Write the phrase as an expression the quotient of 22 and a number [tex]a[/tex].The quotient of 22 and [tex]a[/tex] number = 22/[tex]a[/tex]
Given that
number = 22
quotient = [tex]a[/tex]
To find
The mathematical equation or relation between quotient of 22 and a number [tex]a[/tex].
So according the question
We have
quotient = 22
divisor = [tex]a[/tex]
For finding the relation between given quotient and divisor, let's firstly know about Dividend, Divisor, Quotient and Remainder,
In Mathematics, the dividend is the value that is divided by another value to get the result. The dividend is the base of any division method.
An integer that divides another integer to obtain a result is called a divisor. The result of this division, or quotient, is the dividend, which is the original number that was divided.
Quotient = Dividend ÷ Divisor
When we divide one number by another, the result is a quotient. As an illustration, when we divide 6 by 3, we obtain the answer 2, which is the quotient. A decimal or an integer can both be used as the quotient. When dividing exactly, as when 10 ÷5 = 2, the quotient is an integer, whereas when dividing roughly, as when 12÷ 5 = 2.4, the quotient is a decimal. Although a quotient can be greater than the divisor, it will never be greater than the dividend.
The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). This value is called the remainder.
Now, from question
We have a quotient of 22 that is [tex]a[/tex].
So, 22 fully divided by [tex]a[/tex].
In mathematical form,
= 22/[tex]a[/tex]
The quotient of 22 and [tex]a[/tex] number = 22/[tex]a[/tex]
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let and let be a vector with length that starts at the origin and rotates in the -plane. find the maximum and minimum values of the length of the vector . in what direction does point?
The length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.
What is the maximum and minimum values of the length of the vector? in what direction does point?Generally, the equation for is mathematically given as
Consider the following vector:
[tex]\begin{aligned}\mathbf{v} &=0 \mathbf{i}+4 \mathbf{j}+0 \mathbf{k} \\&=\langle 0,4,0\}\end{aligned}[/tex]
Let us assume that u is a vector that has a length of four, that begins at the origin, and rotates in the x-y plane.
This vector creates a circle with the origin serving as the circle's center and a radius of 4.
So, the coordinates of u can be taken as,
[tex]u=(x\pm \sqrt{4^2-x^2 ,0})[/tex]
Here, 0 [tex]\leq[/tex]x [tex]\leq[/tex] 4.
Now, the cross product of the two vectors u and v is,
[tex]\begin{array}{ccc}\mathbf{i} & \mathbf{j} & \mathbf{k} \\x & \pm \sqrt{4-x^2} & 0 \\0 & 4 & 0\end{array}[/tex]
[tex]&=\mathbf{i}(0-0)-\mathbf{j}(0-0)+\mathbf{k}(4 x-0) \\&=4 x \mathbf{k}\end{aligned}[/tex]
The length of the vector u* v is,
[tex]\begin{aligned}|\mathbf{u} \times \mathbf{v}| &=\sqrt{(4 x)^2} \\&=4 x\end{aligned}[/tex]
Here, 0 <=x <= 4.
If x=4, then u*v is,
[tex]\begin{aligned}\mathbf{u} \times \mathbf{v}| &=4 \times 4 \\&=16 \\|\mathbf{u} \times \mathbf{v}| &=4 \times 0 \\&=0\end{aligned}[/tex]
In conclusion, As a result, the length of the vector u*v has a maximum value of 16 and a minimum value of 0, and it is moving in a positive z-direction.
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CQ
Let v = 4j and let u be a vector with length 4 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u
whats 5 and 1/5 divided by 3
pls help marking brainliest pic attached
Answer:
4
Step-by-step explanation:
16x4=64
Answer:
4 chapters
Step-by-step explanation:
If Raj can read 1 chapter in 16 minutes you need to figure out how many times 16 goes into 64. Divide 64 by 16 and you get 4. Which means Raj can read 4 chapters in 64 minutes.
Find the percent of change in altitude if a weather balloon moves from 100 ft to 103 ft. describe the percent of change as an increase or decrease. round to the nearest tenth if necessary.
The percent of change is an increase in altitude of the weather balloon.
Percentage changeOriginal altitude = 100 ftNew altitude = 103 ftChange in altitude = New altitude - Original altitude
= 103 ft - 100 ft
= 3 ft
Percentage change = Change in altitude / Original altitude × 100
= 3 / 100 × 100
= 3%
Therefore, the percentage change in the altitude of the weather balloon is 3%.
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Find the inequality represented by the graph.
