The Singh family ordered a large pizza with a diameter of 16 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.

200.96 square inches
175.84 square inches
100.48 square inches
25.12 square inches

1. The length of the altitude is 15 units.

2. The perimeter of trapezoid ABCD is 132 units.

An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.

The perimeter of a trapezoid is the sum of all its sides.

From the question;

1. To determine AE,

DE = (DG - EF)/ 2

     = (22 - 6)/ 2          (since AB = EF = 6)

     = 8

DE = 8 units

The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;

/hyp/^2 = /opp/^2 + /adj/^2

AD^2 = DE^" + AE^2

17^2 = 8^2 + AE^2

289 = 64 + AE^2

AE^2 = 225

AE = 15

Thus the length of the altitude is 15 units.

2. To determine the perimeter of the trapezoid, we have;

AE = (AD - EF)/ 2

     = (58 - 16)/ 2           (since BC = EF = 16)

     = 21

AE = 21 units

So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;

/hyp/^2 = /opp/^2 + /adj/^2

AB^2 = BE^2 + AE^2

         = 20^2 + 21^2

AB = 841^1/2

AB = 29

Perimeter of the trapezoid = 29 + 16 + 29 + 58

                       = 132 units

Thus, the perimeter of the trapezoid is 132 units.

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On solving the equation n = za the value of a is obtained as a = n/z.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

To solve for a in the equation n = za, isolate a on one side of the equation.

Do this by dividing both sides by z:

n/z = (za) / z

On the right side, the z's cancel out, leaving -

n/z = a

So the solution is -

a = n/z

Therefore, the value of a that satisfies the equation n = za is equal to n divided by z.

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The monthly amortization on the automobile loan, given the loan amount, the period, and the compounding frequency, is ₱ 18, 901.68

The monthly amortization is constant so it will be an annuity. Seeing as we have the loan amount, this means that the present value of an annuity formula can be used to find the monthly amortization.

First, find the period in months:

= 5 x 12 months a year

= 60 months

The interest in months :

= 9 . 5 % / 12 months per year

= 9.5 / 12 %

The monthly amortization is:

= Loan amount / ( Present value interest factor of annuity, 60 periods, 9.5 / 12 %)

= 900, 000 / 47.614827336156

= ₱ 18, 901.68

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Explanation:

The zeros in 0.00798516 are not considered significant because they are not between nonzero values.

If we had something like 1.207, then that zero would be considered significant.

The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.

Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.

Answer: 0.00799

0.00798516 rounded off to three significant figures is 0.00799

hope that helps...

Answer:

A = 38.5 units²

Step-by-step explanation:

the figure has one pair of parallel sides and is therefore a trapezium.

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

b₁ and b₂ are the parallel bases and h the perpendicular height between them.

here h = 7 , b₁ = 5 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 7 × (5 + 6) = 3.5 × 11 = 38.5 units²

If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

The amount earned In a month is 3250.

There are 12 months In a year.

The total month in 10 years = 10× 12 = 120 months

The total amount in the account for 10years = 120×3250 = 390,000

Therefore there will be 390000 in the account at the end of 10th year.

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The figures for this problem are not scale drawings, as the ratios between the equivalent side lengths are different.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Hence, when a figure is a dilation of another figure, the two figures are scale drawings.

For this problem, the ratio between the bases of the rectangles is given as follows:

12/6 = 2.

The ratio between the height of each rectangle is given as follows:

6/2 = 3.

As the ratios are different, the two figures are not scale drawings of one another.

For them to be scale drawings, it would be needed either a ratio of 2 for the heights or a ratio of 3 for the bases.

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Answer:

742

Step-by-step explanation:

6000

-5258

   742

Answer:

2028

Step-by-step explanation:

156 x 13 = 2028

Answer:

(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180

Step-by-step explanation:

A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:

p = 2w + 2l

We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.

We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.

Plugging these values into our equation we get:

p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.

Or in the form of a quadratic equation:

p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162

=

p = 4k^2 - 24k + 180

Hope this helps!

The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.

The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).

Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.

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So the expanded form of the odometer reading 35,467.219 is:

5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000

A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.

5 stands for 5 x 1,000 miles

3 stands for 3 x 100 miles

4 stands for 4 x 10 miles

6 stands for 6 x 1 miles

7 stands for 7 x 1/10 of a mile

2 stands for 2 x 1/100 of a mile

1 stands for 1 x 1/1000 of a mile

9 stands for 9 x 1/10000 of a mile

So the expanded form of the odometer reading 35,467.219 is:

5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000

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Answer:

yes

Step-by-step explanation:

Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).

The mathematical field of trigonometry investigates relationships between triangle sides and angles. Because every straight-sided form may be reduced to a collection of triangles, trigonometry is a fundamental concept in all of geometry. The relationships between trigonometry and other branches of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly intricate.

