The ratios are not equivalent.
3112 was rounded to the nearest one.
What is the lower bound?
Answer:
3111.5.
Step-by-step explanation:
3112 - 0.5 = 3111.5.
What is the quotient of the following rational expression?
(x ^ 3 + 3x ^ 2 - 4x + 5)/(x ^ 2 - 2)
An expression is defined as a set of numbers, variables, and mathematical operations. The quotient of the following rational expression is (x+3), while the remainder is (-2x+11)/(x²-2).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be solved as,
[tex]\dfrac{x^3+3x^2-4x+5}{x^2-2}\\\\\\= x + \dfrac{3x^2-2x+5}{x^2-2}\\\\\\= x + 3+\dfrac{-2x+11}{x^2-2}[/tex]
Hence, the quotient of the following rational expression is (x+3), while the remainder is (-2x+11)/(x²-2).
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a mother is twice as old as her daughter 5 years from now she will be thrice as old as her daughter how old is the mother five years from now
Representation:
equation:
solution:
answer:
Answer:
Let's define the variables:
M = mother's age
D = daughter's age.
"a mother is twice as old as her daughter"
This can be written as:
M = 2*D
"5 years from now she will be thrice as old as her daughter"
(M + 5) = 3*D
We want to know how old is the mother five years from now.
First, our equations are:
M = 2*D
(M + 5) = 3*D
First, we need to isolate one of the variables in one of the equations, because for the solution we want the mother's age, we should isolate the daughter's age.
Let's isolate D in the first equation:
M/2 = D
Now we can replace this in the other equation:
Now we can replace this on the other equation:
(M + 5) = 3*(M/2)
M + 5 - (3/2)*M = 0
-(1/2)*M + 5 = 0
5 = (1/2)*M
2*5 = M = 10
So the mother is 10 years old (this hasn't a lot of sense, maybe there is a wrong number on the question)
and 5 years from now, the mother will be:
10 + 5 = 15 years old.
How many 1/3 ounce cups can be taken
Answer:
90
Step-by-step explanation:
If we know that for every cup, we can take 3 of 1/3-ounce cups, we can use an equation that looks like this:
number of cups × 3 = total 1/3-ounce cups
If there are 30 cups, then we can simply insert 30 into the equation.
30 × 3 = 90
Therefore, you can make 90 1/3-ounce cups from the cereal box.
6. If sin θ = - 3/5and the terminal side of θ lies in quadrant III, find cosθ .
When sin θ = - 3/5 and the terminal side of θ lies in quadrant III, then cos θ is -4/5
What is terminal side of an angel?The terminal side of an angle refers to the line that intersects the initial line to make an angle
In the problem the terminal side is said to be in the third quadrant and the in the third quadrant sin θ = - 3/5
sin θ = opposite / hypotenuse
using Pythagoras the adjacent is 4, in third quadrant we have -4
cos θ = - adjacent / hypotenuse = -4/5.
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Trapezoid MNPQ is similar to Trapezoid RSTU. What is the length of the "x" on the misside side NP ? Also, what is the length of "y" on the missing side TU?
Answer:
[tex]x = 15[/tex]
[tex]y = 25[/tex]
Step-by-step explanation:
Given
See attachment for MNPQ and RSTU
Required
Find x and y
To solve this question, we make use of equivalent ratios of corresponding side lengths.
The ratio of corresponding sides are:
[tex]MN : RS[/tex]
[tex]NP : ST[/tex]
[tex]PQ : TU[/tex]
[tex]MQ : RU[/tex]
From the attachment, we have:
[tex]MN : RS \to 18 : 30[/tex]
[tex]NP : ST \to x : 25[/tex]
[tex]PQ : TU \to 15 : y[/tex]
To solve for x, we equate [tex]MN : RS[/tex] and [tex]NP : ST[/tex]
[tex]18 : 30 = x : 25[/tex]
Express as fraction
[tex]\frac{18 }{ 30 }= \frac{x }{ 25}[/tex]
Make x the subject
[tex]x = 25 * \frac{18 }{ 30 }[/tex]
[tex]x = \frac{25 * 18 }{ 30 }[/tex]
[tex]x = \frac{450}{ 30 }[/tex]
[tex]x = 15[/tex]
To solve for y, we equate [tex]MN : RS[/tex] and [tex]PQ : TU[/tex]
[tex]18 : 30 = 15 : y[/tex]
Express as fraction
[tex]\frac{18 }{ 30 }= \frac{15 }{ y}[/tex]
Make y the subject
[tex]y = 15 * \frac{30 }{ 18 }[/tex]
[tex]y = \frac{15 *30}{ 18 }[/tex]
[tex]y = \frac{450}{ 18 }[/tex]
[tex]y = 25[/tex]
which answer is this
A.43
B.38
C.61
D.81
Answer:
81
Step-by-step explanation:
by corresponding angles from angle ABC
will GIVE BRAINLIEST!
Answer:
22 ft
Step-by-step explanation:
The circumference of a circle with given diameter d is C = (3.14)d.
