The area of a rectangle is (4x²-49) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show you work.

Answer:

D

Step-by-step explanation:

Only way you apply Pythagoras is if the triangle is a right triangle. it won't work anyway else

The value of b is given as follows:

b = 18.

Similar triangles are triangles that share these two features presented as follows:

The bisection, represented by the altitude segment in this triangle, divides the triangle into two similar triangles, hence the equivalent side lengths are given as follows:

Then the proportional relationship for these side lengths is given as follows:

b/(28 - b) = 27/15

Applying cross multiplication, the value of b is obtained as follows:

15b = 27(28 - b)

42b = 27 x 28

b = 27 x 28/42

b = 18.

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The side of the small square is equal to the length of the rectangles, which is 16cm.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.


We can calculate the area of the small square by using the formula A = side² where A is the area and side is the length of the side of the square. Thus, A = 16² = 256 cm².

Now, the area of the large square is equal to the area of the small square plus the area of the four rectangles. The area of each rectangle is equal to 16 x 4 = 64 cm² Thus, the total area of the large square is 256 + 4(64) = 512 cm²

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(2, -2) does not make the equation y = -5x - 2 true.

Why it is and what is an equation ?

We can check if the point (2, -2) satisfies the equation y = -5x - 2 by plugging in the values of x and y and seeing if the equation is true:

y = -5x - 2

-2 = -5(2) - 2

-2 = -12

Since -2 is not equal to -12, the equation is not true for the point (2, -2). Therefore, (2, -2) does not make the equation y = -5x - 2 true.

An equation is a mathematical statement that shows that two expressions are equal.

It typically consists of one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

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Answer: 10in

Step-by-step explanation: It's been awhile since I have done a problem like this but what you would do first is LxHxW of coarse. I believe you would multiply 5x2=10 3x10=30 30+10=40 40 divided by 4= 10. I'm sorry if it's wrong like I said it's been awhile.

Answer: The function of graph 2 has a higher rate of change than the function of graph 2

Step-by-step explanation:

The correct answer is (c) x's tens digit. , if x = 693, that  yield  9 is (x / 10) % 10

Here's how we have to evaluate the expression:

Substitute x = 693 into the expression to get:

(693 / 10) % 10

Perform the division first:

693 / 10 = 69 with a remainder of 3.

Substitute the result of the division into the expression:

(69 % 10)

To Evaluate the remainder use the modulo operator (%):

69 % 10 = 9

The result, 9, is the tens digit of 693.

=(x / 10) % 10.

The tens digit of a number refers to the digit in the second place from the right, or the digit that represents the multiple of 10. For example, in the number 365, the tens digit is 6 because it represents 6 tens or 60.

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The simplification of the given expression would be = 6

60 minutes = 1 hour

But 0.1 of 60 minutes simply means the quantity of 60 minutes that is 0.1.

This can be calculated through the multiplication of 0.1 by 60 minutes.

That is;

= 0.1 ×60 = 6.

Therefore, the the quantity of 60 minutes that is 0.1 = 6.

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Answer: Really?

Step-by-step explanation:

Answer:

7:11

Step-by-step explanation:

The ratio is 56:88

We simplify by 8 and get the ratio

7:11

We can't simplify anymore, so the answer is 7:11

The amount invested in AAA - bonds is $5353, amount invested in

A - bonds is $1681 and amount invested in B - bonds is $3369. The solution has been obtained by using matrices.

What are matrices?

The term "matrix of order m by n," sometimes known as "m × n matrix," refers to a rectangular array of m × n numbers (real or complex), organised into m rows and n columns.

Such a range is bounded by [ ] or ( ).

We are given equations as

x + y + z = $10300

0.045x + 0.05y + 0.09z = $620

2y − z = 0

From this, we get the matrix as

[tex]\left[\begin{array}{ccc}1&1&1\\0.045&0.05&0.09\\0&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}10300\\620\\0\end{array}\right][/tex]

This shows that AX = B

X = A⁻¹B

[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] [tex]= \left[\begin{array}{ccc}2.42&-31.57&-0.42\\-0.47&10.52&0.47\\-0.94&21.05&-0.05\end{array}\right][/tex]     [tex]\left[\begin{array}{ccc}10300\\620\\0\end{array}\right][/tex]

On solving this, we get

[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]    [tex]=\left[\begin{array}{ccc}5353\\1681\\3369\end{array}\right][/tex]

Hence, the amount invested in AAA - bonds is $5353, amount invested in A - bonds is $1681 and amount invested in B - bonds is $3369.

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Answer:

Estimate: 22,400

Actual Product: 21,828

Step-by-step explanation:

To estimate the product of 68 and 321 by rounding to the nearest ten, you can round 68 to 70 and round 321 to 320. Then you can find the product of 70 and 320:

70 × 320 = 22,400

This is an estimate of the actual product.

To find the actual product, you can multiply 68 and 321:

68 × 321 = 21,828

Therefore, the estimate is 22,400 and the actual product is 21,828.

Moore's law is an observation made by Gordon Moore, co-founder of Intel Corporation, in 1965. It states that the number of transistors on a microchip doubles approximately every two years, while the cost of the chip is halved. Essentially, this means that computing power increases exponentially over time.

Moore's law is associated with exponential functions because it describes a situation in which a quantity (the number of transistors) grows at a rate proportional to its size, resulting in exponential growth. Exponential functions are often used to model phenomena in science, engineering, and other fields that exhibit this kind of behavior. In the case of Moore's law, the rate of growth is approximately 41% per year, or a doubling every 1.5 to 2 years. The formula for exponential growth is:

Where:

Moore's law can be expressed using this formula as:

Where:

For example, if a microchip had 1,000 transistors in 2000, according to Moore's law it would have 2,000 in 2002, 4,000 in 2004, 8,000 in 2006, and so on. The exponential function describes the growth of the number of transistors over time, and the formula allows us to predict future values based on past observations.

~ Zeph

The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]

Multiply the numerator by the reciprocal of the denominator:

[tex]5(\frac{3}{2} )[/tex]

Multiply [tex]5(\frac{3}{2} )[/tex]:

Combine [tex]5[/tex] and [tex]\frac{3}{2}[/tex]:

[tex]\frac{5⋅3}{2}[/tex]

Multiply [tex]5[/tex] by [tex]3[/tex]:

[tex]\frac{15}{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

[tex]\frac{15}{2}[/tex]

Decimal Form:

[tex]7.5[/tex]

Mixed Number Form:

[tex]{7\frac{1}{2}[/tex]

Hence, The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]

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Answer:

Step-by-step explanation:

66666

Answer: 31.5

Step-by-step explanation:  
6*4=24 (Shaded Rectangle)

3*5=15  15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5

The solutions to the equation f(x) = g(x) to the nearest hundredth are:  x = -8.85, -5.1 and x = 0.6

To find the solutions to the equation f(x) = g(x), we need to solve for x such that:

0.15x³ + 2x² + 7x - 3.3 = 1.5x - 7.3

We can simplify this equation by bringing all the terms to one side:

0.15x³ + 2x² + 5.5x - 4 = 0

To find the solutions to the nearest hundredth, we can use a graphing calculator or software to graph the functions f(x) and g(x) and find their points of intersection.

Using a graphing calculator , we can plot the two functions and find that they intersect at two points;

approximately x = -8.85, -5.1 and x = 0.6

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A) note that the above graph is attached accordingly including at least 5 points and the vertex.

(-4, -3)

(-3, 0)

(-2, 1)

(-1, 2)

(0, 1)

(1, 0)

B) The function f(x) is a reflection of the parent function y=|x| over the vertical axis, shifted one unit to the left and two units up.

C) The domain of f(x) is all real numbers since the absolute value of any real number is always non-negative.

