Hi,
Answer:
[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°
Have a good day.
Find the area of the shape shown below.
Answer:
28
Step-by-step explanation:
We divide the shape covenientely, like this, and area 1 is 4*4=16
area 2=4*4/2=8
area 3= 2*4/2=4
Area total = Area 1 + Area 2 + Area 3=16+8+4=28
What is the sum of 3x to the second power +2x-1
Answer:
[tex]3x^2+2x+1[/tex]
Step-by-step explanation:
Sum means to add and second power means that the exponent is "2". So, the expression is:
=> [tex]3x^2+2x+1[/tex]
It cannot be simplified further.
Draw a diagram of this statement,
Fifteen thousand dollars was raised by the booster club. This was two thirds of
the goal.
Use your diagram to determine the percent by which the booster club fell short of their goal
Answer:
The percentage by which the booster club fell short is 33% as shown on the chart
Step-by-step explanation:
To represent the given data pictorially, a pie chart is suitable
The circumference of the pie chart will represent the amount to be raised by the booster club and a sector of the circle which is two-thirds of the circumference represents the amount raised
Given that the amount raised = 2/3×Goal = $15,000, we have;
We represent the amount raised as a sector of the circle as follows;
Sector angle = 2/3×360° = 240°
Total sector of goal amount = Entire circle = 360°
Amount club fell short = 360° - 240° = 120°
The goal amount = 3/2 × $15,000
Percentage by which the club fell short = 120/360×100 = 1/3×100 = 33.33%
Six friends went to a restaurant and agreed to share the bill equally. However, two people forgot their wallets so the other four friends' portions of the bill went up by $7 each. How many dollars was the total bill?
Answer:
The total bill was $84
Step-by-step explanation:
Ok so we know a few things, we know that the total cost of the bill is divisible by both 6 and 4, and we know that if we call the total cost of the bill x and the amount each person would pay if it was divided for 6 people y we can write these equations:
[tex]\frac{x}{6}=y[/tex]
[tex]\frac{x}{4}=y+7[/tex]
Now we can substitute the first equation into the second and solve for x
[tex]\frac{x}{4}=\frac{x}{6}+7\\\frac{x}{4}-\frac{x}{6}=7\\\frac{x}{12}=7\\x=7*12=84[/tex]
Therefore, the total bill was $84
Which best describes the relationship between the lines with equations 5x +y = 4 and 20.0 + 4y = 16?
Answer:
There is no relationship, except they do intersect at the point (1, -1). Hope this helps :)
Brainliest?
Both given lines are going to intersect at ( 1,-1 ) that's it.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that
Line 1 ; 5x +y = 4
Line 2 ; 20 + 4y = 16 ⇒ y = -1
At y = -1 the first line is
5x - 1 = 4 ⇒ x = 1
So,
It is clear that line 1 has a point ( 1 .-1 ) and line 2 also passes
through it hence there will an intersection.
For more about line segment
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Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
Colin leaves school to go home. He walks 3 blocks south and then 9 blocks west. If Colin could walk in a straight line to the school, what is the exact distance between Colin and the school?
Answer:
9.48*
Step-by-step explanation:
This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :
3^2 + 9^2 = C^2
9 + 81 = C^2
90 = C^2
9.48 = C
* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.
Answer:
The answer would be A. 3√10 blocks
Step-by-step explanation:
I have had this question and its 3√10 blocks.
Hope this helps you other people :))
How does the period of f(x)= cos(2x) relate to the period of the parent function cos x?
Answer:
Both have the same period which is 2π
Step-by-step explanation:
Select all that apply. If x^2+b/ax+c/a=0 ; then: The sum of its roots = -b/a? The difference of its roots =-b/a? The product of its roots = c/a?The division of its roots = c/a? I can select multiple.
Answer:
The first and the thirdStep-by-step explanation:
[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]
[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]
[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]
Use De Morgan's laws to write negations for the statement. Sam is an orange belt and Kate is a red belt.
A. Sam is an orange belt or Kate a red belt.
B. Sam is not a red belt and Kate is not an orange belt.
C. Sam is not an orange belt and Kate is not a red belt.
D. Sam is not a red belt or Kate is not an orange belt.
E. Sam is not an orange belt or Kate is not a red belt.
Answer:
C. Same is not an orange belt and Kate is not a red belt.
Step-by-step explanation:
The negation for the statement is Sam is not an orange belt or Kate is not a red belt.
What is Negation of De- Morgan's Law?The negation of a conjunction is equivalent to the disjunction of the negation of the statements making up the conjunction. To negate an “and” statement, negate each part and change the “and” to “or”.
Given statement:
Sam is an orange belt and Kate is a red belt.
Now, to make the negation we have to consider the rule "To negate an “and” statement, negate each part and change the “and” to “or”."
So, the negation statement would be
Sam is not an orange belt or Kate is not a red belt.
Learn more about De Morgan's laws here:
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(pic inside) What is the approximate value of the function at x = 1?
Answer: -2
Step-by-step explanation:
When x = 1, y = -2.
Hope it helps <3
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
The value 4 is a lower bound for the zeros of the function shown below.
f(x) = 4x^3 – 12x^2 – x + 15
A) True
B) False
Answer:
False roots are x = -1 or x = 5/2 or x = 3/2
Step-by-step explanation:
Solve for x:
4 x^3 - 12 x^2 - x + 15 = 0
The left hand side factors into a product with three terms:
(x + 1) (2 x - 5) (2 x - 3) = 0
Split into three equations:
x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0
Subtract 1 from both sides:
x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0
Add 5 to both sides:
x = -1 or 2 x = 5 or 2 x - 3 = 0
Divide both sides by 2:
x = -1 or x = 5/2 or 2 x - 3 = 0
Add 3 to both sides:
x = -1 or x = 5/2 or 2 x = 3
Divide both sides by 2:
Answer: x = -1 or x = 5/2 or x = 3/2
Answer:
False
Step-by-step explanation:
f(x) = 4x³ - 12x² - x + 15
Set output to 0.
Factor the function.
0 = (x + 1)(2x - 3)(2x - 5)
Set factors equal to 0.
x + 1 = 0
x = -1
2x - 3 = 0
2x = 3
x = 3/2
2x - 5 = 0
2x = 5
x = 5/2
4 is not a lower bound for the zeros of the function.
!!!!PLEASE HELP!!!!!
Answer:
inverse = ( log(x+4) + log(4) ) / (2log(4)), or
c. y = ( log_4(x+4) + 1 ) / 2
Step-by-step explanation:
Find inverse of
y = 4^(-6x+5) / 4^(-8x+6) - 4
Exchange x and y and solve for y.
1. exchange x, y
x = 4^(-6y+5) / 4^(-8y+6) - 4
2. solve for y
x = 4^(-6y+5) / 4^(-8y+6) - 4
transpose
x+4 = 4^(-6y+5) / 4^(-8y+6)
using the law of exponents
x+4 = 4^( (-6y+5) - (-8y+6) )
simplify
x+4 = 4^( 2y - 1 )
take log on both sides
log(x+4) = log(4^( 2y - 1 ))
apply power property of logarithm
log(x+4) = (2y-1) log(4)
Transpose
2y - 1 = log(x+4) / log(4)
transpose
2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)
y = ( log(x+4) + log(4) ) / (2log(4))
Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to
y = ( log_4(x+4) + 1 ) / 2
which corresponds to the third answer.
A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
Answer:
$14,580
Step-by-step explanation:
To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form
-In doing that, you get 2,000
-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000
-the value of the car after one year is now $18,000
Now, let's move to the second year. This time find 10% of 18,000
-multiply 18,000 by 0.1 to get 1,800
-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200
-the value of the car after two years is now $16,200
Finally, let's look at the value of the car after three years. Only this time, we will now find 10% of 16,200
-multiply 16,200 by 0.1 to get 1,620
-since value is being depreciated, or lessened, we will once again be subtracting. Subtract 1,620 from 16,200 to get 14,580
Therefore, the value of the car after three years is now $14,580.
Solve the equation and show the solution set on a number line: |x+5|=x+5
Answer: x ≥ -5
Step-by-step explanation:
First, let's see how the function f(x) = IxI works:
if x ≥ 0, IxI = x
if x ≤ 0, IxI = -x
Notice that for 0, I0I = 0.
Ok, we want that:
|x+5| = x+5
Notice that this is equivalent to:
IxI = x
This means that |x+5| = x+5 is only true when:
(x + 5) ≥ 0
from this we can find the possible values of x:
we can subtract 5 to both sides and get:
(x + 5) -5 ≥ 0 - 5
x ≥ -5
So the graph in the number line will be a black dot in x = -5, and all the right region shaded.
something like:
-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...
The vertices of triangle ABC are A(5,2), B(-1,-6), and C(1,5). If triangle DEF is similar to triangle ABC and AB/DE = 5, which could be the coordinates of D and E
Answer:
im pretty sure its the third one
Step-by-step explanation:
i guessed but it might be right
The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 3, negative 1), has an inflection point at (negative 2, 0), and goes through (negative 1, 1). Which equation represents h(x)?
Answer:
The correct option is;
[tex]h(x) = \sqrt[3]{x + 2}[/tex]
Step-by-step explanation:
Given that h(x) is a translation of f(x) = ∛x
From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;
When x = -1, h(x) = 1
When x = -3, h(x) = -1
h''(x) = (-2, 0)
Which gives
d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)
When h(x) = 0, x = -2 which gives;
[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]
Therefore, a = (0/(-2/9))^(-3/5) + 2
a = 2
The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]
We check, that when, x = -1, y = 1 which gives;
h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)
For the point (-3, -1), we have;
h(x) = [tex]\sqrt[3]{-3 + 2} = \sqrt[3]{-1} = -1[/tex]
Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).
Answer: B
Step-by-step explanation:
im stuck on this question helm me out I will mark you as brainliest
Answer: it is =4176000000000000
Step-by-step explanation:
(2.9)(100000)(7.2)(10^2)
5(10^−8)
=
(290000)(7.2)(10^2)
5(10^−8)
=
2088000(10^2)
5(10^−8)
=
(2088000)(100)
5(10^−8)
=
208800000
5(10^−8)
=
208800000
5(1/100000000)=
208800000/1
20000000
=4176000000000000
hope i helped
-lvr
Carrie can inspect a case of watches in 5 hours.James can inspect the same case of watches in 3 hours.After working alone for 1 hour,Carrie stops for lunch.After taking a 40 minute lunch break,Carrie and James work together to inspect the remaining watches.How long do Carrie and James work together to complete the job?
Will mark brainlist if it correct and well explained
Answer:
It takes Carrie and James an hour and a half to finish the job.
Step-by-step explanation:
assuming they have to inspect ONE case of watches.
Carrie can inspect 1/5 case in one hour.
James can inspect 1/3 case in one hour.
Carrie worked alone for 1 hour, so she finished 1/5 of a case.
She leaves 4/5 case to finish.
She had lunch.
After that, Carrie and James worked together for x hours to finish the job.
When they work together, the finish 1/5+1/3 = 8/15 case per hour.
So time to finisher the remaining case
Time = 4/5 / (8/15)
= 4/5 * 15/8
= 3/2 hours
= an hour and a half.
If a cone is 5 meters tall and has a radius of 3 meters, What is its volume? 15π m3 60π m3 45π m3 30π m3
Answer:
V = 15 pi m^3
Step-by-step explanation:
The volume of a cone is
V = 1/3 pi r^2 h
The radius is 3 and the height is 5
V = 1/3 pi ( 3)^2 *5
V = 15 pi m^3
Answer:
15 pi m3
Step-by-step explanation:
[tex] \sqrt[3]{y} = a(c + \frac{1}{x})[/tex]
Greetings from Brasil...
Here we don't have much to go
∛Y = A.(C + 1/X)
∛Y = (AC + A/X)
raising both members to the cube.....
(∛Y)³ = (AC + A/X)³
from Notable Products: (a + b)³ = a³ + 3a²b + 3ab² + b³
Y = (AC)³ + 3(AC)².(A/X) + 3AC(A/X)² + (A/X)³
Y = A³[C³ + (3C²/X) + (3C/X²) + (1/X³)]
greater than (−8) but less than (−2)
Answer:
-8 < x < -2
start number line at -10 and end it at 0
draw an open circle* over the dash indicating -8 and -2
connect the open circles
*open circle because it is less than and greater than, not less than or equal to and greater than or equal to
Answer:
-8<x<-2
Step-by-step explanation:
yw luv :D
An exponential growth function has a base that is____one?
Please help
Answer:
greater than
Step-by-step explanation:
An exponential growth function has a base that is__greater than__one.
If the base is less than one, it will be a decay function.
Note: the above assumes an exponent greater than one as well.
The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (x < 2 mins) _____________________________ b). P (2 < x < 11 mins) _____________________________ c). P (x < 11 mins) ________________________________ d). P (2 < x < 5 mins) _______________________________ e). P (x > 5 mins)
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
A total of $10,000 is invested in two mutual funds. The first account yields 5% and the second account yields 6%. How much was invested in each account if the total interest earned in a year is $575?
Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
Please help me with this question!! TRIGONOMETRY
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = 10/x
x*sin(35) = 10
x = 10/sin(35)
x = 17.434467956211 make sure your calculator is in degree mode
x = 17.4
Answer:
[tex]\boxed{17.4}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{sin(35)}[/tex]
x = 17.4344679562...
x ≈ 17.4
What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : [tex]\dfrac{2}{3}[/tex]
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 14 each week for a number of weeks, w. She writes the expression 100(14)w to find the amount of radioactive substance remaining after w weeks. Ryan starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 40% each week for a number of weeks, w. He writes the expression (1 – 0.4)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Grace’s and Ryan’s expressions mean.
Answer:
100= Initial Amount
1/4= decay factor for each week
w= number of weeks
1/4w= decay factor after w weeks
1 - 0.4= decay factor for each week
w= number of weeks
0.4= percent decrease
Step-by-step explanation: