Answer:
[tex]x=4[/tex] or [tex]x=2[/tex]
Step-by-step explanation:
When given the following equation,
[tex]2(x-4)^2+10=30[/tex]
One must follow the order of operations to solve the equation and get a valid result. The order of operations states the following,
1. Parenthesis
2. Exponents
3. Multiplication/ Division
4. Addition/ Subtraction.
Normally, one would combine the terms in the parenthesis, but since they are unlike terms, one will have to undo the exponents first. Expand the binomial.
[tex]2(x-4)^2 + 10 = 30\\\\2(x^2-8x+16)+10=30[/tex]
Now distribute, multiply every term inside the parenthesis by the term outside,
[tex]2(x^2-8x+16)+10=30\\\\2(x^2)+2(-8)x+2(16) + 10 = 30[/tex]
Simplify,
[tex]2(x^2)+2(-8x)+2(16)+10=30[/tex]
[tex]2x^2 -16x +32 +10 = 30[/tex]
[tex]2x^2 -16x +42=30[/tex]
Inverse operations,
[tex]2x^2 -16x + 42 = 30\\-30\\\\2x^2 - 16x + 12= 0[/tex]
To simplify the equation, divide all terms by (2).
[tex]x^2 - 8x +6=0[/tex]
Factor, rewrite the quadratic equation as a product of linear equations,
[tex](x-4)(x-2)=0[/tex]
Solve using the zero product property. The zero product property states that any number times zero equals zero,
[tex](x-4)(x-2)=0\\\\x=4,x=2[/tex]
36x + 324 = 720 find x
Answer:
x = 11
Step-by-step explanation:
First, subtract 324 from both sides:
36x + 324 = 720
36x = 396
Divide each side by 36:
x = 11
So, the answer is x = 11
Answer:
x=11
Step-by-step explanation:
first get rid of the 324 so we can leave x by itself.
324-324=0
to keep it balanced subtract it from 720
720-324=369
that leaves us with
36x=369
lastly, we have to divide both sides by 36.
36/36=0
369÷36=11
Therefore, x=11
hope this helps
What is the surface area of the sphere below?
5
O A. 125r units2
B. 100% units2
C. 125% 3 units2
D. Cannot be determined
The surface area is B
Principle: $ 250 Rate: 2.5% compounded Semiannually Time: 1.5 yr(s) *
Your answer
Answer:
A=259.43
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r=R/100
r=2.5/100
r=0.025 rate per year,
then solve the equation for A
A=P(1+r/n)
A=250.00(1+0.025/1)
A=250.00(1+0.025)
A=$259.43
What are 64 real square roots
Answer:
8
Step-by-step:
Find the calculator, look for the square root symbol and put 64 in there.
A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1700 feet, what
are the dimensions of the field?
A) Write an equation you can use to answer the given question. Let w be the width of the field. Do not
solve the equation yet.
The equation is
X (Make sure you use the correct variable.)
B) Use your equation to find the dimensions of the field.
The width of the field is
x feet.
The length of the field is
x feet.
Answer:
I. L = 10.35 feet
II. W = 93.15 feet.
Step-by-step explanation:
Let the length of the rectangle be L.
Let the width of the rectangle be W.
Given the following data;
Perimeter of rectangular field = 1700 feet
Translating the word problem into an algebraic expression, we have;
W = 9L
Mathematically, the formula for the perimeter of a rectangle is;
P = 2(L + W)
A. To write an equation;
X = P = 2(L + W)
B. To find the dimensions of the field;
207 = 2(L + 9L)
207 = 2L + 18L
207 = 20L
L = 207/20
L = 10.35 feet
To find the weight;
W = 9L
W = 9 * 10.35
W = 93.15 feet.
Therefore, the width of the field is
93.15 feet and the length of the field is
10.35 feet.
I need the answer fast pls
Answer:
I think D
Hope this helps!!
The following scatter plot represents the number of views a video gets each day.
(b) Use a graphing calculator or other technology to write a regression equation to model the data.
(c) A video is considered viral if it receives more than three million views by the time it has been posted for 10 days. Use the model from Part (b) to determine if the video will receive enough views to be considered a viral video. Show your work.
Answer:
y = 1.0535(4.9512)^x
It can be considered a viral video
Step-by-step explanation:
Using the exponential regression calculator, the regression model obtained is :
y = 1.0535(4.9512)^x
Using the model, we can determine if a video can be considered viral ;
Number of days, x = 10
y = 1.0535(4.9512)^10
y = 1.0535(8853290.1338)
y = 9,326,941.15
Hence, video will receive way over 3 million reviews, a review of about 9,326,941, hence, it can be considered a viral video.
Mrs. Cole gave a math quiz to her classes. Below is a box plot that represents the results of the quiz.
Answer:
Where is the box plot?
Step-by-step explanation:
You did not show the results of the quiz therefore I can not answer. Also there is no question content in the sentences so even if I did have a box plot I still would not be able to answer. Give us more information.
I really need help on this if someone knows the answer pls help
Answer:
14.75
Step-by-step explanation:
x = 1*1*0.5 = 0.5
y = 1.5*1.5 = 2.25
g = ((2.5+1.5)\2) * 2 = 4
t = 4*2 = 8
total = 0.5 +2.25 +4 +8 - 14.75
A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century the mean number of the major hurricanes to strike U.S mainland per year was 0.6. Find the probability that the number of major hurricane to strike U.S mainland in any any give year is: a) Exactly one b) At most one c) More than one
Answer:
a) 0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.
b) 0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.
c) 0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.
Step-by-step explanation:
We have the mean during an interval, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
During the 20th century the mean number of the major hurricanes to strike U.S mainland per year was 0.6.
This means that [tex]\mu = 0.6[/tex]
Find the probability that the number of major hurricane to strike U.S mainland in any any give year is:
a) Exactly one
This is P(X = 1). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293[/tex]
0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.
b) At most one
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.6}*0.6^{0}}{(0)!} = 0.5488[/tex]
[tex]P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5488 + 0.3292 = 0.878[/tex]
0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.
c) More than one
This is:
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.878 = 0.122[/tex]
0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.
David measures a rectangular piece of wood. The length is 8 feet and the width is 2 feet. What is the area, in square feet, of the piece of wood? A = lw
A) 6
B) 15
C) 20
D) 24
E) 30
Correct me if wrong :)
Gabriela has dinner at a cafe and the cost of her meal is \$45.00$45.00dollar sign, 45, point, 00. Because of the service, she wants to leave a 15\%15%15, percent tip.
What is her total bill including tip?
9514 1404 393
Answer:
$51.75
Step-by-step explanation:
The multiplier of the bill with the tip added is 1 +15% = 1.15.
1.15×$45 = $51.75 . . . . Gabriela's total bill
Find x??...................
Answer:
x=8
Step-by-step explanation:
The sides are of equal length
x+2 = 2x-6
Subtract x from each side
x+2-x = 2x-6+x
2 = x-6
Add 6 to each side
2+6 = x-6+6
8 =x
Answer:
X=8
Step-by-step explanation:
x+2=2x-6
-x+2=-6
-x=-8
x=8
The degree of the polynomial 10x^3 + 2x^m y - 4y is 3. What is the value of m?
A.) 1
B.) 2
C.) 3
D.) 4
Answer:
1
Step-by-step explanation:
x is 1 and y is 1 and the total is three so 1
Find the median and mean of the data set below:
14, 25, 41, 4, 23, 8, 32
The largest 2-digit number is 99. How many 2-digit numbers must be in a set in order to apply the pigeonhole principle to conclude that there are two distinct subsets of the numbers whose elements sum to the same value
Answer:
The solution can be defined as follows:
Step-by-step explanation:
[tex]\to n = 10[/tex]
There are 210 = 1,024 sub-sets of 10 entries, however, the number of enters between the lower and upper limits total of 10 different submissions between 1 and 100 can be as low only as 901 (= 955 - 55 + 1). There has to be a minimum level of at least 1 subset with much more subgroups than possible, which equals at least two sets. Call for two main sub, S' and T' equivalent.
Let
[tex]C = S' \cap T'[/tex]
when
[tex]S = S' - C \\\\T = T' - C\\\\[/tex]
Then[tex]S \ and\ T[/tex] are disjoint
[tex]sum(S) = sum(S' - C)\\\\[/tex]
[tex]= sum(S') - sum(C)\\\\= sum(T') - sum(C)\\\\= sum(T' - C)\\\\= sum(T)\\[/tex]
The graph shows the system of equations below.
2x-3y=-6
y= -1/3x=4
Which statement is supported by the graph?
The blue line represents the equation 2x-3y=-6 , and the solution to the system of equations is (–6, –2).
The blue line represents the equation 2x-3y=-6 , and the solution to the system of equations is ( –2, –6).
The red line represents the equation 2x-3y=-6 , and the solution to the system of equations is (2, –4).
The red line represents the equation 2x-3y=-6 , and the solution to the system of equations is (–4, 2).
We want to describe the system of equations by analyzing the graph. We will see that the correct option is:
"The blue line represents the equation 2x -3 y = -6, and the solution to the system of equations is (–6, –2)."
We know that the equations are:
y = (-1/3)*x - 4
2x - 3y = -6
Notice that the y-intercept of the first equation is -4, and the line that intercepts the y-axis at -4 is the red line. So the red line represents the equation y = (-1/3)*x - 4, while the blue line represents the other equation.
Also, remember that the solution of a system of equations is given by the point where the graphs of the equations intercept, here, we can see that the lines intercept at (-6, -2), so the solution of the system is (-6, -2)
Then the correct option is:
The blue line represents the equation 2x-3y=-6, and the solution to the system of equations is (–6, –2).
If you want to learn more, you can read:
https://brainly.com/question/9351049
Answer:
a:The blue line represents the equation 2x-3y=-6 , and the solution to the system of equations is (–6, –2).
Step-by-step explanation:
what is the scientific notation if 36000x10^-8?
Answer:
3.6 * 10^-4
Step-by-step explanation:
36000x10^-8
The number must be between 1 and 10
36000.
Move the decimal 4 places to the left, so add 4 to the exponent
3.6 * 10^(-8+4)
3.6 * 10^-4
Answer:
the scientific notation of
[tex] 36000×10^{-8}=36000/100000000=3.6×10^{4}/10^{-8}[/tex]
[tex]=3.6×10^{4-8}=3.6*10^{-4}[/tex]
simplify 4^9/4^3
can someone help me with this?
Answer:
4096
Step-by-step explanation:
Need to know how you got it? Comment on this answer.
Find the volume of this prism.
9 cm
12 cm
6 cm
Help pls
Answer:
324 cm^3
Step-by-step explanation:
Volume = l x w x h / 2
V = 12 x 6 x 9 / 2
V = 648 / 2
V = 324 cm^3
Answer:
V = 324 cm³
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = area of triangular end × length
A of triangle = [tex]\frac{1}{2}[/tex] × 6 × 9 = 3 × 9 = 27 cm² , then
V = 27 × 12 = 324 cm³
If ß is the small angle is a 3-4-5 right triangle, then sin ß = ?
Answer:
sin β = sin(36.87) ≈ -0.73733168456
Step-by-step explanation:
The small angle in a 3-4-5 triangle is 36.87 and when you put that into a calculator you are left with roughly -0.73733168456.
If a right circular cylinder and oblique cylinder both have a height of 19
inches and diameter of 10 inches, do they have the same volume? (Use
T = 3.14)
Answer:
Yes.
Step-by-step explanation:
The diameters are the same so the radii are the same also.
The volume of both is 3.14r^2h.
The radius r and height h is the same for both cylinders.
The volume = 3.14 * 5^2 * 19 = 1491.5 in^3.
What is the image of F for a dilation with center (0, 0) and a scale factor of 10? (−30, −30) (30, 30) (30, −30) (−30, 30)
Answer: (-30,30)
Step-by-step explanation:
f = -3,3, -3 times 10 = -30 and 3 times 10 = 30 etc
The volume of a rectangular box with a square base remains constant at 500 cm3 as the area of the base increases at a rate of 6 cm2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 15 cm long.
Answer:
the rate at which the height of the box is decreasing is -0.0593 cm/s
Step-by-step explanation:
Given the data in the question;
Constant Volume of a rectangular box with a square base = 500 cm³
area of the base increases at a rate of 6 cm²/sec
so change in the area of the base with respect to time dA/dt = 6 cm²/sec
each side of the base is 15 cm long
so Area of the base = 15 cm × 15 cm = 225 cm²
the rate at which the height of the box is decreasing = ?
Now,
V = Ah
dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0
⇒ dh/dt = -hdA/dt / A
we substitute
dh/dt = [ -( 500 / 225 ) × 6 ] / 225
dh/dt = [ -(2.22222 × 6) ] / 225
dh/dt = [ -13.3333 ] / 225
dh/dt = -0.0593 cm/s
Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s
if i had 4 eggs
My rabbit lays 4 eggs
A thief gives me 3 eggs
My farm rooster lays 5 eggs
How many eggs to i have??
Answer:
Will rabbit lay egg??
Step-by-step explanation:
If it lays in ur case then 4+4+3+5=16
Solve the inequality graphically.
6^x < 3^x
a. X> 1
b. x>0
C. X<1
d. x<0
Answer:
D, X<0
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How do you write an equation of a circle?
Step-by-step explanation:
The equation of a circle is:
(x-h)² + (y-k)² = r² where the center is at (h,k) and r is the radius.
so if you need the equation of a circle centered at (-3,5) and a radius of 7 would be:
(x+3)² + (y-5) = 49
Alguien me ayuda con este ejercicio: 10.- Investiga cuánto tiempo dura el embarazo en otras especies de mamíferos. Elige tres especies de mamíferos y compara la duración de sus embarazos con la duración en el ser humano.
Answer:
22
Step-by-step explanation:
So what would be the answer?
Answer:
i
Step-by-step explanation:
Answer:
did you forget a picture?
Step-by-step explanation:
if you did, either add it in the comments, or make a new question