The range of f(x) is from negative infinity up to (but not including) 2, since the highest value f(x) can attain is 2 due to the vertical shift of the function, and it can take on any value less than 2 (down to negative infinity) due to the reflection and vertical stretching of the absolute value function. In interval notation, the range can be expressed as (-∞, 2).

D) The vertex of the function f(x)=-|x+1|+2 is (-1, 2)

A domain is the set of all possible input values for a function. It specifies the range of values over which the function is defined.

Vertex is the point on the graph of a parabolic function that represents either the maximum or minimum value of the function. It is also known as the "turning point" of the function.

A Parent function is basic or "template" function that represents a particular type or family of functions. It can be transformed to create various related functions.

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15/100

1/10+5/100

step1: di LCM si nye denominator si nye 100..emegbe zã denominator la nàtsɔ ama LCM la ..le ema megbe la, èdzinɛ ɖe edzi kple numerator

10+5/100

afɔɖeɖe 2: ƒo xexlẽdzesifianu la nu ƒu

15/100

ale,1/10+4/100 ƒe ƒuƒoƒo nye 15/100

A quadratic equation can be solved by factoring if its coefficients are rational numbers and its discriminant, which is the expression under the square root in the quadratic formula, is a perfect square.

To determine if a quadratic equation can be solved by factoring, you must first ensure that its coefficients are rational numbers, meaning that they can be expressed as a ratio of two integers. Once you have confirmed this, you can calculate the discriminant of the quadratic equation, which is the expression b²-4ac, where a, b, and c are the coefficients of the quadratic equation in standard form.

If the discriminant is a perfect square, then the quadratic equation can be solved by factoring. If the discriminant is not a perfect square, then the quadratic equation cannot be solved by factoring using rational numbers, but may still be solvable using other methods, such as completing the square or the quadratic formula.

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P is located at the point (31/13, 44/13).

How to determine?

Let A and B be two points on a line segment, and let P be the point that divides AB in the ratio 3:10. We can find the coordinates of P as follows:

Suppose that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2). Then the coordinates of P can be found using the following formula:

P = ( (10 * x1 + 3 * x2) / (10 + 3), (10 * y1 + 3 * y2) / (10 + 3) )

In other words, we add 10 parts of x-coordinates of A to 3 parts of x-coordinates of B, and divide by the sum of the parts (10 + 3 = 13) to get the x-coordinate of P. Similarly, we add 10 parts of y-coordinates of A to 3 parts of y-coordinates of B, and divide by the sum of the parts (10 + 3 = 13) to get the y-coordinate of P.

So if we know the coordinates of A and B, we can plug them into the formula above to find the coordinates of P.

For example, suppose that A has coordinates (1, 2) and B has coordinates (7, 8). Then the coordinates of P can be found as follows:

P = ( (10 * 1 + 3 * 7) / (10 + 3), (10 * 2 + 3 * 8) / (10 + 3) )

= ( (10 + 21) / 13, (20 + 24) / 13 )

= (31/13, 44/13)

Therefore, P is located at the point (31/13, 44/13).

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Answer:

0.5735764

Step-by-step explanation:

sin(55°) = √(1-cos²(55°))

Answer:

The answer is 0.5735764

Step-by-step explanation:

sin(55°) = √(1-cos²(55°)

Hope this helped! Have a GOOD DAY!

Answer:

V = [tex]40in^{3}[/tex]

Step-by-step explanation:

V = [tex]\frac{lwh}{3}[/tex]= [tex]\frac{5*4*6}{3}[/tex]= [tex]40in^{3}[/tex]

The required converted value of the temperature Fahrenheit to Celsius for the value 115°F is given by 46.1111°C .  

To convert Fahrenheit to Celsius use the following formula we have:

( F − 32 ) × ( 5 / 9 ) = °C

Substitute the 115 Fahrenheit to convert into Celsius we get,

= ( 115°F − 32 ) × ( 5 / 9 )

= ( 83 )  × ( 5 / 9 )

= ( 415 / 9 )°C

= 46.1111 °C

Therefore, the converted unit of Fahrenheit to Celsius using standard relation between the two is equal to 46.1111°C .

