Chapter 15 Questions 4) In the diagram below, ABCD is a rectangle and triangle DEF is formed by joining the midpoints of AB and BC. a) determine the area of rectangle ABCD in terms of x and y, b) If the shaded area of triangle DEF is 15m², determine the value of xy. c) Hence, determine the area of triangle EBF​

Answer

14 notebook computers: 3850$

16 desktop computers: 2400$

Step-by-step explanation:

275x14=3850

150x16=2400

Based on the definition of vertical angles, m<A = 36°.

Two angles that are vertically opposite to each other are called vertical angles, and they have congruent angle measures. That is, vertical angles are equal.

Angles A and B are vertical angles, then, they are equal to each other.

m<A = (7x + 22)°

m<B = (8x + 20)°

m<A = m<B

Substitute

7x + 22 = 8x + 20

7x - 8x = -22 + 20

-x = -2

x = 2

m<A = 7x + 22

Plug in the value of x

m<A = 7(2) + 22

m<A = 14 + 22

m<A = 36°

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Answer:

1. Determine the estimate.: Without solving I'd say 200, but you could try to think of your own estimate.
2. Justify.: 5820 rounds up to 6000, and 28 rounds up to 30. 6000/30 = 200
3. 207.85 (I don't know if your teacher makes you do the new way of rounding up, but if it says round to the nearest dollar I'd do $207.)

Step-by-step explanation:

Then you divide. Sorry I can't show you that!!! But I really hope this helped.

Amount after 2 years is $44.1

Compound interest formula

[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]

A= Amount after t years.

P= Principal amount.  

r= Interest rate (decimal)

n=Period of compounding

t= Time

So ,

[tex]A=40(1+\frac{0.05}{1}) ^{1*2}\\ =40(1.05) ^{2}\\ = 40*1.1025\\ = 44.1[/tex]

Amount after 2 years is $44.1

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Answer:

-43

Step-by-step explanation:

(-3)³ - 4² = -27 - 16 = -43

The expression which is equivalent to the expression given in the task content is; 12x +15x² +8.

It follows from the task content that the expression which is an equivalent of the given expression is to be identified.

Given;

15x² +12x + 8

Hence, by re-arranging the terms of the expression; we have;

12x + 15x² +8.

Ultimately, the required equivalent expression is; 12x + 15x² +8.

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The length of the altitude of the equilateral triangle ABC is [tex]\frac{13\sqrt{3} }{2}[/tex].

Equilateral Triangle is defined as the triangle with all the sides equal and all the angles = 60 deg.

Altitude of a Triangle can be defined as the perpendicular drawn from the vertex of a triangle to the opposite side.

According to the question

In the figure given below

In ΔADC

Since ΔADC is a right angle triangle we can apply Pythagoras Theorem.

Let the sides of the equilateral triangle be "a". and "h" be the altitude.

Since the altitude is of equilateral triangle it divides the base i.e. DC=a/2

[tex](AC)^{2} =(AD)^{2}+(DC)^{2}[/tex]

[tex]a^{2} =h^{2}+(\frac{a}{2})^{2}\\ \\ h^{2}=\frac{4a^{2}-a^{2}}{4} \\ \\ h=\sqrt{3} *\frac{1}{2} *a[/tex]

Substituting the value of a=13 we get

Altitude [tex]h=\frac{13\sqrt{3} }{2}[/tex]

Therefore , The length of the altitude of the equilateral ΔABC is [tex]\frac{13\sqrt{3} }{2}[/tex].

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Answer:

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[tex]Solution(1)Digit 1 to 9Lef $x \rightarrow 1, x^{\prime}$$$\lim _{x \rightarrow 1}=1^{\prime}=1$$$\lim _{\lim ^9}=(1)^9=1$$[9$ ways $]$Similarlyt$$\lim _{x \rightarrow 2} x^{\prime}=2^{\prime}=2$$$\lim _{x \rightarrow 2} x^9=\lim _{x \rightarrow 2} 2^9=512 \quad[9$ ways $]$Total no. of ways $=9 \times 9=81$ ways.Required No, of ways $=81$ Ans[/tex]

This article discusses the idea of limit in general. See Limit of a sequence and Limit of a function for additional detailed situations. See Mathematics (limit) for further usage.

Limits are crucial to calculus and mathematical analysis because they are needed to determine continuity, derivatives, and integrals. Limits are the value that a function (or sequence) approaches when the input (or index) approaches some value.

In addition to being closely connected to limit and direct limit in category theory, the idea of a limit of a sequence is further expanded to include the idea of a limit of a topological net.

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The sum of (3x² + 2x + 3) + (x² + 1) will be 4x² + 2x + 4.

The sum of (3x² + 2x + 3) + (x² + 1) will be calculated by simply adding the values.

This will be:

= (3x² + 2x + 3) + (x² + 1)

= 3x² + x² + 2x + 3 + 1

= 4x² + 2x + 4

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By using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

What do you mean by arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given:

Total no. of students is  [tex]30[/tex]

Number of students taken English is [tex]15[/tex]

Number of students taken English but not French is [tex]10[/tex]

(i) Number of students taken French = Total no. of students -  Number of students taken English but not French

                                                             [tex]= 30-10\\=20[/tex]

(ii)  Number of students taken French not English = Number of students taken French - Number of students taken English

                                                                         [tex]=20-15\\=5[/tex]

Therefore, by using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

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Answer:

By using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

What do you mean by arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given:

Total no. of students is  

Number of students taken English is

Number of students taken English but not French is

(i) Number of students taken French = Total no. of students -  Number of students taken English but not French

(ii)  Number of students taken French not English = Number of students taken French - Number of students taken English

Therefore, by using arithmetic operation, we get  Number of students taken French is 20 and Number of students taken French not English is 5

In linear equation ,Jerry's expression is correct.

What in mathematics is a linear equation?

As you can see, starting with border 1, we have 6 daises (white squares) surrounded by 10 tulips (colored squares). Through Jerry's expression we expected:

= 8(b − 1) + 10

= 8(1 − 1) + 10

= 0 + 10

= 10 tulips.

When considering border 2, we expect:

= 8(b − 1) + 10

= 8(2 − 1) + 10

= 8 + 10

= 18 tulips.

Indeed, we have the 10 tulips from border 1 and 8 additional tulips, for a total of 18 tulips.

Then, consider border 3, we expect:

= 8(b − 1) + 10

= 8(3 − 1) + 10

= 16 + 10

= 26 tulips.

Again, this is correct: we have the 10 tulips used in border 1 plus other 16 tulips, for a total of 26.

Therefore, Jerry's expression is correct.

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Answer:

To make a negative exponent positive you put it over 1

[tex]\frac{2}{a^{5} }[/tex]

Step-by-step explanation:

2[tex]a^{-5}[/tex] = [tex]\frac{2}{a^{5} }[/tex]

The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.

Herein we must find what integers are within the interval of a simultaneous linear inequality, whose definition is shown below:

4 < 4 · x + 5 < 175        

Which is equivalent to the following two inequalities:

4 · x + 5 > 4                     (2)

4 · x + 5 < 175                  (3)

By (2):

4 · x + 5 > 4

4 · x > - 1

x > - 1 / 4

x > - 1

By (3):

4 · x + 5 < 175

4 · x < 170

x < 170 / 4

x < 85 / 2

x < 42.5

x < 43

Then, the number of integers within the simultaneous inequality is:

n = 1 + (42 - 1)

n = 42

The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.

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Answer:

z = [tex]\sqrt{30}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it) × ( whole hypotenuse) , so

z² =  3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )

z = [tex]\sqrt{30}[/tex]

By assuming that one of the two integers is even we will reach an absurd, and in that way, prove the given statement.

Remember that an odd integer number is written as:

A = (2n + 1)

While an even number would be written as:

B = 2n

Where n is a random integer.

Then if x times y is an odd integer we can write:

x*y = (2n + 1)

Where n, m ∈ Z.

Where Z is the set of integer numbers.

Now, let's do find an absurd. Let's suppose that one of the two numbers is even, then we can write:

x = 2m

And y can be even or odd, it does not matter, but it is an integer.

Replacing that we get:

x*y = (2m)*y

We can rewrite that as:

(2m)*y = 2*(m*y)

We know that integer numbers are closed under the product, and here m and y are integers, then m*y is also an integer.

Thus, 2*(m*y) is 2 times an integer, then that is an even number, which is absurd because we know that it should be odd. So, if at least one of the two integers is even, then the product will also be even.

Then if the product is odd, neither of the integers can be even, then we conclude that both of the integers are odd integers.

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The viables solutions for the given compound inequality are x ∈ (-3, 5).

According to the given question.

The number of pies baked by Rita is x which is limited by ingredients.

Also, the inequalities which represent the situation are

2x - 3 < 7

And, 5 - x < 8

Since, we have to solve the above inequality and find its solutions.

From the given inequality

2x - 3 <7  we can say that,

2x < 7 + 3

⇒ 2x < 10

⇒ x < 5 ..(i)

And, 5 - x < 8

⇒  5 - 8 < x

⇒ - 3 < x

or, x < -3 ..(ii)

From i and ii we can say that the solution of the given compound inequality are the numbers which lies in between  -3 and 5 or x ∈ (-3, 5).

Hence, the viables solutions for the given compound inequality are

x ∈ (-3, 5).

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Answer:

4x-y+z=2

Step-by-step explanation:

the answer is simple

Based on the definition of complementary angles, the measures are:

m<q = 32°

m<r = 58°

Tow angels are complementary if both angles give a sum of 90 degrees.

The sum of angle q and angle r would give 90 degrees because they are complementary angles. Therefore, we would have the following:

m<r = ?

m<q = m<r - 26

Plug in the values

m<r - 26 + m<r = 90

2(m<r) - 26 = 90

2(m<r) = 90 + 26

2(m<r) = 116

2(m<r)/2 = 116/2

m<r = 58°

m<q = m<r - 26 = 58 - 26

m<q = 32°

Therefore, based on the definition of complementary angles, the measures are:

m<q = 32°

m<r = 58°

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Answer:

see explanation

Step-by-step explanation:

using the formula V = lwh , then

(a)

volume of first box = 3x × x × 2x = 6x³ units³

(b)

volume of second box = 4x × 2x  × x = 8x³ units³

(c)

volume of 2 boxes = 6x³ + 8x³ = 14x³

(d)

if x = 6 , then

volume of 2 boxes = 14x³ = 14(6)³ = 14 × 216 = 3024 units³

Answer:

Hello,

[tex]answer=\boxed{HCF=3*(p+2)}[/tex]

Step-by-step explanation:

[tex]6(p^2+p-2)=6(p+2)(p-1)\\\\15(p^3+8)=15(p+2)(p^2-2p+4)\\\\18(4p^2-p-18)=18(p+2)(4p-9)\\\\\boxed{HCF=3*(p+2)}[/tex]

The phase of inferential statistics is B. Data organization.

The process of arranging raw data in a form that makes sense is known as data organization. Classification, frequency distribution charts, image and graphical representations, among other methods, are used to organize data. Data organization enables us to arrange the information so that it is simple to read and use.

This was illustrated after performing an experiment to determine what time of day adults are most productive, you display your data as a graph to be analyzed. This is data organization.

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The standard error on the mean of these numbers is 1.08

For given question,

suppose your group measures the following three numbers in some experiment: 12.4,7.8,10.2

Mean of these numbers is:

[tex]\bar x=\frac{ 12.4+7.8+10.2}{3}\\\\ \bar x=10.13[/tex]

So the standard deviation would be,

[tex]\sigma=\sqrt{\frac{(12.4-10.13)^2+(7.8-10.13)^2+(10.2-10.13)^2}{3} }\\\\\sigma=1.88[/tex]

Now we find  the standard error on the mean of these numbers.

[tex]\sigma_M=\frac{\sigma}{\sqrt{N} }[/tex]

where, [tex]\sigma_M[/tex] = standard error of the mean

σ = the standard deviation of the original distribution

N = the sample size

[tex]\sigma_M=\frac{1.88}{\sqrt{3} }\\\\\sigma_M=1.08[/tex]

Therefore, the standard error on the mean of these numbers is 1.08

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Answer: 3/10 times 5 equals 15/50

Step-by-step explanation: First you do 3 times 5 which equals 15 and then 10 times 5 to get 50, which together make 15/50 and to make sure it's right check it by finding the greatest common factor they both have.

Answer:

5/5

Step-by-step explanation:

3 will enter 15, 5 times

n 10 will enter 50, 5 times

Answer:

$48

Step-by-step explanation:

The friends have the bus from 5:00 PM to 3:00 AM, so:

3 + 18 − 5 = 15 − 5 = 10 hours.

The cost of renting the bus will be:

$300 + $18 × 10 = $300 + $180 = $480.

The thirty-six students will contribute $12 each for a total of:

$12 × 36 = $432.

So Mr. Jones will pay:

$480 − $432 = $48.

Hope this helped :)

The exact interval for researchers who want real coverage that is at least nominal and a modified version of the variance stabilized interval for those who are OK with approximative coverage.

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Judy's total score is 3.

The difference between the lowest and highest score is -12.

The combined total of the scores from round 1 is -5.

The mathematical operations that would be used to solve this question are addition and subtraction. Addition is the process used to determine the sum of two or more number. The sign used to represent addition is +. Subtraction is the process used to determine the difference between two or more numbers. The sign used to represent subtraction is -.

Judy's total score is the sum of the score in round one and round one.

Judy's total score = -3 + 6 = 3

For negative numbers, the further the number is from 0, the smaller the number. For example, -10 is smaller than -5. For positive numbers, the closer the number is to zero, the smaller the number. For example,1 is smaller than 5.

Looking at the table, the smallest number is -6 and the largest number is 6

The difference : -6 - 6 = -12

The total scores from round 1 =  1 -6 +1 +2 -3 = -5

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Answer:

Step-by-step explanation:

A. 1

B. -3

C. 3

D. -1

The value of x = -1

What is mathematical expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

3x +y+2z=-10  equation 1

x+5y+2z=-12  equation 2

-2x+3y=-1       equation 3

Subtracting equation 1 to equation 2, we get

3x +y+2z - (x+5y+2z)=-10 - (-12)

3x +y+2z - x -5y -2z = -10 + 12

2x - 4y = 2   equation 4

Adding equation 4 to equation 3, we get

2x - 4y -2x+3y = 2 - 1

- y = 1

y = -1

Putting the value of y in equation 4, we get

2x - 4y = 2

2x - 4(-1) = 2

2x +4 = 2

2x = -2

x = -1

Therefore, the value of x = -1

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