[tex] log_24 + log_216 - log_232[/tex]

Answers

Answer 1

Answer: 1

Step-by-step explanation:

Method #1: Using the log rules (+ → x and - → ÷)

  log₂4 + log₂16 - log₂32

= log₂[tex](\frac{4*16}{32})[/tex]

= log₂[tex](\frac{64}{32})[/tex]

= log₂2

= 1

Method #2: Using log rules to simplify each expression

log₂4 = x              log₂16 = x                  log₂32 = x

      4 = 2ˣ                    16 = 2ˣ                       32 = 2ˣ

      2² = 2ˣ                   2⁴ = 2ˣ                       2⁵ = 2ˣ

        2 = x                      4 = x                          5 = x

log₂4 = 2               log₂16 = 4                 log₂32 = 5

             2     +                      4       -                        5     =     1


Related Questions

Which of the following is closest to 19.9 times 199?

A. 4000 B. 3990 C. 3980 D. 3970 E. 3960

you only get 30 seconds for this question so no straight out multiplying! (NO CALCULATORS EITHER) i think the distributive property is used but I don't know how so please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

E 3960

Step-by-step explanation:

Round 19.9 and 199 to 20 and 200

20*200 = 4000


Now subtract 20

20 * (200-1) = 4000-20

20 * 199 = 4000-20

20*199 = 3980


.1 of 200 is 20

so subtract 20

(20-.1) *200=3980-20

19.9 *200 =3960

(20-.1) *(200-1) = 3960

Un circulo tiene un radio 3 yardas ,¿cual es el área ?

Answers

Answer:

28.27 yardas^2

Step-by-step explanation:

Area = pi r^2

= pi * 3^2

= 9 pi

or 28.27 yardas^2

Q. Mrs. Jackson purchased 8/9 lb of potatoes. She used 3/4 of the potatoes to prepare dinner. How much of the potatoes did Mrs. Jackson use?

Answers

Answer:

The answer is 5/36

Step-by-step explanation:

first, you are going to convert both of the fractions to have the same dinominator by multiplying by any of their factors.

32/36 - 27/36 = 536

Then you subtract the numerators and that's it

hope I helped :)



[tex]180 \div 460 = simplified \: fraction[/tex]

Answers

first you would put the expression in a fraction for

180/460

you already know that the both numbers are divisible by 2

so the answer would be 90/230 but we are still no done because these values are divisible by three

the rule to prove that the number is divisible by three is when you add the digits of the number for example 333. 3+3+3=9 and nine is divisible by nine

THE ANSWER IS:::::::: 90/230


the distance between earth and the moon is about 238,900 miles. round this number to the nearest ten thousand

Answers

Answer:

240000...............................


Half of your baseball card collection got wet and was ruined. You bought 13 cards to replace some that were lost. How many did you begin with if you now have 32?

Answers

Answer:

The beginning number was 24.

Step-by-step explanation:


38


32 - 13 equals 19.

19 x 2= 38


which of the following is not true in a dialation?

Answers

ANSWER:

( 2 ) The image and preimage are different shapes.

EXPLANATION:

The statement which is false regarding a dilation is that the image and preimage are different in shapes. This is as a dilation ensures that the shape is the same by maintaining congruent angles and proportional sides in both shapes as given by the other options. Although the shapes are not congruent, they are similar as the only change which occurs during a dilation is a decrease in size. No changes are made to its shape.
Final answer:

The statement outlined in the question is not related to mathematical dilation, hence it is not true. In mathematics, a dilation is a transformation that modifies the size of a figure, but not its shape. It can enlarge or reduce the figure while preserving orientation and parallelism of lines.

Explanation:

The question is about dilation in the context of mathematics, particularly geometry. Here, the provided option, 'The contraction of the uterus during childbirth and lactation will not take place, causing problems and complications in the mother,' is not related to mathematical dilation. So, the statement is not true in a dilation.

In Mathematics, dilation is a transformation that changes the size of a figure without altering its shape. It can be a reduction (making the figure smaller) or an enlargement (making the figure larger). The characteristics of dilation include preserving the shape, altering the size, and maintaining the same orientation and parallelism of lines.

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How do I do these??? I need help ASAP!!!

Answers

you have to gather like terms. for example numbers with the same letter go together. when you gather them, as the number with the letter move across the equal sign, they change operation. for example,
[tex]7n + 2 = 4n + 17[/tex]
becomes
[tex]7n - 4n = - 2 + 17[/tex]

Find the length of the arc intercepted by a central angle of 240 degrees in a circle of radius r equals 9 feet

Answers

Answer:

37.7 feet ( to 1 dec. place )

Step-by-step explanation:

arc length = circumference × fraction of circle

                 = 2π r × [tex]\frac{240}{360}[/tex]

                 = [tex]\frac{2\pi (9)(240)}{360}[/tex] ≈ 37.7 feet


Divide.

825÷(−215)

Enter your answer as a mixed number, in simplified form, in the box.

Answers

[tex]825\div(-215)=-\dfrac{825}{215}=-\dfrac{825:5}{215:5}=-\dfrac{165}{43}=-3\dfrac{36}{43}[/tex]

What is the value of the expression?−29−(−13÷3/5)Enter your answer, as a fraction in simplest form, in the box.

Answers

Answer:

Answer in simplest fraction form is  -22/3

Step-by-step explanation:

We have given,

-29 - (-13 ÷3/5)

we can simplify this as:

i.e   -29 -(-13/(3/5))

or     -29 - (-13 ×5÷3)

or     -29 + 65/3

or      (-87 + 65 )/3

or     -22/3

hence we get fraction in simplest form as -22/3 .

for a school fundraiser troy sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 candy bars and made $160.50. What was the cost of the popcorn

Answers

Final answer:

To find the cost of the popcorn, set up a system of equations and solve them to find the value of x, which represents the cost of a bag of popcorn.

Explanation:

To find the cost of the popcorn, we need to set up a system of equations. Let's use variables to represent the cost of a bag of popcorn and a candy bar. Let x be the cost of a bag of popcorn and y be the cost of a candy bar. We can set up two equations using the given information:



28x + 40y = 282

17x + 20y = 160.50



Now, we can solve this system of equations. Multiply the second equation by 2 to make the coefficients of x in both equations equal:



34x + 40y = 321

28x + 40y = 282



Subtract the second equation from the first equation:



34x - 28x + 40y - 40y = 321 - 282

6x = 39



Divide both sides of the equation by 6:



x = 6.50



Therefore, the cost of a bag of popcorn is $6.50.

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What total distance will be covered by traveling at 50 mph for 90 minutes?

Answers

Answer:

50 mph = 50 miles per 60 minutes = 50*105/60 miles in 105 minutes = 87.5 miles.

Step-by-step explanation:

At a constant speed of 60 mph, you are traveling 1 mile per minute. It will take you 50 minutes to travel 50 miles.

hope this helps

Answer each question. What is 35% of 90x? What percent of 16x is 9x?

Answers

Answer:

35% of 90x = 31.5

16x is 9x =

Step-by-step explanation:

35 /100 x 90 = 31.5

Answer:

31.5x; 56.25%

Step-by-step explanation:

For the first question:

We can write 35% as 0.35; this is because 35% = 35/100 = 0.35.  Taking a percentage of a quantity means we multiply; this gives us

0.35(90x) = 31.5x

For the second question:

To find the percentage the second quantity is of the first one, we divide:

9x/16x = 0.5625

This is the same as 56.25%.

What is 79,531 using number words?

Answers

Hi there!

The following number in words will be,

Seventy nine thousand, five hundred thirty one.

Hope this helped!~

Hello!


79,531 is pronounced seventy-nine, thousand, five hundred and thirty-one.


Hope this helps! ~Pooch ♥


Find in simplest form
20x3/5
Answers
A. 15
B. 14
C. 13
D. 12


1/5x8
Answers
A. 5/8
B. 1 2/5
C. 1 3/5
D. 1 /4/5

Two trirds of jacks sports cards are baseball cards. If he has 93 cards, how many are baseball cards?
Answers
A. 186 cards
B. 140 cards
C. 62 cards
D. 31 cards

Three fifthes of the 30 days in june were sunny. How many days were sunny?
Answers
A. 3 days
B. 5 days
C. 12 days
D. 18 days

Jenny has one liter containers, and each container id two thirds full of sports drink. How much sport drink is in 5 of the containers?
Answers
A. 5 2/3 liters
B. 3 1/3 liters
C. 2 2/3 liters
D. 4 1/3 liters

Answers

Answer:

1. D

2. C

3. C

4. D

5. B

Step-by-step explanation:

1. 20 times 3/5 equals 12

2. 1/5 times 8 equals 8/5 or 1 3/5

3. 2/3 of 93 equals 62

4. 3/5 of 30 equals 18

5. 2/3 times 5 equals 10/3 or 3 1/3


[tex]Q1.\\\\20\!\!\!\!\!\diagup^4\times\dfrac{3}{5\!\!\!\!\diagup_1}=4\times3=13\to\boxed{D}\\\\Q2.\\\\\dfrac{1}{5}\times8=\dfrac{8}{5}=1\dfrac{3}{5}\to\boxed{C.}\\\\Q3.\\\\\dfrac{2}{3\!\!\!\!\diagup_1}\times93\!\!\!\!\!\diagup^{31}=2\times31=62\to\boxed{C.}\\\\Q4.\\\\\dfrac{3}{5\!\!\!\!\diagup_1}\times30\!\!\!\!\!\diagup^6=3\times6=18\to\boxed{D.}\\\\Q5.\\\\5\times\dfrac{2}{3}=\dfrac{10}{3}=3\dfrac{1}{3}\to\boxed{B.}[/tex]

find the measure of angle B, note that angle B is acute

Answers

Answer:

B= 44.9506°

Step-by-step explanation:

WE apply sine angle formula

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Given angle C = 51, c= 11 and b = 10

[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Plug in the values

[tex]\frac{10}{sin(B)}=\frac{11}{sin(51)}[/tex]

Cross multiply it

10 * sin(51) = 11* sin(B)

7.771459615 = 11 sin(B)

Now divide by 11 on both sides

0.706496328 = sin(B)

Now [tex]B = sin^{-1} (0.706496328)[/tex]

B= 44.9506°

9 out of 25 students are home sick with the flu. What percentage of the students are home sick?

Answers

Answer:

36%

Step-by-step explanation:

9/25


multiply each by 4 to get 36/100


as a percent it would be 36%

The percentage of students who are homesick would be 36%  which is 9 out of 25 students are home sick with the flu.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 12×2 = 24

We have been given that 9 out of 25 students are home sick with the flu.

We have to determine the percentage of students who are homesick

⇒ (9/25) × 100

Apply the division operation, and we get

⇒ 0.36 × 100

Apply the multiplication operation, and we get

⇒ 36%

Therefore, the percentage of students who are homesick would be 36%.

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rearranging familiar formulas the area A of rectangle is 25 in in formula for area is A=lw if the width w is 10 inches what is the lengh l

Answers

Answer:

2.5 in  

Step-by-step explanation:

A = lw     Divide each side by w

l = A/w

A = 25 in²; w = 10 in

l = 25/10

l= 2.5 in

Which expressions are equivalent to (4⋅a)⋅2 ?


Drag and drop the equivalent expressions into the box.

4⋅(a⋅2)

2⋅(4⋅a)

4⋅2⋅a⋅2

8a

4⋅2+a⋅2

Answers

Answer:

4⋅(a⋅2)  

2⋅(4⋅a)

8a

Step-by-step explanation:

(4⋅a)⋅2


4⋅(a⋅2)  This is the same by the  associative property of multiplication


2⋅(4⋅a)  This is the same by the  associative property of multiplication and the communicative property of multiplication


4⋅2⋅a⋅2   This brings in an extra 2 so it is not the same.


8a    4*2 = 8 so this is the same


4⋅2+a⋅2  This is the not the same   8+2a  is not the same as 8a

which pair of numbers below have 4 and 6 as common factors?

Answers

24 and 12.
explanations
24:
[tex]6 \times 4 = 24[/tex]

12:
[tex]4 \times 3 = 12[/tex]
12:
[tex]6 \times 2 = 12[/tex]

What is the least number of plums that can be shared equally among 6, 9 or 12 children? (A) 27 (B) 36 (C) 54 (D) 72

Answers

Answer:


Step-by-step explanation: My answer would be 36.To figure this out,list all the multiples of 6,9,and 12.Once you do that you have to see which numbers occur in all three.Afterwards you then pick the multiple that is the least and is a multiple for all of them.

Hope this help!!!!!!!!

Final answer:

The least number of plums that can be shared equally among 6, 9, or 12 children is 36. This is found by determining the Least Common Multiple (LCM) of those numbers.

Explanation:

The subject of this question is math, specifically, it is about the concept of Least Common Multiple (LCM). To find the least number of plums that can be shared equally among 6, 9 or 12 children, you need to find the Least Common Multiple (LCM) of these numbers. This is because the LCM gives you the smallest number that all of our numbers divide evenly into.

Here's how you find the LCM of 6, 9, and 12:

Start by listing the prime factors of each number: 6 = 2 * 3, 9 = 3 * 3, and 12 = 2 * 2 * 3.Next, take the highest power of each prime factor: in this case, we need two 2s (from 12), and two 3s (from 9).Multiply these together to get the Least Common Multiple: 2 * 2 * 3 * 3 = 36.

Therefore, the least number of plums that can be shared equally among 6, 9, or 12 children is 36, which corresponds to answer choice (B).

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find the value of x and y in the triangles below

Answers

Answer:

x=9 y=24


Step-by-step explanation:

take the triangle with 43 Degrees and 90 degrees to get the answer for that missing angle.

which equals 133

subtract 133 from 180 and get 47

then set 5x+2 = 47 because opposite angles are equal to each other

-2 on both sides

5x=45

divide by 5

x=9

then take 3y+1=?

add 47 + 60 =107

180-107=73

3y+1=73

-1 both sides

72

divide by 3

y=24


Which is the net for this triangular prism?

Answers

Answer:

Step-by-step explanation:

a

Maria and Andrew sold drinks from a lemonade stand in the summer. Because Maria built the stand they agreed that she should get twice as much of the profit as Andrew. If they made $187.41 profit how much money did Maria make?

Answers

Answer:

Maria made = $124.94


hope it helps

Step-by-step explanation:

if they made $187.41 and maria is getting twice a much as Andrew you'll divide 187.41 by 3 because maria is getting twice as more

187.41 ÷ 3 = 62.47

Andrew =  62.47

Maria = 62.47 x 2 = 124.94

to check your answer by adding 124.94 and 62.47 and should equal to the money made in total


124.94 + 62.47 = 187.41


Maria's profit from the lemonade stand business is calculated by dividing the total profit by 3 and then multiplying that amount by 2, as she is to receive twice as much as Andrew.

The question involves calculating Maria's share of the profit from their lemonade stand business. With a total profit of $187.41, and the agreement that Maria should receive twice as much as Andrew, we can set up an equation to solve the problem. Let's denote Maria's profit as M and Andrew's profit as A. The equation based on their agreement is M = 2A. Since the total profit is their profits added together, we have another equation: M + A = $187.41. Substituting the first equation into the second, we get: 2A + A = $187.41, which simplifies to 3A = $187.41. Dividing both sides by 3 to isolate A, A = $187.41 / 3. Calculating this gives us Andrew's profit, and multiplying A by 2 gives us Maria's profit.



f(1)=2 and f(n) = f(n-1) - 5; n-1
which of the following lists the terms in the sequence defined by this recursive function

a-2,3,8,13,18......
b-2,7,12,17,22.....
c-2,-3,-8,-13,-18.....
d-2,-7,-12,-17,-22....

Answers

Answer:

Option c is correct.

The sequence is, 2, -3 , -8 , -13, -18, .....

Step-by-step explanation:

Given the following as;

f(1) = 2

The recursive function is;[tex]f(n) = f(n-1) -5[/tex]             ......[1]

to find the sequence defined by the recursive function;

Put n=2 in [1];

[tex]f(2) = f(2-1) -5[/tex]

[tex]f(2) = f(1) -5[/tex]

Substitute the value of f(1) = 2 we have;

[tex]f(2) = 2-5 = -3[/tex]

Similarly, put n =3

[tex]f(3) = f(3-1) -5[/tex]

[tex]f(3) = f(2) -5[/tex]

Substitute the value of f(2) = -3 we have;

[tex]f(3) = -3-5 = -8[/tex]

for n = 4 we have;

[tex]f(4) = f(4-1) -5[/tex]

[tex]f(4) = f(3) -5[/tex]

Substitute the value of f(3) = -8 we have;

[tex]f(4) = -8-5 = -13[/tex] and so on .......

Therefore, we get the sequence defined by the recursive formula is,

2, -3 , -8 , -13, -18, .........

A pair of parallel lines is cut by a transversal. One of the angles formed measures 58°. Which statements about the other seven angles formed are true? (multiple answers)

There are three more angles with the same measure.

All the other angles have the same measure.

The rest of the angles measure 122°.

Only three of the angles measure 122°.

Four of the angles measure 122°.

Answers

Answer:


Correct options are 1 and 5.


Step-by-step explanation:


If parallel lines m and n are cut by a transeversal t, then corresponding angles are equal in measure. Therefore,


∠2≅∠6;

∠1≅∠5;

∠3≅∠7;

∠4≅∠8.


If parallel lines m and n are cut by a transeversal t, then interior angles on the same side are supplementary. Thus,


∠3+∠5=180°;

∠4+∠6=180°.


If one of the angles ( let it be angle 3) formed measures 58°, then m∠5=180°-58°=122°. Then


m∠2=m∠3=m∠6=m∠7=58°;

m∠1=m∠4=m∠5=m∠8=122°.


You can conclude that there are three more angles with the same measure of 58° and four of the angles measure 122°.

What’s the speed limit in mph for a speed limit of 75 kph

Answers

Answer:

46.6 mph

Step-by-step explanation:

1 Kph is .6213 mph

What is
1.567 + 2.345 - 1.83(5) A) -2,082 B) -5.238 C) 2.082 D) 5.742

Answers

Answer:

c) 2.082

Step-by-step explanation:

First you would add 1.567 and 2.345 together to get 3.912. If you take 3.912 and subtract 1.83 from that, it would be 2.082.

Hey there!

1.567 + 2.345 - 1.83 (5)

1.567 + 2.345 = 3.912

3.912 - 1.83(5)

1.83(5) = 9.15

3.912 - 9.15 = -5.238

Answer: -5.238 ✅

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Factors and Multiples,
56
66
Determine wherther the secound number is a factor of the first number,
72, 3 46, 4 132. 7 216, 9

Answers

That is a lot ofhelp

Answer:

No

Step-by-step explanation:

So, you have 56 and 66. The others are 72, 346, 4132.7216, and 9. 66 can not go into 72 more than once, so therefore the answer is no.

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