Answer:
Let x be the number
5 times a number:
5x
The quotient of the number and 2.
5x / 2
Final answer:
The 'quotient of 5 times a number and 2' can be expressed as '5x/2', where 'x' is the unknown number. Important mathematical concepts, such as order of operations, exponents, and percentages, influence how we calculate and understand such expressions.
Explanation:
The statement 'The quotient of 5 times a number and 2' represents a mathematical expression, where you are asked to first multiply a number by 5 and then divide that product by 2. To elucidate, let us assume the unknown number is represented by 'x'. So we multiply 5 by 'x' to get '5x', and then we divide that by 2 to get the final expression, which is '5x/2'. In this case, we are dealing with division, which is opposite to multiplication, and it's important to follow the correct order of operations when solving mathematical problems.
if x:6as3:9,then x is equal to
Answer:
x=2
Step-by-step explanation:
x/6=3/9
simplify 3/9 into 1/3
x/6=1/3
cross product
6*1=3x
6=3x
x=6/3=2
x=2
PLS HURRY! 15 PTS!
Consider the function f(x)=x^3+2x^2-3. (a) Graph the function. (b) What are the x- and y-intercepts of the graph? BE SURE TO ANSWER (a) & (b). also pls show work!
Answer:
x-intercept = 1 and y-intercept = -3
Step-by-step explanation:
The graph of the function is attached with this answer.
I have used some computer program to draw graph but you can draw a rough graph manually on a graph sheet. For that
first of all you need to know basic structure of a cubic polynomial * which is somewhat like a wave (you can have a look at the graph attached to know the basic structure).Then plot some important points which are point of local maxima ** and local minima ***, point of intercepts (which is the second part of the question - has to be done first in order to draw a more accurate rough diagram of the function).To Calculate Some Important Points :
Local Maxima and Minima :These are the points where the the first derivative of the function becomes zero. This means that at these points the graph takes turn, if it was increasing behind this point then it will start decreasing after this point or the other way. The second derivative of the function at these points are either positive or negative (positive for local minima and negative for local maxima).
Intercepts :To calculate the x-intercept, first you need to analyse the graph to know how many x-intercepts are there. According to this graph only one intercept is there, it means that only one real root of this cubic equation is there (a cubic equation has 3 roots in which either one is real and two are imaginary or all the three are real). To calculate roots of a cubic equation there is no specific way. Generally, the first root is through hit and trial method. So, let's start with the simplest number which is x=0
[tex](0)^{3}+2(0)^{2}-3 \neq 0[/tex]
∴ 0 is not a root.
Now, let x=1
[tex](1)^{3}+2(1)^{2}-3=0[/tex]
∴ 1 is a root.
Since 1 is the only real root of the equation, therefore (1,0) is the only x-intercept of the graph.
To calculate y-intercept, simply put x=0 in the equation which is
[tex]f(0)=(0)^{3}+2(0)^{2}-3=-3\\\therefore f(0)=-3[/tex]
Therefore the y intercept is (0,-3).
* Cubic Polynomial : Polynomials which have a degree (highest power of the variable) of 3 are called cubic polynomials.
** Local Maxima : Points at which the left and right neighbours have less function value are called local maxima.
*** Local Minima : Points at which the left and right neighbours have more function value are called local minima.
Answer:
x = 1 and the y = -3
Step-by-step explanation:
here below hope this helps
How many kilograms of lentils will each person get if 3 people share 1/5 of a kilogram of lentils equally?
Answer:
1/15 of a kilogram
Step-by-step explanation:
Answer:1/15 of a kilograms
Step-by-step explanation:
1/5 divided by three is the same as 1/5*1/3. 1*1 =1 and 5*3 =15
Which formula can be used to describe the sequence? -2/3,-4,-24,-144...
The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
Step-by-step explanation:
The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex] , where
a is the first term of the sequencer is the common ratio between each two consecutive terms[tex]r=\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex]∵ The sequence is [tex]\frac{-2}{3}[/tex] , -4 , -24 , -144 , .......
∵ The 1st term is [tex]\frac{-2}{3}[/tex]
∵ The 2nd term is -4
∴ [tex]\frac{-4}{\frac{-2}{3}}=6[/tex]
∵ The 3rd term is -24
∴ [tex]\frac{-24}{-4}=6[/tex]
∵ The 4th term is -144
∴ [tex]\frac{-144}{-24}=6[/tex]
∵ [tex]\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex] = [tex]\frac{a_{4}}{a_{3}}[/tex] = 6
∴ There is a constant ratio between each two consecutive terms
∴ The sequence is a geometric sequence
∵ The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex]
∵ a = [tex]\frac{-2}{3}[/tex]
∵ r = 6
∴ The formula of the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
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Answer:
c - f(x) = -2/3(6)^x − 1
Step-by-step explanation:
Edge 2020
Part one
Find the cost to park for a day and the hourly rate to rent a paddleboat.
Answer:
Total cost for a day=246 dollars
Hourly rate=10 dollars
Step-by-step explanation:
Let the Total cost be a function of 't' (time),i.e. total cost=R(t)
let R(t)=at+b where a and b are some constants belonging to real numbers
Now substitute t=1 in above equation
R(1)=a+b⇒16=a+b
substitute t=2,
R(2)=2a+b⇒26=2a+b
Now solving a+b=16 and 2a+b=26,
we get a=10 dollars/hour and b=6 dollars
Therefore the cost function is, R(t)=10t+6
where 10 dollars/hour is the hourly rate and 6 dollars is the base charge.
To get the Total charge for one day substitute t=24 in R(t)
⇒R(24)=10*24+6=246 dollars
what is the answer of 67 × 27
Answer:
1809
Step-by-step explanation:
Answer:
67 x 27 = 1,809 have a good day
The perimeter of a rectangle is twice the sum
of its length and its width. The perimeter is
40 meters and its length is 2 meters more
than twice its width.
Answer:
The width of the given rectangle = 6 m
The width of the rectangle = 14 m
Step-by-step explanation:
Let us assume the width of the rectangle = k
So, the length of the rectangle = 2 + 2 ( The width) = 2 + 2 k
Perimeter of the rectangle = 40 meters
Now, PERIMETER OF THE RECTANGLE = 2(LENGTH + WIDTH)
or, 40 = 2 ( k + (2 + 2 k))
⇒ 2( 3 k + 2) = 40
or, 2(3 k) + 2(2) = 40
or, 6 k = 40 - 4 = 36
⇒ k = 36 / 6 = 6, or k = 6
Hence, the width of the given rectangle = k = 6 m
The width of the rectangle = 2 + 2 k = 2 + 2(6) = 14 m
x + y = 6
3x - 2y = -2
Answer:
x=2, y=4. (2, 4).
Step-by-step explanation:
x+y=6
3x-2y=-2
---------------
y=6-x
3x-2(6-x)=-2
3x-12+2x=-2
5x-12=-2
5x=-2+12
5x=10
x=10/5
x=2
y=6-(2)=6-2=4
If sin(x) =-1/2 and tan(x) is negative what is cos(2x)
[tex]\( \cos(2x) = \frac{1}{2} \).[/tex]
Given that [tex]\( \sin(x) = -\frac{1}{2} \) and \( \tan(x) \)[/tex] is negative, we can find \[tex]( \cos(2x) \)[/tex]using the trigonometric identities.
First, let's find the value of [tex]\( \cos(x) \)[/tex] using the Pythagorean identity:
[tex]\[ \cos^2(x) = 1 - \sin^2(x) \][/tex]
Given [tex]\( \sin(x) = -\frac{1}{2} \),[/tex] we have:
[tex]\[ \cos^2(x) = 1 - \left(-\frac{1}{2}\right)^2 \][/tex]
[tex]\[ \cos^2(x) = 1 - \frac{1}{4} \][/tex]
[tex]\[ \cos^2(x) = \frac{3}{4} \][/tex]
Taking the square root of both sides, since [tex]\( \cos(x) \)[/tex] is positive in the first and fourth quadrants:
[tex]\[ \cos(x) = \pm \frac{\sqrt{3}}{2} \][/tex]
Given that [tex]\( \tan(x) \)[/tex] is negative, we know that ( x ) lies in either the second or fourth quadrant. In the second quadrant, both [tex]\( \sin(x) \) and \( \cos(x) \)[/tex] are negative. In the fourth quadrant, [tex]\( \sin(x) \)[/tex] is negative but [tex]\( \cos(x) \) i[/tex]s positive.
Since [tex]\( \cos(x) = \pm \frac{\sqrt{3}}{2} \),[/tex] we conclude that [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \)[/tex] (since [tex]\( \cos(x) \)[/tex] is negative in the second quadrant).
Now, using the double angle identity for cosine:
[tex]\[ \cos(2x) = 2\cos^2(x) - 1 \][/tex]
Substituting [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \):[/tex]
[tex]\[ \cos(2x) = 2\left(-\frac{\sqrt{3}}{2}\right)^2 - 1 \][/tex]
[tex]\[ \cos(2x) = 2\left(\frac{3}{4}\right) - 1 \][/tex]
[tex]\[ \cos(2x) = \frac{3}{2} - 1 \][/tex]
[tex]\[ \cos(2x) = \frac{3}{2} - \frac{2}{2} \][/tex]
[tex]\[ \cos(2x) = \frac{1}{2} \][/tex]
So, [tex]\( \cos(2x) = \frac{1}{2} \).[/tex]
find the coordinates of the midpoint of VW with endpoint V(-2,-6) and W(x+2,y+3)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-6})\qquad W(\stackrel{x_2}{x+2}~,~\stackrel{y_2}{y+3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{(x+2)-2}{2}~~,~~\cfrac{(y+3)-6}{2} \right)\implies \left( \cfrac{x}{2}~~,~~\cfrac{y-3}{2} \right)[/tex]
Find the number if:
1.12 of it is 56
Answer:
The number is 50.
Step-by-step explanation:
1.12x=56
x=56/1.12
x=50
Choose the equivalent factored form
A total of 814 tickets were sold for the school play. They were either adult tickets or student tickets. There were 64 more student tickets sold than adult tickets. How many adults tickets were sold?
Final answer:
To solve the problem, we set up an equation with 'x' representing adult tickets and concluded that 375 adult tickets were sold for the school play.
Explanation:
The question involves solving a numerical problem related to ticket sales. To find the number of adult tickets sold for the school play, we can set up an algebraic equation. Let x represent the number of adult tickets and x + 64 represent the number of student tickets (since there were 64 more student tickets sold than adult tickets). The total tickets sold were 814, so we can write the equation as follows:
x + (x + 64) = 814
Combining like terms, we have:
2x + 64 = 814
Subtracting 64 from both sides, we get:
2x = 750
Dividing both sides by 2, we obtain:
x = 375
Therefore, 375 adult tickets were sold for the school play.
The equation 22 = 2y + x represents the perimeter of a flower garden with
length y (in feet) and width x (in feet). Solve for y. Then find the length of the
flower bed when the width is 2 feet, 3 feet, and 4 feet.
Answer:
[tex]y = \frac{22-x}{2}[/tex]
For width = 2 ft, the length of the flower bed = 10 ft.
For width = 3 ft, the length of the flower bed = 9.5 ft.
For width = 4 ft, the length of the flower bed = 9 ft.
Step-by-step explanation:
Here, the Perimeter of the flower garden is given as
22 = 2 y + x
: where, y : Length of the garden
and x : Width of the garden .
Now, solving for y in the above expression,we get
22 = 2 y + x ⇒ 22 - x = 2 y
or, [tex]y = \frac{22-x}{2}[/tex]
Now, when the width (x) = 2 feet
Length of the flower bed [tex]y = \frac{22-x}{2} = \frac{22-2}{2} = \frac{20}{2} = 10[/tex]
or, x = 10 ft
⇒For, the width = 2 ft, the length of the flower bed = 10 ft.
when the width (x) = 3 feet
Length of the flower bed [tex]y = \frac{22-x}{2} = \frac{22-3}{2} = \frac{19}{2} = 9.5[/tex]
or, x = 9.5 ft
⇒For, the width = 3 ft, the length of the flower bed = 9.5 ft.
when the width (x) = 4 feet
Length of the flower bed [tex]y = \frac{22-x}{2} = \frac{22-4}{2} = \frac{18}{2} = 9[/tex]
or, x = 9 ft
⇒For, the width = 4 ft, the length of the flower bed = 9 ft.
