Choose what the expressions below best represent within the context of the word problem.

The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?

x represents
the ones
digit
2x represents
the tens
digit

The two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals

The conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.

The given roots are

[tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex]

They have the same numbers but opposite signs in the middle.

Hence, the two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals

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By solving a system of equations we will see that the two-digit number is 84.

"The tens digit of a number is twice the ones digit"

"The sum of the digits is 12".

A two-digit number can be written as:

a*10 + b

Where a is the tens digit and b is the ones digit.

The word problem can then be written as:

a = 2*b

a + b = 12

So we have a system of equations.

To find the number we need to solve these, if we replace the first equation into the second one:

a + b = 12

(2b) + b = 12

3b = 12

b = 12/3 = 4

Then:

a = 2b = 2*4 = 8

So the two-digit number is 84.

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Answer: e

Step-by-step explanation:

The vertex is at (-3, 1).

This leaves e.

Using it's concept, it is found that the period of the function is of 20 units.

The period of a function is given by the distance between it's repetitions.

Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.

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Answer:

2/3 x - 5 < 11

2/3 x < 16 (add 5 to both sides)

x < 16 * 3/2 (multiply both sides by 3/2)

x < 24

Step-by-step explanation:

Answer:

z=2

Step-by-step explanation:

We are given that a line has a slope of 3.

The line passes through the points (-10, z) and (-8, 8)

We want to find the value of z.

To do that, we can calculate the slope.

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we already have 2 points, let's label their values to avoid any confusion.

[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]

Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.

[tex]\frac{8-z}{-8--10}[/tex] = 3

We can simplify this first.

[tex]\frac{8-z}{-8+10}[/tex] = 3

[tex]\frac{8-z}{2}[/tex] = 3

We can multiply both sides by 2 to clear the fraction and make it easier to calculate.

2([tex]\frac{8-z}{2}[/tex])  = 2(3)

Multiply.

8 - z = 6

Subtract 8 from both sides

-z = - 2

Multiply both sides by -1.

-1(-z) = -1(-2)

Multiply.

z = 2

Answer:

a) 57

b) 19.476

c) 1.106 (rounded)

Step-by-step explanation:

a) note: the very first step here is to find the number of people of age 21 which is found through subtraction. We have a total of 250 people, and we currently have data on 193 (64 + 60 + 69) people.  This means there are (250 - 193 = 57)  57 remaining people of age 21.

The first thing we're trying to find here is the mean, which we sometimes refer to as the average, of this data set.

To find the mean, we add all values together and then divide by the number of values we've combined.

We could write out 18 + 18 + 18... sixty-four times, and then to the same thing for 19's, but that would take a while. So, we can find this value through multiplication (remember, multiplication is the same thing as repeated addition).

18 × 64 = 1152

19 × 60 = 1140

20 × 69 = 1380

21 × 57  = 1197         *see above

Now, we find the sum of our values added together:

Now, we know we have 250 values, so we will divide 4869 by 250:

4869 / 250 = 19.476

So, the mean of this sample is 19.476

Now, we are finding the standard deviation, which is found through the formula:

    ∑ (x - x^(line over x) ) ²

√ _______

       n - 1

(this is hard to write on this website sorry)

find difference between each value and mean  (that's what "x - x^(line over x)" is)

18 - 19.476 = -1.476

19 - 19.476 = -0.476

20 - 19.476 = 0.524

21 - 19.476 = 1.524

square each difference:   (that's what " (x - x^(line over x))² " is)

now, we need to add up our squared values. But first, we must account for how many of each value there are

now, let's add up our squared values:  (that's what "∑" is )  

we now need to divide this number by n - 1 (we have 250 samples, so we need to divide by 250 - 1 (249) to find our variance)

now, we find our standard deviation by taking the square root of the variance that's what the "√" is )

we can round this number to:

1.106 (or any other rounded decimal place, I did it this way to match our previous answer)

So, the standard deviation of this set is 1.106 (rounded)

hope this helps! have a lovely day :)

Answer:

(z+2)(z+3)(x-8)

Step-by-step explanation:

z² + 5z + 6 can be factored into (z+3)(z+2)

zx + 2x − 8z-16 can be factored into (x-8)(z+2)

the LCM would be (z+2)(z+3)(x-8)

if you were to multiply the two expressions together, you would multiply (z+2)^2, which is not necessary for LCM, which is why you factor them first

The true statements are:

The marked up price of chicken before 10pm is $6

The 50% mark down is taken off the marked up price

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Price after the mark up= (1 + mark up) x initial price

1.50 x 4 = $6

Price after the mark down = (1 - percentage mark down) x price after mark up

0.50 x $6 = $3

Here are the options:

The marked up price of chicken before 10pm is 6

The 50% mark down is taken off the marked up price

The chickens sell for $4 after 10pm

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Using proportions, it is found that the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials is of $2.89.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

To pay for the materials, you need to sell 18 paintings at $2.25 each, hence the total is:

T = 18 x 2.25 = $40.5.

If you lose four paintings, you will sell 14, and still need to make $40.5, hence the price will be of:

P = $40.5/14 = $2.89.

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Answer:

C) Experiment

Step-by-step explanation:

With a controlled experiment, a researcher can use a student batch that studied the old curriculum as a control group, and the new batch of students as the 'test' group. To measure student achievement, the researcher would need to either:

1. compare test results for the 2 groups

2. do a longitudinal study - follow the 2 groups of students across several years, and track their 'achievements' (university admissions, jobs, income, etc)

With the other 3 options, the results wouldn't necessarily be accurate or relevant.  

Answer:

523.6

Step-by-step explanation:

Volume of sphere= 4/3πr^3

V=4/3π(5^3)

V=523.6 (correct to 1 dp)

Answer: -2 < x < 1

Step-by-step explanation:

move all terms not containing x from the center section of the inequality

1 < x + 3 < 4

subtract 3 from both terms outside the center

1 - 3 = -2

4 - 3 = 1

therefore our answer is:

-2 < x < 1

Answer:

D

Step-by-step explanation:

Let's start by crossing everything out!

12/3 can be crossed out to 4.

a^3/a^2 can be crossed out to a.

b^6/b^4 can be crossed out into b^2.

c^5/c^5 is just 1.

So which the results we got, we can multiply them, so that it is 4ab^2.

4ab^2 is our final answer!

Answer:

it's

answer

is

32.36

.

.

.

.

.

.

.

..

.

.

..

.

.

.

.

.

Answer:

Step-by-step explanation:

can you show part a nd b for a better understanding of the question

Answer:

30 pupils

Step-by-step explanation:

first you divide 75 and 2.5 to get 30.

Answer:

30 prefer red

Step-by-step explanation:

Multiply the fraction by the number of students:

[tex]75(\frac{2}{5})=\frac{(75)(2)}{5} =\frac{150}{5} =30[/tex]

Hope this helps

Answer: Sorry If I'm wrong but if you are asking for the missing angle on the bottom, I think it is 30 degrees.

Step-by-step explanation: All the angles in a triangle add up to 180 degrees. we already know that one is 50 degrees. The 2nd angle is a bit wider than a 90 degree angle, and the third angle is 30 degrees, so 50 degrees + 100 degrees + 30 degrees add up to 180. So, I think your answer would be 30 degrees.

Answer:

x = 25

Step-by-step explanation:

I added a drawing down below to guide you through!

First, we should remember, that if a line crosses two parallel lines, then the adjacent angles will have the same value. Since Line D and Line E are parallel and line BC is crossing it, angles ABC and 105 will be the same.

Now that we know one of the missing angles, we can find x easily!

All angles in a triangle add up to 180, so in this case, the equation will be: 50 + 105 + x = 180.

155 + x = 180

x = 25.

So x will equal to 25 degrees!

The number of people that studied only one subject is 108.

A set is a collection of well-defined objects.

Objects in a set are called elements or members of a set.

Set notation or the use of Venn diagrams are the methods used to solve set problems.

Analysis:

let P = physics

C = chemistry

M = mathematics

n(P) = 70

n(C) = 46

n(M) = 100

n(M n P n C) = 18

n(M n P) = 30

n(M n P n C') = 30 - 18 = 12

n(M n C) = 28

n(M n C n P') = 28 - 18 = 10

n(P n C ) = 23

n(P n C n M') = 23 - 18 = 5

n(P n C' n M') = 70-(12+18+5) = 70 - 35 = 35

n(P' n C n M') = 46-(18+5+10) = 46-23 = 13

n(P' n C' n M) = 100 - (10+18+12) = 100 - 40 = 60

people that studied only one subject are = 35 + 13 + 60 = 108

In conclusion 108 students studied only one type of subject.

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Considering the volume of the rectangular prism, you will need 2240 bags will be needed for the patio.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, the dimensions are:

l = 14 ft, w = 12 ft, h = 8 ft.

Hence the volume is:

V = 14 x 12 x 8 = 1344 ft³

Each bag yields 0.6 ft³, hence the number of bags is:

n = 1344/0.6 = 2240 bags.

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Answer + Step-by-step explanation:

-2|x| = -6

⇔ 2|x| = 6

⇔ |x| = 3

⇔ x = 3  or  x = -3

Answer:

y-x-1 < 0

Step-by-step explanation:

according to the graph (0,1) and (-1,0) lies on the doted line,

equation of the dotted line is y-x-1=0

shaded region = y-x-1 < 0

The mean is 87 and median is 86.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest.

Given:

79, 91, 93, 85, 86, and 88

So,

79+85+86+88+91+93/6 = 87

and, the median

79, 85, 86, 88, 91, 93

median = 86

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Answer:

134217728

Step-by-step explanation:

The geometric sequence formula is:

[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]

We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:

[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]

Therefore, the 25th term of sequence is 134217728

Answer:

[tex] \small{\boxed{ \sf{Term \: in \: both \: the \: sequence \: is \: 15}}}[/tex]

Step-by-step explanation:

To determine the common term in both the sequence let's solve for each sequence individually.

Let's solve for first sequence

[tex]f(n) = f(n-1)+4[/tex]

we are already told that f(1) = 3

let's solve for f(2),f(3),f(4)........ and so on till we get the highest digit or more than the highest digit from given option.

f(2) = f(2-1)+4 = f(1)+4

f(2) = 3+4

[tex]\small{ \fbox{f(2) = 7}}[/tex]

f(3) = f(3-1)+4 = f(2)+4

f(3) = 7+4

[tex] \small{\fbox{f(3)= 11}}[/tex]

on solving further..

The series obtained is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135.....

Let's solve for second series

[tex]f(n) = 3×5^{n -1}[/tex]

given that f(1) = 3,

f(2) = 3×5¹ = 15

f(3) = 3×5² = 75

f(4) = 3×5³ = 375

The series obtained is 3, 15, 75, 375.....

The term obtained in both the sequence is 15 hence option B is correct Answer.

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