The sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex].
We have two expressions.
We have to add them.
What is Expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it.
According to the question -
f(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex]
g(x) = [tex]-4x^{2} -9x -4x[/tex]
Now -
h(x) = f(x) + g(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex] + ( [tex]-4x^{2} -9x -4x[/tex])
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
Hence, the sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
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URGENT DUE TODAY PLEASE HELP
Lines k and p are parallel. If m<1 = 5x + 1 and m<2 = 8x - 20, find
the measure of angle 2.
how much was the original price of the ticket? Pls help answer with detailed explanation
Answer: the original price of the ticket was $42
Step-by-step explanation:
[tex]Let's\ make\ a\ proportion:[/tex]
$44.92 - 107%
$x - 100%
[tex]\displaystyle\\x=\frac{44.92*100}{107} \\\\x=\frac{4492}{107} \\\\x=42[/tex]
Write an equation of a parabola with the given information.
vertex (0,0) , focus (0, 1/2)
The equation that defines the parabola with vertex at the point and focus at (0, 1/2) is
y = 2x²
What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
In this case we have the vertex of the parabola at the point (0,0) and the focus at the point (0, 1/2) this is displaced on the y-axis upward, so the parabola is of the form.
y = x²
Canonical equation
(y - yo) = 4p(x - xo)
Vertex (0, 0)xo, yo = (0 , 0)
Focus:
f = (0, 0 + p)
(y- 0) = 4*0.5(x - 0)²
y = 2x²
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julia ordered 2 hamburgers and steve ordered 3 hamburgers. If their total bill was $7.50, how much did each hamburger cost?
Answer:
$1.50
Step-by-step explanation:
there are 5 burgers since 2+3 is five. Divide 7.50 by five. The answer is 1.50.
$1.50
Because 2+3=5 and once you 7.5÷5 it equals 1.5.
I need this answered answered please
One is a constant, as it has no variable besides it.
Converting Units of Rates
Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's
rate in miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
Nina's rate in miles per hour is 12.711 and Nina bikes faster than Sophia.
Nina's speed can also be defined as her Average Speed.
Similarly, Sophias's speed can also be defined as her Average Speed.
We have Sophia's speed = 10 miles in hour = 10 miles per hour
What is average speed and average?
Average speed is the total distance travelled by an object to the total time taken. means,
[tex]Average Speed = \frac{Total Distance}{Total Time }\\[/tex]
Total Distance covered by Nina = 63,360ft.
[tex]1 \ mile = 5280 \ feet\\[/tex]
So,Nina's Distance (in miles) [tex]\frac{63360}{5280}= 12 \ miles[/tex]
Nina's Time (in hour) [tex]\frac{3400}{60*60}= 0.944 \ hour[/tex]
Nina's Average Speed = [tex]\frac{12}{0.944}= 12.711 \ miles/hour[/tex]
So, Nina's Average Speed = 12.711 miles per hour
Since, Sophia's Average Speed = 10 miles per hour
Therefore, Nina bikes faster on a average speed of 12.711 miles per hour.
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Nina's rate in miles per hour is 12.711 and Nina bikes faster than Sophia.
Nina's speed can also be defined as her Average Speed.
Similarly, Sophias's speed can also be defined as her Average Speed.
We have Sophia's speed = 10 miles in hour = 10 miles per hour
What is average speed and average?
Average speed is the total distance travelled by an object to the total time taken. means,
[tex]Average Speed = \frac{Total Distance}{Total Time }\\[/tex]
Total Distance covered by Nina = 63,360ft
1 mile = 5280 feet
So,Nina's Distance (in miles) [tex]\frac{63360}{5280}= 12 \ miles[/tex]
Nina's Time (in hour) [tex]\frac{3400}{60*60}= 0.944 \ hour[/tex]
Nina's Average Speed = [tex]\frac{12}{0.944}= 12.711 \ miles \ / \ hour[/tex]
So, Nina's Average Speed = 12.711 miles per hour
Since, Sophia's Average Speed = 10 miles per hour
Therefore, Nina bikes faster on a average speed of 12.711 miles per hour.
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Let f ( x ) = 1 x and g ( x ) = x 2 + 5 x . a. Find (f · g)(x). b. Find the domain and range of (f · g)(x).
The answer to all the subparts are given:
(f · g)(x) = [(f X g)(x) = x + 5]The domain of the given function: (-∞, 0) ∪ (0, ∞)The Range of the given function: (-6.25, 0) ∪ (0, ∞)(A) (f · g)(x):
So,
(f×g)(x)=f(x)*g(x)Plug in:
[tex](f X g)(x)=\frac{1}{x}\left(x^2+5 x\right)[/tex]Simplify as follows:
[tex]\begin{aligned}&(f X g)(x)=\frac{1}{x}(x(x+5)) \\&(f X g)(x)=x+5\end{aligned}[/tex]
(B) Domain:
First, we will determine the domain of f(x), g(x), and (fxg) (x).
Then we can look for a common domain.
The domain of f(x):
[tex]f(x)=\frac{1}{x}[/tex]At x=0, we know that f(x) is undefined.
As a result, the domain will be:
[tex](-\infty, 0)_{\cup}(0, \infty)[/tex]The domain of g(x):
[tex]g(x)=x^2+5 x[/tex]
Because it is polynomial.
As a result, it is defined for all real values of x.We can now find a common domain.As a result, the domain will be:
[tex](-\infty, 0) \cup(0, \infty)[/tex](C) Range:
First, we will determine the range of f(x), g(x), and (fxg) (x).
Then we can determine the common range.
f(x) range:
[tex]f(x)=\frac{1}{x}[/tex]We know that range refers to all possible y values for which x is defined.
Because the horizontal asymptote will be at y=0.
As a result, the range is:
[tex](-\infty, 0) \cup(0, \infty)[/tex]Range of g(x):
[tex]g(x)=x^2+5 x[/tex]Because it is a quadratic equation.
As a result, its range will be:
[tex][-6.25, \infty)[/tex]We can now find a common range.
As a result, the range will be:
[tex](-6.25,0) \cup(0, \infty)[/tex]
Therefore, the answer to all the subparts are given:
(f · g)(x) = [(f X g)(x) = x + 5]The domain of the given function: (-∞, 0) ∪ (0, ∞)The Range of the given function: (-6.25, 0) ∪ (0, ∞)Know more about domain range here:
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If g+9=4 and h-8--3, what is the
value of g + h?
Answer:
g + h = 6
Step-by-step explanation:
We are told that:
• [tex]g + 9 = 4[/tex]
• [tex]h- 8=3[/tex].
To calculate the value of g + h, we have to rearrange the above equations to make g and h their respective subjects:
• [tex]g + 9 = 4[/tex]
⇒ [tex]g + 9 - 9 = 4 - 9[/tex] [Subtracting 9 from both sides]
⇒ [tex]g = \bf -5[/tex]
• [tex]h- 8=3[/tex]
⇒ [tex]h - 8 + 8 = 3 + 8[/tex] [Adding 8 to both sides]
⇒ [tex]h = \bf 11[/tex]
Now that we know the values of g and h, we can find the value of g + h:
[tex]g + h[/tex]
[tex]= -5 + 11[/tex]
[tex]= \bf 6[/tex]
Therefore the value of g + h is 6.
diego compro 12 cuadernos que le costaron 96. 000 ¿cuanto le costo cada uno ?
How should the decimal point in 6.8 be moved to determine the product of 6.8 and 100
The decimal point should be moved two places to the right.
The number we have given is = 6.8
We have to find how many decimal point should be moved when 6.8 is multiplied by 100
We know that when we multiply a decimal number with 10, 100, 1000,…. and so on. We shift the decimal point to the right side according to the number of zeroes present.
According to the question, we have two zeroes therefore we will shift the decimal point to the rights side two times, that is,
6.8 * 100 = 680
Hence the decimal point should be moved two places to the right.
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solve 2x + 5y = -1for y. Then find the value of y when x=-2
solve 2xy - x = 3for y. Then find the value for y when x=2
In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4
In the given statement is
Solve 2x + 5y = -1 for y.
To find the value of y when x= -2
Now, Equation is 2x + 5y = -1 …..(1)
Put the value of x = -2 in eq. 1
2 (-2) + 5y = -1
-4 + 5y = -1
5y = -1 + 4
y = 3/5
Again, Solve 2xy - x = 3 for y
To find the value of y when x = 2
Now, Equation is : 2xy - x = 3 ….(2)
Put the value of x = 2 in eq. (2)
2(2)y - 2 = 3
4y - 2 = 3
4y = 5
y = 5/4
Hence, In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4
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What is the average speed of an
automobile trip of 275 miles that
began at 7:30 in the morning and
ended at 12:30 in the afternoon
The average speed of an automobile is a 55 miles per hour.
According to the statement
We have to find that the value of the average speed of an automobile.
So, For this purpose, we know that the
The average speed is the total distance traveled by the object in a particular time interval.
From the given information:
automobile trip of 275 miles that began at 7:30 in the morning and ended at 12:30 in the afternoon
Then
The total distance covered = 275 miles
And
The total time taken = From 7:30 in the morning to 12:30 in the afternoon
Then
The total time taken = 5 hours,
Then
Average speed = total distance covered / total time taken
Average speed = 275 miles / 5 hours
Then
Average speed = 275 / 5
Average speed = 55 miles per hour.
So, The average speed of an automobile is a 55 miles per hour.
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Choose the number sentence that illustrates the distributive property of multiplication over addition.
A. 5x (7+2) = (5+7) × (5+2)
B. 5x (7+2) = (5 × 7) +2
C. 5x (7+2) = (5 × 7) + (5 × 2)
Answer:its
a80
b16
c60
Step-by-step explanation:
Answer:
Step-by-step explanation:
C. 5 × (7 + 2) = (5 × 7) + (5 × 2)
COORDINATE GEOMETRY Find the measures of the sides of ΔJ K L and classify each triangle by the measures of its sides. (Lesson 4-1)
J(9,9), K(12,14), L(14,6)
The measure of the sides of ΔJKL is 17.26 units.
What do we mean by a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
The formula of perimeter: √√(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(12−9)²+(14−9)²= 17.26 unitsThen, each side of the triangle will be: 17.26 units
Therefore, a measure of the sides of ΔJKL is 17.26 units.
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1. How would you write 2 × 2 × 2 using exponents?
(1 point)
02×3
023
032
2. Rewrite the following expression using exponents.
3×3 × 3× 3 × 3 x3
(1 point)
036
035
O
63
3. What is the value of 4”4? (1 point)
016
064
0256
4. What is the value of 9”2? (1 point)
018
081
0729
5. What is the value of 8”3
024
064
0512
Answer:
[tex]1) \: {2}^{3} \\ 2) \: {3}^{6} \\ 3) \: {4}^{4} = 4 \times 4 \times 4 \times 4 = 256[/tex]
evaluate the expression 13 divided by (2.5 - |-3 1/8|) times 3 to the third power
Answer: -561.6
Step-by-step explanation:
First, recall PEMDAS (Parenthesis, Exponents, Multiply, Divide, Add, Subtract)
In the equation, we need to work through (2.5 - |-3 1/8|) first.
The absolute value of |-3 1/8| is 3 1/8
We change 3 1/8 to a decimal
3 1/8 = 3.125
Now Subtract (2.5 - 3.125)
This equals -0.625
Next, divide 13 by -0.625
13 ÷ -0.625 = -20.8
Then, multiply -20.8 by 3³
3³ = 27
So -20.8 × 27 = -561.6
Calculate the probability of the spinner landing on a purple section of the board. what is the probability that the spinner will land on a purple section of the board? or or
The probability of purple section on spinning is 1/2.
As per the given image of question, we can see there six parts of board. Out of these, three parts of board are purple colored.
Now, the formula of probability is -
Probability = number of favorable outcomes÷total number of outcomes
Number of favorable outcomes = number of purple colored parts of board
Number of favorable outcomes = 3
Number of favorable outcomes = number of colored parts of board
Number of favorable outcomes = 6
Keep the value in formula to find the probability -
Probability = 3/6
Performing division
Probability = 1/2
Hence, the probability that the spinner will land on a purple section of the board is 1/2.
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The complete question is -
Calculate the probability of the spinner landing on a purple section of the board. What is the probability that the spinner will land on a purple section if the board.
A) 1/6
B) 2/6 or 1/3
C) 3/6 or 1/2
6 of 6
Triangles A and B are congruent.
Find the area of triangle A. Give your answer to 1 dp.
area =
17cm
108 cm²
area = cm²
A
Not drawn accurately.
B
12cm
O
F
You may use
Get help
Report a mista
On-screen keyp
Che
Ski
Area of triangle A is 72.2 cm square.
Here, we are given that triangles A and B, as shown in the figure are congruent to each other.
They are also both right angle triangles.
The length of the hypotenuse of A is 17cm
and the height of triangle be = 12cm
But as these two are congruent,
height of triangle A will also be 12cm.
Now, according to Pythagoras theorem,
[tex]hypotenuse^{2} = base^{2} +height^{2}[/tex]
[tex]17^{2}[/tex] = [tex]12^{2}[/tex] + [tex]base^{2}[/tex]
289 = 144 + [tex]base^{2}[/tex]
[tex]base^{2}[/tex] = 145
base = 12.04
Thus, the area of the triangles = 1/2 * base height
= 1/2 x 12 x 12.04
= 72.2
Thus the area of triangle A will be 72.2 cm square.
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Determine the values of y in the equation y2 = 121.
whoever gets it right gets a crown pls help
Answer:
y = 11
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex] \rightarrow \sf \: y {}^{2} =121[/tex]
Step 1: Take square root.
[tex] \sf \: y=± \sqrt{121} [/tex]
y=11 or y=−11
If you dig a 6ft hole, how deep is it?
Answer: 8 feet
Step-by-step explanation:
(18, -7) and (18, 2) m =
Answer:
m = undefined
Step-by-step explanation:
I'm assuming it's "m" as in y=mx+b
(18, -7), (18, 2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2 - (-7) 9
m = ----------- = ------------ = ---------- = undefined
x₂ - x₁ 18 - 18 0
I hope this helps!
Copy trapezoid CDEF and point P . Then use a protractor and ruler to draw a 50° rotation of CDEF about point P .
Repeat steps 1-3 for vertices C,E and F to finish the trapezoid .
Describe the trapezoid shape.
A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.
Step 1 - Draw line DP.
Step 2 - Use a protractor to create a 50° angle with DP'.
Step 3 - Use a ruler to draw D such that DP' = DP
Step 4 - Repeat steps 1-3 for vertices C,E and F to finish the trapezoid .
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Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
10
6
2
13
4m-4=4m
a) many solutions
b) no solutions
Answer: The input is a contradiction: it has no solutions
1st step
4m - 4 = 4m
4m - 4 + 4 = 4m + 4
2nd step -
4m = 4m + 4
3rd step -
4m = 4m +4
4m - 4m = 4m + 4 - 4m
4th step -
Combine like terms
0 = 4
Has No Solutions.
1) |x|-4 = 9
2) |x - 4| = 9
Solve the absolute value for each equation.
Answer:
13 & 5
Step-by-step explanation:
Absolute for x still gives a positive X value
So: X- 4 = 9
X = 9 + 4
X = 13
|x-4| = 9
Gives X + 4 = 9
x = 9 - 4
X = 5
A theater director buys props-for
$116.20 and costumes for $494.85. He
has $194.27 left. How much money did
he have to start?
Answer:
$805.32
Step-by-step explanation:
$116.20 + $494.85 + $194.27 = $805.32
He had $805.32 to start.
The temperature of an object goes up by 1k. how much did it go up in degrees fahrenheit and how much in degrees celsius?
Given that the temperature of an object goes up by 1.0 Kelvin, the rise in degrees Fahrenheit and Celsius are -457.87°F and 272.15°C respectively.
What is the value of 1 Kelvin in in degrees Fahrenheit and Celsius?The formula used in converting temperature from Kelvin to Fahrenheit is expressed as;
(( x - 273.15 ) × 9/5 + 32)°F
Also, to convert temperature form Kelvin to Celsius, we use;
( x - 273.15)°C
Given that;
Temperature goes up by 1 Kelvin1 Kelvin in degrees Fahrenheit = ?1 Kelvin in degrees Celsius = ?Convert 1 Kelvin to degrees Fahrenheit.
(( x - 273.15 ) × 9/5 + 32)°F
(( 1 - 273.15 ) × 9/5 + 32)°F
( 272.15 × 9/5 + 32)°F
( -489.87 + 32)°F
-457.87°F
Convert 1 Kelvin to degrees Celsius.
( x - 273.15)°C
( 1 - 273.15)°C
272.15°C
Given that the temperature of an object goes up by 1.0 Kelvin, the rise in degrees Fahrenheit and Celsius are -457.87°F and 272.15°C respectively.
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identify all the numbered angles that are congruent to the given angle. Justify your answers.
5 times the difference of a number and 3
number meaning x
The value of an unknown number x will be equal to ( 15 / 4).
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that 5 times, the difference between a number and 3 is x. The value of the unknown number will be calculated as:-
5 ( x - 3 ) = x
5x - 15 = x
4x = 15
x = 15 / 4
Therefore, the value of an unknown number x will be equal to ( 15 / 4).
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Evaluate the expression for the given value of the variable
|x-19| ; x = 10
Answer:
|(10)-19| = |-9| = 9
Step-by-step explanation: Just plug it in. Oh btw the absolute value means distance from 0.
