find the area
9 ft
4.8 ft

Answer:

x=2

Step-by-step explanation:

5x - 7=3

Add 7 to each side

5x -7+7 = 3+7

5x = 10

Divide each side by 5

5x/5 = 10/5

x =2

Answer: 177 months

Step-by-step explanation:

Answer: 177 months

Step-by-step explanation:

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].

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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Answer:

your answer should be 7 1/24

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:

$726.34

Step-by-step explanation:

Convert 8.25% to a decimal

8.25/100=0.0825

Multiply the cost by the decimal

670.98*0.0825=53.35585

Add the tax to the cost of the camera

53.35585+670.98=726.33585

Rounded to the nearest cent: 726.34

So, the total cost of the camera is $726.34

Hope this helps!

Answer:726.34

Step-by-step explanation: You have to multiply 670.98 x .0825 and the answer will be around 55. You take that answer and add it to 670.98. There you have to round to the nearest sent and the answer will be 726.335 rounded to 726.34

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

Answer:

Yes, they are equivalent. Something that is not equivalent is 5(9+10x)

Both expressions simplify to 20 + 4x. Distributing 4 in 4(5+x) yields the same result, confirming their equivalence.

Sure, let's break it down step by step:

1. **Start with the first expression**: (5+5+5+5) + (x+x+x+x)

  - First, simplify the terms inside each set of parentheses:

    = (20) + (4x)

  - Then, add the simplified terms together:

    = 20 + 4x

2. **Proceed to the second expression**: 4(5+x)

  - Apply the distributive property, which states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results:

    = 4 × 5 + 4 × x

  - Multiply each term inside the parentheses by 4:

    = 20 + 4x

3. **Compare the results**:

  Both expressions simplify to 20 + 4x.

In both cases, we ended up with the same simplified expression, 20 + 4x. This confirms that the original expressions are equivalent.

To write another equivalent expression, we can distribute the 4 to both terms inside the parentheses in the expression 4(5+x), which results in 20 + 4x. Therefore, the expression 20 + 4x is equivalent to both (5+5+5+5) + (x+x+x+x) and 4(5+x).

Answer:   x ≤ 3

Step-by-step explanation:

4x ≤ 12

divide each side by 4

x≤3

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:

532m^2

Step-by-step explanation:

Please see the attached pictures for full solution.

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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Answer:

2g + 13

Step-by-step explanation:

Times two plus 13.

Answer:

2g+13

Step-by-step explanation:

Since Greg's score id doubled, you would make it 2g.

More is an addition term, so 13 more signals to adding 13, therefore, your answer is

2g+13

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:

answer is

[12  -4  -2]

[-8  -13  8]

[8  15  18]

Step-by-step explanation:

got it right on e2020

To solve the equation X + U = V, subtract the matrix U from both sides and simplify to find the solution for X. The solution is [12 - 4 - 14; -8 - 13 8; 8 15 18].

To solve the equation X + U = V, we need to isolate X. Here is the step-by-step process:

The solution for X is the matrix [12 - 4 - 14; -8 - 13 8; 8 15 18].

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

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

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: 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

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

Step-by-step explanation:

The distance between the 2 given points is 35 units

Step-by-step explanation:

Step 1 :

Let A be the point  (14, 27) and B be the point  (14, −8).

Distance between any 2 points is obtained by the taking  root of the sum of squares of the difference between the x co ordinates and the y co ordinates and is  given by the formula

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

Where [tex](x_{1} , y_{1}) and (x_{2} , y_{2})[/tex] are the 2 points

Step 2 :

Using the above formula , we get the distance between the 2 given points as

[tex]\sqrt({14-14)^{2} + {((-8)-27)^{2} }[/tex]  = [tex]\sqrt{(-35)^{2} }[/tex]   = 35 units

Step 3 :

Answer:

The required distance of the 2 given points is 35 units

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:

  C. 32 cubic feet

Step-by-step explanation:

The volume of a cylinder can be written in terms of diameter as ...

  V = (π/4)d^2·h

If water fills the 6-foot height to only 4.5 feet, then the volume of water is ...

  V = (π/4)(3 ft)^2(4.5 ft) ≈ 31.81 ft^3

The volume of water in the container is about 32 cubic feet.

Answer: D

The relation represents _y_ as a function of x, because each value of _x_ is associated with a single value of _y_.

Step-by-step explanation:

The relation represents y as a function of x, because each value of x is associated with a single value of y.

We have given

A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1).

A function is a relation that describes that there should be only one output for each input.

Here x is the input value and y is the output value of the functions.

A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1)

for the given relation

The relation represents y as a function of x, because each value of x is associated with a single value of y.

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Answer:

The length and width are

r-11 and r+5

Step-by-step explanation:

The given trinomial is

[tex] {r}^{2} - 6r - 55[/tex]

To factor, we need to split the middle term to get:

[tex]{r}^{2} - 11r + 5r - 55[/tex]

We now factor by grouping to obtain;

[tex]{r}(r- 11) + 5(r - 11)[/tex]

We collect common factors again to get:

[tex](r- 11)(r + 5)[/tex]

Therefore the length and width are

r-11 and r+5

The slope of the line is [tex]m=-\frac{3}{7}[/tex]

Explanation:

The points are [tex](-3,1)[/tex] and [tex](4,-2)[/tex]

We need to find the slope of the line that contains the points [tex](-3,1)[/tex] and [tex](4,-2)[/tex]

The slope of the equation can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the points [tex](-3,1)[/tex] and [tex](4,-2)[/tex] in the slope formula, we have,

[tex]m=\frac{-2-1}{4-(-3)}[/tex]

Simplifying the expression, we have,

[tex]m=\frac{-2-1}{4+3}[/tex]

Adding the terms in both numerator and denominator, we have,

[tex]m=\frac{-3}{7}[/tex]

The slope of the line that contains the points [tex](-3,1)[/tex] and [tex](4,-2)[/tex] is [tex]m=-\frac{3}{7}[/tex]

Thus, the slope of the line is [tex]m=-\frac{3}{7}[/tex]

Without additional information about the relationship between the two circles, it is not possible to definitively determine the area of circle B based on the area of circle A. If the circles are identical, the area of circle B is also 72 pi.

Given the area of the circle with the centre A is 72 pi, we find the radius using the formula for the area of a circle: A = πr². Therefore, the radius of circle A, rA, can be found by rearranging the formula to rA = √(A/π). This gives us a radius of √(72) = 8.48 units. Without further information about the relationship between circle A and circle B, we cannot definitively determine the area of circle B. If the two circles are identical, then the area of circle B would also be 72 pi. However, if the radius or diameter of circle B is different, you would have to use that measurement to calculate the area using the formula A = πr².

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