The value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.
We are given the expression:
∛ - 7. ∛ 49
We need to multiply and simplify it.
We will first multiply the expression:
= ∛ - 7 × 49
Solving it, we get that:
= ∛ - 343
Now this can also be written as:
= ∛ (- 7 )³
Now, simplifying the cube root to get the value of the expression:
= - 7
Therefore, we get that, the value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.
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How can you rewrite each function as a piecewise-defined function?
f(x) = -5x - 10|
Value of the given function as a piecewise-defined function is equal to
f(x) = -5x -10 , x ≤ -2
5x +10 , x > -2
As given in the question,
Function as a piecewise-defined function
y = |x| = x , x≥0
-x , x<0
Given function: f(x) = |-5x-10|
-5x -10≥0 ⇒ -5x ≥ 10 ⇒x ≤ -2
-5x -10 <0 ⇒ -5x < 10 ⇒ x> -2
Therefore, value of the given function as a piecewise-defined function is equal to
f(x) = -5x -10 , x ≤ -2
5x +10 , x > -2
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The cost of downloading a book from a certain website is $5.99. The cost of downloading a video is $7.99. Tatum's mom downloads 3 books and 5 videos.
The total required cost of downloading books and videos is $57.92
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the total cost of downloading books and videos?The given parameters are:
Cost of downloading a book = $5.99
Cost of downloading a video = $7.99
The number of books and videos downlaoded are
Books = 3
Videos = 5
So, the total cost of downloading books and videos is
Total cost = Cost of downloading a book * x + Cost of downloading a video * y
This gives
Total cost = Cost of downloading a book * Books + Cost of downloading a video * Videos.
This gives
Total cost = 5.99 * 3 + 7.99 * 5
Evaluate
Total cost = 57.92
So, the total cost of downloading books and videos is $57.92
Hence, the total required cost of downloading books and videos is $57.92
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What is an equation of the line that is perpendicular to y = 3x - 9and that
passes through the point (3, 1)?
y =
Answer:
y = -1/3x + 2
Step-by-step explanation:
The slope of a line that is perpendicular has an opposite inverse of the slope of the line given.
The slope of the line given is 3. The opposite inverse is -1/3.
Use the slope (-1/3), the x(3) and the y(1) to find the y-intercept (b) and to write the equation of the line.
y =mx + b
1 = -1/3(3) + b
1 = -1 + b Add 1 to both sides
2 = b
y = -1/3x + 2
16.) CONSTRUCT ARGUMENTS Mariah is training for a sprint-
distance triathlon. She plans on cycling from her house to
the library, shown on the grid with a scale in miles. If the
cycling portion of the triathlon is 12 miles, will Mariah
2
have cycled at least of that distance during her bike ride?
Justify your argument.
Using the distance between two points, it is found that she cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
What is the missing information?The coordinates are given as follows:
Library (4,9).Mariah's House: (9, 2).It asks if the distance that he cycles from her house to the library is at least 2/3 of 12 miles = 8 miles.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence the distance between her house and the library is:
[tex]D = \sqrt{(9 - 4)^2 + (2 - 9)^2}[/tex]
D = 8.6 miles.
She cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
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Rationalize the denominator of each expression. Assume that all variables are positive. √36 x³/√12y
The rationalization of the given expression is x√3 .
Rationalization can be thought of as the process used to remove the base or imaginary number from the denominator of an algebraic fraction. That is, remove the radical of the fraction so that the denominator contains only rational numbers.Radicals are expressions that use roots such as: B. Square root or cube root. For example, an expression of the form: √(a + b) is a root.The mathematical conjugate of any binomial means another exact binomial with opposite signs between the two terms.We have to rationalize the denominator of the expression √36 x³/√12x ,
where x is positive.
√36 x³/√12x
= √36 x³/√12x × √12x ×√12x
= 6√(x³ × 12x)/√(12x × 12x)
= 6√(x⁴12)/12x
= √(12x⁴)/2x
= √(2 × 2 × 3 × x × x × x × x)/2x
= 2x²√(3)/2x
= x√3
The answer is x√3
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360000/180 in standard form
Answer:
2000
Step-by-step explanation:
Solve 5x-12-6x=-10x+7-1 (please fill out each step)
Step 1. Collect like terms
Step 2.Move variables to one side of the equation (addition/subtraction property of equalities)
Step 3. Move constant to the other side of equation (Addition/subtraction property of equalities)
Step 4.(multiplication/division property of equalities)
5x-12-6x=-10x+7-1
=5x-6x+10x=7-1+12
= 9x=18
=9x/9=18/9
=x=2
0.96 x 0.12 step by step pls
Answer:
0.1152
Step-by-step explanation:
multiply 0.96 by 0.12 to get 0.1152.
You are filling traffic cones with sand to keep them from blowing over. the cone has a radius of 7 inches and a height of 28 inches. approximately how much sand, in cubic inches, can fit inside the cone?
If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.
The volume of the cone can be described as the measure of a 3-D space occupied by matter.
The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,
v = πr²h / 3
As the radius of the cone = 7 inches
Height of the cone = 28 inches
v = π(7)²28 / 3
v = (π)(49)(28) / 3
v = (π)(1372) / 3
As π = 3.14
v = (3.14)(1372) / 3
v = 4308.08 / 3
v = 1436.02 ≈ 1436 cubic inches
Hence, 1436 cubic inches of sand is calculated to fit inside the cone.
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9. Find m
a. 52
b. 38
c. 12
d. 22
Answer:
∠ ABC = 52° , ∠ CBD = 38°
Step-by-step explanation:
the 2 angles form a right angle and sum to 90° , that is
∠ ABC + ∠ CBD = 90
4x + 4 + 5x - 22 = 90
9x - 18 = 90 ( add 18 to both sides )
9x = 108 ( divide both sides by 9 )
x = 12
then
∠ ABC = 4x + 4 = 4(12) + 4 = 48 + 4 = 52°
∠ CBD = 5x - 22 = 5(12) - 22 = 60 - 22 = 38°
Determine the slope of the blue and green line
Answer:
2/-9
Step-by-step explanation:
A rectangular room has an area of 575 square feet. The length of the room is 2 feet less than the width of the room. Find the length and width of the room, in feet, and separate them with a comma.
Answer:
w=17.613
l=15.613
Step-by-step explanation:
w×l=area
l=w-2
therefore w×(w-2)=575
rearrange the equation to make a quadratic
(w^2)-2w-575=0
w=-(b+ or - sqrt (b^2-4ac))/2a
a=1
b=-2
c=-575
using quadraric formula to solve
w=17.613 or -15.613
cant be -15.613
l=w-2
=15.613
HELP PLEASE I NEED HELPPI’ll make you brainlist and it’s Algebra btw
=====================================================
Explanation:
The regression equation is in the form y = mx+b
m = slope = -0.624b = y intercept = 66.022The slope tells us how much the value of y changes each time x goes up by 1. In this case, the scores decrease by 0.624 percentage points each time x goes up by 1
You can think of it like saying
slope = rise/run = -0.624/1rise = -0.624 = y drops by 0.624run = 1 = x increases by 1This is why the answer is 0.624. We don't type the negative sign because that is part of the term "decrease".
5. A bird is at 20 feet above sea level. A fish is 14 feet below sea level. What is the difference? on the number line
Answer:
I think its 34 feet
Step-by-step explanation:
If you subtract 20 to get to 0 its 20, minus another 14 to get to zero is 14. Add them and you get 34 feet. Hope it helps! =)
The difference in their positions on the number line is 34 feet
How to determine the difference on the number linefrom the question, we have the following parameters that can be used in our computation:
Bird = 20 feet above sea level
Fish = 14 feet below sea level
using the above as a guide, we have the following:
Bird = 20 feet
Fish = -14 feet
So, we have
Difference = 20 feet - -14 feet
Evaluate
Difference = 34 feet
Hence, the difference on the number line is 34 feet
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Eve write (1.2x10^5)divided by (3x10^2)
Answer:
1.2 x. 100000
3. x. 100
=120000
300
=400
Determine whether each conjecture is true or false. Give a counterexample for any false conjecture.
1. If AB, BC, and AC are congruent, then A, B, and C and colllinear.
2. If <1 is complementary to <2, and <1 is complementary to <3, then <2 ≅ <3.
The given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.
How to Interpret Conditional Statements?Notice that the given conjecture does not necessarily be always true.
To be precise; there are no reasons as to why A, B and C must be noncollinear.
1. we are given If AB, BC, and AC are congruent, then A, B, and C and colllinear.
A,B ,C are not collinear so it will be false
Therefore, the given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.
A Counter- example of the given statement is that A, B, C are three points that lie on the same line and so they are collinear.
2. We are given If <1 is complementary to <2, and <1 is complementary to <3, then <2 ≅ <3.
It may be true.
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Simplify each expression.
125¹/₃
The questions tests on indices. Write 125 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 125 = 5×5×5
125 = 5^3
(125^3)^(1/3) = 5^(3×1/3) = 5
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For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=-5 when x=3/2
After direct variation y = 10 when x = -3.
What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ -5/3/2 = -10/3That is y = kx ⇒ y = -10/3 × xWhen x = -3:
y = -10/3 × -3 ⇒ y = 10Therefore, y = 10 when x = -3.
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there are two integers between 1 and 100 such that for each: if you divide by 4, the remainder is 3; if you divide by 3, the remainder is 1; if you divide by 5, the remainder is 1. what is the sum of those two integers?
Let [tex]n[/tex] be an integer such that
[tex]\begin{cases} n \equiv 1 \pmod 3 \\ n \equiv 3 \pmod 4 \\ n \equiv 1 \pmod 5 \end{cases}[/tex]
Note that (3, 4, 5) are mutually coprime, so we can use the Chinese remainder theorem.
Starting with
[tex]n = 1 + 3 + 1[/tex]
we adjust to
[tex]n = (1\cdot4\cdot5) + (3\cdot3\cdot5) + (1\cdot3\cdot4)[/tex]
to make computing the residues a bit easier.
• Taken modulo 3, we have
[tex]n \equiv 20 + 0 + 0 \equiv 2 \not\equiv 1 \pmod 3[/tex]
so we need to further adjust the first term by introducing the inverse of 2 modulo 3. We have
[tex]2\cdot2 \equiv 4 \equiv 1 \pmod 3 \implies 2^{-1} \equiv 2 \pmod 3[/tex]
Then
[tex]n = (1\cdot4\cdot5\cdot2) + (3\cdot3\cdot5) + (1\cdot3\cdot4)[/tex]
• Taken modulo 4, we have
[tex]n \equiv 0 + 45 + 0 \equiv 1 \not\equiv 3 \pmod 4[/tex]
We need another inverse; we have
[tex]3\cdot3 \equiv 9 \equiv 1 \pmod 4 \implies 3^{-1} \equiv 3 \pmod 4[/tex]
and so
[tex]n = (1\cdot4\cdot5\cdot2) + (3\cdot3\cdot5\cdot3) + (1\cdot3\cdot4)[/tex]
• Taken modulo 5, we have
[tex]n \equiv 0 + 0 + 12 \equiv 2 \not\equiv 1 \pmod 5[/tex]
One more inverse:
[tex]2\cdot3 \equiv 6 \equiv 1 \pmod 5 \implies 2^{-1} \equiv 3 \pmod 5[/tex]
and so
[tex]n = (1\cdot4\cdot5\cdot2) + (3\cdot3\cdot5\cdot3) + (1\cdot3\cdot4\cdot3)[/tex]
Simplifying, we have [tex]n = 211[/tex], and by the CRT we have
[tex]n \equiv 211 \pmod{3\cdot4\cdot5} \implies n \equiv 31 \pmod{60}[/tex]
which is to say [tex]n=60k + 31[/tex] where [tex]k[/tex] is an integer.
The two integers that fall between 1 and 100 occur for [tex]k\in\{0,1\}[/tex]; they are 31 and 31 + 60 = 91, and their sum is 31 + 91 = 122.
Write each fraction as a percent 17/20
Answer:
85%
Step-by-step explanation:
[tex]\frac{17}{20} * 100 = 85[/tex]
Answer:
85%
Step-by-step explanation:
See attachment for answers.
Karina drinks 42 oz of water in 1 day. In 1 week, Karina drinks 294 oz.
Step-by-step explanation:
???????????????????????
Answer: Your answer is 6.
Step-by-step explanation:
You need to divide 42 from 294.
29.14 × 5.2 estimation step by step please
pls help w this pretty urgent
Answer:
[tex]\textsf{a)} \quad g'(x)=2x-4[/tex]
[tex]\textsf{b)} \quad y=2x[/tex]
[tex]\textsf{c)} \quad x=5[/tex]
Step-by-step explanation:
Given function:
[tex]g(x) = x^2-4x+9[/tex]
Part (a)Differentiate the given function with respect to x:
[tex]\begin{aligned}g(x) & = x^2-4x+9\\\implies g'(x) & = 2 \cdot x^{2-1}-1 \cdot 4x^{1-1}+0\\& = 2x^{1}-4x^{0}\\& = 2x-4(1)\\& = 2x-4 \end{aligned}[/tex]
Part (b)The y-value of the function at x = 3:
[tex]\begin{aligned}\implies g(3) & = (3)^2-4(3)+9\\& = 9-12+9\\& = -3+9\\& = 6\end{aligned}[/tex]
Therefore: (3, 6).
To find the slope of the function at x = 3, substitute x = 3 into the differentiated function:
[tex]\begin{aligned}\implies g'(x) & = 2(3)-4\\& = 6-4\\& = 2\end{aligned}[/tex]
Therefore, the slope of the function at x = 3 is 2.
