Answer:
D. (f+g)(x) = 8x^2 + 4x - 4
Step-by-step explanation:
The notation (f+g)(x) is shorthand for f(x) +g(x).
(f +g)(x) = f(x) +g(x) = (3x^2 -2x +4) +(5x^2 +6x -8)
= (3 +5)x^2 +(-2 +6)x +(4 -8)
(f +g)(x) = 8x^2 +4x -4
Which ordered pairs make both inequalities true? Select two options.
y < 5x + 2
y ≥ 1/2x + 1
A. (-1,3)
B. (0,2)
C. (1,2)
D. (2,-1)
E. (2,2)
B. (0,2) and E (2,2) are the ordered pairings that allow both inequalities to hold.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
We can check which ordered pairs satisfy both inequalities by substituting the x and y values into each inequality and checking if they are both true.
Let's check each option:
A. (-1,3)
The first inequality gives us 3 < 5(-1) + 2, which simplifies to 3 < -3. This is false, so (-1,3) does not satisfy the first inequality.
The second inequality gives us 3 ≥ 1/2(-1) + 1, which simplifies to 3 ≥ 1/2. This is true, so (-1,3) satisfies the second inequality.
B. (0,2)
The first inequality gives us 2 < 5(0) + 2, which simplifies to 2 < 2. This is false, so (0,2) does not satisfy the first inequality.
The second inequality gives us 2 ≥ 1/2(0) + 1, which simplifies to 2 ≥ 1. This is true, so (0,2) satisfies the second inequality.
C. (1,2)
The first inequality gives us 2 < 5(1) + 2, which simplifies to 2 < 7. This is true, so (1,2) satisfies the first inequality.
The second inequality gives us 2 ≥ 1/2(1) + 1, which simplifies to 2 ≥ 3/2. This is true, so (1,2) satisfies the second inequality.
D. (2,-1)
The first inequality gives us -1 < 5(2) + 2, which simplifies to -1 < 12. This is true, so (2,-1) satisfies the first inequality.
The second inequality gives us -1 ≥ 1/2(2) + 1, which simplifies to -1 ≥ 2. This is false, so (2,-1) does not satisfy the second inequality.
E. (2,2)
The first inequality gives us 2 < 5(2) + 2, which simplifies to 2 < 12. This is true, so (2,2) satisfies the first inequality.
The second inequality gives us 2 ≥ 1/2(2) + 1, which simplifies to 2 ≥ 2. This is true, so (2,2) satisfies the second inequality.
Therefore, the ordered pairs that make both inequalities true are B. (0,2) and E. (2,2).
Learn more about inequalities here:
https://brainly.com/question/30231190
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Which of the following shows the less amount from the original value?
a. Gadget of 5000 with 5% discount price
b. Mr Smith bought a leather bag for £25 and sold it for £45.
c. A calculator marked £8.50 and Mr Smith pay 15% VAT for this item.
d. Mr Smith sold of £875 for furniture with a gain of 6%.
and explain why.
Answer:
A
Step-by-step explanation:
This is because it is discounting however in the others it's increasing VAT=Value added Tax,
gain, 45-25=£20 profit therefore it's A.
Answer:
Gadget of 5000 with 5% discount price
Step-by-step explanation:
This is the only option with a discount, not an additional extra on top.
Can you guys help me find the sum TnT
(7−b)+(3b+2)
Answer:
2b+9
Step-by-step explanation:
The number of football games with a score less than or equal to 29 is equal to half the number of basketball games with a score greater than or equal to
.
For both sports, if the only games won were those with scores of 30 or higher, how many more basketball games were won compared to football games won?
What is the difference between the total maximum possible points scored by the basketball team last year and the total maximum possible points scored by the football team last year?
points
Answer:
basketball player scored 40 points in a game. The number of three-point field goals the player made was 22 less than three times the number of free throws (each worth 1 point). Twice the number of two point field goals the player made was 11 more than the number of three point field goals made. Find the number of free-throws, two point field goals, and three point field goals that the player made in the game.
Once I have the equations I understand how to do the problem, but I am obviously doing something wrong because each time I write out the equations I end up getting fractions.
Find the slope for (3,1)and (4,3)
Answer:
2
Step-by-step explanation:
slope formula : [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where the x and y values are derived from known points
We are given the points (3,1)and (4,3)
Given these points we can define our variables
(x1,y1) = (3,1) so x1 = 3 and y1 = 1
(x2,y2) = (4,3) so x2 = 4 and y2 = 3
Now that we have defined our variable, we plug them into the formula
Recall formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
x1 = 3 , y1 = 1 , x2 = 4 , y2 = 3
* plug in values *
[tex]\frac{3-1}{4-3}[/tex]
subtract 3 and 1 , and 4 and 3
[tex]\frac{3-1=2}{4-3=1} =\frac{2}{1} =2[/tex]
the slope is 2
Parallel lines : mastery test
Answer:
I can't see much so take one more than I can help
mr John wants to put a fence around his farm. if the length of one side is 25m and the width is the same length what would be the amount of fencing needed?
Answer:
100 meters
Step-by-step explanation:
4 sides
1 side = 25 m
25m = width as well
so just multiply 25 by 4 to get your answer
Mr John needs to focus on outlining the width and length of the farm. Based on the length and width being the same length, the shape of the farm is a square. To make things simple, multiply the length of one side by four and you will have the exact amount needed to place a fence.
25m x 4 = 100m
So, Mr John needs about 100m of fencing to complete the construction of the fence surrounding his farm.
find the circumference r = 5 cm c [?] cm c=d
Step-by-step explanation:
radius of circle =5 cm
circumference of a circle =2πr
=2π×5
=10π=10×3.14
circumference=31.4 cm
whats the equation? for the problem
Answer: YOU DONT GIVE THE PROBLEM
Step-by-step explanation:
Find the product and simplify answer -3a^3(7a^4 - 5a + 5)
[tex]-3a^3(7a^4 - 5a + 5)\\\\=-21a^7+15a^4-15a^3[/tex]
Which is a better buy?
Answer:
four pack of notebooks for $4.56
Answer:
the 3-pack of note books for 3.33
Step-by-step explanation:
hope this helped have a great day!
Use the following system of equations to determine if each ordered pair is a solution: 1. Is (-4,-2) a solution to the system of equations below? Show your work. -3x+2y=8 x + 2y = -8
Can you convert the stander linear equation 5x-3y=15 into slope intercept form?
Answer: y = (5/3)x - 5
Step-by-step explanation:
5x-3y=15
-3y = -5x + 15
y = (5/3)x - 5
Answer:
In slope intercept form, I think it would be y=5/3x-5
Step-by-step explanation:
5x-3y=15
-subtract 5x on both sides-
-3y=-5x+15
-divide by -3 on both sides-
y=-5/-3x+15/-3
(the negatives on -5/-3 cancel each other out leaving you with a positive 5/3)
y=5/3x-5
Im not sure if all calculations are correct, but i hope this helps! :)
please explain to me how to solve for x and y
Answer:
(x, y) = (6, 2)
Step-by-step explanation:
You solve for x and y by writing equations that reflect the relation applicable to the given geometry.
The diagonals of a parallelogram bisect each other. That means the halves of each diagonal are equal.
2x -4 = 4y . . . . . . down diagonal
x +4 = 7y -4 . . . . . up diagonal
__
We can subtract the first equation from 2 times the second equation to eliminate the x-variable.
2(x +4) -(2x -4) = 2(7y -4) -(4y)
2x +8 -2x +4 = 14y -8 -4y . . . . . . eliminate parentheses
12 = 10y -8 . . . . . . . . . . . . . . . . . collect terms
20 = 10y . . . . . . . . . . . . . . . . . . add 8
2 = y . . . . . . . . . . . . . . . . . . . . divide by 10
Substituting into the second equation gives ...
x +4 = 7(2) -4
x = 6 . . . . . . . . . . . . subtract 4
The values of x and y are (x, y) = (6, 2).
_____
The lengths of the diagonals are 20 and 16.
a) work out the size of angle x.
b) give reasons for your answer.
Answer:
x = 75°
Step-by-step explanation:
180° - 105° = 75°
75° = 75°
Line CG is 180°. The angle of 105° is on this line, and we know that ∠F + 105° = 180° so we can subtract 105° from 180° to find ∠F. Next, ∠F and ∠x are corresponding angles, so they will be equal.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
The proportional relationship between the number of hours Taylor works, h, and her total earnings in dollars and cents, e, can be represented by the equation e=15.9he=15.9h. How much does she make in dollars and cents per hour?
The amount she makes in an hour is $15.90.
The amount Taylor earns is directly proportional to the hours Taylor works.
The equation that can be used to represent direction proportion is:
y = kx
where:
y = dependent variable
k = constant of proportionality
x = independent variable
e = 15.9h
Amount earned in an hour
e = 15.9(1)
e = $15.90
A similar question was answered here: https://brainly.com/question/24799762
What is the equation of g(x)? g(x) = 10x â€"" 3 g(x) = 10x 3 g(x) = 10x â€"" 3 g(x) = 10x 3.
The equation of g(x) is [tex]\rm g(x) = 10^{x-3}[/tex].
Given that,
The graphs of f(x) = 10x and its translation, g(x), are shown.
We have to determine,
What is the equation of g(x)?
According to the question,
The given graphs of two functions f(x) and g(x).
The function f(x) is an exponential function and is given by:
[tex]\rm f(x) = 10^x[/tex]
To find the equation for the transformed function g(x).
We could see that the graph of the function g(x) passes through points (3,1), (4,10), (5,100), and so on.
This means that the equation or the expression for the function g(x) is given by:
[tex]\rm g(x) = 10 ^{x-3}[/tex]
Substitute the value of x = 3 in the function g(x),
[tex]\rm g(x) = 10 ^{x-3}\\\\g(3) = 10^{3-3}\\\\g(3) = 10^0\\\\g(3) = 1[/tex]
Substitute the value of x = 4 in the function g(x),
[tex]\rm g(x) = 10 ^{x-3}\\\\g(4) = 10^{4-3}\\\\g(3) = 10^1\\\\g(3) = 10[/tex]
Hence, The equation of g(x) is [tex]\rm g(x) = 10^{x-3}[/tex].
For more details refer to the link given below.
https://brainly.com/question/13148696
Answer:
the answer is a g(x)= 10x^-3
Step-by-step explanation:
The total amount Y (in dollars) in your savings account after buying x video games is represented by y=70−10x . You have $40 in your account after buying video games. How many video games did you buy?
Answer:
330
Step-by-step explanation:
substitute x for 40 because that is how much you have in your account.
y= 70 - 10(40)
y = 70 - 400
y = 330
Therefore you bought 330 video games!!
Hope this helps, please tell me if I am wrong, I love learning from my mistakes:)
What is 48.5% of 300?
guyssss please help me with this maths problem it's from coordinates I hope you will help me I literally need this one pls will give 8 points
Answer:
find the perpendicular of the angle of pole
A football team has a net yardage of −30 1 3 yards on a series of plays. The team needs a net yardage of 10 yards to get a first down. How many yards do they have to get on their next play to get a first down?
Answer:
36 yards
Step-by-step explanation:
10 yards needed minus 30 then add 1 and 3 and you have your answer
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A recipe calls for 1.25 cups of brown sugar to make a batch
of cookies. How many cups of brown sugar are needed for
5 batches of cookies?
I need help with an equation... I can't understand it I've tried it a couple of times and I still get it wrong...so help plz?
Answer:
(f·g)(x) = x³ -8x² +20x -16
Step-by-step explanation:
The distributive property is useful for this.
(f·g)(x) = f(x)·g(x) = (x² -6x +8)(x -2)
= x(x² -6x +8) -2(x² -6x +8)
= x³ -6x² +8x -2x² +12x -16
(f·g)(x) = x³ -8x² +20x -16
_____
Additional comment
I find it convenient to separate the terms of the shortest polynomial. That way, the distributive property doesn't need to be used quite so many times. Of course, any outside minus sign applies to all terms inside parentheses.
You are a civil engineer working on the design of a new
green space in your city. The space will include gardens,
playgrounds, and picnic areas. One section of the park will
be in the shape of a right triangle. A diagram of the
requirements for the triangular space is shown below.
2x+2 yards
2x yards
2x+4 yards
1. Explain what you know about the space you will be designing. List at least three pieces
of information. (2 points)
Evaluate the function.
f(t)=-2t - 1; Find f(-9)
Answer:
17
Step-by-step explanation:
substitute t = - 9 into f(t) , that is
f(- 9) = - 2(- 9) - 1 = 18 - 1 = 17
write 1+√-32/4 as a complex number in the form a + bi, where a and b are real numbers.
a. 1/4+1/2√2i
b. 1/4+1/4√2i
c. 1/4+√2i
d. 1/4+4√2i
Work Shown:
[tex]\frac{1+\sqrt{-32}}{4}\\\\\frac{1+\sqrt{-1*16*2}}{4}\\\\\frac{1+\sqrt{-1}*\sqrt{16}*\sqrt{2}}{4}\\\\\frac{1+i*4*\sqrt{2}}{4}\\\\\frac{1+4i*\sqrt{2}}{4}\\\\\frac{1}{4}+\frac{4i*\sqrt{2}}{4}\\\\\boldsymbol{\frac{1}{4}+i\sqrt{2}}\\\\[/tex]
This matches with choice C. The imaginary 'i' term is not under the square root.
Factor the following.
Answer:
5. x(x+4)
6. 7x(x-3)
7. 12x(x+5)
8. 4x(2x+5)
help me pls... ....
Step-by-step explanation:
A1
1 yard = 3 feet
1 foot = 12 inches
therefore,
100 yards = 100×3×12 inches = 3600 inches
A2
again, 1 yard = 3 feet
8 ft = 8/3 = 2.67 yards = 2 2/3 yards
A3
1 gallon = 8 pints
A4
1 liter = 1000 milliliters (remember, "mili" means 1/1000).
therefore,
2.2 liters = 2.2×1000 = 2200 milliliters
A5
again, 1 liter = 1000 milliliters
therefore
1 milliliter = 1/1000 liter
670 milliliters = 670 × 1/1000 liter = 670/1000 liter =
= 0.67 liter
B1
1 kg (kilogram) = 1000 grams ("kilo" means 1000).
we have 3 layers.
each layer weighs (cake plus icing)
1/2 kg + 100 g = 500 g + 100 g = 600 g
3 layers then weigh
3×600 g = 1800 g
the additional candle weighs 250 g.
so, the total is
1800 g + 250 g = 2050 g = 2.05 kg
B2
area is 110 m².
1 m = 100 cm ("centi" means 1/100).
and 1 m² is then 100×100 = 10000 cm².
so, the area in cm² is
110 × 10000 = 1,100,000 cm²
the top area of one brick = 10 × 20 = 200 cm²
so, we need
1,100,000 / 200 = 11,000 / 2 = 5500 bricks
First person to get it right will get Brainly and 20 points. Good luck
Answer:
16/20
Step-by-step explanation:
4 is the common factor. 16 % 4 = 4, 20 % 4 = 5. therefore, 16/20 = 4/5
The answer is 16/20 I think.
what is the area of the rectangle.
Answer:
54 units^2
Step-by-step explanation: