9514 1404 393
Answer:
x ≈ 17.3
Step-by-step explanation:
The triangles are all similar, so the side lengths are proportional.
short side / hypotenuse = x/30 = 10/x
x² = 300 . . . . . . cross multiply
x = 10√3 . . . . . . take square root
x ≈ 17.3
An artificial pond is stocked with an initial population of 2,500 fish. The engineers estimate a 24% decline in the fish population over time without restocking or effects of fishing. The following function models the population, where x is the number of years since the pond was made.
f(x) = 2,500(0.76)x
The mathematical range of the function is y > 0. Which statement describes how the reasonable range compares to the mathematical range?
The reasonable range has a minimum value of 2,500.
The reasonable range has a maximum value of 2,500.
The reasonable range has a reasonable minimum that cannot be determined.
The reasonable range has a reasonable maximum that cannot be determined.
Answer:
B) the reasonable range has a maximum value of 2,500
Step-by-step explanation:
The reasonable range has a maximum value of 2500.
What is mathematical range?
'The Range is the difference between the lowest and highest values.'
According to the given problem,
f(x) = 2500 × [tex]0.76^{x}[/tex]
Number of years = x
⇒ x ≥ 0
⇒ f(x) ≤ 2500 × [tex]0.76^{0}[/tex]
= 2500
Hence, we can conclude, the reasonable range has a maximum value of 2500.
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Find the sum of -8x^{2}+9x−8x 2 +9x and -6x^{2}+10x−6x 2 +10x.
Answer:
-14x² +19x
Step-by-step explanation:
You want the sum of the expressions (-8x² +9x) and (-6x² +10x).
SimplificationThe sum is found by adding like terms: terms with the variable to the same power.
(-8x² +9x) + (-6x² +10x)
= (-8 -6)x² +(9 +10)x
= -14x² +19x
What can 7/8 be rewritten as?
Answer:
0.875
Step-by-step explanation:
Answer:
Step-by-step explanation:
u would divide 7 by eight and get 0.875
Find each angle measure in the triangle.
3x°
2xº
4xº
The total measure of angles in a triangle is 180°.
3x° + 2x° + 4x° = 180°
9x° = 180°
x° = 180° ÷ 9
x° = 20
Our 3 angles are:
3(20) = 60°
2(20) = 40°
4(20) = 80°
Done.
Answer:
Step-by-step explanation:
3x+2x+4x=180
9x=180
x=180/9=20
3x=3×20=60°
2x=2×20=40°
4x=4×20=80°
Graph the logarithmic function below by moving the
key point.
y = log₂ (x)
You can only graph integer points
To graph the logarithmic function y = log₂(x), we can use the key point (1,0) and the fact that the logarithmic function is the inverse of the exponential function y = 2ˣ.
Starting at the key point (1,0), we can move to the right by increasing x by a factor of 2, since log₂(2) = 1. This takes us to the point (2,1). Similarly, we can move to the right by a factor of 2 again to get to the point (4,2), and then to (8,3), (16,4), and so on.
If we instead move to the left from the key point (1,0) by a factor of 2, we get to the point (1/2, -1), since log₂(1/2) = -1. We can continue moving to the left by dividing x by 2 to get to (1/4, -2), (1/8, -3), and so on.
The given graph of y = log₂(x) using only integer points.
The graph is symmetric about the line x=1, since log₂(x) = log₂(1/x) = -log₂(x).
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Fred buys flags from a manufacturer. For f dollars each and then sells the flags in his store for a 26% markup . write an expression for the retail price of a flag
Answer:
f - 0.26f
Step-by-step explanation:
please help me asap
Which expressions represent the sum of exactly two terms?
Choose 2 answers:
(Choice A)
xy
(Choice B)
m^4+6n
(Choice C)
3+7s+t
(Choice D)
a+c
Answer:
Step-by-step explanation:
The answer is a+c and 3+7s+t
Bacuase both term have single power
Can someone help with this please?
Answer:
look below
Step-by-step explanation:
slope: 2/1
Y- intercept:1
equation: y= 2x+1
PLZ HELP ME
1: Suraj says the two expressions below are equivalent. Is he correct? 2(3d - 2) and 6d - 2
A: No, when you distribute 2(3d - 2) you get 3d - 4 .Suraj did not distribute correctly.
B: Yes, when you factor 6d - 2 you get 2(3d - 2)
C: No, when you distribute 2(3d - 2) you get 6d - 4. Suraj did not multiply 2 by -2 correctly
D: Yes, when you distribute 2(3d - 2) you get 6d - 2.
2: Using the expressions (3x - 5y) and (4x + 2y),find the sum of the two given expressions.
A: 7x + 7y
B: 7x + 3y
C: x - 7y
D: 7x - 3y
3: Using the expressions (3x - 5y) and (4x + 2y), find the difference of the two given expressions.
A: -x - 7y
B: x - 3y
C: x - 7y
D: x + 3y
4: Factor: 30a + 35b.
A: 5(6a + 7b)
B: 5b(6a + 7)
C: this expression is already factored
D: 5a(6 + 7b)
What story matches the graph?
Answer:
A. Starting from home, Kyle jogs increasing his speed until he gets a cramp. He then slows his pace, begins walking, and returns home.
Explanation:
The line starts from the bottom (starting from home), the line goes up (Kyle jogs increasing) the line goes down (he gets a cramp). the line is at constant speed (he begins walking) the line goes back to his starting point. (and he returns home)
Adult and student tickets to the high school basketball game are sold each week. for every two adult tickets seven students tickets are sold. how many total tickets were sold if 92 adult tickets were sold?
Answer:
414
Step-by-step explanation:
the ratio of adult tickets to student tickets = 2 to 7 num of student tickets / 92 = 7 / 2 ... x = 414 total tickets sold.
Simplify the expression: 6+p–8+7
Answer:
p+5
Step-by-step explanation:
I feel as if I might be oversimplifying my answer, so I may be wrong. But, I simply took the time to add like terms! The variable- p- will stand alone because it does not have a given value. The 6, 7, and -8 can be added together, though! Hence my +5. I hope this helped! :)
PLEASE ANSWER THIS
Review the problem below. Determine when the Associative, Commutative , and Additive Inverse properties are used.
Original problem (5.2 - 4) -4 + 6.2
Step One (5.2 - 4) +(-4) + 6.2
Step Two 1.2 + (-4) + 6.2
Step Three 1.2 + 6.2 + (-4)
Step Four (1.2 + 6.2) + (-4)
Step Five 7.4 + (-4) = 3.4
Answer:
2.5
Step-by-step explanation:
2. Grant works as a salesperson at a seasonal market. During the Christmas season, he
gets a 15 percent commission on every tree he sells. If he sold 12 trees today, with an
average sale price of $35 per tree, what amount of commission will he make?
Grant will make $63 commission on 12 trees he sold.
Given that, Grant works as a salesperson at a seasonal market. He gets a 15 percent commission on every tree he sells. If he sold 12 trees then we have to calculate the amount of commission he will get if the average sales price of a tree is $35.
So, first we will calculate the amount of commission Grant will get if he sold one tree.
∴ The commission on one tree will be equals to 15 percent on the sales price of a tree i.e., $35.
⇒ 15% of $35
= 15/100 x 35
= 5.25
Therefore, Grant will get $5.25 commission on selling one tree.
He sold 12 trees on that day. So, the total amount of commission he will get on 12 trees will be equal to,
= 12 x 5.25
= 63
Therefore, $63 is the amount of commission Grant will made on the sale of 12 trees.
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For a taxi driver, which measures must be accurate? Check all that apply.
A. Price per mile
B. Distance traveled by customer
C. Price if gasoline per gallon
D. Number of customers per day
Answer:
Them all as he has to know how far he travels the customer rate to see is there is an increase of decrease price of gasoline to see if it's affecting g his outcome and price per miles for obvious reasons haha
Answer:
the answer B. Distance traveled by customer
Morris Katz bought four new tires at Goodyear for $95.85 per tire. Goodyear also charged Morris $2.68 per tire for mounting, $2.58 per tire for valve stems, and $4.13 per tire for balancing. Assume no tax.
What was Morris’s total cost for the four tires?
Round your answer to 2 decimal places.
Answer:
$420.96
Step-by-step explanation:
95.85+2.68+2.58+4.13=$105.24
105.24*4=$420.96
PLEASE HELP MEEEEEEEEEEEEEE ILL GIVE U 50 coins for the right answer
Simplify the expression. Explain each step (0+c)+12
Answer:
x+12
Step-by-step explanation:
(0+c)+12
0+c+12
c+12+0
c+12
Hope this helps plz hit the crown :D
The problem to solve is:
(0+c)+12
0+c evaluates to +c
0 + 12 = 12
The answer is 12+c
(0+c)+12 evaluates to 12+c
The final answer is
12+c
IF THE RATIO IN A VALENTINE'S
DAY CANDY BOX OF MILK TO DARK
CHOCOLATES IS 23. HOW MANY
DARK CHOCOLATES ARE THERE IF
THERE ARE 8 MILK CHOCOLATES?
Answer:
12 dark chocolates
Step-by-step explanation:
Let there are 2x milk chocolates and 3x dark chocolates.
Total no of milk chocolates = 8
ATQ,
2x = 8
x = 4
Dark chocolates = 3x
= 3(4)
= 12
Hence, there are 12 dark chocolates.
Scientists are preparing two satellites to be launched. The equation y=8200xy=8200x represents the number of miles, yy, that the satellite, Space Explorer B, flies in xx hours. The satellite, Space Explorer A, flies 28800 miles in 24 hours.
How many fewer miles does Space Explorer A travel in one hour than Space Explorer B?
Answer:
Space Explorer B travels 6800 miles more than Space Explorer A in one hour.
Step-by-step explanation:
Space Explorer A travels 7000 miles less than Space Explorer B in one hour.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Space Explorer A flies 28800 miles in 24 hours.
24 hours = 28800 miles
1 hour = 28800/24 miles
1 hour = 1200 miles
Hence, Space Explorer A travels 1200 miles in 1 hour.
Now, the equation representing the distance, y, traveled by Space Exploral B in x hours is:
y = 8200x
Substitute x = 1:
y = 8200
Therefore, Space Exploral B travels 8200 miles in 1 hour.
The difference between the distance traveled by Space Exploral B and Space Exploral A is:
8200 - 1200
= 7000
Hence, Space Explorer A travels 7000 miles less than Space Explorer B in one hour.
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solve the following two equation X+Y=5
X-2Y=2
Step-by-step explanation:
x=4 and y= 1 because of 4+1=5 and add 2y to both sides
x-2y+2y=2+ 2y
x=2y+2
4-2=2
[tex]\left \{ {{x+y=5} \atop {x-2y=2}} \right.[/tex]
Here we have 2 equations in one system.
System of Equations/Simultaneous Equations are for finding the intercepts of both graphs.
We can solve these Simultaneous Equations in many ways. However, I'll be solving by substitution.
To solve by using substitution, we need to move either x or y to the another side. I'll move x term to another side for the first equation. (We'll substitute the first equation in the second.)
[tex]\left \{ {{y=-x+5} \atop {x-2y=2}} \right.[/tex]
Now we substitute y = -x+5 in x-2y = 2
[tex]x-2(-x+5)=2\\[/tex]
Then distribute -2 in (-x+5) | Note that multiplying the negative will get positive. |
[tex]x-2(-x+5)=2\\x+2x-10=2\\3x=2+10\\3x=12[/tex]
We should get this. When we get this, we move 3 to divide 12 (Opposite when moving to another side so from plus to minus and from multiply to divide.)
[tex]x=4[/tex]
But we are not done yet. We have to find the y-value. After all they are two variables equations.
If we want to find the y-value then we have to substitute x = 4 in any given equations. I'd suggest to substitute in the equation that doesn't have a coefficient with high value.
So I'll be substituting in x + y = 5 instead.
Substitute x = 4 in x + y = 5
[tex]4+y=5\\y=5-4\\y=1[/tex]
Thus, we get both x and y value. Answer in either coordinate point or writing form.
Therefore, the answer is
x = 4 when y = 1 or (4,1)
Both works. Hope this helps.
I NEED HELP PLS ON THIS QUESTION ON MY STUDY GUIDE
Answer:
4(n + 3) = 60
Step-by-step explanation:
In the question it says '3 more than the usual' and that is a big hint that it is 4(n + 3) = 60
The GCF of 18 and 27 is _______. Numerical Answers Expected! Answer for Blank 1:
Answer:
9
Step-by-step explanation:
GCF = Greatest Common Factor
The factors of 18 are 1, 2, 3, 6, 9, 18. The factors of 27 are 1, 3, 9, 27. The common factors of 18 and 27 are 1, 3 and 9. The greatest common factor of 18 and 27 is 9.Answer:
9
Step-by-step explanation:
If Jack's salary went from $15 per hour to $17 per hour this year, find the percent increase
Answer: 13%
Step-by-step explanation:
17$-15$ = 2$
15$ x 0.13 = 1.95$
With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount? Hint: First subtract to find the amount of discount$, then divide it by the original price.
Answer:
14[tex]\frac{2}{7}[/tex]%
Step-by-step explanation:
We can just follow the hint.
Amount of discount = $84 - $72
= $12
Percentage of discount = [tex]\frac{12}{84}[/tex] × 100%
= 14[tex]\frac{2}{7}[/tex]%
Answer:
14.3% discount.
Step-by-step explanation:
Heya! So by the hint that they gave us, I subtracted 72 from 84, and then divided the 12 by 84. The true answer is 0.143 (rounded to the hundredth), getting you close to the initial 12. I hope this helped at least a little bit!
a) Solve by determinant method: x - y = 2, 2x + 3y = 4
Answer:
x = 2
y = 0
Step-by-step explanation:
x - y = 2
2x + 3y = 4
Using creamers rule of determinants, we have;
D =
|1 1|
|2 3|
Thus; D = (1 × 3) - (1 × 2)
D = 1
Dx =
|2 1|
|4 3|
Dx = (2 × 3) - (1 × 4)
Dx = 2
Dy =
|1 2|
|2 4|
Dy = (1 × 4) - (2 × 2)
Dy = 0
Thus;
x = Dx/D = 2/1
x = 2
y = Dy/D = 0/1
y = 0
GIVING BRAINIEST IF CORRECT!!!!
What is the product of 2 rad 5 and 10 rad 30 in simplest radical form?
Answer: 100√6
Step-by-step explanation:
Start out by multiplying the 2 by the 10 to get 20.
Then, multiply √5 and √30 together to get √150. The largest perfect square within √150 is √25 (don't forget about your √6)
√25 is 5. Multiply your 20 and 5 together to get 100, and then put your √6 next to the 100 since it cannot be added or multiplied since they are not like-terms.
Thus, leaving you with an answer of 100√6.
Examine the worked problem and solve the equation.
Four-thirds (x) minus one-third = 9. Four-thirds (x) minus one-third + one-third = 9 + one-third. Four-thirds (x) = StartFraction 28 over 3 EndFraction
The solution is x =
.
Answer:
The answer is 7
Step-by-step explanation:
I don't know how to explain it really but just divide 4/3 by 28/3 and you should get the answer of x
Answer:
7
Step-by-step explanation:
-3 < x -10 Solve for X and simplify please
Hey there!
“-3 < x - 10”
SOME people treat the “<” “>” as an equal sign to make these types of problems easier to solve!
-3 = x - 10
Flip the equation around
x - 10 = -3
ADD both of your sides by 10
Like: x - 10 + 10 = -3 + 10
CANCEL out: -10 + 10 because it gives us 0
Keep: -3 + 10 because it gives us the value of x
-3 + 10 = x
Solve that above and you have your answer: x = 7 ☑️
Overall answer: x < 7
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 -3 2 -9 3 -15 4 -21
Answer:
The numbers:
1, -3, 2, -9, 3, -15, 4, -21,
are not linear.
Step-by-step explanation:
If it was linear:
4, 3, 2, 1, -3, -9, -15, -21