Answer:
Below in bold.
Step-by-step explanation:
f(x) = 3x³ - 4x + 6 and g(x) = x³ + 3x² + x - 3
A. (f+g)x = 3x³ - 4x + 6 + x³ + 3x² + x - 3 = 4x³ + 3x² - 3x + 3.
B. (f-g)x = 3x³ - 4x + 6 - (x³ + 3x² + x - 3) = 2x³ - 3x² - 5x + 9.
C. (3f+2g)(x) = 9x³ - 12x + 18 + 2x³ + 6x² + 2x - 6 = 11x³ + 6x² - 10x - 12.
C. (3f-2g)(x) = 9x³ - 12x + 18 - (2x³ + 6x² + 2x - 6) = 7x³ - 6x² - 14x - 24.
the cost to rent a moving van is $51 plus an additional $7 per hour. If a moving van is rented for 2 hours, what is the cost?
We know that
The cost to rent a moving van is $51 plus an additional $7 per hour.Based on the given information, we define the following
[tex]51+7(2)=51+14=65[/tex]Therefore, the cost is $65.The cost to rent a moving van is $51 plus an additional $7 per hour.
Based on the given information,
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 48.5 (ft) with superscript (3). What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
The dimensions that yield the minimum surface area of the open-top square-based, rectangular metal tank that will have a volume of 48.5 ft³ are:
Length = 3.65 ftWidth = 3.65 ft.What are the dimensions of an area?The dimensions of an area, which is a two-dimensional object, refer to the length and the width.
On the other hand, the dimensions of the volume refer to the length, width, and height.
The volume of the square-based rectangular tank = 48.5ft³.
The length of each side of the surface area = 3.6468 ft (∛48.5ft)
Check:
Volume = height x length x width
= 3.6468 x 3.6468 x 3.6468
= 48.499 ft³
= 48.5 ft³
Thus, the dimensions of the surface area include the length and the width without the height.
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What percentage of the number 1 to 20 contain the digit 2????
The amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We know that the numbers 1 to 20 that contain the digit 2 are 2,12, and 20.
So, the quantity of the numbers is 3
It’s out of 20 numbers, this means 3/20
Calculating percentages indicated above can be readily computed using the formula below:
Percentage = (Value/Total Value) × 100
The amount as a percent = (Value/Total Value) × 100
The amount as a percent = (3/20) × 100
The amount as a percent = 15%
Thus, the amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.
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Please help!!!!
I’ll give you the Brainiest
A triangle has height 4ft and area 32 ft². What is the length of its base?
Step-by-step explanation:
1st
[tex]area = \frac{1}{2} base \times hight[/tex]
2nd
[tex]32 = \frac{1}{2} base \times 4[/tex]
3rd
[tex]32 \div 4 = \frac{1}{2} base[/tex]
4th
[tex]8 \times 2 = base[/tex]
answer
[tex]base = 16ft[/tex]
Given a normal distribution with mean M = 8 and σ = 3,
What is the x value corresponding to z = 0.4?
123
[tex]123 > x = 10 > 6[/tex]
Give a polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −3434 when x=1. Write the polynomial in standard form axn+bxn−1+….
The polynomial in standard form is 2x³+200x-36x²-3600
A polynomial is a mathematical formula that involves only the operations subtraction, addition, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.
It is common to refer to the x of a polynomial as a variable or an indeterminate. The symbol x is fixed and has no significance when the polynomial is viewed as an expression (its value is "indeterminate"). The argument of the function is represented by x, which is referred to as a "variable" when considering the function that the polynomial defines.We know the roots of the polynomial as 18, 10i, and −10i.
therefore the polynomial is of the form.
a(x-18)(x-10i)(x+10i)
= a (x-18)(x²-100i²)
= a (x-18)(x²+100)
= a (x³+100x-18x²-1800)
Now at x =1 The value of the polynomial is -3434
Therefore
-3434 = a(1+100-18-1800)
or, a = 2
Therefore the polynomial is of the form: (2x³+200x-36x²-3600)
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At the beginning of spring, Anand planted a small sunflower in his
backyard. The sunflower's height in inches, h, after w weeks, is given by the equation h = 3.75w+18. What
could the number 3.75 represent in the equation?
Hint: this equation is in slope-intercept form: y=mx+b
The rate of change in the sunflower's height
The sunflower's height after one week
The sunflower's height when it is planted
Answer:
3.75 represents how much the flower grows every week.
Step-by-step explanation:
Find the equation of a line perpendicular to y=x-1 and passes through the point (-1,-5)
A. y+5= -(x+1)
B. y-5=x-1
C. y+5=x+1
D. y-5= -(x-1)
Step-by-step explanation:
d
since you add them up you will have a certain answer that will match up
14/3 = 7y solve for y and simplify your answer as much as possible
Answer:
2/3 = y
Step-by-step explanation:
to solve you got to cancel out the 7
so 7y/7.
whatever you do to one side, you do to the other.
14/3 ÷ 7 = 7y/7
14/3 ÷ 7 = 0.6666... = 2/3 = y
Can someone help me with this please?
Step-by-step explanation:
in general, a linear function is always of the structure
y = ax + b
"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
"b" is the y-intercept (the y-value when x = 0).
so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :
2 = a×1 + b = a + b
1 = a×2 + b = 2a + b
now we can simply subtract the first equation from the second and get
1 = 2a + b
- 2 = a + b
------------------
-1 = a + 0
a = -1
1 = 2×-1 + b = -2 + b
b = 3
and the equation is
y = -x + 3
therefore, when the input is n (that means f(n))
y = output = -n + 3
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42
X
40
Find the unknown side length, x. Write your answer in simplest radical form.
A. 241
B. 4 29
C. 48
D. 58
The unknown side length of the right triangle is 58 units.
What is pythagoras theorem for a right triangle?
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Mathematically, Hypotenuse² = Base² + Perpendicular²
Given, the length of the perpendicular of the right triangle = 42 units
Also, the length of the base of the right triangle = 40 units
Let the length of the hypotenuse of the right triangle = 'x' units
Following the statement of the pythagoras theorem as established in literature, we have: Hypotenuse² = Base² + Perpendicular²
Substituting the values from the question given, we get:
x² = 42² + 40² = 3364 ⇒ x = √3364 ⇒ x = √58² ⇒ x = 58
Therefore, the unknown side length of the right triangle is 58 units.
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a box has 12 red cards and 12 black cards. another box has 24 red cards and 24 black cards. you want to draw two cards randomly from one of the two boxes, one card at a time. which box has a higher probability of getting cards of the same color and why?
Select red from A and B then the probability of getting cards of same color is 12/24 * 24/48 = 1
Box A: 12 Red
12 Black
Box B: 24 Red
24 Black
One card is selected from Box A and placing the selected card into Box B.
One card is selected from Box B.
What is the probability that a red card is selected from Box B?
Two things can occur:
1) Select red from A and B:
12/24 * 24/48 = 1
2) Select black from A and red from B:
12/24 * 24/48 = 1
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A sea turtle is 3 feet below the surface of the sea. If its position can be recorded as −3 feet, what would the position 0 represent in this situation? (4 points)
Group of answer choices
A.) the height of the turtle
B.) the distance above the surface of the sea
C.) the distance below the surface of the sea
D.) the surface of the sea
Answer:
D
Step-by-step explanation:
-3 ft means that it is three feet below zero. That means 0 means the sea level.
Simplify the expression. 1-31
1. 5/6(-2y+3)=
2. 6(3s-2.5-5s)=
3. 3/10(4m-8)+9m=
4. 2.25-2(7.5-4h)=
5. 3(a-7)=
6.-6(2+x)=
7. -5(3m-4)=
8. -9(-5-4c)=
9. 4.5(3s+6)=
10. -1.4(-5+7g)=
11. 2/5(6-5p)=
12. -4/3(3q-10)=
13. 2(3+4y+5)=
Factor the expression using the GCF.=
14. The expression 8x + 2 factored using the GCF is=
15. The expression 3y-24 factored using the GCF is =
16. The expression 14p-28 factored using the GCF is=
17. The expression 6+16k factored using the GCF is=
Factor out the coefficient of the variable term.=
18. The expression 1/7a + 1/7 factored is=
19. The expression 1/3b - 1/3 factored is=
20. The expression 3/8d + 3/4 factored is=
21. The expression 2.2x+ 4.4factored is=
22. The expression 0.15c - 0.072 factored is=
23. The expression 3/8z + 1 factored is=
24. The expression 6s - 3/4 factored is=
25. The expression 5/2k - 2 factored is=
26. Factor -4 out of 8d + 20 The factored expression is=
27. Factor -6 out of 18z - 15 The factored expression is=
28. Factor -0.25 out of 7g + 3.5 The factored expression is=
29. Factor -1/2 out of -1/2x+ 6 The factored expression is=
30. Factor -1.75 out of -14m - 5.25n The factored expression is=
31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=
The answers are given below.
First of all, we will know about GCF and expressions.
GCF (GREATEST COMMON FACTOR) - The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both.
Expression are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
1). 5/6(-2y+3) (simply multiply 5/6 with both terms using expansion)
=-2(5/6)+3(5/6)
=-5/3+5/2
2). 6(3s-2.5-5s)= 18s-15-30s = -12s-15
3). 3/10(4m-8)+9m = 12/10m-24/10+9m
= 6/5m-12/5+9m
=6/5m+9m-12/5
=51/m-12/5
4). 2.25-2(7.5-4h)= 2.25-15+8h
= 8h-12.75
5). 3(a-7)= 3a-21
6). -6(2+x)= -12-6x
7). -5(3m-4)= -15m+20
8). -9(-5-4c)= 45+36c
9). 4.5(3s+6)= 13.5s+27
10). -1.4(-5+7g)= 7-9.8g
11). 2/5(6-5p)= 12/5-2p
12). -4/3(3q-10)= -4q+40/3
13). 2(3+4y+5)= 6+8y+10 = 8y+10
14. The expression 8x + 2 factored using the GCF is= 2(4x+1)
15. The expression 3y-24 factored using the GCF is = 3(y-8)
16. The expression 14p-28 factored using the GCF is= 14(p-2)
17. The expression 6+16k factored using the GCF is= 2(3+8k)
The coefficient of the variable terms of following are given below
18. The expression 1/7a + 1/7 factored is= 1/7
19. The expression 1/3b - 1/3 factored is= 1/3
20. The expression 3/8d + 3/4 factored is= 3/8
21. The expression 2.2x+ 4.4factored is= 2.2
22. The expression 0.15c - 0.072 factored is= 0.15
23. The expression 3/8z + 1 factored is=3/8
24. The expression 6s - 3/4 factored is=6
25. The expression 5/2k - 2 factored is=5/2
26. Factor -4 out of 8d + 20 The factored expression is= -4(-2d-5)
27. Factor -6 out of 18z - 15 The factored expression is=-6(-3z+5/2)
28. Factor -0.25 out of 7g + 3.5 The factored expression is=-0.25(-28g-14)
29. Factor -1/2 out of -1/2x+ 6 The factored expression is=-1/2(x-12)
30. Factor -1.75 out of -14m - 5.25n The factored expression is=-1.75(8m+3n)
31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=-1/4(2x+5y)
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Learn with an example
or Watch a video D
Two cars leave the same parking lot, with one heading north and the other heading east.
After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car
has traveled 4 kilometers. Measured in a straight line, how far apart are the two cars?
kilometers.
The two cars are 5 kilometers far apart from each other.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
Two cars leave the same parking lot, with one heading north and the other heading east.
After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car has traveled 4 kilometers.
Now,
The straight path is find by using the Pythagoras theorem as;
Straight path = √3² + 4²
= √9 + 16
= √25
= 5 km
Therefore,
The two cars are 5 kilometers far apart from each other.
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Consider the line y =
9
7
x-9.
Find the equation of the line that is parallel to this line and passes through the point (-7, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-7, 4).
Answer:
Axis interception points [tex]97x-9[/tex] x intercepts: [tex](\frac{9}{97} ,0),[/tex]Y intercepts:[tex](0,-9)[/tex]
Step-by-step explanation:
Slope of 97x-9 : m=97
Domain: 97 x - 9
Range: 97 x - 9
please answer these question
What age would a dog be in human years if he is 3 in dog years?
what is glow in the dark things made out of?
Answer:
Dog be 28
Phosphors apparently
Step-by-step explanation:
PLEASE HELP
Classify the equation 6x + 4x-1= 2(5x + 4) as having one solution, infinitely many solutions, or no solution by
solving the problem. Solve the equation for x then classify the solution.
Answer: NO SOLUTION
Step-by-step explanation:
6x + 4x - 1 = 2(5x + 4)
10x - 1 = 2(5x+4)
10x - 1 = 10x + 8
-1 = 8
NO SOLUTION
!!!Need Help ASAP
R=42−0.7t
Quinn returned home one summer's day to find it extremely hot. He turned the air conditioner on, and the room's temperature began decreasing at a constant rate. The equation shown above gives the room's temperature, R, in degrees Celsius, t minutes after Quinn turned on the air conditioner. What was the room's temperature, in degrees Celsius, when Quinn returned home?
The room's temperature when Quinn returned home is the y-intercept of the equation, which is: 40 degrees Celsius.
What is the Y-intercept or Initial Value of a Linear Equation?The equation of a linear relationship between two variables, x and y, can be expressed in slope-intercept form as y = mx + b, where we have the initial value or the y-intercept as "b", and the rate of change or unit rate as "m".
Alternatively, it can be rewritten as y = b + mx.
R = 42 - 0.7t represents the equation for the Quinn's room's temperature, R, in degrees Celsius, and t in minutes after Quinn turned on the air conditioner.
Interpreting the equation, we can deduce the following:
The initial value or the y-intercept (b) was the room's temperature when Quinn returned home.
The unit rate or rate of change (m) = -0.7 degrees per minute.
Thus, Quinn's room's temperature when she returned was 40 degrees Celsius.
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What is the length of cd ?
Answer:
7
Step-by-step explanation:
since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that
please someone help me there are only 3 questions
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Definition of the proportionality constant?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
K = y/x is the equation for the proportionality constant. The equation for the slope of a line through the origin, m = y/x, is the same as this. One can determine the value by using the equation for the line's slope.
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A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.
The speed of the boat in still water is 6miles/hour miles per hour.
The speed of the current is 3miles/hour miles per hour.
The distance travelled by the boat downstream(with the flow current of river) is 240 miles.
The distance travelled by the boat upstream(Against the flow current of river) is 240 miles.
Time taken to travel downstream = 20 hours.
Time taken to travel upstream = 60 hours.
Let us say the velocity of the boat is V and the velocity of the current flow of river is U.
The relative velocity of boat with respect to ground while going downstream is,
velocity of boat in downstream = V + U.
As we know,
Velocity = distance/time
Putting values of downstream motion,
V + U = 240/20
V + U = 10
Let us say this is our equation 1.
The relative velocity of boat with respect to ground while going upstream is,
velocity of boat in upstream = V - U
As we already know,
Velocity = distance/time
Putting the values of upstream motion,
V - U = 240/60
V - U = 3
Let us say this is our equation 2.
Now, on adding equation 1 and 2.
V+U+V-U = 10 + 3
2V = 13
V = 6.5 miles per hour.
Rounding off to the nearest integer,
V = 6 miles/hour.
Putting V = 6.5 miles/hour in equation 1,
6.5 + U = 10
U = 3.5 miles/hour.
Rounding off to the nearest integer,
U = 3 miles/hour
The velocity of river current is 3 miles/hour and velocity of boat is 6miles/hour.
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A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours. Use this information to fill in the following blanks.
The speed of the boat in still water is ______ miles per hour.
The speed of the current is ______ miles per hour.
When going out for dinner, Sally left an 18% tip. The tip was 9.50. How much was the dinner bill before the tip?
The dinner bill of Sally before the tip is $53.
Given that, Sally left an 18% tip. The tip was 9.50.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the dinner bill of Sally be x.
Now, 18% of x = 9.50
⇒ 18/100 × x = 9.50
⇒ 0.18x = 9.50
⇒ x = 9.50/0.18
⇒ x = 52.77
≈ 53
Therefore, the dinner bill of Sally before the tip is $53.
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x²y6/xy²
What is the value of the expression above
if x = -2 and y = 2?
answer
11
Step-by-step explanation:
4x+1/3y^24(2)+1/3(3)^28+1/3(9)8+3
A. Solve each absolute value equation. /2.5pts
1)| 3x| = 9
Answer:
x = 3
or
x = -3
(explanation in the picture above)
Answer: x = 3 or x = -3
Step-by-step explanation:
Absolute values make the answer always positive, as they cancel out the negative sign. So to solve an absolute value equation, we must solve for both the positive and negative of the answer.
3x = 9
3x = -9
x = 3 or x = -3
2. Find the slope and y-intercept of the line.
O slope=3 y-intercept=2
O slope 2 y-intercept=3
O slope 3/2 y-intercept=2
O slope 2/3 y-intercept=2
Identify the factors of x2 − 5x − 24. (1 point) (x + 8)(x − 3) (x − 8)(x + 3) (x + 4)(x − 6) (x − 4)(x + 6)
Answer:
(x+3)(x–8)
Step-by-step explanation:
Normally you will always write factors in this form: (variable + smallest number)(variable – largest number)
Correct form: (x+2)(x–8)
Incorrect form: (x–2)(x+8)
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Please help
Name the reciprocals of each equation
Equations in picture
1. (3/4)x = 9. Multiply both sides by the reciprocal of 3/4: (4/3)(3/4)x = (4/3)(9)
x = 12.
2 . -4=4/7*x
4x/7=-4
x=-7
3. -1/5*x=6
-x/5=6
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
x=-30
With an example, what is a reciprocal equation?
An inverse of a number or value is referred to as reciprocal. If x is any real number, then 1/x will be the reciprocal of that number. For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8. 1/8's reciprocal is equal to 8.
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Carmen is about to complete a jigsaw puzzle the puzzle and one remaining piece are shown below what transformation can shark Carmen apply to the final piece to fit into the puzzle
We can see that the holes of the piece are already oriented in a way the piece will fit in the missing hole of the puzzle, so it doesn't need a rotation or reflection.
Then, in order to fit the piece in the hole, we need to move the piece 3 positions to the left and 1 position down.
Therefore the transformation needed is: a translation of 3 units to the left and 1 unit down.