Answer: The correct option is (B) [tex]\dfrac{9}{4}.[/tex]
Step-by-step explanation: We are given to find the term that has to be added to [tex]x^2-3x[/tex] to be a perfect trinomial.
Let, c denote the term to be added.
Then,
[tex]x^2-3x+c\\\\=x^2-2\times x\times \dfrac{3}{2}+c\\\\\\=x^2-2\times x\times \dfrac{3}{2}+\dfrac{9}{4}+c-\dfrac{9}{4}\\\\\\=\left(x-\dfrac{3}{2}\right)+c-\dfrac{9}{4}.[/tex]
Therefore, the given expression will be a perfect trinomial if
[tex]c-\dfrac{9}{4}=0\\\\\\\Rightarrow c=\dfrac{9}{4}.[/tex]
Thus, the required term to be added is [tex]\dfrac{9}{4}.[/tex]
Option (B) is CORRECT,
A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the rectangle is three times the width. How many linear feet of fence must he buy if the perimeter of the rectangle is 320 feet?
Final answer:
The farmer needs to buy 320 linear feet of fence to enclose the rectangular area behind his barn.
Explanation:
Let's represent the width of the rectangle as x. Since the length is three times the width, we can represent the length as 3x. The perimeter of a rectangle is calculated by adding up all four sides, so we have the equation:
2(x + 3x) = 320
Simplifying, we get:
2(4x) = 320
8x = 320
x = 40
So the width of the rectangle is 40 feet, and the length is 3 times that, which is 120 feet. The perimeter is calculated by adding up all four sides: 40 + 120 + 40 + 120 = 320 feet. Therefore, the farmer needs to buy 320 linear feet of fence.
when is a rectangle a square?
a) when its sides are parallel
b) when its angles are right angles
c) when its sides are congruent
d) when its angles are convex angles
A rectangle becomes a square when all of its sides are congruent, which is the defining characteristic that differentiates it from a rectangle. While rectangles do share other attributes such as parallel sides, right angles, and convex angles, these do not specifically define a square.
A rectangle becomes a square when all of its sides are congruent. This by definition means that all four sides of the shape are of equal length. While rectangles do have parallel sides and right angles, these characteristics alone do not suffice to differentiate a square from a rectangle, as rectangles also have these attributes. In the case of convex angles, both squares and rectangles have angles that are convex, so this also cannot be used to distinguish a square from a rectangle.
To specifically address the options provided:
a) when its sides are parallel: This is true for both rectangles and squares, but it doesn't make a rectangle a square.b) when its angles are right angles: Again, both shapes share this characteristic so it doesn't define a square specifically.c) when its sides are congruent: This is the defining characteristic of a square compared to a rectangle.d) when its angles are convex angles: Both rectangles and squares have convex angles, so this does not define a square.Therefore, the most accurate answer is (c) when its sides are congruent.
By what percent will a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%?
40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.
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 "%".
Given that, numerator is decreased by 30% and its denominator is decreased by 50%.
Let x/y be the original fraction.
Then, the new fraction is (x-30% of x)/(y-50% of y)
= 0.7x/0.5y
Now, difference = 0.7x/0.5y-x/y
= 0.7x/0.5y - 0.5x/0.5y
= 0.2x/0.5y
Percentage increase = 0.2x/0.5y ÷ x/y
= 0.2/0.5 ×100
= 40%
Therefore, 40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.
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Jaws made his figure from six congruent squares the edge of each square was 8 inches which figure did Josh construct what is the surface area of his figure
simplify the expression given below
Factorise x^2 + 3x -40
Hazel has an assortment of red, blue, and green balls. The number of red balls is the number of blue balls. The number of green balls is more than the number of blue balls. In total, she has balls.
An equation created to find the number of blue balls will have?
When finding the number of blue balls in the scenario described, the equation will have x + x + x + 1 = 9, where x represents the number of blue balls.
An equation created to find the number of blue balls will have:
Let x be the number of blue balls.
The equation will be x + x + x + 1 = 9.
Solving the equation, we get x = 2.67.
Does the graph represent a function that has an inverse function?
A. Yes
B. No
Answer: A. Yes.
Step-by-step explanation:
To find out if the function represented in the graph has an inverse function, you must apply the Horizontal Line Test, which is used to know if a function is a One-to-one function.
A one-to-one function is that function where each x value has an unique y value.
Therefore, if in the Horizontal Line Test, the horizonal intersects the graph of the function at only and only one point, then the function has an inverse function.
As you can see in the graph attached, the horizontal lines intersect the function at only one point, therefore, you can conclude that it is a One-to-one function and it has an inverse function.
TRUE. The graph represents a function that has an inverse function because it passes the horizontal line test.
Explanation:The graph represents a function that has an inverse function if and only if each horizontal line crosses the graph at most once. This is known as the horizontal line test. If a function passes the horizontal line test, then it has an inverse function. If it fails the horizontal line test, then it does not have an inverse function.
In this case, we can see that the graph passes the horizontal line test because each horizontal line intersects the graph at most once. Therefore, the graph represents a function that has an inverse function.
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The sun is 25 degrees above the horizon. find the length of a shadow cast by a building that is 100 feet tall. round your answer to two decimal places. the length of the shadow is ____ feet.
Answer:
214.45 feet.
Step-by-step explanation:
Please find the attachment.
Let x be the length of building's shadow.
We have been given that the sun is 25 degrees above the horizon. The length of the building is 100 feet tall.
We can see from our attachment that the length of the building is opposite side and the length of the shadow is adjacent side for the angle of 25 degrees.
Since tangent relates the opposite side of right triangle with adjacent side, so we can set an equation to find the length of building's shadow as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(25^{\circ})=\frac{100}{x}[/tex]
[tex]x=\frac{100}{\text{tan}(25^{\circ})}[/tex]
[tex]x=\frac{100}{0.466307658155}[/tex]
[tex]x=214.45069\approx 214.45[/tex]
Therefore, the length of shadow cast by the building is 214.45 feet.
The legs of a right triangle are 13 and 22 inches long. Needa says that the hypotenuse is 17.7 inches long and Monifa says that it is 25.6 inches long. Is either of them correct? Explain
One number is 4 less than twice a second number. find a pair of such numbers so that their product is as small as possible.
Answer:
Numbers are -2 and 1.
Step-by-step explanation:
Let x be the second number,
⇒ First number = 4 less than twice a second number
= 2 × Second number - 4
= 2x - 4
Thus, the product of first and second number is,
[tex]f(x) = x(2x-4)[/tex]
[tex]\implies f(x) = 2x^2 - 4x[/tex]
Differentiating with respect to x,
[tex]f'(x) = 4x -4[/tex]
Again differentiating with respect to x,
[tex]f''(x) = 4[/tex]
Now, for maximum or minimum,
[tex]f'(x)=0[/tex]
[tex]\implies 4x - 4 = 0\implies 4x = 4\implies x = 1[/tex]
Since, for x = 1, f''(x) = Positive,
Therefore, the function f(x) is minimum for x = 1,
⇒ The product is smallest for x = 1,
Hence, the second number = x = 1,
And, first number = 2x - 4 = 2 - 4 = -2
A building in san fransico is shaped like a square pyramid. It has a slant height of 856.1 feet and each side of its base is 145 feet long. Find the lateral area of the building.
In 33,294 how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
The value of the 3 in the ten thousands place is 30,000, while the value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number.
Explanation:The value of the 3 in the ten thousands place in 33,294 is 30,000. The value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number. In this case, the 3 in the ten thousands place is ten times greater than the 3 in the thousands place.
suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is pi/3. what is the length of the third side of the triangle
The length of the third side of the triangle will be 2.65 units.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle C, then we have:
a² + b² – 2ab cos(C) = c²
A triangle has two sides of length 2 and 3 and that the angle between these two sides is π/3.
Then the length of the third side of the triangle will be
c² = 2² + 3² – 2 x 2 x 3 x cos(π/3)
c² = 4 + 9 – 12 x (1/2)
c² = 13 – 6
c² = 7
c = √7
c = 2.65 units
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find the mean and median of these numbers 14, 3, 15, 4, 3, 11
Will someone please do number 8 for me ?
lindsey earn $70 for working 5 hours. how much does she earn for working 12 lawns?
Answer $ 168
as per the question,
money earned for working 5 hours = 70
money earned for working 1 hour = 70/5= 14
money earned for working 12 hours = 12 * 14
money earned for working 12 hours = $168
A jogger ran 3 miles due east of his house. then he ran 5 miles at a heading of 30o east of north (or 30o ne). how far is he from his house after running 8 miles
We want to find how far is the jogger from his house after he runs a total of 8 miles, we will see that the distance is equal to 7 miles.
So we need to define a coordinate axis, the point (0, 0) will be the jogger's house (where he/she starts). North is the positive y-axis and East is the positive x-axis.
Then the jogger starts at (0, 0).
Then he ran 3 miles due East, so the new position is:
(0, 0) + (3mi, 0) = (3mi, 0)
Then he ran 5 miles at 30° East of North (or 60° North of East).
The components are:
x-component = 5mi*cos(60°) = 2.5 miy-component = 5mi*sin(60°) = 4.33 miThen the new position is:
(3mi, 0) + (2.5mi, 4.33 mi) = (5.5mi, 4.33 mi)
The distance to the jogger's house is just the magnitude of that final vector, which is:
|| (5.5mi, 4.33 mi) || = √( (5.5mi)^2 + (4.33mi)^2) = 7mi
So the jogger is at 7 miles from his/her house.
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The jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast after running 8 miles.
Explanation:To find how far the jogger is from his house after running 8 miles, we need to calculate the resultant displacement. The jogger ran 3 miles due east, so his displacement in the east direction is 3 miles. Then, he ran 5 miles at a heading of 30° east of north (or 30° NE). We can split this displacement into the north and east components. The east component can be calculated as 5 miles * cos(30°) = 5 miles * 0.866 = 4.33 miles. The north component can be calculated as 5 miles * sin(30°) = 5 miles * 0.5 = 2.5 miles.
To calculate the resultant displacement, we can use the Pythagorean theorem. The east and north components form a right triangle, with the resultant displacement as the hypotenuse. The magnitude of the resultant displacement can be found as √(3^2 + 4.33^2 + 2.5^2) = √(9 + 18.7489 + 6.25) = √33.9989 = 5.83 miles. The direction of the resultant displacement can be found using trigonometry. tan(θ) = opposite/adjacent = (2.5 miles + 3 miles)/(4.33 miles) = 5.5/4.33. Taking the arctan of both sides, θ = arctan(5.5/4.33) = 51.83°. Therefore, the jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast.
what is the perimeter of a right trianglr whose hypotenuse is the line segment A(-6,4) B(2,-1)
Verify the identity. Show your work. cos(α - β) - cos(α + β) = 2 sin α sin β
Find equations for the tangent plane and the normal line at point upper p 0(3 comma 5 comma 0) on the surface negative 7 cosine left parenthesis pi x right parenthesis plus 3 x squared y plus 5 e superscript xz baseline plus yz equals 147.
starting value 16 increases by 50% with each teem
What is the equation of this circle in general form?
x² + y² + 8x + 10y + 25 = 0
x2+y2−8x−10y+25=0
x2+y2−8x−10y+37=0
x² + y² + 8x + 10y + 37 = 0
Tis the actual answer :)
Math question
Algebra 2, Fundamental Theorem of Algebra, Stste the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots. One root has been given.
x^6 - 3x^5 + 2x^4 - 6x^3 - 15x^2 + 45x = 0; 3
(if possible please provide work)
twice a number x is at most -24. 2x ≥ -24
The value of x should be equal to and greater than -12.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
twice a number x is at most -24.
So, the mathematical expression is
2x ≥ -24
Now, divide both side by 2
2x / 2 ≥ -24 /2
x ≥ -12
So, the value of x should be equal to and greater than -12.
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The lines shown below are parallel. If the green line has a slope of -2, what is the slope of the red line?
Jenny has $25 and she earns $10 for each lawn that she mows. Jenny wants to buy a concert ticket that costs $65. Enter the minimum number of lawns Jenny needs to mow to be able to buy the concert ticket. $$
Answer:
4 Lawns
Step-by-step explanation:
Jenny wants to buy a concert ticket that costs = $65.00
Jenny has $25.00.
She needs more to buy a concert ticket = 65 - 25 = $40.00
For each lawn that she mows she earns = $10.00
For $40 she needs to mow = 40 ÷ 10 = 4 lawns
Jenny needs to mow 4 lawns to be able to buy the concert tickets.
Need the rate of change!!!
Two points: (30, 14) and (34, 17)
In a certain class 40% of students are girls and 20% of the girls wear glasses what percent of the children in the class a girl who wear glasses?
The percentage of the children in the class who is a girl and wears glasses is 8%.
Given that:
Total students in the class = 100%
Percentage of students in the class who are girls = 40%
Percentage of girls who wear glasses = 20%
It is required to find the percentage of students in the class who are girls wearing glasses.
This can be found as:
P = 40% × 20%
= 0.4 × 0.2
= 0.08
Now 0.08 in terms of percentage is 0.08 × 100 = 8%.
Hence the percentage of girls who wear glasses is 8%.
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Dana and her 4 friends are going on a camping trip. Dana wants to see how much fruit she can share so everyone will get the same amount of fruit. There are 5 apples, 10 oranges, 5 strawberries and 10 grapes. How much will each person get?