Look at the equations below. Tell whether each equation is True or False.
a. 2^9/2^-5=2^14
b. (5^0)^3 = 5^3
c. 4^5 x 2^5 = 8^10
d. 3^-9x3^7= 1/3^2

Answer:

Q is the point (3, 4).

Step-by-step explanation:

The formulae for the coordinates of a point (h, k) which divides a line  joining the points (x1, y1) and (x2, y2) in the ratio m : n is:

h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)

Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and

m = 5 and n = 2.

So here, for point Q:

h = (5*5) + 2*-2)/(2+5)

    = 21/7

     = 3.

k = (5*8 + (-6*2) / 7

   = 28/7

    = 4.

Answer:

x=6/5

Step-by-step explanation:

6=2x+3x

5x=6

x=6/5

Answer:

C

Step-by-step explanation:

if you divide the y by x, the answer it will give you will be 2/3 or .6

17 times theo will need to measure the flour for  both the recipes.

Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems. B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.

The order of operations (or operator precedence) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression. For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.

As a result, 1 + (2 3) = 7 rather than 1 + (2 3) = 9 is the value assigned to the expression 1 + 2 3. Exponents were first used in the 16th and 17th centuries, when addition and multiplication were given priority. Exponents could only be used as a superscript to the right of their base. Consequently, 3 + 52 = 28 and 3 52 = 75.

first add the total amount of flour =

   =   [tex]1\frac{1}{2} + 2\frac{3}{4}[/tex]

   = 1.5 + 2.75

   = 4.25

no. of times = 4.25 * 4/1 = 17 times

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Here is a straightforward recursion you may employ to calculate the value.

It should be noted that the formula $2n-1$ for the $1 times n$ case is incorrect if $n=0$.

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Both games A as well as B are unfair.

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Answer:

54

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then

[tex]\sqrt{6}[/tex] × 3[tex]\sqrt{54}[/tex]

= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9(6)}[/tex]

= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{6}[/tex] × [tex]\sqrt{6}[/tex] × 3 × 3

= 6 × 9

= 54

[tex]{ \qquad\qquad\huge\underline{\boxed{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{6} \times 3 \sqrt{54} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{2 \times 3} \times \sqrt{2 \times {3}^{3} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {2}^{2} \times {3}^{4} } [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \times {3}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 \times 9[/tex]

[tex]\qquad \sf  \dashrightarrow \:18[/tex]

Answer:

B. -1

Step-by-step explanation:

Let's solve your equation step-by-step.

−4x+7=2x+13

Step 1: Subtract 2x from both sides.

−4x+7−2x=2x+13−2x

−6x+7=13

Step 2: Subtract 7 from both sides.

−6x+7−7=13−7

−6x=6

Step 3: Divide both sides by -6.

−6x/−6 = 6/−6

x=−1

There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).

In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:

Slope

m = [6.9 - (- 8.5)] / (13.8 - 5)

m = 7 / 4

Intercept

b = - 8.5 - (7 / 4) · 5

b = - 69 / 4

The equation of the line is y = (7 / 4) · x - 69 / 4.

Second, evaluate the equation of the line at different integers:

x= 6

y = (7 / 4) · 6 - 69 / 4

y = - 27 / 4

x = 7

y = (7 / 4) · 7 - 69 / 4

y = - 5

x = 8

y = (7 / 4) · 8 - 69 / 4

y = - 13 / 4

x = 9

y = (7 / 4) · 9 - 69 / 4

y = - 3 / 2

x = 10

y = (7 / 4) · 10 - 69 / 4

y = 1 / 4

x = 11

y = (7 / 4) · 11 - 69 / 4

y = 2

x = 12

y = (7 / 4) · 12 - 69 / 4

y = 15 / 4

x = 13

y = (7 / 4) · 13 - 69 / 4

y = 11 / 2

There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).

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Kyla should babysit for 9.5 hours to buy the dress.

Double number line represents the comparison of numbers by representing them in equal ratio. The required double number line for the question is attached as figure.

The row I indicates the amount earned and row II indicates the number of hours Kyla should babysit. As is evident from the double number line, the average of last two amounts is the amount required by Kyla. Calculations are as follows -

Required amount = (49.5 + 55)/2

Required amount = 52.25

Now, the time between last two columns of row II will also be taken as average for calculation. So, time required to earn 52.25 after earning 49.5: (9 + 10)/2

Time = 0.5

Total time required to babysit = 9 + 0.5

Total time = 9.5 hours

Thus, Kyla should babysit for 9.5 hours to buy the dress.

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The complete question is -

While shopping, Kyla found a dress that she would really like, but it cost $52.25 more than she has. Kyla charges $5.50 an hour for babysitting. She wants to figure out how many hours she must babysit $52.25 to buy the dress. Use a double number line to support your answer.

Answer:(2,2)

Step-by-step explanation:

because if you follow the steps you will end up there

Based on the shape of the back wall of Joe's bedroom and the dimensions of the rectangle, and the cost per square foot, the paper cost of the wall would be $1,105

First, find the area of the back wall of Joe's bedroom because this is the area that would need to be covered by the wall paper:

Area of rectangle = Length x Width

Solving gives:
= 17 x 13

= 221 square foot

The cost to cover the wall based on the cost in dollars of each square foot is:
= Number of square feet x Cost per square foot

= 221 x 5

= $1,105

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Answer:

(a) $126

(b) .453333%

Step-by-step explanation:

(a) 476 - 350 = $126

(b)

[tex]si = p \times r\times t \\ 476 = 350 \times r\times 3 \\ 476 = 1050r \\ \frac{476}{1050} = r \\ r = 0.453333\%[/tex]

The probability that Alysha will win the bet is 0.12013

Let ‘x’ be the number of cute boys from next 20 persons that enter the library

And assume x be the integral values from 0 to 20

Given, the probability is 50% that the next person that enters the library is a cute boy,

total number of trials n=20 and probability of success p=50% = 0.5 = 1/2.

Hence, the p.m.f of X is given by

fX(x) = 20Cx(1/2)x(1−1/2)20−x

=20Cx(1/2)x(1/2)20−x

=20Cx(1/2)20

=20!(20−x)!x!⋅ 1220

=0,1,2,…,19,20

and the probability that X=x,

thus

P(X=x)=20!(20−x)!x!⋅1220

x=0,1,2,…,19,20

P(X=x)=20!(20−x)!x!⋅1220

x=0,1,2,…,19,20.

In particular, for X=x=12

P(X=12)=20!(20−12)!12!⋅1220

=20!8!12!⋅1220

≈0.12013

Hence, the probability that exactly 12 persons of the next 20 persons that walk into the library are cute boys is only approximately 0.12013.

Therefore, 0.1203 is less than 0.5, then it is more probable that Alysha will lose the bet than win it.

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The equation can be modelled to a real scenario where every purchase can be use to calculate sales tax.

The equation to be modelled is as follows:

y = 1 / 20x

let

x = The total price of purchases

y = The  amount of sales tax

This simply means a person pays 1 / 20 or 5% of every purchase he/she makes.

The total price of the purchase(including tax) is x while the actual amount of tax paid is y.

Let's say you buy a goods worth 400 dollars. Let's calculated the tax as follows:

x = $400

Therefore,

y = 1 / 20 × 400

y = 1 / 20 × 400

y = $20

Hence, the tax for a purchase of 400 dollars is 20 dollars.

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Answer:

The answer to the question is 35 degrees

Answer:12.8

Step-by-step explanation: u just round it

Answer:

345 pounds

Step-by-step explanation:

Each bucket dumps out 8 ounces of sand

8 ounces = 1/2 pound

So total sand dumped 10 times  = 1/2 x 10 = 5 pounds

Originally sandbox had 7 x 50 = 350 pounds of sand

Sand left in box = 350 - 5 = 345 pounds

Answer:

yall smart

Step-by-step explanation:

Step-by-step explanation:

Plug in 2x-4 in the function g(x)

[tex]g(f(x)) = {(2x - 4)}^{2} + 6 \\ \\ g(f(x)) = (2x - 4)(2x - 4) + 6 \\ = 4 {x}^{2} - 8x - 8x + 16 + 6 \\ g(f(x)) = 4 {x}^{2} - 16x + 22[/tex]

HOPE THIS HELPS

Answer: You should try to figure out the job you want and do that and maybe make a bucket list. Also, live your future out and your hapiness is what counts.

Step-by-step explanation:

Answer:

Explained through Step-by-step (Showed Work)

Step-by-step explanation:

Question: Show how 2/5 + 4/10 is the same as 4/5

Step-by-step:

2/5 and 4/10 are fractions. (So is 4/5)

To add fractions together, we need the denominators to be the same. This means that the bottom number of 2/5, which is 5 and the bottom number of 4/10 which is 10 have to be the same.

