Answer:
1000Step-by-step explanation:
[tex]log_{10}x = 3 + log_{10}y[/tex][tex]log_{10}x - log_{10}y = 3[/tex][tex]log_{10}(x/y) = 3[/tex][tex]x/y = 10^3[/tex][tex]x/y = 1000[/tex]Answer:
x/y = 10^3 = 1000
Step-by-step explanation:
The rules of logarithms tell you ...
log(x/y) = log(x) -log(y)
__
Here, we have ...
log(x/y) = log(x) -log(y)
= (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)
Taking the antilog, we get ...
log(x/y) = 3
x/y = 10^3 = 1000
_____
Additional comment
The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).
In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).
50 points!!
Solve |y + 2|>6
A. {y|y<-8 or y>4}
B. {y|y<-6 or y>6}
C. {y|y<-4 or y>4}
Answer:
[tex]y < -8[/tex]
[tex]y > 4[/tex]
Step-by-step explanation:
Absolute Value Inequality entered :
|y+2|>6
Step by step solution :
Step 1: Rearrange this Absolute Value Inequality
Absolute value inequalitiy entered
|y+2| > 6
Step 2: Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |y+2|
For the Negative case we'll use -(y+2)
For the Positive case we'll use (y+2)
Step 3: Solve the Negative Case
-(y+2) > 6
Multiply
-y-2 > 6
Rearrange and Add up
-y > 8
Multiply both sides by (-1)
Remember to flip the inequality sign
y < -8
Which is the solution for the Negative Case
Step 4: Solve the Positive Case
(y+2) > 6
Rearrange and Add up
y > 4
Which is the solution for the Positive Case
Step 5:
Wrap up the solution
y < -8
y > 4
Solutions in Interval Notation
(-∞,-8)
(4,+∞)
Solutions on the Number Line
Two solutions were found :
y > 4
y < -8
5 2⁄5 - 3 7⁄10 = What is the correct answer if the answer is wrong I will come and haunt you
[tex] \mathsf\red{♧ANSWER♧}[/tex]
[tex] \mathsf \blue{5 \frac{2}{5} - 3 \frac{7}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{27}{5} - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{2( \frac{27}{5} ) - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{54}{10} - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{17}{10} = 1 \frac{7}{10} = 1.7}[/tex]
A tree is 18 feet tall and casts a shadow
that is 22 feet long. How far is it from the
end of the shadow to the top of the tree?
Show your work.
Answer:
28.42 feet
Step-by-step explanation:
Given
Height of tree = 18 feetLength of shadow = 22 feetTo Find
Distance b/w top of tree and end of shadowSolving
This resembles a right triangle⇒ We can use Pythagorean Theorem!⇒ 18² + 22² = L²⇒ L² = 324 + 484⇒ L² = 808⇒ L = 2√202 ⇒ L = 2 x 14.21⇒ L = 28.42 feetAnswer:
28.4 feet
Step-by-step explanation:
The question can be solved by using Pythagoras Theorem.
Given:-
Height of tree :- 18 feet (Perpendicular)
length of shadow :- 22 feet (Base)
To find:-
Distance of shadow from the end to the top of the tree
Solution:-
We know the Pythagoras theorem,
Which is , H² = P² + B²
So putting the given value , we get
H² = 18²+22²
H² = 324 + 484
H = √ 808 feet
H = 28.4 feet
Which expression is equivalent to 8(a+3)
Answer:
8a + 24
Step-by-step explanation:
Use Distributive property: a(b +c) = a*b + a*c
Here a = 8 ; b= a & c = 3
8(a + 3) = 8*a + 8*3
= 8a + 24
Phoebe rounded a number to the nearest tenth and got 6.5. When she rounded it to the nearest whole number, she got 7. Which number could be the number she rounded?
Answer:
6.7
please give brainliest
(2)Please help with both questions
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Let's think of the boat and wind as vectors:
Boat Vector --> [tex]\langle28cos36^\circ,28sin36^\circ\rangle[/tex]
Wind Vector --> [tex]\langle10cos22^\circ,10sin22^\circ\rangle[/tex]
Now, let's add the vectors:
[tex]\langle28cos36^\circ+10cos22^\circ,28sin36^\circ+10sin22^\circ\rangle[/tex]
Find the magnitude (the true velocity):
[tex]\sqrt{(28cos36^\circ+10cos22^\circ)^2+(28sin36^\circ+10sin22^\circ)}\approx37.78\approx38[/tex]
Find the direction (angle):
[tex]\theta=tan^{-1}(\frac{28sin36^\circ+10sin22^\circ}{28cos36^\circ+10cos22^\circ})\approx32.32^\circ\approx32^\circ[/tex]
Thus, D is the best answer
Problem 2
Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of the vectors and [tex]||u||*||v||[/tex] is the product of each vector's magnitude:
[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{\langle-82,47\rangle\cdot\langle92,80\rangle}{\sqrt{(-82)^2+(47)^2}*\sqrt{(92)^2+(80)^2}})\\\\\theta=cos^{-1}(\frac{(-82)(92)+(47)(80)}{\sqrt{6724+2209}*\sqrt{8464+6400}})\\\\\theta=cos^{-1}(\frac{(-7544)+3760}{\sqrt{8933}*\sqrt{14864}})\\\\\theta=cos^{-1}(\frac{-3784}{\sqrt{132780112}})\\\\\theta\approx109.17^\circ\approx109^\circ[/tex]
Therefore, C is the best answer
if A varies direct as a square of R. Find the % increase in A if R is increase by 20%.
Answer:
20%
Step-by-step explanation:
A=R^2
120/100
=1.2
1.2R= new value of R
original of R=R
A^1/2=R
change/origionalx100%
(1.2A^1/2-A^1/2)
-------------------- x 100%
A^1/2
A^1/2 (1.2-1)
--------------- x100%
A^1/2
0.2
---- x100
1
0.2x100
=20%
99 PTS PLS HELP! Data Set 1 has a mean of 152.7 and a MAD of 2.5.
Data Set 2 has a mean of 170.2 and a MAD of 1.7.
What can be concluded about the two distributions?
Select each correct answer.
The means-to-MAD ratio is 10.
The distributions are different.
The distributions are somewhat similar.
The means-to-MAD ratio is 7.
Answer:
the means to and reroof is 10
the distributions are somewhat similar
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
X =
Answer: x=20
Step-by-step explanation:
(6x-10)=(3x+50) (subtract both sides by 3x)
3x-10=50(add ten to both sides)
3x=60(divide both sides by 3)
x=20
A prize is divided in the ratio 5:1 if the larger share is £65 what is the total prize?
Answer:
£78
Step-by-step explanation:
65 divided by 5= £13
13+65=£78
Answer:
£78
Step-by-step explanation:
Let the total value be T.
£65/T = 5/(5 + 1)£65/T = 5/6T = 65 x 6 / 5T = 13 x 6T = £78a large University with over 40,000 took a recent survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. b = the proportion of students in the sample who claimed to work out 3 at least 3 times a week. What is the standard deviation of the sampling??
Answer:
A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample …
✓ approximately Normal, because we would expect at least 10 success and 10 failures
Step-by-step explanation:
Which of the following units are units of capacity? Select all that apply.
PLEASE HELP PLEASE HELP
Answer:
Acute angle
Step-by-step explanation:
Acute angle = less than 90 degrees
Answer:
acute angles
Step-by-step explanation:
Angles between 0 and 90 degrees (0°< θ <90°) are called acute angles. Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles. Angles that are 90 degrees (θ = 90°) are right angles.
PLSS ANSWER
Ian drinks two and seven eighths liters of water. Farida drinks one and two eighths liters of water. How many more liters of water does Ian drink than Farida?
a. one and five eighths
b. one and one half
c. one half
d. two eighths
6) Over the course of 17 weeks Tiffany collected 18 pounds of cans to recycle and Tom
collected 8 times as much as Tiffany. Tom then put his collection into 6 bags to take to
the recycling center. How many pounds of cans did Tom put into each bag?
Answer:
24 per bag
Step-by-step explanation:
18x8=144 then divide by 6= 144÷6=24
Plsss helppp me find the slope and yint
Answer:
Y-Intercept: (0, -5)
Slope: 1/2
Explanation:
The y-int is when x = 0. The slope formula is (y2 - y1)/(x2 - x1) in which you use 2 points on the line.
A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon. If 750 people go to this store each day, how many people would you expect to use a coupon?
If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon
What is probability?Probability is the likelihood of occurrance of an event. It is given by:
Probability = number of occurrence / total number of possible occurence
A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon.
Probability of using coupon = 32/40 = 0.8
Hence if 750 people go to this store each day, number of people sampled = 75.
Number of people expected to use the coupon = 75 * 0.8 = 60
If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon
Find out more on probability at: https://brainly.com/question/24756209
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Whats the value of the question
Answer:
8
----
125
Step-by-step explanation:
(2/5)³
2 2 2 8
--- x --- x --- = ---------
5 5 5 125
I hope this helps!
Lin’s family needs to travel 325 miles to reach her grandmother’s house. At 377 miles, what percentage of the trip’s distance have they completed?
None of these answer this question and I cant get it anywhere else
Answer:
325/377×100= 116% it means they completed 116%of the trip
What is the perimeter of the pentagon below? 3.2 cm?
Answer:
You didn't attach a picture of the pentagon, but the perimiter can easily be found using one of the following formulae:
Step-by-step explanation:
P = 5s, where s is the length of a side
P = 2r × Sin(180/5), where r is the radius
Look at this parallelogram. Find the value of p.
Answer:
15
Step-by-step explanation:
15 is the answer
If you need solution do let me know in the comments
How many solutions does this system have?
y=-3x
-9x-4y = 21
one
two
an infinite number
no solution
PLEASE HELP ME WITH THIS QUESTION
Answer:
The second option, 1,008 cm²
Step-by-step explanation:
This shape has 5 sides to solve for with reguards to surface area.
Let us solve for them all.
[1 & 2 - the triangles]
12 * 9 = 108 cm²
-> I am not going to divide since we have 2 congruent triangles
[3 - the bottom side]
25 * 12 = 300 cm²
[4 - the side facing away]
25 * 9 = 225 cm²
[5 - the side facing up]
25 * 15 = 375 cm²
Now we will add them together for the total.
108 + 300 + 225 + 375 = 1,008 cm²
The surface area for the triangular prism shown is 1,008 cm².
Answer:
Your answer would be:
C.) 1,350 cm2
Volume = 0.5 x b x h x length
0.5 x (25 x 12) x 9 =
0.5 x 300 x 9 =
= 1,350 cm2
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Find the product of 4+3i and its conjugate.the answer is a +bi where
The value of a and b in the product of 4+3i and its conjugate in the format a + bi are 25 and 0.
What is conjugate?The conjugate is where we change the sign in the middle of two terms. For example:
3y + 1
conjugate of 3y + 1 is 3y - 1.
Therefore, the conjugate of 4 + 3i is 4 - 3i.
The product of 4 + 3i and its conjugate is as follows:
(4 + 3i)(4 - 3i) = 16 - 12i + 12i - 9(i)²
Therefore,
16 - 9i²
i² = -1
Hence,
16 - 9(-1) = 25
It can be written in the form a complex form → (25 + 0.i)
Therefore, a = 25 and b = 0.
learn more on conjugate here: https://brainly.com/question/20757260
I need help with this question?
Answer:
38.5 cm²
Find area of the full rectangle:
Length * Width
6 * 7
42 cm²
Find area of the missing triangle
1/2 * base * height
1/2 * 7 * 1
3.5 cm²
Area of the figure:
42 - 3.5
38.5 cm²
Find the area of the figure.
Pls help
It's a trapezoid
Base=15+5=20cmAnother side=15cmHeight=12cmNow
Area:-
1/2(Sum of parallel sides)(Height)1/2(15+20)(12)6(35)210cm^2Can someone help me please?
Answer:
11/2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
This is because each dot represents one plot, and the only number with one plot above it is 1 and 1/2, aka D
HELPPPPPPPP 50PTSSSSSS!!!!!!!!!
#1
Paved area:-
L(12)=205-7(12)=205-84=121mi#b
Let's see
205-7d=1567d=205-1567d=49d=7daysAnswer:
(a) 121 miles
(b) 7 days
Step-by-step explanation:
Given function:
[tex]\sf L(d)=205-7d[/tex]
Question (a)
When d = 12:
[tex]\sf \implies L(12)=205-7(12)[/tex]
[tex]\sf =205-84[/tex]
[tex]\sf =121 \ miles[/tex]
Therefore, the crew has 121 miles left to pave after 12 days.
Question (b)
When L(d) = 156
[tex]\sf \implies 156=205-7d[/tex]
[tex]\sf \implies 7d=205-156[/tex]
[tex]\sf \implies 7d=49[/tex]
[tex]\sf \implies d=\pm\sqrt{49}[/tex]
[tex]\sf \implies d=\pm7[/tex]
As distance is positive, [tex]\sf d=7[/tex] only
Therefore, the crew has been paving the the road for 7 days.
What the value of q?
Step-by-step explanation:
this is very simple.
you can compare this to the question "in my bag are 70 pieces of fruit. 30 of them are apples. how many pieces of other fruit are there ?"
well, it is 70 - 30 = 40 !
that's it ! that is all there is to it.
so, q = 40°
what is still unclear, please ?