Answer:
[tex]y\le -\frac{1}{3}x + 1[/tex]
Step-by-step explanation:
The equation of the line is y = mx + b
where
m is the slope = rise/run
b = y-intercept ie where the line crosses the y-axis at x = 0
The line crosses the y axis at y = 1 so the y-intercept is 1 and the point at which the line crosses is (0, 1)
We have the equation as
y = mx + 1
To find the slope, take any two points on the line. Find the corresponding difference in the y values and divide this difference by the corresponding difference in the x values
Two convenient points are (0, 1) and (3, 0)
Slope = [tex]\frac{0-1}{3-0} = -\frac{1}{3}[/tex]
Equation of the line :
[tex]y = -\frac{1}{3}x + 1[/tex]
To find out if the inequality in the shaded region is a ≥ or a ≤ inequality, take a point in the shaded region. Determine whether the chosen point x, y values satisfy which of the following equations
[tex]y\le -\frac{1}{3}x + 1[/tex] (1)
or
[tex]y\ge -\frac{1}{3}x + 1[/tex] (2)
The point (0,0) is inside the shaded region
Plug in these values into inequality (1)
[tex]0 = -\frac{1}{3}\cdot0 + 1[/tex] = 1
Is 0 ≤ 1 ?
Indeed it is so the inequality is
[tex]y\le -\frac{1}{3}x + 1[/tex] (Answer)
The region on the opposite side of the line must be a ≥ inqeuality
The attached graph makes it clearer
A soccer ball was kicked toward the goal. the horizontal component of velocity was 22 m/s and the vertical component was 12 m/s . what is the magnitude of the resultant velocity of the soccer ball?
The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .
Let the horizontal component of velocity be [tex]V_{x}[/tex] and the vertical component of velocity be [tex]V_{y}[/tex].
The magnitude of the resultant velocity will be represented by V.
So, we can write
The horizontal component of velocity = [tex]V_{x}[/tex] = 22 m/s
The vertical component of velocity = [tex]V_{y}[/tex] = 12 m/s
The relation between horizontal component, vertical component and resultant velocity is,
[tex]V^{2} = V_{x} ^{2} + V_{y} ^{2}[/tex]
On substituting value of horizontal component and vertical component, we get
[tex]V^{2}[/tex] = [tex](22)^{2} + (12)^{2}[/tex]
[tex]V^{2}[/tex] = 484 + 144
[tex]V^{2}[/tex] = 628
V = [tex]\sqrt{628}[/tex]
V = 25.06 m/s
The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .
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P = 2 ( l + w ) explain how to work this out please
Answer:
2l + 2w
Step-by-step explanation:
using the distributive property
a(b + c) = ab + ac
2(l + w)
= 2l + 2w
A shopping mall has $20,000 to spend on new tiles for the floor. If each tile costs $2, how many tiles can the mall buy
oopss wrong one my bad
THIS IS FOR 50 POINTS AND A BRAINLYS! BUT IF IT WRONG I WILL REPORT YOU!
When you add or subtract whole numbers, always start with the ______.
hundreds
tenths
ones
tens
Answer:
ones
Step-by-step explanation:
always start with the smallest number
Answer:
ones
then tens, tenths, hundreths
Step-by-step explanation:
hope this helps
a radioactive substance decays exponentially. a scientist begins with 180 milligrams of a radioactive substance. after 33 hours, 90 mg of the substance remains. how many milligrams will remain after 43 hours?
The required weight after 43 hours is 72. 96mg
How to determine the valueFrom the information given, we have that;
A Scientist begins with 180 milligrams of a radioactive substance
Let us take Po = 180 milligrams
Using the expression;
[tex]P(t) = Poe^k^t[/tex]
Substituting the values of t = 33, P = 90mg and Po = 180
90 = 180e^33t
[tex]e^3^3^t = \frac{1}{2}[/tex]
Take the log of both sides
[tex]33ln(e^k) = ln (\frac{1}{2} )[/tex]
[tex]k = -\frac{ln 2}{33}[/tex]
k = - 0. 0210
The equation becomes: P(t) = 150e^-0.0210
Substitute t as 43
[tex]P(43) = 180e^-^0^.^0^2^1^0 ^*^4^3[/tex]
P(43) = 72. 96 mg
Hence, 72. 96 mg will remain after 43 hours.
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Find the area of the shaded region in the first quadrant bounded by the line y=3x
The area of the shaded region in the first quadrant is: 0.75 units
What is area under a curve?The area under a curve between two points can be found by doing a definite integral between the two points.
Now,
Given:
x = 0, y = 2Curve: y = 3x - x²To find: area bounded by the given lines and curve in the first quadrant.
Finding:
Now, according to the question, the lines x = 0 and y = 2 intersect at the point (0,2).
Point of Intersection of y = 2 and y = 3x - x²:
2 = 3x - x²
=> x² - 3x + 2 = 0
=> (x - 2)(x - 1) = 0
That is, the line and the curve intersect at two points: ( 1 , 2) and (2,2). But the point that is of our importance is only (1,2).
Thus, area shaded = [tex]\int\limits^1_0 {2 - 3x +x^{2}} \, dx[/tex] = 0.75 square units.
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(COMPLETE QUESTION:
What is the area in the first quadrant bounded by y=3x-x³ and the lines x=0, y=2?)
What is the sum?I need help right now!!!
Answer:
12
Step-by-step explanation:
2 times 2 equals 4, 4 times 3 gets you 12.
the exponent 2 above the original 2 simply means to just times the original number by 2.
Note:
Love your handwriting!
-5x divided by 2 >37
Answer: x < -14.8
Step-by-step explanation:
To solve for x, we will isolate the x-variable.
Given:
[tex]\frac{-5x}{2}[/tex] > 37
Multiply both sides of the equation by 2:
-5x > 74
Divide both sides of the equation by -5:
➜ Since we are dividing by a negative, we will flip the direction of the sign.
x < -14.8
In Exercises 31−34, tell whether the data in the table can be modeled by a linear equation. Explain. If possible, write a linear equation that represents y as a function of x. Help with 34 ; please include a explanation. Thanks
The slope across the values of the table are not the same, therefore, the table cannot be modelled by a linear equation.
How to Determine a Linear Equation Table?If a table can be represented by a linear equation, then the slope/rate of change between every two pairs of values on the table must be the same. If it's not, then it is not a linear equation that represents y as a function of x.
Slope/rate of change between (1, 18) and (2, 15):
Slope = 18 - 15/1 - 2
Slope =-3
Slope/rate of change between (2, 15) and (8, 9):
Slope = 15 - 9 / 2 - 8
Slope = 6/-6 =
Slope = -1
Therefore, the slope across the values of the table are not the same, therefore, the table cannot be modelled by a linear equation.
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In the expression -3 which is the correct order in which operations have been done to x?
5
(1) x was divided by 5 and the result was subtracted from 3.
(2) x had 3 subtracted from it and the result was then divided by 5.
(3) x was divided by 5 and 3 was subtracted from the result.
(4) 5 was divided by x and then 3 was subtracted from the result.
Jason biked 60 miles. he averaged 15 miles per hour. how long did he ride?
Answer:
4 hr
Step-by-step explanation:
A certain vine grows at a rate of three inches per day. A researcher starts observing it
when it is 27 inches long.
I
1) What is the meaning of three inches in the problem?
2) What is 27 inches represent in the problem?
3) How long will be the vine after one day?
after two days?
4) Write an algebraic expression to represent the length of the vine after n days.
+
A certain vine grows at a rate of three inches per day. A researcher starts observing it
when it is 27 inches long.
I
1) What is the meaning of three inches in the problem?
2) What is 27 inches represent in the problem?
3) How long will be the vine after one day?
after two days?
4) Write an algebraic expression to represent the length of the vine after n days.
ans
Multiply numbers with decimals
2.34 x 1.6
Answer:
3.744
Step-by-step explanation:
2.34
* 1.6
-------
1404
+
234
---------
3.744
converse of if a triangle has either two equal sides or two equal angles, then it is an isosceles triangle
It is an isosceles triangle if a triangle has either two equal sides or two equal angles,
What is converse of a statement?The converse of a statement is formed by switching the hypothesis and the conclusion.
Given the statement 'if a triangle has either two equal sides or two equal angles, then it is an isosceles triangle'
Hypothesis - if a triangle has either two equal sides or two equal angles, Conclusion - then it is an isosceles triangle
The converse will be created by switching the hypothesis with conclusion and vice versa to have ' It is an isosceles triangle if a triangle has either two equal sides or two equal angles,
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Drag and drop the correct answer choice to each answer blank.
The length of four rivers in Africa is shown in the table below.
River Length (feet)
Nile 21,800,000
Congo 15,010,000
Ubangi 3,520,000
Zambezi 83,800,000
How is the length of the Zambezi river written in scientific notation?
Answer:
8.38 × 10^7
Step-by-step explanation:
first digit of number X 10 raised to however many digits are after the first
The solution is Option D.
The length of the Zambezi river written in scientific notation is
L = 8.38 x 10⁷ feet
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
The length of the Zambezi river in feet L = 83,800,000 feet
Now , the scientific notation is given by in powers of 10
So ,
The value of L in scientific notation is given by
The value of L = 838 x 10⁵ feet
The value of L = 8.38 x 10² x 10⁵ feet
So , on simplifying the equation , we get
The value of L = 8.38 x 10⁷ feet
Therefore , the value of L is 8.38 x 10⁷ feet
Hence , The length of the Zambezi river written in scientific notation is
L = 8.38 x 10⁷ feet
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Robert wants to buy a digital piano at a yard sale.
explain the GCF method with an example??
Find the value of x.
51 m
h
48 m
51 m
Step-by-step explanation:
there is no "x" in the whole scenario.
you and your teacher mean "h" ?
this we get by using Pythagoras, because h, half of the baseline and one of the 51 m sides create a new right-angled triangle :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.
so, for that new inner triangle we have then
51² = h² + (48/2)² = h² + 24²
2601 = h² + 576
h² = 2025
h = 45 m
Factoring quadratics 15x^2-14x+3
Step-by-step explanation:
15x²-14x+3
Product =45
Sum=-14
=(-9,-5)
15x²-9x-5x+3
3x(5x-3)-1(5x+3)
=(5x-3)(3x-1)
Directions: Use what you have learned this week in class to answer the question. You should show your work or explain your reasoning in mathematical terms. Be specific. Draw a picture if you need to.
please help i need this done HELPPPPPPPASAP
Question:
Evelyn has some paracord with a total length of 5-½ meters. She needs to cut the cord into 12 equal portions. What is the length of each piece written as a fraction? Is this value rational or irrational; why?
Work/Reasoning & Answer:
Answer: Nachelle is 1.35 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 24.15 meters. She stands 19.2 meters away from the tree, so … that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Step-by-step explanation:
A travel agency surveyed 70 of their clients who had visited Europe about international travel. Of the 70 clients who had visited Europe, 60 had traveled to England, France, or both. Of those 60 clients, 45 had visited England, and 50 had visited France.
c. What is the probability that a randomly chosen participant in the survey will have visited both England and France? Explain your reasoning.
The probability that a randomly chosen participant in the survey will have visited both England and France is 0.5
Given data
number of clients = 70
travelled to England , France or both = 60
travelled to England = 45
travelled to France = 50
How to find the probability that a randomly chosen participant in the survey will have visited both England and Francelet:
E represent the client that visited England only,
F represent the number of client that visited France only,
EF represent the number of clients that visited both England and France only
we have
E + F + EF = 60
45 - EF + 50 - EF + EF = 60
45 + 50 - EF = 60
95 - EF = 60
95 - 60 = EF
EF = 35
E = 10
F = 15
probability
Pr = required outcome / possible outcome
= EF / clients surveyed
= 35 / 70
= 0.5
Explanation
EF represents the number of clients that visited England and France only, and it was solved to be 35. probability is the ratio of required outcome which 35 to the possible outcome which is the total number of clients 70. The ratio gives 0.5
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Geometry B.5 Add
Learn with an example
If TU = 14 and UV = 10, what is TV?
5
If 1 kilogram = 2.205 pounds, converting 165 pounds to kilograms and rounding to the nearest tenth gives
The value of 165 pounds is 74.8 kilograms
How to convert the metric units?The given parameter is:
1 kilogram = 2.205 pounds
Multiply both sides by 165
So, we have
165 * 1 kilogram = 2.205 pounds * 165
Divide both sides by 2.205
So, we have
165/2.205 * 1 kilogram = 2.205 pounds * 165/2.205
Evaluate the products
So, we have
74.8 kilogram = 165 pounds
Rewrite as
165 pounds = 74.8 kilogram
Hence, the value of 165 pounds is 74.8 kilograms
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Subtract using the number line.
7- (-1)
+++
-10 -8 -6 -4 -2
Enter your answer in the box.
1
0
2
4
6
+
8 10
Answer:
The question isn't clear but i try to do for 7-(-1) solution only. 7-(-1) =8 mean that 7+1=8
Find the value of b for this line
Answer:
b = - 12
Step-by-step explanation:
substituting m = [tex]\frac{4}{5}[/tex] , x = 10, y = - 4 into y = mx + b , gives
- 4 = ([tex]\frac{4}{5}[/tex] × 10) + b
- 4 = (4 × 2) + b
- 4 = 8 + b ( subtract 8 from both sides )
- 12 = b