The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.
Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Given:
x (x-2) (x + 3) = 18
Divide both sides of the equation by x:
x (x-2) (x + 3) / x = 18 / x
(x-2) (x) + 3) = 18 / x
You can use the following simultaneous equations.
(1) y = (x-2) (x + 3)
(2) y = 18 / x
Using a graphing calculator, we get:
x = 3, y = 6 → point = (x, y) = (3,6)
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Triangle ABC is translated 6 units to the right and 1 units up.
What are the coordinates of C’?
C’(4, –2)
C'(4, –0)
C'(4, 2)
C'(1, 2)
The coordinate of the point C from the given triangle ABC after translation is C' = (4, -2)
Translation of coordinatesA triangle is a 2D figure with 3 sides and angles. Given the coordinate C points of the triangle;
C = (-2, -3)
If these coordinate point is translated 6 units to the right and 1 units up, the resulting coordinate will be at:
C' = (-2 + 6, -3 + 1)
C' = (4, -2)
Hence the coordinate of the point C from the given triangle ABC after translation is C' = (4, -2)
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Answer: the answer is A C'(4, -2)
Step-by-step explanation:
Please help, I can’t really figure out the answer..
Answer:
0.625
Step-by-step explanation:
To find the constant, you do y/x. For the first pair, if we divide 1.25/2, we get 0.625. We can do the same for all the pairs and get 0.625
Hope this helps :)
Answer:
1.6
Step-by-step explanation:
To find the constant of proportionality, we do [tex]\frac{x}{y}[/tex]. We see that 2/1.25=1.6, 4/2.5=1.6, 6/3.75=1.6, and 10/6.25=1.6. This means that the constant of proportionality is equal to 1.6.
10; your car travels for 10 hours.
The algebraic expression that represents the total distance traveled by the car is 10s
How to determine the algebraic expression?The given parameters are:
Speed = s miles per hourTime = 10 hoursThe distance is calculated using:
Distance = Speed * Time
So, we have:
Distance = s* 10
Evaluate
Distance = 10s
Hence, the algebraic expression that represents the total distance traveled by the car is 10s
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Complete question
Your car travels for 10 hours at an average speed of s miles per hour. Write an algebraic expression that represents the total distance traveled by the car
Arianna invests $6,000 into a brokerage
account which earns 3% per year. In 30 years,
how much will Arianna's investment be worth
if interest is compounded quarterly (4 times a
year)? Round to the nearest dollar.
Answer: $14708.14
Step-by-step explanation:
Amount = initial balance(1 + annual rate/periods per year)^(periods per year*years)
A = 6000(1+0.03/4)^4*30
A = 6000(1.0075)^120
A = 6000(2.451)
A = 14708.14
Hope this helps!
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. Assume that the population standard deviation is 2.4 gallons. The mean water usage per family was found to be 19.5 gallons per day for a sample of 3034 families. Construct the 98% confidence interval for the mean usage of water. Round your answers to one decimal place.
The confidence interval for the mean usage of water is (18.7,20.5).
Given population standard deviation of 2.4, mean of 19.5 gallons per day and confidence interval of 98%.
We have to find the confidence interval for the mean usage of water.
To find out the confidence interval we have to first find margin of error.
μ=19.5
σ=2.4
α=0.98
α/2=0.49
We have to find the z value for the p value 0.49 which is z=2.33
Margin of error=z*μ/[tex]\sqrt{n}[/tex]
=2.33*19.5/[tex]\sqrt{3034}[/tex]
=0.82
lower level=mean -m
=19.5-0.82
=18.68
after rounding upto 1 decimal
=18.7
upper mean = mean+m
=19.5+0.82
=20.52
Hence the confidence interval for the usage of water is (18.7,20.52).
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L = 5t + 12
Please choose an answer.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $12 for equipment rental and $5 per hour of use.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $5 for equipment rental and $12 per hour of use.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $5 per rental hour.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $17 per rental hour.
Answer:
Option 1
Step-by-step explanation:
Hello!
We can see that the base price for a canoe is $12, as you have to spend the $12 to get the canoe.
You also have to spend $5 per hour in the canoe, which is why "t" is being multiplied by 5.