Substitute the found slope and point (3, 6) into the point-slope form of linear equation to find the equation of the tangent line of g(x) at x = 3:
[tex]\begin{aligned} y-y_1 & =m(x-x_1)\\\implies y-6 & = 2(x-3)\\y-6 & = 2-6\\y & = 2x-6+6\\y&=2x\end{aligned}[/tex]
Part (c)To find the value of x for which the slope of the graph is equal to 6, set the differentiated function to 6 and solve for x:
[tex]\begin{aligned}g'(x) & = 6\\\implies 2x-4 & = 6\\2x & = 6+4\\2x & = 10\\x & = \dfrac{10}{2}\\x & = 5\end{aligned}[/tex]
What is the logarithmic form of each equation?
a. 36=6²
The logarithmic form is 2log₁₀6
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
loga where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logabc where a is the base is given as logab+logc
loga b/c where a is the base is given as logab-logac
Now it is given to us to find the logarithmic form of 36=6^2
Let us consider the base of the logarithm to be 10
thus log₁₀36=log₁₀[tex]6^{2}[/tex]
log₁₀36=2 log 6
Hence the expression becomes 2log6
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1. What is greenhouse effect?
The heat of the sun penetrates the atmosphere and warms the Earth's surface. The warmed rEarth Radiates and this heat back into the atmosphere.The gases the surround the atmosphere such as carbon dioxide , methane , nitrous oxide and water vapour absorb some of the radiated heat and send it back to the Earth . This trapping of heat from the Sun by excess carbon dioxide and other gases present in the atmosphere is known as the greenhouse effect. The gases involved in the phenomenon are called greenhouse gases.
Hope it helps ~(•‿•)
Fill in the blanks
A(n) ? with a base e is a __________.
When e>1, the base - e exponential function is an increasing function.
What accurately is an exponential function?When the input variable x appears as an exponent in the formula f(x) = ax, it indicates an exponential function.The exponential curve is affected by both the exponential function and the value of x.The exponential function is a fundamental mathematical function whose formula is as follows:f(x) = aˣ
Where a>0 is not equal to 1.x can be any genuine number.If the value of the variable is negative, the function for (-1<x<1) is undefined.Here,
"x" is the variable.The function's base, "a," is a constant.Depending on the exponential function, an exponential curve can increase or decrease.If a quantity increases or decreases by a predetermined percentage on a regular basis, it should exhibit either exponential growth or exponential decay.So,
If b>1:Then the exponential function.So, f(x) = b^x is an increasing function.Therefore, when e>1, the base - e exponential function is an increasing function.
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Give an argument that shows that every polynomial family of degree n>2 contains polynomials that cannot be generated from the basic function y=xⁿ by using stretches, compressions, reflections, and translations.
Answer: because if you have a argument you have all.
Step-by-step explanation:
what do this mean positive number and negative numbers mean in context to sea level
and elevation.
b. An 80 -kg diver stands on a 6 -m diving platform. At what height should a 40 - kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.
The 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.
What is potential energy?Potential energy is the energy held by an object as a result of its position relative to other objects, internal stresses, electric charge, or other factors.The gravitational potential energy of an object, which depends on its mass and distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field are all examples of common types of potential energy. The joule, denoted by the symbol J, is the unit of energy in the International System of Units (SI).The formula of the potential energy of each driver:
Driver 1: PE = gmh = 9.8 · 80 · 6Driver 2: PE = gmh = 9.8 · 40 · hReplace the value of PE for driver 1 with the driver 2 formula.
9.8 · 80 · 6 = 9.8 · 40 · hNow, solve for (h) height:
9.8 · 80 · 6/9.8 · 40 ⇒ h - 12Therefore, the 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.
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Necesito ayuda urgenteee
Un cine tiene 800 butacas: durante la semana la asistencia fue: el lunes
2/5, martes 4/5, miércoles 4/5, jueves 1/5, viernes 3/5, sábado y domingo
completo. El precio de la entrada 8’7 €. ¿Cuál fue la recaudación de toda
la semana?
The total collection is 33408
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total = 800 seats
On Monday 2/5
So, seats= 800*2/5 = 1600/5
=320 seats
On Tuesday
seats = 800 * 4/5
=3200/5
= 640
On Wednesday
seats = 800 * 4/5
=3200/5
= 640
On Thursday
seats = 800 * 1/5
=800/5
= 160
On Friday
seats = 800 * 3/5
=2400/5
= 480
As, the ticket price is €8.7
On Monday price of ticket = 320*8.7=2784On Tuesday price of ticket = 640*8.7=5568On Wednesday price of ticket = 640*8.7= 5568On Thursday price of ticket = 160*8.7=1392On Friday price of ticket = 480*8.7=4176On Saturday price of ticket = 800*8.7=6960On Sunday price of ticket = 800*8.7=6960Hence, the total collection = 33408
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The translation of the complete question is
I need urgent help
A cinema has 800 seats: during the week the attendance was: on Monday
2/5, Tuesday 4/5, Wednesday 4/5, Thursday 1/5, Friday 3/5, Saturday and Sunday complete. The ticket price is €8.7. What was the collection of all
week?