Answer:
f(x) = 4( x + 3/2)^2
Step-by-step explanation:
F(x) =4 x^2 + 12x + 9
= 4 [ x^2 + 3x] + 9
Add (3/2)^2 - (3/2)^2 to the square bracket, we have:
4 [ x^2 + 3x+ (3/2)^2 - (3/2)^2] + 9
4[ (x + 3/2 )^2 - 9/4] + 9
4( x + 3/2)^2 - 9/4 ×4 + 9
4( x + 3/2)^2 - 9 + 9
4( x + 3/2)^2 +0
4( x + 3/2)^2
Note the (3/2)^2 - (3/2)^2 is decoded by dividing b by 2 and squaring it and then subtracting same. Look at the general equation of a circle given below
ax^2 + bx + c
To form a square expression we adopt (b/2)^2 - (b/2)^2 to the general equation provided a = 1;
To make a = 1; we had to factor out 4 from the coefficient of x; making perfect square is of concern when we have ax^2 + bx ; irrespective of 'c' or not.
This is usually referred to as method of completing the square in solving quadratic equation
Determine if the triangles below are similar and explain.
Answer:
The answer would be C the triangles are not similar
Step-by-step explanation:
What is the inverse of the function G(X)=-2(x-4)
Answer:
Step-by-step explanation:
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The inverse of the function G(X)=-2(x-4) is G'(x) = -(1/2)x +4
What is a Function?A function is a law that relates a dependent and an independent variable.
The function is g(x) = -2(x-4)
The inverse of a function is found by interchanging the position of the x an d y variable and then solving for y in terms of x.
g(x) = -2 (x-4)
y = -2(x-4)
Interchanging y to x
x = -2( y-4)
x = -2y +8
(x - 8)/ -2 = y
y = 4 - (1/2)x
To know more about Function
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The function f determines the cost (in dollars) of a new Honda Accord in terms of the number of years t since 2000. That is, f ( t ) represents the cost (in dollars) of a new Honda Accord t years after 2000. Use function notation to represent each of the following. The cost (in dollars) of a new Accord in 2006?
A. How much more a new Accord costs in 2013 as compared to the cost of a new Accord in 2010?
B. A new Accord in 2013 is how many times as expensive as a new Accord in 2010?
C. $980 dollars more than the cost of a new Accord in 2016.
Complete Question
The function f determines the cost (in dollars) of a new Honda Accord in terms of the number of years t since 2000. That is, f ( t ) represents the cost (in dollars) of a new Honda Accord t years after 2000. Use function notation to represent each of the following. The cost (in dollars) of a new Accord in 2006?
A. How much more a new Accord costs in 2013 as compared to the cost of a new Accord in 2010?
B. A new Accord in 2013 is how many times as expensive as a new Accord in 2010?
C. In 2016 , some cars cost $980 more than the cost of a new Accord.How much does the other cars cost (in dollars)in 2016?
Answer:
a
The cost of a new Accord in 2013 compared to 2010 is z = f(13) - f(10)
b
The magnitude at which the cost of a new Accord in 2013 is greater than the cost in 2010 is
[tex]x = \frac{f(13)}{f(10)}[/tex]
c
The cost of the other cars is 2016 is r = 980 + f(16)
Step-by-step explanation:
From the question we are told that
The cost (in dollars) of a new Honda Accord is f(t)
Where t is number of years after 2000
The cost of the Honda Accord at 2013 is
f(2013 - 2000) = f(13)
The cost of the Honda Accord at 2010 is
f(2010 - 2000) = f(10)
So the cost difference between 2013 and 2010 is mathematically evaluated as
z = f(13) - f(10)
Let constant at which the cost of Honda Accord in 2013 is greater than its cost at 2010 be x
So
f(13) = x f(10)
=> [tex]x = \frac{f(13)}{f(10)}[/tex]
The cost of the Honda Accord in 2016 is mathematically evaluated as
f(2016 - 2000) = f(16)
Now the cost of these other cars is mathematically evaluated as
r = 980 + f(16)
The difference between the cost of Accord in 2013 and 2010 is [z = f(13) - f(10)] and this can be determined by using the given data.
Given :
f(t) represents the cost (in dollars) of a new Honda Accord t years after 2000.
A). The cost of Accord in 2013 is given by:
[tex]f(2013-2000) = f(13)[/tex]
The cost of Accord in 2010 is given by:
[tex]f(2010-2000) = f(10)[/tex]
So, the difference between the cost of Accord in 2013 and 2010 is:
z = f(13) - f(10)
B). Let the constant be 'a' then the value of 'a' is:
[tex]a = \dfrac{f(13)}{f(10)}[/tex]
So, the new Accord in 2013 'a' times as expensive as a new Accord in 2010.
