The polynomial that should be subtracted from the dividend first is; x³ + 2x²
How to carry out polynomial long division?
The long division we are given is;
__________
x + 2 ) x³ + 3x² + x
Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².
Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;
(x + 2) * (x²) = x³ + 2x²
Thus, the polynomial to be subtracted is x³ + 2x²
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Find a so that line CD will have the given slope: C(3, -3), D(-3,a); m= -4/3
Work Shown:
m = (y2 - y1)/(x2 - x1)
-4/3 = (a - (-3))/(-3 - 3)
-4/3 = (a+3)/(-6)
-4*(-6) = 3(a+3)
24 = 3a+9
3a+9 = 24
3a = 24-9
3a = 15
a = 15/3
a = 5
These cones are similar. Find the volume
of the smaller cone. Round to the
nearest tenth.
2 cm
Volume = [?] cm³
3 cm
Volume = 66 cm³
Answer:
Hight = 22 cm
Volume of BlueCone= 92 [tex]cm^2[/tex]
Step-by-step explanation:
Finding the Hight of The Red Cone(Check the Image)
Volume of The Blue Cone(Check Image Below)
A puppy weighed 2kg.
Eight weeks later the puppy weighed 3.5kg
What was the percentage increase in the puppy's weight?
Answer:
[tex]3.5 - 2 \times 100 \div 2[/tex]
Answer:
The percentage increase in the puppy's weight is 75%.
Step-by-step explanation:
We can find the percentage increase using the following formula:
[tex]\boxed{\% \space\ \mathrm {increase = \frac{final \space\ - \space\ initial}{initial} \times 100}}[/tex].
In this case,
• initial = 2 kg
• final = 3.5 kg
Substituting these values into the formula:
[tex]{\% \space\ \mathrm {increase = \frac{3.5 \space\ - \space\ 2}{2} \times 100}}[/tex]
⇒ [tex]\frac{1.5}{2} \times 100[/tex]
⇒ [tex]0.75 \times 100[/tex]
⇒ 75%
The exponential model A = 999.8 0.002t describes the population, A, of a country' in millions, t years after 2003. Use
the model to determine when the population of the country will be 1051 million?
The population of the country will be 1051 million in 2014
How to model the population of the country?The exponential model that describes the population of a country' in millions, t years after 2003 is given as:
A = 999.8 e0.002t
Rewrite the function properly as:
A = 999.8 * e^(0.002t)
When the population of the country is 1051 million, it means that:
A = 1051
Substitute the known values in the above equation
So, we have:
1051 = 999.8 * e^(0.002t)
Divide both sides by 999.8
1.0512 = e^(0.002t)
Take the natural logarithm of both sides of the equation
ln(1.0512) = ln(e^(0.002t)
Rewrite the equation as:
ln(e^(0.002t) = log(1.0512)
This gives
0.002t = log(1.0512)
Evaluate the logarithmic expression
0.002t = 0.0216
Divide both sides of the equation by 0.002
t = 0.0216/0.002
Evaluate the quotient
t = 10.8
Approximate 10.8 as 11
t = 11
11 years from 2003 is 2014
Hence, the population of the country will be 1051 million in 2014
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Noah has 22 5 of a pound of rice in his cupboard. He also has 8 9 of that amount in his pantry. Which of the following equations could be used to determine how much rice he has in the pantry?
225/0.88*100%
255.68*100
25,568 pounds in pantry
Solve the system using
elimination:
2x-y=8
3x+2y=5
Answer:2x+y=8
3x-2y=5
Step-by-step explanation:multiply 1 st equation by 2
4x+2y=16
3x-2y=5
7x=21
x=21/7
x=3
2×3+y=8
6+y=8
y=8-6
y=2
What is the independent variable in this function?
Answer:
p.
Step-by-step explanation:
p is the independent variable.
The dependent one is h.
The value of h depends on the value of p.
a 36 foot long pole is cut into two pieces with the ratio lengths equal to 5:7
what is the lengh of the longer piece?
Instructions: Find the missing side length in the image below.
? =
10/
7
?
14.
Using proportions, the missing side length in the image below is of 20.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the side lengths are proportional, being related by the rule of three given as follows:
x/10 = 14/7
Applying cross multiplication:
7x = 14 x 10
7x = 140
x = 140/7
x = 20.
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Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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3. What kind of triangle is represented by the triangle shown below?
Isosceles
Right
O Equilateral
Scalene
Answer:
Isosceles
Step-by-step explanation:
An Isosceles triangle has an acute angle (less than 45°), and this photo shows a triangle with two matching sides with one side being longer.
A right triangle would have a 90° angle which this photo doesn't have
An Equilateral triangle has all 60° sides, since it doesn't have all matching sides, it cannot be the answer.
A Scalene triangle is similar to this photo except it has 30° 60° and 90° angles, which this photo doesn't have.
I hope this helps!
A car is traveling at vx = 36 m/s. the driver applies the brakes and the car decelerates at ax = -6. 0 m/s2. what is the stopping distance?
Answer:
6 Meters
Step-by-step explanation:
If the car is driving at a constant velocity of 36 m/s and accelerates at -6.0 m/s ^2 to a stop, then the distance of the car decelerates to a stop in 6 seconds.
a=v/t ->>> 6= 36/t
Please help what is the answer?
Answer:
C
Step-by-step explanation:
[tex]-15x+60\leq 105 \\ \\ -15x \leq 45 \\ \\ x \geq -3[/tex]
[tex]14x+11 \leq -31 \\ \\ 14x \leq -42 \\ \\ x \leq -3[/tex]
The intersection is x = 3.
The diameter of a circle is 8 mm. What is the circumference of the circle?
25 and 1/7mm?
50 and 2/7mm?
11/28mm?
Or
19 and 1/4mm?
Answer:
25.12 rounded.
Step-by-step explanation:
C = 2[tex]\pi[/tex]r
C=[tex]\pi[/tex]d
C = [tex]\pi[/tex](8)
C = 25.12 rounded.
Answer:
25 and 1/7 mm
Step-by-step explanation:
Diameter = circunference / π
π = 3.1416 aprox.
Then:
8 = citcunference / 3.1416
8 * 3.1416 = circunference
25.1428 = circunference
1/7 = 0.1428
Then:
25.1428 = 25 + 1/7
= 25 1/7
1) The ratio of the number of Mary's stickers to Anne's is 4:7. Mary has 48 stickers. If
Mary buys another 8 stickers, what will be the new ratio of the number of Mary's
stickers to Anne's?
Answer:
2:3
Step-by-step explanation:
ratio = 4:7
4 parts = 48
1 part = 12
Mary has 48
Anne has 84
Mary will have 56
56:84 = 2:3
Find the distance between the given points.
R(O, O) and S(6, 8)
Distance =
Answer:
distance = 10
2/7 /(22) = 10
In the figure below, AD is the perpendicular bisector of CB. Based on this information, which other statement can be proven to be
true?
OA AB AC
OB. AB CB
OCAC CB
OD AD CB
A
C
D
B
Answer:
463833
expand
Medium
Solution
verified
Verified by Toppr
In △ABD and △ACD, we have
DB=DC ∣ Given
∠ADB=∠ADC ∣ since AD⊥BC
AD=AD ∣ Common
∴ by SAS criterion of congruence, we have.
△ABD≅△ACD
⇒AB=AC ∣ Since corresponding parts of congruent triangles are equal
Hence, △ ABC is isosceles.
Answer:
A.
Step-by-step explanation:
With the given information, triangles ABD and ACD can be proved congruent, and by CPCTC, segments AB and AC are congruent.
The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.
Why are the events not mutually exclusive
The events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)
Why are the events not mutually exclusive?The probability values are given as:
P(A) = 0.3
P(B) = 0.6
P(A or B) = 0.8
For mutually exclusive events, we have:
P(A or B) = P(A) + P(B)
Substitute the known values in the above equation
P(A or B) = 0.3 + 0.6
Evaluate the sum
P(A or B) = 0.9
From the given parameters, we have
P(A or B) = 0.8
Hence, the events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)
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Answer:
D
Step-by-step explanation:
edge 2023
The sum of P(A) and P(B) is not equal to P(A or B).
distribute the problem
2(3-8y)
Answer:
6-16yStep-by-step explanation:
Hello!
apply distributive law
[tex]a(b - c) = ab - ac[/tex]
2(3-8y)=2.3-2.8y
2.3=6-2.8y= -16y=6-16y
Hope it helps!
Which of the following equation is an example of inverse variations?
f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B
What are inverse variations?
Inverse variation can be defined as the relationships between variables represented in the form of y = k/x
where;
x and y are two variables k is the constant valueFrom the options given, we can see that;
f(x) = -1/ 3x
f(x) = -z/xy
Both take the form of inverse variations
Thus, f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B
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Use the wave equation to find the speed of a wave given by y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
The speed of the wave is 0.83 m/s.
According to the statement
we have given that the equation and we have to find the speed of the wave.
So, For this purpose, we know that the
The given equation is y(x,t) = (9. 13 mm) sin [(6. 65 m^-1)x - (5. 52 s^-1)t]
Then we have to find the speed of the wave
So, Comparing y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
to the general expression y(x,t)=y m sin(kx−ωt),
Because the general expression is y(x,t)=y m sin(kx−ωt)
we see that k= 6.65 m −1 and ω= 5.52 rad/s.
The speed of the wave is
v=ω/k=(5.52 rad/s)/(6.65 m )= 0.83 m/s
So, The speed of the wave is 0.83 m/s.
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A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. How many customers are on payment plan B? customers How many of the customers on plan B text? customers What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
Answer:
23 customers on payment plan B
13 customers on plan text B
Probability: 13/23
Step-by-step explanation:
Find the expression for f(x) that makes the following equation true for all values of x
9x*3^x+2=3f(x)
what are these questions i need help
177
3 is a root of f(x) = x2–93987. Find the other roots of f(x).
Write your answer as a list of simplified values separated by commas, if there is more than one value.
The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
What are quadratic equations?Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0
How to determine the other roots of the equation?The equation of the function is given as:
f(x) = x^2 - 93987
The above equation is a quadratic equation
Express the equation as a difference of two squares
f(x) = (x - √93987)(x + √93987)
Set the equation of the function to 0
(x - √93987)(x + √93987) = 0
Split the factors of the above function equation as follows
x - √93987 = 0 and x + √93987 = 0
Solve for x in the above equations
x = √93987 and x = -√93987
Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
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Please help !!! Need help !!!
The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answer:
Below in bold.
Step-by-step explanation:
Minimum 24
Lower quartile 29
Median 43
Upper quartile = (49 + 51) / 2 = 50
Maximum = 56
Interquartile range = 50-29 = 21.
How to do 8+(-3)+(-2) three diffrent ways on a number line?
3 ways of computing the sum on the number line are:
Start at 8, then move 2 units to the left, then move 3 units to the left.Start at -3, then move 8 units to the right, then move 2 units to the left.Start at -2, then move 3 units to the left, then move 8 units to the right.How to do the sum in three different ways on a number line?
Here we have the sum:
8 + (-3) + (-2)
The first way of doing the sum in a number line is starting on the first number, which is 8.
Then, we move 3 units to the left, to the 5.Then, we move other 2 units to the left, to the 3.Now, we also can think the sum as:
(-3) + 8 + (-2)
So now we can start at the value -3, then move 8 units to the right, and then 2 units to the left.
Or think the sum as:
(-2) + (-3) + 8
So we start at -2, then we move 3 units to the left, and finally 8 units to the right.
So the different ways of computing the sum on a number line depends on where we start.
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How many different orders of top-three finishers are possible? drag the tiles to the correct locations on the equation. not all tiles will be used.
Orders of top-three finishers that are possible is given as follows:
[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]
What is the permutation?In a broad sense, a permutation of a set is the rearrangement of its elements inside an already ordered set, or the arrangement of its members into a sequence or linear order. The act or process of altering an ordered set's linear order is referred to as "permutation."
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]n P_{r}=\frac{n !}{(n-r) !}[/tex]
The order in which the cars finish is important, hence the permutation formula is used instead of the combination formula.
In this problem, 3 cars are taken from a set of 14, hence the number of different orders is given as follows:
Using the permutation formula, it is found that the number of different orders of top-three finishers that are possible is given as follows:
[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]
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I understand that the question you are looking for is:
How many different orders of top-three finishers are possible? drag the tiles to the correct locations on the equation. not all tiles will be used.
Which of the following graphs has a zero correlation?
Erin’s car uses 6 gallons of gas for every 138 miles she drives. Which equation could be used to find how many gallons,g, Erin needs to drive 92 miles
Answer:
g = 6 / 3 x 2
Step-by-step explanation:
g = 6 / 3 x 2 because 92 / 2 = 46. 46 x 3 = 138. so / 3 = 46 x 2 = 92
Thus, Erin required 4 gallons of gas to drive 92 miles.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.
Let the gallon used by Erin bey and distance traveled be x
Now fuel consumed by Erin is directly proportional to the distance traveled i.e.
y ∝ x
y = ax - - - - - - (1)
where is the constant
Now put y = 6 and x = 138
6 = a * 138
a = 6/138
a = 0.043
Now put a in equation 1
y = 0.043x
The above expression is a required expression that implies how mush gallons of gas Erin used to travel a certain distance.
Erin needs to drive 92 miles,
Put x = 92 in above expression
y = 0.043 * 92
y = 4 gallon
Thus, Erin required 4 gallons of gas to drive 92 miles.
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