First, any number multiplied by 1 yields the result of itself
Therefore, we can rewrite it as 5/3 x 3.
We do the multiplication : 5/3 x 3 = 5/3 x 3/1 = (5x3)/(3x1) = 15/3 = 5.
Rewrite 5 as 5/1 for a fraction result.
A bowl contained 58.3 grams of salt. Then, Brian poured in another 33.47 grams. How much salt does the bowl contain now
translate to an inequality. he runs at least 1.8 hours per day. question content area bottom part 1 let r represent the number of hours of running per day.
g ≥ 1.8 is the number of hours of running per day in inequality .
What are the mathematical inequalities?
An inequality in mathematics depicts the relationship between two values in an unbalanced algebraic expression. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality. Some people receive better and more skilled care in the medical field than others. Additionally, they must pay more for these services.Atleast means the number would be greater than or equal to given number.
g ≥ 1.8
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Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the horizontal component of the friction force f⃗ ?.
Before the drawbridge starts to open, the horizontal component of the friction force f⃗ is zero (0)
The horizontal component of the friction force is the counter force that must overcome the friction force for a body to slide or move.
When the dancer is standing still on the drawbridge, the only force on the dances is the normal force exerted by the bridge. Thus, the horizontal frictional force acting on the dancer
This is given by:
[tex]f_{horizontal} =0[/tex]
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PLS HELP, IT'S ALMOST DUE! I'LL GIVE BRANLIEST TO THE CORRECT/BEST ANSWER. 40 Points! I'd appreciate if you help :)
A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp's incline?
A. 1/3 inch up per foot across
B. 1/2 inch up per foot across
C. 2 inches up per foot across
D. 3 inches up per foot across
Answer:
3 inches up per foot across
Step-by-step explanation:
rate of change = difference of y / difference of x
R = (18 - 12) / ( 6-4) = 6 / 2 = 3 inch / foot
the volume of the ice cream cone is increasing at the rate of 10 units3/sec and its radius is increasing at the rate of 1 14 units/sec when the radius r and height h are (r, h)
The rate of change for the height of the ice cream is [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
What is the rate of change of the height of a cone?
The volume of an ice cream cone (V), in cubic units, is described by the following formula:
V = (1 / 3) · (π · r²) · h (1)
Where:
r - Radius of the cone, in units.h - Height of the cone, in units.The rate of change for the height of the cone is derived from differentiating (1) with respect to time:
V' = (1 / 3) · (2π · r) · h · r' + (1 / 3) · (π · r²) · h'
V' = (2π / 3) · h · r' + (π / 3) · r² · h'
h' = [V' - (2π / 3) · h · r'] / [(π / 3) · r²]
Where:
h' - Rate of change of the height, in units per second.V' - Rate of change of the volume, in cubic units per second.If we know that V' = 10 and r' = 1 / 14, then the rate of change for the height of the cone is:
h' = [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²]
The height of the ice cream cone changes at a rate of [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
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The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?l
The graph could be the graph of f(x) which is the correct answer would be option (B).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We are given the degree of the polynomial function f(x) to be 3; and
the roots of the equation f(x) to be 0 are -1, 0, and 4.
So we will put these values in the polynomial function of degree 3 to get:
f(x) = (x -(-1))(x-0)(x-4)
f(x) = (x + 1)x(x-4) = x³ - 3x² - 4x
According to this, the x-intercepts of this function on the graph will be:
(0, 0)
(-1, 0)
(4, 0)
So we will look for a graph that intercepts the x-axis at these points.
Therefore, the graph of the option (B) at the bottom right satisfies the conditions and is the graph of f(x).
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Sarah created a graph to show the number of gallons in the tank as it is being filled with water over a 10 minute period.
Answer:
Can I see the graph, please?
Step-by-step explanation:
Answer:he graph shows the relationship between the number of miles she drives, y, and the number of gallons of gasoline in her car's tank, x.
Step-by-step explanation:
Make sure you ans
1. A cell phone company offers two texting plans. People who use plan A pay 20 cents for each text sent or received. People who
use plan B pay 14 dollars per month, and then pay an additional 8 cents for each text sent or received.
question
a. Write an inequality to represent the fact that it is cheaper for someone to use plan A than plan B. Use x to represent the number
of texts they send.
b. Solve the inequality.
hey you man what are you going here go to there
There are 2.54 cm in an inch, 100 cm in a meter, 12 inches in 1 foot, and 5,280 feet in 1 mile. Jada ran 1.5 miles. How many centimeters and meters is that?
Answer:
1.5 miles = 241,401.6 centimeters
= 95,040 inches
1.5 miles = 2,414.016 meters
Step-by-step explanation: 5,280 feet x 12 inches = 63,360 inches
2,640 feet x 12 inches = 31, 680 inches
63,360 + 31,680 = 95,040 inches in 1.5 miles
95,040 x 2.54 centimeters per inch = 241,401.6
241,401.6 centimeters / 100 = 2,414.016 meters
please help, i am not sure what to do
cross multiplying
4/3(y-9/10)=5y(2/10)
expanding the bracket and collecting like terms
4y/3 - 6/5=y
4y/3 - y=6/5
((4y-3y)/3)=6/5
y/3=6/5
y=6/5x3
y=18/5
y=3.6
I hope this will help✨
What is the slope of the line that passes through the points (-4, 6) and
(-4, 18)?
The slope of the line passing from the two points is found as infinity.
What is meant by slope of the line?The slope of the line is a measurement of its steepness and direction. Any 2 separate points on a line can be used to calculate the slope of that line. The slope of the a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.For the given question;
The two passing points of the line is given as;
(x1, y1) = (-4, 6)
(x2, y2) = (-4, 18)
The formula for calculating the slope is;
Slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (18 - 6)/ (- 4 + 4)
m = 12/0
m = ∞
It means, the line is parallel to the x axis.
Thus, the slope of the line passing from the two points is found as infinity.
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Question «
Simplify this expression. √24
A 2√6
3√8
8√3
6√2
Answer:
A 2√6
Step-by-step explanation:
- Split the value under root into divisions of factors of 24
[tex]{ \sf{ \sqrt{24} = \sqrt{6 \times 4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times \sqrt{4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times 2 }} \\ \\ { \boxed{ \sf{ \: \sqrt{24} = 2 \sqrt{6} }}}[/tex]
Please helppp :)
Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer
The following data table for two distinct linear functions utilizing identical x values for both functions is displayed:
[tex]\begin{tabular}{|c|c|c|}$\mathrm{x}$ & $\mathrm{y}=2 \mathrm{x}+7$ & $\mathrm{y}=-\mathrm{x}+4$ \\$-3$ & $2(-3)+7=-6+7=1$ & $-(-3)+4=3+4=7$ \\$-2$ & $2(-2)+7=-4+7=3$ & $-(-2)+4=2+4=6$ \\$-1$ & $2(-1)+7=-2+7=5$ & $-(-1)+4=1+4=5$ \\0 & $2(0)+7=0+7=7$ & $-(0)+4=0+4=4$ \\1 & $2(1)+7=2+7=9$ & $-(1)+4=-1+4=3$ \\2 & $2(2)+7=4+7=11$ & $-(2)+4=-2+4=2$ \\3 & $2(3)+7=6+7=13$ & $-(3)+4=-3+4=1$\end{tabular}[/tex]
The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.
As a result, the two functions' graphs will intersect at (1, 5)
First of all, we create 2 LINEAR function, i created the function f(x)=2x+5 and the function h(x)=3x+2, both are linear(without a quadratic term). Then
Choose a group of x values before creating the table. Add each x value from the left side column to the equation. To find the y value, evaluate the equation (middle column). Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.
you replace the x for a number:
Table 1 (F(X)=2X+5) Table 2 (H(X)=3X+2)
X=1----->Y=2+5=7 X=1------>Y=3·1+2=5
X=2---->Y=2·2+5=9 X=2----->Y=3·2+2=8
X=3---->Y=3·3+5=11 X=3----->Y=3·3+2=11
With both tables of data we can see that in the X=3/Y=11 point this two linear functions will intersect so the answer is that the two functions will intersect at (3,11)----->(X,Y)
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A number, x, rounded to 1 decimal place is 3.7
Write down the error interval for x.
The range of the error will be [3.65,3.75.
What is an error interval ?The accuracy range or limit where a number is rounded off or truncated is known as the error interval. This range merely depicts the possible range before rounding.
Given that :A number, x, rounded to 1 decimal place is 3.7
The mistake will be half of 0.1, which is[tex]\frac{0.1}{2} = 0.05[/tex], since the number is rounded to the nearest 0.1 unit.
3.7-0.05=3.65 will then be the lower limit of the error interval.
The error interval's upper limit will be 3.7 + 0.05 = 3.75.
The error will be 3.65≤x<3.75 milliseconds.
If the second decimal unit is more than 5, the first decimal unit will be 6, since we are rounding the first decimal unit. Similar to this, the first decimal unit will be 7 if the second decimal unit is less than 5.
The figures below, when rounded, result in 3.7.
3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74
As a result, the error range will be [3.65,3.75).
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Select Correct or Incorrect for each equation.
Equation
-1+1/-1=1
-1/1=-1
Answer:
first equation: Incorrect
second equation: Correct
Step-by-step explanation:
first equation:
[tex]-1 + (\frac{1}{-1}) = 1[/tex]
[tex]-1 + (-1) = 1[/tex]
[tex]-2 = 1[/tex]
negative 2 isn't the same as positive 1 which isn't true so the answer is incorrect.
second equation:
[tex](\frac{-1}{1} ) = -1[/tex]
[tex](-1) = -1[/tex]
negative 1 is the same as negative 1 so the answer is correct
What is the opposite of each number?
Drag the answer into the box to match each number.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
0.005
12
0
−2
Answer:
0.1 == -0.1
1/7 == -1/7
10 == -10
-7 == 7
Step-by-step explanation:
I took the test
The opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
The numbers are:
0.005, 12, 0, -2
As we know, from the definition of the number, a number is a mathematical entity that can be used to count, measure, or name things.
The opposite of any number can be obtained by changing the sign of the number.
The opposite of the number 0.005 is -0.005
The opposite of the number 12 is -12
The opposite of the number 0 is 0
The opposite of the number -2 is 2
Thus, the opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.
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which show a way to factor 14+35
Answer: The common factors of 14 and 35 are 7, 1, intersecting the two sets above. In the intersection factors of 14 ∩ factors of 35 the greatest element is 7. Therefore, the greatest common factor of 14 and 35 is 7.
Step-by-step explanation:
Shelley buys a volleyball and kneepads to get ready for her season. The volleyball was discounted 30%. The kneepads cost half the original price of the volleyball. She spent a total of $64.08 including $4.08 in tax.
Select all the true statements, where x is the original price of the volleyball.
An equation to model this situation is 0.7x+0.5x+4.08=64.08.
An equation to model this situation is 0.3x+0.5x+4.08=64.08.
The original price of the volleyball was $50.
An equation to model this situation is 0.7x−0.5x+4.08=64.08.
The original price of the volleyball was $75.00.
Avery is the oldest of four siblings whose ages are consecutive odd integers. If the sum of their ages is 112, find Avery's age.
Four siblings whose ages are consecutive odd integers. If the sum of their ages is 112 then The eldest sibling is 31, followed by siblings 29, 27, and 25.
What is consecutive integers ?
Consecutive means in order. Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.
Let x = the 1st sibling
Let x -2 = the second sibling
Let x -4 = the third sibling
Let x-6 = the fourth sibling.
If you add the four siblings together they equal 112
(x) +(x-2)+(x-4)+(x-6) = 112 Combine like terms
4x - 12 = 112
add 12 from both sides
4x - 12 + 12 = 112 + 12
4x = 124
divide 4 both side :
x = 31
The eldest sibling is 31, followed by siblings 29, 27 and 25
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Part 1 of 3
(Type an ordered pair.)
Suppose line h is the line with equation y = -2. Given A(7.-5), B(5,3), and C(-2,-5), what are the coordinates of the vertices of A'B'C' for the reflection?
Rh
The coordinates of the vertices of A'B'C' for the reflection are (7,1),(5,-7), and (-2,1) respectively.
What is reflection?A reflection is a transformation that uses a line to reflect a figure, much like a mirror. The mirror line is also known as the line of reflection.
The given coordinates are A(7,-5), B(5,3), and C(-2,-5).
The line of reflection is y = -2.
We have to determine the coordinates of the vertices of A'B'C' for the reflection.
In this case, the x-coordinate will remain the same and the y-coordinate will vary as the points are reflected across the line y = -2.
From the line of reflection i.e.y = -2, point A(7,-5) is located down at a distance of 3 units so its reflection A' is 3 units up of line y = -2 at (7,1).
From the line of reflection i.e.y = -2, point B(5, 3) is located up at a distance of 5 units so its reflection B' is 5 units down of line y = -2 at (5,-7).
From the line of reflection i.e.y = -2, point C(-2,-5) is located down at a distance of 3 units so its reflection C' is 3 units up of line y = -2 at (-2,1).
Hence, the coordinates of the vertices of A'B'C' for the reflection are (7,1),(5,-7), and (-2,1) respectively.
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2y + k = 6y - ky; y please solve this
Answer:
[tex]y=-\frac{k}{-4+k}; k \neq 4[/tex]
Step-by-step explanation:
2y + k = 6y - ky; solve for y
2y = 6y - ky - k (Subtraction Property of Equality)
2y - (6y - ky) = 6y - ky - k - (6y - ky) (Subtraction Property of Equality)
-4y + ky = -k (Simplify)
y(-4 + k) = -k (Factor)
[tex]\frac{y(-4+k)}{-4+k}=\frac{-k}{-4+k}: k\neq 4[/tex] (Division Property of Equality)
[tex]y=-\frac{k}{-4+k}; k \neq 4[/tex] (Simplify)
The value of y is k/ (4- k).
What is algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to different addition, subtraction, multiplication, and division arithmetic operations.
Given:
2y + k = 6y - ky
Now, solving for y
2y -6y + ky = -k
-4y + ky= -k
y( k-4) = -k
y = -k/(k -4)
y= k/ (4- k)
Hence, the value of y is k/ (4- k).
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(EASY POINTS)
After reviewing the image I know its an expansion and that the top negative answers are incorrect. Its either C or D
Answer:
Its C
Step-by-step explanation:
f(x)=
1
4
x–5 if x<
–
4
x+3 if x≥
–
4
The graph of each function in the piecewise function is added as an attachment
How to determine the plot of the piecewise function?The equation of the piecewise function is given as
f(x) = 1/4x - 5 if x < 4
x + 3 if x ≥ 4
In the above definition of the piecewise function, we have the following functions and the domains
f(x) = 1/4x - 5 at a domain of x < 4
f(x) = x + 3 at a domain of x ≥ 4
Note that:
The domain of the function is the set of input values of the graph
This in other words mean the domain of a function is the set of x values of the graph.
Next, we plot the graph of each function in the piecewise function in their respective domain
See attachment for the graph of each function in the piecewise function,
On the graph, the blue line represents f(x) = 1/4x - 5 while the other line represents f(x) = x + 3
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Possible question
Plot of the piecewise function
f(x) = 1/4x - 5 if x < 4
x + 3 if x ≥ 4
Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberry fewer than Ann and Ben together, what is the total number of strawberries the three of them ate
Answer:
170 strawberries
Step-by-step explanation:
Let strawberries be x, then:
Ann ate 5x, Ben ate 5x, and Cindy ate 7x
7x+30 = 5x+5x
7x+30 = 10x
30 = 3x
10 = x
5x = 50
7x = 70
total: 50+50+70 = 170
9 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in minutes per customer?
The rate at which the customers enter the store in minutes per customer is 2 minutes.
Based on the given question the number of customers is 9 so they take 18 minutes to enter. If each customer takes
(18÷9) minutes = 2 minutes.
Then all the customers will be inside the shop.
Fractions: The number of parts of a full portion is known as a fraction.
It is usually best to show an explanation using the easiest fraction. That is called Simplifying, or Decreasing the Fraction.
We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the total is separated into.
Represented as : [tex]\frac{Numerator}{Denominator}[/tex]
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PLEASE HELP MEEE !!!!!!!!!!!!!!!!!!
Answer:
x=20 degrees
I did what your teacher did down there; I added all the exterior angles and set them equal to 360°
Just combined the like terms and got the answer!
*3x + 4x + 3x = 10x
12 - 10 - 2 = 0
90 + 70 = 160
Put them "as an equation": 10x + 160 = 360
Get rid of what's surrounding the x, so subtract 160 from both sides.
10x = 200
To get rid of whats beside the x *again*, divided 10x by 10 on both sides.
x = 20
1. Directed line segment QR has endpoints Q(8, 4) and R(-2, -1).
Find the coordinates of point Palong directed line segment QR so
that the ratio of QP to PR is 1 to 4.
The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).The x-coordinates of P is 6.2 and y-coordinates of P is 1.4.
Given that,
The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).
We have to find the coordinates of the QR line segment aimed at point P along that QP to PR is a 1 to 4 ratio.
QR has the endpoints Q(8, 4) and R. (-2, -1).
Line segment QR divides at point P in ratio 1:4.
Using section formula:
The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.
P(x,y)=[tex](\frac{mx_{2} +nx_{1} }{m+n},\frac{my_{2} +ny_{1} }{m+n},)[/tex]
Where m is 1 and n is 4. x₁=8,y₁=4 and x₂=-2,y₂=-1.
Substitute in the formulae we get,
P(x,y)=((1×-1+4×8)/1+4,(1×-1+4×4/1+4))
P(x,y)=((-1+32)/5,(-1+8)/5)
P(x,y)=(31/5,7/5)
P(x,y)=(6.2, 1.4)
Therefore, the x-coordinates of P is 6.2 and y-coordinates of P is 1.4
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the difference.
9832 - 6199 =
3633 is the difference of these numbers.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.
Subtraction can be applied in a variety of real-world situations. Assume you had five apples and your friend had three. We may calculate the quantity of remaining apples by subtracting: 5 - 3 = 2.
Given Data
9832 - 6199
Subtracting,
= 9832 - 6199
= 3633
3633 is the difference of these numbers.
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g(x) = 15 - 4x
3
h(x) = x+8
Write g(h(x)) as an expression in terms of x.
g(h(x)) =
Answer:
[tex]g(h(x))=−6x−17
[/tex]
Step-by-step explanation:
given:
[tex] g(x) = 15 - 4x \\ h(x) = \frac{3}{2 } x + 8[/tex]
To find g(h(x)) substitute h(x) instead of every x in g(x)
therefore:
[tex]g(h(x)) = 15 - 4( \frac{3}{2} x + 8) \\ [/tex]
simplify
[tex]g(h(x)) = 15 - 6x - 32 \\ g(h(x)) = - 6x - 17[/tex]
pls helppp!!!
1. Give an example of discrete data that might consist of some decimal numbers.
2. Give an example of continuous data that might not have any numbers with fractional parts
The discrete data might consist of number of legs, number of teeth. The continuous data might consist the length of tail, and the height of dog.
What is discrete data?The discrete data is a data whose value is obtained by counting and they can be described by an integer value. Those random variables, who take only distinct values, are called discrete random variables.
Consider the provided information; Something that will never change
So, the discrete data might consist of number of legs, number of teeth.
A continuous data is defined as a variable whose value is obtained by measuring.
The continuous data might consist the length of tail, and the height of dog.
The continuous variables are random variables, who take any value from a given continuous interval of real numbers.
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