C). Cost of the Honda Accord in 2016 is:
[tex]f(2016-2000) = f(16)[/tex]
The cost of the other cars is:
r = 980 + f(16)
For more information, refer to the link given below:
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(3 1/2 - 9 3/4) ÷ (-2.5)
exact form
5/2
decimal form
2.5
mixed number form
2 1/2
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
JLK = 360-154 (Circle is 360°)
So
JLK = 206
H is directly proportional to the square root of p h=5.4 when p=1.44 find h when p=2.89
Answer:
h=7.65
Step-by-step explanation:
h=k√p
k=h/√p
k=5.4/√1.44
k=4.5
h=4.5√p
when p=2.89
h=4.5√2.89
h=7.65
Answer:
H = 7.65
I hope it helps
[tex]h \: = \sqrt{p} \\ h \: = k \sqrt{p} .....(1) \\ when \: h \: = 5.4 \: p = 1.44 \\ 5.4 = k \: \sqrt{1.44} [/tex]
[tex]5.4 = 1.2k \\ divide \: both \: sides \: by \: 1.2 \\ k \: = 4.5[/tex]
[tex]h \: = 4.5 \sqrt{p} = \: formula \: connecting \: h \: and \: p \\ from \: equation \: .....(1) \\ when \: p \: = 2.89 \: h = \\ when \: p \: = 2.89 \: h \: = \\ h \: = 4.5 \sqrt{2.89} \\ h = [/tex]
[tex]h \: = 4.5 \sqrt{2.89} \\ h = 4.5 \times 1.7 \\ h \: = 7.65[/tex]
need help!!!! asap!!!!
Answer:
number 15 would be B sorry i dont understand number 14
Which ordered pair is a solution of the equation?
y-3=5(x-2) Choose 1 answer:
A
Only (2,3)
B
Only (3,2)
C
Both (2,3) (3,2)
D
Neither
Answer:
A Only (2, 3)
Step-by-step explanation:
The given equation is in point-slope form:
y -k = m(x -h) . . . . . a line with slope m through point (h, k)
The point in the given equation is ...
(h, k) = (2, 3)
so you know the equation is satisfied at that point.
__
When you try the other point, you find ...
For (x, y) = (3, 2), you have
2 -3 = 5(3 -2)
-1 = 5(1) . . . . FALSE
Point (3, 2) does not satisfy the equation.
Only (2, 3) is a solution of the equation
_____
Of course, the equation of a line is satisfied by an infinite number of points. Of the two listed here, only (2, 3) is a solution.
$1,034,473.45 spell it out
Answer:
One million, thirty four thousand, four hundred and seventy three dollars and forty five cents.
Bugs Bunny was
42
4242 meters below ground, digging his way toward Albuquerque, when he realized he wanted to be above ground. He turned and dug through the dirt diagonally for
100
100100 meters until he was above ground.
What is the angle of elevation, in degrees, of Bugs Bunny's climb?
Answer:
24.83 degrees.
Step-by-step explanation:
In the diagram, Bugs Bunny was initially at point A 42 meters below ground and dug diagonally 100 meters to point B.
We are to determine the angle of elevation, [tex]\angle BAX[/tex] of his climb.
Now, [tex]\angle BAX=\angle ABC$ (Alternate Angles)[/tex]
Using Trigonometric ratios
[tex]\sin B=\dfrac{AC}{AB} \\\sin B= \dfrac{42}{100}\\\\B=\arcsin \dfrac{42}{100}\\\\B=24.83^\circ[/tex]
The angle of elevation of Bugs Bunny's climb is 24.83 degrees. (correct to 2 decimal places).
What is the probability of drawing a red marble out of the bag without looking?
Answer:
it depends on how many red marbles are there
Step-by-step explanation:
is there any green or orange or yellow?
Answer:1 over 3
Step-by-step explanation:
99 points for brainliest
Answer:
144
Step-by-step explanation:
4 triangles = 1/2 x 6 x 9 x 4 = 108
1 sq base = 6 x 6 = 36
total surface area = 36 + 108 = 144
if 3 triangles the base wouldn't be a square thus not possible to solve
Answer:
144
Step-by-step explanation:
SA = Area of base + 4 area of triangles
6² + 4(9 × 6 × 1/2)
36 + 4(27)
= 144
WHICH TWO CHOICES ARE EQUIVALENT TO THE FRACTION BELOW?
