Answer:
The answer is [The x-coordinate of the center of the circle decreases by 3.]
Step-by-step explanation:
Does antibiotics help kill the common cold??
explai n how a number and its reciprocal are related
AB=21; AD=28. What is the value of AC+BD?
The value of AC + BD will be 70.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
In rectangle ABCD,
AB = 21
AD = 28
Now,
Since, ABCD is a rectangle.
Hence, We get;
⇒ AC = BD
Here, In rectangle ABCD,
AB = 21
AD = 28
So, By using definition of Pythagoras theorem, we get;
⇒ BD² = AB² + AD²
⇒ BD² = 21² + 28²
⇒ BD² = 441 + 784
⇒ BD² = 1225
⇒ BD = 35
Thus, The value of BD + AC is find as;
⇒ AC + BD = 35 + 35
= 70
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Why is a plane a undefined term
Which answer shows these decimals written in order from greatest to least? 46.95
48.1
46.581
how to write four hundred thousand in numbers?
Katie wants to buy 6 pencils from the school store.Each pencil costs 15¢.How much money will she get back if she pays with a five dollar bill?
Answer: The amount she will get is $4.10
Step-by-step explanation:
My reason is because .15 times 6 since she is buying 6 pencils, it is .90. The you subtract the decimal 5.00-0.90 and you get 4.10. Hope this helps. PLease mark brainliest!!!!!
The ratio of sues age to her fathers age is 2:7 in three years their ages will total 60, how old is sue and her dad right now
how to find a whole number in this question 4% of ... is 56?
In the formula A=\pi r^{2}, if the radius is 6 centimeters, what is the correct unit for the area of the circle?
A)\pi cm
B)cm^2
C)cm
D)cm^3
Determine c so that f(x) is continuous on the entire real line if f(x)= x^2 when x<=3 and c/x when x>3 ...?
The des moines register recently reported the ratings of high school sportsmanship as complied by the iowo high school athletic association. For each school, the participants and coaches were rated by referees, where 1= superior, and 5= unsatisfactory. A regression analysis of the averages scores given to football players and coaches is shown below.
interpret the value of the correlation between the ratings of coaches and participants.
who good at the math
The sensory somatic nervous system controls all _________ responses of the body.
unconscious
voluntary
sequenced
repeated
Answer:
The sensory somatic nervous system controls all voluntary responses of the body.
Step-by-step explanation:
The sensory somatic nervous system controls all voluntary responses of the body.
The movements includes muscles and organs movements and reflex movements. Here the sensory neurons carry impulses to the brain and the spinal cord.
Solve log base(x − 1) 16 = 4.
Answer:
x = 3
Step-by-step explanation:
Given:[tex]\log _{x-1}\left(16\right)=4[/tex]
We have to solve for x.
Consider the given expression [tex]\log _{x-1}\left(16\right)=4[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(b\right)=\frac{\ln \left(b\right)}{\ln \left(a\right)}[/tex]
[tex]\log _{x-1}\left(16\right)=\frac{\ln \left(16\right)}{\ln \left(x-1\right)}[/tex]
Thus, the expression becomes,
[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}=4[/tex]
Multiply both side by [tex]\ln \left(x-1\right)[/tex]
[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}\ln \left(x-1\right)=4\ln \left(x-1\right)[/tex]
Simplify, we get,
[tex]\ln \left(16\right)=4\ln \left(x-1\right)[/tex]
Divide both side by 4, we have,
[tex]\frac{4\ln \left(x-1\right)}{4}=\frac{\ln \left(16\right)}{4}[/tex]
[tex]\frac{\ln \left(16\right)}{4}:\quad \ln \left(2\right)[/tex]
Thus, [tex]\ln \left(x-1\right)=\ln(2)[/tex]
[tex]\mathrm{When\:the\:logs\:have\:the\:same\:base:\:\:}\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]
thus, x - 1 = 2
simplify for x, we have,
x = 3
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)2(x - 8)3
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
The given polynomial has roots -8 with multiplicity 2 and 8 with multiplicity 3. Hence option B is correct.
Use the concept of polynomial defined as:
An expression that contains exponents, variables, and constants that is combined using mathematical operations such as addition, subtraction, multiplication, and division is known as a polynomial.
The given polynomial is:
f(x) = 5(x + 8)²(x - 8)³
To find its root equate this polynomial to 0.
Then,
5(x + 8)²(x - 8)³ = 0
(x + 8)²(x - 8)³ = 0
(x + 8)(x + 8)(x - 8)(x - 8)(x - 8) = 0
Therefore,
x = -8, -8, 8, 8, 8
Hence,
It has root -8 with multiplicity 2 and 8 with multiplicity 3 which is option B.
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The complete question is:
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)²(x - 8)³
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
Hi! Please help... a woman drops a front door key to her husband from their apartment window several stories above the ground. the function h=-16t^2 +64 gives the height h of the key in feet, t seconds after she releases it.
A/ how long does it take the key to reach the ground?
B/ what are the reasonable domain and range for the function h? ...?
Answer:
It would take 2 seconds to the key to reach the ground.
The domain the function is: 0≤t≤2 or in interval notation [0,2].
The range of the function is: 0≤h≤64 or in interval notation [0,64].
Step-by-step explanation:
The provided function is: [tex]h=-16t^2 +64[/tex]
Where h represents the height and t represents the time.
Part(A) how long does it take the key to reach the ground?
When key will be at ground, the height will be 0.
Substitute the value of h=0 in above equation and solve for t.
[tex]-16t^2 +64=0[/tex]
[tex]-16(t^2 -4)=0[/tex]
[tex](t^2 -2^2)=0[/tex]
[tex](t+2)(t-2)=0[/tex]
[tex]t+2=0\ or\ t-2=0[/tex]
[tex]t=-2\ or\ t=2[/tex]
Ignore the negative value of t.
Hence, it would take 2 seconds to the key to reach the ground.
Part (B) what are the reasonable domain and range for the function h?
Time and Distance should be a positive number.
Thus, the value of t and h should be greater or equal to 0.
From the part (a) we know that the after 2 second the key will hit the ground so the value of t can be greater or equal to 0 but should be less or equal to 2.
Thus, the domain the function is: 0≤t≤2 or in interval notation [0,2].
The maximum height of the key will be at t=0.
Thus the maximum value of h can be 64 and minimum value can be 0.
The range of the function is: 0≤h≤64 or in interval notation [0,64].
Watermelons cost $0.35 per pound. Joseph’s watermelon costs between $4.20 and $5.25. Which compound inequality correctly represents the possible weights of his watermelon?
Answer: 12 < x < 15
Step-by-step explanation:
I HATE MATH (and im lazy)
Oliver borrowed $215 from his friend John. He used this money to advertise his tutoring services. Oliver earned 8 times the amount he borrowed in his first month of tutoring. Approximately how much did Oliver earn in his first month of tutoring?
Answer:
then f the teacher
Step-by-step explanation:
Name the property of 11xn=1
Write 16 1/2 as an improper fraction
A1+a2+a3=180 solve for a1
At the beginning of April, Owl Corporation has a balance of $12,000 in the Retained Earnings account. During the month of April, Owl had the following external transactions.
1. Issue common stock for cash, $8,000.
2. Provide services to customers on account, $6,100.
3. Provide services to customers in exchange for cash, $2,400.
4. Purchase equipment and pay cash, $5,600.
5. Pay rent for April, $1,000.
6. Pay workers' salaries for April, $2,500.
7. Pay dividends to stockholders, $1,100.
Using the external transactions above, compute the balance of Retained Earnings at April 30 ...?
graph the line y=3/4x-2
Step-by-step explanation: First, notice that this line is in slope intercept or more commonly known as y = mx + b form because y is by itself on one side of the equation.
Our slope or m therefore is the coefficient of the x-term which in this case is 3/4. Our b or y-intercept is the constant term which in this case is -2.
To graph a line given the slope and y-intercept, we will first start with its y-intercept. The y-intercept of a line is the point where the line crosses the y-axis. Since our y-intercept is -2, we start by plotting the point that is down 2 units on the y-axis and we call that point A.
From there we take our slope of 3/4 so our rise is 3 and our run is 4 and we end up at point B. Now we can connect the two points and we have our line.
I attached the image of the line in the image provided.
Tim is setting up the course for a 9 mile walk.he places a sign every 0.15 mile along the path. how many signs will tim place
A sequence in which each term is found by adding the same number
Sam is flying a kite. the length of the kite string is 80 meters, and it makes an angle of 75° with the ground. the height of the kite from the ground is meters.
Answer:
Height of the kite from ground is 77 m.
Step-by-step explanation:
Given: Length of the kite string = 80 m
Angle of elevation = 75°
To find: Height of the kite from the ground.
Figure is attached.
In ΔABC
using trigonometric ratio,
[tex]sin\,75^{\circ}=\frac{AB}{AC}[/tex]
[tex]0.97=\frac{AB}{80}[/tex]
[tex]AB=0.97\times80[/tex]
AB = 77.27 m
AB = 77 m (approx.)
Therefore, Height of the kite from ground is 77 m.
the circular blade on a saw has a diameter of 7.5 inches and rotates at 2400 revolutions per minute.
A) find the angular speed in radians per sec
B) Find the linear speed of the saw teeth ( in feet per sec) as the contact the wood being cut.
Formulas--> Linear speed= arc length/time= s/t
Angular speed= central angle/time ...?
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The product of 9 and a number is 12 less than three times that number.
What is the number?
Please solve the eqution
Cos4x + cos2x - 2 =0
cos4x = cos2x
We know that:
cos2x = 1-2cos^2 x
==> cos4x = 1-2cos^2 (2x)
Now substitute:
==> 1-2cos^2 (2x) = cos2x
==> 2cos^2 (2x) + cos2x - 1 = 0
Now factor:
==> (2cos2x -1)(cos2x + 1) = 0
==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3
==> x1= pi/6 , 7pi/6
==> x1= pi/6 + 2npi
==> x2= 7pi/6 + 2npi
==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.
==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}
The solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.
Here, we have to solve the equation cos(4x) + cos(2x) - 2 = 0, we can use trigonometric identities to simplify it.
We know the following trigonometric identities:
[tex]cos(2x) = 2cos^2(x) - 1\\cos(4x) = 2cos^2(2x) - 1[/tex]
Now, let's rewrite the equation using these identities:
[tex]2cos^2(2x) - 1 + 2cos^2(x) - 1 - 2 = 0[/tex]
Combine like terms:
[tex]2cos^2(2x) + 2cos^2(x) - 4 = 0[/tex]
Divide the entire equation by 2:
[tex]cos^2(2x) + cos^2(x) - 2 = 0[/tex]
Now, let's simplify further:
We can rewrite [tex]cos^2(2x)[/tex] as [tex](1 - sin^2(2x))[/tex]using the Pythagorean identity: [tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
So, the equation becomes:
[tex](1 - sin^2(2x)) + cos^2(x) - 2 = 0[/tex]
Rearrange the terms:
[tex]cos^2(x) - sin^2(2x) - 1 = 0[/tex]
Now, use the double-angle identity: [tex]sin^2(2x) = 2sin(x)cos(x)[/tex]
[tex]cos^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]
Now, we can rewrite [tex]cos^2(x) as (1 - sin^2(x))[/tex] using the Pythagorean identity:
[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
[tex](1 - sin^2(x)) - 2sin(x)cos(x) - 1 = 0[/tex]
Now, simplify further:
[tex]1 - sin^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]
We can see that [tex](1 - sin^2(x))[/tex] cancels out:
-2sin(x)cos(x) = 0
Divide both sides by -2:
sin(x)cos(x) = 0
Now, there are two possible solutions for this equation:
sin(x) = 0
cos(x) = 0
Let's solve each case:
sin(x) = 0
This occurs when x is an integer multiple of π (π, 2π, 3π, ...). So the solutions are x = nπ, where n is an integer.
cos(x) = 0
This occurs when x is an odd multiple of π/2 (π/2, 3π/2, 5π/2, ...). So the solutions are x = (2n + 1)π/2, where n is an integer.
Therefore, the solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.
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