Insert a rational number and an irrational number between √2 and √3
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The equation of the line in slope-intercept form that passes through the point (-6, -5) with a slope of 6 is y = 6x + 31. The correct answer is option (D).

Given that the line passes through the point (-6, -5) with a slope of 6, we can plug these values into the equation to find the y-intercept (b).

Using the point-slope form of the equation:

y - y₁ = m(x - x₁)

Substitute (-6, -5) and the given slope (m = 6):

y - (-5) = 6(x - (-6))

y + 5 = 6(x + 6)

Now, let's simplify the equation:

y + 5 = 6x + 36

To get the equation in slope-intercept form (y = mx + b), isolate y:

y = 6x + 36 - 5

y = 6x + 31

Thus, the correct answer is option (D).

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The prime factorization of 18 is 2 x 3 x 3.

A prime number is a number that is only divisible by 1 and itself. An example is 11. The factors of a number are numbers that divide another number without leaving any remainder. For example, a factor of 10 is 2. The prime factor of a number is the factors of a number that are prime numbers.

The factors of 18 = 1, 2, 3, 6, 9, 18

Prime factors = 1, 2, 3

Prime factorisation = 2 x 2 x 3

Here is the complete question:
The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3. What is the prime factorization of 18? 2 times 3 2 times 9 2 times 3 times 3 2 times 3 times 9

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Assuming he has the money to make the down payment, my classmate will borrow 90% of the home price.

A down payment is the upfront payment or an initial portion of the total purchase price of expensive property.

It is required that the buyer of a mortgaged property deposits this initial portion before taking the mortgage for the balance.

Mortgage period = 30 years

Interest rate = 3.5% fixed

Down payment = 10%

Balance (Mortgage) = 90% (1 - 10%)

Thus, assuming he has the money to make the down payment, my classmate will borrow 90% of the home price.

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The constant of proportionality between the number of bolts and the number of hours is 2025.

Option B is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Using a ∝ b then a = kb

Where k is the proportionality constant.

Given that;

We substitute into our equation.

a = kb

16200 = k × 8

k = 16200 / 8

k = 2025

The constant of proportionality between the number of bolts and the number of hours is 2025.

Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

The exact time is 93 days

The interest is  $20.38

The maturity value is  $1020.38

The interest is a function of the time, amount borrowed and the interest rate.

Interest = amount borrowed x time x interest rate

Time = June 9 - March 8 = 93 days

1000 x 0.08 x (93/365) = $20.38

Maturity value = 1000 + 20.38 = $1020.38

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The sum of the next 5 consecutive positive integers is w + 25

Let the first five numbers be A - E

So, we have:

A + B + C + D + E = W

The next five numbers would be

A + 5, B + 5...... E + 5

So, we have:

Sum = A + 5 + B + 5 + C + 5 + D + 5 + E + 5

Evaluate the like terms

Sum = A + B + C + D + E + 25

Substitute A + B + C + D + E = W

Sum = W + 25

Hence, the sum of the next 5 consecutive positive integers is w + 25

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The coordinates of B' are 3 and -12. so option D is correct (3, -12)

The point P(x, y) may undergo translation to form P' by using a defined translation rule :

If given the rule T(a, b) synch that P undergoes translation on T; then we will have P'(x+a; y+b)

Therefore,

The point B has its coordinates as B(1, - 5)

Translation rule, T(2, - 7) then the coordination of B after undergoing transformation according to T2;

B(1, - 5) - - - > T(2, - 7) - - - - > B'(1+2 ; - 5+-7)

= B'(3, -12)

Hence, the coordinates of B' are 3 and -12. so option D is correct.

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Answer:

(D)   (3, –12)  

Step-by-step explanation:

If a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'? The answer is (3, –12).

Number of physics textbooks sold was 261 & number of maths textbooks sold was 199.

Let, the number of physics textbooks sold = x

According to the question,

The number of math textbooks sold was 62 less than the number of physics textbooks sold.

So, Number of maths textbooks sold = x-62

The textbook store sold a combined total of 460 physics and math textbooks in a week.

So, the equation becomes,

(x-62)+x = 460

⇒ x-62+x = 460

⇒ 2x-62 = 460

⇒ 2x = 460+62

⇒ 2x = 522

⇒ x = 522/2

⇒ x = 261

So, 261 physics textbooks were sold

(261-62) = 199 maths textbooks were sold.

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The asymptote of the function given in the task content is the line; x = 25.

It follows from the task content that the function given is a rational function and hence, the asymptote of the function is the X-value which renders the function undefined in which case, the denominator is equal to 0.

x - 25 = 0.

x = 25.

The end behaviour of the functions graph is that it approaches the line x = 25 but never touches the line.

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Josiah and Chana travel at constant and different speeds.

Josiah's head start = 10 meters from the start

Josiah's speed = 2 m/s

Chana's speed = 3 m/s

Expressing the distance traveled as an equation, we have;

D = d + s × t

Where;

D = The distance covered

d = The distance from the starting line the runner starts

s = The speed of the runner

t = The time spent running

For Josiah, we have;

D = 10 + 2•t (line a)

For Chana, we have;

D = 0 + 3•t = 3•t (line b)

The above equations are straight line equations.

The point F is on line a, which shows Josiah distance after 25 seconds which is 60 meters. The corresponding point on line b, Chana's distance after 25 minutes is 75 meters.

Therefore;

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Answer:

Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah

Step-by-step explanation:

I got it right on khan.

The triangle KLM is rotated about origin by 90 degrees to form the triangle K'L'M'.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Rotation does not change the size and shape of the geometry.

The triangle KLM is rotated about origin by 90 degrees to create the triangle K'L'M'.

The diagram is given below.

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The equivalent expressions are (b) (7 * 7)^x , (c) 7^x * 7^x and (e) 7^(2x)

The expression is given as:

49^x

Express 49 as 7 * 7

(7 * 7)^x ---- option (b)

Express 7 * 7 as an exponent

7^(2x) ---- option (e)

Express 2x as x + x

7^(x +x)

Expand

7^x * 7^x --- option (c)

Hence, the equivalent expressions are (b), (c) and (e)

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Answer:

The first one: 12/13  > 36/30

Step-by-step explanation:

The first one would be correct as 12/13 is less than 36/30.

To explain why 13/17 is actually less than 24/28, see below:

So when comparing fractions, we must follow steps.

Step One: convert mixed numbers to a fraction, if there are any

There are not mixed numbers to compare, so we can move to the next step.

Step Two: find the least common denominator of the two fractions

Least common denominator = 476

Check out our least common denominator calculator for help on finding this.

Step Three: rewrite each fraction to an equivalent fraction using the denominator 476

To do this, start by dividing 476 by the denominator of the first fraction. Next, multiply the result by the numerator to find the new numerator. To rewrite, put the new numerator over 476. Repeat this for the second fraction

364/476                              408/476

Step Four: compare the numerators

At this point, to compare the fractions, we can simply compare the numerators to see which is larger

364<408

Step Five: rewrite each fraction as the original fraction

13/17<24/28

Therefore, the first statement (12/13 > 36/30) is true.

Answer:

  12/13 < 36/30

Step-by-step explanation:

There are many ways to compare numbers. One way is to compare them to some value that lies between. Another is to consider their difference from a value that does not lie between.

In the first fraction, 12 < 13, so the value of the fraction is less than 1:

  12/13 < 1

In the second fraction, 36 > 30, so the value of the fraction is greater than 1:

  1 < 36/30

Then the order of the fractions is ...

  12/13 < 1 < 36/30

  12/13 < 36/30 . . . . . the given order is True

We notice the difference between numerator and denominator is 4 in each case, so we can write each fraction as a difference from 1:

  (13/17) vs (24/28)

  = (1 - 4/17) vs (1 -4/28) . . . . . fractions rewritten

  = -4/17 vs -4/28 . . . . . . . . . subtract 1 from both

The first fraction, 4/17, has a smaller-value denominator, so its magnitude is larger than that of the fraction 4/28. In other words, the ordering of these fractions is ...

  -4/17 < -4/28

  1 -4/17 < 1 -4/28 . . . . . . add 1 to both sides

  13/17 < 24/28 . . . . . the given order is False

__

Additional comment

One sort of "no brainer" way to compare the fractions is to multiply them by the product of their denominators. This looks like "cross multiplication" where each numerator is multiplied by the opposite denominator. As long as you keep the numerators in the same relative places, the comparison symbol will be the correct one for the fractions.

  12/13 vs 36/30   ⇒   (12·30) vs (13·36)   ⇒   360 < 468

The left fraction is smaller than the right fraction.

Similarly, ...

  13/17 vs 24/28   ⇒   (13·28) vs (17·24)   ⇒   364 < 408

The left fraction is smaller than the right fraction.

__

Here, we have used the fractions "as is." In each case, the fraction on the right could be reduced, possibly making the comparison easier.

The equation of the line represented by the table in slope intercept form is; y = ²/₁₅x + 2

The formula for equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The y-intercept will occur when x = 0. Thus, from the table, it is clear hat the y-intercept will be c = 2.

Let us find the slope using the first two points;

m = (2 - 0)/(0 - (-15))

m = 2/15

Thus, the equation is;

y = ²/₁₅x + 2

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Answer:

7

Step-by-step explanation:

2 = 2

4 = 2²

6 = 2 * 3

8 = 2³

adding the exponents of 2, we get 1+2+1+3 = 7

You will need 252 mL of pure water to obtain 0.25 mL of the desired 25% solution.

If we add X amount of water to the solution, the total amount of solution is 375+X.

And that must be 25%.

The amount of solute in the current amount of solution is

0.6(375)=225.

That amount won't change by adding water.

So we set up the equation so that the amount of solute divided by the new total amount of solution equals 25%.

225/(375+X)=0.25

cross multiply and solve

225/0.25=(375+X)

900-375=X

X=525

The pure water will you need to add to obtain the desired solution is 525.

Then we check 225/(375+525)=0.25.

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Hello !

[tex]F(x) = 5 \times ( \frac{1}{3} ) {}^{x} [/tex]

[tex]F(4) = 5 \times ( \frac{1}{3}) {}^{4} = 5 \times \frac{1 {}^{4} }{3 {}^{4} } = 5 \times \frac{1}{81} = \frac{5}{81} [/tex]

Answer:

{(3,-2), (4,-2),(5,-2), (6,-2)}  this relation is not a function.

The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.

A statement, principle, or policy that creates the link between two variables is known as a function.

A cylinder (round can) has a circular base and a circular top with vertical sides in between.

Let r be the radius of the top of the can and let h be the height.

The surface area of the cylinder (A) is given as

A=2πr² + 2πrh

Part A: Assume that the height of your cylinder is 6 inches.

Consider A as a function of r, so we can write that as

A(r) = 2πr² + 12πr

Then the domain of A(r) will be (0, ∞).

Part B: Continue to assume that the height of your cylinder is 6 inches.

Then the inverse function to A(r) will be

r = 2π[A(r)]² + 12πA(r)

Part C: If the surface area is 175 square inches.

Then the radius will be

                    175 = 2πr² + 12πr

r² + 6r – 27.866 = 0

                        r = 3.07, -9.07

Then the radius will be 3.07 inches.

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The probability that the students gets all the questions correctly is (1/6)^15 .

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability = (number of correct options/ total number of options)^number of questions

(1/6)^15

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Given the radius of 50 miles and the line joining the cities at (0, 56) and (58, 0), the transmitter signal can be picked during 59.24 miles of the drive.

Radius of broadcast of the transmitter = 50 miles

Location of starting point = 56 miles north of the transmitter

Location of destination city = 58 miles east of the transmitter

Therefore we have;

Slope of the line joining the two cities

= 56 ÷ (-58) = -0.966

Which gives the equation of the line as follows;

y = -0.966•x + 56

The equation of the circle is;

[tex] {x}^{2} + {y}^{2} = {50}^{2} [/tex]

[tex] {x}^{2} + { ( - 0.966x + 56)}^{2} = {50}^{2} [/tex]

1.933156•x^2 - 108.192•x + 636 = 0

Which gives;

Therefore;

When x = 6.67, we have;

When x = 49.29, we have;

The length of the drive, during which the driver can pick the signal, l, is therefore;

l = √((49.56-8.4)^2 + (49.29-6.67)^2) = 59.24 miles

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Using scientific notation, the length of the hydrogen atom is given as follows:

[tex]1.9 \times 10^{-10}[/tex]

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

The diameter of a proton is given by:

[tex]1.9 \times 10^{-15}[/tex].

The hydrogen atom has an overall length of 100,000 times the diameter of the proton, hence the length is given by:

[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]

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Answer:

x = 6

Step-by-step explanation:

We want to find x,

[tex]\frac{3}{5} = \frac{x}{10}[/tex]

to get x alone, we multiple both side by 10

[tex]\frac{3}{5} * 10 = \frac{x}{10} *10[/tex]

[tex]\frac{30}{5} = x[/tex]

30 divided by 5 is 6

Check:

We can see that 5 x ____ = 10 where ____ is 2

5 x 2 = 10

so 3 x 2 = 6

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The solution to the given expression is 2

Given the equation 48 ÷ ((2 + 6) × 2) − 1

Using PEMDAS

48 ÷ ((8) × 2) − 1

48÷(16) - 1

3 - 1

2

Hence the solution to the given expression is 2

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Answer:

$26.08.

Step-by-step explanation:

[tex]1. \ \frac{16.95}{0.65} =\frac{x}{1};[/tex]

2) x=16.95/0.65≈$26.076923076923076923

The end behaviour of the function is When x ---> ∞ , f(x) ---> -∞  , when x ---> -∞ f(x) ----> ∞  , Option D is the correct answer.

A function is a mathematical statement that related the independent and the dependent variable.

The function given is

f(x) = [tex]\rm -2 \sqrt[3]{x}[/tex]

To understand the end behaviour the graph is plotted

When x ---> ∞ , f(x) ---> -∞

when x ---> -∞ f(x) ----> ∞

Therefore Option D is the correct answer.

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The units digit of the given exponential expression will be 6

From the question, we are to determine the units digit of the given exponential expression

The given exponential expression is

4⁸⁰⁰

We know that

4¹ = 4

4² = 16

4³ = 64

4⁴ = 256

4⁵ = 1024

4⁶ = 4096

From above, we can observe that the units digit of the odd exponents is 4 while the units digit of the even exponents is 6.

The exponent of the given expression is 800. 800 is an even number.

Hence, the units digit of the given exponential expression will be 6

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Using it's concept, an even function is given by:

B. [tex]F(x) = 2\cos{\frac{1}{2}x}[/tex]

Even functions are functions for which the following statement is true for all values of x.

f(x) = f(-x).

The cosine function, without a phase shift, is an example of an even function, hence option B is correct.

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