Answer:
option B, and D
Step-by-step explanation:
coz when u multiply 2/3 by 2/2, u wud get 4/6,
and when u divide 8/12 by 2/2, u wud agn get 4/6
Answer: 2/3 and 8/12
Step-by-step explanation: When we multiply or divide the numerator and denominator of a fraction by the same number, we get an equivalent fraction.
First write 4/6 in lowest terms by dividing both the numerator and the denominator by 2 to get the equivalent fraction 2/3.
Starting at 4/6 again, if we multiply the numerator and the denominator by 2, we get the equivalent fraction 8/12.
So our two equivalent fractions are 2/3 and 8/12.
It's important to remember the following rule: Whatever you do to the numerator of a fraction, you must also do to the denominator because if you don't, you're changing the value of the fraction.
Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X
Answer:
a. Binomial random variable (n=4, p=0.25)
b. Attached.
c. X=1
Step-by-step explanation:
This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).
a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{4}{k} 0.25^{0}\cdot0.75^{4}[/tex]
The sample space for X is {0,1,2,3,4}
The associated probabilties are:
[tex]P(x=0) = \dbinom{4}{0} p^{0}(1-p)^{4}=1*1*0.3164=0.3164\\\\\\P(x=1) = \dbinom{4}{1} p^{1}(1-p)^{3}=4*0.25*0.4219=0.4219\\\\\\P(x=2) = \dbinom{4}{2} p^{2}(1-p)^{2}=6*0.0625*0.5625=0.2109\\\\\\P(x=3) = \dbinom{4}{3} p^{3}(1-p)^{1}=4*0.0156*0.75=0.0469\\\\\\P(x=4) = \dbinom{4}{4} p^{4}(1-p)^{0}=1*0.0039*1=0.0039\\\\\\[/tex]
b. The histogram is attached.
c. The most likely value for X is the expected value for X (E(X)).
Is calculated as:
[tex]E(X)=np=4\cdot0.25=1[/tex]
what is the solution to -4[2×+6]=-24
Answer:
x=0
Step-by-step explanation:
-4(2x+6) = -24
distribute the -4 to the parentheses
-8x-24 = -24
add the 24 over
-8x=0
divide both sides by -8
x=0
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
p(x)=19x+15
Step-by-step explanation:
Distribution property
Take the values of r and x- you should end up with p(x)=(25x-6x+15)(x)
- 25x minus 6x equals 19x
- form there you distribute the (x) and it will square 19x and multiply with 15
- end answer should be p(x)=19x²+15x
- simply by factoring the ² and 15x and you should get 19x+15
comment if you need clearer step by stepAnswer:
A. p(x) = 19x - 15
Step-by-step explanation:
→Set it up, like so:
[tex](25x)-(6x+15)[/tex]
[tex]25x - 6x-15[/tex]
→Add like terms (25x and -6x):
[tex]19x - 15[/tex]
A 80 kg patient needs a medication x in the amount of 0.25 mg/kg/day. The medication comes in a liquid solution of 50 mg for every 10mg. How many ml of this solution will this patient need in a day
Answer:
v = 100ml
Step-by-step explanation:
0,25mg/kg
-----------> 0,25 * 80 = 20mg
50ml for every 10mg
'v"ml for 20mg
10 * v = 50 * 20
v = 100ml
What is the volume of a hemisphere with a radius of 4.8 ft, rounded to the nearest
tenth of a cubic foot?
Answer: 231.6
Step-by-step explanation:
Answer:
231.6 ft³
Step-by-step explanation:
volume of sphere:
V=[tex]\frac{4}{3} \pi r^{3}[/tex]
radius=4.8
plug in:
[tex]\frac{4}{3} \pi (4.8)^{3}[/tex]
463.246686328
Volume of Hemisphere HALF of Volume of Sphere:
[tex]\frac{463.246686328}{2}[/tex] =231.623343164
≈231.6 ft³
The weight of an object on a particular scale is 145,2 lbs. The measured
weight may vary from the actual weight by at most 0.3 lbs. What is the range
of actual weights of the object?
Answer:
145.2 + .3 = 145.5
145.2 - .3 = 144.9
C. 144.9 <= x <= 145.5
Step-by-step explanation:
Ali wraps a birthday present in a tube that has a length of 14 inches and a diameter of 6 inches.
a. a. How much space can the gift hold?
Answer:
395.84
Step-by-step explanation:
The radius squared is nine. 9 times pi then 14, is 395.84
what is the value of x in the equation 4x +8y, when y =0.8?
Answer:
-1.6
Step-by-step explanation:
4x +8y=0
y=0.8 ⇒
4x+8*0.8=04x+6.4=04x=-6.4x= -6.4/4x= -1.6A sculpture is in the shape of a square pyramid. The sculpture has a height of 36 feet and a volume of 19,200 cubic feet. Find the side length of the square base
Answer:
40ft
Step-by-step explanation:
The volume of a square pyramid is given by:
[tex]V=\frac{l^2h}{3}[/tex]
where V is the volume, l is the length of the square base, and h is the height.
Since we need to find the length, we solve for [tex]l[/tex] in the last equation:
[tex]l^2h=3V\\\\l^2=\frac{3V}{h} \\\\l=\sqrt{\frac{3V}{h} }[/tex]
and now, we substitute the known values:
[tex]V=19,200ft^3\\h=36ft[/tex]
and we get the following:
[tex]l=\sqrt{\frac{3(19,200ft^3)}{36ft} }\\ \\l=40ft[/tex]
the length of the square base is 40ft
Which expressions are equivalent to 30 - 3y - 9?
3(17-y)
3(20-y-3)
17(3-y)
Or 20(3-3y)-9
Answer:
3(20 - y - 3)
Explanation:
If you expand it:
3 · 20 = 30
3 · -y = -3y
3 · -3 = -9
Combine them altogether to get:
30 - 3y - 9
la suma de la longitud de una semicircunferencia y su diametro es 4(pi+2)cm . determine el arrea del circulo
Answer: [tex]16\pi \;cm^2[/tex]
Step-by-step explanation:
La longitud de una semicircunferencia es [tex]l=\pi r[/tex]
[tex]\pi r+2r=4(\pi+2)\\r(\pi+2)=4(\pi+2)\\r = 4\frac{\pi+2}{\pi+2} \\r=4[/tex]
[tex]A = \pi r^2 = \pi (4)^2=16\pi[/tex]
Suppose you take a random sample from a normal population and you want to determine whether there is sufficient statistical evidence to claim that the population variance differs from a corresponding variance specified in a government contract. Which type of test is appropriate, a test of one variance or a test of two variances?
Answer:
A test óf one variance
Step-by-step explanation:
A test of one variance. In this case, one will be testing against the hypothesized variance that was given.
The duration of telephone calls directed by a local telephone company: σ = 3.6 minutes, n = 560, 90% confidence. Round your answer to the nearest thousandth
Answer:
The margin of error for the confidence interval is of 0.25 minutes.
Step-by-step explanation:
With what we are given, the only thing that this question can be asked is the margin of error for the confidence interval of the mean duration of telephone calls directed by a local telephone company.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Using what we are given:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.645*\frac{3.6}{\sqrt{560}}[/tex]
[tex]M = 0.25[/tex]
The margin of error for the confidence interval is of 0.25 minutes.
Evaluate the function at the given values of the independent variable. Simplify the results.
[tex]answers \\ a. \: \: 0 \\ b. \: \: \frac{ - 63}{8} \\ c. \: \: {c}^{3} - {5c}^{2} \\ d. \: \: {t}^{3} + 25t + {10t}^{2} \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
5TH GRADE MATH!!!! PLEASE HELP BRAINLEIST AND 5 STARS!!!!!!!!!!!!!!!!!!!!
Answer with Step-by-step explanation:
1. V= 17*24*32= 13056
2. V=Same as above
3. V= 50*24*22=26400
4. Add them up and total
V= 13056*2+26400
V= 52510 yds
Answer:
So the volume is 52,512 cubic yards or 52,512 yd³
Step-by-step explanation:
1. V = 17 × 24 × 32
V = 13,056
2. Exact same thing as 1 (13,056)
3. V = 50 × 24 × 22
V = 26,400
4. 13,056 + 13,056 + 26,400 = 52,512
Hope that helped :)
3. A sphere has a volume of 4,500Tt cubic inches. What is the radius of the
sphere?
A. 3,375 inches
B. 15 inches
C. 30 inches
D. 225 inches
Answer:
10.24 in
Step-by-step explanation:
Formula for volume of a sphere
= 4/3πr³
This sphere has a volume of
4,500cubic inches= 4500in³
The radius will be equall to
4/3πr³= 4500in³
r³ =( 4500 * 3)/(4π)
r³ = 1074.296
r = 3√1074 296
r = 10.24 in
A cube has sides that are 3 in. long. What is the surface area of the cube?
OA) 72 in2
OB) 54 in 2
OC) 36 in2
OD) 61 in 2
Answer:
B 54in
Step-by-step explanation: