Describe the number and type of roots for the polynomial (how many real and complex?). x3 + 5x2 – 4x – 2 = 0
A quadrilateral has angles that measure 71°, 74°, 113°, and x°. What is the measure of x?
what is the product (7x^3y^3)(3x^5y^8)
a)10x^5y^15
b)10x^10y^24
c)21x^7y^11
d)21x^10y^24
You have studied polynomials consisting of constants and/or variables combined by addition or subtraction. The variables may include exponents. The examples so far have been limited to expressions such as 5x4 + 3x3 – 6x2 + 2x containing one variable, but polynomials can also contain multiple variables. An example of a polynomial with two variables is 4x2y – 2xy2 + x – 7.
Many formulas are polynomials with more than one variable, such as the formula for the surface area of a rectangular prism: 2ab + 2bc + 2ac, where a, b, and c are the lengths of the three sides. By substituting in the values of the lengths, you can determine the value of the surface area. By applying the same principles for polynomials with one variable, you can evaluate or combine like terms in polynomials with more than one variable.
The product of (7x²y³) and (3x⁵y⁸) is obtained by multiplying the coefficients and adding the exponents of like terms, resulting in c) 21x⁷y¹¹.
To find the product of the two algebraic expressions (7x²y³) and (3x⁵y⁸), we simply multiply the coefficients and add the exponents of corresponding variables:
Multiply the coefficients: 7 * 3 = 21
Add the exponents of x: x² * x⁵ = x²⁺⁵ = x⁷
Add the exponents of y: y³ * y⁸ = y³⁺⁸ = y¹¹
Therefore, the product is 21x⁷y¹¹, which corresponds to option (c).
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Algebra 2 Question! I will make sure to give a medal and pin the most helpful answer!
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola. The equation for this parabola is y = -x^2 + 36. (Graph of a parabola opening down at the vertex (0,36) crossing the x–axis at (-6,0) and (6,0))
In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.
Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created with your table positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice.
Are elite runners thinner than the average person? Devon thinks that skin thickness of elite runners is thinner than the average person. He compares a data set of elite runners to regular people by looking at the skin thickness. Which statement correctly compares the two groups?
A) The skin thickness of the elite runners varied by about 11 mm.
B) The skin thickness of the average person varied by about 11 mm.
C) The skin thickness of elite runners is on average about 11 mm thinner than that of the average person.
D) The skin thickness of the average person is on average about 11 mm thinner than that of the elite person.
Answer:
c is the answer
Step-by-step explanation:
The current San Francisco cable railway is driven by two large 14-foot-diameter drive wheels, called sheaves. Because of the figure-eight system used, the cable subtends a central angle of 270°on each sheave. Find the length of cable riding on one of the drive sheaves at any given time.
Answer:
The length of the cable is around 32.97 feet.Step-by-step explanation:
The problem is about a circular sector, where the angle is 270° and the lenght of the subtended arc is the arc is the unknown variable.
The radius of the drive wheel is
[tex]r=\frac{d}{2}=\frac{14}{2}=7ft[/tex]
The central angle is 270°.
The length of the arc is
[tex]L=\frac{2\pi r \theta}{360\°}[/tex]
Replacing all values, we have
[tex]L=\frac{2(3.14)(7)(270\°)}{360\°}=\frac{11869.2}{360} \approx 32.97[/tex]
Thereofre, the length of the cable is around 32.97 feet.
Mrs. Smith and her daughter Laura want to learn ballet. The cost of beginning ballet classes for kids is $3,200 per year, and it increases by 2% every year. The cost of beginning ballet classes for adults is $4,800 per year, and it increases by 2.7% per year. Which function can Mrs. Smith use to determine the total cost of their ballet classes, T(x), after x years?
Solve the equation using square roots. x2 + 10 = 9
A. Plus or minus the square root of 1.
B. no real number solutions
C. 1
D. –1
Answer:
no real number solutions
Step-by-step explanation:
How to estimate the square root of a number that is not a perfect square?
marion is making trail mix for a group camping trip. she buys 3 pounds of granola for $3 per pound and 0.75 pounds of raisins for $2 a pound. what equation can you use to find the price per pound of the trail mix?
It's B on edg. 3(3) + 0.75(2) = (3 + 0.75)x
Anita brings 6 dolls to her grandmas house. These dolls represent 20% of Anita's doll collection. What is the total number of dolls in Anita's dolls collection?
Answer:
30 is your answer
Step-by-step explanation:
One leg of a right triangle measures 8 inches and the hypotenuse 17 inches. determine the length of the other leg.
a. 9 inches
b. 13 inches
c. 15 inches
d. 17 inches
50 POINTS PLEASE HELP show work answer all 3
Answer:
b.) The graph's x-intercepts are similar to ½(x - 5)(x + 2).
a.) [-2, 0], [5, 0]
__________________________________________________________
b.) The graph has a maximum value because the graph opens down [-2 = A].
a.) [-3, -4]
__________________________________________________________
d) [0, -5]
c) -2 = x
b) [-2, -9] → [h, k]
a) -1, 5 = x
Explanation:
b) Both graphs have the binomial of [x - 5][x + 2], so the x-intercepts never altered.
a) Set the binomial equal to zero, and you will get your x-intercepts of [-2, 0] and [5, 0].
__________________________________________________________
b) When A is negative, your graph will have a maximum value [opens down], whereas when A is positive, your graph will have a minimum value [opens up].
a) According to the Vertex Formula, y = A[X - H]² + K, [H, K] represents the vertex, plus, -H gives you the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL labeling your vertex. Additionally, K gives you the NORMAL TERMS.
__________________________________________________________
d) The y-intercept is your C-term, so in this case, it is [0, -5].
c) To find the axis of symmetry, use this formula:
[tex] \frac{-b}{2a} = x[/tex]
Whatever the opposite of your B-term is, you take that and divide it by twice your A-term.
b) To find the vertex, in this case, you have to go from Standard Form to Vertex Form by completing the square, using this formula to get part of your new C-term:
[tex][\frac{b}{2}]^{2} [/tex]
When done, you get this:
[tex]y = {x}^{2} + 4x + 4 \\ \\ y = [x + 2]^{2} [/tex]
Then, you have to deduct some number from 4 that gave you -5 in the first place, and that integer is -9. So, here is the result:
[tex]y = [x + 2]^{2} - 9[/tex]
From here, we can see that our vertex is [-2, -9].
a) When the binomial is set to equal to zero, you get this:
[tex]{x}^{2} + 4x - 5 \\ \\ [x - 1][x + 5] = 0 \\ \\ 1, \: -5 = x[/tex]
e) See above photograph
I am joyous to assist you anytime.
Which graph represents the function?
Solve the system of equations using the substitution method.
{4x+5y=7
{y=3x+9
Enter your answers in the boxes.
x=
y=
I need help on how to convert the radian into degrees for 7pi/10 !!
Which of the following best explains why one graph appears skewed and one graph appears symmetric?
The intervals on the x-axis of the histogram are too large.
The interval on the y-axis of the histogram is too small.
The interval on the x-axis of the histogram is inconsistent.
The interval on the box-and-whisker plot is too small.
Answer:
The interval on the X-Axis of the Histogram is inconsistent
Step-by-step explanation:
edge
The medicine capsule shown consists of a cylinder with a hemisphere at each end. The total length of the capsule is 18 millimeters. The diameter is 7 millimeters. Which choice is the best approximation of the total surface area of the capsule? Use 3.14 to approximate pi.
Answer:396
Step-by-step explanation:
The sum of three numbers is 12. The first number is the difference of the other two numbers. When you add the other two numbers and subtract 8, the result will be the first number. Find the numbers.
2, 4, 6
2, 5, 5
3, 7, 2
5, 10, -3
The marketing department of a sports supply store wants to estimate the percentage of adults in the town who belong to a gym.
Which statement describes a method that will help the marketing department accurately estimate this percentage?
A)Select the store’s first 20 customers every day for one week, and ask each person whether he or she belongs to a gym. Calculate the percentage of the total who say “yes.”
B)Take a random sample of adults at the local park, and ask each person whether he or she belongs to a gym. Calculate the percentage of the total who say “yes.”
C)Take a random sample of adults in the town, and ask each person whether he or she belongs to a gym. Calculate the percentage of the total who say “yes.
D)Take a random sample of the store’s adult customers, and ask what percentage of their friends belong to a gym. Calculate the mean of the responses.
What is the sum of a 6-term geometric series if the first term is 23 and the last term is 1,358,127? 1,395,030 1,461,460 1,527,890?
Answer:
Last term is 1,527,890.
Step-by-step explanation:
In this question a geometric series has been given with
first term A = 23
6th term = 1,358,127
Number of terms n = 6
we have to calculate the sum of this geometric series
we know [tex]T_{n}=a(r)^{n-1}[/tex]
[tex]T_{6}=23.(r)^{6-1}=1358,127[/tex]
[tex]r^{5}=\frac{1358127}{23}=59049[/tex]
[tex]r = 59049^{\frac{1}{5} }[/tex]
r = 9
Now we know the formula to sum a geometric series is
[tex]S=a.\frac{r^{n-1} }{r-1}[/tex]
S = 23 × [tex]\frac{(9^{6-1)} }{(9-1)}[/tex]
S = 23 × [tex]\frac{(531441-1)}{8}[/tex]
S = [tex]\frac{23.(531440)}{8}[/tex] = 23 × 66430
S = 1,527,890
Describe how to find linear expressions for the possible dimensions of a rectangular prism with a volume of 8k^3 +26k^2+ 6k.
Use systems of equations to solve the problem.
A farmer raises wheat and oats on 180 acres. She plants wheat on 20 more acres than she plants oats on. How many acres of each crop does the farmer plants?
You earn $10 a week for doing chores, and you have just been paid for completing eight weeks of chores. If you were paid $8 a week doing chores, how many weeks would it take to earn the same amount of money? weeks
Randy bought a zero coupon bond and a TIPS 5 years ago for $2,500 each. Both had 10 years to maturity. The TIPS's coupon was 2% while the zero coupon bond will be redeemed for $3,000. What should the maximum real value of his bonds be if he tries to sell them today? Select the best answer from the choices provided. $250 $750 $5,250 $5,750
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Find an equation for the circle that has center (−1, 4) and passes through the point (3, −5).
The correct answer for the equation of the circle with center (-1,4) and passes through point (3,-5) is [tex](x+1)^2 + (y-4)^2 = 97[/tex].
Given Co-ordinates:
Centre:
(-1,4)
Point of intersection:
(3,-5)
The standard equation of circle with center (h, k) is:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
(h, k) are co-ordinates of center
Given in question:
h= -1
k = 4
Find radius of the circle:
distance between the center(-1,4) and the given point (3, -5).
[tex]r = [\sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2 }[/tex]
[tex]r = [\sqrt{((3- (-1))^2 + (-5-4)^2 }[/tex]
[tex]= \sqrt{(4)^2 + (-9)^2 }[/tex]
[tex]= \sqrt{16 + 81}[/tex]
[tex]= \sqrt{97}[/tex]
Now, Equation of circle:
[tex](x-(-1))^2 + (y-4)^2 = (\sqrt{97})^2[/tex]
[tex](x+1)^2 + (y-4)^2 = 97[/tex]
The equation of circle is [tex](x+1)^2 + (y-4)^2 = 97[/tex].
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The equation of the circle with center (-1, 4) and passing through the point (3, -5) is (x + 1)² + (y - 4)² = 97.
Explanation:The subject of this question is geometry, specifically about the equations of circles. We start by noting that the general equation of a circle is (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the circle's center and r is the radius of the circle.
Here, the center of the circle is at (-1, 4). We don't know the radius yet, but we know that the circle passes through the point (3, -5). The radius is the distance from the center of the circle to any point on the circle. We can find this using the distance formula which is d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²].
Substituting the given points into the distance formula, we get: r = sqrt[(3 - (-1))² + (-5 - 4)²] which simplifies to r = sqrt[(4)² + (-9)²] = sqrt[16 + 81] = sqrt[97].
Now we can write the equation of the circle, substituting the center and radius values into the equation. This gives us: (x - (-1))² + (y - 4)² = sqrt[97]² which simplifies to (x + 1)² + (y - 4)² = 97.
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Simplify the expression.
A) –24n + 8mn – 100np
B) –6n – 2mn + 25np
C) –6n + 2m – 25np
D) –6n + 2mn – 25np
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. if field has a length that is twice its width, find the area of the field in square meters. ________________________________________