Step-by-step explanation:
6+ 7•log2 x = 21
7.log2 x = 21-6
7. log2 x = 15
log2 x = 15/7
x = 2^(15/7)
x = 4.416 = 4.42
There are 5 red marbles, 15 blue marbles, and 5 green marbles in a bag.If you reach in and randomly draw two marbles without replacing the first, what is the probability that both will be blue.
Answer:
3/5
Step-by-step explanation:
Total number of marbles = 5 + 15 + 5 = 25
Number of blue marbles = 15
Probability of blue marbles:
= 15/25
=3/5
Hope it helps......
9. Simplify by rationalising the denominator: 2+√3 2−√3 + 2−√3 2+√3 .
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { 14 }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } [/tex]
[tex] \\= \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } [/tex]
[tex] \\= \frac{2 \: (2 + \sqrt{3} )+ \sqrt{3} \: (2 + \sqrt{3} )}{ ({2})^{2} - ({ \sqrt{3} })^{2} } + \frac{2 \: (2 - \sqrt{3} ) - \sqrt{3} \: (2 - \sqrt{3} ) }{ ({2})^{2} - ( { \sqrt{3} })^{2} } [/tex]
[tex]\\ = \frac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 }{4 - 3} + \frac{4 - 2 \sqrt{3} - 2 \sqrt{3} + 3}{4 - 3} [/tex]
[tex]\\ = \frac{7 + 4 \sqrt{3} }{1} + \frac{7 - 4 \sqrt{3} }{1} [/tex]
[tex] \\= 7 + 4 \sqrt{3} + (7 - 4 \sqrt{3} )[/tex]
[tex] \\= 7 + 4 \sqrt{3} + 7 -4 \sqrt{3} [/tex]
[tex] \\= 14[/tex]
Note:[tex] (a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
Solve this problem.
A pair of inline skates that usually sells for $40 is on sale at a 30% discount.
What is the sale price?
Answer:
$28
Step-by-step explanation:
original price = $40
discount = 30%
discount amount = 30% of original price
=30/100 * 40
=$1200/100
=$12
sale price = original price - discount amount
=$40 - $12
=$28
Pls help no files just type it in I will mark you
Kyle has run 7 laps around the track. If he plans to run 15 laps, how many more laps must he run?
would i divide or multiply
Answer: 8 more
Step-by-step explanation:
use subtraction
Answer:
8 more laps
Step-by-step explanation:15-7=8
Suppose that every day from Monday through Friday,
you keep the following routine:
You walk directly to school in the moming. On this walk,
you take 1500 steps.
You play at recess.
You play a sport.
You walk directly home from school.
You think you take about as many steps at recess as you
do playing your sport
Your
FitBit says that you have taken a total of 38.000 steps
during the week.
How many steps do you take every day at recess?
Answer: You take around 4,500 steps a day
Step-by-step explanation:
Jonathan and anna have to share $20.64 evenly for the summer festival. how much money will each child recieve.
Answer:
10.32
Step-by-step explanation:
20.64 divided by 2
Which could be the resulting equation when elimination is used to solve the given system of equations ?
Answer:
10·b = 60
Step-by-step explanation:
The given system of equation is presented as follows;
5·a + 5·b = 25...(1)
-5·a + 5·b = 35...(2)
Given that the coefficient of a in equation (1) is equal in magnitude but opposite in sign to the coefficient of 'a' in equation (2), to eliminate the variable 'a' when using the elimination method, we add both equations as follows;
5·a + 5·b + (-5·a + 5·b) = 25 + 35 = 60
5·a - 5·a + 5·b + 5·b = 60
5·a - 5·a = 0
5·b + 5·b = 10·b
∴ 5·a - 5·a + 5·b + 5·b = 60 = 0 + 10·b = 10·b
∴ 10·b = 60
Use the diagram right above
AB=?
m
the difference of 15 and 7 divided by 2
(High points) please solve with explanation
Answer:
The area and the perimeter of the picture are:
Area = 160 cm^2Perimeter = 67.31 cmStep-by-step explanation:
To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:
Area of a rectangle = base * heightAs you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:
Area of a rectangle = 16 cm * 12 cmArea of a rectangle = 192 cm^2Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:
Area of a triangle = (base * height) / 2The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:
Area of a triangle = (8 cm * 8 cm) / 2Area of a triangle = (64 cm^2) / 2Area of a triangle = 32 cm^2We subtract to the found area:
Area of the picture = 192 cm^2 - 32 cm^2Area of the picture = 160 cm^2To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:
[tex]a^{2}+b^{2}=c^{2}[/tex]Where:
a = Opposite leg (8 cm)b = Adjacent leg (8 cm)So, we replace in the theorem:
[tex]a^{2}+b^{2}=c^{2}[/tex][tex](8 cm)^{2}+(8cm)^{2}=c^{2}[/tex] (and we clear c)[tex]\sqrt{(8 cm)^{2}+(8cm)^{2}} =c[/tex] [tex]\sqrt{64 cm^{2}+64cm^{2}} =c[/tex] [tex]\sqrt{128cm^{2}} =c[/tex]c = 11.3137085 cmc ≅ 11.31 cmAt last, we add all the sides of the picture begining by the base and going by the left side:
Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cmPerimeter of the picture = 67.31 cm approximately.Question 4(Multiple Choice Worth 1 points)
(07.02 MC)
An equation is shown below:
4(2x - 3) = 1
Which of the following correctly shows the steps to solve this equation?
Step 1: 6x - 7 = 1; Step 2: 6x = 8
Step 1: 6x + 1 = 1; Step 2: 6x = 0
Step 1: 8x - 12 = 1; Step 2: 8x = 13
Step 1: 8x - 3 = 1; Step 2: 8x = 4
Answer:
Step 1: 8x - 12 = 1; Step 2: 8x = 13
Step-by-step explanation:
Given equation:
4(2x - 3) = 1
Step 1: open the parenthesis
4(2x - 3) = 1
8x - 12 = 1
Step 2: collect like terms
8x - 12 = 1
8x = 1 + 12
8x = 13
step 3: divide both sides by the coefficient of x
8x = 13
x = 13/8
The correct steps to solve the equation:
Step 1: 8x - 12 = 1; Step 2: 8x = 13
please solve this fast.
Question 1 Multiple Choice Worth 1 points)
(01.05 LC)
Solve for x: -7 < X -1 <8
Answer:
-6 < x <9
Step-by-step explanation:
-7 < X -1 <8
Add 1 to all sides
-7+1 < X -1+1 <8+1
-6 < x <9
Answer:
D
Step-by-step explanation:
Maria has an 8-sided die that is numbered from 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8? about 8 times about 12 times about 16 times about 768 times
Answer:
12 Times
Step-by-step explanation:
According To The Question,
The Probability of Rolling An 8 is 1/8 .
Thus , 1/8=X/96
So, X=96/8⇔X=12
Please help me I need this answer to pass high school, math is so difficult man, giving brainliest
Answer:
man you are right it is difficult
In the diagram below of triangle MNO, P is the midpoint of MO and Q is the midpoint of NO. If PQ = 5x + 62, and MN = 6x-4, what is the measure of PQ?
Answer:
29
Step-by-step explanation:
There is a triangle embedded in triangle MNO, which is triangle PQO, and these are similar triangles in that their corresponding sides are always in the same ratio, which in this case is 2:1, as MP = MO due to the midpoint definition, and therefore MO is twice as long as MP. Same for NO and QO.
Now that we know the ratio, we can set 6x-4 = 2(-5x+64)
6x-4 = -10x +108
16x = 112
x = 7
Plug x back in for PQ, -5(7)+64 = 29
The measure of PQ is 22 units.
What is mid point theorem?A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.
Given:
PQ = 5x + 62, and MN = 6x-4
Now, using Mid- Point Theorem
PQ= 1/2 MN
-5x+ 62 = 1/2( 6x - 4)
-5x+ 62 = 3x - 2
-5x- 3x = -2 - 62
-8x = -64
x= 8
and, PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22
Hence, the measure of PQ is 22 units.
Learn more about mid point theorem here:
https://brainly.com/question/13677972
#SPJ2
A planet has a circular orbit around a star. It is a distance of 98,000,000 km from the centre of the star. It orbits at an average speed of 45,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answer:
91 days
Step-by-step explanation:
Given that,
A planet is at a distance of 98,000,000 km from the centre of the star.
It orbits at an average speed of 45,000 km/h.
The speed of an object is given by the distance covered divided by the time taken. So,
[tex]v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{98,000,000}{45,000}\\\\t= $$2177.77\ h[/tex]
or
t = 90.74 days ≅ 91 days
So, the planet take 91 days to orbit the star.
