Answer:
The possible values of the constant b are:
[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]
Step-by-step explanation:
The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.
Expand the cubed part by using the (a + b)³ formula:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Therefore:
[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]
So:
[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]
To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:
[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]
[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]
Therefore, the expression for the coefficient of x² is:
[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]
Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:
[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]
Therefore the possible values of the constant b are:
[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]
Your friend hides a dollar bill under one of three plastic cups. Under the other
two cups is a paper clip. You get to keep whatever is under the cup you
choose, but you don't know which contains the dollar bill. After you choose,
your friend lifts one of the other cups to reveal a paper clip and then gives you
the option of changing your choice.
Should you switch to the other cup?
A. No. The probability of winning the dollar is regardless of the cup
your choose.
B. Yes. If you switch cups, the probability of winning the dollar
increases from to 1/1.
OC. Yes. If you switch cups, the probability of winning the dollar is 3.
D. No. If you switch cups, the probability of winning the dollar is.
Answer: B
Step-by-step explanation:
25 Points! Please help!!
excel ran out of resources while attempting to calculate one or more formulas?
This error message typically occurs when Microsoft Excel is unable to perform a calculation due to running out of memory or system resources.
This can happen when a spreadsheet is extremely large, has many complex formulas or when a large number of calculations are performed simultaneously. To resolve the issue, you can try closing other programs and processes running on your computer, increasing the amount of memory allocated to Excel, breaking down a large spreadsheet into smaller spreadsheets, or simplifying the formulas in your spreadsheet. If these steps do not work, you may need to seek assistance from a technical support expert. This error message typically occurs when Microsoft Excel is unable to perform a calculation due to running out of memory or system resources.
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The function machine at right
follows the equation h(x) = 5x + 2.
a. If the crank is turned backwards, what number should be pulled up into the machine in order to have a 4 come out of the top?
b. Keiko wants to build a new machine that will undo what h(x) does to an input. What must Keiko's machine do to 17 to undo it
and return a value of 3?
c. An "undo" function is called an inverse and has the notation h¹(a). Note that the -1 is not a negative exponent. It is the
mathematical symbol that indicates the inverse function of h(x). Write an equation for h ¹(x), the "undo" function machine.
d. Choose a value for z. Then find a strategy to show that your equation, h¹(x), undoes the effects of the function machine h(x).
Answer: C
Step-by-step explanation: An "undo" function is called an inverse and has the notation h¹(a). Note that the -1 is not a negative exponent. It is the
mathematical symbol that indicates the inverse function of h(x). Write an equation for h ¹(x), the "undo" function machine.
the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4. what are the coordinates of k?
Given that, the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4.
The coordinates of the point k are (9,10)
The concept of section formula asserts that if a line segment is divided into two pieces in a certain ratio, the coordinates at the point of division may be obtained using the formula:
(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = K
where (x1, y1) and (x2, y2) are the line segment's endpoint coordinates, and m:n is the provided ratio by which the line segment is divided.
The ends of the line segment IJ in this example are I(3,5) and J(17,19), and the ratio by which it is divided is 3:4, implying that IK:JK is 3:4.
As a result, m:n = 3:4, implying that m = 3 and n = 4.
When we enter these values into the formula, we get:
K = (3 x 17 + 4 x 3)/(3+4), (3 x 19 + 4 x 5)/(3+4)
When we simplify this expression, we get:
K = ( 51 + 12)/(7), (57 + 20)/(7)
K = (63)/(7),(77)/(7)
K = 9,10
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Relative to a fixed origin O, the point A has position vector (2i + 3j - 4k), the point B has position vector (4i - 2j + 3k), and the point C has position vector (ai + 5j – 2k), where a is a constant and a < 0.
D is the point such that AB = BD.
(a) Find the position vector of D.
Given AC| = 4,
(b) find the value of a.
Answer: (a) To find the position vector of point D, we need to find the midpoint of the line segment AB. We can do this by taking the average of the position vectors of points A and B:
D = (A + B) / 2 = ((2i + 3j - 4k) + (4i - 2j + 3k)) / 2 = (3i + 0.5j - 0.5k)
So, the position vector of point D is (3i + 0.5j - 0.5k).
(b) To find the value of a, we use the fact that the distance between points A and C is 4. We can find the distance between two points by finding the magnitude of the difference between their position vectors. The position vector of point C is (ai + 5j – 2k), so the difference between the position vectors of points A and C is (ai + 5j – 2k) - (2i + 3j - 4k) = (a-2)i + 2j - (-2k).
The magnitude of this difference is given by:
|(ai + 5j - 2k) - (2i + 3j - 4k)| = √((a-2)^2 + 2^2 + 2^2) = 4
So, we have:
√((a-2)^2 + 2^2 + 2^2) = 4
(a-2)^2 + 2^2 + 2^2 = 16
(a-2)^2 = 16 - 4 - 4
(a-2)^2 = 8
a-2 = ±2√2
Since a < 0, we have:
a = 2 - 2√2
So, the value of a is 2 - 2√2.
Step-by-step explanation:
A store purchases battery chargers
from the manufacturer for $10 each.
Calculate the sticker price for the
chargers in order to achieve an 80%
gross margin.
A. $50.00
C. $20.00
B. $12.50
D. $18.00
In order to achieve an 80% gross margin, the store would need to sell the battery chargers for $50 each - A
Finding cost Price of sticker
The gross margin is the difference between the selling price and the cost of the item, expressed as a percentage of the selling price. To achieve an 80% gross margin, we need to set the selling price such that 80% of it represents the profit on the item.
Let's call the selling price of the battery charger S. The profit on the item is S - $10, since that is the cost of the item. So, to achieve an 80% gross margin, we want:
(S - $10) / S = 0.80
Expanding and solving for S:
S - $10 = 0.80S
0.20S = $10
S = $50
So, in order to achieve an 80% gross margin, the store would need to sell the battery chargers for $50 each. That would be the sticker price for the chargers.
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Select the correct answer.
What is the value of x in the triangle?
7√3
60°
OA. 21
OB. 10
O C.
C. 7
O D. 7√3
30%
ratio of heights of 2 triangles is 3:4, area 4:3, ratio of their base?
Ratio of the base of two triangles is 16:9 , if ratio of heights of two triangles is 3:4 and area 4:3.
It is given that the ratio of heights of two triangles is 3:4 and the ratio of area of two triangles is 4:3
We have to find the ratio of their base
The basic formula for the area of a triangle is equal to half the product of its base and height or [tex]\frac{1}{2} \times base \times height[/tex]
Let b₁ , b₂ are the base of two triangles respectively
So, ratio of areas of triangles : [tex]\frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]
[tex]\frac{4}{3} = \frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]
[tex]\frac{b{1}}{b_{2}} =\frac{16}{9}[/tex]
So, ratio of the base of two triangles is 16:9
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PLEASE HURRY
E
B
D
AC = 14 cm
EC = 84 cm
ED = 21 cm
C
Given the following segment lengths,
find the length of segment AB.
The length of the segment AB is 3.5 cm
What is a line segment ?
A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.
We have segments ratio as shown:
BC/AB = CD/ED
=> (AC - AB)/AB = (EC - ED)/ED
=> (14-AB)/AB = (84-21)/21 = 3
Let AB=x
=> (14-x)/x = 3
=> 14-x = 3x
=> 14 = 3x+x = 4x
=> 14/4 = x
=> x=3.5 cm
AB=x = 3.5 cm
The length of the segment AB is 3.5 cm
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WILL GIVE BRAINLIEST
What is JL?
Right triangle J K L has K as its right angle. A segment connects K to M on side J L. Angle J M K is a right angle. K M equals 6 and J M equals 8.
JL =
Answer:
Step-by-step explanation:
To find the length of JL in the right triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, JL is the hypotenuse and JK and KL are the two shorter sides.
Since K is a right angle in triangle JKL, we can find the lengths of JK and KL using the given information. We have KM = 6 and JM = 8, so we can use those values to find JK and KL:
JK = √(JM^2 - KM^2) = √(8^2 - 6^2) = √(64 - 36) = √(28) = 2√(7)
KL = KM = 6
Finally, to find JL, we can use the Pythagorean theorem:
JL = √(JK^2 + KL^2) = √( (2√(7))^2 + 6^2) = √(4 * 7 + 36) = √(52) = 2√(13)
So, JL = 2√(13).
In aright angle triangle,the measure of one acute angle is 6 more than two times the measure of other acute.
The measure of the smaller acute angle is 26 degrees, and the measure of the larger acute angle is 64 degrees.
Let's call one acute angle x and the other acute angle y.
Since they are both acute angles of a right triangle, we know that their sum is 90 degrees:
x + y = 90
We also know that one angle is 2 times the other angle plus 6:
x = 2(y + 6)
Now we can substitute the second equation into the first equation and solve for y:
x + y = 90
2(y + 6) + y = 90
3y + 12 = 90
3y = 78
y = 26
Now that we have the value of y, we can use the second equation to solve for x:
x = 2(y + 6)
x = 2(26 + 6)
x = 64
Therefore, the measure of the smaller acute angle is y = 26 degrees, and the measure of the larger acute angle is x = 64 degrees.
Correct Question :
In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 6. find the measure of each acute angle.
