Answer:
Zeroes : 1, 4 and -5.
Potential roots: [tex]\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20[/tex].
Step-by-step explanation:
The given equation is
[tex]x^3-21x=-20[/tex]
It can be written as
[tex]x^3+0x^2-21x+20=0[/tex]
Splitting the middle terms, we get
[tex]x^3-x^2+x^2-x-20x+20=0[/tex]
[tex]x^2(x-1)+x(x-1)-20(x-1)=0[/tex]
[tex](x-1)(x^2+x-20)=0[/tex]
Splitting the middle terms, we get
[tex](x-1)(x^2+5x-4x-20)=0[/tex]
[tex](x-1)(x(x+5)-4(x+5))=0[/tex]
[tex](x-1)(x+5)(x-4)=0[/tex]
Using zero product property, we get
[tex]x-1=0\Rightarrow x=1[/tex]
[tex]x-4=0\Rightarrow x=4[/tex]
[tex]x+5=0\Rightarrow x=-5[/tex]
Therefore, the zeroes of the equation are 1, 4 and -5.
According to rational root theorem, the potential root of the polynomial are
[tex]x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}[/tex]
Constant = 20
Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.
Leading coefficient= 1
Factors of leading coefficient ±1.
Therefore, the potential root of the polynomial are [tex]\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20[/tex].
58:49 A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix
Answer:
$18
Step-by-step explanation:
1 pound of raisins = $2
1 pound of almonds = $5
Let the number of raisins be represented by a
Let the number of almonds be represented by b
We are told in the question that:
Six pounds of a trail mix contains 2 more pounds of raisins than almonds.
a + b = 6 pounds
Hence, Almonds = 2 pounds
Raisins = 4 pounds
The cost of the 6 pounds of trail mix
= 4 × $2 + 2 × $5
=$8 + $10
= $18
Marissa has a Master's degree and earns an annual salary of $80,400. She works 40 hours per week for 48 weeks per year. Her sister has a Bachelor's degree and earns an average salary of $58,000. She works 40 hours a week for 52 weeks. How much greater is Marissa's hourly wage than her sister's hourly wage? Round your answer to the nearest whole dollar.
Answer:
$14
Step-by-step explanation:
Marissa has a Master's degree and earns annual salary of $80,400.
She works 40 hours per week for 48 weeks per year.
Her sister has a Bachelor's degree and earns an average of $58,000 per year.
She works 40 hours per week for 52 weeks per years.
Marissa works for a total of 40 × 48 = 1920 hours a year.
Her hourly wage = [tex]\frac{80,400}{1920}[/tex] = $42 (rounded up to nearest dollar).
Her sister works for a total of 40 × 52 = 2080 hours
Her hourly wage = [tex]\frac{58,000}{2080}[/tex] = $28 (rounded up to nearest dollar)
So Marissa's hourly wage is $42 - $28 = $14 more than her sister's hourly wage.
E Question Help
1.3.AP-9
Two hikers are 22 miles apart and walking toward each other. They meet in 4 hours. Find the rate of each hiker if one hiker walks 1.1 mph faster than the other
The speed of the slow hiker is mph, and the speed of the fast hiker is mph.
Step-by-step explanation:
Since, the hiker are walking at different speeds they meet at a point not in the middle.
Let distance travelled by Hiker A (slower) be x at speed s.
So, distance travelled by Hiker B (faster) is (22 - x) at a speed (s + 1.1) .
[tex]speed \: = \frac{distance}{time} [/tex]
s = x / 4s + 1.1 = 22 - x / 4Solving equations 1 and 2, we get :
x = 8.8m and s = 2.2mph
Therefore,
Speed of Hiker A = 2.2 mph
Speed of Hiker A = 2.2 mphSpeed of Hiker B = 3.3 mph
Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
apples, went to market and sold all their apples at the same price, and each
received the same sum of money. What was the price?
Answer:
The amount each took home was 20 unit currency.
Step-by-step explanation:
We are given that Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140 apples, went to market and sold all their apples at the same price, and each received the same sum of money.
Formula : [tex]a \times n + (n - 1)[/tex], [tex](a + b)\cdot n + (n - 2)[/tex], [tex](a + 2 \cdot b) \cdot n + (n - 3)[/tex], [tex](a + 3 \cdot b) \cdot n + (n - 4)[/tex], [tex](a + 4 \cdot b) \cdot n + (n - 5)[/tex], [tex](a + 5 \cdot b) \cdot n + (n - 6)[/tex], [tex](a + 6 \cdot b) \cdot n + (n - 7)[/tex]
[tex]a \cdot n + (n - 1) = 20[/tex]
[tex](a + b) \cdot n + (n - 2)=40[/tex]
[tex](a + 2 \cdot b) \cdot n + (n - 3) = 60[/tex]
[tex](a + 3 \cdot b) \cdot n + (n - 4) = 80[/tex]
[tex](a + 4 \cdot b) \cdot n + (n - 5) = 100[/tex]
[tex](a + 5 \cdot b) \cdot n + (n - 6) = 120[/tex]
[tex](a + 6 \cdot b) \cdot n + (n - 7) = 140[/tex]
On solving :
n = 7, a = 2, b = 3
So,
[tex]2 \times 7 + 6 = 20[/tex]
[tex]5 \times 7 + 5=40[/tex]
[tex]8 \times 7 + 4 = 60[/tex]
[tex]11 \times 7 + 3 = 80[/tex]
[tex]14 \times 7 + 2 = 100[/tex]
[tex]17 \times 7 + 1 = 120[/tex]
Based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount :
2×1 + 6×3 = 20
5×1 + 5×3=20
8×1 + 4×3 = 20
11×1 + 3×3 = 20
14×1 + 2×3 = 20
17×1 + 1×3 = 20
20×1 = 20
Therefore, the amount each took home was 20 unit currency.
Insert two rational numbers between each of the following,
a. 5 and 11
c. 2 and 8
b. 26 and 34
d. 14 and 24
Answer:
a. 6 and 8.
c. 4 and 7
b. 29 and 30.
d. 17 and 23.
Step-by-step explanation:
The cost of a cell phone is $700. According to the cellular device contract, you will need to be $0.22 per minute for first 500. Write the function that models the total cost of the cell phone bill for the first 500 min. What is the domain of the function?
Answer:
[tex]C = 700+0.22m[/tex]
Domain is [0,500] or [tex]0 \leq m\leq 500[/tex]
Step-by-step explanation:
We are given that:
Cost of cell phone is $700.
Cost per minute for the first 500 calls is $0.22 per minute.
To find:
Function to model total cost of the cell phone bill for the first 500 minutes.
And domain of the function = ?
Solution:
Here, Total Cost is the sum of cost of cell phone, plus the cost of calls.
Total Cost = Cost of cell Phone + Cost of calls
We have the cost of cell phone as $700.
and cost of calls is $0.22 per minute up to 500 minutes.
Let the number of minutes for the calls is m. (m [tex]\leq[/tex] 500)
So, cost for m number of minutes of calls = m [tex]\times[/tex] cost per minute
cost for m number of minutes of calls = [tex]0.22 \times m[/tex]
Let the Total Cost be represented as C.
So, we can write the cost function as:
[tex]C = 700+0.22m \ \{0\leq m\leq500\}[/tex]
Domain of a function is the valid input value to the function for which the output is defined.
Here, the domain is [0, 500] i.e. 0 and 500 are inclusive.
So, the answer is:
[tex]C = 700+0.22m[/tex]
Domain is [0,500] or [tex]0 \leq m\leq 500[/tex]
PLEASE HELP, Write the quotient as a mixed number.
23 divided by 6 = 3 R5
Answer:
3 and 5/6
Step-by-step explanation:
First you place the highest number divible by 6.
There is 18 that is divisble by 6.
3 and 5/6
(3(6) + 5)/6
23/6
The quotient as a mixed number 23 divided by 6 is [tex]3\frac{5}{6}[/tex]
The given fraction is 23/6
Twenty three divided by six
Twenty three is the numerator and six is the denominator
23/6 being an improper fraction, it can be further written as a mixed number consisting of a whole and a fractional part.
The quotient of 23 divided by 6 is 3 with a remainder of 5.
Therefore, it can be written as a mixed number as follows:
23 ÷ 6 = 3 remainder 5
23/6 = 3 and 5/6
Hence, the quotient as a mixed number 23 divided by 6 is [tex]3\frac{5}{6}[/tex]
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I can some one help me please
Answer:
b
Step-by-step explanation:
Answer:
i have nom idea
Step-by-step explanation:
i have no idea
Michael has saved $22.40. Kevin saved 3/4 of the amount that Michael saved. Jack saved 5 times as much as Kevin. What is the total saved amount of all three?
Answer:
123.2 is the answer
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $7.50 fee and $14 She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60. Each pizza is cut into 8. She wonders how many total slices she can afford.
Answer:
The answer is 24
Step-by-step explanation:
If the restaurant fee is $7.5 and the price is $14 per pizza, she has $52.5 to spend on the pizzas after we deduct the restaurant fee.
That means she can get 52.5 / 14 = 3.75 pizzas.
Since she can't get .75 pizza, we can assume that she will order 3, which in total makes 8 x 3 = 24 slices.If she can however order 3.75 pizzas, .75 x 8 makes 6 slices so it is a total of 30 slices for 3.75 pizzas.I hope this answer helps.
The total slices she can afford is 30 and this can be determined by using the unitary method and forming the linear equation.
Given :
Jacque needs to buy some pizzas for a party at her office.She's ordering from a restaurant that charges a $7.50 fee and $14 for delivery.She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60.The following steps can be used to determine the total slices she can afford:
Step 1 - Total cost to order one pizza is given by:
= 7.5 + 14
= $21.5
Step 2 - Let the total number of pizzas she can order be 'x'. So, the delivery fee plus the cost of the pizzas under $60 is represented by the equation:
14x + 7.5 = 60
14x = 52.5
x = 3.75
Step 3 - Now, according to the given data if one pizza contains 8 slices then 3.75 pizza contains:
[tex]= 3.75\times 8[/tex]
= 30 slices
The total slices she can afford is 30.
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is the sqrt of 1 - sin^2 theta = cos theta true? If so, in which quadrants does angle theta terminate?
A. false
B. true; quadrants 1 and 4
C. true; quadrants 2 and 3
D. true; quadrants 1 and 3
Answer:
Answer: The answer is option B.
Step-by-step explanation:
Here,
We have,
[tex] { \sin }^{2} theta \: + {cos}^{2}theta = 1[/tex]
[tex] {cos}^{2} \: theta = 1 - {sin}^{2} \: theta[/tex]
[tex]cos \: theta = \sqrt{1 - { \sin }^{2}theta } [/tex]
So, it's true; and it lies in quadrant 1 and 4.
The reason according to the "CAST" rule cos theta is in 1st and 3rd quadrant cos theta is positive.
The house Trevor's family lives in has 6 66 people (including Trevor) and 3 33 bathrooms. In the past month, each person showered for an average of 480 480480 minutes and used an average 72 7272 liters of shower water (over the entire month). Water costs 0.20 0.200, point, 20 dollars per liter. How much did Trevor's family pay per minute on shower water?
Answer:
The amount Trevor's family pay per minute on shower water is $0.005.
Step-by-step explanation:
The cost of water is,
Cost = $0.20/liter
Amount of water used over the entire month:
Amount of water used = 72 liters
Compute the total water cost as follows:
Total water cost = Amount of water used × Cost
= 72 × 0.20
= $14.4/liter
The average number of minutes each person showered is:
Average number of minutes = 480 minutes.
The number of people in Trevor's house:
N = 6
Compute the total amount of time the 6 person showered as follows:
Total amount of time = Average number of minutes × N
= 480 × 6
= 2880 minutes
Compute the pay per minute on shower water as follows:
Pay per minute on water = Total water cost ÷ Total amount of time
= $14.4 ÷ 2880
= $0.005
Thus, the amount Trevor's family pay per minute on shower water is $0.005.
Answer:
0.03
Step-by-step explanation:
Select the equivalent expression. (8^-5/2^-2)^-4 = ?
Choose 1 answer:
A. 1/8*2^2
B. 2^6/8^9
C. 8^20/2^8
Please
Answer:
C. 8^20/2^8
Step-by-step explanation:
(8^5/2²)^4
8^20/2^8
What is the coefficient, constant, or variable for a+3b
Answer:
variables: 'a' and 'b'coefficient: 3Step-by-step explanation:
The variables are 'a' and 'b'. The number 3 is a coefficient.
__
The coefficient of 'a' is 1. A coefficient of 1 is rarely shown.
how would you show 2,500 using exactly seven blocks?
Answer:
see below
Step-by-step explanation:
You would use ...
2 thousands cubes5 hundreds sheetshelp.....ASAP!!!.....
Answer:
B
Step-by-step explanation:
[tex] \sqrt{19} + \frac{7}{2} \: is \: irrational \: \\ \because \: \sqrt{19} \: is \: irrational \: and \: \frac{7}{2} is \: rational \\ adding \: any \: rational \: number \: in \: irrational \: number \\ results \: in \: irrational \: number.[/tex]
OABCD is a pyramid with a rectangular base of sides 15cm by 9cm.Given that the slant height OQ is 16cm find its
i)height
ii)volume
Hello! Your answer is below... Remember : h = height and v = volume
Answer:
H = 15.35 cm
V = 690.75 m^
Step-by-step explanation:
(H= height, V = volume, ^= square, √ = square root )
1. divide 9/2
=4.5 cm
2. use the pythagorean theorem
H=√16^-4.5^
H=15.35
if your looking for volume
1. use the formula for volume of the pyramid which is:
1/3 x base area x height
or
base area x height /3
2. then you substitute
1/3 x (9)(15) x 15.35
or
(9)(15) x 15.35 /3
V= 690.75 m^
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
:)
Answer:
height = h = 13.4 cm
volume = V = 602.8 cm³
Step-by-step explanation:
area of a square base = 15 cm x 9 cm = 135 cm²
slant height of pyramid = 16m
solving height: (see attached image)
first step is to take the diagonal base:
side of base 15 = 15 / 2 = 7.5cm
side of base 9 = 9 / 2 = 4.5m
diagonal base = sqrt ( 7.5² + 4.5²) = 8.75 cm
therefore
height² = slant height² - diagonal base²
h² = 16² - 8.75²
h = 13.4 cm
solving the volume:
V = 1/3 * area of square base * h
V = 1/3 * 135 * 13.4
V = 602.8 cm³
PLEASE help me. I am stuck on this question for a long time.
Answer:
b.28% of the patients tested received the medication and experienced a decrease in blood pressure
Answer:
The second one
Step-by-step explanation:
The total of patients is 100% wich is equivalent to 1.
● 0.5 of them received medication and ● 0.54 of them experienced a decrease in blood pressure.
The intersection of both is worth 0.28
So out of 1, 0.28 took medication and experienced a blood pressure decrease
Translate the statement 9n+3>5n
Three more than nine times a number is at least five times the number.
The next term of the AP root 8, root 18,root 32 is...........
Answer:
root 50
Step-by-step explanation:
Root 8 = 2root 2root 18 = 3root 2root32 =4root 2common difference = 4root 2 - 3root 2=root2 next term = 5root2 = root50.
What is 18/100 written as a decimal?
Answer:
18/100 as a decimal is:
0.18
Hope this helps! （づ￣3￣）づ╭❤～
Step-by-step explanation:
Answer:
0.18
Step-by-step explanation:
18 divided by 100 is 0.18 18 divided by 1000 is 0.018
you move the decimal to the left when you divided a number by ten how many zeros is how many times you move the decimal. every number is a decimal like if you have a number 20 it actually looks like 20. so when you divide it by a 10 or 100 to move the decimal to the left the same number of zeros in 100 so that would be 0.20 hope you understand
What is this and whats the steps?
-4(-5h-4)=2(10h+8) *
Answer:
this is an algebraic equation because it has an unknown which is the alphabet
Step-by-step explanation:
-4(-5h-4)=2(10h+8)
-4 will multiply the ones in the bracket beside it
-4*-5h=20h
-4*-4=16
20h+16=
2 will multiply the ones in the bracket beside it
2*10h=20h
2*8=16
20h+16=
so we have 20h+16=20h+16
we take like terms
20h-20h=16-16
h=0
6=1-2n+5 can you please solve it
Answer:
n = 0
Step-by-step explanation:
6 = 1 - 2n + 5
6 = 6 -2n
0 = -2n
n = 0
The value of n after solving the given equation 6 = 1 - 2n + 5 is the number, n = 0.
Given an equation:
6 = 1 - 2n + 5
It is required to find the value of n.
In order to find the value of n, the variable n has to be isolated to one side of the equation with the constant on the other.
Here, the variable is n.
The equation can be written as:
6 = -2n + 6
Subtract 6 from both sides.
0 = -2n
Now, divide both sides by -2.
0 = n
Hence, the value of n is 0.
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Find the indicated side of the triangle
Answer:
[tex]a = 17 \sqrt{2} [/tex]Step-by-step explanation:
To find a we use sine
sin ∅ = opposite / hypotenuse
From the question
a is the hypotenuse
17 is the opposite
Substitute the values into the above formula
That's
[tex] \sin(45) = \frac{17}{a} [/tex][tex]a \sin(45) = 17[/tex][tex]a = \frac{17}{ \sin(45) } [/tex][tex] \sin(45) = \frac{ \sqrt{2} }{2} [/tex][tex]a = \frac{17}{ \frac{ \sqrt{2} }{2} } [/tex]We have the final answer as
[tex]a = 17 \sqrt{2} [/tex]Hope this helps you
what should be multiplied to 288 to become it a perfect square
Greetings from Brasil...
Follow the reasoning.
288 ÷ 2 = 144
and 144 its a perfect square (144 = 12²)
It is visible that if we multiply 288 by 1/2, we will obtain a perfect square, but we will do this via a simple equation
288 · X = 144
X = 144 ÷ 288
X = 0,5 ⇔ X = 1/2
Andre's school has 20 clubs, which is five times as many as his cousin's school.
His cousin's school has x clubs.
Answer:
4
Step-by-step explanation:
you would do 20÷5=x
to check it it would be 5x=20
5×4=20
Answer: X=4
Step-by-step explanation:
If your school has 20 clubs, 20 divided by 5 is 4
Find mNMKˆ. A. 222 B. 183 C. 213 D. 246
Answer:
B. 183 degrees.
Step-by-step explanation:
m arc MN = 360 - 107 - 177
= 360 - 284
= 76
m NMK = 76 + 107
= 183
The measure of the arc NMK will be 183°. Then the correct option is B.
What is a circle?The circle is at equidistant of points drawn from the center. The radius of a circle is the distance between the center and the circumference.
The measure of the angle ∠MLK is 35°.
The major and minor arc is 117x and 107x.
We know that the angle ∠MLK is the half of the difference of the major arc to minor arc.
∠MLK = (arc KN – arc KM) / 2
35° = (177x - 107x) / 2
70° = 70x
x = 1°
Then the measure of the arc KN will be
Arc NK = 177 x 1
Arc NK = 177°
We know that the sum of the arc KN and KMN will be 360°.
mNK + mNMK = 360°
177° + mNMK = 360°
mNMK = 360° – 177°
mNMK = 183°
The measure of the arc NMK will be 183°.
Then the correct option is B.
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Simplify the following:
3c² + 30²
Answer: 3c^2+900
Step-by-step explanation: 30^2 is the only thing that can be simplified
Add or Subtract to Simplify:
(4x - 2x3) + (5x3 - 4x + 5)
Answer:
3x³ + 5Step-by-step explanation:
( 4x - 2x³ ) + ( 5x³ - 4x + 5)
Remove the parenthesis
That's
4x - 2x³ + 5x³ - 4x + 5
Group like terms
We have
5x³ - 2x³ + 4x - 4x + 5
We have the final answer as
3x³ + 5Hope this helps you
In the figure below, O is the center of the circle. Name a radius of the circle. A. HK←→ B. FG←→ C. AB¯¯¯¯¯¯¯¯ D. AO¯¯¯¯¯¯¯¯
Answer:
D. AO
Step-by-step explanation:
The radius can be made with a line from a point in the circumference (end) to the middle.
Point A is on the circumference. Point O is in the middle. So, line segment AO is the radius.
The radius of a circle is a line drawn from the center of the circle to any point on the circumference of the circle.
The radius of the circle are AO, CO and BO.
From the attached diagram of the circle, we have:
[tex]O \to[/tex] center
There are three lines from center O to the circumference of the circle. The three points are: A, C and B.
This means that the radius of the circle are AO, CO and BO.
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