Answer:
a) factors of polynomial are: (x+1)(x-2)(x-5)
b) the required polynomial in standard form is: [tex]\mathbf{x^3-6x^2+3x+10}[/tex]
Step-by-step explanation:
The polynomial has zeros at -1,2,5
Part A) Write the three factors of the polynomial
we have x=-1, x=2 and x=5 as zeros of polynomial
so factors will be:
(x+1)=0, (x-2)=0, (x-5)=0
So, factors of polynomial are: (x+1)(x-2)(x-5)
Part B) Write the polynomial in standard form
For finding polynomial, we will multiply all the factors i.e
(x+1)(x-2)(x-5)
[tex](x+1)(x-2)(x-5)\\=(x(x-2)+1(x-2))(x-5)\\=(x^2-2x+x-2)(x-5)\\=(x^2-x-2)(x-5)\\=x(x^2-x-2)-5(x^2-x-2)\\=x^3-x^2-2x-5x^2+5x+10\\=x^3-x^2-5x^2+5x-2x+10\\=x^3-6x^2+3x+10[/tex]
So, the required polynomial in standard form is: [tex]x^3-6x^2+3x+10[/tex]
At a homecoming game, there are 630 students and 1080 alumni in attendance. Express the
ratio of students to alumni as a fraction in simplest form. Explain its meaning,
Answer:
7/12
There are 7 students for every 12 alumni
Step-by-step explanation:
So, the ratio of students to alumni is 630/1080. This means there are 630 students for every 1080 alumni.
However, we can simplify this. If you treat this like a fraction and simplify, it will be much easier. Both numerator and denominator can be divided by 90, so that's what we'll do. 630/90 is 7. 1080/90 is 12.
Therefore, the correct answer is 7/12!
Hope I helped!!!!!!
A tower is 234 meters tall. Jaylon is looking up at the top of the tower and thinking it would be cool to string a zip line from the top of the tower to a platform that is 1.9 meters high. If the angle formed between the zip line and tower would be 76 degrees how many meters of the line is neded?
Answer:
A length of 959.401 meters is needed for the zip line is needed to string it from the top of the tower to the platform.
Step-by-step explanation:
The geometrical representation of the statement is summarized in the figure below attached. The length of the line is represented by hypotenuse of the right triangle, whose value is calculated by the help of trigonometrical relations:
[tex]\cos \alpha = \frac{h}{r}[/tex] (1)
Where:
[tex]\alpha[/tex] - Angle formed between the zip line and the tower, measured in sexagesimal degrees.
[tex]h[/tex] - Vertical distance between the tower and the platform, measured in meters.
[tex]r[/tex] - Length of the zip line, measured in meters.
If we know that [tex]\alpha = 76^{\circ}[/tex] and [tex]h = 232.1\,m[/tex], then the length of the zip line is:
[tex]r = \frac{h}{\cos \alpha}[/tex]
[tex]r = \frac{232.1\,m}{\cos 76^{\circ}}[/tex]
[tex]r = 959.401\,m[/tex]
A length of 959.401 meters is needed for the zip line is needed to string it from the top of the tower to the platform.
The a value of the equation y = a(b)^x represents which of the following?
Answer:
initial starting value.
Step-by-step explanation:
how can i solve this?
Answer:
About $804.70
Step-by-step explanation:
So, for this you will need the formula: "A = B(1 + r)^t" It is + 1 since it is an increase.
B = Initial Value
r = rate
t = time
A = B(1 + r)^t
A = 523(1 + 0.09)^5
A = 523(1.09)^5
A = 523(1.5386239549)
A = 804.700328413
A ≈ 804.70
Vinnie Testerverte is standing on the 40 yard line of the Washington Redskins when he throws a pass towards his end zone. The
equation that represents the path of the ball is y = -0.0975x2 + 3.9x + 6 where x represents the number of yards from 40 yard line and y
represents the number of feet the ball is above the ground.
1. How high is the ball when it crosses the
a) 30 yd line?
b) 15 yd line?
C) 5 yd line?
Answer:
a.35.25
b. 42.56
c.23.06
Step-by-step explantion
Just subsitute 30, 15, and 5 for x each time for each question
ex:
y=-0.0975(5)^(2)+3.9(5)+6
Please Help Me With A Paper For Math Class!!!
Hopeful this is helpful!
Step-by-step explanation:
a. p is 20% of 190. How many pennies do you have?
p=.20 x 190=p p= 38 pennies
b. 190 is 200% of r. How many rare coins do you have?
190/2=r r(rare coins) = 95 rare coins
c. n is 60% of r. How many nickels do you have?
n=.60 x 95=n n= 57 nickels
:)
Can someone help Eri? ^w^" circumference --- 25 points
Answer: same thing for me
Step-by-step explanation:
answer the question for n
Answer:
el pepe
Step-by-step explanation:
Dontrelle received 30% off when he purchased a rare book
regularly priced at $96.50. How much did Dontrelle pay?
HELP PLEASE!!
Answer:
28.85
Step-by-step explanation:
30% 30% of $96.50 is $28.95
Answer:
$67.55
Step-by-step explanation:
30% off that was 28.95 so you subtract
Which graph represents the function f(x) = -x + 3)?
Answer: y=−x+3
Step-by-step explanation: the line starts from top left between - 8 and -6 and goes through right under 4 / half a square intercepts on the x axis right onto the 4 and to the part stopping between - 8 and -6 once again, so it basically goes diagonal just be sure to make those marks
Someone can help???
A ladder is leaning against a house. The distance to the house's edge from the bottom step is 3 ft. and the distance from the edge to the top step is 4 ft. What is the slant of the ladder?
Answer:
The slant of the ladder is 5 ft
Step-by-step explanation:
Look at the attached figure to understand this situation
∵ a represents the distance from the edge to the top step
∵ The distance from the edge to the top step is 4 ft
∴ a = 4 ft
∵ b represents the distance to the house's edge from the bottom step
∵ The distance to the house's edge from the bottom step is 3 ft
∴ b = 3 ft
∵ c represents the slant of the ladder
∴ We need to find c
→ By using the Pythagoras Theorem
∵ c = [tex]\sqrt{a^{2}+b^{2}}[/tex]
∴ c = [tex]\sqrt{(4)^{2}+(3)^{2}}=\sqrt{16+9}=\sqrt{25}[/tex]
∵ [tex]\sqrt{25}[/tex] = 5
∴ c = 5 ft
∴ The slant of the ladder is 5 ft
There are 7 girls and 13 boys in a class at a Private
School. Of these students, 5 girls and 3 boys are in
the Running Club. What percentage of the students
at this Private School are in the Running Club?
Answer:
40%
Step-by-step explanation:
the total amount of students are 20
the people in running club are 8
8/20 = .40
.40 as a % is 40%
Answer:
40%
Step-by-step explanation:
What is 2 (x-3) -(6x-4)
Answer:
simplify = - 4 x -2 factored = 2 (-2x - 1)
Step-by-step explanation:
Salvador’s investment of $2,200 in the stock market earned $528 in two years. Find the simple interest rate for this investment.
Answer:
24%Step-by-step explanation:
Step one:
given data
Principal= $2,200
SImple interest =$528
Time = 2years
Rate = ?
Required:
Rate R
The simple interest is expressed mathematically as
SI=PRT/100
substitute we have
528=2200*R*2/100
cross multiply
528*100=2200R
divide both sides by 2200
R=52800/2200
R=24%
Cindy did an experiment. She started out with 600 bacteria cells. She found that the growth rate of the bacteria cells was 4.1%. Create an equation for the situation that would work for any time, x.
Pls Help thx
Answer: P(t) = 600*(1.041)^t.
Step-by-step explanation:
An exponential growth can be written as:
P(t) = A*(1 + r)^t
Where:
A = initial population = 600
r = rate of growth in decimals = 4.1%/100% = 0.041.
t = number of units of time.
Now we have a problem, we know that the growth rate is 4.1 %, but we do not know in which time units are we working.
Because is not the same if the bacteria grows a 4.1% in one day, than if the bacteria grows a 4.1% in a hour.
But that does not matter for the actual equation, because we can just define "t" as the time (like the question asks) and the equation will be:
P(t) = 600*(1 + 0.041)^t
P(t) = 600*(1.041)^t.
The table shows the temperature (y) at different altitudes (x).
This is a linear relationship. (Example 2)
2)Find the slope of this relationship
3)Find the y-intercept for this relationship
4)Write an equation in slop intercept form that represents this relationship
5)Use the equation to determine the temperature at an altitude of 5000 feet
Answer/Step-by-step explanation:
2. Using two pairs of values, (0, 59) and (2,000, 51),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{51 - 59}{2,000 - 0} = \frac{-8}{2,000} = -\frac{1}{250} [/tex]
3. The y-intercept is the value of y when x = 0. Thus, x = 0, when y = 59. Therefore,
y-intercept (b) = 59
4. To write an equation in slope-intercept form, simply substitute m = -¹/250, and b = 59, in [tex] y = mx + b [/tex]
✅[tex] y = -\frac{1}{250}x + 59 [/tex]
5. Substitute x = 5,000 in [tex] y = -\frac{1}{250}x + 59 [/tex].
[tex] y = -\frac{1}{250}(5,000) + 59 [/tex]
[tex] y = -20 + 59 [/tex]
[tex] y = 39 [/tex]
At an altitude of 5,000 ft, temperature would be 39°F
Geometry, need help answering this.
Answer:
HI = GJ ( GIVEN) s
GH = IJ ( given) s
Gi = Gi ( common side) s
And boom
GHI = Gji ( mention above eq, being SSS)
S mean side
Harvard University accepts 6 students for every 100 applicants. How many students will be accepted if 850 applicants apply for admission?Immersive Reader (1 Point)
Answer:
51 students will be accepted if 850 applicants apply for admission.
Step-by-step explanation:
With the information provided, you can use a rule of three to find the amount of students that will be accepted if 850 applicants apply for admission given that you know that Harvard University accepts 6 students for every 100 applicants:
100 → 6
850 → x
x=(850*6)/100= 51
According to this, the answer is that 51 students will be accepted if 850 applicants apply for admission.
I need help with the question below
Answer:
27
Step-by-step explanation:
In Luke's grade, there are 200 students. Currently, 25% of them are enrolled in health. How many students are enrolled in health?
Answer:
50
Step-by-step explanation:
I’m really stuck please help me
Answer:
well the question asked for the point (2,2)
Answer:
2,2
Step-by-step explanation:
You look at where the x is on the x axis, then you look at where the x is on the y axis to find the number, the x number always is written first.
A pound of swiss cheese costs $4.00 at the grocery store. Use the
fact that 16 ounces = 1 pound to help you find the cost of 5/6 pound
of swiss cheese. pls help ASAP
Answer:
3.
..2330
Step-by-step explanation:
What was R-kelly doing in the basement
Right answers only ;-;
Answer:
Sum he wasn't suupposed to be doing....... ;-;
Step-by-step explanation:
1/2(23-5) ??????????????
Answer:
9
Step-by-step explanation:
The first step is the stuff in the parenthesis which equals to 1/2(18). The next step is to multiply 18 by 1/2. That is super simple because it is just taking one half of 18 which is 9. Plz vote brainliest
What are the solutions of 3x^2-x+4=0
Answer: x= 1 + i √ 47/6
Step-by-step explanation: solve using the quadratic formula
Solve using the quadratic formula.
Answer:
the answer would be B
Step-by-step explanation:
solve using quadriatic formula because we are doing quadriatics
Help please helppppp ASAP
Find the slope between these two points: (2,-1) and (10,-13)
Answer:
-3/2
Step-by-step explanation:
Answer:
-3/2
Step-by-step explanation:
(y2-y1) / (x2-x1)
(-13-(-1)) / (10-2)
=-12/8
simplify
= -3/2
This assignment is hard as heck lol!
Answer:
z = 3[tex]\sqrt{13}[/tex]
Step-by-step explanation:
Using the altitude- on- hypotenuse theorem
( leg of large Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse )
z² = 9 × (9 + 4) = 9 × 13 = 117 ( take square root of both sides )
z = [tex]\sqrt{117}[/tex]
= [tex]\sqrt{9(13)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]
= 3[tex]\sqrt{13}[/tex]
What is the equation of the line that passes through the point (6,8) and has a slope of 1/2
Answer:
y = 1/2 + 11
Also:
Plz mark brainliest if this helped :)
I’m confused on this type of math
Answer:
all you do is add
Step-by-step explanation: