The expression is written as a product of binomials as;
a) (x + 2) (5x + 3)
b) (x - 5) ( 3x + 2)
What is Distributive property?
Distributive property is said to be multiplying the sum of two or more number will give the same result as multiplying each addend individually by the number and then adding the products together.
Now, For solving the expression by using the distributive property "backwards" , we can find the GCD of each term using in the expression as;
(a) x(x+2) + 3(x+2) + 4x(x+2)
GCD of x(x + 2), 3(x + 2), 4x(x + 2) = (x + 2)
Hence, Firstly take (x + 2) as common term we get;
x (x + 2) + 3(x + 2)+ 4x(x + 2) = (x +2) ( x + 3 + 4x)
= (x + 2) (5x + 3)
The expression is written as a product of binomials as;
a) x (x + 2) + 3(x + 2)+ 4x(x + 2) = (x + 2) (5x + 3)
And, (b) 2x(x-5) + 3(x-5) + (x-1) (x-5)
GCD of 2x(x-5) , 3(x-5) , (x-1) (x-5) = (x - 5)
Hence, Firstly take (x - 5) as common term we get;
2x(x-5) + 3(x-5) + (x-1) (x-5) = (x - 5) (2x + 3 + x - 1)
= (x - 5) ( 3x + 2)
So, The expression is written as a product of binomials as;
b) 2x(x-5) + 3(x-5) + (x-1) (x-5) = (x - 5) ( 3x + 2)
Therefore, The expression is written as a product of binomials as;
a) (x + 2) (5x + 3)
b) (x - 5) ( 3x + 2)
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Solve. Check for extraneous solutions. (2 x+3)³/₄-3=5
x = 13/2 is not an extraneous solution.
[tex](2x+3)^{3/4}[/tex] - 3 = 5
Adding 3 on both the sides of the equation, we get
[tex](2x+3)^{3/4}[/tex] - 3 + 3= 5 + 3
[tex](2x+3)^{3/4}[/tex] = 8
On the right hand side of the equation, 8 can also be written as
[tex](2x+3)^{3/4} = 2^{(3/4)*4}[/tex]
Taking power 4/3 on both the side of the equation, we get
(2x + 3) = 2⁴
2x + 3 = 16
2x = 13
x = 13/2
Check for extraneous solution and putting x = 13/2 in the original equation, we get
[tex](2(13/2) + 3)^{3/4}[/tex] - 3 = 5
[tex]16^{3/4}[/tex] - 3 = 5
8 - 3 = 5
5 = 5
⇒ LHS = RHS
∴ x = 13/2 is not an extraneous solution.
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A frog is about to hop from the bank of a creek. The path of the jump can be modeled
by the equation h(x) = -x² + 4x + 1, where h(x) is the frog's height above the water and
x is the number of seconds since the frog jumped. A fly is cruising at a height of 5 feet
above the water. Is it possible for the frog to catch the fly, given the equation of the
frog's jump?
Answer:
The frog will catch the fly after 2 seconds of his jump.
Step-by-step explanation:
It is given that a frog is about to hop from the bank of a creek. The path of the jump can be modeled by the equation h(x) = -x² + 4x + 1, where h(x) is the frog's height above the water and x is the number of seconds since the frog jumped and a fly is cruising at a height of 5 feet above the water.
Now, let us assume that the frog catches the fly that is cruising at a height of 5 feet above the water;
=> h = 5 feet
So, let us put the value of h = 5 for time x;
=> h(x) = -x² + 4x + 1
=> 5 = -x² + 4x + 1
=> x² - 4x - 1 + 5 = 0
=> x² - 4x + 4 = 0
Now, on solving the above equation we get;
=> x² - 4x + 4 = 0
=> x² - (2 + 2)x + 4 = 0
=> x² - 2x - 2x + 4 = 0
=> x (x - 2) - 2 (x - 2) = 0
=> (x - 2) (x - 2) = 0
On comparing and solving for the value of x we get;
=> (x - 2) = 0
=> x = 2
and
=> (x - 2) = 0
=> x = 2
Therefore, the frog will catch the fly after 2 seconds of his jump.
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Write each expression in simplest form. (√y-√3)(√y+2√3)
We write the expression in its simplest form and we are left with.
y²√3 + y - 6
Before proceeding let's define an algebraic expression.
