Answer:
x=4+√73 or x=4−√73
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x^2−8x−48=9
Step 2: Add 48 to both sides.
x^2−8x−48+48=9+48
x^2−8x=57
Step 3: The coefficient of -8x is -8. Let b=-8. Then we need to add (b/2)^2=16 to both sides to complete the square.
Add 16 to both sides.
x^2−8x+16=57+16
x^2−8x+16=73
Step 4: Factor left side.
(x−4)^2=73
Step 5: Take the square root.
x−4=±√73
Step 6: Add 4 to both sides.
x−4+4=4±√73
x=4±√73
x=4+√73 or x=4−√73
Answer:
x=4+√73 or x=4−√73
If this answer helped you, I would greatly appreciate it if you gave me brainliest :D.
1 Jill always buys the same kind of
shampoo in an 11.5-ounce bottle. She is
at the store buying more and sees that
the bottle is now bigger and has 20%
more for the same price. How many
ounces of shampoo are in the
new bottle?
A 11.5
B 13.8
C 17.3
D 23.0n in
Answer:
B 13.8 oz
Step-by-step explanation:
20 % is .20 in decimal
.20 * 11.5 oz = 2.3 oz more than 11.5
2.3 + 11.5 =13.8 oz
Find the SURFACE AREA of the shape below.
Step-by-step explanation:
The given shape is a cube.
SURFACE AREA
= 6(a²)
= 6(5²)
= 6(25)
= 150cm²
Answer:
150 cm²
Step-by-step explanation:
Given figure is of a cube, probably like an ICE cube.
Surface area = ?
We know that,
SA of cube = 6a^2Here a denotes edge.
Given that edge is 5 .
Substituting,
6(5^2)6(25)150 cm^2SA of cube = 150 cm²
a number, x, rounded to 1 decimal place is 3.7. write down the error interval for x
Answer:
3.65 ≤ x < 3.75
Step-by-step explanation:
We are finding the lower and upper bounds:
The lowest possible number that can be rounded to 3.7 is 3.65 as the 5 makes the 6 go next.
The maximum possible number to 2 d.p that will be 3.74 as the 4 keeps it at 3.7.
But someone can say 3.749 is a bigger number that 3.74 that will get rounded to 3.7
Someone else can argue with 3.7499.
So to solve this argumnet we put 3.75 but we don't include it.
Therefore our final answer is :
3.65 ≤ x < 3.75
Hope this helped and branliest please.
Do the following lengths form a right triangle? (Also how to tell that they do form a right triangle)
Answer: Yes this is a right triangle
We can determine this by using the converse of the pythagorean theorem.
a = 5, b = 12, c = 13
[tex]a^2 + b^2 = c^2\\\\5^2 + 12^2 = 13^2\\\\25 + 144 = 169\\\\169 = 169 \ \ \checkmark\\\\[/tex]
Since those a,b,c values work in the pythagorean theorem, this proves we have a right triangle.
what is the domain of h
Which expressions in the box have a value less than 1·· 2, between 1··2and 1, or greater than 1? Write each expression in the correct column in the table. 4 6··82 1 1··81··91 1··41 1··32 7··85··61 4··52 3··42 1 2··31··31 3··5Less than 1··2Between 1··2and 1 Greater than 1
Answer:
less then 1..2
Step-by-step explanation:
hese are equivalent because 42+35=77 and 7(6+5)=77.
Merle has found that the probability of randomly drawing a bag of green tea out of a box of assorted tea bags is . If Merle draws 25 tea bags out of the box, which of the following is the best prediction of the number of tea bags that will be green tea?
Answer:
its dont make since bro what is the fraction?
Step-by-step explanation
divide
Assume another planet is 10^8 million miles away from Earth. If an astronaut in the future can travel 10^5 million miles per week, about how many weeks would it take for her to reach the other planet?
Answer:
x=1000
Step-by-step explanation:
10⁵x= 10⁸
x= 1000
Which expressions represent the area of the entire shaded region, including the light and dark shading? select three options. 12a cm2 2b cm2 (6a – b) cm2 (12a 2b) cm2 (6a b) cm2
A triangle is a polygon. The total area of the figure can be represented by 12a, (6a+b), and 2b cm².
What is a triangle?A triangle is a polygon with 3 sides and 3 vertices.
Since the area of a single triangle is a cm², and the shape is formed of 12 triangles, therefore, the area of the 12 triangles will be equal to,
[tex]\text{Area of the complete figure} = 12 \times a = 12a\rm \ cm^2[/tex]
Given that the area of the complete dark portion is b cm², therefore, the area of the 6 triangles with a cm² of area each, and the black portion can be written as,
[tex]\text{Area of the complete figure} = (6 \times a)+b = (6a+b)\rm \ cm^2[/tex]
As the dark portion also consists of 6 triangles with an area of a cm² each and the total sum of this dark area is b cm². Also, the light portion consists of 6 triangles with an area of a cm². Therefore, the total area can be written as,
[tex]\text{Total area} = 6a+6a = b+b = 2b\rm\ cm^2[/tex]
Thus, the total area of the figure can be represented by 12a, (6a+b), and 2b cm².
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1. Mrs. Grape has 90 students. On her last test, 3/10 of these students earned an A. Of those students, 1/9 got a perfect score. How many students got a perfect score?
2. Using the information from the problem above, what fraction of the total students got a perfect score on the test?
Answer: 1/30
Step-by-step explanation:
3/10 of 90 = 27
1/9 of 27 = 3
3/90 = 1/30
Answer:
3 1/30
Step-by-step explanation:
90 * 3/10 got A
of these 1/9 = perfect
90 * 3/10 * 1/ 9 = 3
3 out of 90 = 3/90 = 1/30
What is the multiplication problem that means the same thing as the division 1/3 ÷ 7 problem ?
3 x 1/7
1/7 x 1/21
1/3 x 1/7
1/3 x 7
Answer:
1/3 x 1/7
Step-by-step explanation:
when dividing fraction you take the reciprocal of the divisor and multiply.
Answer:
1/3 x 1/7
Step-by-step explanation:
1/3 x 1/7
Multiplying the reciprocal.
Which expression is equivalent to 6x - 24?
A. 6(x-24)
B. 6(x-18)
C. 6(x-4)
D. 24(x-6)
Answer:
C
Step-by-step explanation:
If you factorise 6x-24 you will get 6(x-4) as 6 times x equals 6x and 6 times -4 equals -24.
What is the median?
1 ,1 ,2 ,1 ,2
Answer:
1
Step-by-step explanation:
Median is the middle number when the numbers are arranged least to greatest.
So:
1, 1, 1, 2, 2
1, 1, 1, 2, 2
1 is the middle number in this data set.
Hope this helps! :D
For the function f (x) = 4x - e determine
X such that f (x) 0
Answer:
derivative is a function which measures the slope. It depends upon x in some way, and is found by differentiating a function of the form y = f (x). When x is substituted into the derivative, the result is the slope of the original function y = f (x).
There are many different ways to indicate the operation of differentiation, also known as finding or taking the derivative. The choice of notation depends on the type of function being evaluated and upon personal preference.
Suppose you have a general function: y = f(x). All of the following notations can be read as "the derivative of y with respect to x" or less formally, "the derivative of the function."
f'(x) f' y' df/dx dy/dx d/dx [f(x)].
[HINT: don't read the last three terms as fractions, read them as an operation.
For example, read: " dx/dy = 3x"
As: "the function that gives the slope is equal to 3x"
Let's try some examples. Suppose we have the function : y = 4x3 + x2 + 3.
After applying the rules of differentiation, we end up with the following result:
dy/dx = 12x2 + 2x.
How do we interpret this? First, decide what part of the original function (y = 4x3 + x2 + 3) you are interested in. For example, suppose you would like to know the slope of y when the variable x takes on a value of 2. Substitute x = 2 into the function of the slope and solve:
dy/dx = 12 ( 2 )2 + 2 ( 2 ) = 48 + 4 = 52.
Therefore, we have found that when x = 2, the function y has a slope of + 52.
Now for the practical part. How do we actually determine the function of the slope? Almost all functions you will see in economics can be differentiated using a fairly short list of rules or formulas, which will be presented
Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction pi over 4 endfraction)) minus 2 y = negative 3 sine (2 (x startfraction pi over 4 endfraction)) minus 2 y = 3 cosine (2 (x startfraction pi over 4 endfraction)) minus 2 y = negative 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2
The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
How to convert sine of an angle to some angle of cosine?We can use the fact that:
[tex]\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)[/tex]
to convert the sine to cosine.
Which trigonometric functions are positive in which quadrant?In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.In second quadrant(π/2 < θ < π), only sin and cosec are positive.In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)
Here, the given function is:
[tex]y= 3\cos(2(x + \pi/2)) - 2[/tex]
The options are:
[tex]y= 3\sin(2(x + \pi/4)) - 2[/tex][tex]y= -3\sin(2(x + \pi/4)) - 2[/tex][tex]y= 3\cos(2(x + \pi/4)) - 2[/tex][tex]y= -3\cos(2(x + \pi/2)) - 2[/tex]Checking all the options one by one:
Option 1: [tex]y= 3\sin(2(x + \pi/4)) - 2[/tex][tex]y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2[/tex]
(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.
This option if would be true, then from option 1 and this option, we'd get:
[tex]-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0[/tex]
which isn't true for all values of x.
Thus, this option is not same as the given function.
Option 3: [tex]y= 3\cos(2(x + \pi/4)) - 2[/tex]The given function is [tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]
This option's function simplifies as:
[tex]y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2[/tex]
Thus, this option isn't true since [tex]\sin(2x) \neq \cos(2x)[/tex] always (they are equal for some values of x but not for all).
Option 4: [tex]y= -3\cos(2(x + \pi/2)) - 2[/tex]The given function simplifies to:[tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]
The given option simplifies to:
[tex]y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2[/tex]
Thus, this function is not same as the given function.
Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
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Answer:
a
Step-by-step explanation:
Can someone solve this today please
Answer:
B
Step-by-step explanation:
4,000 is a constant so i cannot be a rate. That instantly eliminates 'D' as an option. If x = 0 at the very start that means the 4,000 must be how many gallons of water there is initially.
Vector u has an initial point at (−5, 2) and a terminal point at (−7, 9). Which of the following represents u in trigonometric form?
u = 7.28(cos 74.055°i + sin 74.055j)
u = 7.28(cos 105.945°i + sin 105.945°j)
u = 7.28(sin 74.055°i + cos 74.055°j)
u = 7.28(sin 105.945°i + cos 105.945°j)
The vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j).
How to determine a vector in polar form
Let be a vector in rectangular form, that is, a vector of the form (x, y). A vector in polar (trigonometric) form is defined by the following expression: (r, θ)
And the magnitude (r) and direction of the vector (θ), in degrees, are, respectively:
Magnitude[tex]r = \sqrt{x^{2}+y^{2}}[/tex] (1)
Direction[tex]\theta = \tan^{-1}\frac{y}{x}[/tex]
And the vector in rectangular form is described below:
(x,y) = (-7, 9) - (-5, 2)
(x,y) = (-2, 7)
And its polar form is determined below:
[tex]r = \sqrt{(-2)^{2}+7^{2}}[/tex]
[tex]r = \sqrt{53}[/tex]
r ≈ 7.280
θ = tan⁻¹ (-7/2)
θ ≈ 105.945°
And the vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j). [tex]\blacksquare[/tex]
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what makes an equation a perfect square
Answer:
the way you form it or the material you use should be perfect
PLS HELP ME ONLY GOT 5 MIN LEFT!!!! LOTS OF POINTS
Answer:
G is the correct answer
.
.
need help asapppl !!!!
Answer:
After 12 days both bamboo plants were 9ft tall
Find the value of each variable. Show all the work
Answer:
x° = 45°
y° = 90°
z° = 45°
Step-by-step explanation:
Angles on a straight line add up to 180°
⇒ z° + 135° = 180°
⇒ z° = 180° - 135°
⇒ z° = 45°
The dashes on the side lengths mean that the sides are of equal length. Therefore this is an isosceles triangle. The base angles of an isosceles triangle are equal.
⇒ x° = z°
⇒ x° = 45°
The sum of the interior angles of a triangle is 180°
⇒ x° + y° + z° = 180°
⇒ 45° + y° + 45° = 180°
⇒ y° = 180° - 45° - 45°
⇒ y° = 90°
A hot air balloon is 1,200 feet above the ground. The angle of depression from the basket of the hot air balloon to the base of a monument is 54°.
Which equation can be used to determine the distance, d, in feet, from the basket of the hot air balloon to the base of the monument?
Answer:
c
Step-by-step explanation:
And The opposite of the 54 is 1200s. That 1200 go on top and then below the hypothesis D. So Since it's opposite of hypotenuse opposite over hypotenuse, we signed 54 is 1200 over d. Here's what he says, Another way to look at this is like this 1200 Indians. This dash line drew is also 1200 And when it comes to this 54° angle, it's the same thing opposite. 1200 divided by the hypothesis of D.
select expression that is equivalent to (x^2-9) please help
Answer:
D (x-3)(x+3)
It's the difference of two squares
simplifi the expresion 3^-3
Answer:
0,(037)
Step-by-step explanation:
At this question, if I understood correctly, the answer for that is 0,037037037037...
You can write it as 0,(037)
I hope that I helped :)
what is the area of a circle with the radius of 5ft
Answer:
25pi or 78.54
Step-by-step explanation:
The formula for the area of a circle is pi*r^2
We know that r=5ft
A=pi*(5ft)^2
A=25pi ft2
You can write it as 25pi ft2 but you can also write as 25*pi ft2 which is about 78.54 ft2
Hope that I helped :)
Please help
In a class of 147 students, 95 are taking math (M), 73 are taking science (S), and 52 are taking both math and science. One student is picked at random. Find each probability.
P(taking math but not science)
Answer:
The probability that a student taking only math will get picked is approximately 29%
Step-by-step explanation: This is because out of the total number of students taking math (95), 52 of such students are also taking science. In order to get the number of students only taking math you have to do 95-52=43 and to put that against the amount of total students the ratio would be 43:147 or 42/147 and if you plug 42/147 into a calculator you will recieve a long decimal that you can then round to 29%.
Arnold has recorded the number of chirps per minute ( x) that crickets make
at different temperatures (y).
He has determined that the association is linear and that the line of best fit is y= 1/4x + 50.
What is the interpretation of the slope and y-intercept of this equation?
Answer:
A)
Step-by-step explanation:
The slope predicts a temperature increase of about [tex]\frac{1}{4}[/tex]º for every increase of 1 chirp per minute. The y-intercepct shows that when the crickets are not chirping (x = 0), the temperature is 50º
Which of the following exponential regression equations best fits the data shown below?
X -4 -3 -2 -1 0 1 2 3 4
y 0.01 0.04 0.16 0.75 5 16 65 276 1251
OA. y = 2.08 -2.61^x
OB. y= 3.53 4.37^x
O C. y=6.37.5.02^x
OD. y= 7.13 6.09^x
Answer:
B. 3.53*4.37^x
Step-by-step explanation:
See attached graph.
The exponential regression equations that best fits the data is y = 3.53(4.37)ˣ
What is exponential regression equation?The equation of an exponential regression model takes the following form: y = abˣ where: y: The response variable x: The predictor variable a, b: The regression coefficients that describe the relationship between x and y.
Given is a table, we need to determine the exponential regression equation, for the same,
So,
The general exponential regression equations is, y = abˣ
where, a is initial value and b is growth factor.
Using graph calculator, we get,
a = 3.53
b = 4.37
Put the value of a and b in general equation, to find the exponential regression equation.
y = 3.53(4.37)ˣ
Hence the option B is correct.
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Drag the tiles to the correct boxes to complete the pairs. Match the events described to the likelihood of their occurrence. unlikely impossible certain neither likely nar unlikely Event Likelihood Edna has a bag of chocolates. There are 12 milk chocolates, 14 dark chocolates, and 9 chocolate-covered almonds. She reaches into the bag without looking and picks one chocolate. What is the likelihood that Edna picks a chocolate-covered cherry from the bag? Neal used magnetic letters to spell the word communication on his file cabinet One of the magnets fell on the floor. What is the likelihood that an a fell on the floor? Each letter of the word Mississippr(including repeating letters) is written on a separate card, and the cards are placed on a table with the letters facing down. If you randomly pick a card, what is the likelihood that it will be either an sor a o? Dorothy is a fourth-grade teacher at an all-girls school. She calls on one of her students to give a presentation on the different parts of a plant. What is the likelihood that she will choose a girl to make the presentation?
NEED HELP ASAP WILL GIVE BRAINIST TO BEST AWNSER
The probability of picking a chocolate-covered cherry is 0.
The probability that an a fell on the floor is 0.08
The probability that an a or a o would be picked is 0.36
The probability a girl would be picked is 1.
What is the probability?
Probability is used to calculate the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of picking a chocolate-covered cherry is zero because there is no chocolate-covered cherry in the bag.
The probability that an a fell on the floor = number of a in the letter / total number of letters
= 1/13 = 0.08
The probability that an s or a o would be picked is = (number of s in the letter / total number of letters) + (number of 0 in the letter / total number of letters)
= 4/11 + 0 = 4/11 = 0.36
The probability a girl would be picked is one since its an all-girls school.
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1. The length and width of a certain rectangle with an area of 12 units² can be expressed as x + 2 and
x + 3 respectively. What is the value of x? NOTE: only an algebraic solution will earn credit.
[tex]~~~~(x+2)(x+3) = 12\\\\\implies x^2+3x+2x+6 -12=0\\ \\\implies x^2 +5x -6 = 0\\\\\implies x^2 +6x-x-6 = 0\\\\\implies x(x+6) -(x+6) =0\\\\\implies (x+6)(x-1)=0\\\\\implies x=1~~~~~~~~~;[x\neq -6~ \text{because length cannot be negative.}}][/tex]