.

Since we do not have specific values for [tex]\( l \)[/tex] and [tex]\( w \)[/tex], we can consider a few scenarios:

1. If rectangle B is a square itself, then [tex]\( l = w \)[/tex], and the area of rectangle B would be [tex]\( l^2 \)[/tex]. For the square drawn by Lena to have a greater area, the side length [tex]\( s \)[/tex] must be greater than [tex]\( l \)[/tex]. So, any value of [tex]\( s \)[/tex] greater than [tex]\( l \)[/tex] would be a possible side length for Lena's square.

2. If rectangle B is not a square, then [tex]\( l \neq w \)[/tex]. Without loss of generality, let's assume [tex]\( l > w \)[/tex]. To ensure that [tex]\( s^2 > l \times w \)[/tex], [tex]\( s \)[/tex] must be greater than the square root of [tex]\( l \times w \)[/tex].

The solution to the system of equations is (7, 13/3).

We have Equations,

y= 1/3x + 2,

y= 4/3 x - 5

Solving above two equations we get

1/3 x + 2 = 4/ 3 x - 5

1/3 x - 4/3 x = -5 - 2

-3/3 x = -7

-x = -7

x = 7

and, y = 4/3(7) - 5 = 28/3-5 = 13/3

Thus, the solution of equation is (7, 13/3).

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Answer:

6,440.5

Step-by-step explanation:

So the car starts at 16,200. For the first part of the equation it's 16,200 × x raised to the y. X in this equation would be 1-.1425 = 0.8575. 16,200×(.8575)^y. Y is the number of years after you purchased the car. So, 16,200×(.8575)^6 and that equals 6,440.5

Answer:

$6440.5

Step-by-step explanation:

I hope this helps!

Length of the rectangle is 8m and width is 6m

Step-by-step explanation:

48 = x (x - 2)

48 = x² - 2x

x² - 2x - 48 = 0

x² - 8x + 6x - 48 = 0

x(x - 8) + 6(x - 8) = 0

(x + 6)(x - 8) = 0

x = -6, 8 (neglecting the negative value)

∴ Length of the rectangle = 8m

∴ Width of the rectangle = 8 - 2 = 6m

Answer:

$2

Step-by-step explanation:

$30 ÷ 15 pounds

30 ÷ 15 = 2

Answer: $2 per pound

The unit price of apple per pound is $2.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Given, Honeycrisp apples are on sale if you buy a crate, 15 pounds for $30.

To find the unit price,

we divide the total cost to total pound of a crate.

unit price of an apple

= $30 / 15

= $2

Therefore, the unit price of an apple per pound is $2.

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Equivalent expression for x + x + x + x + x is 5x and that of 18y - 12 are 6·3y - 6·2 and 6(3y - 2)

Step-by-step explanation:

Equivalent expressions are 6·3y - 6·2 and 6(3y - 2)

Answer:

$2.16

Step-by-step explanation:

7.56 ÷ 7 = 1.08

1.08 × 2 = 2.16

Answer:

$2.16

Step-by-step explanation:

7 oranges -----> costs $7.56

Find the unit rate (i.e the cost of 1 orange)

Unit rate ---> cost of 1 orange =  $7.56/7 =  $1.08

Cost of 2 oranges

= unit rate x 2 oranges

= $1.08 x 2

= $2.16

1. Recall the vertical line equation.

2. Plug in the x that we know.

3. Write down the final equation

Pls mark me brainiest :)

Answer:

x= 12

Step-by-step explanation:

Please see attached picture for full solution.

Answer: THIRD OPTION.

Step-by-step explanation:

For this case it is important to know that  by definition, there are three possible cases for the solution of a System of equations. These are shown below:

 1. If the lines intersect each other, then the System of equations has ONE SOLUTION.

2. If the lines are parallel, then the System of equations has NO SOLUTION.

3. If the two equations are the same line, then the System of equations has INFINITELY MANY SOLUTIONS.

Observe the graphs attached in the exercise.

You can notice in the third graph that the "line a" and the "line b" are exactly the same line.

Therefore, based on the explained before, you can conclude that the third graph given in the exercise contains a System of equations with Infinitely many solutions.

Answer:

Choice 3

Step-by-step explanation:

First of all, I got 100% on EDGE. Secondly, to lines that coincide and go in the same direction have infinitely many solutions. Finally, it is correct on EDGE 2020

In isosceles triangle ABC with AB=AC=4, and AH=3HC, the length of BC is [tex]\( \frac{4\sqrt{5}}{5} \)[/tex] units, determined using the Pythagorean Theorem and the given relationship between AH and HC.

In isosceles triangle ABC, let BH be the altitude from B to side AC. Given AB = AC = 4 and AH = [tex]3 \cdot[/tex] HC, we can use the Pythagorean Theorem in right triangle ABH:

[tex]\[ BH^2 + AH^2 = AB^2 \][/tex]

Substitute the given values:

[tex]\[ BH^2 + (3HC)^2 = 4^2 \][/tex]

Simplify:

[tex]\[ BH^2 + 9HC^2 = 16 \][/tex]

Since BH = HC in an isosceles triangle, substitute BH with HC:

[tex]\[ HC^2 + 9HC^2 = 16 \][/tex]

Combine like terms:

[tex]\[ 10HC^2 = 16 \][/tex]

Solve for HC :

[tex]\[ HC^2 = \frac{8}{5} \][/tex]

Now, use the Pythagorean Theorem in right triangle BHC:

[tex]\[ BC^2 = BH^2 + HC^2 \][/tex]

Substitute the known values:

[tex]\[ BC^2 = HC^2 + HC^2 \]\[ BC^2 = 2HC^2 \]\[ BC^2 = 2 \cdot \frac{8}{5} \]\[ BC^2 = \frac{16}{5} \][/tex]

Therefore, BC is the square root of [tex]\( \frac{16}{5} \)[/tex], which simplifies to [tex]\( \frac{4}{\sqrt{5}} \)[/tex] or [tex]\( \frac{4\sqrt{5}}{5} \)[/tex].

The length of BC in an isosceles triangle with sides AB=AC=4 and altitude BH, where AH=3(HC), is 2√2 units.

To determine the length of BC in an isosceles triangle ABC with sides AB=AC=4 and altitude BH, where AH=3(HC), we can use the properties of similar triangles and the Pythagorean theorem.

Since the triangle is isosceles, the altitude BH will bisect the base AC at H, creating two right triangles ABH and CBH. We know that AH=3(HC), which can be expressed as AH=3x and HC=x for some value x. Therefore, AC = AH + HC = 3x + x = 4x.

Using the Pythagorean theorem (a² + b² = c²), in triangle ABH, we get:

And in triangle HBC, we have:

Since we want to find BC, we first solve for BH from the first right triangle:

Substitute BH² into the second equation:

To find x, we use AC = 4x = 4, thus x = 1. Substituting x into the equation for BC, we get:

Answer:

63

Step-by-step explanation:

When dividing by a fraction, it is the same a multiplying that fraction but the reciprocal of it.

21 / 1/3 is same as 21 * 3/1

63

Answer:  63

Answer:

The balance after four years is $1129.27

Step-by-step explanation:

The formula for compound interest, including principal sum, is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

∵ $800 is deposited in an account

∴ P = 800

∵ The account pays 9% annual interest

∴ r = 9% = 9 ÷ 100 = 0.09

∵ The interest is compounded annually

∴ n = 1

∵ The time is 4 years

∴ t = 4

- Substitute the values of P, r, n, and t in the formula above

∵ [tex]A=800(1+\frac{0.09}{1})^{(1)(4)}[/tex]

∴ [tex]A=800(1.09)^{4}[/tex]

∴ A = 1129.265

∴ The balance after four years is $1129.27

Answer: the answer is 907.46 in^2 so the answer is the first choice

Step-by-step explanation:

Answer:   x ≤ 3

Step-by-step explanation:

4x ≤ 12

divide each side by 4

x≤3

Answer:

If one number is x, the other is (96 - x)...since if you add those two together, you will get 96..and the product is x(96 - x) = 96x - x^2

Since this is a quadratic function (x to the power of 2), it is a parabola. More specifically, it is a parabola opening downwards, because there is a negative in front of the x squared. Because it downward facing the maximum value of x is going to be where the vertex is. The x value of the vertex can be found by taking the negative of b (which is the number in front of teh x) over a squared (which is the number in front of the x squared which in this case is 1)

So x = -96 / 2(-1) = -96/-2 = 48

Since as we first stated one number is x, the first number is 48

The second number will be 48, because we stated the second number to be 96-x

Therefore 48 times 48 will give you the maximum product 2304.  

Hope This Helps!!!!!!!!!!!!!!

Answer:

3,600

Step-by-step explanation:

x + y = 120

y = 120 - x

Product "P"

P = x × y = x(120-x) = 120x - x²

P = -(x² - 20x)

= -(x² - 2(x)(60) + 60² - 60²)

= -(x - 60)² + 3600

Max value is 3,600

Answer:

X = 29

fyfufubivih8g8hih

Answer: X = 29

X + 61 = 90

x+61−61=90−61

x=29

Answer:

Step-by-step explanation:$40.00 is the original price of denim shirts if they are marked down to $29.99 you subtract $40.00 from $29.99 = $10.01 then you add the difference in price $10.01 x 2 to get the total savings the answer is $20.02

ΔABC and ΔDEF are similar by AAA similarity.

Solution:

Sum of the interior angles = 180°

In triangle ABC,

60° + 60° + m∠C = 180°

120° +m∠C = 180°

Subtract 120° from both sides, we get

m∠C = 60°

In triangle DEF,

60° + 60° + m∠F = 180°

120° +m∠F = 180°

Subtract 120° from both sides, we get

m∠F = 60°

Consider ΔABC and ΔDEF,

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Therefore by AAA similarity ΔABC ≅ ΔDEF.

ΔABC and ΔDEF are similar triangles.

Answer: The answer above is correct.

Answer:

b

Step-by-step explanation:

The flavor most likely to sell best if stocked by the grocery chain is B. Salsa Crisps, as it has the highest probability of purchase at 0.35.

To determine which flavor of potato crisps is most likely to sell best if stocked by the grocery chain, we need to compare the given probabilities.

From these calculations, we can see that Salsa Crisps have the highest probability (0.35) of being bought. Therefore, Salsa Crisps are the most likely to sell best if stocked by the grocery chain.

The correct answer is Salsa Crisps.

Answer:

wf

axStep-by-step explanation:

Answer:

Her ride is about 15.1 miles long.

Step-by-step explanation:

40.03 = 6.75 + 3.20m

33.28 = 3.20m

ISOLATE M

m = 15.1272

m = 15.1

Part a: Domain : [tex]\{2,5,-1,6\}[/tex]

Part b: Range : [tex]\{3,-2\}[/tex]

Part c: The relation is a function

Explanation:

Part a: The domain of the relation is the set of all input values in the relation. In other words, the domain is the set of all x - coordinates of the ordered pairs in the relation.

Hence, from the given relation, the domain is given by

[tex]\{2,5,-1,6\}[/tex]

Therefore, the domain of the given relation is [tex]\{2,5,-1,6\}[/tex]

Part b: The range of the relation is the set of all output values in the relation. In other words, the range is the set of all y - coordinates of the ordered pairs in the relation.

Hence, from the given relation, the range is given by

[tex]\{3,-2\}[/tex]

Therefore, the range of the given relation is [tex]\{3,-2\}[/tex]

Part c: A relation is said to be a function if each element in the input value of the relation is mapped to exactly one element in the output value.

Hence, from the given relation, it is obvious that the each element in the input is mapped to exactly one element in the output value.

Thus, the given relation is a function.

Answer:

10percent

Step-by-step explanation:

I think

Elle experienced a 22.22% decrease in earnings from babysitting, from $45 to $35. This is calculated by finding the difference between the two amounts, dividing by the original amount, and then multiplying by 100 to convert to a percentage.

Elle's decrease in earnings can be calculated using the formula for calculating the percentage decrease, which is [(Original value - New value)/(Original value)] * 100.

In Elle's case, the original value is $45 (the amount she earned last month), and the new value is $35 (the amount she earned this month). So, follow the formula:

So, Elle experienced a 22.22% decrease in her earnings from babysitting.

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Option D:

x = 8

Solution:

Given data:

m∠FGH = 148° , m∠FGL = (x + 12)°  and m∠LGH = (16x)°

To find the value of x:

m∠FGL + m∠LGH = m∠FGH

⇒ (x + 12)°  + (16x)° = 148°

⇒ x° + 12°  + 16x° = 148°

⇒ 17x° + 12° = 148°

Subtract 12° from both sides of the equation.

⇒ 17x° = 136°

Divide by 17 on both sides, we get

⇒ x° = 8°

⇒ x = 8

Option D is the correct answer.

Answer:D

Step-by-step explanation:I did it on usatestprep trust me.

Answer:

since PQ ||BC,

Angle A is common for both triangles angle P = angle B

triangles ABC, APQ are similar,then their corresponding sides are in proportion

AP/PB =AQ/QC

4/8=x/16

x=8

Do you know basic proportionality theorem ? You can solve the problem easily by this.

In short: BPT is if a line is parallel to a side of the triangle which intersects the other sides imto two distinct points, then the line divides those sides in proportion.

In your problem, it's given that the mutual lines are parallel (PQ || BC), so it makes it divide |AP| with |AB| and |AQ| with |AC| proportionally.

|AP| / |AB| = |AQ| / |QC|

4/12 = x/16+x

4(16+x) = 12x

x=8

Hope it helps!

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Answer: 25

Step-by-step explanation:

3² + 4 ² = ?

(3x3) + (4x4) = ?

9 + 16 = 25

Answer:

  25

Step-by-step explanation:

3² +4² = 9 +16 = 25

_____

Your calculator can help you figure this.

_____

25 = 5², which means that the lengths 3, 4, and 5 could be the sides of a right triangle. They are the smallest integer solution to the equation ...

  a² +b² = c²

Answer:

False

Step-by-step explanation:

if it was counter clockwise it be in the 2 and 3 quadrants