Answer:
area after 8 years is 2156km²
Step-by-step explanation:
Area of forest=4900 km²
decrease in area in 1 year=4900km² × 7%
decrease in area in 1 year= 343km²
decrease area in 8 years=343km² × 8
=2744km²
Remaining area= (4900-2744)km²
=2156km²
Note:If you have any question about it please ask.
Select the correct answer.
Which algebraic expression is equivalent to the expression below?
The sun of three numbers is 40. The second number is 6 more than the first. The third number is 1 less than 5 times the first. Find all three numbers.
Answer:
first n = 5
sec n = 11
third n = 24
Step-by-step explanation:
40-6+1 = 35
35/7 = 5
1st no = 5
2nd no = first + 6
= 5+6
= 11
3rd no = 5(first) - 1
= 5(5) - 1
= 25-1
= 24
double check total = 1st + 2nd + 3rd
= 5 + 11 + 24
= 40
Harry is painting a wall in his house that is 20 by 18 feet. He has two windows that he does not want to paint. What is the total area he will need to paint?
340
200
289.73
Step-by-step explanation:
total area is 18 × 20 = 360
but by excluding window it will be less than 360
here U have not given lenght of windows so i can not find answer
-6+-3-(-18)? what is the answer to this problem?
The answer to this problem is 9.
-6+(-3)-(-18)
Since (+)(-)=(-) and (-)(-)=(+),
-6-3+18
-9+18
9
Answer:
9
Step-by-step explanation:
-6 + -3 - (-18)
-6 - 3 + 18
-9 + 18
9
- (-) = +
+ (+) = +
- (+) = -
+ (-) = -
PLEASE HELP!!!
Ken Runfast is the star of the cross-country team. During a recent morning run, Ken averaged a speed of 5.8 m/s for 12.9 minutes. Ken then averaged a speed of 6.10 m/s for 7.1 minutes. Determine the total distance which Ken ran during his 20 minute jog.
Answer:
7087.8m or 7.09km
Step-by-step explanation:
formula used:
distance = speed * time
total distance = distance1 + distance2
let d1 be distance1, d2 be distance2, s1 be speed1, s2 be speed2, t1 be time1, and t2 e time2:
s1 = 5.8m/s, t1 = 12.9 min or 774 sec, s2 = 6.10m/s, t1 = 7.1 min or 426 second
d1 = s1 * t1
= 5.8 m/s * 774 s
= 4489.2 m
d2 = s2 * t2
= 6.10 m/s * 426 s
= 2598.6 m
total distance = d1 + d2
= 4489.2m + 2598.6m
= 7087.8 meter or 7.09 kilometer
What is the solution set to this equation?
log4 (x + 3) + log4x =1
A. x=0
B. x=1
C. x=1 and x= -4
D. x=-3 and x=0
Answer:
B
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log (xy)
[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex]
Given
[tex]log_{4}[/tex] (x + 3) + [tex]log_{4}[/tex] x = 1 , then
[tex]log_{4}[/tex] x(x + 3) = 1
x(x + 3) = [tex]4^{1}[/tex] = 4
x² + 3x = 4 ( subtract 4 from both sides )
x² + 3x - 4 = 0 ← in standard form
(x + 4)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 1 = 0 ⇒ x = 1
However, x > 0 , thus x = 1
What is the correct domain and range in set notation
Answer:
The one on the middle left.
Explanation:
x goes infinitely in the positive direction.
y does not show any sign of not going infinitely positively or negatively.
3. Based on the graph of the trigonometric function,
what is the period?
4. Based on the graph of the trigonometric function,
what is the amplitude?
Answer:
4. ☐ A [tex]\displaystyle \frac{1}{3}[/tex]
☐ B [tex]\displaystyle 2[/tex]
☑ C [tex]\displaystyle 3[/tex]
3. ☐ A [tex]\displaystyle \frac{\pi}{3}[/tex]
☐ B [tex]\displaystyle \pi[/tex]
☑ C [tex]\displaystyle 6\pi[/tex]
Step-by-step explanation:
[tex]\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}) \\ y = -2cos\:\frac{1}{3}x[/tex]
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1\frac{1}{2}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{1}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6\pi} \hookrightarrow \frac{2}{\frac{1}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
The above information can help you interpret the graph much better. First off, JUST IN CASE you needed to know the trigonometric equation(s) of this graph, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = -2sin\:\frac{1}{3}x,[/tex] in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle 1\frac{1}{2}\pi\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle 1\frac{1}{2}\pi\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-1\frac{1}{2}\pi} = \frac{-\frac{\pi}{2}}{\frac{1}{3}}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -2sin\:(\frac{1}{3}x + \frac{\pi}{2}).[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -2],[/tex] from there to [tex]\displaystyle [-6\pi, -2],[/tex] they are obviously [tex]\displaystyle 6\pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 6\pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow. Now, in this case, you were probably wondering why the negative was inserted in front of the amplitude in the equation(s). Well, here is why:
[tex]\displaystyle y = sin\:x \\ y = cos\:x[/tex]
Knowing your parent functions, sine commenses upright from the origin, while cosine commenses one unit above the origin [tex]\displaystyle [0, 1].[/tex] This should tell you that inserting a negative in front of the amplitude will REFLECT each crest over the midline. Well, there you have it.
I am delighted to assist you at any time.
3.7 as a mixed fraction
let x =
10x =
9x =
x =
So 3.7 repeating is equal to...
Answer:
37/9Step-by-step explanation:
we have3.77777... :- is a repeating decimalLetx = 3.7...so10x =37.7...10x - x = 37.7... -3.7...9x=34x= 34/9convert to mixed number34/9=(27/9)+(7/9)=3+(7/9) =37/9 I hope this may help you.find the solutions of the following equation. b^2 = 16/121 choose all answers that apply:
a. b= 2/7
b. b= - 2/7
c. b= 4/11
d. b= -4/11
e. none of the above
tysm <3
Answer:
c. b= 4/11
d. b= -4/11
Step-by-step explanation:
b^2 = 16/121
Take the square root of each side
sqrt(b^2) =± sqrt(16/121)
b = ±4/11
b² = -16/121
16 is 4² and 121 is 11²
b² = -4²/11²
b² = -(4/11)²
When exponents are common they are eliminated. Here, 2 is common
b = ±4/11
Hence, the answer is ±4/11OPTION c and d IS CORRECT
The main rotor of a helicopter is spinning at a constant rate. The rotor makes 80 revolutions every 12 seconds. At what rate, in revolutions per minute, is the rotor spinning?
Answer:
B/16
Step-by-step explanation:
if the rotor is spinning 80 reveloutions every 12 seconds and, a minute is 60 seconds
12 divided by 60 = 0.2
0.2 times 80 = 16.
hope this helped
rachel states that -5.5 is an integer because it is negative. is she correct? why or why not?
Answer:
no
Step-by-step explanation:
-5.5=-55/10=-11/2
-11/2 is not an integer because it is not a whole number. even if it is negative, as long as it is in fraction form it is not an integer. therefore rachel is not correct
F(x)=5x-2 & g(x) =1-2x find f/g(c)
Answer these 2 questions please
9514 1404 393
Answer:
(a) 9x -10x^2 -2(c) 25Step-by-step explanation:
1) (fg)(x) = f(x)·g(x) = (5x -2)·(1 -2x)
= (5x)(1) -(2)(1) +(5x)(-2x) +(-2)(-2x)
= 5x -2 -10x^2 +4x
= 9x -10x^2 -2 . . . . matches A
__
2) (f+g)(-2) = f(-2) +g(-2) = (-5(-2) +1) +(-6(-2) +2)
= 10+1 +12 +2 = 25 . . . . matches C
even more math.......
Answer:
A
Step-by-step explanation:
We don't know the height of the building, and it's changeable because we multiplied it by 1/2, also, the rest of the values are revealed, so the answer is A.
Distance & midpoint
Step-by-step explanation:
All steps are in picture above.
Note:if you need to ask any question please let me know.
anyone help me? Solve this problem
the answer is in the picture I mentioned as the answer ok ◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉◉‿◉
(SHOW WORK) Write the slope-intercept form of the equation:
passes through (-2, 3) and is perpendicular to y = 1/4x - 4
Answer:
[tex]\displaystyle y = -4x - 5[/tex]
Step-by-step explanation:
We want to find the slope-intercept form of the equation that passes through the point (-2, 3) and is perpendicular to the line:
[tex]\displaystyle y = \frac{1}{4} x - 4[/tex]
Note that this line has a slope of 1/4.
