The value of Q(x) = x² - 1
R(x) = 4
What is Long Division?
Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.
By long Division method:
x² - 1
_______________________________
(3x - 4) | 3x³ - 4x² - 3x
3x³ - 4x²
_________________
0 - 0 - 3x
- 3x + 4
___________________
0 + 4
Q(x) = x² - 1
R(x) = 4
Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1 ) + 4
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Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
27
Select all that apply.
A. natural numbers
B. whole numbers
C. rational numbers
D. real numbers
E. integers
. F. irrational numbers
The number 27 is a natural number, whole number, rational, real and an integer .
The number 27
And this number is a natural number and thus it is a natural number and a rational number too.
This is also an integer .
Reason: Natural number : A natural number is one that naturally and frequently appears. It is a whole, non-negative number as a result. N, the collection of natural numbers, can be defined in one of two ways: N = {0, 1, 2, 3, ...}
whole number: the sum of all natural numbers plus zero. neither a decimal nor a fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. 0, the negative, or a counting number.
Rational number: A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.
Real number: Rational, irrational, entire, and natural numbers are all examples of real numbers. Negative, positive, and zero numbers are all examples of integers.
Integer : An integer, pronounced is a whole number that can be positive, negative, or zero and is not a fraction.
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Grayson has $1.20 worth of nickels and dimes. He has twice as many nickels as dimes. Determine the number of nickels and the number of dimes that Grayson has.
The determined value of the number of nickels and the number of dimes that Grayson has is
x=6y=2This is further explained below.
What is the determined value of the number of nickels and the number of dimes that Grayson?Generally, The following phrase represents Jayden's complete financial worth:
Nickels are worth $0.05 each.
The dime value is equal to $0.10
The total value is equal to the sum of the values of the nickels and dimes.
where;
[tex]1.20= (0.05*2 x) +(0.1*x)[/tex]
0.1 x+0.1 x=1.2
0.2 x=1.2
[tex]x=\frac{1.2}{0.2}[/tex]
x=6
y=2
In conclusion, the Total number of dimes=6
Total number of nickels=12
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The distance between city an and city b is 500 miles. A length of 1.7 feet represents this distance on a certain wall map. City c and city d are 2.38 feet apart on this map. What is the actual distance between city c and city d
PLEASE HELP ASAP DUE AT 11:59PM
The actual distance between city c and city d represented by 2.38 feet on the map as required in the task content is; 700 miles.
What is the actual distance between city c and city d?It follows from the task content that the actual distance between city c and city d be determined according to the map's scale factor given.
It follows from the task content that the distance between cities a and b which is 500 miles is represented by 1.7 feet on the map;
1.7 feet ===== 500 miles
Hence, let x = the actual distance between the cities c and d represented by 2.38 on the map is; so that we have;
1.7 feet ====== 500 miles
2.38 feet ====== x miles.
x = (500 × 2.38)/1.7
x = 700 miles.
Therefore, the actual distance between the two cities c and d is; 700 miles.
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use your equation from part b to predict the highway MPG for a car that gets 68 MPG in the city.part b equation:[tex]y = \frac{7x}{9} + \frac{125}{9} [/tex]
ok
[tex]\begin{gathered} \text{ y = }\frac{7(68)}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{476}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{601}{9} \\ \\ \text{ y = 66.8 } \end{gathered}[/tex]MPG = 66.8
The table shown below gives the approximate distance from the sun for a few different planets. How much further (in km) from the sun is Saturn than Venus? Express your answer in scientific notation. Planet Approximate distance from the Sun (in km) Mercury 5.8 \cdot 10^75.8⋅10 7 5, point, 8, dot, 10, start superscript, 7, end superscript Venus 1.1 \cdot 10^81.1⋅10 8 1, point, 1, dot, 10, start superscript, 8, end superscript Earth 1.5 \cdot 10^81.5⋅10 8 1, point, 5, dot, 10, start superscript, 8, end superscript Saturn 1.4 \cdot 10^91.4⋅10 9 1, point, 4, dot, 10, start superscript, 9, end superscript Uranus 3\cdot10^93⋅10 9 3, dot, 10, start superscript, 9, end superscript
It is to be noted that Saturn is 1.29 *x 10⁹ km further from the sun than Venus.
What is the computation justifying the above results?Recall that we are given:
approximate distance from the sun for a few different planets.
Hence, to detect how much farther (in km) from the sun Saturn is than Venus we initiate a series of subtractions.
Recall that
Planet approximate distance from the sun ( km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
The distance of Saturn form the sun and Venus is given as
= Distance of Saturn from Sun - Distance of Venus from Sun
= 1.4 x 10⁹ - 1.1 * 10⁸ [Multiply 1.4 x 10 and we've got]
= 14 x 10⁸ - 1.1 * 10⁸
= (14 - 1.1) * 10⁸ [ Collect like terms and consolidate]
= 12.9 x 10⁸ [Revert back to the power of 9 and we have]
= 1.29 x 10⁹ km
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Full Question:
The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.
Planet Approximate distance from the Sun (in km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
It is found that Saturn is 1.29 x 10⁹ km further from the sun than Venus.
How do scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
We have been given that the approximate distance from the sun for a few different planets.
Hence, to determine the farthest distance (in km) from the sun Saturn is than Venus, we get;
Planet the approximate distance from the sun ( km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
The distance between Saturn from the sun and Venus can be calculated as;
= Distance of Saturn from Sun - Distance of Venus from Sun
= 1.4 x 10⁹ - 1.1 x 10⁸
= 14 x 10⁸ - 1.1 x 10⁸
= (14 - 1.1) x 10⁸
= 12.9 x 10⁸
= 1.29 x 10⁹ km
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1. Explain why the slope of line a is 2/6
What is the slope of a line perpendicular to the line whose equation is x - y = 6. Fully reduce your answer. Answer: Submit Answer
Answer:
Explanation:
The standard form of an equation is expressed as y = mx+b
m is the slope
Given the equation x - y = 6
Rewrite in standard form;
-y = -x + 6
Multiply through by -1
-(-y) = -(-x) - 6
y = x - 6
Compare with the standard equation
mx = 1x
mx+b
m is the slope
Given
evaluate T^T -[tex]x^{2}[/tex]+3x for x=-3
Answer:
The answer is -18
Step-by-step explanation:
- [tex](-3)^{2}[/tex] + 3(-3)
-9 + -9 = -18
PLEASE HELP !!! QUICKKK !!
A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.
The rate of change will be 3/4.
What is meant by linear function?A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function. Here, a stands for the line's gradient, and b for the y-axis intercept (which is sometimes called the vertical intercept).
The rate of change of y with respect to x, can be calculated utilizing any two of the pairs of values of the table, say, (3, -5) and (7, -2).
Rate of change [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]
Let, (3, -5) = (x1, y1) and (7, -2) = (x1, y1).
Rate of change [tex]$=\frac{(-5)-(-2)}{7-3}$[/tex]
Rate of change = 3/4.
Therefore, the correct answer is option c) 3/4.
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Please help me this is due in an hour
Answer:
Your missing number is -87.5.
Step-by-step explanation:
You want to follow reverse order of operations to isolate your variable x
First, you plug in y= 700 to get::
700 = (24x)/7 +1000
Then subtract 1000 from both sides to get:
-300 = (24x)/7
Then multiply both sides by 7 to get:
-2100 = 24x
Then, divide by 24 to get:
-87.5 = x
Thus, your answer x= -87.5
Megan is in charge of housekeeping at the Seaside Hotel. She makes sure there are enough clean towels for each room that has been booked for the night.
There is a proportional relationship between the number of rooms booked, x, and the number of towels Megan needs to supply, y.
By the analysis of the graph, the constant of proportionality is 2.
By analyzing the graph given we can infer that If five rooms are reserved, he must provide ten towels.
So x is the number booked and y is the number of towels, Then
x is directly proportional to y,
The given graph is linear in nature, as we increase x, there will be a significant increase increase in y, The constant of proportionality(k) tells us how much y will change when x changes.
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
Now, 10= k *5
[tex]k =\frac{10}{5} \\k =2[/tex]
Hence, the constant of proportionality k is 2.
and the equation of the given graph is y = 2x
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Help me with this ,8th grade math look at attachment
100 points
Answer:7
Step-by-step explanation:
Answer:
its 7!!!!
Step-by-step explanation: i just got it right im in 8th grade also!
When you looked at the thermometer last night, the temperature was 5° C. By morning, the temperature had risen 13°. By afternoon, the temperature had risen another 5°. Afterwards, the temperature dropped 10°. What is the temperature now?
Answer:
Step-by-step explanation:
13
The figures below are congruent. Name the corresponding angles.
Answer:
A goes to K. C goes to M. B goes to L.
Step-by-step explanation:
:)
What is the probability of tossing an odd number with 6 sided number cube ?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested probability, so we obtain the following:
Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :
Probability of an event=Favorable Cases/Possible Cases
Probability of tossing an odd number with 6 sided number cube =3/6
Probability of tossing an odd number with 6 sided number cube =1/2
Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.
when 64 is increased in the ratio 9 : 8, it becomes?
Recall that the ratio 9:8 can be written as follows:
[tex]\frac{9}{8},[/tex]therefore, when 64 is increased in the ratio 9:8 we get:
[tex]64\times\frac{9}{8}=72.[/tex]Answer: 72.
Answer:
72
Step-by-step explanation:
Since X : 64 = 9 : 8
Then we know X/64 = 9/8
Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64
X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72
Therefore 72 : 64 = 9 : 8
10b4 +3b²-11 can you help
Answer: your answer in in the screenshot
Step-by-step explanation:
A piece of rope 60 meters long is cut into two
pieces so that the longer piece is twice the
length of the shorter. How long are the two
pieces?
Answer:
short piece = 20
Longer piece = 40
Step-by-step explanation:
Comment
Let the shorter piece be x
Then the longer piece is 2x
Givens
The rope is 60 meters long
Equation
x + 2x = 60 meters Combine like terms
Solution
3x = 60 Divide by 3
3x/3=60/3
x = 20
A certain map shows two roads. Road A is 2 road B on the map? miles long but is 1 inches long on the map. What is the unit rate for inches per mile on this map? If road B is 15 miles long, how long is
The unit rate per inch on the map is 5/4 , and the length of road B is 18.75 miles.
in the question ,
it is given that ,
On the map [tex]1\frac{1}{2}[/tex] miles is equal to [tex]1\frac{7}{8}[/tex] inches .
we first convert the mixed fraction to normal fractions ,
we get
[tex]1\frac{1}{2}[/tex] miles = (1*2+1)/2 = 3/2 miles
and
[tex]1\frac{7}{8}[/tex] inches = (8+7)/8 = 15/8 inches
So, the statement becomes
On the map 3/2 miles is equal to 15/8 inches .
So 1 mile = (15/8)/(3/2) = (15*2)/(8*3) = 30/24 = 5/4
so , the unite rate is 5/4 inches per mile .
given the road B is 15 miles long .
and the unit rate is 5/4 .
so 15 miles = 15 *(5/4) = 75/4 = 18.75 inches
Therefore , The unit rate per inch on the map is 5/4 , and the length of road B is 18.75 miles.
The given question is incomplete , the complete question is
A certain map shows two roads. Road A is [tex]1\frac{1}{2}[/tex] miles long but is [tex]1\frac{7}{8}[/tex] inches long on the map. What is the unit rate for inches per mile on this map? If road B is 8 miles long, how long is road B on the map?
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Step 1: Add 7 to
x
.
Step 2: Multiply by 6
The final term after following the steps is ( 42 + 6x ).
We are provided with some steps that we have to follow to reach the final answer or expression. The steps we have to follow to reach the final answer or expression are mentioned below;
Step 1: Add 7 to x
In the first steps we need to add 7 to the x. Mathematically this can be written as,
7 + x
Step 2: Multiply by 6
In the second step we need to multiply the entire term obtained in step 1 by 6 . Mathematically this can be written as,
( 7 + x ) × 6
= 42 + 6x
Thus, the final term is ( 42 + 6x ).
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Express given equations in standard form:-
(a) 2x-5y =4 (b) 6x+ 3y = 12
Answer: a) [tex]y = \frac{2}5x} - \frac{4}{5}[/tex] b) y = -2x + 4
Step-by-step explanation:
2x - 5y = 4
2x - 4 = 5y
[tex]y = \frac{2}5x} - \frac{4}{5}[/tex]
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
4. What is the equation of the line that represents your initial climb?
Question 19
There are 118 different elements in the periodic table. While giving a presentation, Clark says that there are 128 different
elements. Select each true statement.
A) There are actually 118 elements
B) The amount of error in Clark's estimate is 10.
C) The amount of error in Clark's estimate is 118.
D) To the nearest tenth percent, the percent error in Clark's estimate is 8.5%.
E) To the nearest tenth percent, the percent error in Clark's estimate is 10%.
Next Question Check Answer
Four friends on a ski trip pay $210 each to share the rent of a cabin. The cost per person varies inversely
the number of persons. How many people sharing the rent would make the cost $120 per person?
Seven people sharing the rent would make the cost $120 per person.
What is Inversely Proportional?When two quantities are inversely proportional, that is, when an increase in one causes a decrease in the other and vice versa, they are said to be inversely proportional.
The general equation for inverse variation is y = k/x, where k is the proportionality constant and x and y are two variables.
Given:
The price paid by Four friends on a ski trip to share the rent of a cabin = $210
The cost per person varies inversely with the number of persons.
Let the cost be C and the number of persons be n,
C ∝ 1/n
So, the equation becomes, k = Cn.
Putting the values in the equation we obtain the value of k,
k = 210×4 = 840
We have to find the number of people sharing the rent that would make the cost $120 per person.
Using the equation,
k = Cn
840 = 120 × n
n = 840/120 = 7
Therefore, seven people sharing the rent would make the cost $120 per person.
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On “2 fer Tuesday” 2 bagels with cream cheese cost $2.50. Jimmy wants to buy 2 dozen bagels (24 bagels). How much will this cost?
a+B
A-b
2b+ a
A+b+c
A+2b-c
Please answer fast
Use segments a, b, and c to complete the following constructions of segments with length
equal to the indicated segments
Answer:
3A+B+2a+4b
Step-by-step explanation:
A rectangular prism has a length that is 3 inches shorter than the height and a width that is 5 inches longer than the height. Fill in the blanks to create an equation for the volume of the prism as a function of the height.
An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.
We are given a rectangular prism.A rectangular prism is no different than a cuboid.Let the height of the rectangular prism be "h".The length of the rectangular prism is "h-3".The width of the rectangular prism is "h+5".The volume of the rectangular prism is the same as that of the cuboid.The volume of the rectangular prism is the product of its length, its width, and its height.The volume of the rectangular prism is (h - 3)*(h + 5)*h.An equation for the volume of the prism as a function of the height is :Volume = (h - 3)*(h + 5)*hVolume = (h² + 2h - 15)*hVolume = h³ + 2h² - 15hTo learn more about prism, visit :
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Approximate −12 + the square root of thirty-two to the nearest tenth
The approximate value of the expression given will be equal to -6.3.
An approximation may be defined bringing the value of a certain entity which is almost similar, but not exactly equal to the correct value. The expression can be written as −12 + √32. The value of √32 can be written as 5.656. Since, after decimal 6 to the right of 5 is greater than 5 so to the nearest tenth, we can write as 5.66. Therefore, √32 = 5.66
For the required value of the expression we can write,
−12 + √32
Putting the value of √32 = 5.66 in the expression we get
-12 + √32 = -12 + 5.66
After solving we get
⇒ -12 + √32 = -6.34
To the nearest tenth it will be -6.3.
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Let f (x) = px 2 + qx - 4 p, where p 0. Find the number of roots for the equation f (x) = 0 . Justify your answer.
Answer:
f(x) = 0
px^2 + qx - 4p = 0
abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)
x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)
x = (-q ± √(q^2 + 4^2·p^2))/(2·p)
Because q^2 + 4^2·p^2 > 0 there are two roots.
Because the dividend is the same for all three expressions the larger the divisor the__the quotient
Given:
Because the dividend is the same for all three expressions the larger the divisor the__the quotient
the answer will be: smaller or least