To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.
Explanation:To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:
First, we calculate (-3)^2, which is equal to 9.Next, we substitute the values in the expression: (-2)(9) - 2(2 - 5).Then, we simplify the expression inside the parentheses: (-2)(9) - 2(-3).Multiplying -2 by 9 gives us -18, and multiplying 2 by -3 gives us -6.Finally, we subtract -6 from -18 to get the final result, which is -12.Therefore, the simplified expression is -12.
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A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample? 52 days 60 days 74 days 136 days
Answer:
74 days
Step-by-step explanation:
The proportion left after d days is ...
p = (1/2)^(d/100)
When that proportion is 60%, we have ...
.60 = .50^(d/100)
log(.60) = (d/100)log(.50) . . . . . take logarithms
100·log(.60)/log(.50) = d ≈ 73.697 ≈ 74 . . . days
Question 25 Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice’s fence if the area of her garden is 5,670 square feet?
A) 342 feet
B) 318 feet
C) 300 feet
D) 270 feet
Answer:
Option A - 342 feet
Step-by-step explanation:
Given : Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width.
To find : What is the perimeter of Janice fence if the area of her garden is 5,670 square feet?
Solution :
Let the width of the garden be w=x feet.
The garden has a length that is 9 feet less than 3 times its width.
The length of the garden be l=3x-9 feet
The area of the garden is A=5670 square feet.
The formula of area of garden is [tex]A=l\times w[/tex]
[tex]5670=(3x-9)\times x[/tex]
[tex]5670=3x^2-9x[/tex]
[tex]3x^2-9x-5670=0[/tex]
[tex]x^2-3x-1890=0[/tex]
[tex]x^2-45x+42x-1890=0[/tex]
[tex]x(x-45)+42(x-45)=0[/tex]
[tex](x-45)(x+42)=0[/tex]
[tex]x=45,-42[/tex]
Reject x=-42 as measurement cannot be negative.
The width of the garden is w=45 feet.
The length of the garden is l=3(45)-9=135-9=126 feet.
The perimeter of the garden is [tex]P=2(l+w)[/tex]
[tex]P=2(126+45)[/tex]
[tex]P=2(171)[/tex]
[tex]P=342[/tex]
The perimeter of Janice fence is 342 feet.
Therefore, Option A is correct.
The perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]
To determine the perimeter of Janice's garden, let's follow these steps:
Step 1: Define Variables
Let ( w ) be the width of the garden in feet.
The length ( l ) of the garden is given by: [tex]\[ l = 3w - 9 \][/tex]
Step 2: Set Up the Area Equation
The area of the rectangular garden is given as 5,670 square feet:
[tex]\[ \text{Area} = l \times w \][/tex]
[tex]\[ 5670 = (3w - 9) \times w \][/tex]
Step 3: Solve the Quadratic Equation
Expand and simplify the equation:
[tex]\[ 5670 = 3w^2 - 9w \][/tex]
Rearrange it to standard quadratic form:
[tex]\[ 3w^2 - 9w - 5670 = 0 \][/tex]
Step 4: Factor or Use the Quadratic Formula
Divide through by 3 to simplify:
[tex]\[ w^2 - 3w - 1890 = 0 \][/tex]
Solve using the quadratic formula [tex]\( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]:
[tex]\[ a = 1, \, b = -3, \, c = -1890 \][/tex]
[tex]\[ w = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1890)}}{2 \cdot 1} \][/tex]
[tex]\[ w = \frac{3 \pm \sqrt{9 + 7560}}{2} \][/tex]
[tex]\[ w = \frac{3 \pm \sqrt{7569}}{2} \][/tex]
[tex]\[ w = \frac{3 \pm 87}{2} \][/tex]
This gives two potential solutions:
[tex]\[ w = \frac{90}{2} = 45 \][/tex]
[tex]\[ w = \frac{-84}{2} = -42 \][/tex]
Since width cannot be negative:
[tex]\[ w = 45 \][/tex]
Step 5: Find the Length
Substitute ( w = 45 ) into the length equation:
[tex]\[ l = 3(45) - 9 \][/tex]
[tex]\[ l = 135 - 9 \][/tex]
[tex]\[ l = 126 \][/tex]
Step 6: Calculate the Perimeter
[tex]\[ P = 2l + 2w \][/tex]
[tex]\[ P = 2(126) + 2(45) \][/tex]
[tex]\[ P = 252 + 90 \][/tex]
[tex]\[ P = 342 \][/tex]
Thus, the perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]
Jack has 63 pennies, dimes, and quarters worth $6.30. If the number of dimes is three less than the number of quarters, how many of each coin does he have? Three variable application
Answer:
18 quarters
30 pennies
15 dimes
Step-by-step explanation:
Let number of quarters be q, number of pennies be p, number of dimes be d
The value of pennies is 0.01, the value of quarters is 0.25 and value of dimes is 0.10.