Latoya, Henry, and Manuel served a total of 112 orders Monday at the school cafeteria. Latoya served 7 more orders than Henry. Manuel served 3 times as many orders as Henry. How many orders did they each serve?
Answer:
Henry: 21
Latoya: 28
Manuel = 63
Step-by-step explanation:
x = orders henry served
x + 7 = orders latoya served
3x = orders manuel served
x + (x + 7) + 3x = 112
5x + 7 = 112
5x = 105
x = 21
x + 7 = 21 + 7 = 28
3x = 3 * 21 = 63
In regular mathematics what is nine times nine
Answer:
81
Step-by-step explanation:
2y÷8-2y=-10
pls answer by today
Answer:
40/7
Step-by-step explanation:
Answer: y=5.7 approx.
Step-by-step explanation:
2y÷8-2y=-10
follow order of operations and simplify a bit first
2y÷8-2y=-10 becomes 1/4y-2y=-10
you can keep on going
so 1/4y-2y=-10 becomes -7/4y=10
y=5.7 approx.
What is the equation?
Step-by-step explanation:
the segments are equal to each other because O is the midpoint of the segment
If there are 32 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
4/7
Step-by-step explanation:
32/56=4/7
Answer:
The number of boys = 32
The number of girls = 56
therefore, to fine the possible ratio, you divided 32 and 56 to their lowest terms.
i.e 32: 56. 32÷8 : 56÷8 = 4:7
what is the simplified answer to 5+3w+3-w
Answer:
5 + 3w + 3 - w = 2w + 8Step-by-step explanation:
[tex]5+3w+3-w\qquad\text{combine like terms}\\\\=(3w-w)+(5+3)\\\\=2w+8[/tex]
A television at Best Buy is on sale for 35% off. If the tv's original price was $1,800, what is the sale price?
The tv is on sale for
Final answer:
The sale price of the television, after a 35% discount on the original price of $1,800, is $1,170.
Explanation:
To calculate the sale price of the television that was originally priced at $1,800 and now has a 35% discount, we need to determine what 35% of the original price is and subtract it from the original price.
Step-by-Step Calculation
Find 35% of $1,800:
(35/100) × $1,800 = $630.
Subtract the discount from the original price:
$1,800 - $630 = $1,170.
Therefore, the sale price of the television is $1,170.
The diameter of a truck tire is 22inches Approximately how fat will the truck have traveled after 5 rotations of these tires
Answer:
The truck have travelled 345.5 inches after 5 rotations of the tires
Step-by-step explanation:
Given:
Diameter of the tyre= 22 inches
Number of rotations= 5
To find:
Distance travelled after 5 rotations=?
Solution:
We have given with diameter,
So let radius be r
r= [tex]\frac{diameter}{2}[/tex]
[tex]r=\frac{22}{2}[/tex]
r=11 inches
The distance covered by one rotation is given by circumference
Circumference =[tex]2\pi r[/tex]
Substituting the values, we get
Circumference =[tex]2\times\pi\times r[/tex]
Circumference =[tex]2\times\pi\times 11[/tex]
Circumference =[tex]2\times\3.14\times 11[/tex]
Circumference =[tex]6.28\times 11[/tex]
Circumference = 69.11
Now for 5 rotation,
Distance travelled = [tex]5\times(\text{circumference value})[/tex]
Distance travelled = [tex]5\times(69.11)[/tex]
Distance travelled = [tex]5\times(69.11)[/tex]
The truck will travel 345.5 inches.
if a population of 5000 doubles in size every 55 years what will the population be 220 years from now
Answer: 40 000
Step-by-step explanation:
Population doubles in first 55 years =
5000 * 2 = 10 000
In 220 years from now, 220/55 = 4
Hence, 10 000 * 4 = 40 000 population
I will mark Brainliest and 5 s.
Here is part one I will post part two after I get an answer for this one.
Thank you so much!❤️
Answer:
Part 1) The rate of change of the linear function is [tex]\frac{1}{3}[/tex]
Part 2) The initial value is -4
Step-by-step explanation:
Part 1) Find the rate of change
we know that
The rate of change of the linear function is the same that the slope of the linear function
To determine the slope we need two points
Looking at the graph
take the points (0,-4) and (3,-3)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-3+4}{3-0}[/tex]
[tex]m=\frac{1}{3}[/tex]
therefore
The rate of change of the linear function is [tex]\frac{1}{3}[/tex]
Part 2) Find the initial value
we know that
The initial value or y-intercept is the value of y when the value of x is equal to zero
Looking at the graph
when the value of x is equal to zero
The value of y is equal to -4
so
The y-intercept is the point (0,-4)
therefore
The initial value is -4
What is the answer? Solve 4 ⋅ (−6)
three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle. find the measure of the angle
Answer:
Step-by-step explanation:3(180-x)=8(90-x)
540-3x=720-8x
540=720-5x
-180=-5x
36=x
x=36
the angle is 36,supplement is 144,complement is 54.
The angle is 36, the supplement is 144, complement is 54.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles.
Two angles whose sum is 90° are called complementary angles.
Given;
The three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle.
So, 3(180-x)=8(90-x)
Solve for x;
540-3x=720-8x
540=720-5x
-180=-5x
36=x
x=36
Hence, the angle is 36, the supplement is 144, complement is 54.
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A shade of green paint is to be mixed with 3 parts blue and 2 parts yellow Ten gailions of green paint are to be mixed
How many gallions of yellow paint must be used?
4
2
5
6 2/3
Answer:
4
Step-by-step explanation:
If we were to work backwards, 4 would be the 2 part in the equation, already done. 2x2=4. so that means that the other number must also be multiplied by 2, making the number 6. 6+4 is 10, meaning ten gallons. message me with any remaining questions!
There are 4 gallons of yellow paint are needed to mixed with the ten gallons of green paint.
To calculate how many gallons of yellow paint must be used to mix with blue paint in order to make ten gallons of green paint, using a ratio of 3 parts blue to 2 parts yellow, we first need to understand the total ratio parts. The ratio given is 3:2, which means there are 3 + 2 = 5 parts in total. Since we want to mix ten gallons of green paint, we need to split these ten gallons according to the ratio.
First, we calculate the value of one part by dividing the total gallons of green paint by the total number of parts:
10 gallons / 5 parts = 2 gallons per part
Now, since we have 2 parts yellow, we need:
2 parts imes 2 gallons per part = 4 gallons
Therefore, to make ten gallons of green paint with the given ratio, 4 gallons of yellow paint must be used.
please help with question below!
Answer:
45
Step-by-step explanation:
45 is constant, because no mater how many miles you drive, you will always be charged $45. It stays the same
Answer:
45
Step-by-step explanation:
your equation would be y= 45+22x and no matter what x equals, you will always have the set $45, so that is your constant.
The bears at the zoo eat
875 pounds of food each week. How
much do they eat per day?
Answer:
They eat 125lbs of food a day
Step-by-step explanation:
You do 875 divide by 7 for the days of the week and you get 125
Answer:
125 pounds
Step-by-step explanation:
One week is equivalent to 7 days
If the bears eat 875 pounds each week all we have to do to get the answer is divide 875 by 7.
875 ÷ 7 = 125
Hope I helped!
A plumber is making steel ring to fit around a pipe with diameter
of 5 centimeters. How long does the steel ring need to be to fit
around the pipe? (Use 3.14 for Pi.)
A. 15.7 cm
B. 19.63 cm
C. 31.4 cm
D. 78.5 cm
Answer:
The circumference of the pipe can be derived by 2(pi) r = 2 (3.14) (2.5)= 15.7. Hence the steel ring needs to be 15.7 cm. (option A).
The length of the steel ring necessary to fit around a pipe with a diameter of 5 cm is 15.7 cm, found using the formula for the circumference of a circle. This formula is Circumference = Pi * Diameter.
Explanation:The student wants to find out how long a steel ring needs to be to fit around a pipe with a diameter of 5 centimeters. This involves finding the circumference of a circle, which uses the formula Circumference = Pi* Diameter. So, to find the needed length of the steel ring, we substitute the given diameter into the formula.
Step 1: Write down the formula: Circumference = Pi*Diameter.
Step 2: Substitute the given diameter of 5 cm into the formula: Circumference = 3.14 * 5 cm.
Step 3: Calculate the circumference: Circumference = 15.7 cm.
Therefore, the steel ring needs to be 15.7 cm long to fit perfectly around the pipe. So, the answer is A. 15.7 cm.
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