Rewrite it in the form a^2 - 2ab + b^2, where a = d and b = 2
d^2 - 2(d)(2) + 2^2
Use the Square of Difference: (a - b)^2 = a^2 - 2ab + b^2
(d - 2)^2
Answer:
(d - 2)²
Step-by-step explanation:
d² - 4d + 4 ← is a perfect square of the form
(x ± a )² = x² ± 2ax + a²
compare coefficients of like terms
- 2a = - 4 ⇒ a = 2 and a² = 4, hence
d² - 4d + 4 = (d - 2)²
What is the value of the expression? tan 5π3
Answer:
[tex]tan(\frac{5\pi}{3})=\sqrt{3}[/tex]
Step-by-step explanation:
we are given
[tex]tan(\frac{5\pi}{3})[/tex]
we know that
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
so, we can write our expression as
[tex]tan(\frac{5\pi}{3})=\frac{sin(\frac{5\pi}{3})}{cos(\frac{5\pi}{3})}[/tex]
now, we can use unit circle
[tex]sin(\frac{5\pi}{3})=-\frac{\sqrt{3} }{2}[/tex]
[tex]cos(\frac{5\pi}{3})=-\frac{1}{2}[/tex]
now, we can plug values
[tex]tan(\frac{5\pi}{3})=\frac{-\frac{\sqrt{3} }{2}}{-\frac{1}{2}}[/tex]
[tex]tan(\frac{5\pi}{3})=\sqrt{3}[/tex]
What is the 1st step? 2x-7=18
Answer:
The first step is to add 7 to each side
Step-by-step explanation:
2x-7 = 18
To solve this equation, the first step is to add 7 to each side
2x-7+7 = 18+7
2x = 25
Answer:
the first step is to add 7 to both sides.
Step-by-step explanation:
2x-7 = 18
+7 +7
2x = 25
divide by 2
25/2 = 12.5
so x= 12.5
Why did Vanderbilt close the Albany bridge
The closing of the Albany bridge by Commodore Cornelius Vanderbilt was likely a strategic decision to protect and enhance his railroad enterprise, demonstrating the importance of controlling transportation infrastructure in the 19th century.
Explanation:Commodore Cornelius Vanderbilt, known for his vast railroad empire, consolidated several smaller railroad lines to form the powerful New York Central Railroad Company. This consolidation allowed for more efficient connections from Midwestern suppliers to eastern markets, which was of great economic importance. The closing of the Albany bridge by Vanderbilt would have been one such strategic decision to enhance his railroad network and protect the interests of his enterprise.
The incident at Ebenezer Creek, where Union General Jefferson C. Davis ordered the cutting of the pontoon bridge to strand fleeing slaves and prevent them from crossing, shows the harsh decisions made during the Civil War. While this event does not directly relate to Vanderbilt closing the Albany bridge, it demonstrates the kind of pivotal and often harsh decisions made regarding bridges and the movement of people during that era for military or strategic reasons.
A 5 gallon bucket of paint costs $97.45. What is the price per gallon?
Answer:
19.49 per gallon
hope it helps
Step-by-step explanation:
total pay ÷ number of gallon = the cost of each gallon
97.45 / 5 = 19.49 per gallon
BRAINLIEST + Points please help me
John and Ted have a reputation for being late to events. If John is late 20% of the time, and Ted is late 40% of the time, what is the probability that both John and Ted will be on time? Show your work or explain how you got your answer.
The answer is:
The probability that both John and Ted will be on time is 48%.
Why?Since we are dealing with percentages, in order to make it easy to understand, let's remember that percentages are used to simplify the way we refer to something, talking in numeric terms. For example, meaning 100% it's equal to say that somethinh is complete, or absolute. Also, we can see the percentage as a ratio that is expressed as a fraction of the number 100 or [tex]\frac{1}{100}[/tex]
From the statement the know that John is late 20% of the time, making it easy to understand, it's equal to say that from 100 times, John is late 20 times.
So, calculating we have:
For John:
[tex]Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-20=80[/tex]
So, we have that the probability that John will be on time is 80%.
For Ted:
[tex]Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-40=60[/tex]
So, we have that the probability that Ted will be on time is 60%.
Now, to calculate the probability that both John and Ted will be on time, we need to calculate the combined probability. It can be calculated using the following equation:
[tex]CombinedProbability=Probability_{1}*Probability_{2}[/tex]
Let be:
[tex]Probability_{1}=80(percent)=\frac{80}{100}=0.8\\\\Probability_{2}=60(percent)=\frac{60}{100}=0.6[/tex]
So, substituting and calculating we have:
[tex]CombinedProbability=Probability_{1}*Probability_{2}[/tex]
[tex]CombinedProbability=0.8*0.6=0.48=48(percent)[/tex]
Hence, we have that the probability that both John and Ted will be on time is 48%.
Have a nice day!
Solve: 7|x| = 42 brainliest thanks and ratting for help!
–6
–6 or 6
No solution
6
Answer:
–6 or 6
Step-by-step explanation:
7|x| = 42
We need to isolate the absolute value, so we will divide each side by 7
7|x|/7 = 42/7
|x| = 6
Now we remove the absolute values and set what is inside the absolute value equal to plus and minus what is on the right hand side
x = + 6 and x = -6
Answer:
Solve for x over the integers:
7 abs(x) = 42
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides by 7:
abs(x) = 6
Hint: | Eliminate the absolute value.
Split the equation into two possible cases:
Answer: x = 6 or x = -6
Step-by-step explanation:
Which circle shows AB that measures 60 degrees?
Answer:
Can you put a picture?
Step-by-step explanation:
Answer:
i need a picture
Step-by-step explanation:
(2/9 v)-(-1/3v +5/9)
Answer:
(5/9)(v – 1)
Step-by-step explanation:
(2/9)v - ((-1/3)v +5/9) Remove parentheses
= (2/9)v + (1/3)v - 5/9 Multiply each term by 9/9
= (2/9)v + (3/9)v - 5/9 Combine like terms
= (2v + 3v)/9 -5/9 Combine like terms
= 5v/9 - 5/9 Factor out 5/9
= (5/9)(v – 1)
find the x intercept of the graph of the equation y equals -2.65 x + 25. what does the x intercept mean in terms of the situation
The x-intercept of the equation y = -2.65x + 25 is approximately 9.43. The x-intercept generally represents the value of x at which y is zero or the point where correlation between x and y starts.
Explanation:The x-intercept of a graph is the point at which the line crosses the x-axis. In terms of your equation y = -2.65x + 25, the x-intercept is found when y equals 0. By setting y equal to 0 and solving for x, we get: 0 = -2.65x + 25. Isolate x by dividing both sides by -2.65 and adding 25. This calculates to x ≈ 9.43. In terms of real life situations, the x-intercept often represents the value of x where y is nil or where the correlation between x and y begins. However, the real-world interpretation of this value depends on the context of the problem.
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Kendra lost one half of her allowance but her mother gave her four more dollars now she has $9 how much was her allowance
Final answer:
Kendra's original allowance was $10.
Explanation:
To find out how much Kendra's allowance was, we can use algebraic equations. Let 'x' represent Kendra's original allowance.
Kendra lost half of her allowance, which means she had x/2 left.
Then her mother gave her four more dollars, so now she has x/2 + 4.
Given that Kendra has $9, we can set up the equation x/2 + 4 = 9 and solve for x.
x/2 + 4 = 9
x/2 = 9 - 4
x/2 = 5
Multiplying both sides of the equation by 2, we get x = 10.
Therefore, Kendra's allowance was $10.
PLEASE HELP
[02.03] Solve for x: |2x + 6| − 4 = 20
x = 9 and x = 11
x = −9 and x = 15
x = 9 and x = −15
No solution
Answer:
x = 9 and x = −15
Step-by-step explanation:
|2x + 6| − 4 = 20
Add 4 to each side
|2x + 6| − 4+4 = 20+4
|2x + 6| = 24
Now we have an absolute value equation that has the absolute value isolated. We can separate them, have two equations, one positive and one negative.
2x+6 =24 and 2x+6=-24
Subtract 6 from each side
2x+6-6=24 -6 2x+6-6 = -24-6
2x = 18 2x =-30
Divide by 2
2x/2 = 18/2 2x/2 = -30/2
x =9 x=-15
Please help im on the verge of tears.
Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies.
Who gains altitude more quickly, a pilot traveling 400 mph and rising at an angle of 30 degrees, or a pilot traveling 300 mph and rising at an angle of 40 degrees?
Answer: The pilot traveling 400 mph rising at an angle 30 degrees is going to gain more altitude faster
======================================================
Explanation:
Draw out the triangles as you see in the attached image below. We'll use the sine rule because we want to tie together the unknown height (h) which is the opposite side of the reference angle, to the known hypotenuse (the speed of the aircraft)
For the first plane,
sin(angle) = opposite/hypotenuse
sin(30) = h/400
h = 400*sin(30)
h = 200
so the first plane is gaining altitude at 200 mph (each hour, the plane is 200 miles higher up)
For the second plane
sin(angle) = opposite/hypotenuse
sin(40) = h/300
h = 300*sin(40)
h = 192.836282905961
h = 192.84
which is smaller than the previous result (200)
So we see that the first plane is rising faster
Answer:
a pilot traveling 400 mph and rising at an angle of 30 degrees
Step-by-step explanation:
29 us. 2ft. 11 in. + 55 yd. 1 ft. 10 in. + 13 yd. 1 ft.3 in.
Answer:
99 yd
Step-by-step explanation:
When I add these, I line them up vertically
29 yd. 2ft. 11 in.
+ 55 yd. 1 ft. 10 in.
+ 13 yd. 1 ft. 3 in.
---------------------------
97 yd 4ft 24 in
We know that 12 in = 1 ft
so 24 in = 2ft
Subtract 24 in and add 2 ft
97 yd 4ft 24 in
+2ft -24 in
------------------------------
97 yd 6ft
We know 3 ft = 1yd
so 6ft = 2yd
Subtract 6ft and add 2 yd
97 yd 6ft
+2yd - 6ft
-------------------
99 yd
Tyler makes $10 per hour at his job.The function f(x)=10x gives the amount of money Tyler makes after x hours.Graph this function and give its domain and range.
You will have the points: (0,0) and (1,10) and (2,20) and (3,30) etc etc
Plot at least 2 of these points. Then draw a line through them.
Each point has an x,y pair such that the y value is ten times the x value
For example, if x = 2, then
y = 10*x = 10*2 = 20
so that shows how (2,20) is one of the points.
-------------------
The domain would be the set of positive whole numbers assuming Tyler can only work a whole number of hours. If partial time values are accepted, then the domain would be the set of positive real numbers. Negative x values are not allowed as Tyler can't work negative 3 hours for instance.
In a similar fashion, the range is the set {0, 10, 20, 30, 40, ...} incrementing by multiples of 10 if x is the set of positive whole numbers. If x is the set of positive real numbers, then y can be 0 or larger which sets up the range of y being the set of positive real numbers as well.
Which graph represents a direct variation between the quantities x and y
Answer:
Any graph which passes through the origin(0,0)
Step-by-step explanation:
To check a graph if it represents direct variation or not, one needs to check whether it passes through the origin or not .
So any graph which passes through the origin is of direct variation.
And in equation form : [tex]y=kx\\ y=mx +b\\[/tex]
⇒b=0 , m=k
So it is of direct variation if it passes through the origin (0,0)
Answer: its c
Step-by-step explanation: i just got it right
I’m supposed to find the slope intercept form. The x intercept is (2,0) and the y intercept is (0,6). I keep getting 6/2. But, the graph goes down?
[tex]\bf \stackrel{x-intercept}{(\stackrel{x_1}{2}~,~\stackrel{y_1}{0})}\qquad \stackrel{y-intercept}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{6})} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{0-2}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=-3(x-2)\implies y=-3x+6[/tex]
What's ten of the second power times 25.89
As an estimation we are told 5 miles is 8 km.
Convert 13.5 miles to km
Answer:
Step-by-step explanation:
5/13.5 x 8/x (cross multiple) 108/5 (divide) = 21.6
Question
As an estimation we are told 5 miles is 8 km.
Convert 13.5 miles to km
Answer:
21.6 KmStep-by-step explanation:
you can solve with an equation
5 : 8 = 13.5 : x
x = 8 * 13.5 : 5
x = 21.6
What is the best estimate for 5.07 x 0.81 ?
A. 0.4
B. 4
C. 4.5
D. 5
Please help and if so correct and answered then I’ll mark you as Brainiest Answered.
Thank you.
Answer: 5
Step-by-step explanation: 5.07 rounds to 5
0.81 rounds to 1
so the best estimate for 5.07 x 0.81 = 5(1) = 5.......ANS
Answer:
4.05
Step-by-step explanation:
5 X 0.81 = 4.05 so I say C
The domain of the following relation R:
Answer:
{-3, 1, 6 }
Step-by-step explanation:
the domain is the values of x ( input) from the relation in ascending order.
Values are not repeated.
domain {- 3, 1, 6 }
Answer:
{- 3, 1, 6 }
Step-by-step explanation:
The domain is the values of x inputs from the relation in ascending order. Values cannot be repeated.
Which number can be used to fill in the blanks to make both statements true? 144÷12=____ and 12 x ____ = 144
Answer:
12
Step-by-step explanation:
144/12 = 12
12 x 12 = 144
Answer:
12
Step-by-step explanation:
divide 12 by 144
a process of rounding the number to the first digit is called
Answer:
Rounding to the whole number or an estimation.
Step-by-step explanation: Pretty sure there isn't really a name for this
Rounding a number to its first digit is known as rounding to the nearest whole number. This method simplifies calculations while maintaining a number's approximate value.
Explanation:The process of rounding a number to its first digit is often referred to as rounding to the nearest whole number. For example, if you have a number like 4.58, rounded to the nearest whole number it's 5, because the number next to 4 is 5 which is equal or higher than 5. But if the number was 4.42, rounded to the nearest whole number it's 4, because the number next to 4 is 2 which is less than 5. This rounding method applies when you want to make calculations simpler, while still keeping the number's value close to what it was.
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102 - 42 , 33y-11y can I get four equivalent expressions plzzz
Final answer:
The equivalent expressions for 102 - 42 are 60, -42, 60 - 42, and 102 - 42. The equivalent expressions for 33y - 11y are 22y, 22y - 11y, 33y - 11y, and 11y.
Explanation:
Equivalent expressions for 102 - 42:
60-4260 - 42102 - 42Equivalent expressions for 33y - 11y:
22y22y - 11y33y - 11y11yConsider the steps to simplify the expression. Which property is used to reach Step 3? Expression: -4 3/7 + 7 + (-3 4/7 )
Step 1: = -4 3/7+(-3 4/7) + 7
Step 2: = -4 + (-3/7) + (-3) + (-4/7) + 7
Step 3: = -4 + (-3/7) + (-4/7) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
A) The associate property of addition.
B) The commutative property of addition.
C) The opposite of a sum is the sum of its opposites.
D) Subtracting a number is the same as adding its inverse.
Answer:
B) The commutative property of addition.Step-by-step explanation:
Given expression :
Step 1: = -4 3/7+(-3 4/7) + 7
Step 2: = -4 + (-3/7) + (-3) + (-4/7) + 7
Step 3: = -4 + (-3/7) + (-4/7) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
In 3rd step they just swap the positions of (-4/7) and (-3) to bring the like fractions with common denominator together.
Swapping the numbers is the Commutative Property of Addition.
Therefore, correct option is B) The commutative property of addition.What Is the solution to the system 5X plus 7Y equals 32 and 8X plus 6Y equals 46
[tex]\bf \begin{cases} 5x+7y=32\\ 8x+6y=46 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 5x+7y=32\implies 7y=32-5x\implies \boxed{y}=\cfrac{32-5x}{7} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{8x+6\left(\boxed{ \cfrac{32-5x}{7}} \right)}=46\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7\left( 8x+6\left( \cfrac{32-5x}{7} \right) \right)=7(46)} \\\\\\ 56x+6(32-5x)=322\implies 56x+192-30x=322[/tex]
[tex]\bf 26x+192=322\implies 26x=130\implies x=\cfrac{130}{26}\implies \blacktriangleright x=5 \blacktriangleleft \\\\\\ \stackrel{\textit{subsituting \underline{x} in the 1st equation}}{5(5)+7y=32}\implies 25+7y=32\implies 7y=7 \\\\\\ y=\cfrac{7}{7}\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,1)~\hfill[/tex]
What is the ratio forms a proportion with 16/20
4/10
32/50
8/12
4/5
Answer: D) 4/5
================================================
Explanation:
There are a few ways to see how this is the answer.
----------------
The first is to notice how 16/20 = 0.80 when using long division or a calculator. At the same time, 4/5 = 0.80 as well. So that means 16/20 = 4/5.
---------------
Another way to see how this works is to multiply top and bottom of 4/5 by 4. So we have 4*4 = 16 as the new numerator and 5*4 = 20 as the new denominator. Going in reverse, you can divide each piece of 16/20 by the GCF 4 to reduce this fraction into 4/5.
---------------
Finally, we can equate the two fractions and cross multiply
16/20 = 4/5
16*5 = 20*4
80 = 80
Both sides are the same value, so that confirms the original equation is true as well.
1188 kilograms of rice divided into 7 sacks
Answer: 169.7
Step-by-step explanation:
Answer:
There are 1,014 kilograms of rice in 6 stacks of rice. 5 kilograms of rice remain.
Step-by-step explanation:
7 ÷ 1188 = 169
169 × 6 = 1,014
What’s a complex conjugate in math
Answer:
Step-by-step explanation:
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4i is 3 − 4i. In polar form, the conjugate of is.
A complex conjugate is the element of a complex number that has the same real part but an opposite-sign imaginary part, and multiplying a complex number by its conjugate yields a real number.
Explanation:A complex conjugate in mathematics is a paired element of a complex number that has the same real part but an opposite-sign imaginary part. When you have a complex number, let's call it A, which can be expressed in the form (a + ib) where 'a' is the real part and 'b' is the imaginary part, the complex conjugate of A, denoted as A*, would be (a - ib). One important property of complex conjugates is that when you multiply a complex number by its conjugate, you get a real number. This is because the product A* A = (a + ib) (a - ib) = a² + b².
For example, if a complex number is a = 3 + 4i, its complex conjugate would be a* = 3 - 4i. Multiplying a by its conjugate, we get a* a = (3 + 4i) (3 - 4i) = 9 + 16 = 25, which is a real number. This property is very useful, especially in fields such as quantum mechanics, where physical measurements must yield real numbers.
Michael took his younger brother to the movies. Michael paid regular price, but it cost $2 less for his brother at the child price. It cost Michael $12 total for the movie. How much did it cost for his brother?
Answer:
$5
Step-by-step explanation:
So we know that altogether Michael paid $12 right?
So if his brother's price is x then his price is x+2
so 2x+2=12 x=5
Michael's brother's price was $5
and his was $7
In this mathematics problem, Michael's brother's movie ticket cost $10, arrived at by subtracting $2 from the total cost of $12.
Explanation:This is a simple subtraction problem. According to the problem, Michael paid $12 total, with his brother's ticket costing $2 less. Therefore, if we subtract $2 from Michael's ticket, we will have the cost of his brother's ticket.
Here are the steps:
Michael paid $12 in total,His brother's ticket was $2 less,So, subtract $2 from $12, which equals $10.Therefore, his brother's ticket cost $10.
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What is the value of h?