Why should money be your motivation?
[tex] \huge{ \green{ \boxed{ \boxed{ \sf{ \blue{hi}}}}}}[/tex]
My AnswerMoney is a crucial incentive to work motivation. It is a medium of exchange and the means by which employees can purchase things to satisfy their needs and desires. It also serves as a scorecard by which employees assess the value that the organization places on their services
#CarryonLearningBrainliest please
i don’t understand help me pls
Answer:
AC = 7.42
Step-by-step explanation:
Draw a picture!
∠ACB = 90 - 38 = 52º
Use Law of Sines
AC/sin38 = 9.5/sin52
AC = 9.5/sin52 * sin38
Use calculator
AC = 7.422213451813815
AC = 7.42 Rounded to 3SF
what is the answer to 15y − 1 = 11/2y + 2
Answer:
y= 6/19
hope it helps
Select all the numbers that are irrational.
9514 1404 393
Answer:
π, √3, 3√2
Step-by-step explanation:
A number is irrational if it is not a decimal number of finite length or a repeating decimal number.
The irrational numbers in the group are shown below.
(2x6)3/4 using rational exponents
Answer:
the answer is 9 divided by 1
AVERAGES 1. Find the mean, mode and median of: (a) 1.5, 1.2, 1.3, 1.5, 1.4 (b) 2.3, 1.2, 2.4, 1.2
Answer:
Look at Step by step
Step-by-step explanation:
Mean: (a) 1.38
Mean: (b) 1.7
median (a) 1.3
Pacx '?
a]g.;//
>Dc.cccccccccccccccccccccccccccccx;;;;;;;;;;;;;;;;;;;;;;;;;|;z
;zzx';
[c' / v\Zcccccccc
Answer:
A)mean is 1.38 mode is 1.5 median is 1.4
B)mean is 1.775 mode is 1.2 median is 1.75
Step-by-step explanation:
the mean is the average of the numbers added together divided by how many numbers are listed. 1.5+1.2+1.3+1.5+1.4=6.9 6.9 divided by 5 = 1.38
mode is the number that shows up in the list the most.
median is the number that is in the middle of the list of numbers when listed highest to lowest or vice versa.
In the instance of (B) since there were only 4 numbers and could not get exact middle number you take the 2 middle numbers and add them together and divide by 2 to get the average of those 2 numbers
ethan invests £500 in the bank for 2 years he earned £40 simple interest
Answer:
Rate = 4%
Step-by-step explanation:
principal = £500
time = 2 years
simple interest = £40
rate = ?
simple interest = PTR / 100
£40 = £500*2*R /100
£40*100 = £1000*R
£4000/£1000 = R
4 % = R
John is twice as old as Mary. The sum of thelr ages is 21. How old Is Mary?
Answer: 7 years
Step-by-step explanation:
let x be the age of Mary
so John's age will be 2x
the equation becomes
2x+x=21
3x=21
x=21/3
x=7
Answer:
Step-by-step explanation:
Let Mary's age = x years
John's age = 2 * x = 2x
The sum of their ages = 21
x + 2x = 21
3x = 21
Divide both sides by 3
x = 21/3
x = 7
Mary's age = 7 years
if the probability that it will rain tomorrow is 1/5
what is the probability that it will not rain tomorrow?
Answer:
If the probability is that it WILL rain 1/5. Then the remaining chances are the number it will not rain. The denominator tells us that there are at total of 5 chances. That leaves a 4/5 chance it will not rain.
Step-by-step explanation:
CAN SOMEONE HELP ME OUT WITH THIS PLEAS AND THANK YOU.
Answer:
5 11/30
Step-by-step explanation:
convert both to least common denominator then solve
Answer:
the answer to this question is 5.366666666
What additional information is needed to prove the triangles are congruent by HL?
Answer:
bce is 90
Step-by-step explanation:
Which graph or equation represents a Nonpoportional relationship A B C or D
Answer:
A
Step-by-step explanation:
A graph that represents a proportional relationship usually has the line cutting through the line of origin (0, 0).
The graph in option A does not have the line passing through the point of origin (0, 0), therefore, it does not represent a proportional relationship.
For an equation that represents a proportional relationship, it is written in the form of y = kx
Where, k is the constant of proportionality.
Therefore, the two equations given represents a proportional relationship.