If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.
How can the acceleration be calculated?We were told that the constant force acts upon an object, and the acceleration of the object varies inversely with its mass, which can be interpreted as :
A = k/M
where M is the mass of the object.
A = acceleration
the k= proportionality constant
then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2
then substitute into the equation as:
25 =k*3
k= 25/3
then we were told that when mass is 5 kg, then acceleration will be ?
A= (25/3 )/5 = 1.667m/s^2.
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A number x is such that dividing the number by 5 and then adding 2 gives the same outcome as adding 22 and then dividing by 10. Write down and solve an equation satisfied by x. Enter your answer in the box below as a number, rounded to one decimal place if necessary.
Answer:
x = 2
Step-by-step explanation:
You want x such that dividing by 5 and then adding 2 gives the same outcome as adding 22 and then dividing by 10.
Setup(x/5) +2 . . . . the value after dividing by 5 and adding 2
(x +22)/10 . . . . the value after adding 22, then dividing by 10
These two outcomes are the same:
x/5 +2 = (x +22)/10
SolutionMultiplying the equation by 10 gives ...
2x +20 = x +22
x = 2 . . . . . . . . . . . . subtract x+20
The number is x = 2.
__
Additional comment
The outcome in each case is 2.4.
hellp foo You are considering different investment strategies to save for your retirement.
Option 1: You invest $25/ month at a rate of 3.25% APR compounded monthly for 30 years.
Option 2: You invest $75/ quarter at a rate of 4.00% APR compounded monthly for 30 years.
Option 3: You invest $1,000 at a rate of 6.25% APR compounded monthly for 30 years.
1) Which option was the least amount invested and what was the investment plan?
2) Which option yielded the highest amount at the end of the 30 years and what was the basis of the plan?
3) What is the difference in the principal invested for the highest and lowest final balances? What is the difference in the interest earned?
4) Is it better to invest more money in the beginning or the end of the 30 years?
1) Option 3 had the least amount invested. The investment plan was to invest a certain amount in the beginning and let it grow at an interest of 6.25% APR compounded monthly for 30 years.
2) Option 2 yielded the highest amount at the end of 30 years. The plan was to invest $75/quarterly i.e, $25/monthly at an interest of 4.00% APR compounded monthly for 30 years.
3) Difference in principle is $8000 and the difference is interest is $2976.83
4) It is better to invest more at the end of 30 years.
Define interest.
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The loan's interest rate is denoted by this proportion.
Solution Explained:
First, let's calculate the amount after adding the compound interest using
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex], where P is principal, r = interest rate, n = number of times interest is compounded monthly, and t = time
After calculation (For Op 1 and 2, the principal is $9000 and 3 is $1000)
Option 1 has $15275.50
Option 2 has $17467
Option 3 has $6489.17
Interest for Option 1 = $6275.50
Interest for Option 2 = $8466
Interest for Option 3 = $5489.17
After this solving the questions will be easy to understand.
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Answer:
contributions:
1 $25/ month at a rate of 3.25% APR
2 $75/ quarter at a rate of 4.00%
3 $1,000 at a rate of 6.25% APR
total interest rate:
1 $6275.50
2 $8466
3 $5489.17
final balances:
1 $15275.50
2 $17467
3 $6489.17
questions 1-4
1: Option 3 had the least amount invested
2: option 2
3: Difference is $8000 – and interest difference in $2976.83
4: it’s better to invest more at the end of 30 years
Step-by-step explanation:
i did the assignment
How do I solve this question
Answer: [tex]6/(x-7) +( -5)/(x-5)[/tex]
Step-by-step explanation:
Let
[tex](x+5)/(x-7)(x-5) = A/(x-7) +B/(x-5)[/tex]
⇒[tex](x+5)/(x-7)(x-5)=( A(x-5) +B(x-7))/(x-7)(x-5)[/tex]
Comparing both the sides
[tex](x+5)= A(x-5)+B(x-7)\\x+5=Ax-5A+Bx-7B\\x+5= (A+B)x + (-5A-7B)\\[/tex]
Comparing both sides of the equation we get,
[tex]A+B= 1[/tex] ....eq(1)
[tex]-5A-5B=5[/tex] ..... eq(2)
solving eq(1) and eq(2),
we get B=-5 and A=6.