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Answer: Jessica's average clothing budget for the first six months of 2001 was $102.

Explanation: To calculate the average amount of money that Jessica's budget allowed for clothing in the first six months of 2001, we first need to find her monthly budget.

We can do this by dividing her annual salary by 12 (the number of months in a year):

$48,960 / 12 = $4,080 per month

Next, we need to find her clothing budget for one month. We're told that her clothing budget is 5% of her monthly budget, so we can calculate this as follows:

5% of $4,080 = (5/100) x $4,080 = $204

Therefore, Jessica's clothing budget for one month is $204.To find her average clothing budget for the first six months of 2001, we simply need to multiply her monthly clothing budget by the number of months (i.e., 6):

$204 x 6 = $1,224

Finally, we divide this total by the number of months to find the average: $1,224 / 6 = $102

The required value of 112 kilograms into pounds using standard conversion relation is equal to 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )

One kilograms is equal to 2.20462 pounds.

We need to convert 112 kilograms into pounds :

This implies :

⇒ 112 kilograms = ( 112 × 2.20462 ) pounds

⇒ 112 kilograms = ( 246.91744 ) pounds

⇒ 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )

Therefore, the converting value of kilogram to pounds is given by :

112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places ) .

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Answer:

To convert GB to MB multiply the value of a GB by 1000 to get mb.

1gb x 1000 equals 1000 mb

The measure of the angles required are,

Angle A = 58.3deg

Angle B = 121.7deg

If two angles sum up to 180 degrees, they are referred to as supplementary angles. When paired, supplementary angles result in a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this case, Angles 1 and 2 are referred to as "supplements" of one another.

Supplementary angles, by definition, add to to a sum of 180deg.

So what we know is:

Angle B + Angle A = 180deg

Angle B - 63.4deg = Angle A

By substitution:

Angle B + (Angle B - 63.4deg) = 180deg

Using the commutative property of addition, we can re-write the equation as:

(Angle B + Angle B) - 63.4deg = 180deg

We can add 63.4deg to both sides of the equation:

(Angle B + Angle B) - 63.4deg + 63.4deg = 180deg + 63.4deg

By simplifying, that gives us:

2(Angle B) = 243.4deg

Dividing both sides of the equation by 2, we can determine the measure of Angle B:

Angle B = 243.4deg/2 = 121.7deg

Now we have the measure of one of the angles, which we can plug back into our first equation:

Angle B + Angle A = 180deg

121.7deg + Angle A = 180deg

Subtracting 121.7deg from both sides, we get:

Angle A = 180deg - 121.7deg = 58.3deg

There’s your answer:

Angle A = 58.3deg

Angle B = 121.7deg

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Answer: Correct option is B

Step-by-step explanation:  3/6 + 2/6 = 5/6

The conversion of mass unit lbs, 163 lbs to other mass unit kilogram is equals to the 73.93555631 kg.

Kilogram (kg) and pound (lbs) are used to measure the mass of the substance/objects. Kilogram is used for mass in the International System of Units, whereas pound is used in the imperial and US customary systems. To convert lbs to kg, multiply the particular lbs value by 0.45359237 kg. For example, to convert x lbs to kilogram, multiply the x lbs by 0.45359237 kg. So,x lbs = x × 0.45359237 kg

x lbs = 0.45359237x kg, if x = 6

Therefore, 6 lbs is approximately equal to 2.72155422 kg. It is very important skill to convert the lbs to kilograms in mass measurment. Now, we have 163 lbs. We know that one lbs = 0.45359237 kg

Therefore, 163 lbs = 163 x 0.45359237 kg

163 lbs = 73.93555631 kg.

Hence, 163 lbs is equal to 73.93555631 kg.

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