Algebraic expressionAn algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The first thing we will do is to write the expression:
(√y-√3)(√y+2√3)
Then we perform the multiplication, with the distributive property, which gives as a result
(y + 2√3y - √3y - 6)
y²√3 + y - 6
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Use the dropdown menus to complete the definition of a midpoint. please help
image below
given that x is (near, between, or before) a and b, x is the midpoint of segment ab (if or if and only if) ax= (xa, ax,ab,xb)
select the right answers for each
X is between A and B, X is the midpoint of segment AB if and only if
AX = XB.
What is a midpoint?A midpoint is a point lying between two points and is in the middle of the line joining the two points.
We have,
A_____X_____B
Given that X is ___________A and B, X is the midpoint of segment AB____________ AX= ______
We need to fill in the blanks.
X would be in between A and B.
X is a midpoint of segment AB if and only if AX = XB.
Thus,
X is between A and B, X is the midpoint of segment AB if and only if
AX= XB.
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9/53
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
The proof of DE is parallel to BC in the given triangle is shown.
What is defined as the parallel line?Parallel lines are defined as two lines that remain the same distance away and never intersect. To be parallel, two lines must be driven in the same plane, which is a perfectly flat surface such as a wall or sheet of paper.As per the given data in the question;
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)B has coordinates (2,-2)C has coordinates (-2,-4)Whereas,
D lies at the midpoint of AB.
E lies at the midpoint of AC.
The mid piont formula is;
Mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
The coordinates of D is found by the mid point formula of coordinates.
Put the coordinates of A (4, 6) and B (2,-2).
D = (4 + 2 / 2, 6 - 2 / 2)
D = (3, 2)
The coordinates of E is found by the mid point formula of coordinates.
Put the coordinates of A (4, 6) and C (-2,-4)
E = (4 - 2 / 2, 6 - 4 / 2)
E = (1, 1)
Now, the slope is calculated by;
m of DE = (y₂ - y₁)/(x₂ - x₁)
The slope of E is
m of DE = (1 - 2)/(1 - 3) = 1/3
Slope of BC
M of BC = (-4 + 2)/(-4 - 2)
M of BC = 1/2
As, the slope of both line DE and BC are equal. Thus, both line are parallel to each other.
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Find the least integer greater than each number. Do not use a calculator.
log√₇ √50
It follows that the least integer greater than log√₇ √50 is 3.
We have a logarithm function that is given to us.
Let x = log√₇ √50
We get that:√ 7 ˣ = √ 50
So, we must find an integer x, such that √ 7 ˣ > √ 50.
We know that √ 49 = 7
√ 7 ˣ > 7
7 ⁰°⁵ˣ > √ 7
x / 2 > 1
x > 2
In this case, x = 3 will be the least integer to satisfy this inequality.
Therefore, it follows that the least integer greater than log√₇ √50 is 3.
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What are the vertex and x-intercepts of the graph of the function below?
y=(x+4)(x+2)
ООС
A. Vertex: (1,-5); Intercepts: x= -4,2
B. Vertex: (1, -9); Intercepts: x= 4,-2
C. Vertex: (-4, 2); Intercepts: x= 3, -3
OD. Vertex: (-3,-1); Intercepts: x = -4,-2
can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ig
can somebody help me with these questions! helping me instead of giving me the answers is what i want but answers only is okay too ?
Here, in the figure we can see a diagram with 3 lines and few points.
1.Name a line that contains point A is A point is an intersection point of 2 lines that are line "l" and line "n".
2.Name a line that contains point D is D point is an intersection point of 2 lines that are "n" and line "m".
3.What is the another name of line m is line BD, B and D point are on the line "m" so we can say as line BD.
4.what is the another name of line n is line AD, A and D points are on the line "n" so we can say as line AD.
5.Name a point not on line AC is there are two points that are not on line AC is D and E points.
6. Name a point not on line BD is there are three points that are not on line BD is A,C and E points.
7.Name the intersection of AC and DB, B is the intersection of AC and DB.
8. Name the intersection of AD and AC, A is the intersection of AD and AC.
9. Name a point not on line l or line m is point E.
10.Name a point not on line n or line m is point E.
Intersection is nothing but a point where lines intersect is the intersection.
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This is a question from line segments part of geometry.
1. A line that contains point A is line l.
2. A line that contains point D is line n.
3. Another name for line m is line BD.
4. Another name for line n is line AD.
5. A point not on the line AC is the point D.
6. A point not on the line BD is the point A.
7. The intersection point of line AC and line DB is the point B.
8. The intersection point of line AC and line AD is the point A.
9. A point not on the line l or line n is the point E.
10. A point not on the line m or line n is the point D.
Geometry is a branch of mathematics that broadly deals with the measurement, characteristics, and connections of points, lines, angles, surfaces, and solids: the study of the characteristics of given elements that hold true even after being transformed in a certain way.
It is from line segments part of geometry.
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Solve. Check for extraneous solutions. x¹/₂-(x-5)¹/₂=2
No extraneous solution to the equation:
The equation is:
[tex]x^{1/2}[/tex] - [tex](x- 5)^{1/2}[/tex] = 2
To know whether the equation has an extraneous solution first we need to find the value of x.
[tex]x^{1/2}[/tex] - 2 = [tex](x - 5)^{1/2}[/tex]
[tex]x^{1/2} - 2[/tex] = [tex](x - 5)^{1/2}[/tex]
Now squaring both sides of the equation we have:
[tex](x^{1/2} - 2)^{2}[/tex] = x - 5
x - 4[tex]x^{1/2}[/tex] + 4 = x -5
[tex]x^{1/2}[/tex] = -9/4
x = 81/16
Now we have to put the value of x in the equation.
[tex](81/16)^{1/2}[/tex] - [tex](81/16 - 5)^{1/2}[/tex] =2
9/4 - 1/4 =2
8/4 = 2
2 =2
Therefore we get to know that there is no extraneous solution to the equation.
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What is the product of (p3)(2p2 - 4p)(3p2 - 1)? 6p7 4p4 6p7- 2p5 - 12p5 4p3 6p7 - 12p6 - 2p5 4p4 6p12 - 14p6 4p3
The product is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
We are provided with expressions in three brackets. Performing multiplication between first two brackets first. This will be followed by multiplication of the product of first two brackets with the expression of third bracket.
For multiplication, the rule of exponents to be used is -
aᵇ×aⁿ = aᵇ⁺ⁿ
Rewriting the expression
Product = (p³)(2p² - 4p) (3p² - 1)
Performing multiplication of first two brackets -
Product = (p³ × 2p² - p³ × 4p) (3p² - 1)
Product = (2p⁵ - 4p⁴) (3p² - 1)
Further performing multiplication of product with third bracket -
Product = (2p⁵ × 3p² - 2p⁵ × 1 - 4p⁴ × 3p² - 4p⁴ × - 1)
Product = 6p⁷ - 2p⁵ - 12⁶ + 4p⁴
Hence, the product of given expressions is 6p⁷ - 2p⁵ - 12⁶ + 4p⁴.
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Answer:
C: 6p7 - 12p6 - 2p5 + 4p4
Step-by-step explanation:
Source: Trust me bro
Can someone please help me?
Answer: that’s easily C because look down
Step-by-step explanation:
calculator lol I saw it don’t worry niu
what shape do i draw?
Answer:
You draw the exact same shape but at a different scale
Step-by-step explanation:
You just draw it bigger.
A stop sign is a regular octagon, formed by cutting triangles off the corners of a square. If a stop sign measures 36 in. from top to bottom, what is the length of each side?
The length of each side will be 14.8 inches approx.
It's given that an Octagon sign is drawn out of a square by cutting out triangles from its corners and the total length of the stop sign is 36 inches. We know that squares are Right Angled at each side so in the picture mentioned below, we apply Pythagoras' theorem to find an equation for the side of the sign.
=> [tex]s^{2} = x^{2} + x^{2}[/tex]
=> [tex]s^{2} = 2x^{2}[/tex] ----> Eq. 1
Also, it is a square. So, the measurement of length from side to side
=> 2x + s = 36 inch ----> Eq. 2
By solving Eq.1 we get s = (√2)(x), Putting this value in Eq.2
=> s = 36 - 2x => (√2)(x) = 36 - 2x
=> x(2 + √2 ) = 36 => x = 36/(2+√2)
Putting this value of x in Eq.1 , s^2 = 2(x^2)
=> s = √2.(x) => s = √2 (36/(2 + √2)
=> s = 14.8
Hence, the length of each side of the sign will be 14.81-inch approx.
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fraction in simplest form. 48 over 64
A hexagon has three sides of length (2x+5) in and three sides of length (x-6) in. What is the length of the longest side of the hexagon if the perimeter is 60 in?
Help I'm Being Timed!!
Answer:
varies inversely as √t
Step-by-step explanation:
Answer:
a hexagon has three sides of length (2)+ in and other three side is equal to
the length of longest side
Step-by-step explanation:
Describe how the variables in the given equation are related.
p= k q r t / s
k, q, r, t are directly proportional to p and s is inversely proportional to p.
What is inversely proportional ?The inversely proportional property state that two values are opposite to each other. If there will increase in one value or quantity then the another quantity will automatically decrease with the same ratio and if one quantity will decrease then another will increase with that ratio.
Say if x and y are inversely proportional, then mathematically
x ∝ 1 / y
What is Directly proportional ?The directly proportional property state that two values are same to each other. If there will increase in one value or quantity then the another quantity will automatically increase with the same ratio and if one quantity will decrease then another will also decrease with that ratio.
Say if x and y are directly proportional, then mathematically
x ∝ y
In the given equation,
k, q, r, t are directly proportional to p and s is inversely proportional to p.
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Solve for t.
4t + 2 + =18
Please help
Answer:
4
Step-by-step explanation:
18 - 2= 16
16/4=4
the quotient of a number x and five is half the difference of the number and four. write an equation that represents the statement.
The equation that represent the statement "quotient of a number x and five is half the difference of the number and four" is x / 5 = 4 - 1/2x
EquationQuotient means divisionThe unknown number = xx / 5 = 4 - 1/2x
collect like termsx/5 + 1/2x = 4
(2x+5x) / 10 = 4
7/10x = 4
divide both sides by 7/10x = 4 ÷ 7/10
= 4 × 10/7
= 40/7
= 5.714285714285714
Approximately,
x = 5.7
Therefore, the value of x in the equation is approximately 5.7
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Simplify a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
The simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶
Given,
a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed.
The expression : ( a⁻⁴ / 2 × b² )³
Simplify the expression :
( a⁻⁴ / 2 × b² )³
= a⁻⁴⁽³⁾ / 2³ ˣ b²⁽³⁾
= a⁻¹² / 2³ ˣ b⁶
= a⁻¹² / 8b⁶
Therefore, the simplified form of the expression ( a⁻⁴ / 2 × b² )³ is a⁻¹² / 8b⁶
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Thomas withdrew $55 from his account and later added $30. What was the overall change in his account balance?
It should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance is -$25.
How to illustrate the information?It should be noted that regarding a bank account, it should be noted that the withdrawal has to do with the amount of money that the person removes from the account.
It should be noted that deposit is an addition to the amount in the account while the withdrawal is the subtraction.
Therefore, should be noted that when Thomas withdrew $55 from his account and later added $30, the overall change in his account balance will be:
= -$55 + $30
= -$25.
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6. Jordan rounds a number, X, to one decimal place.
The result is 6.3.
Write down the error interval for X
If the approximated number is given as 6.3 Then the error interval of x is 6.24≤x≤6.35
What is Approximation?A value or quantity that is nearly but not exactly correct.
The number is given as x.
So, we have:
x = 6.3
The smallest number that can be approximated to 6.3 is 6.25 (to 1 decimal place), while the largest number is 6.34
Given that there are possibilities of error, the lower and upper bound of the error interval would be:
6.25-0.01≤x≤6.34+0.01
6.24≤x≤6.35
Hence, the error interval of x is 6.24≤x≤6.35
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Does the function below represent a linear function, an exponential function, a quadratic function, or none of these?
function----> f(x)=5*2^x
Question 1 options:
linear
exponential
quadratic
none of these
The equation of the function given as (x)= 5 * 2^x is an exponential function
How to determine the function type?The equation of the function is given as
f(x)= 5 * 2^x
An exponential function is represented as
f(x) = a * b^x
Where
Initial value = a
Rate = b
This means that
a = 5
b = 2
Hence, the equation of the function given as (x)= 5 * 2^x is an exponential function
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m∠ABC=(6x+8)° and m∠DEF=(12x−8)°. If ∠ABC and ∠DEF are supplementary, what is the measure of each angle?
Given that ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.
What is the measure of each angle?Supplementary angles are angles that sum up to 180 degrees.
Given the data in the question;
∠ABC and ∠DEF are supplementaryMeasure of ∠ABC = (6x + 8)°Measure of ∠DEF = (12x − 8)°Since ∠ABC and ∠DEF are supplementary, it means they sum up to 180 degrees.
Measure of ∠ABC + Measure of ∠DEF = 180°
Plug in the given values and solve for x
(6x + 8) + (12x − 8) = 180
6x + 8 + 12x − 8 = 180
6x + 12x + 8 - 8 = 180
18x + 0 = 180
18x = 180
x = 180/18
x = 10
Now, the numerical measure of each angle will be;
Measure of ∠ABC = (6x + 8)° = 6(10) + 8 = 60 + 8 = 68°
Measure of ∠DEF = (12x − 8)° = 12(10) - 8 = 120 - 8 = 112°
Given that ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.
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pleasem help i dont remember
The line of the graph is a solid line and the region to be shaded depends on the type of the inequality
How to use the graph to determine whether the line will be dashed or solid?The graph represents the given parameter
On the graph, we have a straight continuous line
A straight continuous line is an illustration of a solid line
This means that the line of the graph is a solid line
Hence, the line of the graph is a solid line
How to use the graph to determine whether the graph would be shaded above or below?
The graph represents the given parameter
On the graph, we can see that no region of the graph is shaded
This means that the shaded region would be determined by the type of the inequality
≥ means that the region would be shaded above
≤ means that the region would be shaded below
Hence, the region to be shaded depends on the type of the inequality
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What is each expression in simplest form?
b. (9x ⁴√y)³/²
Fractions are in their simplest form when they have no common divisors other than one at their top and bottom. The top and bottom cannot be divided further and remain integers.
You may also hear the simplest form called "lowest term."
In preferred, an expression is in only form while it's far easiest to use not unusual methods to help you simplify:
Combine Like termsFactoringincreasing (the opposite of factoring)clean out fractions by multiplyingrecognizing a pattern you have seen earlier than, just like the difference of squaresExpand the following:
(9×4 x sqrt(y)) ^(3/2)
9×4 = 36:
(36 x sqrt(y))^(3/2)
(36 x sqrt(y))^(3/2) = 36^(3/2) (x sqrt(y))^(3/2):
36^(3/2) (x sqrt(y))^(3/2)
36^(3/2) = 36^(2/2 + 1/2) = 36^(2/2)×sqrt(36):
36^(2/2) sqrt(36) (x sqrt(y))^(3/2)
2/2 = 1
Answer:
36 sqrt(36) (x sqrt(y))^(3/2).
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(5x^2+8x-4)+(7x^2-11x+3) simplify
Which of the following is not viable in order to solve the following systems of equations using Substitution?
The only option that is not viable to solve the systems of equations is:
D. Substitute y = 6/5x - 12 into the first equation
How to Solve Equations?Given the systems of equations,
2x + y = 20 ----> equation 1
6x - 5y = 12 ----> equation 2
In order to solve the system of equations using the substitution method, rewrite 2x + y = 20:
2x + y - 2x = 20 - 2x
y = 20 - 2x
Or
2x = 20 - y
x = 10 - 1/2y
Or
6x - 5y = 12
-5y = -6x + 12
y = -6/5x - 12/5
or
6x = 12 + 5y
x = 2 + 5/6y
Therefore, the only option that is not viable to solve the systems of equations is:
D. Substitute y = 6/5x - 12 into the first equation
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Evaluate the expression. – 2 5 ÷ – 1 3 – 3 5 × – 2 3 Write your answer as a fraction or as a whole or mixed number.
The solution of the expression – 25 ÷ – 13 – 35 × – 23 is 806 12/13
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
– 25 ÷ – 13 – 35 × – 23
Evaluate the quotient
So, we have
– 25 ÷ – 13 – 35 × – 23 = 25/13 – 35 × – 23
Evaluate the product
So, we have
– 25 ÷ – 13 – 35 × – 23 = 25/13 + 805
Evaluate the sum
So, we have
– 25 ÷ – 13 – 35 × – 23 = 805 25/13
Divide the fraction
So, we have
– 25 ÷ – 13 – 35 × – 23 = 805 + 1 12/13
Evaluate the sum
So, we have
– 25 ÷ – 13 – 35 × – 23 = 806 12/13
Hence, the solution of the expression – 25 ÷ – 13 – 35 × – 23 is 806 12/13
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Help very much needed 30 points.
Answer:
1. 32/80 2. 9/3 3. 1/3 4. 12/4 5. 4/1 6. 3/6 or 1/2 7. 21/18 8. 24/15 9. 25/5 10. 7/21
Step-by-step explanation:
good fraction brain
Nick estimates that 50% of his income goes toward living expenses. Of the rest 50% goes to paying for his car and 25% of what is left goes to. his other expenses. IF nick has $300 remaining at the end of the month how much does he earn?
Based on the amount that Nick is left with at the end of the month, the amount he earns is $2,400
What does Nick earn?The amount of $300 that is left is 25% of 50% of Nick's income as the other 75% of the 50% went to paying for the car and other expenses.
25% of 50% is:
= 25% x 50%
= 12.5%
The amount Nick makes per month is:
= Amount remaining / Amount remaining in percentage terms
= 300 / 12.5%
= $2,400
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