Answer:
2^(-n^2+n+1)
Step-by-step explanation:
2^(n+2)*2^(n-1)*2^(-n(n-1))=2^((n+2)+(n-1)-(n^2-n))=2^(-n^2+3n+1)
I can do it because they have the same base, so I can add the exponents.
I can write 4^n=2^2n. So I have 2^(-n^2+3n+1) / 2^2n and they have the same base again (2), so we can subtract the exponents.
2^((-n^2+3n+1)-2n)=2^(-n^2+n+1)
At midnight the temperature was -2 degrees C. By noon the following day the temperature was 8 degrees C. Find the temperature change.
Which is equivalent to the expression? x2 + 6x + 4 A) (x + 3)2 + 5 B) (x + 3)2 − 5 C) (x − 3)2 + 5 D) (x − 3)2 − 5
Answer:
Step-by-step explanation:
(x + 3)² − 5 because :
(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4
Answer:
B) [tex](x + 3)^2 - 5[/tex]
Step-by-step explanation:
the equation is: [tex]x^2 + 6x + 4[/tex]
we have an equation of the form
[tex]ax^2+bx+c[/tex]
where
[tex]a=1,b=6,c=4[/tex]
and we must complete the square to obtain a perfect square binomial,
we must add and substract the following:
[tex](\frac{b}{2a} )^2[/tex]
which is:
[tex](\frac{6}{2*1} )^2=3^2[/tex]
and then the equation becomes:
[tex]x^2 + 6x + 4+3^2-3^2[/tex]
where the terms [tex]x^2+6x+3^2[/tex] are the components of the perfect square binomial: [tex](x+3)^2[/tex]
and thus, the equation now is:
[tex](x+3)^2+4-3^2\\=(x-3)^2+4-9\\=(x+3)^2-5[/tex]
the answer is: B) [tex](x + 3)^2 - 5[/tex]
If a pair of shoes costs $52.50 including a 7.25% tax, what is the original cost of the item before taxes are added?
No other symbols other than the number rounded to the second decimal.
Answer:
The original cost of the pair of shoes before tax is $48.95
Step-by-step explanation:
* Lets explain how to solve the problem
- Assume that the cost of the pair of shoes is 100% before taxes
∵ The cost of the pair of shoes is 100% before taxes
∵ The tax is 7.25%
∴ The price of the pair of shoes after tax = 100% + 7.25% = 107.25%
- This 107.25% equivalent to the price of the pair of shoes including
the tax
∵ The cost of the pair of shoes including tax is $52.50
- Lets use the cross multiplication to find the cost of the pair of
shoes before tax
∵ 100% ⇒ 107.25%
? ⇒ 52.50
- ? represents the cost of the pair of shoes before tax
∴ ? = [tex]\frac{100*52.50}{107.25}=48.95[/tex]
∴ The original cost of the pair of shoes before tax is $48.95
Point A is located at (3, -5). After it is transformed, point A' is located at (3, 5). How was the point transformed?
A. It was reflected in the x-axis.
B. It was rotated 90° around the origin.
C. It was reflected in the y-axis.
D. It was rotated 180°.
Answer:
A
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Under a rotation about the origin of 90°
a point (x, y ) → (- y, x )
Under a reflection in the y- axis
a point (x, y ) → (- x, y )
Under a rotation of 180°
a point (x, y ) → (- x. - y )
Here A(3, - 5 ) → A'(3, 5 ) → A
Nidhi has $185 to spend on bottles of wine for a party. Each bottle of wine costs $22.87. What is the maximum number of bottles of wine she can buy?
Answer:8
Step-by-step explanation:
Divide the amount of money she has by the amount the bottles cost. And you will get 8! Check your answer by multiplying 8 by 22.87
Final answer:
Nidhi can buy a maximum of 8 bottles of wine with her $185 budget, as each bottle costs $22.87.
Explanation:
The question involves finding out the maximum number of bottles of wine Nidhi can buy with her budget of $185, given that each bottle costs $22.87. To find the answer, we need to divide the total amount of money Nidhi has by the cost of one bottle of wine.
Step 1: Calculate the total number of bottles by dividing the total budget by the cost per bottle:
Total Number of Bottles = Total Budget / Cost per Bottle
Total Number of Bottles = $185 / $22.87
Step 2: Perform the calculation:
Total Number of Bottles ≈ 8.09
Since Nidhi cannot buy a fraction of a bottle, she can purchase a maximum of 8 bottles of wine with her budget of $185.
Cilia cycles 4.2 km every morning. How many feet are in 4.2 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet ?
A. 13,782.47 feet
B. 22,176.00 feet
C. 35,681.18 feet
D. 44,352,00 feet
Answer:
There are 13,782.47 feet in 4.2 kilometers ⇒ answer A
Step-by-step explanation:
- Cilia cycles 4.2 km every morning
- We need to convert the kilometers to feet
- 1 mile = 1.609 kilometers
- 1 mile = 5,280 feet
* Lets do that
∵ 1 mile = 1.609 km
∵ 1 mile = 5,280 feet
- Equate them
∴ 1.609 km = 5, 280 miles
* Now we can use the cross multiplication to find how many feet in
4.2 kilometers
→ km : feet
→ 1.609 : 5,280
→ 4.2 : x
- By using cross multiplication
∴ 1.609 x = 4.2 × 5,280
- Multiply 4.2 by 5,280
∴ 1.609 x = 22176
- Divide both sides by 1.609
∴ x = 13782.47
∵ x represents the number of feet in 4.2 kilometers
∴ There are 13,782.47 feet in 4.2 kilometers
Answer:
yeah eggs dee
Step-by-step explanation:
the genius up top is right
ABCD is a rectangular wall in which AB=3.15 m and BC = 1.77m. Find the
length of the diagonal BD.
(2x - 1) + (3y + 2)i = 5 – 4i
Solve for x and y
Answer:
The solution for x and y in (2x - 1) + (3y + 2)i = 5 – 4i cannot be determined.
Solution:
From question, the equation given is
(2x - 1) + (3y + 2)i = 5 – 4i
Multiplying the terms inside the bracket (3y + 2) with i, the above equation becomes,
(2x – 1) + 3iy + 2i = 5 – 4i
Removing the parenthesis in (2x – 1), the above equation becomes,
2x -1 + 3iy + 2i = 5 - 4i
2x – 1 + 3iy + 2i – 5 + 4i = 0
Rearranging the terms, the above equation becomes
2x + 3iy + 4i + 2i -1 -5 = 0
2x + 3iy + 6i – 6 = 0
The above equation cannot be simplified further. Hence the solution for x and y cannot be determined.
Five times the sum of a number and 6 is 48
The number is 3.6
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values.
Given statement:
Five times the sum of a number and 6 is 48.
Let the number be x.
5(x+6)=48
x+6= 9.6
x= 9.6-6
x= 3.6
Hence, the number is 3.6.
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8,407,47
is divisible by 3.
Answer:
Yes, it is divisible by three. The answer would be 280,249
Step-by-step explanation:
If BA [a= (-2,-3) b= (1,2)] is extended all the way through A creating a BF and A becomes the midpoint of BF, then what are the coordinates
Answer:
(-5,-8)
Step-by-step explanation:
If M(x,y) is the midpoint of the segment CD, where [tex]C(x_1,y_1),\ D(x_2,y_2),[/tex] then
[tex]x=\dfrac{x_1+x_2}{2}\\ \\y=\dfrac{y_1+y_2}{2}[/tex]
You are given two points A(-2,-3) and B(1,2), let point F be the point with coordinates (x,y). Yuo know, that point A is the midpoint of BF, then
[tex]x_A=\dfrac{x_B+x_F}{2}\\ \\y_A=\dfrac{y_B+y_F}{2}[/tex]
Substitute known coordinates:
[tex]-2=\dfrac{1+x}{2}\Rightarrow 1+x=-4,\ \ x=-5\\ \\-3=\dfrac{2+y}{2}\Rightarrow 2+y=-6,\ \ y=-8[/tex]
So, point F has coordinates (-5,-8)
What is the solution to 5x+y=13
−x+2y=−7 ?
also What is the solution to
4x+5y=35
−3x+2y=−9 ?
A)
5x+y=13
−x+2y=−7
Multiply each term in the first equation by -2:
5x + y = 13 x -2 = -10x - 2y = -26
Now add that to the second equation:
-10x - 2y = -26 + −x+2y=−7
= -11x = -33
Divide each side by -11
X = -33 / -11
X = 3
Now you have x, replace it in the first equation and solve for y:
5(3) + y = 13
Simplify:
15 + y = 13
Subtract 15 from both sides:
y = 13 -15
y = -2
Solution = (3,-2)
B)
4x+5y=35
−3x+2y=−9
Multiply each term in the second equation by -2.5:
7.5x -5y = 22.5
Add this to the first equation:
4x+5y=35 + 7.5x -5y = 22.5
= 11.5x = 57.5
Divide both sides by 11.5:
x = 57.5 / 11.5
x = 5
Now you have x, replace x in one of the equations to solve for y:
4(5) + 5y = 35
Simplify:
20 + 5y = 35
Subtract 20 from both sides:
5y = 15
Divide both sides by 5:
y = 15/5
y = 3
Solution = (5,3)
A quadrilateral has vertices at A(-5,5), B(1,8), C(4,2), and D(-2,-2). Use slope to determine if the quadrilateral is a rectangle. Show your work.
Answer:
The quadrilateral is not a rectangle
Step-by-step explanation:
we know that
If a quadrilateral ABCD is a rectangle
then
Opposite sides are congruent and parallel and adjacent sides are perpendicular
Remember that
If two lines are parallel, then their slopes are the same
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
A(-5,5), B(1,8), C(4,2), and D(-2,-2)
Plot the figure to better understand the problem
see the attached figure
Find the slope of the four sides and then compare
step 1
Find slope AB
A(-5,5), B(1,8)
substitute in the formula
[tex]m=\frac{8-5}{1+5}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m_A_B=\frac{1}{2}[/tex]
step 2
Find slope BC
B(1,8), C(4,2)
substitute in the formula
[tex]m=\frac{2-8}{4-1}[/tex]
[tex]m=\frac{-6}{3}[/tex]
[tex]m_B_C=-2[/tex]
step 3
Find slope CD
C(4,2), and D(-2,-2)
substitute in the formula
[tex]m=\frac{-2-2}{-2-4}[/tex]
[tex]m=\frac{-4}{-6}[/tex]
[tex]m_C_D=\frac{2}{3}[/tex]
step 4
Find slope AD
A(-5,5), D(-2,-2)
substitute in the formula
[tex]m=\frac{-2-5}{-2+5}[/tex]
[tex]m=\frac{-7}{3}[/tex]
[tex]m_A_D=-\frac{7}{3}[/tex]
step 5
Verify if the opposites are parallel
Remember that
If two lines are parallel, then their slopes are the same
The opposite sides are
AB and CD
BC and AD
we have
[tex]m_A_B=\frac{1}{2}[/tex]
[tex]m_C_D=\frac{2}{3}[/tex]
so
[tex]m_A_B \neq m_C_D[/tex]
It is not necessary to continue verifying, because two of the opposite sides are not parallel
therefore
The quadrilateral is not a rectangle
Hank’s pickup can travel 75 miles on 5 gallons of gas. How many gallons will Hank’s pickup need to travel 60 miles?
Hank’s pickup will need blank gallons of gas to travel 60 miles.
Answer:
The Answer is 4
Step-by-step explanation:
75 Miles divided by 5 Gallons is 15. Take that and divide 60 miles by 15. Your answer is 4 Gallons.
Hank's pickup consumes gas at a rate of 15 miles per gallon. To travel 60 miles, it would need 4 gallons of gas.
Explanation:To solve this problem, you need to first establish the rate of gas consumption for Hank's pickup. According to the data given, we know that Hank's pickup travels 75 miles with 5 gallons of gas which gives us a rate of 15 miles per gallon. The next step is to find out how much gas Hank's pickup will consume to travel 60 miles. So you divide the 60 miles by the rate of consumption which is 15 miles per gallon. The result is 4 gallons. Therefore, Hank's pickup will need 4 gallons of gas to travel 60 miles.
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If square root of x has a decimal approximation of 3.4, then x is between which two integers? In your final answer, include all calculations.
Answer:
You know that √x = 3.4, therefore x = 3.4² = 11.56
Hope I helped :)
If the square root of x has a decimal approximation of 3.4, then x is between 11 and 12.
We have,
If the square root of x has a decimal approximation of 3.4, we can write this as:
√x ≈ 3.4
To find the range of integers that x could fall between, we can square both sides of the equation:
x ≈ (3.4)²
x ≈ 11.56
So, x is approximately 11.56.
The two consecutive integers that x falls between are 11 and 12.
Thus,
If the square root of x has a decimal approximation of 3.4, then x is between 11 and 12.
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Express 0.000000018 in scientific notation.
Answer:
Step-by-step explanation:
0.000000018 = 1.8 * 10^-8
Final answer:
To express the number 0.000000018 in scientific notation, it is written as 1.8 × 10⁻⁸. Additionally, to multiply 0.00000000552 by 0.0000000006188 in scientific notation, the result is 3.415776 × 10⁻¹⁸.
Explanation:
To express the number 0.000000018 in scientific notation, we need to place the decimal after the first non-zero digit, and then count the number of places the decimal has moved. In this case, we move the decimal to the right of the 1 (the first non-zero digit), so it moves 8 places to the right. Therefore, 0.000000018 can be expressed as 1.8 × 10⁻⁸.
For the additional exercise, we'll convert each number to scientific notation and then multiply them:
0.00000000552 is written as 5.52 × 10⁻⁹0.0000000006188 is written as 6.188 × 10⁻¹⁰Now, multiplying these we get:
5.52 × 10⁻⁹ × 6.188 × 10⁻¹⁰ = 34.15776 × 10⁻¹⁹ which simplifies to 3.415776 × 10⁻¹⁸ in scientific notation.
Multiplication Property of Equality---- If 6x divided by 8 = 40, then______
A.) 6x * 8=320
B.) 40=6x*8
C.) 6x=320
D.)40=6x divided by 8
whats the corrects answer and why?? plz help
Answer:
Option C.) 6x=320
Step-by-step explanation:
we know that
The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal
we have
[tex]\frac{6x}{8}=40[/tex]
Apply the multiplication property of equality
Multiply by 8 both sides
[tex]\frac{6x}{8}(8)=40(8)[/tex]
[tex]6x=320[/tex]
therefore
The answer is the Option C
Answer:
Option C.
Step-by-step explanation:
Multiplication property of equality states that "if a number is multiplied to one side of the equation then other side of the equation should be multiplied with the same number".
The given equation is [tex]\frac{6x}{8}=40[/tex]
By the multiplication property of equality,
[tex]\frac{6x}{8}\times 8=40\times 8[/tex]
6x = 320
Option C will be the correct option.
Two lines are perpendicular. The first line passes through (1, –3) and has a y-intercept of (0, 3). Which of the following cannot be the equation of the second line?
Answer:
u tell me
Step-by-step explanation:
its been 3 years. did u figure it out?
Two Containers have leaks. Container A begins with 80 ounces and leaks at a rate of 0.6 ounces per minute. Container B begins with 100 ounces and leaks at a rate of 1 ounce per minute. How many minutes before the containers have the same amount of ounces?
Answer:
50 mins
Step-by-step explanation:
Set up the following equation:
80-0.6m=100-1m
1) Add 1m to both sides:
80+0.4m=100
2) Subtract 80 from both sides:
0.4m=20
3) Divide both sides by 0.4:
m=50
Let me know if you have any difficulty understanding how I set up the equation!
Andre says that 5 3/4 + 2 1/4 = 7 1/2 because 7 4/8 = 7 1/2. Identify his mistake. Draw a picture to prove that he is wrong.
Andre's Mistake in reasoning is assuming that 7 4/8 is equal to 7 1/2. Drawing a number line can prove that the fractions may be equivalent, but the whole numbers are not.
Andre made a mistake in his reasoning.
He incorrectly assumed that 7 4/8 is equal to 7 1/2. The fractions 4/8 and 1/2 are actually equivalent, but the whole numbers 7 and 7 are not.
To prove this, you can draw a number line and divide it into equal parts.
Taking the fractions 4/8 and 1/2, you will see that they represent the same distance, but they start at different points on the number line.
Therefore, 5 3/4 + 2 1/4 is not equal to 7 1/2.
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mmath help pls, will reward!! O_O
Answer:
x = -4, y = 8.
Step-by-step explanation:
Question 16.
8x + y = -24 ........(A)
-3x - 2y = -4 ........(B)
Multiply (A) by 2:
16x + 2y = -48 Adding this to equation (B):
13x = -52
x = -4
Substituting this value of x in Equation (A):
8(-4) + y = -24
y = -24 + 32 = 8.
Answer:
Answer for the first part of question 16 is y =-24 - 8x
1st subtract 8x from both sides: 8x + y - 8x = -24 - 8x
2nd simplify: -24 - 8x
Answer for the 2nd part of Q. 16 is y = -(-4+3x)/2
1st add 3x to both sides: -3x - 2y + 3x = -4 + 3x
2nd simplify: -2y = -4 + 3x
3rd divide both sides by -2: -2y ÷ -2 = 4 ÷ -2 +3x ÷ -2
4th simplify: (-4 + 3x)/2
Answer to the 1st part of Q. 17 is y = (-1 - 2x)/3
1st subtract 2x from both sides 2x + 3y - 2x = -1 - 2x
2nd simplify: -3y= -1 - 2x
3rd divide both sides by -3: -3y ÷ -3 = 1 ÷ -3 - 2x ÷ -3
4th simplify: y = (-1 - 2x)/3
Answer to 2nd part of Q.17: y = 6 + 7x ÷ 10
1st Add 7x to both sides: -7x + 10y + 7x = 6 + 7x
2nd simplify: 10y=6+7x
3rd divide both sides by 10: 10y ÷ 10 = 6 ÷ 10 + 7x ÷ 10
4th simplify: y = 6 + 7x ÷ 10
sorry, but I don't know the answer to Q.18 but I hope I helped on questions 16 and 17 :)
Find the area of a circle whose radius is 12 in. Round to the nearest tenth.
452.4 in2
113.1 in 2
75.4 in2
37.7 in 2
Answer:
Well to find the area of a circle given the radius you do: pi*12^2 Which is 452.4 in2
Step-by-step explanation:
506 students went on a field trip. Nine buses
were filled and 29 students traveled in cars.
How many students were in each bus?
Answer:
53 students on each bus
Step-by-step explanation:
506-29=477 (take out the students that went by car)
477/9 = 53 (distribute 477 students evenly in 9 buses)
On a number line, what number is located 8 units away from -11 in the positive direction?
Answer:
-3
Step-by-step explanation:
Take negative 11 and add positive 8 to it because you are going in the positive direction.
Am i correct about this or no? Need answer asap.
Answer: Yep! I agree
Step-by-step explanation: Ok to shows the 10 and 30 are proportional... This means 8 and n would be too
Which accurately describes a circle with radius 12 centimeters and center Q?
A.
the collection of all points located 6 centimeters from point Q
B.
the collection of all points on the same plane located 6 centimeters from point Q
C.
the collection of all points located 12 centimeters from point Q
D.
the collection of all points on the same plane located 12 centimeters from point Q
Answer:
option D is correct
the collection of all points on the same plane located 12cm from point Q
Answer:
Option D is correct
Step-by-step explanation:
A circle is a planar shape which has a point called center. All the points on the circle keep equal distance from the centre and the equal distance is called radius.
Here given that radius is 12 cm. Since it is a circle it should be in a plane only. Otherwise this will form a sphere. So this lies in a plane with all points keeping equal distance of [tex]12 cm[/tex] from the center
Option D) the collection of all points on the same plane located 12 centimeters from point Q
What is the rate of change of the function represented by the table
X Y
1. 5
2. 5
3. 5
4. 5
Answer:
I believe that the rate of change would be zero.
Step-by-step explanation:
When you look at the y value you notice that the 5 is repeated so this means that the rate of change is 0. i hope this helps.
Stephen is baking cookies for his school bake sale. He bakes 300 cookies.
1/2 are chocolate chip cookies
3/20 are peanut butter cookies
1/10 are sugar cookies
The rest are lemon cookies
How many cookies are lemon cookies?
Answer:
The number of lemon cookies is 75
Step-by-step explanation:
we know that
The total cookies are 300
Let
x ----> the number of lemon cookies
[tex]x=300(1-\frac{1}{2} -\frac{3}{20}-\frac{1}{10})[/tex]
Multiply by 20 both sides to remove the fractions
[tex]20x=300(20)-300(10)-300(3)-300(2)[/tex]
[tex]20x=1,500[/tex]
[tex]x=75[/tex]
therefore
The number of lemon cookies is 75
Answer:the geezer is right
Step-by-step explanation:
14.25 devised by1.9 what is the answer
How do you change a percent to a decimal?
To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100. Let's say we wanted to convert 82% to a decimal. We can think of 82% as the ratio 82 to 100 or 82 ÷ 100. When we divide by 100, it moves the decimal point 2 places to the left so 82 ÷ 100 would move the decimal point 2 places to the left which would give us .82. Therefore, 82% would = 0.82.
Final answer:
To convert a percent to a decimal, represent the percent as a fraction with a denominator of 100 and divide the numerator by the denominator. A percent is a ratio whose denominator is 100, making this conversion straightforward.
Explanation:
To change a percent to a decimal, you need to express the percent value as a fraction with a denominator of 100. For example, if you have a percent like 75%, you represent it as the fraction 75/100. Then, you divide the numerator by the denominator, which in this case is 75 divided by 100, giving you a decimal of 0.75.
When calculating percents, it's essential to understand that a percent is a ratio with a denominator of 100. So every percent can be written as a fraction over 100, simplified if possible, and then easily converted to a decimal.
To illustrate the reverse process, for converting a decimal to a percent, you'd take a decimal such as 0.45, write it as the fraction 45/100 (which is already simplified since the denominator is 100), then express it as a percent, which would be 45%.