The answer is:
The second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.
Why?Since we are given two forces acting at distance, torque will be created. We are given two forces and one distance, so, to calculate the other distance required to balance the system (solve this fulcrum problem), we need to write the following equation:
[tex]Torque_{1}=Torque_{2}[/tex]
Where,
[tex]Torque=F*Distance[/tex]
We are given,
[tex]Force_{1}=Weight_{1}=150lb\\Force_{2}=Weight_{2}=30lb\\distance_{1}=15ft\\[/tex]
So, substituting and calculating, we have:
[tex]Torque_{1}=Torque_{2}[/tex]
[tex]Weight_{1}*distance_{1}=Weight_{2}*distance_{2}[/tex]
[tex]150lb*15ft=300lb*distance_{2}[/tex]
[tex]distance_{2}=\frac{150lb*15ft}{300lb}=7.5ft[/tex]
Hence, the second distance ([tex]distance_{2}[/tex]) is equal to 7.5 feet.
It's a logical solution since the second force is twice the first force and it means that the second distance must be equal to half the first distance in order to maintain the equilibrium condition.
Have a nice day!
4/5-3/10???? Help plzzz
Answer:0.5
Step-by-step explanation:4 divided by 5=0.8, 3 divided by 10=0.3
0.8-0.3=0.5
Answer:
1/2
Step-by-step explanation:
First you can make common denominators which will be
8/10-3/10 which equals 5/10
If you simplify 5/10 you will get 1/2
A sphere has a height of 26. Find the surface area, volume and density (D=m/v , where m is 72)
Answer:
Surface Area: 2123.72
Volume: 9202.77
Density: 0.0078
Step-by-step explanation:
For a sphere, the height is the diameter.
Also we know the radius is half of the diameter.
Since height is 26, diameter is 26 as well. Thus, radius is half of 26, which is 13.
Formulas:
Surface area of sphere = 4πr^2
Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex]
Density = mass/volume
Firstly, the surface area:
[tex]4\pi r^2\\=4\pi (13)^2\\=2123.72[/tex]
Next, the volume:
[tex]\frac{4}{3}\pi r^3\\=\frac{4}{3}\pi (13)^3\\\\=9202.77[/tex]
Lastly, density:
[tex]\frac{Mass}{Volume}\\=\frac{72}{9202.77}\\=0.0078[/tex]
*Note: all answers are given as is since no units were given
How much did hazel spend on the felt
Answer:
$47.52
Step-by-step explanation:
First find the area in square inches. - 6*11*8=528
Then multiply the cost per square inch by the area - 528*9=1452
Convert the number into dollars - $14.52
Answer:
C
Step-by-step explanation:
Calculate the SA.
[tex]SA = 2(6*11)+2(11*8)+2(6*8) \\ \\ SA=2(66)+2(88)+2(48) \\ \\ SA=132+176+96 \\ \\ SA=404[/tex]
Now since we know it costs $0.09 per square inch, we can multiply 0.09 by the SA.
[tex]404*0.09=36.36[/tex]
It costs $36.36 in all.
Graph 4x2+4y2=64. What are the domain and range?
ANSWER
EXPLANATION
The given equation is
[tex]4 {x}^{2} + 4 {y}^{2} = 64[/tex]
We divide through by 4 to obtain;
[tex]{x}^{2} + {y}^{2} = 16[/tex]
This can again be written as:
[tex]{x}^{2} + {y}^{2} = {4}^{2} [/tex]
This is the equation of a circle centered at the origin with radius 4 units.
The graph is shown in the attachment.
Answer:
Domain: [-4,4]
Range : [-4,4]
Step-by-step explanation:
Given equation is [tex]4x^2+4y^2=64[/tex].
Now we need to graph and find about what are domain and range of the given problem.
[tex]4x^2+4y^2=64[/tex]
divide both sides by 4
[tex]x^2+y^2=16[/tex]
[tex]x^2+y^2=4^2[/tex]
Which looks similar to the formula of circle
[tex]x^2+y^2=r^2[/tex]
that means it is a circle with radius 4. whose centre is at the origin.
From graph we can easily see that
Domain: [-4,4]
Range : [-4,4]
Which of the two solids below are similar ?
A. I and II
B. I and II
C. II and II
D. I, II and I
E. None of the solids are similar.
Answer: I and II.
Step-by-step explanation:
By definition, two solids are similar if their corresponding sides are in the same ratio.
Knowing this, let's find which solids are similar:
Corresponding sides ratio of solids I and II:
[tex]\frac{3}{2}=\frac{2}{\frac{4}{3}}=\frac{5}{\frac{10}{3}}[/tex]
[tex]\frac{3}{2}=\frac{3}{2}=\frac{3}{2}[/tex]
Corresponding sides ratio of solids I and III:
[tex]\frac{3}{\frac{9}{2}}=\frac{2}{3}=\frac{5}{8}[/tex]
[tex]\frac{2}{3}=\frac{2}{3}=\frac{5}{8}[/tex]
Corresponding sides ratio of solids II and III:
[tex]\frac{2}{\frac{9}{2}}=\frac{\frac{4}{3}}{3}}=\frac{\frac{10}{3}}{8}}[/tex]
[tex]\frac{4}{9}=\frac{4}{9}=\frac{5}{12}[/tex]
You can observe that the solids I and II are similar.
Find the value of x. Round to the nearest tenth.
Please help me!!
Answer:
x ≈ 4.4 in
Step-by-step explanation:
The segment from the centre to the chord is a perpendicular bisector.
The third side of the right triangle = 7.4 ÷ 2 = 3.7
Consider the right triangle with legs 3.7 and 2.4 and hypotenuse x
Using Pythagoras' identity
x² = 2.4² + 3.7² = 5.76 + 13.69 = 19.45
Take the square root of both sides
x = [tex]\sqrt{19.45}[/tex] ≈ 4.4
What is the value of y?
Enter your answer in the box.
Answer:
Y = 64°
Step-by-step explanation:
The internal angles of a triangle sum to 180°
So by subtracting the known angles from the angle sum you can find Y
Y = 180° - 37° - 79° = 64°
Answer:
64
Step-by-step explanation:
Add up the first two angles, 79+37=116
Subtract this from 180, 180-116=64
Theres your answer
Holly had $5,000 in her bank account. She withdrew $800 to buy a new bike. What is the percent decrease in the balance of her account? The percent decrease is 1.6%. The percent decrease is 16%. The percent decrease is 84%. The percent decrease is 120%.
16% is the most accurate answer
16% is the answer to this question
Classify the triangle by its sides and by its angles (picture)
Answer:
It is A for sure because all of the angles are acute so yes A
The correct answer is a
Classifying quadrilaterals
Answer:
A quadrilateral is a polygon with four sides.
Practicly anything with 4 sides like square, Rectangle ,and rhombas
Im sorry if i didn't answer your question but i did not get what you were saying but here is an image that can maybe help you
The quadrilateral has includes 7 types that are parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid.
Quadrilaterals:The quadrilateral is a four-sided polygon having four angles.
Types of quadrilaterals:
A parallelogram has parallel pairs at opposite ends.The rectangle is a parallelogram with 4 right angles. Contrary to popular opinion, which isn't true for all quadrilaterals and parallelograms, they are rectangles.A parallelogram with 4 congruent sides is known as a rhombus. It possesses all of the qualities of a parallelogram, including diagonal intersections at right angles.A square is a rhombus that also happens to be a rectangle. The parallelogram has 4 (congruent sides and right angles).A trapezoid is a quadrilateral with one parallel pair of sides.An isosceles trapezoid is a trapezoid with congruent non-parallel sides.A four-sided polygon with no congruent sides is known as a scalene quadrilateral.Find out more information about the Classify quadrilaterals here:
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Consider the diagram. The congruence theorem that can be used to prove △LON ≅ △LMN is SSS. ASA. SAS. HL.
Answer:
The answer is SSS
Step-by-step explanation:
Answer:
SSS
Step-by-step explanation:
What is the value of 4,029 x 26 ?
4029*26= 104754
Answer:104754
My answer is right.
Answer:
100,400,754
Step-by-step explanation:
Two binomials that are factors of x^2+8x+12
Answer:
(x+2) (x+6)
Step-by-step explanation:
x^2+8x+12
What 2 numbers multiply together to give you 12 and add together to give you 8
2*6 = 12
2+6 = 8
(x+2) (x+6)
Answer: (x+2) (x+6)
Step-by-step explanation: a p e x
use the substitution method to solve the system of equations. y=-8x and 4x-y=3
Answer:
x = 1/4 and y = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=-8x&(1)\\4x-y=3&(2)\end{array}\right\qquad\text{put (1) to (2):}\\\\4x-(-8x)=3\\4x+8x=3\\12x=3\qquad\text{divide both sides by 12}\\x=\dfrac{3}{12}\to x=\dfrac{1}{4}\\\\\text{put the value of x to (1):}\\\\y=-8\left(\dfrac{1}{4}\right)=-2[/tex]
Answer:
x = 1/4 and y = -2
The answer I need to see if it’s correct
Answer:
I believe you, by the looking of it, I would do the same
Step-by-step explanation:
9. Jonathan can rent an unfurnished apartment for
$600 per month or a furnished apartment for $190
per week. He will need to pay a one month deposit,
plus a $350 security deposit for the unfurnished
apartment. He will need to purchase furniture, which
he has found for $850. Which is the better deal if
Jonathan plans to stay 1 year?
A. unfurnished apartment
B. furnished apartment
The cost of the unfurnished and furnished apartments for 1 year would be $8,650 and $9,880 respectively. Therefore, the unfurnished apartment is the better deal for Jonathan.
Explanation:The cost for the unfurnished apartment for one year would be $600 (monthly rent) * 12 (months) + $600 (one month deposit) + $350 (security deposit) + $850 (furniture cost) = $8,650.
The cost for the furnished apartment for one year would be $190 (rent per week) * 52 (weeks in a year) = $9,880.
Therefore, the unfurnished apartment offers a better deal for Jonathan if he plans to stay for 1 year.
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A rule of thumb refers to______
A. Rules everyone follows
B. A set process people follow
C. A general rule most people follow
D. A way to measure growth
Answer: C. A general rule most people follow
Step-by-step explanation: A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation.
The term 'rule of thumb' refers to a general rule or principle that people often follow, based on practical experience and wisdom. It isn't universally true for all situations but serves as a useful guideline.
Explanation:A rule of thumb generally refers to an option C, which is a general rule that people tend to follow, but it isn't necessarily universally true or applicable to every situation. It's a guideline or heuristic that helps simplify or solve problems, based on practical experience rather than theory.
For example, a common rule of thumb in cooking may be that 'one cup of uncooked rice serves two people'. However, this may vary depending on the individuals' appetites, age, and more.
So, from options given, a rule of thumb most closely aligns with 'C: A general rule most people follow'.
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Simplify the following expression.
2x^2-9-17x^2+10+7x
Answer:
- 15x² + 7x + 1
Step-by-step explanation:
Given
2x² - 9 - 17x² + 10 + 7x ← collect like terms
= (2x² - 17x² ) + 7x + 1
= - 15x² + 7x + 1
Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for h(f(x)).
Answer:
h(f(x)) = 2x - 11
Step-by-step explanation:
h(f(x)) is a "composite function." We use the function f(x) as the input to the function h(x):
h(x) = 2x + 3, or 2( x ) + 3; replacing x with f(x), or x - 7, we get:
h(f(x)) = 2(x - 7) + 3, or
h(f(x)) = 2x - 14 + 3, or
h(f(x)) = 2x - 11
Answer: h(f(x)) = 2x - 11
Step-by-step explanation:
A, B, C, OR IS IT D pls answer
What is your question
What is the question
PLEASE HELP! WILL MARK BRAINLIEST!! :D
Given the explicit formula for a geometric sequence, find the first 5 terms and the 8th term. (I already have the answers for the 8th term, I just need help finding the first 5 terms)
aN = 3^8-1 = 2,187
aN = 2 * (1/4)^8-1 = 0.000122
aN = -2.5 * 4^8-1 = -40,960
aN = -4 * 3^8-1 = -8,748
Hope this helps
Given a term in a geometric sequence and the common ratio find the first five terms, the explicit formula, and the recursive formula. Given two terms in a geometric sequence find the 8th term and the recursive formula. Determine if the sequence is geometric. If it is, find the common ratio.
A cell phone plan costs $23.70 per month for 700 minutes of talk time. It costs an additional $0.06 per minute for each minute over 700 minutes. To get e-mail access it costs 20% of the price for 700 minutes of talk time. Your bill wich includes e-mail is the same each month for 6 months. The total cost for all 6 months is $195.12. Write and solve an equation to find the minutes of talk time you use each month.
Your equation is...
195.12=6(0.06m+23.70+0.20(23.70))
You use_____ minutes talk time each month
Final answer:
The equation can then be solved to find the value of 'm', representing the minutes of talk time. In this case, the answer is 68 minutes of talk time each month.
Explanation:
To find the minutes of talk time you use each month, we can set up an equation based on the given information. Let's assume that the number of minutes of talk time you use each month is represented by 'm'.
The total cost for all 6 months is $195.12, which is equal to the sum of the monthly costs. Each month, the cost of the cell phone plan is $23.70 for 700 minutes of talk time, plus an additional $0.06 per minute for each minute over 700 minutes. Additionally, to get email access, it costs 20% of the price for 700 minutes of talk time.
Based on this information, the equation is: 195.12 = 6(0.06m + 23.70 + 0.20(23.70))
To solve the equation, we can simplify it: 195.12 = 6(0.06m + 23.70 + 4.74)
195.12 = 6(0.06m + 28.44)
Divide both sides of the equation by 6, we get: 32.52 = 0.06m + 28.44
Subtract 28.44 from both sides of the equation, we get: 32.52 - 28.44 = 0.06m
4.08 = 0.06m
Divide both sides of the equation by 0.06, we get: m = 68
Therefore, you use 68 minutes of talk time each month.
Final answer:
After setting up the equation based on the total cost for 6 months, we calculate that the user talks for a total of 768 minutes each month. This includes the 700 minutes in the plan and an additional 68 minutes of talk time.
Explanation:
To solve for the number of minutes of talk time used each month, we first set up an equation based on the information given. The total cost for 6 months is $195.12 which includes the monthly plan cost, the additional cost per minute after 700 minutes, and the email cost which is 20% of the 700 minutes talk time plan.
The equation, therefore, is 195.12 = 6(0.06m + 23.70 + 0.20(23.70)), where m is the number of minutes used over 700. Let's solve the equation step-by-step:
Start with the original equation: 195.12 = 6(0.06m + 23.70 + 0.20 × 23.70).Calculate 20% of 23.70 which is 0.20 × 23.70 = 4.74.Add the monthly plan cost and the e-mail access cost: 23.70 + 4.74 = 28.44.Substitute the sum into the equation: 195.12 = 6(0.06m + 28.44).Distribute the 6: 195.12 = 0.36m + 170.64.Subtract 170.64 from both sides: 195.12 - 170.64 = 0.36m, which simplifies to 24.48 = 0.36m.Divide by 0.36 to find m: m = 24.48 / 0.36 = 68.Therefore, you use 68 minutes over the 700 included minutes, which means you use a total of 700 + 68 = 768 minutes of talk time each month.
An equation that sets two fractions equal to each other is called a
Answer:
proportion
Step-by-step explanation:
An equation that sets two fractions equal to each other is called a proportion. A proportion is a name we give to a statement that two ratios are equal. When two ratios are equal, then the cross products of the ratios are equal.
Which graph represents the linear function y = x 3/4– 4?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=\frac{3}{4}x-4[/tex]
This is a linear equation (the graph is a line)
To identify the graph find out the intercepts
Find out the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y=\frac{3}{4}(0)-4=-4[/tex]
The y-intercept is the point (0,-4)
Find out the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0=\frac{3}{4}x-4[/tex]
[tex]\frac{3}{4}x=4[/tex]
[tex]x=16/3=5.33[/tex]
The x-intercept is the point (5.33,0)
therefore
The graph in the attached figure
The graph of the linear function y = x 3/4–4 can be generated by understanding that '3/4' is the slope and '-4' is the y-intercept. This implies for every horizontal increase of 4 units, there's a vertical rise of 3 units. The function intersects the y-axis at -4.
Explanation:The linear function in question, y = x 3/4–4, can be graphed by understanding how the terms within the equation shape the line. The term '3/4' in the equation is the slope of the line and '–4' is the y-intercept. The slope or the rate of change is less than 1 which means for every increasing step in 'x', 'y' increases by less of a step (3/4 of a step, in this case). The linear function intersects the y-axis at -4. Therefore, when you plot x and y values, keep in mind that for every rise of 3 on the vertical axis, there's an increase of 4 on the horizontal axis. Start by marking the y-intercept (0, -4) and use the slope (3/4) to find the next points. From the y-intercept, move 3 units up and 4 units to the right. Repeat this pattern to generate other points that lie on the line.
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write an equation and find slope for the points (0,8) (6,8)
Answer:
equation: (8-8) ÷ (0-6)
answer: 0
Step-by-step explanation:
I need the answer to question 8. 50 points up for grabs
Let iron = x
There is 1.5 times the amount of zinc that there is iron, so you get zinc = 1.5x
There is 3 times as much copper as there is zinc, so 1.5 x 3 = 4.5, so copper equals 4.5x
Now all three need to equal the total weight of 210:
X + 1.5x + 4.5x = 210
Simplify:
7x = 210
Divide both sides by 7:
x = 210 /7
x = 30
Now you have a value for x, you can solve for the amount of each material.
Iron = x = 30 g
Zinc = 1.5x = 1.5(30) = 45 g
Copper = 4.5x = 4.5(30) = 135g
There is 45 g of zinc.
Let iron =x
There is 1.5 times the amount of zinc then there is iron, so zinc = 1.5x
There is 3 times as much copper then there is zinc, so 1.5*3=4.5, so copper equals 4.5x
What is the importance of discrete mathematics in Information Technology?
discr etemathematics deals with objects that can assume only distinct, separate values like integers. information technology needs separate values so as to be accepted
Final answer:
Discrete mathematics is crucial in Information Technology for creating efficient algorithms in cryptography, network communication, and software development, as well as for driving insights from data analysis.
Explanation:
The importance of discrete mathematics in Information Technology cannot be understated, particularly due to its fundamental role in various IT applications. Discrete mathematics provides the theoretical underpinning for computer science and information technology, where discontinuous structures are observed, such as computer algorithms, software development, and data structures. It allows IT professionals to design efficient algorithms for data encryption, network communication, and software development.In cryptography, discrete mathematics helps in securing online transactions by creating algorithms that are easy to compute in one direction (like multiplying large numbers) but challenging to reverse (like factoring into primes). Moreover, discrete mathematics is central to understanding and working with concepts such as recursion, combinatorics, and graph theory which are essential in programming and data analysis.Its principles also facilitate the quantification of information as noted by C. Shannon, aiding in the differentiation between mere data and valuable information that can drive insights and business decisions. Discrete mathematics also provides the tools for approximating continuous mathematical operations, which is vital in scientific computing and the practical implementation of IT solutions.HELPPP PLEASE!!!!!!!
Answer:
the first answer is 135
Step-by-step explanation:
What is the measure of angle B?
d. 128°
have a nice day!!
PLEASE HELP
WILL MARK MOST-BRAINLY-EST
Evaluate 9 C 4
3,024
24
1,008
126
Answer:
126
Step-by-step explanation:
Using the definition of n [tex]C_{r}[/tex] = n! / r ! (n - r) !
where n ! = n(n - 1)(n - 2) ........ × 3 × 2 × 1
9 [tex]C_{4}[/tex]
= 9 ! / 4 ! 5 ! ← cancel 5 ! on numerator/ denominator
= [tex]\frac{9(8)(7)(6)}{4(3)(2)(1)}[/tex]
= [tex]\frac{3024}{24}[/tex]
= 126
Answer:
126 mayihavebrainly
Step-by-step explanation: