Hope the quality is somewhat better geometry worksheet

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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[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 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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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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Check the picture below, which is just a template for transformations.

so hmmm if we grab f(x) and move it downwards by 8 units, that means that the value for "D" gets a -8 added to it, so let's do that.

[tex]f(x)=3x^2+1\qquad \implies f(x)=\stackrel{A}{3}(\stackrel{B}{1}x+\stackrel{C}{0})^2+\stackrel{D}{1} \\\\\\ g(x)=3(1x+0)^2+1+(-8)\implies {\LARGE \begin{array}{llll} g(x)=3x^2-7 \end{array}}[/tex]

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]

Similarly, Q1 is obtained as the median of the lower half as (7+1)/2th = 4th observation i.e 60.

Similarly, Q3 is obtained for the upper half as 79 (4th upper half)

IQR (Interquartile Range) = Q3 - Q1 = 79 - 60 = 19

The interquartile range is a gauge for where a data set's "middle fifty" lies. An interquartile range (IQR) measures where most of the values lay, whereas a range measures where a set's start and finish are. For this reason, it is preferable when reporting things like academic performance or SAT scores over many other measures of spread.

The interquartile range IQR is 19

In ascending order we have: 48,51,57,60,63,65,69,71,72,73,75,79,85,88,97

Also, we get sample size (n) = 15 (odd)

So, Median = Q2 = (n+1)/2th observation

Median = (15+1)/2th term = 8th observation

Median = Q2 = 71

The formula for the interquartile range is the first quartile less the third quartile:

IQR = Q3 - Q1.

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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

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

14 notebook computers: 3850$

16 desktop computers: 2400$

Step-by-step explanation:

275x14=3850

150x16=2400

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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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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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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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

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

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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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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Answer:

Substitution property.

Step-by-step explanation:

The substitution property is just like saying, "If a variable, b, equals c, then b will be substituted for c, and it goes for c being substituted as b, too."

➲ Hope this helps.

The equation to model the maximum and minimum scores is given by |x - 76| = 5

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the student score. All students scored within 5 points of the average, hence:

|x - 76| = 5

The equation to model the maximum and minimum scores is given by |x - 76| = 5

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No, there is only one outlier at 58 minutes.

An observation that differs abnormally from other values in a population-based random sample is referred to as an outlier. In a way, this definition defers to the analyst's (or a consensus process') judgment as to what constitutes aberrant behavior. It is vital to define typical observations before distinguishing aberrant ones.

A data point is considered an outlier if it is more than 1.5 times the IQR below the first quartile or more than 1.5 times the IQR above the third quartile, according to the general criterion for utilizing it to compute outliers. The first and third quartile percentiles must be known in order to compute the IQR.

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.

9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim?

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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:

24

Step-by-step explanation:

Let x be shirts.

Write an equation.

13x=321

Divide 13 from both sides.

x≈24.69

So, the soccer team can only buy 24 shirts, because it cannot go over the budget.

Hope this helps!

Please mark as brainliest if correct!

Answer:

1. Not Linear

2. Linear

3. Linear

4. Linear

Step-by-step explanation:

Linear means it follows the form y = mx + b

1. The x value increases by 2 each time, but the y value doubles each time. They are increasing at different rates, so they are not linear.

2. The x value is increasing by 3 each time, and the y value is deceasing by 1 each time. Slope (m) of this line would be -1/3

3. The x value is increasing by 4 each time, the y value is increasing by 3 each time. Slope (m) of this line would be 4/3

4. The x value is increasing by 1 each time, the y value is constantly -3. This means that the line is a horizontal line, which is linear with a slope of 0. So the equation of this line would be y = 0x -3 ---->  y = -3

Answer:

1.1512, 2.1, 2.106, 2.16

Answer:

1.1512, 2.1, 2.106, 2.16

Step-by-step explanation:

1.1512 is the lowest cause it starts with 1

then 2.1 cause it has no more numbers to make it larger than the last two

then 2.106 because there is a 0 separating the 1 and 6 which makes the number smaller

which leaves you with 2.16 as the lasrgest

Volume of a regular Octagon pyramid is = 96.55 [tex]feet^3[/tex]

In the given statement is:

The greenhouse at the right is a regular octagonal pyramid with a height of 5 feet. The base has side lengths of 2 feet.

To find the Volume of the greenhouse

We know that the :

Area of Regular Octagonal Pyramid is [tex]2a^{2}(1+\sqrt{2} )[/tex]

a = side of an octagonal

and, a= 2 feet

Let's find Area of Octagonal :

Now, putting the value of a in above formula:

[tex]2(2^{2} )(1+\sqrt{2} )\\\\8(1+\sqrt{2} )\\\\=19.31 feet^{2}[/tex]

Now, Volume of the green house

Volume of a regular Octagon pyramid is = Area of an Octagon x height

Height = 5 feet

Now,   Volume of a regular Octagon pyramid is = 19.31×5

Volume of a regular Octagon pyramid is = 96.55 [tex]feet^3[/tex]

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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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The final answer for this is $36.95.

Now, if we se the explanation

We have, the cost for pizza and pasta for four people is $24.99

and,

the cost of drink for single person is $2.99

Now, if we calculate the cost of drinks for all the four person,

it would be $2.99 × 4 = $11.96.

It is the cost of drinks only for four people.

we have already given the cost of eat I.e. $24.99

total cost for four people to eat and drink is

= $11.96 + $24.99

=  $36.95

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