We can also look at this graphically.
The x-axis is the number of hours, while the y-axis is the price. When x is 0 (no hours on canoe), you can see that the price is $12. But as it increases by 1 hour, the price increases by $5.
PLEASE REFER THE ATTACHMENT. THANK YOU
The solution is given below:
What is price index?An index number expressing the level of a group of commodity prices relative to the level of the prices of the same commodities during an arbitrarily chosen base period and used to indicate changes in the level of prices from one period to another.
Given:
Comm. p0 q0 p1 q1 p0q0 p1q0 p1q1 p0q1
A 25 750 30 960 18750 750 28800 24000
B 30 450 25 550 13500 750 13750 16500
C 5 250 6 360 1250 30 2160 1800
D 6 90 7 210 540 42 1470 1260
E 10 140 10 190 1400 100 1900 1900
F 4 48 5 65 192 240 365 260
Now,
[tex]\sum[/tex]p0q0 = 35632
[tex]\sum[/tex]p1q0 = 1912
[tex]\sum[/tex]p1q1 = 48445
[tex]\sum[/tex]p0q1= 45720
1) P01(L) = [tex]\sum[/tex]p1q0/[tex]\sum[/tex]p0q0 * 100
= 5.36
2) P01(L) = [tex]\sum[/tex]p1q1/[tex]\sum[/tex]p0q1 * 100
= 105.96
Dorbish- Bowley
= 5.36+ 105.96/2
=55.66
Marshall- Edgeworth
= 1912+ 48445/35632 + 45720
= 50357/ 81352
= 0.619 *100= 61.9
Fisher's price index
=( 5.36 * 105.96 )^ 0.5
=23.831
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Can someone pls help with these geometry questions, it’s urgent.
Answer:
6. x + x + 14 = 90
2x + 14 = 90
2x = 76
x = 38
angle b = 38 + 14 = 52°
7. angles on a straight line add up to 180°
x + x - 32 = 180
2x = 212
x = 106°
angle d = 106 - 32 = 74°
8. vertically opposite angles are equal
7x - 80 = 3x
-80 = -4x
20 = x
angle 1 = 7(20) - 80 = 60°
angle 2 = 3(20) = 60°
In a hospital maternity ward there are only five babies. Baby 1 is heavier, with red hair. Baby 2 is male and thin, with the same colour hair as Baby 3, who is blonde and wears a bonnet. Baby 4 is one of the three female babies and Baby 5 wears sunglasses and is heavier. All babies wear bonnets and at least one of the females wears sunglasses.
A thin, red-haired baby wearing a bonnet is the oldest of the group. Who can it be?
Answer:
Baby 4
Step-by-step explanation:
This is because the baby we are finding is thin and red haired.
This takes out Baby 1 because he is heavier. This takes out Baby 2 because he has blonde hair. This takes out Baby 3 who is blonde. This takes out Baby 5 who is heavier.
help meeeeeee please
Please help!
On a certain Saturday, the number of adult tickets sold was 1/3 (one third) of the children tickets sold. What was the greatest number of adult tickets sold if the box office receipts was not more than $3,190?
Adult admission fee: $8.50
Children admission fee: $5.50
The greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.
How to find the greatest number of adult tickets sold ?let
number of children tickets = x
number of adult ticket sold = 1 / 3 x
The greatest number of adult tickets sold if the box office receipts was not more than $3,190 can be calculated as follows:
The equations that represent the situation is as follows:
5.50x + 8.50 (1/3 x) = 3190
5.50x + 2.83333333333x = 3190
8.33333333333x = 3190
x = 3190 / 8.33333333333
x = 982.839313573
x ≈ 983
Therefore,
adult ticket = 983/3 = 328
Therefore, the greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.
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The product of 8 and the sum of 4 and a number is 112. What is the number?
Which equation could be used to solve for the number?
8 + 4n = 112
O 8 x 4 + n = 112
8(4 + n) = 112
Answer:
8(4 + n) = 112Step-by-step explanation:
Let's start by reading the problem since it maybe is a bit confusing at first.
The product of 8
Now we know that it starts with 8 multiplied by another number. We do not know that number yet, so let's put 8 * () and fill in the parentheses later.
So far, our equation is:
8()
.. And the sum of 4 and a number
So, 4 + n
We can enter that into our equation
8(4+n)
The next line says "..Is 112"
So, the solution to our equation is 112
Our equation becomes:
8(4+n)=112
Translate into an algebraic expression:
How much x% of sugar syrup can you make if you have 100 grams of sugar?
(Need Urgent Help)
The algebraic expression is: x% * 100
How to translate the expression?The statement is given as:
How much x% of sugar syrup can you make if you have 100 grams of sugar?
The amount of sugar is given as:
100 grams
So, the algebraic expression is:
x% * 100
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2- The doctor prescribed 50 grams of sodium polystyrene sulfonate rectally. The medication is supplied as a 15 g/60 mL suspension. How many milliliters of sodium polystyrene sulfonate should the nurse Flora administer? Record your answer as a whole number.
The number of milliliters of sodium polystyrene sulfonate that the nurse Flora should administer is; 200 mL
How to carry out conversion rates?We are told that;
Medication dosage supply = 60mL for each 15 grams
Now, if the doctor prescribes 50 grams of the drug sodium polystyrene sulfonate rectally, then the volume to be administered is;
V = (50 * 60)/15
V = 200 mL
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URGENT!! WORTH 27 POINTS
Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,900 calories per day. How many calories does he have left to consume for the day? Is 1,100 a viable solution to this problem?
a. yes, 1,100 is less than 1,500.
b. no, 1,100 is more than the 400 he burned off at the gym.
c. no, 1,100 will cause him to exceed 1,900.
d. yes, 1,100 is less than 1,900.
Answer:
Step-by-step explanation:
1,500-400=1,100 he has 800 calories left so no if he ate 1,100 more calories he would go over his goal of 1,900 so C is the answer hope this helps
Which of the following data sets has the mean, median, mode, and range as the same number?
A. 6, 11,14,14,19,20
B. 10,12,14,16,18,20
C. 8,11,13,15,19,22
D. 3,4,5,6,7,8
Answer:
A.
Step-by-step explanation:
6, 11,14,14,19,20
Adding these 6 numbers we get 84.
84 / 6 = 14 = mean.
Median = middle number(s) = 14
Mode = number occurring most = 14.
A board is 90 inches long. How long is it in feet and inches?
Answer:
feet: 7.5
Inches: 90
Step-by-step explanation:
Which equations should Amber graph?
Answer:
amber should graph the second equation
Determine the area of the figure.
The area of the trapezoid is x+11 cm.
Given a trapezoid has one side of (x+6) cm, the other side is 5 cm, and the height is 2 cm.
A two-dimensional quadrilateral consisting of the sum of non-adjacent parallel sides and a suitable non-parallel side is denoted as a trapezoid.
Now we will use the formula to find the area of a trapezoid
Area = 1/2 × (base 1 + base 2) × height
Here base 1 = (x+6) cm, base 2 = 5cm and height = 2cm
Substituting the values into the formula, we get
Area = 1/2 × (x+6+5) × 2
Area = 1/2 × (x+11) × 2
Area = x+11
Thus, the area of the given figure when one side is x+6, the other side is 5 cm and the height is 2 cm is x+11 cm.
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Write the following as an equation. then solve. twice the difference of a number and 8 is equal to three times the sum of the number and 3. find the number. the equation is (type an equation using x as the
The equation representing the given case is 2(x - 8) = 3(x + 3), where x is the number.
The number satisfying this equation is -25.
In the question, we are asked to find the number when twice the difference of the number and 8 is equal to thrice the sum of the number and 3.
We assume the number to be x.
The expression representing twice the difference between the number and 8, can be shown as 2(x - 8).
The expression representing thrice the sum of the number and 3, can be shown as 3(x + 3).
We are informed that these two expressions are equal. This can be shown as the equation:
2(x - 8) = 3(x + 3).
Thus, the equation representing the given case is 2(x - 8) = 3(x + 3), where x is the number.
Now, to find the number, we solve the equation as follows:
2(x - 8) = 3(x + 3),
or, 2x - 16 = 3x + 9 {Simplifying},
or, 2x - 16 + (16 - 3x) = 3x + 9 + (16 - 3x) {Adding (16 - 3x) to both sides of the equation},
or, 2x - 16 + 16 - 3x = 3x + 9 + 16 - 3x {Simplifying},
or, -x = 25 {Simplifying},
or, -x(-1) = 25(-1) {Multiplying both sides of the equation with -1},
or, x = -25 {Simplifying}.
Thus, the number satisfying the equation is -25.
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What does 64. 75 inch height mean?
Answer:
5'4.75 feetStep-by-step explanation:
60 inches is 5 feet, so just add on the remaining inches to get
5 feet and 4.75 inches
P is a rectangle with a length of 40cm and width of x cm
Q is a rectangle with a width of y cm
the length of Q is 25% more than the length of P
the area of Q is 10% less than the area of P
work out the ratio of x:y
The ratio x:y as required in the task content is; 25:18.
What is the ratio x:y as required?It follows from the information given in the task content that;
The area of rectangle P is; 40x.
The area of rectangle Q is; y × (1.25 × 40) = 50y.
Hence, since the area of Q is 10% less than the area of P, it follows that A(q) = 0.9A(p).
And, A(p)/A(q) = 10/9
Hence, 10/9 = 40x/50y
x/y= 50/36 = 25/18
Hence, the required ratio is; 25: 18.
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Whoever helps me with this problem will have brainlist.
By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number [tex]0.\overline{333}[/tex]
How to find the quotient of a fraction
The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.
[tex]\frac{1}{3} = 0.\overline{333}[/tex]
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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.
How to find the quotient of a fraction?
Quotient is described as the quantity produced by the division of two numbers.
Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;
0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.
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Mwakio bought an item after being offered a discount of 30%. if this discount represented a reduction of sh 210, what was the price of the item before discount?
Answer:
The answer is Sh 700
Step-by-step explanation:
Let's set x as the original price
30% * x = 210
0.3 * x = 210
x = 210/0.3
x = 700
Use the Algebra Tiles to construct the algebraic expression for this situation:
What is this expression in simplified form?
`-4x -3 + 5x -2`
The given expression in simplified form is x - 5
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
-4x -3 + 5x -2
To simplify the expression, we collect like terms and then simplify
That is,
-4x + 5x -3 -2
= x - 5
Hence, the given expression in simplified form is x - 5
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Select the equivalent expression:
Please explain why it is changed from a fraction to a multiplication problem!
Answer:
On opening the bracket, we have (x^-28)/(x^56)
This is the same as (x^-28) . 1 / (x^56)
Following the law of indices 1/(x^a) = x^-a, we have 1 / (x^56) = (x^-56)
Hence (x^-28) . (x^-56)
If all the values in a set of data are the same, which of the following is true? (Check all that apply.)
(A) The median and mode are the same.
(B) The range is zero.
(C) The range and mode are the same.
(D) The low and high values are the same.
C
H
A
Which is the value of this expression when =-2 and x=-1?
O-64
12
2
01/22
064
3
The value of this expression when =-2 and x=-1 is: 3.
Value of the expressionGiven equation:
-2 and x=-1
Solving the value of the given equation
-2 and x=-1
Hence:
=-(-1)+2
=1+2
=3
Therefore the value of this expression when =-2 and x=-1 is: 3.
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AC is a tangent to the circle below at point B. Calculate the sizes of angle x, angle y and angle z. Justify each of your answers. .
[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)
[tex]x=78^{\circ}[/tex] (alternate segment theorem)
[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)
3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.
Which inequality explains why these three segments cannot be used to construct a triangle?
EF + FD > DE
ED + EF < DF
ED + EF > DF
EF + FD < DE
The inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF
InequalitiesFrom the question, we are to determine which of the given inequalities explains why the three segments cannot be used to construct a triangle
From the given information,
Line DE is about half the length of line DF
That is,
ED = 1/2 DF
Also,
Line FE is about one-third of the length of line DF
That is,
EF = 1/3 DF
Then, we can write that
ED + EF = 1/2DF + 1/3DF
ED + EF = 5/6 DF
Since,
5/6 DF < DF
Then,
ED + EF < DF
Hence, the inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF
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