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Please help (will mark as brainlest)
Answer:
(9y + 4)(5x + 7)
Step-by-step explanation:
factoriser les expressions :
16x+4
Answer:
4(4x+1)
Step-by-step explanation:
16x+4
Factor out 4,
4(4x+1)
A right triangle has side lengths 7, 24 and 25as shown below.
Use these lengths to find tan L, sin L, and cos L.
In the given right angle triangle the measure of tanL, sinL, and cosL is 73.74°.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecent/hypotenuse and
tan = opposite/adjacent.
Given, A right-angled triangle has side lengths 7, 24, and 25.
Here, Hypotenuse is 25, Adjacent is 7 and opposite is 24.
Now, tan = opposite/adjacent.
tanL = 24/7.
L = tan⁻¹(24/7).
L = 73.74°.
Similarly,
sinL = 24/25.
L = sin⁻¹(24/25).
L = 73.74°.
And,
cosL = 7/25.
L = cos⁻¹(7/25).
L = 73.74°.
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Pls show your work thank you will mark the Brainliest
Answer D
Step-by-step explanation:
what is the solution to 2j=16+4j
Answer: j = -8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
2j = 16 + 4j
collecting like terms, you would have
2j - 4j = 16
-2j = 16
divide both sides by 2
j = 16/(-2)
j = -8
Simplify g³ x g³‼️‼️‼️
Answer:
[tex]g^6[/tex]
Step-by-step explanation:
When multiplying exponents, for example
[tex]x^2 * x^5[/tex]
Their power values are added together to get
[tex]x^2 * x^5 = x * x * x* x* x* x* x = x^7[/tex]
Answer:
[tex]g^6[/tex]
Step-by-step explanation:
because, [tex]g^3*g^3[/tex] is basically [tex]g^(^3^+^3^)[/tex] which is [tex]g^(^6^)[/tex] = [tex]g^6[/tex]
Sin (x-30)*cos (x/2) >0
Answer:
15
Step-by-step explanation:
Use the Slope Formula to calculate the slope of a line with these two points. Find the slope of the line that passes through (1, 9) and (8, 8).
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }[/tex]
Line l is a straight line. 2 line intersect line l to form 4 angles. From top left, clockwise, the angle are: x, y, z, w.
Which statements are true about the angles in the figure? Select two options.
Angle x and angle y are supplementary angles.
Angle W and angle Z are a linear pair.
Angle W and angle Y are adjacent angles.
Angle X and Angle Z are vertical angles.
The statements are A. ∠x and ∠y are supplementary angles, B. ∠w and ∠z are a linear pair.
Describe an angle and its types?Angle is the void between two surfaces or lines that meet. The angle is also expressed in degrees. The angle is 360 degrees for a full rotation.
Supplementary angle: When two angles add up to 180 degrees, they are considered to be supplementary angles.
Corresponding angle: The third line if two lines are parallel. Equal angles are formed by the matching angles.
Angles that are vertically opposed to one another are equal when two lines intersect.
Alternate angle: When two lines are parallel, a third line forms a z-angle, which is an equal angle to the parallel lines.
Complementary angle - When two angles add up to 90 degrees, they are considered to be complementary angles.
Angle x and angle y are supplementary angles. True.
Angle w and angle z are a linear pair. True.
Angle w and angle y are adjacent angles. False.
Angle x and Angle z are vertical angles. False.
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Make a prediction about what might happen if you have ten birds.
Answers:
1.There is no relationship.
2.You'll have nine angry neighbors.
3.You'll have either five or six angry neighbors.
4.You'll have six angry neighbors.
5.You'll have either seven or eight angry neighbors.
The prediction about what might happen if you have ten birds will be 5. You'll have either seven or eight angry neighbors
What is a word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, it should be noted that as the number of birds increase, the number of angry neighbor increased too. Therefore, the prediction about what might happen if you have ten birds will be that you'll have either seven or eight angry neighbors.
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How do you multiply polynomials step by step?
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, we can be multiply two polynomials step by step.
Distribute each term of the first polynomial to every term of the second polynomial.
Combine like terms by adding the coefficients of the terms that have the same variables raised to the same powers.
Simplify the result by arranging the terms in descending order of the exponent of the variable.
For example, let's say you want to multiply (2x + 3) and (x - 4):
(2x + 3) * (x - 4) = 2x * x - 2x * 4 + 3 * x - 3 * 4
Simplify the terms: 2x^2 - 8x + 3x - 12
Combine like terms: 2x^2 - 5x - 12
Therefore, the product of (2x + 3) and (x - 4) is 2x^2 - 5x - 12.
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The equations represent the elevations, y, of two hikers, in meters, after x hour. Wich ordered pair, (0, 0), (1, 7) or (2, 10), is a solution to the system? will the hikers ever be the same elevation? explain. Y = 6x + 1
y = 3x + 4
yes. the hikers will ever be the same elevation.6+1=7 the same elevation.
Y = 6x + 1
FIll the value of y in this equation
3x + 4= 6x + 1
3x=4-1
x=3/3=1
Y = 6x + 1
FIll the value of x in this equation
6+1=7. The height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface. Elevation should not be confused with the angular separation from the Earth's center. The summits of Mount Everest and Chimborazo have the highest elevation and greatest geocentric distance, respectively, because of the equatorial bulge.
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Quanto é
78+34789+1+234+5678
the answer is 40780
I would show you my calculations but I don't know how to add pictures to your answer .sorry
I hope that helped
A composite figure is shown.
Which of the following represents the total area of the figure?
A. 222 cm2
B. 240 cm2
C. 258 cm2
D. 294 cm2
The total area of the composite figure is 258 squared centimeters.
What is the area of the composite figure?The figure in the diagram is composed of two triangle and a rectangle?
The area of a triangle = 1/2 × base × height
Area of a rectangle = length × width
From the diagram;
Triangle 1
base = 4cmheight = 12cmTriangle 2
base = 12cmheight = 3cmRectangle
length = 18cmwidth = 12cmTo find the area of the composite figure, we find the area of the two triangle and rectangle and add.
Area = area of triangle 1 + area of triangle 2 + area of rectangle.
Area = ( 1/2 × base × height ) + ( 1/2 × base × height ) + ( length × width )
Area = ( 1/2 × 4 × 12 ) + ( 1/2 × 12 × 3 ) + ( 18 × 12 )
Area = ( 2 × 12 ) + ( 6 × 3 ) + ( 18 × 12 )
Area = 24 + 18 + 216
Area = 258cm²
Therefore, the area is 258 squared centimeters.
Option C) 258cm² is the correct answer.
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Answer:
258cm^2
Step-by-step explanation:
A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of multiplication problems to total problems?
Answer as a fraction in simplest form.
Answer: 1/3
Step-by-step explanation: The ratio of multiplication problems to total problems is 12:36, which can be simplified to 1:3.
Answer:
A
Step-by-step explanation:
Hi there.
We know this math exam has 12 multiplication and 24 division problems, making the overall exam questions 36 problems. (12+24=36)
The ratio is the fraction equivalent comparison between two variables. In this case, it's multiplication problems over total problems.
We know multiplication problems as 12, and we calculated the total, which is 36.
The answer would be 12/36; but it's divisible by 12 and can be further simplified to 1/3.
WILL GIVE BRAINLIEST, PLEASE HURRY
Which transformations take the graph of f(x)=6x to the graph of g(x)=6x−4+2?
Choose each correct answer.
Responses
The graph is translated to the right 4 units.
The graph is translated up 2 units.
The graph is translated down 4 units.
The graph is translated to the right 2 units.
The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.
What is Graph?
In mathematics, a graph is a collection of points, called vertices or nodes, and a collection of lines, called edges, that connect pairs of vertices. Graphs are used to represent relationships between objects, such as the connections between different parts of a network or the dependencies between different variables in a system. They are commonly used in fields such as computer science, operations research, and engineering to model and solve problems involving complex systems.
The correct transformations are:
The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.
The graph is translated up 2 units. This is because there is a constant term of +2 added to the function, which means the function has a vertical shift upwards by 2 units.
Therefore, the correct answers are:
The graph is translated to the right 2 units.
The graph is translated up 2 units.
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the probability that a specific vulnerability within an organization will be attacked by a threat is known as . a. determinism b. externality c. potential
The probability that a specific vulnerability within an organization will be attacked by a threat is known as potential.
Potential refers to the likelihood that a specific vulnerability in an organization's security will be exploited by a threat actor or attacker. In the field of information security, the concept of potential is used to assess the risk associated with a particular vulnerability.
This risk assessment helps organizations to prioritize their security efforts and allocate resources where they are most needed. Determinism is a philosophical and scientific concept that refers to the idea that events are determined by prior causes, rather than by random chance.
Externality is an economic term that refers to the impact of an economic activity on parties not directly involved in the activity. For example, pollution from a factory may have externalities that affect the health and well-being of people who live near the factory.
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Jack Tupp, an auto parts dealer, earns 15% commission on his first $2,000 in
auto part sales, and 5% on the balance. Jack sold earned $5,975 worth of
auto parts last week. How much commission did Jack make?
Answer: Jack made $898.25 in commission
Step-by-step explanation:
Jack made $898.25 in commission. ($2,000 x 15%) + ($3,975 x 5%) = $898.25
[tex]5975-2000=3975[/tex] this is the amount jack earns 5% commission on
