The number of square feet in the area of a square is 5 more than the number of feet in the perimeter of the square. Find the length of a side.
Answer:5
Step-by-step explanation:The area of a 5x5 square is 25, and the perimeter would be 20. A 5x5 square's area is 5 more than the perimeter.
Ahmad is riding his bike. The distance he travels varies directly with the number of revolutions (turns) his wheels make. See the graph below.
Question 1) how far does he travel per revolution
Question 2) what is the slope?
Given that Ahmad is riding his bike. The distance he travels varies directly with the number of revolutions (turns) his wheels make. A) Ahmed travels 8 feet per revolution. B) the slope here is 8.
The slope is the measure of rate of change in y (dependent variable) due to change in x (independent variable).
In the given question, a graph is given.
On y axis we are given distance travelled, making it the dependent variable.
On x axis we are given the number of revolutions, making it the independent variable.
On reading from the graph, coordinate (2,16) clearly lies on the graph.
It implies, distance travelled in 2 revolutions = 16 feet.
By unitary method,
distance travelled in 1 revolution = [tex]\frac{16}{2} = 8[/tex] feet.
Since, distance travelled in 1 revolution is 8 feet, the change in distance travelled on unit change of revolution is 8, making the slope of the line equals to 8.
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Use the work shown to find the solutions of the quadratic equation. x2 – x –3/4=0 x2 – x = 3/4
Answer:
x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
x² - x - [tex]\frac{3}{4}[/tex] = 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
The solutions are x = 3 and x = -7.
To solve the quadratic equation, we first need to bring it to the standard form of ax2 + bx + c = 0. In the example given, we have the equation x2 + 4x - 21 = 0, where a = 1, b = 4, and c = -21. To find the solutions for x, we will use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).
Substituting the values of a, b, and c into the quadratic formula, we get:
x = (-(4) ± √((4)2 - 4(1)(-21))) / (2(1))
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √100) / 2
x = (-4 ± 10) / 2
Which gives us two solutions:
x = (6 / 2) = 3
x = (-14 / 2) = -7
Therefore, the solutions to the quadratic equation x2 + 4x - 21 = 0 are x = 3 and x = -7.
Three workers have to do a certain job. The first worker can finish the job in 8 hours. The second worker can finish the job in 4 hours. The third worker can also finish the job in 4 hours. How long will it take the three workers to finish the job if they work together?
PLS help
Working together three workers would take 1 hour 36 minutes to finish the job
Solution:
Given that first worker can finish the job in 8 hours
So in one hour, first worker can do [tex]\frac{1}{8}[/tex] th of the work
The second worker can finish the job in 4 hours
So in one hour, second worker can do [tex]\frac{1}{4}[/tex] th of the work
The third worker can also finish the job in 4 hours
So in one hour, third worker can do [tex]\frac{1}{4}[/tex] th of the work
The three workers working together in 1 hour can do:
[tex]\frac{1}{8} + \frac{1}{4} + \frac{1}{4} = \frac{1 + 2 + 2}{8} = \frac{5}{8}[/tex]
The three worker can thus do [tex]\frac{5}{8}[/tex] th of the work in one hour
Hence the three of them together can finish the work in [tex]\frac{8}{5}[/tex] hours
[tex]\frac{8}{5} = 1\frac{3}{5}[/tex] hours
Thus working together three workers would take 1 hour 36 minutes to finish the job
Determine the point that lies on the equation y = -5x - 3.
(4, 12)
(4, -12)
(4, 23)
(4, -23)
Answer:
(4, -23)
Step-by-step explanation:
To see if a point is on the equation, substitute its "x" and "y" coordinates into the equation. The points are written as (x, y). If the left side equals the right side, the point is on the line. (LS = RS)
Try (4, 12)
y = -5x - 3
12 = -5(4) - 3
12 = -20 - 3
12 = -23
LS ≠ RS
The point is not on the line.
Try (4, -12)
y = -5x - 3
-12 = -5(4) - 3
-12 = -20 - 3
-12 = -23
LS ≠ RS
The point is not on the line.
Try (4, 23)
y = -5x - 3
23 = -5(4) - 3
23 = -20 - 3
23 = -23
LS ≠ RS
The point is not on the line.
Try (4, -23)
y = -5x - 3
-23 = -5(4) - 3
-23 = -20 - 3
-23 = -23
LS = RS
The point (4, -23) is on the line.
Which expression is equivalent to 6(x – 4)?
6x + 4
6x-4
0 6x - 24
6x + 24
Answer:
6x-24
Step-by-step explanation:
6(x-4)=6x-24
Answer:
hi there!
The correct answer is: 6x - 24
Step-by-step explanation:
you distribute 6 into the parenthesis
you first multiply 6 by x and you get 6x
then you multiply 6 by -4 and you get -24
then you combine both to get 6x-24
Why does multiplying 37.4 times 0.01 give a product that is less than 37.4
Answer: When you multiply by 0.1 it is the same as dividing by 10. So it gives you a product that is less than 37.4.
The dot plot represents an order of varying shirt sizes. A number line going from 8 to 26. 0 dots are above 8. 1 dot is above 10. 3 dots are above 12. 3 dots are above 14. 5 dots are above 16. 4 dots are above 18. 2 dots are above 20. 1 dot is above 22. 1 dot is above 24. 0 dots are above 26. Which histogram represents the same data?
The Answer is:
The histogram on Answer C.
The histogram will reflect the frequency of shirt sizes as shown in the dot plot, with bars representing the number of shirts for each size range; no bar for size 8, bars of height 1, 3, 5, 4, 2, 1, and 1 for sizes 10 through 24 respectively.
Explanation:The question relates to the representation of data using a histogram based on the information given for a dot plot. A histogram is a type of graph that depicts the distribution of data through contiguous boxes, where the x-axis often represents the data categories (like a number line indicating shirt sizes) and the y-axis shows frequencies or relative frequencies.
To represent the same data as the described dot plot in a histogram, we need to create intervals or bins that will encompass the range of shirt sizes, and each interval will have a frequency corresponding to the number of dots in that size range from the dot plot. We could have intervals such as 8-10, 10-12, 12-14, and so on, with the height of each bar representing the frequency of shirts in each size range.
Histogram bars will correspond to dot plot points as follows: no bar for size 8, a single bar reaching up to 1 for size 10, a bar up to 3 for both sizes 12 and 14, a bar up to 5 for size 16, a bar up to 4 for size 18, bars up to 2 and 1 for sizes 20 and 22 respectively, and a final bar reaching up to 1 for size 24.
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solve sin x - (3sin x-1) = 0
Answer:
[tex]\large\boxed{x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]\sin x-(3\sin x-1)=0\\\\\sin x-3\sin x+1=0\qquad\text{subtract 1 from both sides}\\\\-2\sin x=-1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}[/tex]
[tex]\text{Equation:}\\\\\sin x=a\\\\\text{has solutions}\\\\x=\theta+2k\pi\ \vee\ x=(\pi-\theta)+2k\pi\\\\\text{Why}\ 2k\pi?\\\text{Because the sine function has a period of}\ 2\pi.[/tex]
[tex]\text{look at the table}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}[/tex]
[tex]\text{Other solution:}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\sin^{-1}\dfrac{1}{2}\\\\x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi[/tex]
For which pair of functions is (g circle f) (a) = StartAbsoluteValue a EndAbsoluteValue minus 2?
Answer:
C
Step-by-step explanation:
The pair of functions are f(a) = 5 + a² and g(a) = √(a - 5) - 2 option third is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
(gof)(a) = |a| - 2
Let f(a) = 5 + a²
g(a) = √(a - 5) - 2
(gof)(a) = g(f(a)) = √(5 + a² - 5) - 2
(gof)(a) = |a| - 2
Thus, the pair of functions are f(a) = 5 + a² and g(a) = √(a - 5) - 2 option third is correct.
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A population of 45 foxes in a wildlife preserve triples in size every 13 years. The function y equals 45 * 3to the x power, where x is the number of 13-year periods, models the population growth. How many foxes will there be after 39 years?
Answer:
1,215
Step-by-step explanation:
39/13=3
45*(3)^x
45*(3)^3
45*(27)
1,215
Final answer:
To find the number of foxes after 39 years, use the population growth function y = 45 *[tex]3^x[/tex]. Since 39 years corresponds to 3 periods of 13 years each, the equation becomes y = 45 * [tex]3^3,[/tex] resulting in 1215 foxes.
Explanation:
The student has asked how many foxes will there be after 39 years, given the population growth function y equals 45 times 3 to the x power, where x represents the number of 13-year periods. To solve this, we calculate the value of x by dividing the total time of population observation (39 years) by the duration of one population tripling period (13 years). This gives us:
x = 39 years / 13 years/period = 3 periods
We then substitute x into the equation and get:
y = 45 *[tex]3^3,[/tex] = 45 * 27 = 1215 foxes
Therefore, there will be 1215 foxes in the wildlife preserve after 39 years.
The cost of renting a bicycle is $9 for the first hour plus another $4 for each
additional hour. Which of the following represents this situation, where Cis
the total cost of renting a bicycle for h hours?
The missing choices are:
A. C = 9h + 4
B. C = 4h + 9
C. C = 4(h - 1) + 9
D. C = 13h
C = 4(h - 1) + 9 represents this situation ⇒ answer C
Step-by-step explanation:
The given is:
The cost of renting a bicycle is $9 for the first hourAnother $4 for each additional hourC is the total cost of renting a bicycle for h hoursWe need to find which of the following represents this situation
∵ The cost of renting a bicycle is $9 for the first hour
∵ Another $4 for each additional hour
∵ h represents the number of hours
- Add the cost of the first hour to the cost of the remaining hours
∵ The remaining hours = h - 1
∴ The cost of the remaining hours = 4(h - 1)
∵ C is the cost of renting the bicycle for h hour
- Add 9 to 4(h - 1) to find C
∴ C = 4(h -1) + 9
C = 4(h - 1) + 9 represents this situation
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Which of the following represent the three sides of the right triangle shown below? Select all that
apply
answer choices:
-5.55
-6
-7
-10
-11.66
-12
-16
Answer:
10, 6 and 11.66
Step-by-step explanation:
10, 6 and the hypothenous is equal to : √(10^2 + 6^2)
= √(100+36)
= √136
= 11.66
Answer:
10,6 and 11.66
Step-by-step explanation:
A right angled triangle has three sides which are the adjacent, the opposite and the hypotenuse.
Looking at the triangle in question, the longest side is the hypotenuse while the other two sides are opposite and adjacent respectively.
Before we can get the hypotenuse, we need to know the value of the other sides first.
Based on the diagram the height of the triangle is (20-10) = 10
The base of the triangle = (7-1) = 6
This are gotten be subtracting the initial point from the final point on which the triangle is standing in space.
Hypotenuse is gotten using the Pythagoras theorem expressed as;
Hypotenuse² = Adjacent² + opposite²
Hypotenuse² = 10²+6²
Hypotenuse² = 100+36
Hypotenuse² = 136
Hypotenuse = √136
Hypotenuse = 11.66
The three sides of the triangles are therefore 10, 6 and 11.66
2y+8x=1 write in slope intercept form
Answer:
y=-4x+1/2
Step-by-step explanation:
2y+8x=1
2y=1-8x
2y=-8x+1
y=-8/2x+1/2
y=-4x+1/2
what is the mean proportion between 10 and 40?
Answer:
Step-by-step explanation:
10, 20, 30, 40
Answer:25
which set of side lengths can be used to form a right triangle?
Answer:
30, 40, 50
Step-by-step explanation:
30 x 30 + 40 x 40 = 900 + 1600 = 2500
500 x 500 = 2500
sum of two legs² equals hypotenuse²
Answer:
Step-by-step explanation:
30,50,40
Given f(x)=2x^2+3x-5 for what values of x is f(x) positive
Answer:
x< -2.5 or x>1
Step-by-step explanation:
Please see attached picture for full solution.
To find the values of x for which f(x) is positive, we can set f(x) greater than zero and solve for x using factoring or the quadratic formula.
Explanation:
To determine the values of x for which f(x) is positive in the quadratic function f(x) = 2x^2 + 3x - 5, we need to find the values that make the function output positive values.
First, let's set f(x) greater than zero: f(x) > 0.Next, we can factor the quadratic function to solve for the roots: 2x^2 + 3x - 5 = 0.Using factoring or the quadratic formula, we can find the roots which are x = -1 and x = 2.5.We can see that the quadratic function is positive in the intervals (-∞, -1) and (2.5, ∞).Therefore, the values of x that make f(x) positive are x < -1 and x > 2.5.
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What is 3(23d+4d)-18d=
The answer I can’t do it I don’t understand it
Answer: -23 feet to sea level
Step-by-step explanation:
start with 0 (sea level)
he dives twenty, -20
he dives ten more, -20 - 10 = -30
he swims up twelve feet; -18
he goes down 5 more; -23 feet
Answer:
20 + 10 = 30
30 - 12 = 18
18 + 5 = 23
His elevation is 23ft below the sea level
a film canister in the shape of a cylinder has a height of 8 centimeters and a volume of the film canister. write an equation for the volume of the film canister.
Answer:
Part a) The equation for the volume of the film canister is
[tex]32\pi=\pi r^{2}(8)[/tex]
Part b) The radius of the film canister is [tex]2\ cm[/tex]
Step-by-step explanation:
The complete question is
A film canister in the shape of a cylinder has a height of 8 centimeters and a volume of 32π cubic centimeters.
a. Write an equation for the volume of the film canister.
b. What is the radius of the film canister?
Part a) Write an equation for the volume of the film canister
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
where
r is the radius of the circular base
h is the height of the cylinder
we have
[tex]V=32\pi\ cm^3[/tex]
[tex]h=8\ cm[/tex]
substitute
[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister
Part b) What is the radius of the film canister?
we have
[tex]32\pi=\pi r^{2}(8)[/tex]
[tex]32\pi=8\pi r^{2}[/tex]
Simplify
Divide by 8π both sides
[tex]4=r^{2}[/tex]
square root both sides
[tex]r=2\ cm[/tex]
A computer can sort x objects in t seconds, as modeled by the function
below:
t=0.007x2 + 0.003x
How many objects are required to keep the computer busy for exactly 9
seconds?
Round to the nearest whole object.
Answer:
36 objects
Step-by-step explanation:
You want the value of x when t=9, so you're solving ...
9 = 0.007x^2 +0.003x
9 = 0.007(x^2 + 3/7x)
From here, we observe that an approximation is probably sufficient.
9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2
x ≈ 3/√.007 ≈ 35.9 ≈ 36
We can check:
.007(36)(36 3/7) = 9.18
.007(35)(35 3/7) = 8.68
To keep the computer busy for 9 seconds, it needs to sort 36 objects.
Sue drives 12 kilometers and passes 24 street lights set along the road. Find the number of street lights she passed in 1 kilometer.
Answer:
2
Step-by-step explanation:
You have to find unit rate (I feel like this is wrong, sorry in advance!)
Answer:
she passes 2 per 1 kilometer
Step-by-step explanation:
24 / 2 = 12
12 x 2 = 24
24 / 12 = 2
-13g+12g+9=15 solve for g
PLEASE HELP ASAP! WORTH 8 POINTS
"Four-fifths of the pieces of fruit in Maria's basket are apples. Three-fourths of the apples are McIntosh apples.
This model represents the fraction of the fruit in Maria's basket that are McIntosh apples.
What fraction of the fruit in Maria's basket are McIntosh apples?"
Answer:
3/5
Step-by-step explanation:
4/5 * 3/4 = 12 / 20 = 3 / 5
The second side of a triangle is 7 inches more than the first side. The third side is 4 inches less than 3 times the first. The perimeter is 28 inches. Find the length of the three sides of the triangle.
Answer:
First side; 5 in
second side: 12 in
third side: 11 in
Step-by-step explanation:
A: first side B: second side C: third side
b = a + 7
c = 3a -4
a + b + c = 28
a + (a + 7) + (3a -4) =28
5a + 3 = 28
5a = 28 -3 = 25
a = 5
b = 12
c = 11
The length of the sides of a triangle is 5, 12, and 11.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
Let's say the first second and third side of the triangle is a, b and c respectively.
Now,
The second side of a triangle is 7 inches more than the first side.
b = a + 7
The third side is 4 inches less than 3 times the first.
c = 3a - 4
Now,
Perimeter = 28
a + b + c = 28
By substituting,
a + a + 7 + 3a - 4 = 28
5a + 3 = 28
a = 5
b = 5 + 7 = 12
c = 3(5) - 4 =11
Hence "The length of the sides of a triangle is 5, 12, and 11".
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A cylinder has a base diameter of 12m and a height of 10m. What is its volume in cubic m, to the nearest tenths place?
The volume is approximately 1130.5 m³.
A cylinder's volume can be calculated using the formula
V = π r² h
Given a base diameter of 12m (radius = 6m) and a height of 10m,
we substitute these values into the formula and get the volume:
V = 3.142 × (6m)² × 10m
V = 1130.52 m³
Pls help! three arithmetic sequences are given below.
Sequence A: 5, 7, 9, 11,...
Sequence B: 34, 43, 52, 61
Sequence C: -9, -4, 1, 6..
Which of the following lists the sequences in order from least common difference to greatest common difference?
The common difference is basically the number at which the pattern increases.
A's common difference: 2
B's common difference: 9
C's common difference: 5
answer: A, C, B
Is angle ABC congruent to angle DCE
Answer:
I do not think I can answer this without any pictures.
Step-by-step explanation:
Sorry, but could you attach a link or maybe sketch it out?
which expression shows a way to find 35% of 10
Answer:
10 X 0.35
OR
10 X 35%
Final answer:
To find 35% of 10, convert the percentage to a decimal (0.35) and multiply by 10, which equals 3.5.
Explanation:
The expression that shows a way to find 35% of 10 is 0.35 *10. To calculate this, you convert the percentage to a decimal by dividing by 100 and then multiplying it by the number you want to find the percentage of. So, to find 35% of 10, you calculate 0.35 *10 which equals 3.5.
To find 35% of 10, you can use the following expression:
(35/100) x 10
This can be simplified to 0.35 x 10 = 3.5. Therefore, 35% of 10 is 3.5.
What is the answer with the remainder
Answer:
0.0007
Step-by-step explanation: