In algebra, the variable 'm' in the expression 'm + 8' can indeed take on any value; therefore, the statement is true because variables are meant to be placeholders for a wide range of numbers.
Explanation:In the expression m + 8, it is true that the variable m can have any value, which means that this expression does not impose any restrictions on the possible values of m. This type of statement involving a variable is common in mathematics, particularly in algebra where variables represent unknown quantities that can take on various values.
When evaluating statements for truth or false, the statement 'in m + 8, the variable m can have any value' is true. Variables, by their nature, are symbols that can represent any number, so unless specific limitations are given, we assume variables to have the full set of numbers (real numbers, integers, etc.) as potential values.
The figure is a cylinder with a sphere within it.
To the nearest whole number, what is the approximate volume of the shaded part of this figure?
Use 3.14 for Pi.
Drag the correct value to the box.
Answer:
[tex]2713cm^3[/tex]
Step-by-step explanation:
From the given figure, the radius of the cylinder is=8cm, height of cylinder is =18cm and the radius of the sphere is= 6cm.
Thus, [tex]Volume of cylinder={\pi}r^2h[/tex]
[tex]V=3.14(8)^{2}(18)[/tex]
[tex]V=3.14(64)(18)[/tex]
[tex]V=3617.28cm^3[/tex]
And [tex]volume of sphere=\frac{4}{3}{\pi}r^3[/tex]
[tex]V=\frac{4}{3}(3.14)(6)^3[/tex]
[tex]V=\frac{4}{3}(3.14)(216)[/tex]
[tex]V=904.31cm^3[/tex]
Thus, the volume of the shaded part of the figure=Volume of cylinder-volume of sphere
⇒volume of the shaded part of the figure=[tex]3617.28-904.31[/tex]
=[tex]2712.97[/tex]
≈[tex]2713cm^3[/tex]
Thus,volume of the shaded part of the figure=[tex]2713cm^3[/tex]
What are the coordinates of the hole in the graph of the function f(x) ?
f(x)=x2−9x−3
Answer:
(3,6)
Step-by-step explanation:
Believe me this is correct I just did the test
There is no hole in the graph of the function f(x) = x^2 - 9x - 3.
Explanation:To find the coordinates of the hole in the graph of the function f(x) = x^2 - 9x - 3, we need to determine the x-value at which the function is undefined. This occurs when the denominator of the function is equal to zero. In this case, the function has no denominator, so there is no hole in the graph.
Write the resultant if the 2 vectors as an ordered pair.
<5, -2> and <0,0>
A car travels 20 mph slower in a bad rain storm than in sunny weather. the car travels the same distance in 2 hrs in sunny weather as it does in 3 hrs in rainy weather. find the speed of the car in sunny weather. PLEASE SHOW YOUR WORK.
The speed of the car in sunny weather is calculated to be 60 mph, given that it travels the same distance in less time compared to its speed in a rainy weather, which is 20 mph slower.
Finding the Car's Speed in Sunny Weather:
Let's assume the speed of the car in sunny weather is s mph. Therefore, the speed of the car in a rain storm would be (s - 20) mph. Given that the car travels the same distance in both weathers, we can use the formula distance = speed * time to express the distance travelled in sunny weather and rainy weather.
In sunny weather, the car travels for 2 hours, hence the distance covered is 2s miles. In rainy weather, it travels for 3 hours, covering a distance of 3(s - 20) miles.
Since the distances are equal, we can equate them and solve for s:
2s = 3(s - 20)
2s = 3s - 60
s = 60 mph
Therefore, the speed of the car in sunny weather is 60 mph.
Help please! Not sure what this is
Mr.Johansson's truck weighs 3 tons. How many ounces does it weigh
Final answer:
To convert the 3-ton weight of Mr. Johansson's truck to ounces, we multiply 3 tons by 2,000 to get pounds and then multiply that figure by 16 to get 96,000 ounces.
Explanation:
Mr. Johansson's truck weighs 3 tons. To convert this weight to ounces, we need to know that one ton is equal to 2,000 pounds and one pound is equal to 16 ounces.
First, we convert tons to pounds:
3 tons x 2,000 pounds/ton = 6,000 pounds
Next, we convert pounds to ounces:
6,000 pounds x 16 ounces/pound = 96,000 ounces
Therefore, the weight of Mr. Johansson's truck is 96,000 ounces. This conversion showcases the application of the conversion factors between tons, pounds, and ounces, providing a precise measure of the truck's weight in a more universally comprehensible unit.
Final answer:
The truck weighs 96,000 ounces.
Explanation:
To convert tons to ounces, we can use the conversion factor that 1 ton is equal to 32,000 ounces.
So, to find how many ounces the truck weighs, we can multiply the weight of the truck in tons by the conversion factor.
Weight of the truck in ounces = Weight of the truck in tons x Conversion factor
Weight of the truck in ounces = 3 tons x 32,000 ounces/ton
Weight of the truck in ounces = 96,000 ounces.
the hour hand on a clock is 7.5 centimeters long. What distance does the tip travel in one complete rotation,to the nearest centimeter?
A news anchorman can read 7.5 lines in 0.5 minutes. How many lines can he read in 8.5 minutes? Round the answer to the nearest tenth, if necessary.
A. 15.0 lines B. 127.5 lines
C. 31.9 lines D. 2.7 lines
which function defines the sequence -6, -10, -14, -18, where f(6)=-26
Mathematics defines function as an expression that points a relationship between two variables.
Sequence is a list of numbers in certain order.
The function that defines the sequence -6,-10,-14,-18 is [tex]\rm f(x)= -4x-2[/tex]
To justify above answer, following calculations are required:Given:
[tex]\rm f(1)=-6\\f(2)=-10\\f(3)=-14\\f(4)=-18\\f(6)=-26[/tex]
Substituting x=1 in function [tex]\rm f(x)= -4x-2[/tex]
[tex]\begin{aligned}\rm f(1)&= -4(1)-2\\&=-6\end[/tex]
x=2
[tex]\begin{aligned} \rm f(2)&= -4(2)-2\\&=-10\end[/tex]
x=6
[tex]\begin{aligned}\rm f(6)&= -4(6)-2\\&=26\end[/tex]
Therefore the function [tex]\rm f(x)= -4x-2[/tex] defines the sequence.
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Work out the circumference of this circle.
Take pi to be 3.142 and give your answer to 1 decimal place
The radius is 4cm
Circumference of the circle is 25.136 cm with radius 4 cm.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The radius of circle = 4 cm
We know that;
The circumference of circle = 2πr
Where, 'r' is radius of circle.
So, We get;
The circumference of circle = 2πr
= 2 × 3.142 × 4
= 25.136 cm
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Solve the following equation for x: 6(4x+5)= 3(x+8)+3. Round to the nearest hundredth.
A car travels 120 miles in 3 hours (with a constant speed). How far will it take to travel 200 miles?
I need the right answer please
If AB represents 50% , what is the length of a line segment that is 100%
A ----------------------------------------------B. . 3in.
What is the period of the function f(x) shown in the graph?
The area of a rectangle is 1,176 square meters.The width of the rectangle is 21 meters.What is the length of the rectangle?
area/width
=length
=1176÷21
=56m
Answer:
Length = 56 meters
Step-by-step explanation:
We can find the length of the rectangle which has an area of 1,176 square meters and width of 21 meters with this formula:
[tex]\boxed{Area(A)=length(l)\times width(w)}[/tex]
Given:
[tex]A=1,176\ m^2[/tex][tex]w=21\ m[/tex]Then:
[tex]\begin{aligned}A&=l\times w\\1,176&=l\times21\\l&=1,176\div21\\l&=56\ m\end{aligned}[/tex]
The sum of five consecutive even integers is 120, what is the 5th number in the sequence
I don't understand this
What is 20 percent of 60
Amount Saved = Original Price x Discount % / 100. So,
Amount Saved = 60 x 20 / 100
Amount Saved = 1200 / 100
Amount Saved = $12 (answer)
the graph below could be the graph of which exponential function
Answer:
The correct option is C.
Step-by-step explanation:
∵ The given graph is of increasing nature.
∴The base of the exponential will be greater than 1.
∴ option A is incorrect.
Also, at x=0 the value of y=3, but in option B at x=0 ⇒y= 3^0 =1
∴ option B is also incorrect.
At x=0, y=3 for option 3 which satisfies the graph.
∴ the option C is correct.
option D is incorrect because the base of an exponential can never be negative.
An architect is designing square windows with an area of ( x 2 + 20x + 100) ft2 . The dimensions of the windows are of the form ax + b, where a and b are whole numbers.
a. Find the dimensions of each square window.
b. Find an expression for the perimeter of a window.
c. Find the perimeter of a window when x = 4.
how many times does a person blink in 1.5 min
Help with this question please
A rectangle 7 feet longer than it is wide find the dimensions of the rectangle if its area is one 198 sq ft.
Which equation represents a football player who runs 5yds/sec and starts on the 25 yard line?
Question 1 options:
y = 5x + 25
y = 5x - 25
y = 25x + 5
y = 25x - 5
Based on these equations, which one represents the greatest rate?
Question 2 options:
y = 1/2 x + 8
y = 2x + 4
y = 4x + 2
y = 7x + 5
Solution:
Question 1:
we are given that
A football player who runs 5yds/sec and starts on the 25 yard line.
So here rate is 5yds/sec
and 25 yards is the y- intercept.
Hence it can be written as
[tex]y=5x+25[/tex]
Question 2:
Based on the given equations, which one represents the greatest rate?
As we know in the standard form of equation of starlight line
[tex]y=mx+b[/tex]
m represents the rate or gradient.
As we can observe from the given options [tex]y = 7x + 5[/tex] has the greatest gradient.
Hence the correct option is [tex]y = 7x + 5[/tex]
If the ratio of boys to girls is 1:4 and there are 20 girls in your class, how many boys are there?
Please help!!!!
Question on image and question below.
Find the missing value to nearest hundredth.
cos____=7/18
A data set contains three points, and two of the residuals are -10 and -20. What is the third residual?
The residuals of any data set should get added to zero. If there are three residuals (say A, B, and C) in any data set, then it could be written as A + B + C = 0.
Given are the two residuals -10 and -20 out of three point in a particular data set.
Let's assume A = -10 and B = -20, so that we could find third value C of the given data set.
We know A + B + C = 0
(-10) + (-20) + C = 0
(-30) + C = 0
C = 30
It means that third residual must be 30.
Hence, the final answer is 30.
Answer:
30
Step-by-step explanation:
What is the solution of the system? Use either the substitution method or the elimination method. 4x + 2y = 104x + 2y = 10 x − y = 13x − y = 13
There is no solution.
(3.5, −1)
(6, −7)
(−7.5, 2)
Alfred made 21 goals in 3.5 minutes. What is Alfred’s unit rate?