The factorization of the polynomial 10x² - 3x - 4 by grouping is (2x + 1)(5x - 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A polynomial is an expression involving addition, subtraction and multiplication of variables. A quadratic equation is a polynomial of degree two.
Given the polynomial:
10x² - 3x - 4
= 10x² - 8x + 5x - 4
= 2x(5x - 4) + 1(5x - 4)
= (2x + 1)(5x - 4)
The factorization of the polynomial 10x² - 3x - 4 by grouping is (2x + 1)(5x - 4)
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Isabel is on a ride at an amusement park that slides the rider to the right, and then rotates counterclockwise about its own center 60° every 2 seconds. How many seconds pass before Isabel completes one full rotation?
Isabel to complete one full rotation is 12 seconds.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.P ( E ) = Number of favourable outcome Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.In every 2 seconds the ride rotates 60º.
So, it takes 6 turns to rotate 6 × 60º or 360º.
Therefore, the time it takes
Isabel to complete one full rotation is 12 seconds.
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round 13.891 to the nearest tenth, i need help with math homework
Answer:
13.9
Step-by-step explanation:
13.891
the 9 is greater than 4 so it can round up the 8 to a 9
what is y if 3y+20=5y-16
Answer:
y is equal to 18
Step-by-step explanation:
[tex]3y+20-20=5y-16-20\\3y=5y-36\\3y-5y=5y-36-5y\\-2y=-36\\\frac{-2(y)}{-2}=\frac{-36}{-2}\\(\frac{-a}{-b} = \frac{a}{yb}) =\frac{2y}{2}\\\frac{2(y)}{2}=y\\=\frac{36}{2}\\=18\\y = 18[/tex]
I've been trying to figure this out for a while now, can I get some help? -53<9x+1<-26
Answer:
- 9 < x < - 3
Step-by-step explanation:
- 53 < 9x + 1 < - 26 ( subtract 1 from each interval )
- 54 < 9x < - 27 ( divide each interval by 9 )
- 6 < x < - 3
4. Drew is going to try out for the basketball team, so he decides to shoot free throws every day at the park. On the first day, he shoots 15 free throws. On the second day, he shoots 25 free throws. On the third day, he shoots 35 free throws, Drew continues to increase the number of free throws he shoots each day by the same amount. a) If Drew continues to follow this pattern, how many free throws will Drew shoot on the 20th day? b) What is the total number of free throws Drew shot during those 20 days?
Answer:
He shot a total of 2,415 free throws. He shot 255 on the 20th day.
Step-by-step explanation:
Find the value of each variable (3x+31)° (2x-6)°
Answer:
x = 31°Step-by-step explanation:
Angle (3x+31)° and angle (2x-6)° are supplementary angles
(3x + 31)° + (2x - 6)° = 180°
5x + 25° = 180°
5x = 155°
x = 31°
-----------------
check
3 * 31 + 31 + 2 * 31 - 6 = 180
180 = 180 (remember PEMDAS)
the answer is good
3(4x −2)=2(5x +3) yo i need this fast
Answer:
x=2
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
3(4x-2)=2(5x+3)
12x-6=10x+6
+6 +6
12x=10x+12
-10x -10x
2x=12
Divide by 2.
x=6
Hope this helps.
A 3-gallon bottle of fabric softener costs $40.32. What is the price per pint?
the andersons can set up 6 tables in 1 hour how many tables can they set up in 5 hours
They can set up total 30 tables in 5 hours.
How is a multiplication explained?Multiply in mathematics refers to the continual addition of sets of same size.
2 × 3 = 6
It can be interpreted this way:
Three times two equals six.
Three times two equals six.
Six is two threes.
Given,
Andersons can set up 6 tables in 1 hour
Tables they can set up in 5 hours = 5 × 6
= 30
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Divide the quantity 3.185 times ten raised to the seventeenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.. write the final answer in scientific notation. 3.5 x 108 0.35 x 109 3.5 x 109 0.35 x 1025
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .
The quantity 3.185 times ten raised to the seventeenth power can written as 3.185 × [tex]10^{17}[/tex] .
The quantity 9.1 times ten raised to the eighth power can written as 9.1 × [tex]10^{8}[/tex] .
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] ,
( 3.185 × [tex]10^{17}[/tex] )/( 9.1 × [tex]10^{8}[/tex] ) = 0.35 × [tex]10^{17-8}[/tex] = 0.35 ×[tex]10^{9}[/tex] = 3.5 ×[tex]10^{8}[/tex] (in scientific notation)
Scientific notation is a floating-point system in which the numbers are expressed as the products consisting of a number between one to ten multiplied by an appropriate power of ten.
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .
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i need help pleaseee
Answer:
UT=27
ST=18
RV=15
US=15
Step-by-step explanation:
If the entirety of RT is 30, then you'd divide that by 2 to receive the number for both RV and VT. 30 divided by 2 is 15.
Because RVS and UVT are vertical, they are both 27. Similarly, RVU and SVT are vertical to each other, so SVT is the same as RVU which is 18.
Hope this helps.
Use each recursive definition to write an explicit formula for the sequence. a₁ = 10, an =2 a n ₋ ₁
The explicit formula is [tex]a_n = 2^{n-1}.10[/tex]
What is a sequence ?A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence. There are many types of sequences such as recursive sequences, arithmetic sequences, special sequences, quadratic sequences, geometric sequences etc.
Some examples for sequence are :
2,4,6,8,10,12
3,9,27,81,243
What is recursive sequence ?The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.
In a sequence , first term always known as initial term.
and difference between two terms are known as common difference. It is denoted by d.
General form of sequence is :
[tex]a_1,a_2,a_3,----,a_n[/tex]
where , [tex]a_n[/tex] = last term in sequence.
According to question,
[tex]a_1 = 10[/tex] and [tex]a_n=2a_{n-1}[/tex]
first find the sequence ,
[tex]a_2= 2 a_{2-1} = 2 a_1 = 2(10) = 20\\\\a_3= 2 a_{3-1} = 2 a_2= 2(20) = 40\\\\a_4= 2 a_{4-1} = 2 a_3= 2(40) = 80[/tex]
Thus sequence is 10,20,40,80,...
and the explicit formula for sequence is :
[tex]a_n = 2a_{n-1}\\= > a_n = 2(2a_{n-2}) = 2^2 a_{n-2}\\= > a_n = 2^2 (2a_{n-3}) = 2^3 a_{n-3}\\ .\\.\\= > a_n = 2^{n-1} a_{n-(n-1)} \\ = > a_n = 2^{n-1} .a_1 = 2^{n-1}.10[/tex]
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A. Solves each equation by extracting square root.
1.) x² = 16
2.) x² = 49
3.) x² = 128
4.) x² = 108
5.) x² = 121
6.) x²-169 = 0
7.) x²-80=0
8.) x²-63=0
9.) 5x2 – 125 = 0
10.) 3x²-132-0
can you answer this please
Question below, only answer if you know
Answer:
1. translate
2.rotate
explanation:
first, translate a to the next quadrant.
second, rotate it 180 degrees.
Answer:
Figure A translated 2 figures down and mirrored to the right.
Figure A then rotated 180 degrees.
7
2-2
3-3
Question 6(Multiple Choice Worth 1 points)
(02.05 MC)
If the parent function f(x) = |x| is transformed to g(x) = |x - 3|, what transformation occurs from f(x) to g(x)?
The graph of f(x) is shifted upward to create g(x).
The graph of f(x) is shifted downward to create g(x).
The graph of f(x) is shifted to the right to create g(x).
The graph of f(x) is shifted to the left to create g(x).
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
Set
Answer: The graph of f(x) is shifted to the right to create g(x).
Step-by-step explanation:
g(x) is the graph of f(x) shifted right 3 units.
Please resolve it and list the steps the simplest way possible, thanks. ASAP if possible
Step-by-step explanation:
Looks like it's a piecewise defined function. Where you see a circle, means it's not inclusive so at f(1) it should be define at y=3
Draw a right triangle with side lengths that form a Pythagorean triple. If you double the length of each side, is the resulting triangle acute, right, or obtuse? if you halve the length of each side? Explain.
If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.
Pythagoras Theorem states that the sum square of two sides of triangle is equal to the square of longest side.
Let us take Pythagorean triplet as (6,8,10).
where base=6
perpendicular = 8
hypotenuse = 10
Part(a)
Let us double the length of each value
base = 12
perpendicular = 16
hypotenuse = 20
By Pythagoras Theorem
[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}[/tex]
[tex]12^{2} +16^{2} =20^{2} \\ \\ 144+256=400\\ \\ 400=400[/tex]
Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.
Part (b)
Let us halve the length of each value
base=3
perpendicular = 4
hypotenuse = 5
By Pythagoras Theorem
[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}\\\\3^{2} +4^{2} =5^{2}[/tex]
[tex]9+16=25\\ \\ 25=25[/tex]
Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.
Therefore , If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.
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[tex]\frac{1}{4} + \frac{-3}{4}[/tex]
Answer:
-1/2
[tex] - \frac{1 }{2} [/tex]
First the two fours cancel out so it's becomes
[tex] \frac{1 - 3}{4} [/tex]
then subtract
[tex] \frac{ - 2}{4} [/tex]
simplify
[tex] \frac{ - 1}{2} [/tex]
A negative sign indicates the ______ of the number?
Answer:
opposite
Step-by-step explanation:
Write an equation of a circle with the given center and radius. Check your answers.
center (-6,10) , radius 1
The equation of the circle with radius 1 and center at (-6 , 10) is (x + 6)^2 + (y - 10)^2 = 1.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-6 , 10)
r = 1
(x - -6)^2 + (y - 10)^2 = 1^2
(x + 6)^2 + (y - 10)^2 = 1
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A 3-gallon bucket of paint costs $ 81.60. What is the price per pint?
Answer: $3.40 per pint
Step-by-step explanation:
1 gallon=8 pints
3 gallons * 8 pints/1 gallon=
3*8/1=
3*8=24 pints in 3 gallons
$81.6 for 24 pints of paint
81.6/24=$3.40 per pint
Rita had a 28-mile head start.
Roger had a 26-mile head start.
Roger had a 25-mile head start.
Rita had a 22-mile head start.
Rita has a head start, has she began her race 28 Mile ahead of the starting point.
How to illustrate the information?Since they moved at a constant speed, then there speed is the same through out the journey.
Speed is given by the slope:
(y2 - y1) / (x2 - x1) = (130 - 65) / (2 - 1) = 65 / 1 = 65 mph
Roger's starting position, when t = 0
t = 1 ; distance = 65 miles
t = 0 ; 65 - speed per hour = 65
At t = 0 ; 65 - 65 = 0 miles
Hence, Roger does not have a head start.
For Rita :
Speed is also constant :
Speed or rate = slope of the graph :
(y2 - y1) / (x2 - x1) = (158 - 93) / (2 - 1) = 65 / 1 = 65 mph
Rita's starting position, when t = 0
t = 1 ; distance = 93 miles
t = 0 ; 93 - speed per hour
At t = 0 ; 93 - 65 = 28 miles
Hence, Rita has a head start of 28 miles.
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Determine whether the given function is linear. f(x) = 3 + 1/3x
you can either graph this or plug in values.
[tex]f(x)=3+\frac{1}{3}x[/tex]
[tex]f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}[/tex]
[tex]\therefore[/tex] we can conclude that this function is linear.
Also here is a graph
If x = −4 and y = −5, what is the value of 5x + 3y + 14? A. −49
B. −21 C.41 D. 49
Answer:
the value it's -21
Step-by-step explanation:
5×(-4)+3×(-5)+14=
-20 + (-15) + 14=
-20 -15 + 14=
-35 + 14=
-21.
Simplify each expression.
8. (-3)+4
8. (-3)+4
= -24 +4
= -20
What is algebric equation?In algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few field, regularly the field of the rational numbers.
algebraic equation, statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.
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In the expression 38+27 y , which number is a coefficient?
27 is the number that is a coefficient.
An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.
A coefficient is a number or an alphabet that is multiplied by a variable of a single term or the terms of a polynomial. For example, in the term 7x, 7 is the coefficient. The coefficient of x in the term 3xy is 3y.
The variable is a symbol for a value we don't know yet. It is usually a letter like x or y.
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
In the expression 38 + 27y the coefficient of y is 27, 38 is the constant and y is the variable.
we can identify a coefficient since it is always associated with a variable.
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f(x) = -5x − 3 and g(x) = 6x - 2. Find f g and its domain.
The domain is f[tex]o[/tex]g(x)= -30x+7
The domain is all the real numbers.
Given that f(x)=-5x-3 and g(x)=6x-2.
f[tex]o[/tex]g=f(g(x))
=f(6x-2)-3
=-5(6x-2)-3
=-30x+10-3
f[tex]o[/tex]g =-30x+7
The domain is all the real numbers.
What is domain?
Specific to the internet, the term domain can refer to how the internet is structured, and domain also refers to how an organization's network resources are organized. In general, a domain is an area of control or a sphere of knowledge.
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9.233050612 es el número racional o irracional
9.233050612 is a rational number.
What are rational and irrational numbers?Real numbers that can be expressed as a ratio of two integers, such as P/Q, where Q is not equal to zero, are referred to as rational numbers. Finite or repeating numbers are included in the category of rational numbers.
Real numbers are referred to as irrational numbers if they cannot be represented as the ratio of two integers. These are composed entirely of non-terminating, non-repeating numbers.
The given number 9.233050612 can be written in the form P/Q as :
9.233050612 = [tex]\frac{9.233050612}{1000000000}[/tex]
Hence, the given number is a rational number.
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The correct question is:
"9.233050612 is a rational or irrational number"
The measure of an angle is 51.1°. What is the measure of its complementary angle?
Answer:
let the complementary angle be x
51.1°+x=90°
x=90°-51.1°
x=38.9°
Write the equation of the line in slope-intercept form.
(x/6) - (5/12)y = 5/8
The equation of the line in slope-intercept form is y = (2/5)x + (-3/2) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is (x/6) - (5/12)y = 5/8 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
(x/6) - (5/12)y = 5/8
On multiplying both sides of above equation by (12/5), we will get
(2/5)x - y = 3/2
⇒ y = (2/5)x + (-3/2) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 2/5
Intercept = c = -3/2
The equation of the line in slope-intercept form is y = (2/5)x + (-3/2) .
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