The difference in elevations between a scuba diver at -8 meters and a shark at -29 meters is calculated as: -8 - (-29) = 21 meters.
Explanation:The subject in question involves finding the difference in elevations. In this context, the scuba diver is swimming at an elevation of -8 meters, and the shark is at -29 meters. To find the difference, we subtract the lower number (-8) from the higher number (-29).
However, due to the negative signs, the difference will be calculated as follows: -8 - (-29) = -8 + 29 = 21 meters. Therefore, the difference in elevations between the shark and the scuba diver is 21 meters.
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given: m = 1/2 and b=4
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y-intercept )
here m = [tex]\frac{1}{2}[/tex] and b = 4, hence
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
Answer:
where is the question?
5|-6+r|=55
[tex]5 | - 6 + r| = 55[/tex]
Answer:
r= -5 , r= 17
Step-by-step explanation:
5|-6+r|=55
solve for 'r'
First we isolate absolute function
We divide both sides by 5
|-6+r| = 11
for absolute function we consider two cases, one with positive and one with negative. Now we make two equations
-6+r = 11 or -6+r = -11
Now solve both equations
-6 + r= 11
Add 6 on both sides
so , r= 17
-6 + r= -11
add 6 on both sides , so r= -5
PLEASE HURRY!
There is a geometric theorem that says "If twp lines in a plane are perpendicular to the same line, they are parallel to each other." Explain why this is true by writing and comparing equations for two different lines that are perpendicular to y= -1/3x.
Two lines perpendicular to a third line are parallel to each other because they both inherit the slope from their perpendicularity. The resulting lines only differ in their y-intercepts, indicating they run parallel.
Explanation:The theorem you're referring to essentially relates to the slope of the lines. If two lines are each perpendicular to the same line, this means the slope of all three lines are related. This occurs because the slope of any line perpendicular to y=-1/3x is 3, the negative reciprocal of -1/3. For example, if we have two lines L1: y = 3x + b1 and L2: y = 3x + b2 which are both perpendicular to y= -1/3x (and thus parallel to each other), their formulas would only differ by their y-intercepts (b1 and b2). Since the coefficient of x (the slope) remains the same (3), we can conclude that these two lines are indeed parallel to each other which confirms the mentioned geometric theorem.
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3rs - 5cr - 15cs + 25c2
[tex]3rs-5cr-15cs+25c^2=r(3s-5c)-5c(3s-5c)\\\\=(3s-5c)(r-5c)\\\\Answer:\ \boxed{3rs-5cr-15cs+25c^2=(3s-5c)(r-5c)}[/tex]
I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?
The maximum number of trees the student can plant per row is 10. This is found by identifying the greatest common divisor of the total number of apple trees and peach trees he has which is 10.
Explanation:To solve this problem, you need to find the greatest common divisor of 50 (the number of apple trees) and 30 (the number of peach trees). The greatest common divisor is the highest number that can divide both numbers without a remainder.
Both 50 and 30 can be divided by 10 without any remainder, but they can't be divided evenly by any number higher than 10. Therefore, 10 is the greatest common divisor of 50 and 30.
In this context, being able to divide the number of trees evenly means that you can plant the same number of each type of tree in each row. So, given the total numbers of apple and peach trees, the maximum number of trees you can plant per row is 10.
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To determine the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with uniformity, calculate the greatest common divisor (GCD) of the two quantities, which is 10. This means the maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.
The question involves finding the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with the same number and type of trees per row. To find this number, we need to determine the greatest common divisor (GCD) of the two quantities, which will tell us the largest number of trees that can uniformly fit into each row for both types of trees.
First, list the factors of 50 (1, 2, 5, 10, 25, 50) and the factors of 30 (1, 2, 3, 5, 6, 10, 15, 30).
Find the largest factor that appears in both lists. In this case, it is 10.
The maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.
Therefore, you can plant up to 10 trees per row for a neat and organized orchard layout.
3/4( 1/6 x+16)= 3/7 (4 3/8 x−21)
Answer:
x=12
Step-by-step explanation:
Solve for x:
(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7
Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:
(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7
8×4 = 32:
(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7
32/8 + 3/8 = (32 + 3)/8:
(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7
32 + 3 = 35:
(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7
Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:
3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7
x/6 + 96/6 = (x + 96)/6:
3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7
3/6 = 3/(3×2) = 1/2:
(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7
Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:
(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8
(35 x)/8 - 168/8 = (35 x - 168)/8:
(x + 96)/(2×4) = 3/7 (35 x - 168)/8
2×4 = 8:
(x + 96)/8 = (3 (35 x - 168))/(8×7)
8×7 = 56:
(x + 96)/8 = (3 (35 x - 168))/56
Multiply both sides by 56:
(56 (x + 96))/8 = (56×3 (35 x - 168))/56
56/8 = (8×7)/8 = 7:
7 (x + 96) = (56×3 (35 x - 168))/56
(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):
7 (x + 96) = 3 (35 x - 168)
Expand out terms of the left hand side:
7 x + 672 = 3 (35 x - 168)
Expand out terms of the right hand side:
7 x + 672 = 105 x - 504
Subtract 105 x from both sides:
(7 x - 105 x) + 672 = (105 x - 105 x) - 504
7 x - 105 x = -98 x:
-98 x + 672 = (105 x - 105 x) - 504
105 x - 105 x = 0:
672 - 98 x = -504
Subtract 672 from both sides:
(672 - 672) - 98 x = -672 - 504
672 - 672 = 0:
-98 x = -672 - 504
-672 - 504 = -1176:
-98 x = -1176
Divide both sides of -98 x = -1176 by -98:
(-98 x)/(-98) = (-1176)/(-98)
(-98)/(-98) = 1:
x = (-1176)/(-98)
The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:
Answer: x = 12
9/10+7/100 WHAT DOES THE EQUAL
Answer:
97/100
Step-by-step explanation:
9/10 = 90/100
90/100 + 7/100 = 97/100
How to solve for b in p=2(a+b)
[tex]2(a+b)=p\qquad\text{divide both sides by 2}\\\\a+b=\dfrac{p}{2}\qquad\text{subtract a from both sides}\\\\\boxed{b=\dfrac{p}{2}-a}\\\\or\\\\2(a+b)=p\qquad\text{use distributive property}\\\\2a+2b=p\qquad\text{subtract 2a from both sides}\\\\2b=p-2a\qquad\text{divide both sides by 2}\\\\\boxed{b=\dfrac{p-2a}{2}}[/tex]
Please help! Thank you
M and O are congruent
N, M and O are similar
Your answer is: M and N are similar but not congruentM and N are similar because the sides of M are proportional to sides of N:
[tex]\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Two figures are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
To make a sandwich, Steve uses 1/8 1b of ham and 1/5 1b of cheese how much more cheese than ham does he use?
A 1/3
B 3/40
C 1/20
D 1/10. PLEASE ANSWER THIS
Answer: B - 3/40
Step-by-step explanation: in order to find their difference, set up their common denominators equally, resulting in them having 5/40 and 8/40. subtract and you will get 3/40 as your final answer.
What is the probability of someone being born on Feb.28 given that they were born in February?
Answer:
4/113
Step-by-step explanation:
1/28 for non leap years and 1/29 for leap years
However if u put those together it would be 4/113 overall
This is because every 4 years there are 113 days in February and 4 of those days will be the 28th.
Final answer:
The probability of someone being born on February 28th given that they were born in February is 1/28, assuming a non-leap year scenario.
Explanation:
The student is asking about the probability of being born on February 28th, given that they were born in February. Given that February usually has 28 days, except for leap years when it has 29 days, to find this probability, we consider a non-leap year scenario.
The total number of possible birth dates in February, in a non-leap year, is 28. Since being born on any given day in February is equally likely, the probability of being born on February 28th is simply 1 divided by the number of days in February.
Therefore, the probability is:
P(born on Feb. 28) = 1/28
I will give a thanks and a 5star is you answer ASAP
Answer: -2,0,2,4,6
The solution of the inequality is x<1
Step-by-step explanation:
Answer:
x < 1
Step-by-step explanation:
2x < 2
Divide 2 on both sides
x < 1
------------------------------------------------------------------------
Table: (I think)
-2 , 0 , 2 , 4 , 6
0.7(3x−0.2)=0.3(0.8−2x)
URGENT
20 Points!
Please Help!!!
Answer:
x = .140741
Step-by-step explanation:
0.7(3x−0.2)=0.3(0.8−2x)
Distribute
.7 * 3x - .7*.2 = .3*.8 - .3 * 2x
2.1x - .14 = .24 - .6x
Add .6x to each side
2.1x +.6x -.14 = .24 -.6x+.6x
2.7x -.14 = .24
Add .14 to each side
2.7x -.14+.14 = .24+.14
2.7x = .38
Divide by 2.7 on each side
2.7x/2.7 = .38/2.7
x = .140741
How would you do this problem?
(7+√6)(7+√6)
BEST ANSWER GETS BRANLIEST AND 99 POINTS
Answer:
55 + 14 sqrt(6)
Step-by-step explanation:
(7+√6)(7+√6)
We can figure out this problem by FOILing
First : 7*7 = 49
Outer: 7* sqrt(6) = 7 sqrt(6)
Inner: 7* sqrt(6) = 7 sqrt(6)
Last: sqrt(6) * sqrt(6) = 6
Add these together
49+ 7 sqrt(6)+ 7 sqrt(6)+6
55 + 14 sqrt(6)
A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket
Answer:
Step-by-step explanation:
35 x .08 = $2.80
35 + 2.80 = 37.80
Answer:
T = 0.08 × 35
Step-by-step explanation:
The cost of a jacket = $35
The tax rate on the jacket = 8% = [tex]\frac{8}{100}[/tex]
= 0.08
The expression to find the cost of the tax on the jacket would be
T = 0.08 × 35
find the value of x in 2x+20=3x-8
Answer:
X=28
Step-by-step explanation:
3x-8=2x+20. So x=28
How do I show that x5-y5=(x-y)(x4+x3y+x2y2+xy3+y4)
The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex] is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.
Explanation:Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.
Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]
Expand the expression on the right-hand side: [tex](x - y)(x^4 + x^3y + x2y^2 + xy^3 + y^4).[/tex]You do this by distributing x to all the terms in the parenthesis and then y to all the terms in the parenthesis.When you simplify this expression, you will find that it equals to x5 - y5.
This demonstrates that the original formula you asked about is accurate.
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a man pays 20% of his salary as tax and has 24,000$ left. How much did he pay as tax
Answer:
He paid $6,000 in taxes.
Step-by-step explanation:
His final amount after taxes is $24000. In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%). In other words if he was taxed 20% he took home 80% of what he was paid. Therefore mathematically we have:
[tex]0.8A_{pre-tax}=A_{taxed}[/tex]
Since we know he was left with $24000 after taxes then:
[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]
So originally he had $30,000. So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:
$30,000 - $24,000= $6,000 taxed
please help me with this question!!
Answer:
40
Step-by-step explanation:
5+1 3/8n=60
Subtract 5
1 3/8n=55
11/8n=55
8/11(55/1)
n=40
In a group of 25 students, 12 students play basketball, 11 students play football. Five students play both sports. A student is chosen randomly from this group.
What is the probability that the student plays both basketball or football?
Answer:
2/25 chance for both.
Step-by-step explanation:
There is a total of 25 students = 25 as my denominator.
11 + 12 = 23.
25 -23 = 2
Therefore my numerator is 2.
----> 2/25
if 4x+41=3x+45, what is the value for x
Answer:
x = 4
Step-by-step explanation:
4x+41=3x+45
Subtract 3x from both sides
x + 41 = 45
Subtract 41 from both sides
x = 4
n first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 1,850 r.p.m. Transmission in second gear Drive-shaft speed =
Answer:
Consider the following cases
Case 1: In n first gear, an automobile's engine runs about three times as fast as the drive shaft.
So, if Speed of Engine = 1,850 r.p.m
Then Speed of Drive Shaft [tex]=\frac{1850}{3}=616.67[/tex] r.p.m
Case 2 : In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft.
So, if Speed of Engine = 1,850 r.p.m
Then Speed of Drive Shaft [tex]=\frac{1850}{1.6}=1156.25[/tex] r.p.m
Case 3: Finally, in third, or high gear, the engine runs at the same speed as the drive shaft.
So, if Speed of Engine = 1,850 r.p.m
Then Speed of Drive Shaft is also equal to 1,850 r.p.m
what expression represents a number one fourth as great as 10-2
Answer:
The expression represents
[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is [tex]a \geq 0.0025[/tex]
Step-by-step explanation:
Given : Expression represents a number one fourth as great as [tex]10^{-2}[/tex]
To find : What is the expression?
Solution :
Let the number be 'a'.
According to question,
A number one fourth as great as [tex]10^{-2}[/tex]
i.e. [tex]a\geq \frac{1}{4}\times (10^{-2})[/tex]
Now, we solve the expression
[tex]a \geq \frac{1}{4}\times\frac{1}{100}[/tex]
[tex]a \geq\frac{1}{400}[/tex]
[tex]a \geq 0.0025[/tex]
Therefore, The expression represents
[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is [tex]a \geq 0.0025[/tex]
PLEASE HURRY
Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth.
A 0.137 B 0.138 C 0.394 D 0.707
Answer:
0.707 to nearest thousandth
Step-by-step explanation:
People who go at least 2 times a month = 219 + 180 + 96
= 495
So the required probability = 495 / 700
= 0.707 14
Please help please help
Answer:
D
Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3
Answer:
B is the one here as well
can someone help with this
Answer:
(1,3)
Step-by-step explanation:
From the graph, determine the coordinates of the point of intersection of the two. They are x=1 and y=3: (1,3)
This is the last of the four given possible answers.
Answer:
(1,3)
Step-by-step explanation:
The solution to a system of equations that is graphed is where the two graphs intersect. The two lines intersection at 1, 3. We can check this by putting them into the equation
y = 3x
3 = 3*1
True
y =x+2
3 = 1+2
3=3
True
This is the solution to the system of equations
Need an educated answer fast
Answer:
y-2 = 2/3(x-8)
Step-by-step explanation:
We have the line 6x-9y = -7
Let's rewrite it in the form y=mx+b
6x-9y = -7
Subtract 6x from each side
6x-6x-9y = -7 -6x
-9y = -6x-7
Divide by -9
-9y/-9 = -6x/-9 -7/-9
y = 2/3 x + 7/9
The slope is 2/3
If the line is parallel, the slope will be the same so the slope will be 2/3
We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line
y-y1 = m(x-x1)
y-2 = 2/3(x-8)
at the amusement park each student is given $16 for food this covers the cost of two meals plus $4 for snacks how much money does the school expect the students to spend per meal. which equation could be used to represent this dituation
6. Maya is driving 120 miles to her grandmother’s house. She drives 35% of the distance before stopping for lunch. How far does she drive before lunch? (1 point)
Answer:
42 miles
Step-by-step explanation:
She drove 35% of 120 miles.
To find a percent of a number, multiply the percent by the number.
35% of 120 miles =
= 35% * 120 miles
= 0.35 * 120
= 42
Which inequality matches the graph?
A) x > -2
B) x < -2
C) x = -2
D) x ≤ -2
Answer:
D) x ≤ -2
Step-by-step explanation:
The dot is at -2 = -2
the dot is filled in = ≤ or ≥ because its means equal too
think of ≤ or ≥ like arrows = it points left.
so its x ≤ -2
Note on using the ≤ or ≥ like pointing arrows
this only works if its written:
variable < constant form,
which is the way they are usually seen, like x < 5
but it could be 5 > x which means the > points the opposite way
Hello! :)
Answer:
D. x≤-2
*The answer must have a negative sign and less than or equal to.*
Step-by-step explanation:
Lesson: It's about the graphing inequalities
An inequality is a statement that compares mathematical expressions that are not equal. The expressions are separated by an inequality symbol (<,>, ≤, ≥, or ≠).
The arrow points to the left. The circle is closed.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thanks!