Answer:
36 cm^2
Step-by-step explanation:
Find the fuction h (x) =f(x) - g (x) if f (x)=3^x and g (x)= 3^2x - 3^x
To find h(x) = f(x) - g(x), we substitute and simplify the given functions. The result is h(x) = 2 × 3ˣ - 3²ˣ. This solution involves basic algebraic manipulation and exponent rules.
Let's start by defining the given functions:
f(x) = 3ˣg(x) = 3²ˣ - 3ˣWe need to find h(x) = f(x) - g(x). Substitute the expressions for f(x) and g(x):
h(x) = 3ˣ - (3²ˣ - 3ˣ)Now simplify the expression inside the parentheses:
h(x) = 3ˣ - 3²ˣ + 3ˣCombine like terms:
h(x) = 3ˣ+ 3ˣ - 3²ˣh(x) = 2 × 3ˣ - 3²ˣThus, the function h(x) = 2 × 3ˣ - 3²ˣ is found by subtracting g(x) from f(x).
what is the product 4^3* 4^-3
The product 4^3×4^(-3) is equal to 1.
Take care of the exponents.
4^3= 4*4*4
4^3= 64
=4^-3
What is the product?The product meaning in maths is a number that you get to by multiplying two or more other numbers together.
Make it a fraction to make the power positive.
[tex]=\frac{1}{4^3}[/tex]
Now, simplify.
[tex]=\frac{1}{64}[/tex]
=64* 1/64= 1
Therefore, The product 4^3×4^(-3) is equal to 1.
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What is the area of the figure?
Express your answer as a mixed number in simplest form.
? m2
Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a height of 10 meters and a circular base with a radius of 8 meters
Answer: Volume of an oblique cylinder is 2011.43 sq.m.
Step-by-step explanation:
Since we have given that
Radius of a cylinder = 8 meters
Height of a cylinder = 10 meters
Cavelieri's Principle states that volume of an oblique cylinder is same as the volume of right circular cylinder with equal radius and height.
As we know the formula for "Volume of cylinder":
[tex]Volume=\pi r^2h\\\\V=\frac{22}{7}\times 8\times 8\times10\\\\V=\frac{14080}{7}\\\\V=2011.43[/tex]
Hence, Volume of an oblique cylinder is 2011.43 sq.m.
Help with this question
7b divided by 12=4.2 what is b
To solve for b in the equation 7b divided by 12 equals 4.2, multiply both sides by 12 and then divide by 7, resulting in b being equal to 7.2.
Explanation:To solve the equation 7b ÷ 12 = 4.2 for b, we must isolate b on one side of the equation. We can begin by multiplying both sides of the equation by 12 to cancel out the division by 12 on the left side. This results in the equation 7b = 4.2 × 12. To find the value of b, we then divide both sides of the equation by 7:
Multiply both sides by 12: 7b ÷ 12 × 12 = 4.2 × 12Simplify: 7b = 50.4Divide both sides by 7: 7b ÷ 7 = 50.4 ÷ 7b = 7.2Therefore, the value of b is 7.2.
To find the value of b in the equation 7b/12 = 4.2, multiply both sides by 12 and then divide by 7 to get b = 7.2. The value of b is 7.2.
Explanation:The student is asking how to find the value of b in the equation 7b divided by 12 equals 4.2. To solve for b, you can follow these steps:
Write down the original equation: 7b / 12 = 4.2.Multiply both sides of the equation by 12 to eliminate the denominator: 12 * (7b / 12) = 12 * 4.2, which simplifies to 7b = 50.4.Divide both sides by 7 to solve for b: 7b / 7 = 50.4 / 7, which gives b = 7.2.Therefore, the value of b is 7.2.
sin(76)cos(31)-cos(76)sin(31)
What is the solution set to the inequality-3x 5.92-15.4 for x in the set (-10,-5, 0, 5, 10)?
Final answer:
The solution set to the given inequality '-3x < 5.92 - 15.4' is {5, 10}.
Explanation:
The student's question seems to be about solving an inequality to find which values from a given set satisfy it. While the inequality itself appears to be incorrectly written or has a typo, I'll assume it's meant to be '-3x < 5.92 - 15.4'.
We can begin by simplifying the right side of the inequality:
5.92 - 15.4 = -9.48
So the inequality becomes:
-3x < -9.48
To solve for x, we divide both sides by -3, remembering to reverse the inequality sign because we are dividing by a negative number:
x > 9.48 / 3
x > 3.16
Now we can compare this result to the set of numbers given: (-10, -5, 0, 5, 10).
The only numbers greater than 3.16 are 5 and 10.
Therefore, the solution set to the inequality is {5, 10}.
Last summer we took an auto trip of 3427 miles . After we had driven 1578 miles , how many are left ?
the area of this circle is 72π m^2 what is the area of a 45° sector of this circle
The left and right page numbers of an open book are two consecutive integers whose sum is 423.
three friends are in the same algebra class. Their scores on a recent test are three consecutive odd intergers whose sum is 279. find each score
I need some help what 9 + 10?
Determine the taylor series about the point x0=2 for the function 11−x. determine the radius of convergence of the series.
Sam is training for an upcoming wrestling match. He trains for 3.5 hours each day Monday through Wednesday. He trains 2.5 hours on Thursday and Friday. How many hours will he train if he trains for six weeks
Mah problem, in class no substitute beed help
can someone help me with this
The system of equations 4x-y=4(x+1) , y = 6 has:
A. one solution
B. infinitely many solutions
C. no solution
The system of equations 4x-y=4(x+1) and y=6 has no solution.
To determine the solution(s) of the system of equations, let's analyze each equation:
Equation 1: 4x - y = 4(x + 1)
Equation 2: y = 6
To simplify Equation 1, we can distribute 4 on the right side:
4x - y = 4x + 4
By rearranging terms, we have:
- y = 4
Comparing Equation 2 with this result, we see that the two equations are contradictory. Equation 2 states that y = 6, while the modified Equation 1 states that y = -4. This means there is no value of y that can simultaneously satisfy both equations.
Thus, the system of equations has no solution.
Therefore, the correct answer is C. no solution.
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Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter.
A Bird Is flying 5 m/s. How far will it travel if it flies for 3minutes
A. 15m
B. 5m
C. 900m
D. 36m
What is the right answer for this? Need this module done before tomorrow so If y’all could help that’ll be great
You have a $50 gift card to the same site. You want to buy an album with 16 tracks for $12.99 and then use the rest of the gift card for single tracks. How many songs can you buy with the gift card?
Final answer:
After purchasing an album for $12.99 from the $50 gift card, the remaining balance is $37.01, which allows the purchase of 37 more single tracks, assuming each track costs $1.
Explanation:
To determine how many songs can be bought with a $50 gift card after purchasing an album for $12.99, we need to subtract the cost of the album from the total amount on the gift card. So, we have:
Total amount on gift card: $50Cost of album: $12.99Subtracting the cost of the album from the gift card amount gives us:
$50 - $12.99 = $37.01
Assuming that each single track costs $1 as per the scenario provided, we can divide the remaining balance by the cost per single track:
$37.01 ÷ $1 per track = 37 tracks
This means that you can purchase 37 more single tracks with the remaining balance on the gift card.
Write 4/10 as a fraction with a denominator of 100. Then write 4/10 as a decimal.
Would it be 4/100 or 40/100? The decimal would be 0.4 ?
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle.
Opposite angles in a cyclic quadrilateral add to 180 degrees. Quadrilateral ABCD is a cyclic quadrilateral.
< A+<C=180
Substituting <A and <B values given in figure:
x+2+x-2=180
Adding like terms:
2x=180
Dividing both sides by 2
x=90°
<A=x+2=90+2=92°
<C=x-2=90-2=88°
<D=x-10=90-10=80°
<B+<D=180
<B=180-80=100°
The angles of the quadrilateral ABCD are
<A=92°
<B=100°
<C=88°
<D=80°
Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the difference. 1. (–3x3 + 5x2 + 4x – 7) + (–6x3 + 2x – 3) 2. (–3x3) + 5x2 + 4x + (–7) + (–6x3) + 2x + (–3) 3. [(–3x3) + (–6x3)] + [4x + 2x] + [(–7) + (–3)] + [5x2] 4. –9x3 + 6x + (–10) + 5x2 5. –9x3 + 5x2 + 6x – 10
To find the polynomial difference, Lorne transformed the subtraction into addition of the opposite, combined like terms, and simplified the expression to get the result of -9x³ + 5x² + 6x - 10.
To find the difference between the two polynomials, Lorne correctly followed the steps of subtraction by changing the subtraction to the addition of the opposite. The process is outlined below:
Add the opposite of the second polynomial to the first polynomial by changing the sign of each term in the second polynomial.
Combine like terms by adding the coefficients of terms with the same degree of x.
Rearrange the terms in descending order of their degrees.
Write down the final simplified form of the polynomial.
By following these steps, the result would be:
Step 1:
(-3x³ + 5x² + 4x - 7) + (-6x³ + 2x - 3)
Step 2:
(-3x³ + 5x² + 4x - 7) + (-6x³) + 2x + (-3)
Step 3:
[(-3x³) + (-6x³)] + [4x + 2x] + [(-7) + (-3)] + [5x²]
Step 4:
-9x³ + 6x + (-10) + 5x2
Step 5:
-9x³ + 5x² + 6x - 10
Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]
The steps Lorne used to find the difference between [tex]-3x^{3} +5x^{2} +4x-7[/tex] and [tex]6x^{3} -2x+3[/tex] are:
[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]
So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]
Lorne first added the two polynomials by combining like terms, then simplified the result by collecting like terms. The final expression represents the difference between the two polynomials after combining and simplifying.
COMPLETE QUESTION:
Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. Use the drop-down menus to identify the steps Lorne used to find the difference.
[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]
What is the completely factored form of x2y – 2xy – 24y?
Answer:
C: y(x + 4)(x – 6)
Step-by-step explanation:
I took the test on Edge -2022
Tim and Maria went on a cruise together, but agreed to divide their expenses. The cost of the room was R. The cost of the horseback riding excursion was $125 per person. The historic tour was $214 per couple. Tim and Maria equally split the cost of the room, but Tim also paid for both his and Maria's horseback riding excursion. Maria was to pay for the historic tour but only had to paid half price because the cruise line scratched their luggage, so they offered to pay the other half.
What is the solution set for 3x>6?
Mrs. Bell has a rain gauge outside. On a very rainy day, the gauge measured 2.5 inches. The actual amount of rain that fell was 2.3 inches. To the nearest tenth, what is the percent error in Mrs. Bell's measurement?
Miguel’s teacher asks him to color for 4/8 of his grid. He must use three colors: red blue and green. There must be more green sections then red sections. How can Miguel color the section service grid to follow all the rules?