Answer:
n = 2 + 2√3 and n = 2 - 2√3
Step-by-step explanation:
Let the number be n.
Then n² + 1 = 4n.
Rearranging this in proper quadratic format:
n² - 4n + 1
Here the coefficients are a = 1, b = -4 and c = 1.
Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.
By applying the quadratic formula, we find that the roots are:
- (-4) ± √12
n = ------------------
2
or n = 2 + 2√3 and n = 2 - 2√3
Answer:
3.732 or 0.268 to the nearest thousandth.
Exact values are 2 + √12/2 or 2 - √12/2.
Step-by-step explanation:
Let the original number be x, then:
x^2 + 1 = 4x
x^2 - 4x + 1 = 0
x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2
x = (4 + sqrt12)/ 2 , (4 - sqrt12) / 2
= 3.732, 0.268.
Help me please!!! What is the mean of the following data values?
A. 33
B. 27
C. 37
D. 43
Answer:
By mean, find the average. Add them all up and divide by how many numbers are there.
22+37+49+15+92= 215
215/5= 43.
Therefore, the answer is D, 43.
To find the mean, you add up all the values and then divide by the number of values. In this case, the mean is 43, which corresponds to option D.
To find the mean (average) of a set of data values, you sum all the values and then divide by the total number of values. In this case, you have the following data values: 22, 37, 49, 15, and 92.
Mean = (22 + 37 + 49 + 15 + 92) / 5
Mean = (215) / 5
Mean = 43
So, the mean of the given data values is 43.
The correct answer is D. 43.
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Help me plz. Haven’t been able to answer this problem. Even my TEACHER is stumped. (Mark brainliest)
Answer:
K 48 inches
Step-by-step explanation:
First lets determine how big of table cloth we need
The table is 3 ft in diameter which is 36 inches
That means the radius is d/2 = 36/2 = 18 inches
We need to add 5 inches to the radius to hang over the edge
18+5 = 23
We need to add the hem which is 1 inch
23+1 = 24
The radius is 24 inches
The diameter would be 2r = 2*24 = 48 inches
the perimeter and area of each figure:
a. A square with a side length of 3.5 inches.
[tex]3.5 \times 3.5 = 12.25 \: for \: are \\ 3.5 \times 4 = 14 \: for \: perimeter[/tex]
rationalize the denomintaors 3square root of 3 - 3 square root of 3
Answer:
Please see attached image
Step-by-step explanation:
An analysis of the expression can be seen in the image below
See attached figure
Jonathan borrowed $475 at a simple annual interest rate of 2%. How many years will it take him to repay the loan if he wants to pay $38 in interest?
A. 4
B. 5
C. 6
D. 7
Answer:
a
Step-by-step explanation:
The ratio of cats to dogs at the pet store is 2:3. There are 14 cats. How many dogs are there at the pet store?
Answer:
21 dogs
Step-by-step explanation:
In your question, we need to find how many dogs are in the store.
To find the answer to your question, we would need to use the information given in the question
Given Information:
Ratio of cats to dogs (respectively) is 2:3
There are 14 cats
With the information above, we can solve the question.
We know that there are 2 cats for every 3 dogs.
The question says that there are 14 cats.
We need to change the amount of cats there are in the ratio.
We would multiply 2 by 7 to fit the story, due to the fact that 2 times 7 makes 14.
Whatever you do to the left, you would do to the right. This means that you would multiply 3 by 7.
2 : 3
×7 ×7
14 : 21
When you multiply, you should get 21. This means that there are 21 dogs at the pet store when there are 14 cats.
I hope this helps you out.Good luck on your academics.Have a fantastic day!There are 21 dogs at the pet store.
To find how many dogs are at the pet store, use the given ratio of cats to dogs and the number of cats. Apply the ratio to determine the number of dogs. There are 21 dogs at the pet store.
To find the number of dogs at the pet store, you can use the ratio of cats to dogs, which is 2:3.
Since there are 14 cats, first determine the number of parts in the ratio that represent cats. In this case, each part represents 14/2 = 7 cats.Next, calculate the number of parts representing dogs by multiplying the number of parts representing cats by the part of dogs in the ratio. 7 parts * 3 (for dogs) = 21 dogs.Therefore, there are 21 dogs at the pet store.
Which point on the y-axis lies on the line that passes through
point C and is perpendicular to line AB?
O(-6,0)
O (0, -6)
O (0, 2)
O (2,0)
Answer:
0(0,2)
Step-by-step explanation:
0(0,2)
0(0,-6)
0(2,0)
0(-6,0)
The line perpendicular to the line AB passes through the point (0, 2)
What are perpendicular line?Two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot.
The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.
Given is a graph of a line, we need to find the which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB,
From the given figure in the question it is observed that the line AB passes through the points (-2, 4) and (2, -8)
The coordinate of point C is, (6, 4)
Obtain the slope of the line AB.
-8-4 / 2+2 = -3
Consider the slope of AB as, m1
m1 = -3
Consider a line which is perpendicular to the line AB passing through the point C.
Assume the slope of the perpendicular line as m2,
The product of the slope of two mutually perpendicular lines is always equal to -1
The equation formed for the slope is as follows: 1/3
Finding the equation of the line,
y-y₁ = m(x-x₁)
3y - x = 6
Therefore, the equation of the perpendicular line is 3y - x = 6
In option 3 it is given that the line perpendicular to AB passes through the point (0, 2)
The equation of the line which is perpendicular to AB is 3y - x = 6
Substitute for in the above equation
3y - (0) = 6
3y = 6
y = 2
From the above calculation it is concluded that the line passes through the point (0, 2).
This implies that option 3 is correct.
Hence, the line perpendicular to the line AB passes through the point (0, 2)
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select the action you would use to solve x-3=12 . then select the property that justifies the action
The x is a placeholder for some currently unknown number. Let's say that number was 10. So we replace x with 10 to get 10-3 = 12. That statement is false because 10-3 is actually 7. What you can do is keep guessing until you get the right answer.
A much better approach is to undo what is happening to x. We have x and we subtract off 3 to get 12. Following this in reverse, we need to add 3 to both sides so that x is isolated.
x-3 = 12
x-3+3 = 12+3
x = 15
Let's replace x with 15 and see if the equation is true
x - 3 = 12
15 - 3 = 12
12 = 12
Sure enough we get the right answer.
The idea of adding 3 to both sides is possible through the additive property of equality (if a = b, then a+c = b+c)
==========================================
In summary, I added 3 to both sides using the additive property of equality. Doing this isolated x to get x = 15.
Simplify the expression. cos x csc x tan x
Answer:
1
Step-by-step explanation:
Using the trigonometric identities
• csc x = [tex]\frac{1}{sinx}[/tex]
• tan x = [tex]\frac{sinx}{cosx}[/tex]
cos x × [tex]\frac{1}{sinx}[/tex] × [tex]\frac{sinx}{cosx}[/tex]
Cancel sin x and cos x on the numerator/ denominator leaving
1
Answer:
1
Step-by-step explanation:
cscx=1/sinx
tanx=sinx/cosx
cosx*(1/sinx)*(sinx/cosx)
Cancel out common factors on top and bottom.
1
Differentiate x^2/4-x^3
Answer:
x^4 + 8x
-----------------
(4-x^3)^2
Step-by-step explanation:
d /dx (x^2/(4-x^3))
When we differentiate a fraction u/v
df/dx = u/v
= v du/dx-u dv/dx
---------------------------
v^2
we know u = x^2 so du/dx = 2x
v = (4-x^3) so dv/dx = -3x^2
d dx = (4-x^3) (2x)- x^2 ( -3x^2)
-------------------------------------
(4-x^3)^2
Combining terms
(8x-2x^4) --3x^4
-------------------------------------
(4-x^3)^2
8x-2x^4 +3x^4
-------------------------------------
(4-x^3)^2
x^4 + 8x
-------------------------------------
(4-x^3)^2
The probability of spinning a 7 on a spinner is 0.083. If you spun 250 times, approximately how many times would the spinner land on 7
Answer:
21 times
Step-by-step explanation:
To find out how many times the spinner would land on the 7, take the probability times the number of times spun
250 * .083
20.75
It would land on 7 approximately 21 times
Answer:
The spinner will land on 7 approximately 21 times
Step-by-step explanation:
According to your question. The probability of spinning a 7 on the spinner is 0.083 (8.3%). You spin the spinner 250 times and you would like to know how many times the spinner would land on 7 based on the previous probability. To do this we will need to multiply the probability of the spinner landing on 7 in one spin with the amount of total spins.
[tex]250*0.083 = 20.75[/tex]
As shown above we can see that with a probability of 8.3% on 250 spins, the spinner will land on 7 approximately 21 times.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
9 cu yd 113 cu in - 4 cu ft 129 cu in
Answer:
=8 yd³ 22 ft³ 1712 in³
Step-by-step explanation:
To perform the indicated operation we need to convert the given measurements of volume to common units.
1 yd = 3 ft
1 yd³=27ft³
1 ft³=1728 in³
Thus 9 yd³=(27×9)ft³
=243 ft³
113 in³ into ft= 113/1728
9 yd³ 113 in³= 243 113/1728 ft³
4 ft³ 129 in³= 4 129/1728 ft³ = 4 43/576 ft³
Performing the operation given in the equation:
243 113/1728 ft³ - 4 43/576 ft³ = 238 1712/1728 ft³
238 ft³= 8 yd³ 22 ft³ + (1712/1728) × 1728
=8 yd³ 22 ft³ 1712 in³
If sin x = -1/2, and 270° < x < 360°, what is cos(x - 30°)?
Answer:
x = -30
cos(x - 30) = ½
Step-by-step explanation:
Look at the picture
(0201 LC)
Melissa made some chocolate pudding For every 3 cups of chocolate, she added 7 cups of milk. The ratio of chocolate to milk in Melissa's chocolate pudding is
Answer:
its c
3 : 7
3/7
Step-by-step explanation:
Answer:
3/7
Ratio is explained in sentence: For every 3 cups of chocolate, she added 7 cups of milk.
This is another way to say/show a ratio. It is also said as: 3:7, 3/7, and 3 to 7
Solve the equation.1/8+c=4/5
Answer:
27/40
Step-by-step explanation:
We want to isolate the variable c. In order to do so, we have to subtract 1/8 from both sides. Then, on the left side, we have c, and on the right side we have 4/5-1/8. The fractions 4/5 and 1/8 do not have a common denominator, so we need to multiply 4/5 by 8/8 and 1/8 by 5/5 in order to reach a common denominator of 40 (5 and 8's least common multiple). Then, we get 32/40-5/40, or 27/40.
Side note: we are able to multiply by 8/8 and 5/5 because both of those fractions equal 1.
There are 3,280.84 feet in a kilometer. There are 5,280 feet in a mile. To the nearest hundredth, how many kilometers are in a mile?
Answer:
1.61
Step-by-step explanation:
1 mile × (5280 ft / 1 mile) × (1 kilometer / 3280.84 ft) = 1.61 kilometers
To convert miles to kilometers, divide the number of feet in a mile (5,280) by the number of feet in a kilometer (3,280.84). This calculation reveals that there are approximately 1.61 kilometers in a mile, a conversion factor that facilitates precise and efficient measurement conversions.
The question asks how many kilometers are in a mile, given that there are 3,280.84 feet in a kilometer and 5,280 feet in a mile. To find the answer, you can use the information that 1 kilometer equals 3,280.84 feet. Therefore, to convert feet to kilometers, you divide the number of feet by 3,280.84.
To find how many kilometers are in a mile, you follow these steps:
Start with the conversion factor that 1 mile = 5,280 feet.Since 1 kilometer = 3,280.84 feet, we divide the total feet in a mile by the number of feet in a kilometer to convert miles to kilometers. That calculation would be 5,280 feet / 3,280.84 feet per kilometer = 1.60934 kilometers.
To the nearest hundredth, there are 1.61 kilometers in a mile. This conversion is useful for making quick and accurate estimates between the two units of measurement commonly used in many parts of the world.
3x + 7y + 6 = 0 what is the y intercept
Answer:
The y-intercept is located at (0, -6/7)
Step-by-step explanation:
First, we should convert this equation from Standard Form(ax+by+c=0) into Slope-Intercept Form(y = mx+b), with b being the y-value of the y-intercept.
Work:
3x+7y+6=0
First, isolate the variables by subtracting 6 from both sides to keep the equation equal
3x+7y = -6
Next, isolate the y-variable by subtracting 3x from both sides to keep the equation equal
7y = -3x - 6
Then, divide by +7 on both sides to keep the equation equal and to simplify the left side even more, to completely isolate the variable
y = -3x/7 -6/7
The y-intercept is located at (0, -6/7)
A chef used one- third of a bag of potatoes for a meal. If the potatoes fed 7 people, what fraction of the bag did each person get?
Answer: 1/21 of the bag
Step-by-step explanation:
If only one person eats the meal they are consuming 1/3 of a bag of potatoes. However if more than one person is eating the potatoes we need to multiply 1/3 by the reciprocal of how many people are eating.
For example:
2 people 1/3*1/2=1/6
3 people 1/3*1/3=1/9
So then we apply this principle for seven people.
7 people 1/3*1/7=1/21
We can check our answer by working backwards
1/21*7=7/21=1/3
So each person got 1/21 of the bag.
The total cost f(x), in dollars, for renting a houseboat for x days is shown:
f(x) = 15 + 150x
What does f(15) represent?
A.The number of dollars it costs for 15 people to rent the houseboat
B.The number of houseboats that can be rented for 15 days
C.The number of dollars it costs to rent the houseboat for 15 days.
D.The number of days the houseboat can be rented for a cost of $150
Answer:
C.The number of dollars it costs to rent the houseboatfor 15 days.Step-by-step explanation:
f(x) - total cost in dollars, for renting a houseboat for x days.
f(15) → x = 15 - number of days
f(x) = 15 + 150x → f(15) = 15 + 150(15) = 2,265 - total cost in dollars for 15 days
Answer: Option 'c' is correct.
Step-by-step explanation:
Since we have given that
f(x) = 15+150x
Here, x represents the number of days,
f(x) represents the total cost.
If we calculate f(15), we get that
[tex]f(15)=15+150\times 15\\\\f(15)=15+2250\\\\f(15)=2265[/tex]
$2265 is the cost for 15 days.
So, it shows the number of dollars it costs to rent the houseboat for 15 days.
Hence, Option 'c' is correct.
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Answer:
im kinda sure the answer is 120 degrees
Step-by-step explanation:
but maybe not
Susan Pollack had worked at Carl’s Garage as a receptionist for 22 years when she became permanently disabled. She was 55 years old at the time and had planned to retire at age 60. Her final average salary was $48,600 a year. Her rate of benefits is 2%. What is her annual disability benefit?
A. $26,244
B. $29,001
C. $25,667
D. $22,500
Answer:
it is C
Step-by-step explanation:
Answer:
The is A. Not c
Step-by-step explanation:
need the answer asap !! #34 !!
Answer:
A) 46 mph
Step-by-step explanation:
Step 1: To find the speed, you need to find the distance and time to travel between Chicago and Cleveland.
Distance = 354 miles
Time = 9: 50 am to 5: 30 pm
Time = 7 hours 40 minutes
Step 2: Convert time to hours
1 hour = 60 minutes
40 minutes = 60/40 = 2/3 hours
Step 3: Find the speed
Speed = Distance/Time
Speed = 354/7 + 2/3
Speed = 1062/23
Speed = 46.17 miles per hour rounded off to 46 mph
Therefore, A is the correct answer.
!!
Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4
Answer:
Refer to pics
Step-by-step explanation:
Vertical angles are two angles which are vertically opposite and have the same measure. Thus, the two angles are to be congruent.
Vertical angles are often formed when two straight lines intersect at a point.
From the given question, the steps to prove that angle 2 and angle 4 are congruent are:
With reference to the sketch attached to this answer;
<AOC + <AOD + <BOC + <BOD = [tex]360^{o}[/tex] (sum of angle at a point)
Thus,
<AOC + <AOD = [tex]180^{o}[/tex] (supplementary angle property)
also,
<BOC + BOD = [tex]180^{o}[/tex] (supplementary angle property)
So that;
<AOD ≅ <BOC (vertically opposite angle property)
Therefore,
<2 and <4 are congruent (vertically opposite angle property)
It can be concluded that vertically opposite angles are equal in measure, thus congruent.
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If one kilogram equals 2.2 pounds, how many kilograms equal 112 pounds? Round your answer to the nearest hundredth, if necessary.
Answer:
50.91
Step-by-step explanation:
Write a proportion:
1 kg / 2.2 lb = x kg / 112 lb
Cross multiply:
2.2 x = 112
Divide:
x = 50.91
50.91 kg equals 112 pounds.
PLEASE HELP URGENT!!!
Robin is giving toy cars to some children at a carnival. He has 2 black toy cars, 7 blue toy cars, and 3 yellow toy cars. If Robin selects a toy car randomly without looking, what is the probability that he will give a yellow toy car to the first child and then a blue toy car to the second child? 3 over 12 multiplied by 7 over 11 is equal to 21 over 132 3 over 12 multiplied by 7 over 12 is equal to 21 over 144 3 over 12 plus 7 over 11 is equal to 117 over 132 3 over 12 plus 7 over 12 is equal to 10 over 12
Answer: Choice A
3 over 12 multiplied by 7 over 11
(3/12) * (7/11)
=============================================
Explanation:
There are 3 yellow cars out of 2+7+3 = 12 total. The probability of selecting yellow is therefore 3/12. We can reduce this, but the answer choices decide not to, so we'll do the same.
After picking a yellow car, we have 12-1 = 11 left over. The amount of blue cars do not go down (because we haven't selected it yet). There are 7 blue cars out of the 11 total, so the probability of picking blue for this case is 7/11
Multiply the two fractions to get (3/12)*(7/11) which is a shorthand way of writing "3 over 12 multiplied by 7 over 11".
Answer:
the guy on top of me is correct give him brainliest and 5 star ratings because he is a freaking genius btw
Step-by-step explanation:
Y varies directly with x and inversely with the source root of z if y =4 when x=z and z=4 what is y when x=6 and z=9
Answer:
8
I made a couple of assumptions so you might want to make sure I made the right assumptions.
I assumed you meant square root of z; not source of z.
I also assumed you meant x=2 not x=z.
Step-by-step explanation:
y varies directly with means y=k times something where k is a constant.
Inversely means to divide by whatever it says it varies inversely with.
So we have:
[tex]y=k \cdot \frac{x}{\sqrt{z}}[/tex]
We are given y=4 and x=2 and z=4, which means:
[tex]4=k \cdot \frac{2}{\sqrt{4}}[/tex]
[tex]4=k \cdot \frac{2}{2}[/tex]
[tex]4=k(1)[/tex]
[tex]4=k[/tex]
So the constant is k which means the equation for any (x,y,z) is:
[tex]y=4 \cdot \frac{x}{\sqrt{z}}[/tex]
We want to know y when x=6 and y=9:
[tex]y=4 \cdot \frac{6}{\sqrt{9}}[/tex]
[tex]y=4 \cdot \frac{6}{3}[/tex]
[tex]y=4 \cdot 2[/tex]
[tex]y=8[/tex]
is a number less than 10 the same as the difference of a number and 10?
Answer:
Ten more than x x + 10
Step-by-step explanation:
Answer:
No.
10-x and x-10 are only the same when x=10.
They are not the same because subtraction is not commutative.
Step-by-step explanation:
A number less than 10 is 10-x .
The difference of a number and 10 means x-10.
10-x is not the same as x-10
We can find out when they are the same by solving:
10-x=x-10
Add x on both sides:
10=2x-10
Add 10 on both sides:
20=2x
Divide both sides by 2:
10=x
So they are only the same when x=10.
It is mainly not an identity because subtraction isn't commutative.
What are the factors of x squared minus 4x minus 5?
Answer:
(x-5) (x+1)
Step-by-step explanation:
x^2 -4x-5
What 2 numbers multiply to -5 and add to -4
-5*1 = -5
-5+1 = -4
(x-5) (x+1)
Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 3x+5y=1.
Answer:
[tex]\large\boxed{a)\ y=\dfrac{5}{3}x+\dfrac{22}{3}}\\\boxed{b)\ 5x-3y=-22}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================\\\\\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope-intercept form.}\\\\3x+5y=1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\5y=-3x+1\qquad\text{divide both sides bvy 5}\\\\y=-\dfrac{3}{5}x+\dfrac{1}{5}\to m_1=-\dfrac{3}{5}[/tex]
[tex]a)\\\\y=m_2x+b\\\\m_1=-\dfrac{3}{5}\to m_2=-\dfrac{1}{-\frac{3}{5}}=\dfrac{5}{3}\\\\\text{Put the value of slope and the coordinates of the given point (1, 9)}\\\text{to the equation of a line:}\\\\9=\dfrac{5}{3}(1)+b\\\\9=\dfrac{5}{3}+b\qquad\text{subtract}\ \dfrac{5}{3}\ \text{from both sides}\\\\\dfrac{27}{3}-\dfrac{5}{3}=b\\\\\dfrac{22}{3}=b\\\\\text{Finally:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}[/tex]
[tex]b)\\\\\text{The standard form of an equation of a line:}\\\\Ax+By=C\\\\\text{Convert the equation}\ y=\dfrac{5}{3}x+\dfrac{22}{3}\ \text{to the standard form:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}\qquad\text{multiply both sides by 3}\\\\3y=5x+22\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+3y=22\qquad\text{change the signs}\\\\5x-3y=-22[/tex]
What is the distance between (8, -3), (4,-7)?
A.- 6
B. 9
C.[tex]\sqrt{35}[/tex]
D.[tex]\sqrt{42}[/tex]
Thank You!
Answer:
[tex]4\sqrt{2}[/tex] which is none of your choices....
Did you mean (8,-3) and (4,-7)?
Step-by-step explanation:
We need to first find the distance between the x's.
Then the distance between the y's.
The distance between the x's is 8-4=4.
The distance between the y's is -3-(-7)=4.
So the distance between two points [tex](x_1,y1)\text{ and }(x_2,y_2)[/tex] is [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex].
So we already found x1-x2 and y1-y2 so now we have:
[tex]\sqrt{(4)^2+(4)^2}[/tex]
[tex]\sqrt{16+16}[/tex]
[tex]\sqrt{2(16)[/tex]
[tex]\sqrt{16}\sqrt{2}[/tex]
[tex]4\sqrt{2}[/tex]