Here,

[tex]e^{x}[/tex] is a function that increases across all of space  (d[[tex]e^{x}[/tex] ]/dx = [tex]e^{x}[/tex]  which is never negative), it must be that so it must be that [tex]e^{u}[/tex] crosses y=1 just once, or at u = 0. To demonstrate this:

In[tex]e^{sinx}[/tex]= In 1

sin x = 0

And when x = "0, 0", "2", we would have that sin x = 0 in [0, 2"]. In general, we would then have that x = n, where n Z, because of the periodicity of sin (where n is an integer).

Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).

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The total length is 2.077m (2177 cm).

Length is a measurement of size, distance, or duration. It can refer to physical size (length of a field, length of an object, etc.), distance (length of a journey, length of a river, etc.), or duration (length of a movie, length of a school day, etc.). Length can also refer to the duration of time it takes to complete something (length of a task, length of a process, etc.). Length is typically measured in units such as meters, feet, inches, miles, kilometers, and seconds.

The given measurements can be added together to calculate a total length. The addition of 1.8m, 77cm, and 210mm can be expressed in the form of a sum equation. The equation would be 1.8m + 77cm + 210mm = ?.

To solve this equation, the measurements need to be converted to the same unit of measurement. In this case, all measurements can be converted to cm. 1.8m is equal to 1800cm, 77cm is equal to 77cm, and 210mm is equal to 21cm.

Therefore, the sum equation becomes 1800cm + 77cm + 21cm = ?. To find the total length, the numbers can be added together.

The total length is 1977cm. However, since the measurements are expressed in decimals, the answer must also be expressed in decimals. Therefore, the total length is 2.077m (2177 cm).

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The component vectors to a linear combination is given by the equation

A = 20 i^ + 14 j^ - 23 k^

The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by

u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃

An equivalent definition, typically used in physics, is

u ⋅ v = ∣u∣ ∣v∣ cos θ,

where θ is the angle between u and v

Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero

Given data ,

Let the component vectors be represented as A

The value of A is

< 20 , 14 , -23 >   be equation (1)

On simplifying the equation to the linear combination , we get

< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^

So , the linear combination of the vectors is given by the equation ,

A = 20 i^ + 14 j^ - 23 k^

Hence , the equation is 20 i^ + 14 j^ - 23 k^

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On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x)

[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

True

Step-by-step explanation:

First, you need to subtract a then that would make a 0

Answer: true

Step-by-step explanation: c and d are the same, so a+c and a+d will be the same

There is a 2/17 difference between 16/17 and 14/17 as 17 is the shared denominator of both fractions.

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.

Given,

To get the difference between 16/17 and 14/17, discover their common denominator first.

17 is the shared denominator of both fractions.

To solve, multiply the result by the numerator of the fractions, then divide the sum by the common denominator:

16 - 14/17 (16 - 14) = 2/17 is the solution.

Therefore, there is a 2/17 difference between 16/17 and 14/17.

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Need to find the x and y: The Graph asking in question is attached below:

A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.

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Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way

Here,

Given :  complementary angle one of the angle is 35°

=>  x+ 35° = 90°

=> x = 55°

Let y be the supplement of angle x

=> x+ y = 180°

=>55° + y =180°

=>y =125°

Therefore , the solution of the given problem of angle comes out to be

x = 55° and y =125°.

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Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give 1.74 mL

To calculate the appropriate dosage of Neupogen to give to the patient, we need to convert the patient's weight from pounds to kilograms and then use the dosage provided in the order (10 mcg/kg/d IV).

First, we have to convert the patient's weight from pounds to kilograms:

115 pounds = 52.16 kg

Now we can use the dosage provided in the order (10 mcg/kg/d IV) to calculate the appropriate dosage for the patient:

10 mcg/kg/d IV

= 10 mcg/kg/day * 52.16 kg

= 521.6 mcg/day

Then, since the Neupogen is available in a solution of 300 mcg/ml, we can use the following formula to calculate the required volume of solution to give to the patient:

Volume = Dosage / Concentration

= 521.6 mcg / 300 mcg/ml

= 1.74 ml

So, the education order reads 24 hours after bone marrow transfusion, give 1.74 mL of Neupogen at a concentration of 300 mcg/mL IV.

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Answer:

102200

Step-by-step explanation:

564+458= 1022

1 decagram=100 decigram

So multiply the sum by 100

1022*100=102200

Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.

A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages ​​are:

L1, which has exactly one "a" but any number of "bs".

L2, which has an odd number of "as" and an even number of "bs".

L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.

L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".

L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.

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Answer:

S = pi^2 * (8^2 - 10^2)

= pi^2 * (-4)

= -12.57 pi^2

The value of S is approximately -12.57 * pi^2. To express this value to three significant figures, we would round it to -13 * pi^2, which is the same as -12.6 * pi^2. So the final answer is -12.6 * pi^2.

Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

Answer:

The answer would be the second and fourth options.

Step-by-step explanation:

This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!