in the polynomial function F(x)=1/2x^2+8-5x^3-19x what is the leading the coefficient
Answer:
-5
Step-by-step explanation:
The leading term in a polynomial consist on the highest degree term. To get the highest degree term, we need to reorder the polynomial from left to right, starting with the highest degree term.
In this case:
[tex]f(x)=\frac{1}{2} x^{2} +8-5x^{3} -19x[/tex]
reordering
[tex]f(x)=-5x^{3} +\frac{1}{2}x^{2} -19x+8[/tex]
So, the leading coefficient is the one with the leading term:
[tex]-5x^{3}[/tex]
So, it is -5
Solve the following quadratic equation using the quadratic formula.
5x^2 − 8x + 5 = 0
Write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form.
x = r − si/t,x = r + si/t
Quadratic equations can be solved using several methods; one of them, is by using quadratic formula
The solution to [tex]5x^2 - 8x + 5 = 0[/tex] is: [tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]
The equation is given as:
[tex]5x^2 - 8x + 5 = 0[/tex]
The quadratic formula is:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
In the given equation;
[tex]a = 5\\b = -8\\c = 5[/tex]
So:
[tex]x = \frac{-(-8) \± \sqrt{(-8)^2 - 4 \times 5 \times 5}}{2 \times 5}[/tex]
[tex]x = \frac{8 \± \sqrt{-36}}{10}[/tex]
Expand
[tex]x = \frac{8 \± \sqrt{36} \times \sqrt{-1}}{10}[/tex]
[tex]x = \frac{8 \± 6 \times \sqrt{-1}}{10}[/tex]
In complex numbers;
[tex]i = \sqrt{-1}[/tex]
So, we have:
[tex]x = \frac{8 \± 6 \times i}{10}[/tex]
[tex]x = \frac{8 \± 6i}{10}[/tex]
Simplify
[tex]x = \frac{4 \± 3i}{5}[/tex]
Split
[tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]
Hence, the solution to [tex]5x^2 - 8x + 5 = 0[/tex] is: [tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]
Read more about quadratic formulas at:
https://brainly.com/question/9701183
Frank owns 250 acres of land. If he divides the land into 1/3 acre plots, how many plots will he have?
You are required to choose two topics from a list of six to write about on your science test. How many different pairings are possible?
10
15
20
12
Brenda’s bank offers car financing for 3, 4 or 5 years. If brenda chooses 5-year financing, how many monthly payments will she have?
An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?
A. 8 units
B. 6 units
C. 5 units
D. 3 units
Answer
The answer is 6
Step-by-step explanation:
A triangular flag has an area of 187.5 square inches. The base of the flag measures 25 inch How tall is the triangular flag?
Answer:
To find the height, you would do the area divided by the base, or in this case,187.5 / 25 which equals 7.5 inches
Step-by-step explanation:
A drawer of loose socks contains 2 red socks, 2 green socks, and 6 white socks. Which best describes how to determine the probability of pulling out a white sock, not replacing it, and pulling out another white sock?
Answer:
The probability that the first sock is white is 6/10 and that the second sock is white is 5/9, so the probability of choosing a pair of white socks is 30/90 = 1/3! Hope that helps.
Step-by-step explanation:
Original tv cost: 700$
Current tv cost: 500$
Find the percent of decrease
Round to the nearest whole percent
Hi
The answer : the percent of decrease is 29%
The length of a rectangle is twice it’s width.The length is 12cm.Work out the area of the rectangle
Answer:
Step-by-step explanation:
As with all word problems we first have to convert it to an equation or equations.
L = length of the Rectangle and W = its width
So L = 2 * W
A = area of the rectangle which is 128 cm^2
So A = L * W = 128 cm^2
substitute 2W for L from the 1st equation to give A = 2 * W * W = 2 * W^2 = 128 cm^2
Thus W^2 = 64 cm^2
finally W = 8 cm and therefore L = 2 * W = 16 cm
The perimeter P = 2 * (L+W) = 2* (8cm + 16cm) = 2 * 24cm = 48 cm
Will mark 5 stars
The variable used to show correlation is r, which is also known as the correlation complement.
A.True
B.False
help me please...
Problem: The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:
Complete the square showing all your work to convert to Standard Form:
If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.
Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.
Verify the equation below with each of the values listed for t to find a solution.
4 = 2t +8
simplify
can u plz help me on this its a math question !!!!!
theres an image below!!!
Answer:
6
----------- 6 over 729
729
Step-by-step explanation:
2/9 * 2/9 * 2/9
If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square
An equation of a function y(t) is shown.
y(t)=−t²+14t−40
Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?
a. The value of y(t) increases over the interval 6≤t≤7
b. The value of y(t) increases over the interval 7≤t≤8
c. The average rate of change over the interval 6≤t≤8 is 0
d. The value of y(t) is constant over the interval 6≤t≤8
e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8
The graph of y(t) increases over the interval 6≤t≤7 because the derivative is positive. The average rate of change over the interval 6≤t≤8 is 0 due to symmetry about the vertex of the parabola at t=7. The rate of change over the intervals 6≤t≤7 and 7≤t≤8 are equal in magnitude but opposite in direction.
Given the quadratic function y(t)=-t²+14t-40, we need to analyze its behavior over the interval 6≤t≤8. The first derivative y'(t) of the function, which represents the slope of the tangent line to the graph at any point t, is -2t + 14. To determine the intervals of increase and decrease, we can set the first derivative to zero to find the vertex of the parabola, yielding t=7, which means the function increases on the interval 6≤t≤7 and decreases on 7≤t≤8.
The average rate of change over an interval is calculated by taking the difference in the function values at the endpoints of the interval over the difference in t. For the interval 6≤t≤8, since this is a symmetrical interval around the vertex, the average rate of change is 0. Furthermore, it follows from symmetry that the average rate of change over the intervals 6≤t≤7 and 7≤t≤8 should be equal in magnitude but opposite in sign.
Considering the stated properties and analyzing the equation, we can conclude that:
The value of y(t) increases over the interval 6≤t≤7.The value of y(t) decreases over the interval 7≤t≤8, so statement b is false.The average rate of change over the interval 6≤t≤8 is 0, making statement c true.The value of y(t) is not constant over the interval 6≤t≤8.The average rates of change over both intervals 6≤t≤7 and 7≤t≤8 are not equal in value; they are opposite, making e false.ABCD is an isosceles trapezoid with legs AB and CD, and base BC. If the length of AB = 6y +5, the length of BC= 4y - 6, and the length of CD= 2y +1, what is the value of y?
To find the value of y in the given isosceles trapezoid ABCD, we can set up an equation AB = CD and solve for y.
Explanation:To find the value of y in the given isosceles trapezoid ABCD, we can set up the equation AB = CD and solve for y.
Given that AB = 6y + 5 and CD = 2y + 1, we have the equation 6y + 5 = 2y + 1.
Simplifying this equation, we can subtract 2y from both sides to get 4y + 5 = 1.
Finally, subtracting 5 from both sides gives us 4y = -4.
Dividing both sides of the equation by 4, we find that y = -1.
To find the value of y in an isosceles trapezoid ABCD with given side lengths in terms of y, we set the equations for the congruent legs, AB = 6y + 5 and CD = 2y + 1, equal to each other and solve for y, arriving at y = -1.
Explanation:To find the value of y in an isosceles trapezoid where the lengths of the sides are given in terms of y, we can utilize the properties of an isosceles trapezoid. In an isosceles trapezoid, the legs (non-parallel sides) are congruent. Given that AB = 6y + 5 and CD = 2y + 1, and these lengths must be equal for ABCD to be an isosceles trapezoid, we can set up the following equation:
6y + 5 = 2y + 1
Solving for y, we subtract 2y from both sides to get:
4y + 5 = 1
Now, subtract 5 from both sides:
4y = -4
And finally, divide by 4 to find y:
y = -1
Thus, the value of y is -1.
Dustin is driving his car at speed of 50 kilometres per hour. he going to texas which is located 345 kilometres from his starting point.how long will it take him to reach texas?
The ratio of boys to gils in art class is 1:2 there a 12 girls in the class. how many boys are there
Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β < α.
sin(7x − 15) = cos(3x + 5)
Answer:
The answer is B). 35
Step-by-step explanation:
I did it on USA Test Prep
A shipping box in the shape of a rectangular prism has a volume of 18x^3+5x^2-2x. what are three expressions that can represent possible dimensions of the shipping box?
Answer:
[tex](x), (9x-2), (2x+1)[/tex]
Step-by-step explanation:
[tex]18x^3+5x^2-2x=x(18x^2+5x-2)=x(9x-2)(2x+1)[/tex]
Are the two events “choosing a sophomore” and “choosing someone who replied ‘Yes’” independent events?
PLEASE PLEASE HELP
question is attached
Short Answer
x1 = 4.8284
x2 = - 0.828
Remark
Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y.
Step one
Solve for y in the first equation. Subtract x from both sides.
y = 2 - x
Step Two
Equate the two ys.
2 - x = - 1/4x^2 + 3
Step Three
Bring the left side over to the right side.
0 = -1/4 x^2 + x + 3 - 2 Combine the like terms.
0 = -1/4 x^2 + x + 1
Step Four
0 = -1/4 x^2 + x + 1 Multiply through by 4
0 = - x^2 + 4x + 4
Step five
This won't factor. The only thing you can do is use the quadratic equation for roots.
a = - 1
b = 4
c = 4
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.8284
I hope this helps
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.82
In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is the value of x?
a. 60 degrees
b. 90 degrees
c. 100 degrees
d. 120 degrees
Answer:
(D) 120 degrees
Step-by-step explanation:
From the figure drawn, we have
∠ABC=60°
And ∠OAB=∠OCB=90° (angles made by tangent on the circle is 90°)
Thus, ∠AOC+∠OCB∠CBA+∠OAB=360° (Angles sum property of quadrilateral)
[tex]x+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}[/tex]
[tex]x+240^{\circ}=360^{\circ}[/tex]
[tex]x=120^{\circ}[/tex]
Therefore, the value of x is [tex]120^{\circ}[/tex]
Hence, option D is correct.
Answer: d. 120 degrees
Step-by-step explanation:
From the given figure drawn, we can see that
∠ABC=60°
Also we know that tangents are radius are perpendicular at the point of tangency
And ∠OAB=∠OCB=90° (∵ tangents are radius are perpendicular at the point of tangency)
Therefore, we have
[tex]\angle{AOC}+\angle{OCB}+\angle{ABC}+\angle{OAB}=360^{\circ}\text{ ( By Angle sum property of quadrilateral)}\\\\\Rightrarrow\ x+90^{\circ}+60^{\circ}+90^{\circ}=360^{\circ}\\\\\Rightarrow\ x=360^{\circ}-240^{\circ}\\\\\Rightarrow\ x=120^{\circ} [/tex]
Consider the function graphed below
Which of the following would triple the volume of the Egyptian square-based Pyramid below?
A. Multiply only the height by 3.
B. Add 3 to each dimension of the Pyramid.
C. Multiply every dimension of the Pyramid by 3.
D. Add 3 to the slant height.
Final answer:
To triple the volume of a square-based Egyptian pyramid, you must multiply every dimension of the pyramid by 3. This is because volume is proportional to all three dimensions of the shape, and changing just one dimension won't achieve the desired effect.
Explanation:
The question asks which action would triple the volume of a square-based Egyptian pyramid. The volume (V) of a pyramid is calculated using the formula V = (1/3) × base area × height. To triple the volume, you would need to triple the factor of each dimension because volume is a three-dimensional measurement, and changing one dimension alone would not be sufficient.
Option A suggests multiplying only the height by 3, but this would not triple the volume as the base area remains the same. Option B suggests adding 3 to each dimension, but adding a constant to linear dimensions does not maintain a proportional relationship to volume.
Option D suggests adding 3 to the slant height, which does not directly correlate to the volume. Therefore, option C is correct: Multiplying every dimension of the Pyramid by 3 would indeed triple the volume because changing each dimension equally maintains the proportion. This is similar to how if a block's dimensions were doubled (2L × 2L × 2L), the new volume would be 8 times the original (8L³).
A number is chosen at random from 1 to 50. find the probability of selecting numbers with 3 in the tens places
If GP=PH, GA =17, mED = 37, and mAB = 87, find each measure.
ONE LAST QUESTION!!!!!!!!!!WILL GIVE THE BRAIN!!!!!!!!!!
Given a possible triangle ABC with a=5,b=11,and a=23, find a possible value for