Here, C = (3.14)(7 ft) = 21.98 ft, or approximately 22 ft
Answer:
22ftStep-by-step explanation:
Here,
It gives the diameter of a [tex]\huge{\bigcirc}[/tex]d=7feet,
Here,
[tex]\pi = 3.14[/tex]
Then the circumference of that circle is
[tex]\bold{ \pi×d }[/tex] 3.14×721.98ft[tex]\bold{\approx{22} }[/tex]ftHence
The circumference of that circle is 23ft
How do you tell if a set of ordered pairs satisfies an exponential function?
The following presumption has to be verified in order to establish whether the collection of ordered pairs fulfills an exponential function: The x-coordinates must have the same increment or a consistent difference.
What is an exponential function?A mathematical function of form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the foundation for exponential functions that are most frequently utilized.
Characteristics are:
The fact that a⁰ = 1 causes them all to include the point (0, 1). Always an asymptote, the x-axis. If (0 < a < 1) or (1 < a), they are decreasing and growing, respectively.To know more about exponential function refer to:
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Please please help me no links
Does the table represent a linear or nonlinear function?
Answer:
Linear
Step-by-step explanation:
Linear means the graph is a straight line. If you plot the points, the line will be straight, therefore it is linear.
20 workers can paint a building in 21 days. If work has to be finished in 15 days, find the number of extra workers required.
Step-by-step explanation:
20 workers finish work in 21 days.
the necessary work effort is 20×21 = 420 workdays.
the same effort is needed even if the overall time is shorter.
x workers in 15 days.
x × 15 = 420
x = 420/15 = 28 workers.
so, 28-20 = 8 additional workers are needed to finish the work in 15 days.
Find the largest prime number that divides the quantity 0! + (1!) x 1 + (2!) x 2 + (3!) x 3 + ... + (50!) x 50
The largest prime number that divides the quantity is the largest prime number less than 5.5e+22.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.
We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.
0! = 1
1! = 1
2! = 2
3! = 6
...
50! = 30414093201713378043612608166064768844377641568960512000000000000
Now we can write the expression as
(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)
We can notice that the number is very large, and it's impractical to factorize it using traditional methods.
We can use the property that if n is not divisible by a prime number p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.
The next step would be to check if the remaining number is divisible by any prime numbers.
Since it's impractical to check for all the prime numbers, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)
Which is approximately 5.5e+22.
Therefore, the largest prime number that divides the quantity is the largest prime number less than 5.5e+22.
It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.
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1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
x = 6 does not satisfy the given equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that an equation, 5(x – 3) = x + 13
Checking if x = 6 satisfy the equation or not,
5(x – 3) ? x + 13
5(6-3) ? 6+13
5×3 ? 19
15 ≠ 19
Hence, x = 6 does not satisfy the equation.
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n% of 400 = 150
please HELLPPP
Answer:
150 of 400 can be written as:
150400To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
150400 × 100100= (150 × 100400) × 1100 = 37.5100Therefore, the answer is 37.5%
If you are using a calculator, simply enter 150÷400×100 which will give you 37.5 as the answer.
How do you know if a graph is wider or narrower than the parent function?
The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.
Define the condition for wider graph of the parent function?The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.
The parabola ends point up when the quadratic coefficient is positive.The parabola's ends point down when the quadratic coefficient is negative.The parabola narrows as the quadratic coefficient increases.The parabola's width increases as the quadratic coefficient decreases.The axis of symmetry is moved away from the y-axis by the linear-term coefficient b. The quadratic coefficient's sign and the linear coefficient's sign both affect the shift's direction.The y-intercept is impacted by the constant term c. The intercept point just on y-axis increases higher the higher the number is.To know more about the parent function, here
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Simplifying algebraic expressions
Answer:
Step-by-step explanation:
Plug in 5 for h
6(5)+7(5)
30+35=65
65
Answer:
[tex] \sf \: 6h + 7h = 65[/tex]
Step-by-step explanation:
Given information,
→ 6h + 7h
→ h = 5
Now the final value will be,
→ 6h + 7h
→ 6(5) + 7(5)
→ 30 + 35
→ 65 => final value
Hence, the answer is 65.
Nora needs at least $115 for a new cell phone. She has already saved $45. She earns $7 an hour at her job. Write and solve an inequality to find how many hours she will need to work to buy the phone.
Answer:
Nora needs to work 10 hours to get 70 dollars to be able to have 115 to buy the new phone.
Step-by-step explanation:
45+7x = 115
45+7(10)
45+70
115
(Hope this helped! If you have any questions about this please comment) :D
PLEASE HELP ITS ATEST I BEG U. NEED HELP
Answer:
36 degrees
Step-by-step explanation:
angle 1 and 2 are the same
good luck!
Complementary angles are of 90°.
So, angle 1 + angle 2 = 90°
=> 36° + angle 2 = 90°
=> angle 2 = 90° - 36°
=> angle 2 = 54°
Which graph represents a relation that is NOT a function
Answer:
3) if you were to draw vertical lines through this graph you would have instances where an 'x' value would have more than one unique 'y' value
Step-by-step explanation:
functions must have one unique 'y' value for each 'x' value
The third graph represent a relation that is not a function
What is a function?A relation is a function if it has only One y-value for each x-value.
The third one doesn't represent a function, because for some values of "x", you get two different values for "y" (which should not happen, if that were a function).
In order to see it better, you can trace a vertical line onto that graph.
If that line and the graph intersects in more than one point, then that graph doesn't represent a function.
In every function, you must have a single "y" value for each "x" in the domain.
Hence, the third graph represent a relation that is not a function
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Please help me !!
this the last question !!
Answer:
2 ≥ p
Step-by-step explanation:
-14 ≤ -7p
Divided both sides by -7. Because divided by a negative number, the < will turn to >
So, the equation is
2 ≥ p
Because there is an equal, the circle will be close and to the left of 2.
Answer:
2 ≥ p
Step-by-step explanation:
Have a great day :) <3
Uppose you have a bag of marbles and of the marbles are . If you choose one without looking, the probability you choose marble is
. How can you write this probability as a decimal? Write this probability as a decimal. Use a word or phrase to describe this probability.
How do you change the fraction to a decimal?
A. Multiply the numerator and denominator by .
B. Divide the denominator by the numerator.
C Divide the numerator by the denominator..
D. Multiply the numerator by the denominator.
What are the coordinates of point (x,y) when it is reflected across the line y=−x?
The coordinate of the reflection is (-y, -x)
How to determine the coordinate of the reflectionFrom the question, we have the following parameters that can be used in our computation:
Point = (x, y)
Reflection: Across the line y=−x
Using the above as a guide, we have the following:
The reflection of a point over the line y = -x implies that, the x-coordinate and y-coordinate change places Then they are negated (the signs are changed)So, we have
Image = (-y, -x)
Hence, the image is (-y, -x)
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(NEED HELP ASAP!!)
What are the coordinates of the focus of the parabola?
A: (8, 6)
B: (-8, 6)
C: (-8, 2)
D: (8, 2)
Answer:
C: (-8, 2)
Step-by-step explanation:
Given parabola:
[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]
For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.
Therefore, the x-value of the vertex of the given parabola is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]
To find the y-value of the vertex, input x = -8 into the given equation:
[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]
Therefore, the vertex (h, k) of the parabola is (-8, 4).
The focus of the parabola is (h, k+p) where:
(h, k) is the vertex[tex]p=\dfrac{1}{4a}[/tex]Therefore:
[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]
Help me please, worth 20 points
Answer:
It's actually worth 10 points
A voltage of 20 volts flow through a wire of 2.5ohm's resistance. Calculate the current
Answer:
8 A
Step-by-step explanation:
V = 20 volts
R = 2.5 ohms
I=?
By Ohm's Law
[tex] \because \: I \: = \frac{V}{R} \\ \\ \therefore \: I= \frac{20}{2.5} = \frac{200}{25} = 8 \: Ampere[/tex]
GUYS I NEED HELP WHAT IS (8x[1 +(20 - 6)]} divided by 1/2
Answer:
240x is=f simplfied.
Step-by-step explanation:
Please help with this question!
Answer:
3. 17.2°
Step-by-step explanation:
The angles for the right triangle are 90°, 72.8°, and 17.2°.
In the interval 0° < x < 360°, find the values of x for which tan x = -0.8645
Answer:
Step-by-step explanation:
x=tan^{-1}(-0.8645) \approx -40.84°,-40.84+180,-40.84+360
x=139.16°,319.16°
The values of x in the interval 0° < x < 360° for which tan(x) = -0.8645 are approximately 139.18° and 299.18°.
To find the values of x in the interval 0° < x < 360° for which tan(x) = -0.8645, you can use the inverse tangent function (also known as arctan or atan). The inverse tangent function will give you the angle whose tangent is equal to the given value.
Using a calculator or a math software that supports trigonometric functions, you can take the inverse tangent (arctan) of -0.8645 to find the angle:
arctan(-0.8645) ≈ -40.82°
Since tangent is a periodic function with a period of 180°, you can find other angles that satisfy the equation by adding or subtracting multiples of 180°:
-40.82° + 180° ≈ 139.18°
-40.82° + 2 * 180° ≈ 299.18°
So, the values of x in the interval 0° < x < 360° for which tan(x) = -0.8645 are approximately 139.18° and 299.18°.
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HELP ASAP
|x+12|, if x>-11
Answer:
it should be x+12
Step-by-step explanation:
if x is bigger than -11, then the answer will always be positive
We have given a function; [tex]|x+12|, if x > -11[/tex] if x is bigger than -11, then the answer will always be positive.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
We have given a function;
[tex]|x+12|, if x > -11[/tex]
The modulus of any number always gives the positive term.
if x is bigger than -11, then the answer will always be positive.
Let x = 2
then we get
[tex]|x+12| = |2+12| \\\\= 14[/tex]
So, we can see that the answer is positive.
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