Jack has 63 pennies, dimes, and quarters worth $6.30:
We can write:
p + q + d = 63
0.01p + 0.25q + 0.10d = 6.30
Also, the number of dimes is three less than the number of quarters:
We can write:
d = q - 3
Now we have written 3 equations. Replacing 3rd equation in 1st gives us:
p + q + (q-3) = 63
p + 2q -3 = 63
p + 2q = 66
Solving for p:
p = 66 - 2q
Now we can use this and the 3rd equation and replace p and d with q:
0.01p + 0.25q + 0.10d = 6.30
0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30
Solving for q, gives us:
[tex]0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30\\0.66-0.02q+0.25q+0.10q-0.3=6.30\\0.36+0.33q=6.30\\0.33q=5.94\\q=18[/tex]
There are 18 quarters
Since, p = 66 - 2q, there are:
p = 66 - 2 (18) = 30 pennies
Also,
d = q - 3, so d = 18 - 3 = 15 dimes
Hence, there are:
18 quarters
30 pennies
15 dimes
What is a point on a line and all points of the line to one side of it called?
Answer:
ray
Step-by-step explanation:
A ray is a line that extends in one direction from its end point.
Can anyone help me solve this?
The answer will be 13
since he give you the C and X
you just need to add them and then subtract them from 90 degree
51+26-90=13
I hope this will helps you.
Help PLease. A vector is defined as having magnitude of 15 m and a direction of East. Multiply this vector by the scalar value of –6. What is the resultant vector’s magnitude and direction?
What are the components of a vector C→ if its magnitude is 8.9 m/s and it makes an angle of –40° with the +x-axis?
Answer:
90 m West(6.82, -5.72) m/sStep-by-step explanation:
1. The magnitude of the multiplier is 6, so the magnitude of the new vector is 6×(15 m) = 90 m. The sign on the multiplier is negative, so the new vector will be in the opposite direction of East. It will be 90 m West.
__
2. The components can be found from ...
(8.9 m/s)(cos(-40°), sin(-40°)) ≈ (6.82, -5.72) m/s
__
One or both of the components will usually be irrational if the angle is a rational number of degrees not a multiple of 90°. Here, we have rounded to 2 decimal places.
Peter wrote the equation 4x - 2 = 10, and Andres wrote the equation 16x - 8 = 40. The teachers looked at their equations and asked them to compare them. Describe one way they are similar?
Answer:
The Andrew equitation is 4 times more bigger than Peter equation.
Step-by-step explanation:
(16x-8x=40) is:
4*(4x-2=10)=(16x-8=40)
The result of subtracting (4x2 − x) from -3x2 is .
the result of subtracting[tex]\( (4x^2 - x) \)[/tex] from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]
To subtract [tex]\( (4x^2 - x) \) from \( -3x^2 \)[/tex], we need to distribute the negative sign to each term inside the parentheses and then perform the subtraction.
Given:
[tex]\( -3x^2 - (4x^2 - x) \)[/tex]
Step 1: Distribute the negative sign inside the parentheses:
[tex]\( -3x^2 - 4x^2 + x \)[/tex]
Step 2: Combine like terms:
[tex]\( (-3x^2 - 4x^2) + x \)[/tex]
[tex]\( = -7x^2 + x \)[/tex]
Therefore, the result of subtracting[tex]\( (4x^2 - x) \)[/tex] from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]
How do I solve this word problem?
Eight hundred tickets were sold for a movie production and the receipts for the performance wear $8600. The tickets for adults and students sold for $12.50 and $7.50, respectively. How many of each ticket were sold?
Answer:
280 student tickets520 adult ticketsStep-by-step explanation:
You may recognize that you are given two relationships between two unknowns. You can write equations for that.
You are asked for numbers of adult tickets and of student tickets. It often works well to let the values you're asked for be represented by variables. We can choose "a" for the number of adult tickets, and "s" for the number of student tickets. Then the problem statement tells us the relationships ...
a + s = 800 . . . . . . 800 tickets were sold
12.50a + 7.50s = 8600 . . . . . . . revenue from sales was 8600
(You are supposed to know that the revenue from selling "a" adult tickets is found by multiplying the ticket price by the number of tickets: 12.50a.)
___
You can solve these two equations any number of ways. One way is to do it by elimination. We can multiply the first equation by 12.50 and subtract the second equation:
12.50(a +s) -(12.50a +7.50s) = 12.50(800) -(8600)
5s = 1400 . . . . simplify. (The "a" variable has been eliminated.)
s = 280 . . . . . . divide by 5
Then the number of adult tickets can be found from the first equation:
a + 280 = 800
a = 520
280 student tickets and 520 adult tickets were sold.
520 adult tickets and 280 student tickets were sold.
To solve this problem, we need to set up a system of two linear equations using the given information and then solve for the number of adult and student tickets sold.
Let x be the number of adult tickets sold, and y be the number of student tickets sold.
Given information:
- Total number of tickets sold: [tex]x + y = 800[/tex]
- Total receipts: [tex]12.50x + 7.50y = 8600[/tex]
We have a system of two equations with two unknowns:
[tex]x + y = 800[/tex]
[tex]12.50x + 7.50y = 8600[/tex]
We can solve this system using the substitution method or the elimination method.
Using the substitution method:
From the first equation, [tex]y = 800 - x[/tex]
Substituting this into the second equation:
[tex]12.50x + 7.50(800 - x) = 8600[/tex]
[tex]12.50x + 6000 - 7.50x = 8600[/tex]
[tex]5x = 2600[/tex]
[tex]x = 520[/tex]
Substituting [tex]x = 520[/tex] into the first equation:
[tex]y = 800 - 520 = 280[/tex]
Therefore, 520 adult tickets and 280 student tickets were sold.
By setting up a system of linear equations based on the given information and solving them using algebraic methods, we can find the number of adult and student tickets sold that satisfy the conditions of the total number of tickets and the total receipts.
Consider the graph shown. Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning.
Answer:
the quantities do NOT vary directly
Step-by-step explanation:
A graph showing a proportional relationship is a straight line through the origin. This graph goes through (0, 100), so does NOT show a proportional relationship. y does NOT vary directly with x.
please helpppppppppppppppppppp
I think it 8 I think this is the right answer
Answer:
g(3) = 34
Step-by-step explanation:
To evaluate g(3) substitute x = 3 into g(x), that is
g(3) = 4(3)² - 3(3) + 7 = (4 × 9) - 9 + 7 = 36 - 9 + 7 = 34
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $61. A season ski pass costs $400. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answer:
Step-by-step explanation:One of the things you can use for that is RAP so here's how this goes:
R:A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $61. A season ski pass costs $400. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
A:what do we want to know?(Understand the problem)
How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes
What do we already know?
A daily pass costs $61,A season ski pass costs $400,The skier would have to rent skis with either pass for $25 per day.
what is the plan??
Carry out the plan.Show work for your solution
Hopefully I helped a little
blessings,lilabear
Mrs. Kellen's most recent math test consisted of 50 questions. Some of the questions were worth two points and the rest of the questions were worth 3 points. If there were 115 points available on the test, how many questions were worth 2 points?
Answer:
The answer to your question is: 35 questions worth 2 points and 15 questions worth 3 points.
Step-by-step explanation:
Data
Number of questions = 50
Total points = 115
x = questions worth 2 points
y = questions worth 3 points
Process
write to equations
(1) --------------- x + y = 50
(2) -------------- 2x + 3y = 115
Solve them by substitution
x = 50 - y
2 (50 - y) + 3y = 115
100 - 2y + 3y = 115
3y -2 y = 115 - 100
y = 15
x = 50 - 15
x = 35
Complete the equation. Round to the nearest hundredth where necessary.
(Recall: 1 mi ≈ 1.61 km)
a.
6.21
b.
9.43
c.
10.60
d.
16.10
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
There are 1.61 km in 1 mi.
10 mi × (1.61 km/mi) = 16.1 km
A pool company has learned that, by pricing a newly released noodle at $2, sales will reach 10,000 noodles per day during the summer. raising the price to $6 will cuase the sales to fall to 2,000 noodles per day [Hint: The line must pass through (2,10000) and (6,2000).]
a.) assume that the relationship between sales price and number of noodles sold is linear and write an equation describing this relationship. WILL GIVE 50 POINTS :(
Answer:
[tex]y = - 2000x + 14000[/tex]
SHOW YOUR WORK Multiply.
(3 x 10^6)x (1.4 x 10^-8)
a.
4.2 x 10^-48
b.
4.4 x 10^-48
C.
4.2 x 10^-2
d. 4.4 x 10^-2
Answer:
The answer to your question is: 4.2 x 10⁻²
Step-by-step explanation:
Information: (3 x 10⁶) x (1.4 x 10⁻⁸)
3 x 1.4 = 4.2 we just multiply the integers
10⁶ + 10⁻⁸ = -2 then we add 6 and -8
4.2 x 10⁻² now join the results and -2 will be a power of ten.
what is the estimated product when 620 and 374 are rounded to the nearest hundred and multiplied?
The answer is 240000
Step-by-step explanation:
When you round 620 to the nearest hundred,you will get 600
and when you round 374 to the nearest hundred,you will get 400
multiplying the product after rounding them will give 600×400
=240000
The estimated product when 620 and 374 are rounded to the nearest hundred and multiplied is 240000.
What is a Product?Product is the output obtained when two numbers are multiplied.
The product has to be obtained of numbers 620 and 374
Rounding to nearest hundred
620 can be written as 600
374 can be written as 400
=> 600 * 400
= 240000
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A certain liquid has a density of 2.67 g/cm3. 30.5 mL of this liquid would have a mass of ________ Kg.
0.0114
11.4
0.0814
0.0875 81.4
Answer:
One ml is equal to a cm3, then
m=2.67g/cm3*30.5cm3
m=81.435g
If we divide this quantity by 1000 to pass this to Kg we get:
m=81.435/1000=0.081435kg
Step-by-step explanation:
Remember the formula of density is density=mass/volume, if we solve for mass we get:
mass=density*volume
Which of the following is a factor of 24x6 − 1029y3?
24
2x2 + 7y
4x4 + 14x2y + 49y2
All of the above
Answer:
C - 4x4+14x2y+49y2
Step-by-step explanation:
Just took the test
To determine which option is a factor of the given expression, we need to check each option individually. After checking, we find that option 2, 2x^2 + 7y, is a factor.
Explanation:To determine which of the given options is a factor of the expression 24x^6 - 1029y^3, we need to check each option individually.
Option 1: 24 - We can verify if 24 is a factor by dividing 24x^6 - 1029y^3 by 24 and checking if there is no remainder.
Option 2: 2x^2 + 7y - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.
Option 3: 4x^4 + 14x^2y + 49y^2 - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.
After checking each option, we can determine that option 2, 2x^2 + 7y, is a factor of the expression 24x^6 - 1029y^3.
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A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. Use the result to find the coordinates of the endpoint of a line segment when the coordinates of the other endpoint and midpoint are, respectively, (1, −9), (2, −1) and (−2, 18), (5, 9).
Answer:
(3,7) for the first line, and (12,0) for the second one.
Step-by-step explanation:
Hi Isabella,
1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:
[tex]x_{m}=\frac{x_{1} +x_{2} } {2}, y_{m} =\frac{y_{1}+ y_{2} }{2}[/tex]
2) Each segment has two endpoints, and their midpoints, namely:
a) (1,-9) and its midpoint (2,-1)
b) (-2,18) and its midpoint (5,9)
3) Calculating. You need to be careful to not sum the wrong coordinates.
So be attentive!
The first line a
[tex]2=\frac{1+x_{2} }{2}\\ 4=1+x_{2}\\ 4-1=-1+1+x_{2} \\ x_{2}=3\\-1=\frac{y_{2}-9}{2}\\-2=y_{2}-9\\+2-2=y_{2}-9+2\\ y_{2}=-7[/tex]
So (3,7) is the other endpoint whose segment starts at (1,-9)
The second line b endpoint at (-2,18) and its midpoint (5,9)
[tex]5=\frac{-2+x_{2} }{2} \\ 10=-2+x_{2} \\ +2+10=+2-2+x_{2}\\ x_{2}=12 \\ \\ 9=\frac{18+y_{2} }{2} \\ 18=18+y_{2} \\ -18+18=-18+18+y_{2}\\ y_{2} =0[/tex]
So (12,0) it is the other endpoint.
Take a look at the graph below:
Answer:(3,7) for the first line, and (12,0) for the second one.
Step-by-step explanation:
Hi Isabella,
1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:
Step-by-step explanation:
Tom took a trip of 1,300 miles. He traveled by train at 50 miles an hour and the same number of hours by plane at 275 mph. How many hours did the trip take?
Answer:
Let the number of hours traveled by train be "x".
The x = the number of hours traveled by plane.
-------------------------------------------------
Equation:
train distance + plane distance = 1300 miles
50x + 275x = 1300
x(325) = 1300
x = 4 hours
---
The trip took 8 hrs.
Step-by-step explanation:
Trust me
Answer:
The answer to your question is: time = 4 hours
Step-by-step explanation:
Data
Total distance = 1300 miles
train v = 50 mi/h time is the same distance = x
plane v = 275 mi/h distance = 1300 - x
t = ?
Formula
v = d/t
Process
Train t = d/v t = x / 50
Plane t = d/ v t = (1300 - x) / 275
x / 50 = (1300 - x) / 275
275 x = 50 (1300 - x)
275 x = 65000 - 50x solve for x
275x + 50x = 65000
325x = 65000
x = 65000/325
x = 200
Time with train
t = 200 / 50 = 4 hours
Time with plane
t = (1300 - 200) / 275
t = 1100 / 275 = 4 hours
Can anyone help? Thank you.
Answer:
91.8 ft
Step-by-step explanation:
So we can talk about the diagram, let's name a couple of points. The base of the tree is point T, and the top of the tree is point H. We want to find the length of TH given the length AB and the angles HAT and ABT.
The tangent function is useful here. By its definition, we know that ...
TA/BA = tan(∠ABT)
and
TH/TA = tan(∠HAT)
Then we can solve for TH by substituting for TA. From the first equation, ...
TA = BA·tan(∠ABT)
From the second equation, ...
TH = TA·tan(∠HAT) = (BA·tan(∠ABT))·tan(∠HAT)
Filling in the values, we get ...
TH = (24.8 ft)tan(87.3°)tan(9.9°) ≈ 91.8 ft
The height h of the tree is about 91.8 ft.
Line segment CD begins at (−1,1) and ends at (4,1). The segment is translated 2 units down to form line segment C'D'. Line segment C'D' begins at (−1,−1). Enter the coordinates for the end of line segment C'D'. ( , )
Answer:
D' = (4, -1)
Step-by-step explanation:
Translation down by 2 units subtracts 2 from the y-coordinate. The x-coordinate remains unchanged. You can see this in the descriptions of C and C':
C = (-1, 1)C' = (-1, -1) . . . . . 2 is subtracted from y=1 to get y=-1Likewise:
D = (4, 1)D' = (4, -1)__
The translated segment is still a horizontal segment, now at y=-1 instead of at its previous position of y=1.
Last year at a certain high school, there were 132 boys on the honor roll and 90 girls on the honor roll. This year, the number of boys on the honor roll increased by 25% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
23
Step-by-step explanation:
or 2.8 but try 23 frist
The percentage of increase of total number of students on the honor roll is obtained as 22.97%.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
And to convert a fraction or a decimal into percentage, they are multiplied by 100.
The number of boys and girls on the honor code last year is given as 132 and 90.
Then, the total number is 132 + 90 = 222.
When, the number of boys increased by 25%, it can be obtained as,
⇒ 132 + 25% × 132 = 165
And, the number of girls increased by 20% can be obtained as,
⇒ 90 + 20% × 90 = 108
Now, the total number of students is 165 + 108 = 273.
The percent increase can be obtained as follows,
Change in the total number ÷ Initial number × 100
⇒ (273 - 222) ÷ 222 × 100 = 22.97%
Hence, the percent value of the increase in the number is 22.97%.
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A man with a mass of 65 kg skis down a frictionless hill that is 4.7 m high. At the bottom of the hill the terrain levels out. As the man reaches the horizontal section, he grabs a 23 kg backpack and skis off a 1.7 m high ledge. At what horizontal distance from the edge of the ledge does the man land?
Answer: 4,85 meters
Step-by-step explanation:
Using energy we get the velocity when the man gets to the bottom of the hill
mgh=1/2 m v^2
Then the velocity is the squareroot of two times the mass times the gravity constant =9,598 m/s2
Using energy again, we can get the velocity on the edge of the ledge (using the second mass, the one of the man plus the backpack)
1/2 M1 V1^2=1/2 M2 V2^2
We get V2=8,24 m/s2
Then we have to analyze the jump, horizontally, with constant velocity, and vertically, with constant acceleration equals to the gravity constant.
To get the time we analyze the vertical move
Y=1/2 g t^2
t=59 seconds
To get the horizontal distance we use
X= v t
X=4,85 meters.
PLEASE HELP!!!
WILL MARK BRAINLY
Factor.
10x5+5x2−15
5x2(2x3+x−3)
10(x5+5x2−15)
5(2x5+x2−3)
5(2x5+5x2−15)
The correct answer is:
Option C: 5(2x^5+x^2−3)
A Quick Check:
5*2x^5 is 10x^5
5*x^2 is 5x^2
and 5*-3 is -15
making the equations match
The factored form of the expression 10x⁵ + 5x² - 15 is 5(x⁵ + x² - 3).
What are factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Given, A polynomial of degree five which is 10x⁵ + 5x² - 15.
Now, The HCF of 10, 15, and 5 is 5, and the HCF of x⁵, x², and x⁰ is x⁰ = 1.
Therefore,
10x⁵ + 5x² - 15.
= 5x⁰(x⁵ + x² - 3).
= 5(x⁵ + x² - 3).
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4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail
Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
[tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex] ⇒ answer D
Step-by-step explanation:
* Lets explain how to find the inverse of a function
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y = [tex]f^{-1}(x)[/tex]
* Lets use these steps to solve the problems
∵ [tex]f(x)=\sqrt{x-3}[/tex]
∵ f(x) = y
∴ [tex]y=\sqrt{x-3}[/tex]
- Exchange x and y
∴ [tex]x=\sqrt{y-3}[/tex]
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by [tex]f^{-1}(x)[/tex]
∴ [tex]f^{-1}(x)=x^{2}+3[/tex]
∵ g(x) = x² + 3
∴ [tex]f^{-1}(x)=g(x)[/tex]
∴ The functions are inverses to each other
* Now lets find f(g(x))
- To find f(g(x)) substitute x in f(x) by g(x)
∵ [tex]f(x)=\sqrt{x-3}[/tex]
∵ g(x) = x² + 3
∴ [tex]f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x[/tex]
∴ f(g(x)) = x
∴ The functions are inverses; f(g(x)) = x
* Lets find the inverse of h(x)
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴ [tex]\frac{x + 1}{3}=y^{2}[/tex]
- Take √ for both sides
∴ ± [tex]\sqrt{\frac{x+1}{3}}=y[/tex]
∵ x ≥ 0
∴ We will chose the positive value of the square root
∴ [tex]\sqrt{\frac{x+1}{3}}=y[/tex]
- replace y by [tex]h^{-1}(x)[/tex]
∴ [tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex]
A storm dumps 1.0 cm of rain on a city 6 km wide and 8 km long in a 2-h period. How many metric tons (1 metric ton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 g = 10−3 kg.) How many gallons of water was this?
Answer:
4660194 metric ton
126802560 gallon
Step-by-step explanation:
1 cm = 0.01 m
6 km = 6000 m
8 km = 8000 m
Volume = 0.01 m x 6000 m x 8000 m = 480000 m³
480000 m³ = 480000000 kg of water (density of water = 1000kg/m³)
103 kg = 1 metric ton
480000000 kg = 480000000 / 103 = 4660194 metric ton
1 m³ = 264.17 gallon
480000 m³ = 480000 x 264.172 = 126802560 gallon
A total of 480,000 metric tons of water fell on the city, which is equivalent to approximately 126,802,560 gallons of water.
Explanation:To calculate the amount of water in metric tons that fell on the city, we need to first determine the volume of the rainfall which can be calculated by taking the product of the rainfall's depth (1.0 cm), and the area of the city (6 km x 8 km).
Firstly, convert all dimensions into the same unit. Let's use meters: 1.0 cm = 0.01 m, 6 km = 6000 m, 8 km = 8000 m. Therefore, the volume equals 0.01 m x 6000 m x 8000 m = 480,000 m³.
The mass of the water is then found by multiplying the volume by the density of water. Given that the density of water is 1 g/cm³ (or 1000 kg/m³, which is more useful here, as mass needs to be in kg), this calculation gives us a mass of 480,000,000 kg = 480,000 metric tons.
To convert this to gallons, we use the fact that 1 m³ = 264.172 gallons. Therefore, 480,000 m³ = 480,000 x 264.172 = 126,802,560 gallons.
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answer for the square root(5x-9)+1=x
[tex]\bf \sqrt{5x-9}+1=x\implies \sqrt{5x-9}=x-1\implies 5x-9 = (x-1)^2 \\\\\\ 5x-9=\stackrel{\mathbb{FOIL}}{x^2-2x+1}\implies 5x=x^2-2x+10\implies 0=x^2-7x+10 \\\\\\ 0=(x-5)(x-2)\implies x= \begin{cases} 5\\ 2 \end{cases}[/tex]
Find the value of k in the data set such that the data set represents a linear function. HELP ASAP!!
Answer:
k=3
I mean the third choice
Step-by-step explanation:
f(x) = x-1
The required value of k is 3. Option C is correct.
Given that,
To find the value of k in the data set such that the data set represents a linear function.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The slope of the function,
x, f(x) = (7,6) and (9,8)
Slope = 8 - 6 / 9 - 7
Slope = 2 / 2 = 1
Equation,
y + 3 = 1 (x + 2)
y = x - 1
Now at x = 4 : f(x) = k
k = 4 - 1
k = 3
Thus, the required value of k is 3. Option C is correct.
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