The fourth term on expansion of the expression (d - 4b)^3 is d. [tex] {-64b}^{3} [/tex].
To find the fourth term in the expression in question, [tex] {(d - 4b)}^{3} [/tex] will be calculated by expanding the expression. The expression will be expanded based on the formula -
[tex] {(a - b)}^{3} [/tex] = a³ - 3a²b + 3ab² - [tex] {b}^{3} [/tex]. This expanded form of the expression has four terms. Hence, keeping the values on Left Hand Side, we will get four terms for the expression mentioned in question.
So, expanding the expression according to formula by keeping the values of a and b as d and 4b -
[tex] {(d - 4b)}^{3} [/tex] = d³ + 3d²4b + 3d16b² - [tex] {-64b}^{3} [/tex]
Now, depending on this expansion of the question mentioned in expression, [tex] {-64b}^{3} [/tex] is the fourth term. Thus it is the correct option.
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The complete question is -
What is the fourth term of (d - 4b)^3?
a. b^3
b. -b^3
c. 64b^3
d. -64b^3
A Fibonacci-type sequence that has been studied by mathematicians is the Lucas sequence, named after a French mathematician of the nineteenth century. The first ten terms of the Lucas sequence are 1, 3,
4,7, 11, 18, 29, 47, 76,123 what
is the
term of the Lucas
The eleventh term of the Lucas sequence is?
The eleventh term of the Lucas' sequence is 199
How to determine the eleventh term of the sequence?From the question, we have the following parameters that can be used in our computation:
1, 3, 4,7, 11, 18, 29, 47, 76,123
As a general rule of Fibonacci, the current term of a sequence is the sum of the two previous terms
This means that
11th term = 10th term + 9th term
Substitute the known values in the above equation, so, we have the following representation
11th term = 123 + 76
Evaluate the sum
11th term = 199
Hence, the 11th term is 199
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percent proportions and equations what do you call a destroyed angle
The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
Given, a destroyed angle
A destroyed angle is called a figure in Geometry also known as Rectangle.
A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
Therefore, the destroyed angle is a rectangle.
Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
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Sample Test 4: Cartesian Graphing
Score: 38 / 200 \quad 4 / 20 answered
Question 14
Determine the slope of the line represented by the equation: 3 x+1 y=3
Slope DO NOT USE 1 AS THE DENOMINATOR!
Write answer as an integer or a reduced fraction.
The slope of the line is - 3
How to calculate the slope of a line?The equation of the line is given by,
3x + 1y = 3
y = -3x + 3 ---(1)
The slope- intercept form of a line is given by ,
y = mx + c ---(2)
where ,m is the slope
c is the y intercept
Comparing (1) and (2)
The slope of the line is , m = -3
What is a slope?A value known as slope can be used to define a line's direction and steepness. It is represented by the letter m in variable format. The gradient or rate of change of a line is another name for its slope. The line gets steeper as the slope's magnitude goes up. The line grows less steep as the slope's magnitude diminishes, which is the opposite of what happens. A line's direction can also be determined by a slope. A line that extends from left to right and has an upward slope is said to be growing.To learn more about slope, refer:
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4. If there were
10,164 total votes, how many yes votes were there?
Answer:
There are 6468 yes votes
Step-by-step explanation:
10164÷(7+4)×7
=10164÷11×7
=924×7
=6468
How do you find the missing side of a congruent triangle?
Triangles that are exactly the same in size and shape are said to be congruent. Two triangles are said to be congruent when their corresponding sides and angles are also congruent.
What is Traingle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Using the Triangle Sum Theorem, we can determine the third angle in a triangle when only two angles are known.
The two angles' combined angles are subtracted from 180 degrees.
The diagram needs a third angle. Try to match the angles and sides of two triangles with the provided information if the congruence statement is not provided in the problem.
List the corresponding vertices in the same order once the vertices of the two triangles have been matched. The congruence assertion reads as follows if vertex A relates to vertex D, vertex B to E, and vertex C to F:
△ABC≅△DEF
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles are still congruent even if we flip, spin, or otherwise alter one of them.
Two triangles must have the same angles and, as a result, must be congruent if their sides are the same. If two triangles are congruent or not, we may determine this simply by looking at their sides.
These two triangles are also equivalent if we know that two sides of one triangle and the angle between them are congruent to two sides and the angle between them of another triangle.
Likely, these two triangles are congruent if we know that two angles and the side between them in one triangle are congruent with two angles and the side between them in another triangle.
When two angles and a non-included side in a triangle are congruent to one another, this is the final scenario that results in congruent triangles.
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How do you find the solution to a linear equation?
The solution to a linear equation can be found by balancing the variables.
A linear equation is one that carries a degree of one as its maximum value. None of the variables in these equations, thus, has an exponent greater than one. Moreover, the graph of these equations will always also be a straight line. A mathematical equation resembles a balance scale with identical weights on either side.
An equation remains valid even if the same integer is added to or subtracted from both sides. Similarly to this, an equation is accurate if the same integer is multiplied or divided into both sides. We place the constant on one side of the equation, and the variables on the other, and then we calculate the value of the unknown variable. This is how a linear equation with a single variable is solved.
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what is the value of this expression when w 5 w2 3w 11 a 51 b 36 c 16 d 1
The value of this expression when w = -5 in w² + 3w - 11 is -1
Algebraic expressions comprises of at least one variable and one operation, it is an expression built up from integer constants, variables, and the algebraic operations
We need to find the value of this expression when w = -5 in w² + 3w - 11
After substituting the value of x as 5, we get the expression as
5² + 3(-5) - 11
25 - 15 - 11
25 - 26
= -1
Therefore, the value of this expression when w = -5 in w² + 3w - 11 is -1
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What is 6\9 reritten.
Answer:
Simplied:
2/3
Step-by-step explanation:
So basically so look at the factors and find that 6 and 9 both divided by 3 so 6/3=2 and 9/3=3
so 2/3
But if you are looking for equivalent:
8/12
6/9= 0.66 repeating which is 60/90 (I think)
HOPE THIS HELPS!!
How do you read and analyze a Punnett square?
The Punnett square is a square diagram that is used to predict the genotypes of a particular cross or breeding experiment.
The genotypes of a certain cross or breeding experiment are predicted using the Punnett square, a square diagram. It bears Reginald C. Punnett's name, who developed the method in 1905. Biologists use the graphic to estimate the likelihood that a child will have a specific genotype.
The likelihood that a cross would produce children with a specific genotype is represented by a Punnett square. It does not depict live children. For instance, the Punnett square in Figure 3 demonstrates that there is a 25% chance that the cross Aa x Aa will produce homozygous recessive offspring.
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Determine the value of x.
Answer:
14.5
Step-by-step explanation:
You would use cos for this. 12/cos 56 = 14.5...Therefore you would have 14.5
The value of x in the triangle using trigonometric identities is 14.5 units.
Option A is the correct answer.
We have,
Sin x = Perpendicular / Hypotenuse
Now,
From the triangle,
Sin 56 = 12/x
0.83 = 12/x
x = 12/0.83
x = 14.46
x = 14.5
Thus,
The value of x in the triangle is 14.5 units.
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Help with my math please
Answer:
$27,000 at 8%$3,000 at 7%Step-by-step explanation:
You want the amounts invested in each of two accounts, one earning 7% and the other earning 8% simple interest, when the total investment of $30,000 earns total interest of $2370.
SetupLet x represent the amount invested at 8%. Then the amount invested at 7% is 30000-x. The total interest earned is ...
0.08(x) +0.07(30000-x) = 2370
Solution0.01x +2100 = 2370 . . . . simplify
0.01x = 270 . . . . . . . . subtract 2100
x = 27000 . . . . . . . multiply by 100
30000-x = 3000
Deshaun invested $27,000 at 8% and $3,000 at 7%.
The product of 5 and the sum of 3 and a number is 20.
Answer:
The product of 5 and the sum of 3 and 1 is 20
Step-by-step explanation:
Equation:
5*(3+x)=20
15+5x=20
5x=5
x=1
What are 2 ways to solve a division problem?
Answer: Put it as a fraction then divide the numerator by the denominator but they have to be divided by the same number. Or just divide.
Step-by-step explanation:
For each function, select whether it’s inverse is a function or not a function. refer to the attached picture.
Function
y=x⁴
y=x⁹
y=x⁸
y=x¹¹
The inverses of the functions y= x⁹ and y= x¹¹ are functions.
The inverses of the functions y = x⁴ and y= x⁸ are not functions.
How is the functionality of the given functions determined?(a )Consider ,the inverse of the function is a function
(2 ) y= x⁹
The inverse of the function is given by,
x = [tex]\sqrt[9]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
So, this is a function.
(4) y= x¹¹
The inverse of the function is given by,
x = [tex]\sqrt[11]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
Similarly , this is a function.
(b ) Consider ,the inverse of the function is a not a function
(1 )y = x⁴
The inverse of the function is given by,
x = [tex]\sqrt[4]{y}[/tex] (y ≥0)
It is of one- one correspondence,
when y = 4 ,
x = ±√2
Thus, it is not a function.
(3) y= x⁸
The inverse of the function is given by,
x = [tex]\sqrt[8]{y}[/tex]
Likewise , this is not a function.
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What type of triangle is def?
An isosceles triangle therefore has both two equal sides and two equal angles.
What is traiangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the previous illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg).
An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces. The isosceles right triangle is yet another unique instance of an isosceles triangle.
The Pythagorean theorem can be used to determine the height of the isosceles triangle shown in figure:
[tex]h = \sqrt{b^2-\frac{1}{4}a^2 }[/tex]
Consequently, the region is given by:
A=1/2ah
A = [tex]\frac{1}{2}a\sqrt{b^2-\frac{1}{4}a^2 }[/tex]
[tex]A = \frac{1}{2}a^2\sqrt{\frac{b^2}{a^2}-\frac{1}{4} }[/tex]
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Identify the recursive formula for the sequence 900, 850, 800, 750,...
C (3rd Answer)
1st term is 900 and as n increases (number of terms increase), each time it goes down by 50 if n is greater than 1.
which function is positive for the entire interval 3 2
The graph is representing the function that is positive for the entire interval [-3 , -2] .
In the question ,
four graphs are given ,
we need to identify the graph of the function that is positive for the interval [-3 , -2] .
From the graphs given , we observed that
Graph1 :
the value of the function at -3 is 0 , and it is decreasing from [-3 , -2] . Thus the function is negative in the interval.
Grpaph2:
we can clearly see that the function has a positive value, through the interval [-3 , -2] .
In Graph3 :the value of the function is negative in the given interval . and in Graph4 : the value of the function is both positive and negative in the given interval .
Therefore , the function represented by Graph 2 is positive .
The given question is incomplete , the complete question is
Which function is positive for the entire interval [-3 , -2] from the given graphs ?
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please I need help on question 8
Answer:
BM = 20m
YZ = 13m
m∠B = 39
m∠M = 34
m∠Y = 107
Step-by-step explanation:
CM = 16m
BM = 20m
YZ = 13m
m∠B = 39
m∠M = 34
m∠Y = 107
May I please have a brainliest? Thank you!
A rectangular parking lot has an area of 2/3 of a square kilometer. The width is 1/2 of a kilometer. What is the length, in kilometers, of the parking lot?
Group of answer choices
5/3 km
2/3 km
1/3 km
4/3 km
Answer:
Step-by-step explanation:
2/3 = 1/2x
2/3 / 1/3 = x
x = 4/3
Answer: The answer is 4/3
Step-by-step explanation: I have my ways ;>
What is the point of concurrence of perpendicular bisectors of a triangle?
The points of concurrency of perpendicular bisectors of triangle is circumcenter.
A point of concurrency shared by three or more lines is referred to as a single point of concurrency. Constructed lines in triangle interiors are excellent places to look for points of convergence.
When you construct a triangle's medians, perpendicular bisectors, angle bisectors, or altitudes, you create a point of concurrency for each of them.
Because the triangle can have four distinct types of line segments, it can have four distinct points of convergence. Each point of concurrency represents the intersection of a particular type of line segment: centroid, circumcenter, incenter, and orthocenter.
The centroid of the triangle is the point of convergence shared by the three medians.The point at which the triangle's three angle bisectors intersect is known as the incenter.The three perpendicular bisectors will intersect at the circumcenter, which is a point of convergence.The orthocenter is the point at which the three altitudes/heights of a triangle intersect.Thus, the points of concurrency of perpendicular bisectors of triangle is circumcenter.
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The equation of line T, shown below, can be written in the form y=mx+c.
What are the values of m and c?
Give each of your answers as an integer or as a fraction in its simplest form.
The straight line has the equation, y = 5x - 4.
What is the equation of a straight line?A straight line is made up of an infinite number of points that are joined on both sides of the point.
Any straight line's slope 'm' is given by:
m = y2 - y1 / x2 - x1
In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.
The obtained points from the graph are (0,-4) and (1,1)
The slope is ,
m = 1-(-4) / 1-0
= 5/1
= 5
Because it intersects the y-axis at the point where the intercept C = -4,
The line's equation will be:
⇒ y = mx + c
⇒ y = 5x + (-4)
⇒ y = 5x - 4
As a result, the equation for the straight line shown below is y = 5x - 4.
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What is root domain example?
The root domain in the DNS system of the Internet is a domain that is indicated by an empty name (i.e., containing no characters).
Each domain is split from the next when you enter a domain name, and there may also be a dot at the end of the name to demarcate the empty name for the root domain. If this dot is present and in its proper location, such as "www.example.com," the domain name is regarded as full (absolute). The name is regarded as relative if there isn't a dot at the end ("www.example" or "www.example.com").
Even if the phrase "root domain" was frequently used, the primary domain name of the website is the one that must be purchased or registered with a TLD extension.
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(b) Circle the two pairs of numbers that have
Highest Common Factor (HCF) 4 \4 and
Least Common Multiple (LCM) 60
The pairs of numbers that have HCF 4 and LCM 60 are : 4 and 60 , 12 and 20.
What is LCM and HCF?In this case, we must use the following relationship between HCF and LCM:
Number 1 + Number 2 = HCF x LCM
In other words, multiplying both factors equals multiplying the given numbers that we are looking for. We don't know the numbers yet, but we can get an idea of what they could be by calculating the product of the factors:
4 x 60 = 240
We know that the products should be 240 and that if the HCF is 4 , then both numbers can be divided by 4 as the highest factor, so let's write the multiple of 7:
4-digit multiples:
4, 8, 12, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
By using, we can get an idea: if 60 x 4 = 240, all we need to do is find the other two numbers that result in 240:
So the pairs of numbers are 4 and 60 , 12 and 20.
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ASAP
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
23.04
19.2
10.0
2.8
The value of variable x is 19.20.
How to solve equations ?Let's find the value of variable x in the equation.
A variable is a number represented with letters in an equation.
Therefore,
x / 6 + 4 / 10 = 3 + 6 / 10
Therefore, let's find the variable x.
10x + 24 / 60 = 30 + 6 / 10
10x + 24 / 60 = 36 / 10
60 × 36 = 10(10x + 24)
2160 = 100x + 240
2160 - 240 = 100x
1920 = 100x
divide both sides by 100
x = 1920 / 100
x = 19.20
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Expand.
Your answer should be a polynomial in standard form.
−5qx^{2} ( − q − 5 ) =
The expansion of the polynomial expression is −5q²x² + 25qx²
How to expand the polynomial expression?The polynomial expression is given as
−5qx^{2} ( − q − 5 ) =
Rewrite the expression properly
So, we have the following representation
−5qx²(−q − 5)
Remove the bracket
So, the expression becomes
−5qx²(−q − 5) = −5qx² * −q −5qx² * − 5
Evaluate the products
−5qx²(−q − 5) = −5q²x² + 25qx²
Hence, the expanded expression is −5q²x² + 25qx²
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Evaluate 732,178 + 167 - 542,137 =
Answer: 190208
Step-by-step explanation:
A dairy farmer wants to mix a 45% protein supplement and a standard 15% protein ration to make 1200 pounds of a high-grade 40% protein ration. How many pounds of each should he use?
A dairy farmer needs to mix 450 pounds of protein supplement, 30 pounds of protein ration and 480 pounds of high-grade protein ration.
Given that, a dairy farmer wants to mix a 45% protein supplement.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let x be number of pounds farmer wants to mix a 45% protein supplement.
Here,
0.45x + 0.15(1200-x) = 0.40(1200)
⇒ 0.45x +180-0.15x = 480
⇒ 0.30x=480-180
⇒ 0.30x=300
⇒ x=300/0.30
⇒ x=1000
Here, 45% of 1000
= 450 pounds
15% of (1200-100)
= 0.15×200
= 30 pounds
40% of 1200
= 480 pounds
Therefore, a dairy farmer needs to mix 450 pounds of protein supplement, 30 pounds of protein ration and 480 pounds of high-grade protein ration.
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Function and function notation
Please help asap
The value of function f(1/2) = 9.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between input variables in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x seems to be the input. A function is typically represented as y = f. (x). In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) as well as their outputs (also referred to as the codomain), where each input does have exactly one output and the output could be linked to its input.
Given function f(x) = (4+x)/x
put x = 1/2,
f(x) = (4+1/2)/1/2
f(x) = 9/2/1/2
f(1/2) = 9
Now f(3) = (4+3)/3
=7/3
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A box is 36 inches long,18 inches wide, and 6 inches deep. How many
cubic feet are in the box?
A 2.25 cubic feet
B) 4.5 cubic feet
C) 5 cubic feet
D) 3 cubic feet
Answer:
A
Step-by-step explanation:
The volume in cubic inches is [tex](36)(18)(6)=3888[/tex].
This is equal to [tex]3888/12^3=2.25[/tex] cubic feet.
Express each of the following ratios in the form 1:N
8:13
Answer:
Step-by-step explanation:
i just need the points bro