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
Since the slope of our old line is 1/4, the slope of its perpendicular line must be -4.
We are also given that it passes through the point (-2, 3). So, we can consider using point-slope form:
[tex]\displaystyle y - y_1 = m(x - x_1)[/tex]
Let (-2, 3) be (x₁, y₁) and substitute -4 for the slope m. Hence:
[tex]\displaystyle y - (3)= -4 (x - (-2))[/tex]
Convert into slope-intercept form. Simplify:
[tex]\displaystyle \begin{aligned} y -3 &= -4 (x + 2) \\ y - 3 &= -4x - 8 \\ y &= -4x -5\end{aligned}[/tex]
In conclusion, the perpendicular line that passes through the point (-2, 3) is given by:
[tex]\displaystyle y = -4x - 5[/tex]
Passes through (3,4) and is parallel to the line containing (3,5) and (0,2). Write answer in slope intercept form.
Answer:
should be 0
Step-by-step explanation:
Find the equation of the line passes through ( -3, 4) and parallel to the line 2y-4x + 2 = 0
Answer:
[tex]y = x + 1[/tex]
Step-by-step explanation:
We want to determine the equation of the line that passes through the point (3, 4) and is parallel to the line containing the points (3, 5) and (0, 2).
Recall that parallel lines have equivalent slopes.
Hence, first find the slope of the line containing the points (3, 5) and (0, 2):
[tex]\displaystyle m = \frac{\Delta y }{\Delta x} = \frac{(2)-(5)}{(0)-(3)} = \frac{-3}{-3} = 1[/tex]
Therefore, the slope of our new line must also be 1.
We are given that it passes through the point (3, 4). Since we are given a slope and a point, we can consider using point-slope form:
[tex]\displaystyle y - y_1 = m(x - x_1)[/tex]
Substitute:
[tex]\displaystyle y - (4) = (1)(x - (3))[/tex]
Simplify:
[tex]y - 4 = x - 3[/tex]
And add. Hence, our equation in slope-intercept form is:
[tex]y = x + 1[/tex]
In conclusion, the line that passes through the point (3, 4) and is parallel to the line containing the two points (3, 5) and (0, 2) is:
[tex]y = x + 1[/tex]
3,
8.
If TU = 23 and TV = 5x + 6, then x = ?
23
U
Sxt6
10.
If PQ = 6x - 1 and PR = 15x - 29,
then QR = ?
P
Q
R
Problem 1
Answer: x = 8----------------------------------
Explanation:
The tickmarks say that TU and UV are the same length. Both are 23 units each. They combine to TU+UV = 23+23 = 46, which is the length of TV
TV = 5x+6
TV = 46
5x+6 = 46
5x = 46-6
5x = 40
x = 40/5
x = 8
===========================================================
Problem 2
Answer: QR = 53----------------------------------
Explanation:
We use the same idea as the previous problem.
PQ = 6x-1 is the same length as QR
PQ+QR = (6x-1)+(6x-1) = 12x-2 = PR
Since PR = 15x-29, we can then say,
PR = 12x-2
15x-29 = 12x-2
15x-12x = -2+29
3x = 27
x = 27/3
x = 9
From there,
PQ = 6x-1 = 6(9)-1 = 53QR = 53 since PQ and QR are the same lengthPQ+QR = 53+53 = 106PR = 15x-29 = 15(9)-29 = 135-29 = 106This shows that PQ+QR = PR is true and it helps confirm the answer.
The 4,000 accounts receivable of GHI Company have a total book value of $60,000. Bob Smith, CPA, has selected and audited a sample of 100 accounts with a total book value of $1,600. Using the mean-per-unit estimation technique, Smith has properly estimated a projected misstatement of a $8,000 overstatement for the entire population. The audited value of Smith's sample is:
Answer:
The answer is $1,300
Step-by-step explanation:
step by step
-5x-y=12
x+y=4
-6x+9y=11
Answer:
1. x = -12+y / 5 , y = -12-5x
2. x = 4 - y , y = 4 - x
3. x = -11 - 9y / 6 , y = 11 + 6x / 9
( for the numbers in fractions such as the x value for #1 and x & y value for #3, put the negative sign in front of the fraction, not the number okay? )
Step-by-step explanation:
-5x - y = 12---> -5x - y = 12 -5x - y = 12
= -5x - y = 12 = +5x +5x
+y +y ---------------------
--------------------- -y = 12 + 5x
-5x = 12 + y /-1 /-1
/-5 /-5 ----------------------
--------------------- y = -12-5x
x = -12+y / 5
-------------------------------------------------------------------------------------------
x + y = 4---> x + y = 4 x + y = 4
= -y -y = -x -x
--------------------- ----------------
x = 4 - y y = 4 - x
--------------------------------------------------------------------------------------------
-6x + 9y = 11-----> -6x + 9y = 11 -6x + 9y = 11
= -9y -9y = +6x +6x
------------------------------ ------------------------
-6x = 11 - 9y 9y = 11 + 6x
/-6 /-6 /9 /9
------------------------------- --------------------------
x = -11 - 9y / 6 y = 11 + 6x / 9
soy nuevo nesesito ayuda
Answer:
867 plz make me brien list
A mix weighs 38 pounds.the mix is 80% sand by weight.about how many pounds of sand are in the mix???
PLZZZ HELPP MEE RNNN
Does anyone know the answer 1 through 4?If not you can solve whatever you can.Please help me I’m so tired
Answer:
1. x minus twenty
2. five n plus two
3. a raised to the third power / a cubed
4. n raised to the fourth power then minus one
Step-by-step explanation:
Ight I got u. Im a AP calc bc student so trust xd
Which is the least positive integer that should be multiplied with 2 × 2 × 2 × 3 so that we get
a perfect square?
Answer:
3
Step-by-step explanation:
In order to have a perfect square you have to have at least two prime factors, and since three is quite clearly not in a pair, the answer is three.
1
Write down the temperature that is 7 °C below -3°C.
ES
Answer:
-10 [tex]^\circ C[/tex]
Step-by-step explanation:
Subtract 7 from -3. -3 - 7 = 0=-10
The temperature that is 7°C below -3°C is equal to -10°C.
To find the temperature that is 7°C below -3°C, we need to subtract 7 from -3. When subtracting a positive number from a negative number, the result becomes more negative.
Starting with -3°C, we subtract 7°C:
-3°C - 7°C = -10°C
A negative temperature indicates a temperature below zero on the Celsius scale. In this case, -10°C means that the temperature is 10 degrees below freezing point.
The Celsius scale is based on the freezing and boiling points of water, with 0°C representing the freezing point and 100°C representing the boiling point at standard atmospheric pressure.
Since we are subtracting 7°C, we are moving further below the freezing point. So, -10°C indicates a colder temperature than -3°C.
To learn more about temperature click on,
https://brainly.com/question/28827315
#SPJ2
Complete question is:
Write down the temperature that is 7 °C below -3°C?
Help Me!
In this figure QR = XY ?
write the reason and find the pairs of matching angles.
Answer:
Yes
Step-by-step explanation:
I think you just rotate the triangle...
But since angle P and angle Z are the same, they fix the position the rays will go and since ZY=PQ=6cm and ZX=RP=4cm, they are the same triangle so QR=XY.
Pairs of matching angles would be angle R= angle X and angle Q = angle Y
Answer:
Yes,By CPCT
Step-by-step explanation:
SEE the image for solution.
HOPE it helps
Have a great day
how many sides has a cuboid
Answer:
[tex]6faces \\ thank \: you[/tex]
how to find standard form given 2 points
9514 1404 393
Answer:
(y2 -y1)x -(x2 -x1)y = (y2 -y1)(x1) -(x2 -x1)(y1)
Step-by-step explanation:
The standard form equation of a line is of the form ...
ax +by = c
where a, b, c are mutually prime integers. The leading coefficient must be positive.
__
The standard form equation of a line can be found for the two points (x1, y1) and (x2, y2) using the formula ...
(y2 -y1)x -(x2 -x1)y = (y2 -y1)(x1) -(x2 -x1)(y1)
Using this equation, you must choose y2>y1. If y2=y1, you must choose x1>x2.
You will need to eliminate any fractions by multiplying the equation by an appropriate number. Once you have the numbers figured out, you need to factor out any common factors from the coefficients and the constant, so they are all mutually prime.
What is greater 8 + the square root of 50 or 5 + the square root of 65
Answer:
8+the square root of 50 is greater.
Step-by-step explanation: