Answer:
Below
Step-by-step explanation:
x^2 + 32 + 116 = 12x 1st intermediate step: put everything on one side
x^2 -12x + 148 = 0 2nd intermediate step : re-arrange with constant on R
x^2 -12x = -148 3 rd intermediate step : take 1/2 of the 'x' coefficient
square it and add to both sides
x^2 -12x + 36 = -148 + 36 4th intermediate step : simplify
(x-6)^2 = -112
The product of 5 and a number is the same as 11 less than 6 times the number. Find the number.
a. Write an equation that represents the given statement.
b. Solve the problem.
The number is 11.
Lets assume that the P is the product of the number 'x' and 5, then the equation will become :
P = 5x .......i
now given that the product P is same as the 11 less than 6 times the number 'x'., therefore the equation will become :
P = 6x -11 ......ii
Now from i and ii,
5x = 6x -11 ,
11 = 6x - 5x
therefore, x = 11.
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(3,6) relfect it across the line -x+2y=30
The equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.
Given equation is -x+2y = 30
and passing through the point (3,6).
If two lines are parallel, their slopes will be equal.
We know that equation for parallel lines is y = 3x+c
Now, -x + 2y = 30
= 2y = 30 + x
[tex]= y = \frac{30+x}{2}[/tex]
[tex]= y = \frac{30}{2} +\frac{x}{2} \\\\= y = 15 + \frac{x}{2}[/tex]
Therefore slope = [tex]\frac{1}{2}[/tex]
Equation of line with slope and passing through (3,6)
[tex]y-y_{1} = m(x-x_{1}) \\\\y - 6 = \frac{1}{2} (x-3)\\\\[/tex]
2(y-6) = 1(x-3)
2y - 12 = x - 3
x - 2y + 9 = 0
Hence the answer is the equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.
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The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73% of
in the carbon-14 expected in living matter, when did the tree die?
The tree died about ] years ago.
Do not round until the final answer. Then round to the nearest whole number.)
Answer:
Time 2 540 years
Step-by-step explanation:
T = 5 600 yares - Half-life
73% - Carbon content
N = 0.73·N₀
Decay constant:
λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124 (years)⁻¹
Law of radioactive decay:
N = N₀·e^(-λ·t)
0.73·N₀ = N₀·e^(-λ·t)
0.73 = e^(-λ·t)
ln (0.73) = -λ·t
t = ln (0.73) / (-λ) = ln (0.73) / (- 0.000124) ≈ 2 540 years
write an equation of the line that contains point (-2,2) and is perpendicular to x - 2y = 5 in standard form.
Answer:
[tex]y = -2x-2[/tex]
Step-by-step explanation:
A line being perpendicular means that it has a slope that is an opposite reciprocal of the other line.
In this case:
[tex]x - 2y = 5\\-2y = -x + 5\\y = \frac{x}{2} - \frac{5}{2}[/tex]
The slope of this line is [tex]\frac{1}{2}[/tex] and so the perpendicular slope would be [tex]-2[/tex].
Using the point slope form:
[tex]y - y_1 = m(x-x_1)\\[/tex]
Substitute values:
[tex]y - y_1 = m(x-x_1)\\y - 2 = -2(x+2)\\y -2 = -2x-4\\y = -2x-2[/tex]
The side of a square field is 125 m. There are two paths running inside it along the sides, crossing each other at the centre. The width of the lengthwise path is 3 m and the width of the breadthwise path is 5 m. Find the area of the two pathways.
The area of lengthwise pathway is 610 m²
The area of breadthwise pathway is 360 m²
The total area of the two pathways is 985 m²
Given,
The side of square field = 125 m
The width of the lengthwise path = 3 m
The width of the breadthwise path = 5 m
We have to find the area of the two pathways.
Here,
Area of path on length wise = (125 - 3) × 5 = 610 m².
Area of path on breadth wise = (125 - 5 ) × 3 = 360 m²
Area of rectangle at intersection of paths = 5 × 3 = 15 m².
Thus the Total area of two pathways = 610 + 360+15 = 985 m²
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A swimming pool is in the shape of the following figure. The homeowner wishes to build a fence around the perimeter of the pool. How many feet of fencing are required?
Round your answer to the nearest hundredth, if necessary.
71.849 feet of fencing are required.
Given:
In a rectangle two sides are 13 feet and 12 feet.
In right angled triangle sides are 15 feet and 13 feet.
Let x be the hypotenuse of the triangle.
From rectangle opposite sides are equal so the other two sides are equal to 12 feet and 13 feet.
According to pythagorean theorem:
[tex]15^{2} +13^{2} =x^{2}[/tex]
x = [tex]\sqrt{225+169}[/tex]
x = 19.849
The perimeter of the pool = 15 + 12 + 13 + 12 + 19.849
= 27 + 13 + 12 + 19.849
= 52+19.849
= 71.849 feet.
Therefore 71.849 feet of fencing are required.
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help you have 3/8 of a pound of chips if 1/6 of a pound is a serving how many servings are their
Answer:
2 1/4 servingsStep-by-step explanation:
Given
Total amount of chips = 3/8 of a pound,Each serving = 1/6 of a pound.Number of servings:
3/8 ÷ 1/6 = 3/8 × 6 = 9/4 = 2 1/4Need an answer quick please
The required amount in the savings account=$2704.05
What is simple interest?
Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.
P=2700, r=0.3%=0.003, t= 0.5 year
A= P(1+rt)
= 2700(1+ 0.003*0.5)
= 2700(1+ 0.0015)
= 2700(1.0015)
= 2704.05
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Complete the calculation to convert
18
pounds
(lbs)
to grams
(g)
given that
1
lb.
=
453.92
grams.
The conversion of 19 pounds to grams is 8170.74 grams.
How to calculate the value?From the information illustrated, it should be noted that it was illustrated that 1 pound = 453.93 grams.
In this case, in order to fund the value of 18 pounds, we will have to multiply 18 by 453.93 grams.
This will be calculated as:
18lb = 18 × 453.93 grams.
= 8170.74 grams
The value is 8170.74 grams.
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PLS HELP ASAPPPP URGENT
Answer: 4 + (2*3)^2
Step-by-step explanation:
Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels four miles per hour. The southbound boat goes eight miles per hour. How many hours will it take them to be 66 miles apart?
It will take the boat going north 16.5hrs and the boat going south will take it 8.25hrs
Step-by-step explanation:
divide 66/4 for the north boat and 66/8 for the south boat
Which integer makes the following sentence true? -10 < ? < -1
Answer:
Any of the following will work: -9,-8,-7,-6,-5,-4,-3, or -2,
Step-by-step explanation:
What does < mean?
The less than sign shows that the number being compared is LESS than the other number.
Think: 9 < 100 showing that the number 9 is less than the number 100
What does > mean?
The greater than sign shows that the number being compared is GREATER than the other number.
Think: 100 > 9 showing that 100 is greater than the number 9
What is an integer?
Integers are all whole positive and negative numbers including zero.
Think: -13 and 13 are integers but 13.445 or -13.445 are not.
How can we prove these answers?
Simply looking at a number line, we can fill in what numbers would be greater than -10 but less than -1. Remember, these numbers must be whole numbers.
After a flood, a creeks water level changes by -2 4/5 ft in 3 1/2 h. What is the average change in the creeks water level each hour
Answer
0.8 ft/hr
Explanation
2 4/5 ÷ 3 1/2 = 2.8 ÷ 3.5 = 0.8
Question 6(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Can a triangle be formed with side lengths 13, 7, and 5? Explain.
O Yes, because 13 +7 > 5
O Yes, because 13+5<7
O No, because 5+7 < 13
O No, because 5+7 > 13
Answer:
the first one
Step-by-step explanation:
one because 13+7= 20 and 20 is a bigger than 5 so there for it i one
Question is attached in the photo! Please answer with the local maximums, minimums, and extrema's! Thank you :)
local maximum(s) :
local minimums(s) :
local extrema :
The number local extremas to the function is given as follows:
3.
They are classified as follows:
Local maximum: 2.Local minimum: 1.What are the local extremas of a function?The local extremas of a function are the turning points of the graph of the function, and they are classified as follows:
Local maximum: the function changes from increasing to decreasing.Local minimum: the function changes from decreasing to increasing.The graph of the function has three turning points, and they are defined as follows:
Local maximum close to x = -4, as the function changes from increasing to decreasing.Local minimum close to x = 2, as the function changes from decreasing to increasing.Local maximum close to x = 1, as the function changes from increasing to decreasing.More can be learned about the local extremas of a function at https://brainly.com/question/24367710
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4. Look at the following inequality.
x(5+2) > 22
Which value will make this inequality true?
A. 1
B.2
C.3
D.4
Answer:
D.4
Step-by-step explanation:
You can try replacing x value with the answer one by one.
A. 1(7) > 22 = 7 > 22, false, 7 smaller than 22
B. 2(7) > 22 = 14 > 22, false, 14 smaller than 22
C. 3(7) > 22 = 21 > 22, false, 21 smaller than 22
D. 4(7) > 22 = 28 > 22, true, 28 is larger than 22
5. Minnie had 9 coins in her
purse. If they were nickels
and dimes and totaled
$0.65, how many of each
coin did she have?
Answer:
5 nickels and 4 dimes
Step-by-step explanation:
5 nickels = 25 (5 x 5)
4 dimes = 40 (4 x 10)
can anyone help me with these please and thank you ?
Membership costs for belonging to a gym for a certain number of months are shown in the table below.
Answer:
y = 35.5x - 10
Step-by-step explanation:
If we graph the function with the help of the given table,
Since, there is a common difference in each term of 'cost of gym membership'
d = 61 - 25.5 = 35.5
d = 96.5 - 61 = 35.5
Graph will represent a linear function.
Let the equation of the line is,
y - y' = m(x - x')
where (x', y') is a point lying on the graph and 'm' is the slope.
Two points lying on the graph are (1, 25.5) and (2, 61).
Slope of the line =
=
= 35.5
Equation of the line passing through (1, 25.5) having slope 'm' = 35.5
y - 25.5 = 35.5(x - 1)
y = 35.5x - 35.5 + 25.5
y = 35.5x - 10
Here x = duration of membership
y = membership price
Therefore, equation representing Fit Zoom's membership price equation will be,
y = 35.5x - 10
someone please help me ty
Answer:
40
Step-by-step explanation:
We divide 317 by 8 to see how much for each table
317/8 is 39.625
We round up for the next whole number since the last table is probably not filled all the way
So we need 40 tables
Hopes this helps please mark brainliest
Answer:
40 tables
Step-by-step explanation:
317 divided by 8 equals 39.625
Round the answer.
Since the number after the decimal is bigger than 4, round up to the nearest whole number which is 40.
P.S. this is simple math. No offense, but you should have been able to figure this out yourself. It's not that hard. Again, not trying to offend you. Just letting you know.
if a interior angle of a regular polygon is 174.5 how many sides does it have
Answer: 177.936.....
Step-by-step explanation:but since this number is not a natural number its not possible
- Given the table below write an explicit
equation .
n
1
2
3
4
5
f(n)
5
58
13
20
29
The explicit equation for the table is,
f(n) = n² + 4
Given, the values of an explicit function,
Let the function be,
f(n) = an² + bn + c
f(1) = a(1)² + b(1) + c
5 = a + b + c
f(2) = a(2)² + b(2) + c
8 = 4a + 2b + c
f(3) = a(3)² + b(3) + c
13 = 9a + 3b + c
On subtracting the equations, we get
5 = 5a + b
3 = 3a + b
Again, on subtracting we get
2 = 2a
a = 1
On putting the values we get,
b = 0.
a + b + c = 5
1 + 0 + c = 5
c = 4
Hence, the explicit equation for the table is,
f(n) = n² + 4
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A ABC has a right angle at C, BC = 9.2 centimeters, and mA = 63°.
What is CA?
In the right-angled triangle ABC, CA is 4.2cm.
What is a right-angled triangle? How to identify it?
Any angle that is a right angle or has one of its interior angles equal to 90 degrees is considered to be in a right-angled triangle. This triangle is also known as the right triangle or the 90-degree triangle for this reason. Trigonometry heavily utilizes the right triangle. In this article, let's learn more about this triangle.
By applying Pythagoras' theorem, one can determine whether a triangle has a right angle. If the squares of the triangle's two shorter sides equal the square of the hypotenuse, a right angle is present.
Solution explained:
A/Q, we have
BC = 9.2cm and m∠A = 63°
Using the tangent ratio formula (ratio of a side that is not the hypotenuse to a side that is near to an angle), we get
[tex]tanA = \frac{BC}{CA}[/tex]
tan 63° = [tex]\frac{9.2}{CA}[/tex]
CA = [tex]\frac{9.2}{1.96}[/tex] (tan 63° = 1.96)
CA = 4.687 ≅ 4.7cm
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Simplify the complex numbers and match them with the correct values.
Answer:
-i, 1, i, -1, 1, -1
Step-by-step explanation:
You want the simplified form of various expressions involving powers of i.
Powers of iThe definition of i is ...
i = √(-1) or i² = -1
This value can be used to find other powers:
i³ = (i²)(i) = -i
i⁴ = (i²)² = (-1)² = 1
This means any power of i is equivalent to that power modulo 4.
Application[tex]-i^{25}=-i^1 = \boxed{-i}\\\\i^{16}=i^0=\boxed{1}\\\\i^{17}=i^1=\boxed{i}\\\\-i^{32}=-i^0=\boxed{-1}\\\\i^{-9}\times -i^{11}=-i^{-9+11}=-i^2=-(-1)=\boxed{1}\\\\\dfrac{i^{23}}{-i^{11}}=-i^{23-11}=-i^{12}=-i^0=\boxed{-1}[/tex]
1 point
An arrow is launched upwards. The height of the arrow, in meters, after seconds can be modeled by the function h (t) = -2.1t2 +32t-0.03. After how many seconds will the arrow
first reach an altitude of 60 meters?
3.4 seconds
-8 seconds
2.2 seconds
13 seconds
The arrow first reach an altitude of 60 meters is 13 seconds.
A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.Use addition or subtraction to isolate the variable term on one side of the equation.Use multiplication or division to solve for the variable.Finding the value of the given equation's unknown variables is a step in the equation-solving process.The value of the variable satisfies the requirement that the two expressions are equal. When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used.h (t) = -2.1t² +32t-0.03 ---(i)
The arrow first reach an altitude of 60 meters:
h(t) = 60 -- (ii)
Equate the (i) and (ii)
60 = -2.1t² +32t-0.03
2.1t² - 32t + 0.03 + 60 = 0
2.1t² - 32t + 600.3 + = 0
t = -13, 13
Hence, The arrow first reach an altitude of 60 meters is 13 seconds.
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Select the correct answer.
Here are four decimal numbers:
0.702, 0.76, 0.91, 0.73
Choose the list that shows the numbers in order from smallest to largest.
O
O
0.702, 0.91, 0.73, 0.76
0.702, 0.73, 0.76, 0.91
0.91, 0.702, 0.76, 0.73
0.91, 0.76, 0.73, 0.702
702, 0.91, 0.73, 0.76 shows the decimal numbers in order from smallest to largest.
What is a decimal number?
A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. The decimal point is the dot that separates the whole number from the fractional part of the number. An example of a decimal number is 34.5.Here are four decimal numbers:
0.702, 0.76, 0.91, 0.73
the numbers in order from smallest to largest.
702, 0.91, 0.73, 0.76
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Answer:
B) 0.702, 0.73, 0.76, 0.91
Step-by-step explanation:
The given set of decimal numbers (in any order) is:
0.702, 0.76, 0.91, 0.73Each number has zero units.
Comparing the digits in the tenth place, all the numbers have 7 tenths except 0.91 which has 9 tenths. Therefore, 0.91 is the largest number as 9 > 7.
Comparing the digits in the hundredths place of the other three numbers, 0.702 is the smallest number as it has zero hundredths.
As 0.73 has 3 hundredths and 0.76 has 6 hundredths, this means that 0.73 is the second smallest number as 3 < 6.
Therefore, the given set of decimals in order from smallest to largest is:
0.702, 0.73, 0.76, 0.91Can someone help me with this question please !!
I have to know how to solve it to pass my exam
I'll give brainly to the right answer .
Answer:
Step-by-step explanation:
you'll need to know L'Hôpital's Rule. Obviously this problem goes to zero in the denominator if you let x go to zero, which is a big problem :P sooo use L'Hopital's rule to solve this messy problem.
L'Hoptial's rule takes the advantage that you can find the derivative of something but still find it's limit just like you didn't take a derivative. soo
take derivative of numerator and denominator separately
remember how to take derivative of sin^2(3x) ??
pull the two down, then chain rule
d/dx (sin^2(3x) = 2sin(3x) * cos(3x) * 3 = 6*sin(3x)*cos(3x)
d/dx (4x^2) = 8x
we still have the same issue if we take the limit if x goes to zero :0
but it's okay... just take L'Hopitals' again :P
d/dx (6*sin(3x)*cos(3x)) = 6*cos(3x) *3 *(-sin(3x)*3 = 54*cos(3x)*(-sin(3x))
d/dx (8x) = 8
now we can let the limit go to zero
lim ( x ->0)[54*cos(3x)*(-sin(3x)) / 8]
we can see that sin(x) will get closer and closer to zero so we have 0/8
so we can fairly say, without guessing, that yes... this limit goes to zero as X goes to zero. :) nice
Calculate the percentage of alcohol in a lotion containing 2liters of which hazel (14% of alcohol), 1liter of alcohol (95%) and enough boric acid solution to make 5liters
from the reading above, doesn't seem the boric acid has any alcohol at all, so we can say 0% alcohol.
now let's see how many liters we have hmmm 2 of hazel, 1 of alcohol and the rest in boric acid, to make a total of 5 liters, so boric acid must be 2, since 2 + 1 + 2 = 5.
how much alcohol is there in 14% of 2 liters?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{14\% of 2}}{\left( \cfrac{14}{100} \right)2}\implies 0.28[/tex]
how much alcohol is there in 95% of 1? well, no to bore you to death, is just 0.95 liters, and we know the boric acid has no alcohol.
so in the 5 liters of the lotion, we have 0.28 liters plus 0.95 liters of alcohol total, that's 1.23 liters total.
now, if we know the 100% of the lotion is the 5 liters, how much is 1.23 liters off of it in percentage?
[tex]\begin{array}{ccll} liters&\%\\ \cline{1-2} 5 & 100\\ 1.23& x \end{array} \implies \cfrac{5}{1.23}~~=~~\cfrac{100}{x} \\\\\\ 5x=123\implies x=\cfrac{123}{5}\implies x=\stackrel{\%}{24.6}[/tex]
You are solving a measurement problem where the numbers 3.0471 x 10^9 and 2.4 x 10^-4 are divided. How many significant digits should the quotient have?
A. 2
B. 3
C. 4
D. 5
Answer:
5(d)
Step-by-step explanation:
(3.0471×10⁹)/2.4×10^-4
30471×10^9-4÷24×10^-4-1
30471×10⁵÷24×10^-5
(30471÷24)×10^5-(-5)
1269.625×10^5+5
1269.625×10¹⁰
1.269625×10^10-3
1.269625×10⁷
1.2696 to 5s.f
Rewrite the function by completing the square. h ( x ) = x 2 + 3 x − 18 h(x)=x 2 +3x−18
The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
We are given a quadratic function:
h (x) = x^2 + 3x − 18
We need to rewrite the function by completing the square.
We can see the coefficient of x is 3.
So, we will add and subtract the square of half that.
So, find the square of half of 3, we will get;
(3 / 2)^2 = 9 / 4 = 2.25
add and subtract the square of half of 3 from the given function, we will get;
h(x) = x^2 +3x + -18 2.25 -2.25
arrange the expression, we will get;
h(x) = (x^2 +3x +2.25) -18 -2.25
write the expression in parentheses as a square, and simplify the constant, we will get;
h(x) = (x + 1.5)^2 - 20.25
So, the square function is written as h(x) = (x + 1.5)^2 - 20.25.
Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
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brainliest if you answer :) thanksss
AC is congruent to SU