One factor of the function f(x) = x ^ 3 - 8x ^ 2 + 17x - 10.5(x - 5) Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technologyShow your work and include all intercepts in your answer.
Answers
Answer:
x-intercept(s): (−1.9900717, 0)
y-intercept(s): (0, 52.5)
Step-by-step explanation:
To find the x-intercept, substitute in [tex]0[/tex] for [tex]y[/tex] and solve for [tex]x[/tex]. To find the y-intercept, substitute in [tex]0[/tex] for [tex]x[/tex] and solve for [tex]y[/tex] .
[tex]f(x)=y[/tex]
[tex](x)=x[/tex]
x-intercept
To find the x-intercept(s), substitute in [tex]0[/tex] for [tex]y[/tex] and solve for [tex]x[/tex] .
[tex]f(x) = x ^ 3 - 8x ^ 2 + 17x - 10.5(x - 5[/tex]
[tex]=\bold{0}=x^3-8x^2+17x-10.5\left(x-5\right)[/tex]
[tex]=0\cdot \:10=x^3\cdot \:10-8x^2\cdot \:10+17x\cdot \:10-10.5\left(x-5\right)\cdot \:10[/tex]
[tex]=0=10x^3-80x^2+170x-105\left(x-5\right)[/tex]
[tex]=0=10x^3-80x^2+65x+525[/tex]
[tex]=10x^3-80x^2+65x+525=0[/tex]
[tex]=10x^2-99.90071\dots x+263.80959\dots \approx \:0[/tex]
[tex]\bold{x\approx \:-1.99007\dots}[/tex]
y-intercept
[tex]f(x) = x ^ 3 - 8x ^ 2 + 17x - 10.5(x - 5[/tex]
[tex]=y=\bold{0}^3-8(\bold{0})^2+17(\bold{0})-10.5\left(\bold{0}-5\right)[/tex]
[tex]=y=0-8\cdot \:0+17\left(0\right)-10.5\left(0-5\right)[/tex]
[tex]=y=0-8\cdot \:0+17\cdot \:0-10.5\left(0-5\right)[/tex]
[tex]=y=0-0+0-\left(-52.5\right)[/tex]
[tex]=0-0+0+52.5[/tex]
[tex]\bold{y=52.5}[/tex]
Related Questions
Can someone please help me
Answers
Answer:
Option 2: y = a(x + 1)² - 9
Step-by-step explanation:
Given the graph of an upward-facing parabola, whose vertex occurs at point (-1, -9) as its minimum point.
Vertex FormUsing the vertex form of the quadratic equation, y = a(x - h)² + k:
where:
a = determines the wideness and the direction of where the graph opens.
(h, k) = vertex
h = determines the horizontal translation of the graph
k = determines the vertical translation of the graph
Using the vertex, (-1, -9), and another point from the graph, (2, 0), substitute these values into the vertex form to solve for the value of a:
y = a(x - h)² + k0 = a[2 - (-1)]² - 9
0 = a(2 + 1)² - 9
0 = a(9) - 9
Add 9 to both sides to isolate a:
0 + 9 = 9a - 9 + 9
9 = 9a
Divide both sides by 9 to isolate a:
[tex]\displaystyle\mathsf{\frac{9}{9}\:=\:\frac{9a}{9}}[/tex]
a = 1
Final answer:Therefore, the vertex form of the given parabola is: y = a(x + 1)² - 9.
EXERCISE 11D
1. Draw MON = 81° and bisect it.
2. Draw an angle of measure 175°.
3. Construct a right angle and then bisect it.
4. Draw ABC= 162º and divide it into four equal parts.
5. Construct the following angles using a ruler and compass. a 60° b. 30° C. 120° d. 135°
6. Draw an angle of 107° and make a copy of it. Verify your construction by ac measurement. a.
7. Draw an angle of 83º. Make a copy of its complementary angle.
✅help me to solve this
Answers
1. Draw MON = 81° and bisect it.
2. Draw an angle of measure 175
3. Construct a right angle and then bisect it.
Draw ABC = 162° and divide it into four equal parts.
5. Construct the following angles using a ruler and compass.
120°
May has 10 sticker sheets with 8 stickers each and 15 pages with y stickers each. How many stickers does she have total.
A. (10 x 8) + (15y)
B 10 x ( 9 + 15 + y)
C. 10 + 8 + 15 + y
D, (10 x 15) + (8y)
Answers
Answer:
A
Step-by-step explanation:
1 meter is equal to 100 centimeters or 1,000 millimeters. How many millimeters are in 2 meters, 17 millimeters?
Answers
Answer:
2,017
Step-by-step explanation: 2 meters= 2,000
So, 2,000+17= 2,017
2017 millimeters are in 2 meters, 17 millimeters as per the given unit conversion rate.
What is Unit conversion?A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).
Given, 1 meter is equal to 100 centimeters or 1,000 millimeters.
To calculate the total number of millimeters in 2 meters, 17 millimeters.
Since,
millimeters in 1 meter = 1000
Thus,
millimeters in 2 meter = 2000
millimeters in 2 meters, 17 millimeters = 2017
Therefore, there is 2017 mm in 2meteres, 17 mm as per the given unit conversion.
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1 gallon is equal to 4 quarts or 8 pints. How many pints are in 3 gallons?
Answers
Answer:
24 pints
Step-by-step explanation:
if 1 gallon is = to 8
then 3 gallons is 24
There are 24 pints in 3 gallons.
To determine how many pints are in 3 gallons, we can use the conversion factor provided: 1 gallon equals 8 pints.
Step 1: Calculate the number of pints in 1 gallon.
Since 1 gallon equals 8 pints, we can write this as 1 gallon = 8 pints.
Step 2: Multiply the number of pints in 1 gallon by the number of gallons.
To find the number of pints in 3 gallons, we multiply the number of pints in 1 gallon (8 pints) by 3 gallons:
3 gallons × 8 pints/gallon = 24 pints.
Therefore, there are 24 pints in 3 gallons.
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If [tex]f(x) = x[/tex]² [tex]-x+3[/tex], then what is the reaminder when [tex]f(x)[/tex] is divided by [tex]x+9[/tex]?
Answers
Answer:
Remainder is 93
Step-by-step explanation:
Use synthetic division:
-9 | 1 -1 3
____ -9 90
1 -10 | 93
Therefore, the remainder is 93
Ann received a $90 gift card for a coffee store. She used it in buying some coffee that cost $8.04 per pound. After buying the coffee, she had $65.88 left on her
card. How many pounds of coffee did she buy?
pounds
5
?
Answers
Answer:
3 lbs of coffee
Step-by-step explanation:
$90.00 - $65.88 =$24.12 (spent 24.12 on the coffee)
24.12/8.04 = 3
Answer:
3 ponds of Coffee. take what she spent, and subtract it from the total. Then divide that number by the cost of 1 lb. of coffe. You get 3. 3 pounds.
Help help help help math math math math help
Answers
because 7 (14) + 9 is equal to 9 (14) - 19
Answer:
14
Step-by-step explanation:
because both sides need to be equal so if u plug in the 14 in x it gives you the same number for both sides 107.
Salaar, Waleed and Muazzam share $ 256. Waleed;s share is four times as much as Salaar. And Salaar's share is one-third of muazzam's. How much is each of their share?
Answers
Answer:
S 32, W 128, M 96
Step-by-step explanation:
W = 4S
S = 1/3M, or 3S = M
S + W + M = 256
Substitute
S + 4S + 3S = 256
8S = 256, S = 32
S = 32
W = 4S = 128
M = 3S = 96
how do you solve x^0.5=8
Answers
Answer:
The answer is x=64Step-by-step explanation:
Hello !Because, [tex]x {}^{0.5} = 8 \\ x {}^{ \frac{1}{2} } = 8...changing \: it \: to \: fraction \\(x {}^{ \frac{1}{2} } ) {}^{2} = 8 {}^{2} ...squaring \: both \: sides \\ (x {}^{ \frac{1}{2} } ) {}^{2} = x \\ 8 { }^{2} = 64 \\ therefore \: the \: value \: of \: x = 64.[/tex]When buddy ran away after his dad yelled at him dad and step brother searched 10% of New York for him what is this number as a fraction written in simplest form
Answers
Answer:
1/10
Step-by-step explanation:
they searched 1/10of New york
10%=10/100
=10%=1/10
Answer : 1/10
Step - by - step explanation :
10% = 10/100 ( because percentages are always out of 100 )
10/100 divided by 10/10 = 1/10
help me please please
Answers
Answer:
C? yikes if im wrong mb
Step-by-step explanation:
5/6 in simpliest, its C id have to assume
Mrs. Lovejoy and Christi spent the day baking cookies. When they divided them into 8 stacks, they had 14 cookies in each stack. How many cookies did they have? Solve and label the word problem. Please I need help.
Answers
Answer:
they had 112 cookies
Step-by-step explanation:
14×8 = 112
Find the next two terms in the sequence -3, 0, 3, 6
Answers
The rule is add 3 so yeah lol
Answer:
9, 12
Step-by-step explanation:
the rule is +3 for each step in the sequence
in digging a well, crew records the location of the bottom of the hole relative to ground
level. After 4 hours the hole is 164.4 feet deep. What integer represents the change in
location in feet after 1 hour?
Answers
164.4 / 4, gets answer/ unit rate
Requires integer so it would be 41 not 41.1
You are playing a game where you flip 3 coins, if you get all tails you lose $15, for each heads you get $3. What is your expected profit from this game?
Answers
Answer:
expected profit=$-3
Step-by-step explanation:
1 tail=-5
1 head=3
3/2=1.5
1.5*3=4.5
1.5*-5=-7.5
4.5-7.5=-3
$-3
What is 5,783 divided by 6 ?
Answers
A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent?
Answers
Answer:
5.3
Step-by-step explanation:
8^2 - 6^2 = x^2
64 - 36 = x^2
28 = x^2
Square root of 28 is approx 5.3
David invests $10,000 in a savings account that pays 3.5% simple interest. If David
makes no withdrawals or deposits to the account, how much will be in the
account after 7 years.
Answers
Answer:
David will have $12,450 if he makes no withdrawals.
What is the horizontal asymptote of j(x)=14x^3+45/2x^3+x+9
Answers
Answer:
It's C! y = 7
Step-by-step explanation:
71.841 to the nearest tenth
Answers
71.8
Step-by-step explanation:71.841:
The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.
How?In order to round, we need to remember how to round numbers:
If the digit is less than 5, the number to the left stays the same.If the digit is greater than, or equal to 5, the number to the left rounds up, or increases by 1. Solve:First, 4<5, meaning that 4 is less than 5.
#1 above is stating that the number to the left of 4 stays the same.
If we use that rule:
71.8 is our answer.
Find the total amount and total interest after one year if the interest is compounded half yearly
Principal = 4000
Rate of interest = 10% per annum
Total amount =
Total interest =
Answers
Total amount=p(1+(r/k))^(k*t)
p=principal
r=rate
k=number of times compounder per year
t=number of years
So 4000(1+(.10/2)^(2*1)=4410
4410 is the total amount owed
4410-4000=410
410 is the total interest owed
A bath tub drained at a constant rate. The table shows the number of gallons of water left in the tub after being drained for two amounts of time
Answers
The rate at which the water was drained from the tank is 6 gallons of water per minute (option A)
To know the speed at which the tank was drained, we must carry out the following operations:
Taking into account the information provided by the table we establish how much water has been drained from the tank in 20 minutes.
450 gallons - 330 gallons = 120 gallons.
Subsequently, we must divide the amount of water (120 gallons) that was drained by the time it was drained (20 minutes).
120 gallons ÷ 20 minutes = 6 gallons / minute.
According to the above, we can establish that the bath drain rate is 6 gallons / minute (option A).
Note: This question is incomplete because there is some missing information. Here is the complete information:
What is the rate at which the water was drained from the tank?
6 gallons of water per minute. 11 gallons of water per minute. 45 gallons of water per minute. 120 gallons of water per minute.
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1. Find the area of the sector by multiplying the area of the circle by the ratio of the _________________________ to 360.
2. Subtract the area of the triangle from the area of the sector.
length of the radius
length of the diameter
measure of the central angle
circumference of the circle
Answers
Answer: measure of the central angle
Step-by-step explanation: trust
Answer:
measure of the central angle
Step-by-step explanation:
Math isn't really my thing, so if you could help I would really, really appreciate!!
Answers
Answer:
1. 0.25
2. 105-40
3. 0.375
4. 0.5
5. 0.4 same as the number 6
Step-by-step explanation:
i hope it helpful i guess?
Help help help math math
Answers
Answer:
Function
Step-by-step explanation:
Hope it help !!
4781/32 without a decimal
Answers
Answer:
149(13/32)
Step-by-step explanation:
4781/32 and then take the remainder to make it an improper fraction
Look back at the plans these students used to solve the word problem below.
Who found a correct solution?
- STEP 4: LOOK BACK
According to soap box derby rules, a racer must weigh 250
pounds or less. The Math Club's car weighed in at 266
pounds on the day of the derby. How many pounds did the
Math Club need to remove from their soap box racer?
Dana added the weight limit to the Hector subtracted the weight limit
racer's weight. Since
from the racer's weight. Since
250 +266 = 516, the Math Club 266 - 250 = 16, the Math Club
needed to remove 516 pounds from needed to remove 16 pounds
the racer
from the racer
O A. Dana
B. Hector
Answers
which holds the more capacity 0.75 litres or 350ml
Answers
Answer:
0.75 liters
Step-by-step explanation:
1000ml in 1 liter so 0.75*1000=750ml
750ml > 350ml
LCM of two numbers is 1134 and HCF is 18. if one of the numbers is 162, find the other. number.
Answers
=====================================================
Work Shown:
Let x and y be the two numbers.
We're given x = 162 and the variable y is unknown.
We're also given LCM = 1134 and HCF = 18
So,
LCM = (x*y)/HCF
1134 = 162*y/18
1134 = (162/18)y
1134 = 9y
9y = 1134
y = 1134/9
y = 126
The other number is 126
---------------------
Notice that
162 = 18*9126 = 18*7showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.
Now let,
A = multiples of 162B = multiples of 126So,
A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.