The easiest way to do this is to simplify 4/10. To simplify 4/10, we divide both the numerator (top number) and the denominator (bottom number) by the Greatest Common Factor.

In this case, 2 is the Greatest Common Factor because 4 divided by 2 is 2 and 10 divided by 2 is 5.

so, 4/10 can be simplified to 2/5.

Now, we can add 2/5 and 2/5 together by only adding the numerators. 2 + 2 = 4

so, 2/5 + 2/5 = 4/5

4/5 = 4/5

Therefore, 2/5 + 4/10 is the same as 4/5.

Hope this helps

If the salary of Sam is $25000 and Charlie earns $30000 and each get a raise of $2000 then the statement "The raises are the same in absolute terms, but Charlie's is larger in relative terms" is true.

Salary of Sam = $25000

Raise in Sam's Salary = $2000

New Total Salary = $25000 + $2000 = $27000

Salary of Charlie = $30000

Raise in Charlie's Salary = $2000

New Total Salary = $30000 + $2000 = $32000

Hence the absolute value of their salaries are same but Charlie will get more in relative terms.

Hence, option d is correct.

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For the given function f(x) = x^2 - 2x + 1, the difference quotient is {2x + h - 2]

Here we have the function f(x) = x^2 - 2x + 1

And we want to find the difference quotient, which is:

( f(x + h) - f(x))/h

Replacing the actual function there we get:

[ (x + h)^2 - 2*(x + h) + 1 - x^2 + 2x - 1]/h

Now we can simplify the numerator, we will get:

[ x^2 + 2xh + h^2 - 2x - 2h + 1 - x^2 + 2x  -1]/h

[2xh + h^2 - 2h]/h

Taking the quotient we get:

{2x + h - 2]

That is the difference quotient for the function f(x).

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The standard form the linear function is f(x)= -3x-3.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+3. Where:

m= the slope. It can be calculated for Δy/Δx .

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=3.

You should replace in the minimum two given values for x and y in the standard form for a linear equation mx+b . Thus, you will write a system linear where from it, you can find the coefficients m and b. See below.

       y=mx+b

      -3=0*m+b

      -3=b

       y=mx+b

      3= -2*m+b

Now, you find b=-3, then

      3= -2*m-3

      3+3= -2m

       6=-2m

       m= -3

Thus, you can write f(x)= -3x-3.

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Answer:

[tex] \sf \large \: x=7 or x=−3[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

|x+8|=|2x+1|

Solve Absolute Value.

|x+8|=|2x+1|

We know eitherx+8=2x+1orx+8=−(2x+1)

x+8=2x+1(Possibility 1)

x+8−2x=2x+1−2x(Subtract 2x from both sides)

−x+8=1

−x+8−8=1−8(Subtract 8 from both sides)

−x=−7

−x/−1 = −7/−1

(Divide both sides by -1)

x=7

x+8=−(2x+1)(Possibility 2)

x+8=−2x−1(Simplify both sides of the equation)

x+8+2x=−2x−1+2x(Add 2x to both sides)

3x+8=−1

3x+8−8=−1−8(Subtract 8 from both sides)

3x=−9

3x/3 = −9/3

(Divide both sides by 3)

x=−3

Check answers. (Plug them in to make sure they work.)

x=7(Works in original equation)

x=−3(Works in original equation)

Answer:

7

Step-by-step explanation:

x+8=2x+1

Subtract x on both sides. Subtract 1 on both sides

x=7

Yes parallel line exist in spherical geometry. The radius or diameter and the tangent can be a pair of parallel line in spherical geometry

The tangent of the sphere refers to a line that make contact with only a point in the sphere. The tangent is perpendicular to the center and the radius can be drawn to be parallel to the tangent.

The radius refers to a line running from the center to an end of the circle. Two radius can be drawn say radius A and radius B. Radius A will be drawn perpendicular to the tangent and radius B drawn perpendicular to radius A.

The pair of lines tangent and radius B will be parallel to each other.

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Answer:

Less; $25.90 less than at the beginning of the week

Step-by-step explanation:

162-(63.50+23.25+26.45)=162-113.20=48.80

48.80+87.30=136.10; 162>136.10

162-136.10=Δ$25.90

$25.90 less