Answer:
The correct option is D.
Step-by-step explanation:
Let x denote the years.
The information provided is:
The population of Metro City is 7420.The population is decreasing by 152 people per year.The population of Smallville is consistently 1200 less than half of Metro City.From the provided data derive the equation for the population of Smallville x years after as follows:
[tex]Y = [\frac{1}{2}\cdot (7420-152x)]-1200[/tex]
The population of Smallville is 2282 after x years.
Compute the value of x as follows:
[tex]2282= [\frac{1}{2}\cdot (7420-152x)]-1200[/tex]
[tex]\frac{7420-152x}{2}=2282+1200\\\\7420-152x=3482\times 2\\\\152x=7420-6964\\\\152x=456\\\\x=3[/tex]
Thus, the time it will take for Smallville's population to reach 2282 is 3 years.
The correct option is D.
What is (7.8 x 10) • (1.0 x 10)
780 is the answer. Hope this helps :)
If the domain of the sqaure root function f(x) is x <= 7, which statement must be true?
A) 7 is subtracted from from the x term inside the radical.
B) The radical is multiplied by a negative number.
C) 7 is added to the radical term.
D) The x-term inside the radical has a negative coefficient.
Answer:
D
Explanition:
Maria walked 3 km west and 4 km south. Calculate how far she is from her starting point
Distance will be the hypotenuse of a right triangle.
Distance^2 = 3^2 + 4^2 = 9 + 16 = 25
Distance = 5 km
HELP will mark branniest answer
what do you notice about the picture
Answer:
Transversal line
Step-by-step explanation:
That is a picture of a Transversal line, a Transversal line intersects 2 or more parallel lines.
what is the graph of the equation Y= 66x - 1200
Answer:the answer is b :)
Step-by-step explanation:
A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?
Answer:
Step-by-step explanation:
A comparison between the cups of milk and cups of water can be written as a ratio: Note that:1/3 >1/4
1/3 : 1/4 ← x 12 to get rid of fractions 12/1 x 1/3 : 12/1 x 1/4=4:3 4 cups of milk are used with 3 cups of water ←÷ 41 cup of milk is used with 3/4 cup of water
is 0.523 a rational number?
Answer:
no
Step-by-step explanation:
Answer:
yes, it doesn't go on infinitely it stops at thousandths
if pqr=tsr what are the congruent corresponding parts
Answer: The congruent corresponding parts:
∠P≅∠T (first letter) , ∠Q≅∠S (second letter), ∠R≅∠R (third letter)
segment PQ ≅ segment TS , segment QR≅ segment SR , segment PR ≅ segment TR.
Step-by-step explanation:
We know that if two triangles area congruent then the corresponding parts area congruent.
Given: ΔPQR ≅ ΔTSR
Then, ∠P≅∠T (first letter) , ∠Q≅∠S (second letter), ∠R≅∠R (third letter)
segment PQ ≅ segment TS , segment QR≅ segment SR , segment PR ≅ segment TR.
Hence, the congruent corresponding parts:
∠P≅∠T (first letter) , ∠Q≅∠S (second letter), ∠R≅∠R (third letter)
segment PQ ≅ segment TS , segment QR≅ segment SR , segment PR ≅ segment TR.
The corresponding parts of a triangle are parts that have the same measurement.
The corresponding parts are: P & T, Q & S and R & R
The given parameter is:
[tex]\mathbf{\triangle pqr \cong \triangle tsr}[/tex]
The above congruence equation means that:
[tex]\mathbf{\angle p \cong \angle t}[/tex]
[tex]\mathbf{\angle q \cong \angle s}[/tex]
[tex]\mathbf{\angle r \cong \angle r}[/tex]
Hence, the corresponding parts are:
P & T, Q & S and R & R
The above highlight means that:
P corresponds to TQ corresponds to SR corresponds to RRead more about corresponding parts at:
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Find the minimum or maximum value of the function y=9x2+7. Describe the domain and range of the function, and where the function is increasing and decreasing. The minimum value is Response area. The domain is Response area and the range is Response area. The function is decreasing to the Response area of x= Response area and increasing to the Response area of x= Response area.
The given function is [tex]y=x^2+7[/tex].
Minimum or maximum value:
At the extremum (maximum or minimum) value, the function will have zero slope. So, differentiate the given function once and equate it to zero to get the extremum point.
dy/dx=0
[tex]\Rightarrow 18x=0\cdots(i)[/tex]
[tex]\Rightarrow x=0[/tex]
Now, check whether the point x=0 is corresponding to the maximum value or minimum value by differentiating the function twice,
[tex]\frac {d^2y}{dx^2}=18[/tex]
As [tex]\frac {d^2y}{dx^2} >0[/tex] for all value of x, so x=0 is the point corresponding to minima.
Put x=0 in the given function to get the minimum value.
[tex]y_{min}=9(0^2)+7[/tex]
[tex]y_{min}=7[/tex]
Domain and range:
The function defined for all the values of the independent variable, x.
So, the domain is [tex](-\infty, \infty)[/tex].
The range of the function is the possible value of y.
The minimum value, for x=0, is y=7.
The maximum value, as [tex]x\rightarrow \infty \;or\; -\infty, y\rightarrow \infty[/tex].
Hence the range of the function is [tex][7,\infty)[/tex].
The value of x for which the function is increasing and decreasing:
If the slope of the function is negative than the function is decreasing, so
Then, from equation (i), the value of x for which dy/dx<0,
18x<0
[tex]\Rightarrow x<0[/tex]
Hence, the function is decreasing for [tex]x\in {-\infty, 0)[/tex] .
While if the slope of the function is positive than the function is increasing, so
Then, from equation (i), the value of x for which dy/dx<0,
18x>0
[tex]\Rightarrow x>0[/tex]
Hence, the function is increasing for [tex]x\in {0,\infty)[/tex]
Solve for y in the following equation.
Answer: The last one.... -9
hope this helped :>
PLEASE HURRY!!! 10 POINTS Which ordered pair would form a proportional relationship with the point graphed below?
100ty
90
80
70
60
50
40
30
20
10
45.30)
10 20 30 40 50 60 70 80 90
(10, 10)
(25, 35)
(70, 50)
Answer:
50
Step-by-step explanation:50 is the right answer!!
Please help ASAP!!!!
a scale on a map reads 2in 150ft find the actual distance if the length on a map is 4.5 inches
Answer:
4.5 in. is equivalent to 337.5 ft.
Step-by-step explanation:
The given parameters are;
The scale of the scale map is 2 in. to 150 ft.
The measured length on the scale map = 4.5 inches
The actual distance of the location is given as follows;
2 in. is equivalent to 150 ft.
Therefore;
1 in. is equivalent to 150 ft./2 = 75 ft.
4.5 in. will be equivalent to 4.5 × 75 ft. = 337.5 ft.
4.5 in. will be equivalent to 337.5 ft.
fb + 3b = d solve for b
Answer: the answer is d/f+3
sorry i couldnt find my work for this problem but i hope it helps !
An equation is formed of two equal expressions. When in the given equation the value fo b is d/(f+3).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
fb + 3b = d
Take b as a common term from both the terms on the left side of the equation,
b(f + 3) = d
Divide both the sides of the equation by (f+3),
b(f + 3)/(f+3) = d/(f+3)
Simplify,
b = d/(f+3)
Hence, when in the given equation the value fo b is d/(f+3).
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I need the answer to this question please.
Answer:
√1 is a rational number as it is 1. The other three options are irrational.
Answer:
1 4 6 10
----------------------------------------------
2. Tyler is solving this system of equations:
4p + 2g = 62
8p - q = 59
He can think of two ways to eliminate a variable and solve the system:
o Multiply 4p + 2g = 62 by 2, then subtract 8p - q= 59 from the result.
• Multiply 8p-q=59 by 2, then add the result to 4p + 2q = 62.
Do both strategies work for solving the system? Explain or show your reasoning.
please help out ://
Answer:
Both of them work
Step-by-step explanation:
by multiplying the first equation by 2 it creates the same coefficient in front of "p" for both equations. same for the second equation and "q".
Both strategies works since we can easily eliminate a variable from both equations.
Given the simultaneous equation solved by Tyler
4p + 2q = 62
8p - q = 59
In order for him to eliminate a variable to solve the system of equations, he must ensure that the coeffiecient of the variable to be eliminated are equations in both expressions. To do that;
Multiply 4p + 2g = 62 by 2, then subtract 8p - q= 59 from the result. This will give;8p + 4g = 124
8p - q = 59
Subtract
4q + q = 124 + 59
5q = 183
The second required strategy is to Multiply 8p-q=59 by 2, then add the result to 4p + 2q = 62, to have:
16p-2q=118
4p + 2q = 62
Adding up
16p + 4p = 118 + 62
20p = 180
p = 9
We can see that both strategies works since we can easily eliminate a variable from both equations.
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Find he percent of change from 1250 to 1,755mi
A secretary earns $12 an hour and worked a total of 47 hours last week she earns time and a half for work beyond 40hours calculate her pay
Answer:
$606
Step-by-step explanation:
For the first 40 hours, she was making $12. With this, we can do 12x40, which is 480$. We can store that in a safe space for later access. Afterwards, since the problem says that "after 40 hours she earns time and a half for her work" we can assume she gets 1.5x her pay after 40 hours, which is $18 (We can get this by 12 / 2 = 6. Then do 12 + 6 = 18). Then we can do 18x7 because she worked 7 hours over 40. With that, we get 126$. Now we can do 480$ + 126$ = 606$. So, she earned 606$.
Write an expression to represent the submarine’s elevation after its final dive. Then simplify the expression to find its elevation
Answer:
-502.5 − 115 = -617.5
The submarine’s elevation after its final dive is -617.5 feet, or 617.5 feet below sea level.
Step-by-step explanation:
Plato answer
Answer:
63 1/4
Step-by-step explanation:
I did the edmentum
HELP , ILL GIVE BRAINLIEST. Answer 5-8 please .
Answer:
#5. 17, #6. 22, #7. 14, and #8. 13
Step-by-step explanation:
Can anyone help this is for a study guide I'll mark you the brainliest if the answer is right.
Answer: The answer has to be
d. t and u
Step-by-step explanation:
Write 56/49 in simplest form
Answer:
8/7 or 1 1/7
Step-by-step explanation:
Answer:
8/7
Step-by-step explanation:
A music player app has 2 gigabytes of storage and can hold about 500 songs. A similar, but larger app has 80
gigabytes of storage. About how many songs can the larger app hold?
Answer:
20,000
Step-by-step explanation:
Penelope has a birdhouse that is 4 and 9/10 feet
above the roof of her garage. She has a second
birdhouse that is 5.36 feet below the roof of
her garage. What is the distance between the
birdhouses?
Answer:
The distance between the bird houses are 10.26 feet
Step-by-step explanation:
The distance between the birdhouses is 10.26 feet.
What is simplification?A mathematical expression gets simpler when it is transformed into an equivalent, frequently shorter statement. One strategy for promoting uniformity in job effort, cost, and time is procedure simplification. It lessens diversity and variation that is harmful, unwanted, or unneeded.
Given, Penelope has a birdhouse that is 4 and 9/10 feet above the roof of her garage. She has a second birdhouse that is 5.36 feet below the roof of her garage. thus,
Distance between garage roof and birdhouse = 4.9 feet
Distance between garage roof and second birdhouse = 5.36 feet
Since these birdhouses are in the opposite directions of the garage roof
Hence the total distance between them = 4.9 + 5.36
the total distance between birdhouses is 10.26 feet
Therefore, the Two birdhouses are 10.26 feet apart from each other.
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Find the measure of the angle indicated below. 162 130 ?
Answer:
162 is greater than 130.. if that's what your are talking about..
A triangle has two sides of length 19 and 3. What is the largest possible whole number length for the third side?
========================================================
Explanation:
Consider a triangle with side lengths a,b,c such that a < b < c
a = 3 and b = 19 are the two known sides
Let c be the missing side length
The missing side has the property that...
b-a < c < b+a
19-3 < c < 19+3
16 < c < 22
Meaning that if c is a whole number then it can take on any of these values {17, 18, 19, 20, 21}
So c = 21 is the largest possible third side, where only whole number sides are considered.
We can't have a third side of 22 because the two other sides add to a+b = 3+19 = 22 and a triangle wouldn't form (instead only a straight line would). I recommend cutting out strings of paper trying this out yourself.
---------------
Side note: The inequality b-a < c < b+a is a variation of the triangle inequality theorem.
Point AAA is at {(6, -6)}(6,−6)left parenthesis, 6, comma, minus, 6, right parenthesis and point CCC is at {(-6,-2)}(−6,−2)left parenthesis, minus, 6, comma, minus, 2, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that AB=\dfrac34ACAB= 4 3 ACA, B, equals, start fraction, 3, divided by, 4, end fraction, A, C.
Answer:
B(-3, -3)
Step-by-step explanation:
If a point O(x, y) divides line segment XY in the ratio of n:m and the endpoints of the segment are [tex]X(x_1,y_1)\ and\ Y(x_2,y_2)[/tex], the coordinates of O is:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]
Given that A(6, -6) and C(-6, 2). Pont B is on AC such that:
AB = (3/4)AC
AB/AC = 3/4
Therefore point B divides the line AC in the ratio of 3:1. Let point B be at (x, y), therefore:
[tex]x=\frac{3}{3+1}(-6-6)+6=\frac{3}{4}(-12)+6=-9+6=-3\\ \\y=x=\frac{3}{3+1}(-2-(-6))-6=\frac{3}{4}(4)-6=3-6=-3[/tex]
Therefore the location of B is at (-3, -3)
Answer: (-3, -3)
Step-by-step explanation: Khan academy
A hole is accidentally made in a water tank. On the first day, 32 gallons of water leak from the tank. Each day after that, workers are able to decrease the number of gallons leaking by 8% of the leakage on the day before. What is the total number of gallons of water that leaked from the tank?
Answer: 34.78 gallon
Step-by-step explanation:
Exponential equation for decay:
[tex]A=P(1-r)^t[/tex] , where p = initial amount, r= rate of decay , t= taime
As per given,
r= 8% = 0.08
For days 1 , i.e. at t= 0 , P= 32 gallons
[tex]1=32(1-0.08)^t\\\\\Rightarrow\ \dfrac{1}{32}=(1-0.08)^t \\\\\Rightarrow\ \ln \left(\frac{1}{32}\right)=t\log (0.92)\\\\\Rightarrow\ t=-\frac{5\ln \left(2\right)}{\ln \left(0.92\right)}=41.5\approx42[/tex]
Total water = [tex]\dfrac{a(1-r^n)}{1-r}=\dfrac{32(1-0.08^{42})}{1-0.08}=34.782[/tex]
hence, the the total number of gallons of water that leaked from the tank = 34.78 gallon approx.
A calculator screen shows a number in scientific notation as 4.67e-8 write this number in standard form
Answer:
467 000 000
Step-by-step explanation:
4.67e-8 is rewritten as 4.67 x 10^-8.
Negative -> decimal with lots of places, Positive -> big, big number
Move the decimal place right 8 times so you end up with a small decimal.
4.67 -> 467000000
Finish the proportion using the figure below:
a = c
j ?
A. D
B. K
C. B
D. A
