Answers
Justification:
1) For a function to have inverse function, the original function has to be one to one. This is for the original function two (or more) images cannot have different inputs. That condition is satisfied by the function m(x) = - 7x, since it is a straigh line.
2) the function b (x) = x^2 + 3 is a parabola. That means that, except by the vertex, every image is realated with two inputs.
For example, b(x) = 103 => x^2 = 103 - 3 = 100 => x = 10 and x = -10.
3) For the function d(x) = - 9, you cannot tell the input value for the image because it is the same image for any value of x.
4) The function p(x) = |x| also has a pair of images for the same value of x (excpet for the vertex).
For example, for x = - 100 and x = 100, p(x) = 100, so you cannot tell the x value given the p(x) value.
Related Questions
A sporting goods store offers a 40% discount on all golf clubs. Rocco spent 20% of the money in his savings account on a golf putter. He paid $48 for the putter after the discount. How much money did Rocco have in his savings before buyin the putter?
Answers
Rocco originally had $240
Explanation:
Before we begin, note that the price of the putter is given AFTER the discount. This means that the value of the discount doesn't affect the solution.
Assume that the amount Rocco had originally is x
Now, we are given that:
price of putter = $48
Price of putter represents 20% of what Rocco had
This means that:
price of putter = 20% * amount Rocco had
48 = 20% * x
48 = 0.2x
x = 48 / 0.2
x = $240
This means that Rocco originally had $240
Hope this helps :)
Select the expression for the following word phrase.
12 less than v
Answers
For this case, the first thing we are going to assume is that we have the following terms:
Number = 12
Variable = v
We then have the following expression:
12 less than v
Writing the expression in algebraic form we have:
12 <v
Answer:
the expression for the word phrase is:
12 <v
Matias stacked his cubes to make this rectangular prism.
rectangular prism with grid lines
How many cubes did Matias use?
cubes
Answers
SEE ATTACHED IMAGE.
The problem can be modeled as a pair of matrices:
First matrix:
(4) * (4) = 16
Second matrix:
(16) * (5) = 80
Since the second matrix depends on the first, then the number of cubes is:
N = 80
Answer
80 cubes.
Answer:
The answer is 80
how do you do #8,9,10 ?? thank you !!
Answers
.. 3 represents a vertical expansion factor of 3
.. 2 represents a left shift of 2 units
9. g(x) = -2f(x)
.. 2 represents a vertical expansion factor of 2
.. the minus sign is a reflection across the x-axis
10. g(x) = f(x -1) +3
.. 3 represents a vertical shift upward by 3 units
.. -1 represent s right shift of 1 unit
A toy manufacturer ships a toy in one of two different size boxes. The small box contains 6 of the toy and the large box contains 10 of the toy.
A client orders no fewer than 100 of the toy. Based on his storage and sales needs, the client requires that he receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.
The cost to the client for a small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200 for his order of toys.
Let x represent the number of small boxes and y represent the number of large boxes.
What constraints are placed on the variables in this situation?
Answers
Answer:
Let x represent the number of small boxes.
Let y represent the number of large boxes.
The client receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.
[tex]x \geq 6[/tex]
[tex]y \leq 8[/tex]
The cost of small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200.
[tex]4x+ 6y \leq 200[/tex]
The small box contains 6 of the toy and the large box contains 10 of the toy. A client orders no fewer than 100 of the toy.
[tex]6x+10y \geq 100[/tex]
What is the perimeter of this square?
A.
19 in.
B.
28.5 in.
C.
30.5 in.
D.
38 in.
Answers
A) –2n + 9m – 17p
B) –2n – 9mn + 17np
C) –2n + 9mn – 17np
D) –18n + 81mn – 153np
Answers
All you do is simplify the equation by distributing and multiplying the 1/3n to each of the numbers.
Hope this helps!
_____________________________________________________
[tex] \frac{1}{3} [/tex] n (−6 + 27m − 51p) =
( [tex] \frac{1}{3} [/tex] n * −6 ) + ( [tex] \frac{1}{3} [/tex] n * 27m ) −
( [tex] \frac{1}{3} [/tex] n * 51p ) ;
= −2n + 9mn − 17np ; which is: Answer choice: [C]: " −2n + 9mn − 17np" .
__________________________________________________________
Which equation of the least squares regression line most closely matches the data set?
Note: The variable x represents the years after 1970.
Y= -5.7x-67
Y= -0.98x+65
Y= -0.17x+76
Y= -5.7x +67
Answers
The 4th selection is appropriate.
Answer:
D. [tex]y = -5.7x + 67[/tex]
Step-by-step explanation:
Let us take the year 1970 as the 0th year.
So, the corresponding table of values is,
x y
0 65
2 58
4 45
6 32
8 21
Using the linear regression calculator, we see that,
The closest equation of the regression line is [tex]y = -5.7x + 67[/tex].
PLEASSE HELLP! // 99 points // look at the picture below
Answers
Parallelogram is your answer
The opposite sides are parallel to each other, and are congruent.
hope this helps
LCD for 13/4x and 27/3x^2
Answers
In the least common denominator, LCD, we consider the terms that are in the denominator of the fractions; therefore in this case, our focus will be on:
[tex]4x,3x^{2}[/tex]
Now,
Let us find LCD of the above two terms:
[tex]4x[/tex] = 2*2*[tex]x[/tex]
[tex]3x^{2}[/tex] = 3*[tex]x^{2}[/tex]
Therefore, the LCD = 2*2*3*[tex]x^{2}[/tex] (always go for the highest level exponent for LCD)
Ans: LCD = 12[tex]x^{2}[/tex]
suppose that the amount of algae in a pond doubles every 4 hours. if the pond initially contains 90 pounds of algae, how much algae will be in the pound after 12 hours?
720 pounds
360 pounds
1,440 pounds
114 pounds
Answers
Here is your answer:
The proper answer to this question is option B "360 pounds".
Here is how:
All you need to do is multiply 4 by 90 pounds to get your answer....
4*90=360 pounds
Your answer is B.
If you need anymore help feel free to ask me!
Hope this helps!
Which of the following sets of points forms a linear function?
A. (0, 5) (1, 8) ( 2, 11) (3, 14)
B. (1, 2) (2, 4) (3, 8) (4, 16)
C. (-2, 5) (-1, 2) (0, 1) (1, 2)
D. (-4, 8) (-3, 3) (-2, 0) (1, 3)
Answers
x=1, y=a*1+5=8, a=8-5, a=3
x=2, y=2*3+5=11
x=3, y=3*3+5=14
A is the answer
BRAINLIESTTTT!!!!
Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
(x − 4)2 = 3
(x − 3)2 = 2
(x − 2)2 = 1
(x − 1)2 = 4
Answers
x² − 2x − 3 = 0
Step 1
isolate the variable terms
x² - 2x = 3
Step 2
complete the square
x² - 2x + 1² = 3 + 1²
(x-1)² = 4
the answer is the option (x-1)² = 4
guys please assist me
this is a system of equation word problem
Answers
.. 20t +100h = 10000 . . . . . . the total value of the payment was $10,000
.. t - h = 20 . . . . . . . . . . . . . . . she gave him 20 more twenties than hundreds
Using an augmented matrix, the solution can be found to be
.. t = 100
.. h = 80
She gave the crook only 100 20s, so did not meet the requirement for 105 twenty-dollar bills. Polly did not give him enough.
Is this pattern a net for the three dimensional figure ?
Answers
The pattern net is not for the three-dimensional figure which is a hexagon prism the answer is No.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have a three-dimensional figure is shown in the picture.
As we know,
In the hexagonal prism, there are only two hexagons but in the net, there are three hexagons shown.
Thus, the pattern net is not for the three-dimensional figure which is a hexagon prism the answer is No.
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Two armies face each other for battle. One army has 1220 soldiers and the other has 549 soldiers. Both armies are divided into smaller groups of equal size called platoons. Find the largest possible number of soldiers in a platoon if the platoon size is equal for the two armies.
Answers
The largest possible number of soldiers in a platoon is 61.
What is the greatest common factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.
Given that, two armies face each other for battle. One army has 1220 soldiers and the other has 549 soldiers.
Factors of 1220 and 549 are
1220 = 2×2×5×61
549 = 3×3×61
So, GCF is 61
Therefore, the largest possible number of soldiers in a platoon is 61.
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A toy plush weighed 1/5 of a pound. a flimsy box can hold 3 pounds. how many toy plushes could the box hold?
Answers
total weight = 1/5 times the amount of toys
3 = 1/5 x
rewrite
3 = 1x /5
multiply both sides by 5
15 = 1x
15 = x
The flimsy box can hold 15 toy plushes.
Hope this helps
30 POINTS!!! HELP PLEASE!
Model each scenario with an equation and a sketch. Solve for the missing value and u. Use complete sentences to interpret the solution. In your final answer, include your equation, sketch, interpretation, and all calculations necessary for the solution.
1.) To get home from school, Bob walks four blocks north and three blocks east. What is the straight line distance between Bob’s house and his school?
2.)One of the requirements of your summer window-washing job is to provide yourself with all of the necessary supplies, including a fourteen foot ladder. When you arrive at your first job, you place your ladder on the ground six feet from the base of the house and lean it towards a second story window, only to realize that the ladder doesn’t reach the window. Given the length of the ladder and its current position, what is one possible height of the second story window? (Hint: There is more than one correct answer.)
3.) In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.
4.) A sailboat drifts 600 meters west, makes a turn and sails 800 meters south. How far is the sailboat from its original position?
Answers
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. Using our coordinates we have:
[tex]d=\sqrt{(4-1)^2+(5-1)^2} \\=\sqrt{3^2+4^2} \\=\sqrt{9+16} \\=\sqrt{25} \\=5[/tex] His house is 5 blocks from the school in a straight line.
#2) The ladder (14 ft) forms the hypotenuse of a right triangle, with the legs being the distance from the house (6 ft) and the height of the ladder (b ft). This gives us:
[tex]6^2+b^2=14^2 \\36+b^2=196[/tex]
Subtract 36 from both sides:
[tex]36+b^2-36=196-36 \\b^2=160[/tex]
Take the square root of both sides:
[tex]\sqrt{b^2}=\sqrt{160} \\b=12.6[/tex]
One possibility for the height of the second story window is 13 feet, since it is longer than 12.6.
#3) The distance from 1st base to 3rd base forms the hypotenuse of a right triangle, with each leg being equal to s, the side length of the square formed by the baseball diamond. Using the Pythagorean theorem we have:
[tex]s^2+s^2=d^2[/tex], where d is the distance from 1st to 3rd. Combining like terms gives us [tex]2s^2=d^2[/tex]. Taking the square root of both sides we have [tex]\sqrt{2s^2}=\sqrt{d^2} \\s\sqrt{2}=d[/tex] (this is due to the fact that square root cancels a squared variable, so s comes out of the radical sign).
#4) The straight distance from the boat's original position to its new position forms the hypotenuse of a right triangle, with the legs being the distance west (600) and the distance south (800) it traveled. Using the Pythagorean theorem we have:
[tex]600^2+800^2=d^2 \\360000+640000=d^2 \\1000000=d^2[/tex]
Taking the square root of both sides we have
[tex]\sqrt{1000000}=\sqrt{d^2} \\1000=d[/tex]
The straight distance between the two points would be 1000 meters.
Solve 1-12 or any of them please.
Answers
2. y = -x + 4
3. y = 1/3x +1
4. y = ----
5. y = 1/7x + 2
6. y = -4x + 2.75
7. y = 3x + 5
8.
9.
10.
11.
12.
.. x/(x-intercept) +y/(y-intercept) = 1
2) x/4 +y/4 = 1 . . . . . an equation
.. x + y = 4 . . . . . . . . the equation in standard form
3) x/-3 +y/1 = 1 . . . . an equation
.. x -3y = -3 . . . . . . . the equation in standard form
10) x/4 +y/2 = 1
.. x +2y = 4 . . . . . . . in standard form
11) x/-3 +y/5 = 1
.. 5x -3y = -15 . . . . . in standard form
12) x/-10 +y/16 = 1
.. 8x -5y = -80 . . . . . in standard form
For the rest, the 2-point form of the equation of a line will work.
For points (x1, y1) and (x2, y2), the line through them can be written as
.. y = (y2 -y1)/(x2 -x1)*(x -x1) +y1
1) y = (1 -(-3))/(1 -0)*(x -0) +(-3)
.. y = 4x -3
Cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of cylinder B? V = 270 cm3 V = 360 cm3 V = 480 cm3 V = 600 cm3
Answers
This is because the volume of the cylinder is dependent on the base and the perpendicular height, therefore, the slanting of the cylinder wont change its volume
Step-by-step explanation:
ndkfkasdjfkjdasl;fkjalksdfjlasdjf
Jimmy is trying to figure out how many pennies are in his bank. He asked his mother to help him figure out the total. He tells her to let the amount in the bank equal 21x^3+18x^2+9x and each penny equal 3x. Can you help them figure out how many pennies are in the bank?
Answers
plzz hellp :( i will mark you the brainlist if some on helps (A rectangular prism has a length of 1 1/4 yards, a width of 2 1/2 yards, and a height of 4 yards.
Enter the volume of the prism as a mixed number in simplest form in the box.
Answers
So the volume V of prism with length [tex]1 \frac{1}{4} [/tex] yards, width [tex]2 \frac{1}{2} [/tex] yards and height of 4 yards will be:
[tex]V=1 \frac{1}{4} * 2 \frac{1}{2} *4 \\ \\ V= \frac{5}{4}* \frac{5}{2}*4 \\ \\ V= \frac{25}{2} \\ \\ V=12 \frac{1}{2} [/tex]
Thus the volume of prism as a mixed number in simplest form will be [tex]12 \frac{1}{2} [/tex] cubic yards
Please help quickly for 5 stars and brainliest!!
1. Omar set off a rocket in a field. The height h of the rocket in feet can be roughly estimated using the formula
h = -16t^2 + 128t, where t is the time in seconds. How long will it take the rocket to reach a height of 240 feet?
2. Josefina tosses a ball upward with an initial velocity of 76 feet per second.
She tosses it from an initial height of 2 feet. Find the approximate time that the ball hits the ground.
Use the function h(t) = -16t^2 + 76t + 2
Round to the nearest second.
3. Brandi, an amateur skier, begins on the "bunny hill," which has a vertical drop of 200 feet.
Her speed at the bottom of the hill is given by the equation v^2 = 64h, where the velocity v is in feet per second
and the height h of the hill is in feet. Assuming there is no friction, approximate Brandi's velocity at the bottom of the hill.
Answers
Height h = 240 feet
We insert it into formula.
[tex]240 = -16 t^{2} +128t[/tex]
Now we solve this for t:
[tex]16 t^{2} -128t +240 = 0 /16 \\ t^{2} - 8t +15 =0 \\ t_{1} = 5 t_{2} = 3[/tex]
We have two answers as the rocket will pass this height on it's way up and down.
2.
Height h = 0 feet
We insert it into formula.
[tex]0=-16 t^{2} +76t + 2[/tex]
Now we solve this for t:
[tex]16 t^{2} - 76t -2 = 0 /2 \\ 8t^{2} - 38t - 1 = 0 \\ t_{1} = 5 t_{2} = -1[/tex]
We do not consider solution -1 as the time can not be negative. Our solution is 5s.
3.
Height at bottom of hill h = 0 feet
We insert it into formula.
[tex] v^{2} = 64 * 0 = 0 ft/s[/tex]
what is the answer for Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number.
Answers
2 solutions: perimeter=6+5+5=16 or 8+5+5=18.
A hybrid car averages 609 miles on a 12.5 gallon tank of gas. Manuel is planning a 1290- mile vacation in his hybrid car. Find how many gallons of gas he can expect to burn.
Answers
1 miles = 12.5 / 609
1 mile = 0.0205 gallon
1290 miles = 0.0205 gallons x 1290
= 26. 48 gallons
Using ratio and proportion, we deduced that Manuel's hybrid car travels 48.72 miles per gallon. Based on this, we estimated that Manuel would need around 26.5 gallons of gas for his 1290-mile vacation.
Explanation:The subject at hand requires the utilization of ratio and proportion in mathematics, specifically in the context of fuel economy of cars. The hybrid car Manuel owns averages 609 miles on a 12.5 gallon tank. This implies that for every one gallon of gas, the car can travel 609 / 12.5 = 48.72 miles.
Now Manuel is planning for a 1290-mile trip. To ascertain how many gallons of gas he might expect to consume, we divide the total distance of the vacation by the miles per gallon for his car: 1290 miles / 48.72 miles/gallon = 26.5 gallons.
Therefore, Manuel can expect to consume approximately 26.5 gallons of gas for his 1290-mile vacation.
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The function f(x) = −(x + 5)(x + 1) is shown.
What is the range of the function?
a.all real numbers less than or equal to 4
b.all real numbers less than or equal to −3
c.all real numbers greater than or equal to 4
d.all real numbers greater than or equal to −3
Answers
Since the shading would go from 4 all the way to negative infinity, the answer is all real numbers less than or equal to 4.
Best of luck!
Range of the given function is all real numbers less than or equals to 4.
What is the range of the function?The range of a function is the set of all its output values.
According to the given equation we have
f(x) = -(x+5)(x+1)
Let, y = -(x+5)(x+1)
To find the range of the given function, we will substitute different values of x.
At, x = -5
y = f(-5) = -(-5 +5)(-5+1) =0
At, x = -4
y = f(-4) = -(-4 + 5)(-4 + 1) = -(1)(-3) = 3
At, x = -2
y = f(-2) = -(-2+5)(-2+1) = -(3)(-1) =3
At, x = -3
y = f(-3) = -(-3 + 5)(-3 + 1) = -(2)(-2) =4
Similarly, we will find for the other values of x.
So, the coordinates are (-5, 0), (-4, 3), (-3, 4), (-2,3)
And the graph using this coordinates are already given. Here, the set of outputs are the values of y. So we can see that the range of the given function is all real numbers less than or equals to 4.
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4.2(3.9r – 5.9s) + 7.9s – 9.53r
A.
16.88r + 6.85s
B.
10.82r + 31.15s
C.
10.82r – 31.15s
D.
6.85r – 16.88s
Answers
Answer:
D. 6.85r – 16.88s
Step-by-step explanation:
Use the distributive property to eliminate parentheses, then collect terms.
4.2(3.9r -5.9s) +7.9s -9.53r
= 16.38r -24.78s +7.9s -9.53r
= (16.38 -9.53)r +(-24.78 +7.9)s
= 6.85r -16.88s
Solving quadratics by factoring 3x^2+33x+30=0
Answers
3(x^2+11x+10)=0
3(x+10)(x+1)=0
x=-10,-1
x = -1 and -10
Hope this helps!!
Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
Answers
The first five terms of a complex sequence are 4, 7, 10, 16, and 28.
Let's consider a non-trivial sequence.
Let's say the first term of our sequence, a1, is 4.
From then on, the sequence increases by 3 times the previous term, but instead of simply multiplying by 3, we will multiply by 3 raised to the power of one less than the term's position in the sequence. However, we are given that the general expression for the nth term is 4 + 3 x 2(n-2), except for the first term which remains 4.
This gives us a starting point for both our formulas.
To find the first five terms of this sequence, we can manually calculate them using the explicit formula given:
a1 = 4 (by definition)a2 = 4 + 3 x 2(2-2) = 4 + 3 x 1 = 7a3 = 4 + 3 x 2(3-2) = 4 + 3 x 2 = 10a4 = 4 + 3 x 2(4-2) = 4 + 3 x 4 = 16a5 = 4 + 3 x2(5-2) = 4 + 3 x 8 = 28Therefore, the first five terms are 4, 7, 10, 16, and 28.
Explicit Formula:
The explicit formula for any term an in the sequence is:
an = 4 + 3 x 2(n-2) for n > 1, with a1 = 4.
Recursive Formula:
The recursive formula builds each term based on the preceding term. For n > 1, the recursive formula is an = an-1 + 3 imes 2(n-2), with a1 still equal to 4.
In the game of roulette, a player can place a $55 bet on the number 3434 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3434, the player gets to keep the $55 paid to play the game and the player is awarded an additional $175175. otherwise, the player is awarded nothing and the casino takes the player's $55. what is the expected value of the game to the player
Answers
In the game of roulette, a player can place a $5 bet on the number 34 and have a 1/38 probability of winning. if the metal ball lands on 34, the player gets to keep the $5 paid to play the game and the player is awarded an additional $175. otherwise, the player is awarded nothing and the casino takes the player's $5. what is the expected value of the game to the player
we know that
P(winning) = 1/38
P(losing) = 1-1/38 = 37/38
Expected value = 175*1/38 - 5*37/38
175/38 - 185/38 = - 10/38 =-$0.2632
The player's expected value is -$0.2632 ( is losing)