Answer:
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2} < - InsertQuadraticFormula[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:6\sqrt{3}}{2\cdot \:2}[/tex]
[tex]x_1=\frac{-\left(-6\right)+6\sqrt{3}}{2\cdot \:2},\:x_2=\frac{-\left(-6\right)-6\sqrt{3}}{2\cdot \:2} < - Separate THE Solutions[/tex]
[tex]x=\frac{3\left(1+\sqrt{3}\right)}{2},\:x=\frac{3\left(1-\sqrt{3}\right)}{2}[/tex]
what is (8^5)^4 (answer must include an exponent )
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](8^5)^{4}[/tex] = [tex]8^{5(4)}[/tex] = [tex]8^{20}[/tex]
Two angles are complementary if their sum is 90°. A larger angle measures three degrees less than
twice the measure of the smaller angle. If x represents the measure of the smaller angle and these two
angles are complementary, find the measure of each angle.
Answer:
31 and 59
Step-by-step explanation:
We can figure this out by putting the words into an equation
"three degrees less than twice the measure of the smaller angle"
we know the smaller angle = x, so:
twice the smaller angle=2x
3 degrees less=-3
you then put those into an equation where they all add up to equal 90 and simplify
x+2x-3=90
3x-3=90
3x=93
x=31
you then plug that into the equation we would have for the second angle:
2x-3
2(31)-3
62-3
59
the first angle would be 31 and the second angle would be 59
:D
The governor of state A earns $49,485 more than the governor of state B. If the total of their salaries is $288,035, find the salaries of each.
need to find a and b
Answer:
a) $168,760
b) $119,275
Step-by-step explanation:
For this, I believe you do $288,035 - $49,485. This equals $238,550.
Then divide this by 2 to get the salary for state B, which is $119,275 .
$168,760 remains, so it's the salary for state A.
Answer:
Governor of state A = 168,760
Governor of state B = 119,275
Step-by-step explanation:
A = 49485 + B Eq. 1
A + B = 288035 Eq. 2
A = Earns of governor of state A
B = Earns of governor of state B
Replacing Eq. 1 in Eq. 2:
(49485+B) + B =288035
2B + 49485 = 288035
2B = 288035 - 49485
2B = 238550
B = 238550/2
B = 119275
From eq. 1
A = 49485 + 119275
A = 168760
Check:
from eq. 2:
A + B = 288035
168760 + 119275 = 288035
If 7cakes cost $6.30 what is the cost of 12 such cakes
Answer:
$10.8
Step-by-step explanation:
First, to determine the price of one cake divide 6.30/7
You will determine one cake costs 90 cents.
So, multiply 0.90 by 12, and you get $10.8
all real numbers greater than or equal to 55
The set notation of the numbers is {x | x < 50 ∪ x > 50}
How to determine the set notation of the numbers?The set is given as
The set of all real numbers less than 50 or greater than 50
Let the number be represented by x
So, we have
x less than 50 or x greater than 50
When represented as an inequality, we have
x < 50 or x > 50
Using set notation, we have
{x | x < 50 ∪ x > 50}
Hence, the set notation of the numbers is {x | x < 50 ∪ x > 50}
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You buy a new computer for $1500. The value of the computer decreases by 6% every year. How much is the computer worth after 4 years?
Answer: Your computer will be worth $1,171.12
Step-by-step explanation:
[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]
The perimeter of a rectangle is 32 m. The length is 4 m more than two times the width. Find the length and the width of the rectangle.
The length of the rectangle is 12 meters and its width is 4 meters.
A rectangle is a four sided figure, whose opposite sides are equal and the angle formed by any two adjacent sides is 90 degrees.
Here, we are given that the perimeter of the rectangle is 32 meters.
Let the length of the rectangle be L and breadth or width be B
We known that perimeter of a rectangle = 2(L + B)
Now, it is given that the length is 4 m more than two times the width
⇒ L = 4 + 2B
Thus, the area of the perimeter will be-
Perimeter = 2(4 + 2B + B)
⇒ 32 = 2(4 + 2B + B)
32/2 = 4 + 2B + B
16 = 4 + 3B
16 - 4 = 3B
12 = 3B
or 3B = 12
B = 12/3
B = 4
Thus, the width of the rectangle is 4 meters.
Therefore, L = 4 + 2(4)
L = 4 + 8
L = 12
Thus, the length of the rectangle is 12 meters.
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HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
Please help on the middle!!
Answer: I just points so rate this a 10
Step-by-step explanation:
Answer:
owi4w85e963696w95witote5iw47e
For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
For the linear function x - y = 3, three ordered pairs are given as follows:
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.Using points (3,0) and (0,-3), the graph of the function is given at the end of the problem.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the function is:
x - y = 3.
In standard notation:
y = x - 3.
Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.The graph of the function is given at the end of the answer.
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What are the approximate x-intercepts for y=(x+4)^2 -7
Answer:
44
Step-by-step explanation:
because if u pit it together 44 is what u get
Please help!!!!!!! thx xxx
Start by dividing both sides by G, giving us
[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].
Finally, divide both sides by m2.
[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]
Hope this helps! This was a tough problem for me too.
Select all figures that have at least one line of symmetry.
Answer:the heart and planet are the only ones
Step-by-step explanation:
the clover looks like maybe but the stem is curved. the planet the line goes verticle through the rings
The length of a rectangle is 1 fr more than double the width, and the area of the rectangle is 45 ft^2. Find the dimensions of the rectangle.
The length and width of rectangle is 10 feet and 4.5 feet.
This problem is related to the area and perimeter of plane figures. We have to find the dimensions of the rectangle using the data given.
Given, the length is 1 feet more than twice the width.
Let the width be a feet.
So, length = (2a+1) feet
Now according to question,
[tex](2a+1)(a)=45\\[/tex]
⇒ [tex]2a^{2} +a-45=0[/tex]
On solving the above quadratic equation we get a=4.5 feet.
So, length = 10 feet.
The dimension of rectangle is 10 feet × 4.5 feet.
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If y’all can’t se it just zoom in because that’s the best I can get it please help me thank u please don’t comment on my stuff just for points I really need help with this
Answer:
the answer is 42
Step-by-step explanation:
you add 217+153+88=458
500-458=42
the distance between two cities on a map measures 3.75 inches. the scale shows that 2 inches is equal to 50 miles . how many miles apart are the cities
If y= 50 degrees and z=85 degrees, then x in degree is=?
the answer will be 55 degrees. please solve
Answer:
Step-by-step explanation:
NO LINKS!! Please help me with these problems. Part 10a1
y = √(x - 2)
Answer:
Domain: [2, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain [2, ∞).Minimum point at (2, 0).Increasing function: (2, ∞)Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.Step-by-step explanation:
Given function:
[tex]y=\sqrt{x-2}[/tex]
DomainThe domain is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken, the domain of the given function is restricted.
[tex]x-2\geq 0 \implies x\geq 2[/tex]
Therefore, the domain of the given function is [2, ∞).
RangeThe range is the set of all possible output values (y-values).
As the square root of a negative number cannot be taken, the range of the given function is restricted.
Therefore, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain [2, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]
Therefore, there are no stationary points.
As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (2, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: [2, ∞)
Range: [0, ∞)
Continuity: Function is continuous on its domain [2, ∞).
Minimum point at (2, 0).
Increasing function: (2, ∞)
Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.
9x = 7x + 22 need help
Answer:
x=11
Step-by-step explanation:
9x=7x+22
9x-7x=22
2x=22
2x/2=22/2
x=11
How many times larger is (1.143 x 101) than (9 x 10−1)?
0.127
7.87
10.287
12.7
how did you get your answer?
(1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7
Calculating magnitudeFrom the question, we are to determine the factor by which 1.143 × 10¹ is larger than 9 × 10⁻¹
To determine how many times larger the number is, we will divide 1.143 × 10¹ by 9 × 10⁻¹
Carrying out the division operation
(1.143 × 10¹) ÷ (9 × 10⁻¹)
= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)
= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)
= 0.127 × (10¹ ⁻ ⁽⁻¹⁾)
= 0.127 × (10¹ ⁺ ¹)
= 0.127 × (10²)
= 0.127 × 10²
= 12.7
Hence, (1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7
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Jordan will hike the trail at a rate of 4mph. Write a linear equation to represent the distance Jordan still has to walk after x hours what does the y intercept represent
The linear equation would be y = 18 - 4x which represents the distance Jordan still has to walk after x hours.
The y-intercept represents the total distance Jordan has to walk.
What is the distance?Distance is defined as the product of speed and time.
We have to determine the distance.
So distance = speed× time
Given that his speed is 4 mph and x hours of walking, then:
So distance = 4 × x
Let it Start of the trail: 0 miles
And the end of the trail: 18 miles
The trail length is 18 miles, so if he walked 1 mile, 18 - 1 = 17 miles are left, in general:
⇒ y = 17 - 4(x)
Here y would be the distance Jordan still has to walk.
The y-intercept would be if substitute x = 0, then:
⇒ y = 17- 4(0)
⇒ y = 17
This represents the total distance Jordan has to walk
Hence, the linear equation would be y = 18 - 4x which represents the distance Jordan still has to walk after x hours.
The y-intercept represents the total distance Jordan has to walk.
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A shopkeeper allows a discount of 10% on the marked price of an article.What was the marked price of the article which costs him 1800 and makes profit of 15%.
Answer:
$243 is his profit
Step-by-step explanation:
Answer: $4100
Step-by-step explanation:
discount = [tex]\frac{1800}{90}[/tex]×100 = 2000
profit = [tex]\frac{115}{100}[/tex]×2000 = 2300
market price = 2300 + 1800 = 4100
Fill in all missing terms and select all missing descriptions.
Answer:
Add all like terms
12s = 0
s = 0
Step-by-step explanation:
8s + 6 + 4s = 6
12s + 6 = 6
-6 -6
12s = 0
÷12 ÷12
s = 0
I hope this helps!
Lucia walked of the length of the Tremont Trail before
stopping for a rest. How far had Lucía walked on the trail?
Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail
We are told in the question that
Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.
From the question, the length of the Tremont Trail = 3 1/2 miles
Hence, the distance (how far )Linda has walked =
3/4 of 3 1/2 miles
= 3/4 × 3 1/2 miles
= 3/4 × 7/2 miles
= 21/8 miles
= 2 5/8 miles or 2.625 miles
Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.
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The length of a rectangle is 1 in. less than 3 times the width. If the perimeter of the rectangle is 46 in., find the length and the width.
[tex] \Large {\mathbb {SOLUTION: }}[/tex]
[tex] \: \: \text{L = 3w - 1}[/tex]
[tex] \: \: \text{P=46}[/tex]
[tex] \: \: \text{2(3w-1) + 2w = 46}[/tex]
[tex] \: \: \text{6w - 2 + 2w = 46}[/tex]
[tex] \: \: \text{8w = 48}[/tex]
[tex] \: \: \text {W = 6 }[/tex]
[tex] \: \: \text{L = 17}[/tex]
[tex] \: \: \text{Applying the inequalities:}[/tex]
[tex] \: \: \text{L>=17 and w=6}[/tex]
[tex] \: \: \text{The perimeter is at least 46.}[/tex]
Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of gigabytes 400. (Recall that giga means billion.)
My new music player has a capacity of _ enter your response here bytes.
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
4 x 10¹¹
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
400 billion in scientific notation = 4 x 10¹¹
We can complete the sentence as,
My new music player has a capacity of 4 x 10¹¹
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Ettwice is three times as old as mavis. the sum of their age is 60. how old each
the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps
Step-by-step explanation:
15 * 3 = 45
45 + 15 = 60
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
The product of 3 and the difference of 5 and a number.
The sentence "5 is subtracted from the square of a number" represented as an algebraic expression is x² -5.
Algebraic expressions: what are they?
A group of integers or variables combined using the operations +, -, o, or constitute an expression. algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.Given,
Let the number be x and 3 is subtracted from a number.
Represent it in expression.
Step 2
3 is subtracted from a number means 3 is subtracted from x.
Here we have to subtract 3 from x. It can be represented as = x - 3
Let the number be x.
In this exercise, you're required to write an algebraic expression to represent the word problem (sentence). Also, the number would be denoted by the letter x and no need for further simplification of the algebraic expression.
Translating the word problem (sentence) into an algebraic expression, we have;
Square of a number (x) = x²
Subtracting 5 from the the square of x, we have x² -5 .
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A line passes through ( - 1, - 1) and ( - 3, 5).
What is the equation of the line in slope-intercept form?
Answer:
y= -3x-4.
Step-by-step explanation:
1) the slope-interception form is:
y=slope*x+i, where i - interception;
2) using the given two points it is possible to calculate the slope:
[tex]slope=\frac{5+1}{-3+1}=-3;[/tex]
then the required equation has the form:
y=-3x+i;
3) in order to calculate the 'i', it is enough to substitute the coordinates of the one point into this form of the required equation:
-1=-3*(-1)+i; ⇒ i=-4.
4) finally, the required equation is:
y=-3x-4.
P.S. the suggested way is not the shortest one.
.Solve 2x−1<4 or −5x−3>−3 and write the solution in interval notation.
The interval notation is { 5/ 2 < x > 0 }
How to determine the valueGiven the inequalities;
2x−1<4−5x−3>−3To determine the value of x, we have;
2x - 1 < 4
collect like terms
2x < 4 + 1
2x < 5
Make 'x' the subject
x < 5/ 2
−5x −3 > −3
collect like terms
-5x > -3 + 3
-5x > 0
x > 0
Thus, the interval notation is { 5/ 2 < x > 0 }
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