Hence the solution is [tex]6/(x-7) +( -5)/(x-5)[/tex]
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How many liters of paint are in a 5 gallon bucket round your answer to the nearest liter
Answer:
19 liters
Step-by-step explanation:
use f(x)=|x|
f(x) is shifted down 4 and right 3 to create h(x)
which answer shows the correct function for h(x)
Answer:
h(x)= |x-3|-4
Step-by-step explanation:
If f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4
The function is given
f(x) = |x|
Translation of the shape mean the displacement of the shape from one place to another place. Some usually used displacements are shifted to right / left and shifted to up / down etc.
First f(x) is shifted down 4
Then the function will become
f(x) = |x| - 4
Then the function shifted right 3
Then the function will be
h(x) = |x - 3| - 4
Hence, if f(x) = |x| is shifted down 4 and right 3 to create h(x), then h(x) = |x - 3| - 4
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Which expression is equivalent to 3x – 5?
Answer:
2x – 4 – 1 + x
Step-by-step explanation:
Answer:
Step-by-step explanation: -15
8x^(3)-27=0
find the roots of x
Answer:
[tex] \sf Root \: of \: x \: are \: \dfrac{3}{2} \: and \: \dfrac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]
Step-by-step explanation:
[tex] \rm \implies 8 {x}^{3} - 27 = 0 \\ \\ \rm \implies (2 \times 2 \times 2) {x}^{3} - (3 \times 3 \times 3) = 0 \\ \\ \rm \implies {(2x)}^{3} - {3}^{3} = 0 \\ \\ \boxed{ \rm {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )} \\ \\ \rm \implies (2x - 3)( {(2x)}^{2} + (2x)(3) + {3}^{2} ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^{2} + 6x + 9 = 0 \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{36 - 144} }{8} \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]
Katelyn’s older brother borrowed money for school. He took out a loan that charges 6% simple interest. He will end up paying $720 in interest after 6 years. How much did Katelyn’s brother borrow for school?
The amount of money that Katelyn’s brother borrowed for school would be = $ 2,000.
What is interest?Interest in the amount of money that an individual pays in extra with a borrowed amount of money either from an individual or from the bank.
The formula for simple interest= Principal ×Time × Rate/100
Rate of payment= 6%
Time = 6 years
Simple interest = $720
Principal= X
From the formula above, make principal the subject of formula;
Principal = SI × 100/ T× R
= 720 × 100/ 6×6
= 72000/36
=$ 2,000
Therefore, the amount of money that Katelyn’s brother borrowed for school is $2,000.
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Two times the sum of a number and 3 is 8.
Use the variable c for the unknown number.
My answer is : 2(c+3)=8
The " is" throwing my brain off, thanks so much
Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.
Let the value of the unknown number or variable be c.
Given,
"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.
If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.
The equation will be:
2(c + 3) = 8
=> 2c + 6 = 8
=> 2c = 8- 6
=> 2c = 2
=> c = 2/2
=> c = 1.
Hence, the value of the unknown number c will be 1.
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I've been stuck on this problem for awile can anyone help?
7z-4=12+3z
Answer:
z = 4
Step-by-step explanation:
7z - 4 = 12 + 3z
1) We want to first move the z values to one side of the equation. This means we would subtract 3z from both sides to move it to the left side. This would give us 4z - 4 = 12.
2) We then want to isolate the z value. This means we want to move the -4 to the right side. We would add 4 to both sides and get 4z = 16.
3) We can then divide both sides by 4 and get the value for z.
This gives us z = 4.
Use the quadratic formula to solve for the "solutions", or "zeros" of the equation. Did
you get 2 real answers, I real answer, or 2 imaginary answers?
Show your work F(x) =3x^2 - 40x + 180
We get 2 complex answers
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.
Given that F(x) = 3x2 - 40x + 180
Set F(x) to 0, and you get ax2 + bx + c = 3x2 -40x + 180.
[-b +/- (b2 -4ac)(1/2)] is the quadratic formula. / 2a.
The stuff under the square root / radical (b2 - 4ac) is the KEY to your answer, and it determines whether you have two real, one real, or two imaginary answers. The discriminant is the term (b2 - 4ac).
Obviously, if (b2 - 4ac) > 0, you have two real answers, because the square root of a positive number is also a (positive) real number. And -b multiplied by a real number (and divided by 2a) yields two (real) answers.
If (b2 - 4ac) = 0, you have one correct answer because the square root of 0 is zero. And -b multiplied by a 0 real number (and divided by 2a) yields 1 (real) answer.
(b2 - 4ac) 0 yields two fictitious answers, because the square root of a negative number is a fictitious number. And -b multiplied by an imaginary number (and divided by 2a) yields two (complex) answers.
In this case, (b2 - 4ac) = ((-40)2 - 4(3)(180)) = 1600 - 2160 0 As a result of the discriminant is negative, the quadratic formula yields two complex answers.
Therefore we get two complex answers
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Answer:
[tex]x=\dfrac{20 +2\sqrt{35}\:i}{3}, \quad x=\dfrac{20 -2\sqrt{35}\:i}{3}[/tex]
2 imaginary answers.
Step-by-step explanation:
Given quadratic function:
[tex]f(x) =3x^2 - 40x + 180[/tex]
The zeros of a quadratic function can be found when f(x) = 0:
[tex]\implies 3x^2 - 40x + 180=0[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore:
a = 3b = -40c = 180Substitute the values of a, b and c into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-40) \pm \sqrt{(-40)^2-4(3)(180)}}{2(3)}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{1600-2160}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{-560}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{16 \cdot 35 \cdot -1}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{16}\sqrt{35}\sqrt{-1}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\sqrt{-1}}{6}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex]:
[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\:i}{6}[/tex]
[tex]\implies x=\dfrac{20 \pm 2\sqrt{35}\:i}{3}[/tex]
Therefore, the solution is 2 imaginary answers.
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].
Lets sets A and B be defined as follows:
A= {25, 26, 27, 28, 29}
B is the set of integers greater than or equal to -6 and less than or equal to 1.
(picture attached below)
a) The value sets of n(A) = 5, n(B) = 8
b) 33 ∈ A is false, -4 ∈ B is true, 25 ∈ A is true, 5 ∉ B is true.
What is set?Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.
A = { 25, 26, 27, 28, 29}
B ( is greater or equal to -6 and equal to 1) = { -6, -5, -4, -3, -2, -1, 0, 1}
n(A) = number of elements in A which is 5 and n(B) = 8
33 ∈ A The symbol ∈ means element of. so 33 is not an element of A.
-4 is an element of B so it is true, -4 ∈ B is true
25 ∈ A is true because 25 is an element of A
5 ∉ B is true because 5 is not an element of B
In conclusion, n(A) = 5, n(B) = 8
-4 is an element of B so it is true, -4 ∈ B is true
25 ∈ A is true because 25 is an element of A
5 ∉ B is true because 5 is not an element of B
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Expand the brackets in each expression and then
combine like terms where possible.
a -7(7a + 4b) + 10a - 10b
4x-10 y
b 6(2x+6y) -
The expanded form of 7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.
What is expanded form?
The expanding form can be used to indicate the value of each digit in a number in arithmetic. Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.
It is given that,
a) 7(7a + 4b) + 10a - 10b
b) 6(2x+6y) -
a)
[tex]=7(7a + 4b) + 10a - 10b \\\\ =49a+28b+10a-10b \\\\ =49a+10a+28b-10b \\\\ =59a+28b-10b \\\\ =59a+18b[/tex]
b)
= 6(2x+6y) -
=12x+12y
Thus, the expanded form of 7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.
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A man has 25 coins in His pocket all of which are dimes and quarters. If the total value of his change is 475 cents, how many dimes and how many quarters does he have
Answer:
10 dimes15 quartersStep-by-step explanation:
You want to know the numbers of dimes and quarters that make 475 cents using 25 coins.
SetupLet q represent the number of quarters. Then 25-q is the number of dimes, and the total value of the coins is ...
25q +10(25-q) = 475
SolutionSimplifying the above equation gives ...
15q +250 = 475
15q = 225 . . . . . . . subtract 250
q = 15 . . . . . . . . . divide by 15; number of quarters
25 -q = 10 . . . . number of dimes
The man has 10 dimes and 15 quarters.
What is tan 67 degrees
Solve 2x-7 = 3x-2(x+8) for x
Answer:
x = -11
Step-by-step explanation:
2x - 7 = 3x - 2x - 18
2x - 7 = x - 18
collect like terms
2x - x = 7 - 18
x = -11
suppose v varies directly as g,and v=36 when x=4.Find v when g=11
Answer:
v = 99
Step-by-step explanation:
given v varies directly as g then the equation relating them is
v = kg ← k is the constant of variation
to find k use the condition v = 36 when g = 4 , then
36 = 4k ( divide both sides by 4 )
9 = k
v = 9g ← equation of variation
when g = 11 , then
v = 9 × 11 = 99
Car A is travelling east at a steady speed .......
Answer:
for 20 miles per hour
Step-by-step explanation:
.
What happened to the native economies and cultures of Asia, Africa, and the Americas as a result of the Age of
Exploration?
They joined together to resist the attempts of Europeans to change them.
What was the Age of Exploration What major changes did it cause in the world?People have been captivated by global exploration and learning about new locations and civilizations for thousands of years. Traveling by sea was historically one of the most effective methods of globetrotting. Greeks in antiquity to medieval SpanishKings, because it provided the possibility of new business ventures and trade routes, exploration was a top priority for governments. Spanish ships, for instance, could travel to China and return with Chinese spices and silks (which were not accessible in continental Europe) to sell in Spanish marketplaces.In order to avoid deviating from their intended course, early explorers used a navigational system known as "dead reckoning," which involves calculating their position based on previous positions (such as landmasses). However, this technique may not be an exact science. Exploration became increasingly crucial as far as Europe's economic interests were concerned.Innovative tools that made exploration simpler and more accurate were created.Learn more about Age of Exploration refer to :
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Seven factory workers take part in a charity swim. Altogether they swim 179 lengths of a pool. How many lengths does each worker swim on average?
The length of each factory worker on average is 25.57 lengths
How to determine the length of each on average?From the question, we have the following parameters that can be used in our computation:
Total length of the pool = 179 lengths
Number of workers = 7
The length of each on average is calculated as
Average length = Total length of the pool/Number of workers
Substitute the known values in the above equation
So, we have the following equation
Average length = 179/7
Evaluate the quotient
Average length = 25.57
Hence, the average length is 25.57 lengths
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A room is 12 m long,10m broad and 6 m high. It has a door of size 1m×2m and a windows of size 2m × 1.5m. Calculate the cost of plastering the walls at the rate of Rs 15/m².
The cost of plastering the rectangle walls at rate of Rs.15/[tex]m^2[/tex] is Rs.5565.
What is rectangle?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.
Given,
Length of room =12m
Breadth of room =10m
Height of room =6m
So, Area of four walls =2(l+b)×h
=>area of four wall=2(12+10)×6=264[tex]m^2[/tex]
Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)
=> area of 2 doors and 3 windows = 13[tex]m^2[/tex]
Area of ceiling =l×b=12×10=120 [tex]m^2[/tex]
Thus, total area for plastering =(264−13+120)= 371[tex]m^2[/tex]
Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.
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Zahra and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags
of popcorn and 5 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Total cost, 8 bags of popcorn and 5 drinks:
Total cost, p bags of popcorn and d drinks:
Convert a person's weight of 122 pounds to kilograms. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
Ihs ✓
CLASSIFYING A FUNCTION. Is the function represented by the ordered pairs linear or nonlinear? Explain your reasoning.
How many ways can the letters in the word CHEWY be arranged to form a five letter code
Answer:
60 ways;
GOOD LUCK!
Step-by-step explanation:
The word CHEWY has 5 letters, Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.
How do I calculate the area and perimeter of this triangle?
Step-by-step explanation:
to find the perimeter first:
13×3=39
13×3=39
5×3=15
5×3=15
39+39+15+15=108
P=108
i hope it's useful
I need help please answer
Two triangles are shown below. 3 5 15 9 6 18 Which statement best describes the relationship between the two triangles ? The triangles are not similar all corresponding angles are not equal . The triangles are not similar ; all corresponding sides are not proportional . The triangles are similar ; the similarity ratio is 1: 3. The triangles are similar ; the similarity ratio is 2 :3.
The statement that best describes the relationship between the two triangles is the option;
The triangles are not similar; all the corresponding sides are not proportionalWhat are the conditions for the similarity of two triangles?Two triangles are similar if they satisfy the following conditions.
Two angles of one triangle are congruent to two angles in the other triangle (AA, Angle-Angle similarity postulate)Two sides of one triangle are proportional to two sides of the other triangle and the included angle of the two sides in each triangle are congruent (SAS, Side-Angle-Side similarity postulate)The three sides of one triangle are proportional to the three sides of the other triangle (SSS, Side-Side-Side, similarity postulate)The length of the sides of the triangles are;
First triangle, a₁ = 3, b₁ = 5. c₁ = 15
Second triangle. a₂ = 9, b₂ = 6, c₂ = 18
The ratio of the corresponding sides is therefore;
[tex]\dfrac{a_1}{a_2} = \dfrac{3}{9} =\dfrac{1}{3}[/tex]
[tex]\dfrac{b_1}{b_2} = \dfrac{5}{6}[/tex]
[tex]\dfrac{c_1}{c_2} = \dfrac{15}{18} =\dfrac{5}{6}[/tex]
The ratio of the three corresponding sides of the triangles are not the same such that the corresponding sides of the triangles are not constantly proportional.
Therefore the two triangles are not similar because all the corresponding sides are not proportional.
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Use the pie chart to answer the following questions:
STEP
1. How many studer ts would you expect to like Comedy in a class of 300
2. How many students would you expect to like Action in a class of 400?
3.How maby studeptstwould you expect to like Romance in a class of 350?
4. How many students would you expect to like Foreign in a class of 225?
5. How many students would you expect to like Horror in a class of 200?
6. How many students would you expect to like Science Fiction in a class of 175?
Comedy 27%
Action 18%
Romance 14%
Drama 14%
Horror 11%
Foreign 8%
Science 8%
fiction
1. The number of students like Comedy in a class of 300 are 81.
2. The number of students like Action in a class of 400 are 72.
3. The number of students like Romance in a class of 350 are 49.
4. The number of students like Foreign in a class of 225 are 18.
5. The number of students like Horror in a class of 200 are 22.
6. The number of students like Science friction in a class of 175 are 14.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The pie chart is,
Comedy 27%
Action 18%
Romance 14%
Drama 14%
Horror 11%
Foreign 8%
Science 8%
Now,
1. The number of students like Comedy in a class of 300 are;
= 27% of 300
= 27/100 x 300
= 81
Thus, The number of students like Comedy in a class of 300 are 81.
2. The number of students like Action in a class of 400 are;
= 18% of 400
= 18/100 x 400
= 72
Thus, The number of students like Action in a class of 400 are 72.
3. The number of students like Romance in a class of 350 are;
= 14% of 350
= 14/100 x 350
= 49
4. The number of students like Foreign in a class of 225 are;
= 8% of 225
= 8/100 x 225
= 18
5. The number of students like Horror in a class of 200 are;
= 11% of 200
= 11/100 x 200
= 22
6. The number of students like Science friction in a class of 175 are;
= 8% of 175
= 8/100 x 175
= 14
Thus, 1. The number of students like Comedy in a class of 300 are 81.
2. The number of students like Action in a class of 400 are 72.
3. The number of students like Romance in a class of 350 are 49.
4. The number of students like Foreign in a class of 225 are 18.
5. The number of students like Horror in a class of 200 are 22.
6. The number of students like Science friction in a class of 175 are 14.
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please help I need to find X
Answer:
x = 12
Step-by-step explanation:
if l and m are parallel that means that since the two angles are consecutive interior they add to 180
so add them both and set that to 180
9x - 4 + 5x + 16 = 180
now combine like terms
14x + 12 = 180
subtract 12 from both sides
14x = 168
divide everything by 14
x = 12
that is the answer
Answer:
[tex]\sf x=12^o[/tex]Step-by-step explanation:
Let's find x:-
[tex]\sf 9x-4+5x+16=180^o[/tex]
Combine like terms:-
[tex]\sf 9x+5x-4+16=180[/tex]
[tex]\sf 14x-4+16=180[/tex]
[tex]\sf 14x+12=180[/tex]
Add/Subtract numbers:-
[tex]\sf 14x+12-12=180-12[/tex]
[tex]\sf 14x=168[/tex]
Divide both sides by 14:-
[tex]\sf \cfrac{14x}{14}=\cfrac{168}{14}[/tex]
[tex]\sf x=12^o[/tex]
__________________
Hope this helps!
Have a great day!
