Answer:
2.5
Step-by-step explanation:
56(t+1/2)=70 t
56T + 28= 70T
28=70T-56T
28=14
2=T
s=T+ 1/2
S=2+ 1/2
S=2.5 hours
Tina traveled for 2 hours at a speed of 70 miles per hour, covering a distance of 140 miles.
Stephanie traveled for 2.5 hours at a speed of 56 miles per hour, also covering a distance of 140 miles.
What's the expression about?The distance traveled by a vehicle is given by the formula: distance = speed × time.
For Stephanie:
Distance_stephanie = Speed_stephanie × Time_stephanie
Distance_stephanie = 56 × (t + 0.5)
For Tina:
Distance_tina = Speed_tina × Time_tina
Distance_tina = 70 × t
Since both Stephanie and Tina are traveling the same route, the distances they travel should be equal:
Distance_stephanie = Distance_tina
Substitute the expressions for distances:
56 × (t + 0.5) = 70 × t
Now solve for "t":
56t + 28 = 70t
28 = 14t
t = 28 / 14
t = 2
So, Tina traveled for 2 hours.
Now we can find the distance traveled by both Stephanie and Tina:
Distance_tina = 70 × t
Distance_tina = 70 × 2
Distance_tina = 140 miles
Distance_stephanie = 56 × (t + 0.5)
Distance_stephanie = 56 × (2 + 0.5)
Distance_stephanie = 56 × 2.5
Distance_stephanie = 140 miles
Both Stephanie and Tina traveled a distance of 140 miles.
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2. Ryan gets a raise. He now earns $9 an hour. Ryan decides to
start saving for a car. He works 9 hours a week.
Part A
How many hours does Ryan need to work to earn
enough money to buy the car, as well as pay for the
taxes, title, and plates as shown? Draw bar diagrams
to help write and solve equations.
Used car: 52,753
Taxes, title, and
plates: $235
Part B
About how many weeks will Ryan need to work to buy the car and pay
for the taxes, title, and plates? Explain.
Part
How many actual weeks does Ryan need to work to buy the car and pay
for the taxes, title, and plates? Show your computations. Explain why your
solution is reasonable.
Answer:
A. He has to work 5,887hrs and 55 min
B. 3,504 weeks
Step-by-step explanation:
A. He earns $9 an hr. He works 9hrs a week, or 1hr 17 min a day. $11.52 per day.
The car costs $52,753, + $235(taxes, titles, and plates)= $52,988.
52,988/9=5,887:55
B. One week= 168 hrs. 5,887:55/168=3,504 weeks
Ryan needs to work approximately 5888 hours, which translates to about 654 weeks or 12.5 years, to save enough to buy a used car and pay for taxes, title, and plates at his current wage of $9 an hour.
To determine how many hours Ryan needs to work to afford a used car plus additional costs, we first add the price of the car to the taxes, titles, and plates. The cost of the used car is $52,753, and the taxes, titles and plates amount to $235, giving us a total cost of $52,988.
Ryan earns $9 per hour. To find out how many hours he needs to work to earn $52,988, we divide the total cost by his hourly wage.
$52,988 / $9 per hour = 5887.555... hours
Ryan would need to work approximately 5888 hours to afford the car and the extra costs.
For part B, we calculate how many weeks Ryan needs to work. Since Ryan works 9 hours a week, we divide the total hours needed by his weekly hours.
5888 hours / 9 hours per week = 654.222... weeks
Ryan would need to work approximately 654 weeks, which is roughly 12.5 years, assuming he works every week without any breaks or holidays.
Dora is conducting a performance appraisal for Sue, one of her employees. The company's performance appraisal form asks her to rate Sue's performance on various items like "Submits reports on time with minimal errors" on a scale from 1 to 5.
The correct answer is "behaviorally anchored rating scale."
Further Explanation:
This type of testing is used by employers to rate an employees patterns of behaviors or their performance. This testing is also known as BARS. They use a scale system from either 1-5 or 5-9. This helps to see how the employee or trainee will do in certain situations.
This is commonly used by Human Resource departments, supervisors, or other higher ups in a company. This is used to benefit the company in the long run in case the employee or trainee doesn't work out during the appraisal. This can also be done during a yearly review of a seasoned employee.
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Diana has an end table in the shape of a right triangle. The triangular tabletop is twice as high as it is wide at the base. If the area of the tabletop is 4 square feet (4ft2), what is the width of the base of this triangular tabletop in feet?
Answer:
The width of the base is 2.828 feet
Explanation:
Given the area of the table top is 4 square feet
The triangular table top is twice as high as it is wide at the base
Therefore, we can say that height = base
Area of a right angled triangle is calculated by, Area = ½ * base * height
In this case, height = base
Therefore, area =[tex]\frac{1}{2}\times (base)^2[/tex]
Substituting the values,
4 = [tex]\frac{1}{2}\times (base)^2[/tex]
[tex](base)^2[/tex] = 8
Base = 2√2 = 2 * 1.414 = 2.828 feet
Therefore, the width of the base is 2.828 feet
What is the mean of the following data? 53, 71, 89, 10, 62
62. If you add up all of the numbers, you get 310, then take this number and divide it by 5. you divide it by five because there are five numbers given.
Answer:
57 is the mean.
When you add up all of the numbers, you get 285.
Divide 285 by 5 and you get 57.
(
4.
What is the volume of the composite
figure?
he composite vi
10x7
6 in.
2 in
7 in
360
10 in.
6x2.212
3
Answer: I think something is missing ?? sorry comment down below
Step-by-step explanation:
(–x^2y^3m)^5 write the monomial in standard form
Answer:
-m^5*x^10*y^15
Step-by-step explanation:
remember alphabetical order
The standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (–x²y³m)⁵. The standard form of the number will be written as,
E = (–x²y³m)⁵
Solve the exponents and simplify.
E = -m⁵x¹⁰y¹⁵
Therefore, the standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
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the equations below are. parallel perpendicular or neither
Answer:
b
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange both equations into this form
x - 6y = - 30 (subtract x from both sides )
- 6y = - x - 30 ( divide all terms by - 6 )
y = [tex]\frac{1}{6}[/tex] x + 5 ← in slope- intercept form
with slope m = [tex]\frac{1}{6}[/tex]
y = - 6x + 5 ← in slope- intercept form
with slope m = - 6
Parallel lines have equal slopes.
Clearly the lines are not parallel.
The product of the slope of perpendicular lines equals - 1, thus
[tex]\frac{1}{6}[/tex] × - 6 = - 1
Hence the lines are perpendicular → b
Please answer this correctly
Answer:
6:32 is my answer to this question
so if it is three minutes to one that means it is
12:57
in 6 hours and 34 minutes will be
12:57 + 6= 6:57
if you add 34 (i didnt do it above to make it easier) to 57 you get 91.
because minutes dont go past 60 you have to subtract..
91 - 60 = 31 and because you only subtracted 60 once you only add one hour..
so your answer is 7:31
i hope this helps you !!!
There are 1/35 of the students in the school that are allergic to seafood. there are 1/15 of the students in school that are allegic to peanuts? Are there more students allergic to seafood or peanuts?
More people are allergic to peanuts because the smaller the denominator, the bigger the fraction.
There are 12 chairs in the meeting hall and odd number of tables each table has the same number of chairs how many tables are there use prime factorization to solve two different ways
Answer:
There may be 3 tables or 1 table.
Step-by-step explanation:
If we factorize 12 into its prime factors then we get 12 = 2 × 2 × 3
If there are an odd number of tables and each table has an equal number of chairs and there are a total of 12 chairs, then the possibilities of the number of tables are 1 and 3.
{Since 1 and 3 both are odd numbers}
Now, for 3 tables there will be 4 chairs each to make the total chairs (3 × 4) = 12 and for 1 table there will be 12 chairs in the table to make the total number of chairs (1 × 12) = 12. (Answer)
To solve using prime factorization, the factors of 12 are 2, 2, and 3. We need an odd number of tables, so only the factor 3 is used. There are 3 tables with 4 chairs each.
Explanation:The question involves a scenario where there are 12 chairs in a meeting hall and an odd number of tables. Each table has the same number of chairs. The question prompts us to use prime factorization to determine how many tables there could be. Since there is a fixed total of 12 chairs, we need to find the factors of 12 that are odd numbers because the number of tables has to be odd.
Using prime factorization, 12 can be broken down into its prime factors: 2 x 2 x 3. To have an odd number of tables, we cannot include the factor of 2 because it would result in an even number of tables. Hence, we only consider the factor of 3. In this scenario, this would mean there are 3 tables with 4 chairs each because 3 (an odd number) times 4 equals 12 (total number of chairs).
Another way to use prime factorization to solve this is to look for combinations of the factors that multiply to 12 but in groups that have an odd factor. The only possible combination is again 3 tables with 4 chairs each, as any other multiplication involving the factor 2 would result in an even number of tables.
0.5x+7/3 = 21/4 cross multiply
Answer:
Step-by-step explanation:
I'm not sure I would cross multiply as my first step.
How about subtracting 7/3 first.
0.5x = 21/4 - 7/3
0.5x = 21*3/(4*3) - 7*4/(3*4)
0.5x = 63 / 12 - 28/12
0.5x = 35/ 12 Now multiply by 2
2*0.5x = 35*2 / 12
x = 70/12
x = 5 10/12 or
x = 5 5/6 or
x = 5.8333333
There might be a slightly easier way of doing this.
Suppose you multiply by 2 to begin with
x + 14/3 = 42/4
x + 14/3 = 21/2
x = 21/2 - 14/3
x = 63/6 - 28/6
x = 35/6
x = 5 5/6
I don't think there is much difference in how you do it. The numbers are just plain ugly.
q.15ab with step pls
Answer:
(a) The cost of 1 model house A = $24
(b) YES, with $200 Victor can purchase 3 A model & 4 B model houses.
Step-by-step explanation:
Let us assume the cost of model house B = $ m
So, the cost of model house A =$ ( m - 6)
So, the price of 5 A model house = 5 x ( Rate of 1 model house A)
= 5(m-6)
And, the price of 3 B model house = 3 x ( Rate of 1 model house B)
= 3 x (m) = 3 m
So, the cost of 3 B house + 5 A house = 5(m-6) + 3 m
⇒5(m-6) + 3 m = $210
or, 5 m - 30 + 3 m = 210
or, 8 m = 240
or, m = 30
So, the cost of 1 B house = m = $30
And the cost of 1 house A = (m -6) = (30 - 6) = $24
Now, The cost of 3 A model + 4 B model
= 3( 24) + 4(30) = 72 + 120 = 192
So, The cost of 3 A model + 4 B model = $192 and $192 < $200
Hence, YES, with $200 Victor can purchase 3 A model + 4 B model houses.
euben's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Reuben $5.70 per pound, and type B coffee costs $4.30 per pound. This month, Reuben made 167 pounds of the blend, for a total cost of $820.30. How many pounds of type A coffee did he use?
Answer:
The quantity of type A coffee is 73 pounds
The quantity of type B coffee is 94 pounds .
Step-by-step explanation:
Given as :
The price of Type A coffee costs = $ 5.70 per pound
The price of Type B coffee costs = $ 4.30 per pound
The total quantity of coffee does Reuben purchases = 167 pounds
The total cost of the coffee for 167 pounds = $ 820.30
Let The quantity for type A coffee = a pounds
And The quantity of type B coffee = b pounds
Now, According to question
a + b = 167 pounds And
$ 5.70 × a + $ 4.30 × b = $ 820.30
Now solving equations
5.70 × ( a + b ) = 5.70 × 167
or, 5.70 a + 5.70 b = 951.9
Now ,
( 5.70 a + 5.70 b ) - ( 5.70 a + 4.30 b ) = 951.9 - 820.30
or, ( 5.70 a - 5.70 a ) + ( 5.70 b - 4.30 b ) = 131.6
Or, 0 + 1.4 b = 131.6
∴ b = [tex]\frac{131.6}{1.4}[/tex]
I.e b = 94 pounds
Put the value of b to get a value
So, a = 167 pounds - b
Or, a = 167 - 94
∴ a = 73 pounds
Hence The quantity of type A coffee is 73 pounds
And The quantity of type B coffee is 94 pounds . Answer
Think of something in your home or community that could be described as a proportional relationship. List at least three examples.
Answer in 3 complete sentences.
Answer:
The 3 examples are given below.
Step-by-step explanation:
1. While decorating my home the amount of paint required ([tex]A_{m}[/tex]) for the wall is proportional to the area of the wall (A),
or [tex]A_{m}[/tex] ∝ A .
2. The no. of tiles required(T) to fill the floor of a house is proportional to the area of the floor(F) provided area of each tile(t) is constant here,
or T ∝ F when t is constant
3.The tuition fee (M) taken by my sister's school for her studies is proportional to the no. of months(H) she is in that school,
or M ∝ H
Final answer:
Examples of proportional relationships include electricity bills proportionate to usage, water in a tank related to tap flow time, and pay from a job based on the number of performed tasks.
Explanation:
Proportional relationships involve constants of proportionality which indicate a direct or inverse relationship between two quantities. For example, in a household setting, the electricity bill is directly proportional to the amount of electrical usage; the higher the usage, the higher the bill. Similarly, the amount of water in a tank can be seen as directly proportional to the time the tap runs if the flow rate is constant. Additionally, the pay for a college work-study job, such as making calls for donations, can be directly proportional to the number of calls made; if you're paid $2.50 per call, doubling the number of calls doubles your pay.
The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the population to quadruple according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
There are 16 years will it take for the population to quadruple i.e. four times the initial population.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
Given that a population of a country grows exponentially and continuously at a rate of 9% per year.
The number of years it takes for the population to quadruple i.e. four times the initial population.
As per the given condition, the required solution would be as:
⇒ 4p = p[tex]e^{0.09t}[/tex]
Divided by p into both sides of the above equation,
⇒ 4p/p = p[tex]e^{0.09t}[/tex]/p
⇒ 4 = [tex]e^{0.09t}[/tex]
Take the natural logarithm of both sides of the equation,
⇒ ln 4 = ln [tex]e^{0.09t}[/tex]
⇒ ln 4 = 0.09t ln e
∵ ln e = 1
⇒ ln 4 = 0.09t
Divided by 0.09 into both sides of the above equation,
⇒ ln 4 / 0.09 = 0.09t / 0.09
⇒ t = 16
Thus, there are 16 years will it take for the population to quadruple.
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5x + y = 10
5y = 3x - 6
Solution: (0,0)
Solve for system of equations
Answer:
x=2, y=0. (2, 0).
Step-by-step explanation:
5x+y=10
5y=3x-6
-------------
y=10-5x
5(10-5x)=3x-6
50-25x=3x-6
50-25x-3x=-6
50-28x=-6
28x=50-(-6)
28x=50+6
28x=56
x=56/28
x=2
5(2)+y=10
10+y=10
y=10-10
y=0
Express the ratio of the area of the circle to the area of the square
Answer:
π/4
Step-by-step explanation:
The area of the circle is A = π(2x)^2 = 4πx².
The length of one side of the square is 2(2x), or 4x, so the area of the square is A = 16x².
The ratio of the area of the circle to the area of the square is
4πx²
ratio = ------------- and this reduces to ratio = π/4.
16x²
10/3 = 5y how do I find y
Answer: y= 2/3
Step-by-step explanation:
Divide 10 by 5 and you get the 2 so you keep the denominator and it makes 2/3
Sixty-four tickets are issued for a school
dance, and 96 brownies are ordered for
the refreshment table. Each student gets
the same number of tickets as every
other student. Each student also gets the
same number of brownies as every other
student.
Each student will get — tickets and _
brownies.
Answer:
Each students will get 3 tickets and 2 brownies .
Step-by-step explanation:
Given as :
The total number of tickets issued for the school dance = 64
The number of brownies ordered for refreshment table = 96
Let the number of tickets given to each student = x
And The number of brownie given to each student = y
Now,
According to question
The tickets and brownies is distributed equally among students
So , Now, consider the tickets and brownies = n
Or, [tex]\dfrac{n}{64}[/tex] - [tex]\dfrac{n}{96}[/tex] = 1
Or, Taking LCM we get
[tex]\dfrac{3 n - 2 n}{192}[/tex] = 1
Or, [tex]\dfrac{n}{192}[/tex] = 1
∴ n = 192
Now,
The number of tickets given to each student = x = [tex]\dfrac{192}{64}[/tex]
I.e x = 3
And The number of brownie given to each student = y = [tex]\dfrac{192}{96}[/tex]
I.e y = 2
Hence Each students will get 3 tickets and 2 brownies . Answer
To ensure each student gets an equal number of tickets and brownies, we distribute 64 tickets and 96 brownies among the students. Each student gets 2 tickets and 3 brownies.
To determine how many tickets and brownies each student gets, follow these steps:
Identify the variables: Let the number of students be denoted by x.Equate the tickets: Each student gets an equal number of tickets. Thus, 64 tickets are distributed equally among x students, so each student gets 64/x tickets.Equate the brownies: Similarly, 96 brownies are distributed equally among x students, so each student gets 96/x brownies.Find common divisors: To ensure each student gets an equal and whole number of tickets and brownies, x must be a common divisor of both 64 and 96.Calculate the greatest common divisor (GCD): The GCD of 64 and 96 is 32. Therefore, there are 32 students.Determine distribution: Each student gets 64/32 = 2 tickets and 96/32 = 3 brownies.Hence, Each student will get 2 tickets and 3 brownies.
Seniors at a high school were asked what color car they drive. The results were put in a circle graph. The measure of each central angle is shown. If a senior is chosen at random from this school, find the probability of each response.
What Color Is Your Car?
Car color is not red or blue.
options:
0.51
0.47
0.53
0.49
Answer:
P(The color of the car is red) is 0.32 .
P(The color of the car is white) is 0.34 .
P(The color of the car is silver) is 0.19 .
P(The color of the car is blue) is 0.15 .
P(car color is not red or blue) is 0.53 .
Step-by-step explanation:
We know that total angle subtended at the center by a complete circle is
360° .
According to the question,
P(The color of the car is red)
= [tex]\frac {115.2}{360}[/tex]
= 0.32
P(The color of the car is white)
= [tex]\frac {122.4}{360}[/tex]
= 0.34
P(The color of the car is silver)
= [tex]\frac {68.4}{360}[/tex]
= 0.19
P(The color of the car is blue)
= [tex]\frac {54}{360}[/tex]
= 0.15
So
P(car color is not red or blue)
= 1 - (0.15 + 0.32)
= 0.53
Answer:
0.53 is the correct answer.
Step-by-step explanation:
How do u solve 4(3x-1)=9-x
Answer:
x = 1
Step-by-step explanation:
Well the first step is to apply the distributive property:
4(3x - 1) is equal to (12x - 4). You DISTRIBUTE a '4' to what is inside the parentheses.
And btw, to make it easier, you can make 9 - x so that x is first. For example, (-x + 9). They're both the same thing, just written differently.
Your new equation is 12x - 4 = -x + 9. You want to now solve the equation.
Add the (-x) to both sides. It cancels out on the right side and you add it to 12x on the left side.
[If there's no number in front of a variable, you can always just put 1 in order to make it easier]
12x + 1x = 13x. Your new equation is 13x - 4 = 9. This should look very familiar. You simply add 4 to both sides. 9 + 4 = 13
Finally, 13x = 13. Divide 13 ÷ 13 to get 1.
x = 1
The ratio of quarters to dimes in a coin collection is 5:3. You add the same number of new quarters as dimes
to the collection. Is the ratio of quarters to dimes still 5 : 3
The ratio of quarters to dimes is not still 5 : 3
Solution:
Given that ratio of quarters to dimes in a coin collection is 5:3 .
You add same number of new quarters as dimes to the collection .
Need to check if ratio of quarters to dimes is still 5 : 3
As ratio of dimes and quarters is 5 : 3
lets assume initially number of quarters = 5x and number of dimes = 3x.
Now add same number of new quarters as dimes to the collection
Let add "x" number of quarters and "x" number of dimes
So After adding,
Number of quarters = initially number of quarters + added number of quarters = 5x + x = 6x
Number of dimes = initially number of dimes + added number of dimes
= 3x + x = 4x
New ratio of quarters to dimes is 6x : 4x = 3 : 2
So we have seen here ratio get change when same number of new quarters and dimes is added to the collection
Ratio get change from 5 : 3 when same number of new quarters and dimes is added to the collection and new ratio will depend on number of quarters and dimes added to collection.
Is the expression 3(x+1 1/2)-3 equivalent to 3x+1 1/2
Answer:
No
Step-by-step explanation:
3(x+11/2)-3 = 3x + 33/2 -3 = 3x + (33-6)2 = 3x + 27/2
The expression 3(x+1 1/2)-3 is equivalent to 3x+1 1/2 once the distributive property is applied and the constants are combined.
The expression 3(x+1 1/2)-3 is not equivalent to 3x+1 1/2. To determine the equivalency, we need to apply the distributive property to the expression on the left-hand side. The distributive property states that we can multiply the outside term by each term inside the parentheses. Thus, the expression 3(x+1 1/2) becomes 3x + 4 1/2. When we subsequently subtract 3 from 4 1/2, we get 1 1/2, which results in the final expression of 3x + 1 1/2. This confirms the expressions are equivalent.
Write in vertex form y=x^2+16-71
The vertex form of y = x² + 16x - 71 is (x + 8)² - 135
Step-by-step explanation:
The vertex form of the quadratic function y = ax² + bx + c, is
y = a(x - h)² + k, where
a is the coefficient of x²b is the coefficient of xc is the y-intercept (numerical term)(h , k) are the coordinates of the vertex point of the parabola which represents the quadratic function graphicallyh = [tex]\frac{-b}{2a}[/tex] and k = y when x = h∵ The quadratic function is y = x² + 16x - 17
- Compare it with the general form of the quadratic function above
∴ a = 1 , b = 16 and c = -71
∵ [tex]h=\frac{-b}{a}[/tex]
- Substitute the value of a and b is h
∴ [tex]h=\frac{-16}{2(1)}[/tex]
∴ [tex]h=\frac{-16}{2}=-8[/tex]
∵ k = y when x = h
- Substitute x by -8 in the function above
∴ k = (-8)² + 16(-8) - 71
∴ k = 64 - 128 - 71
∴ k = -135
∴ The vertex point is (-8 , -135)
∵ The vertex form is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -135
- Substitute these values in the vertex form above
∴ y = 1(x - (-8))² + (-135)
∴ y = (x + 8)² - 135
The vertex form of y = x² + 16x - 71 is (x + 8)² - 135
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what is the percentage of 35
Answer:
0.35
Step-by-step explanation:
Answer:
it is 0.35
Step-by-step explanation:
this is because 35/100= 0.35
Please simplify.
13[tex]\frac{1}{3}[/tex] - 7[tex]\frac{7}{9}[/tex]
A. 6[tex]\frac{8}{27}[/tex]
B. 5[tex]\frac{5}{9}[/tex]
C. 7
D. 6[tex]\frac{2}{3}[/tex]
Answer:
B) 5 5/9
Step-by-step explanation:
13 1/3=40/3
7 7/9=70/9
-----------------
40/3-70/9=120/9-70/9=50/9=5 5/9
Tours of the art museum are offered every 1/3 hr from 10:00 A.M. until closing at 4:00 P.M. How many tours are offered each day?
Answer: 3 Each hour × (difference in 10 am and 4 pm= 5) = 15.
Step-by-step explanation:
Answer:
18 tours are offered
Step-by-step explanation:
So 1/3 of a hour is 20 mins, so every 20 mins a tour is offered so we know 1 hour equals to 3 tours offered so
10:00 to 11:00 is 3, 11:00 to 12:00 is 3, 12:00 to 1:00 is 3, 1:00 to 2:00 is 3, 2:00 to 3:00 is 3, 3:00 to 4:00 is 3.
6 hours times 3 equals, 18 tours are offered
3x - 4y = -16
2x - 4y = -8
what is x and y
Answer:
x = -8 , y = -2
Step-by-step explanation:
Solve the following system:
{3 x - 4 y = -16 | (equation 1)
2 x - 4 y = -8 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{3 x - 4 y = -16 | (equation 1)
0 x - (4 y)/3 = 8/3 | (equation 2)
Multiply equation 2 by 3/4:
{3 x - 4 y = -16 | (equation 1)
0 x - y = 2 | (equation 2)
Multiply equation 2 by -1:
{3 x - 4 y = -16 | (equation 1)
0 x+y = -2 | (equation 2)
Add 4 × (equation 2) to equation 1:
{3 x+0 y = -24 | (equation 1)
0 x+y = -2 | (equation 2)
Divide equation 1 by 3:
{x+0 y = -8 | (equation 1)
0 x+y = -2 | (equation 2)
Collect results:
Answer: {x = -8 , y = -2
the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method here.
Given equations:
1.[tex]\(3x - 4y = -16\)[/tex]
2.[tex]\(2x - 4y = -8\)[/tex]
We can see that both equations have the same term ( -4y), so we can eliminate ( y) by subtracting equation 2 from equation 1:
[tex]\[(3x - 4y) - (2x - 4y) = (-16) - (-8)\][/tex]
[tex]\[3x - 4y - 2x + 4y = -16 + 8\][/tex]
[tex]\[(3x - 2x) - 4y + 4y = -16 + 8\][/tex]
[tex]\[x = -8\][/tex]
Now that we have found ( x = -8 ), we can substitute this value into either of the original equations to find ( y ).
Let's substitute ( x = -8 ) into equation 1:
[tex]\[3(-8) - 4y = -16\][/tex]
[tex]\[-24 - 4y = -16\][/tex]
[tex]\[-4y = -16 + 24\][/tex]
[tex]\[-4y = 8\][/tex]
[tex]\[y = \frac{8}{-4}\][/tex]
[tex]\[y = -2\][/tex]
So, the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]
An isosceles triangle has an angle that measures 40 degrees. Which other angles could be in that isosceles triangle? Choose all that apply
• 70
• 40
• 100
• 20
An isosceles triangle has an angle that measures 40 degrees. 70 and 100 are other angles could be in that isosceles triangle
Solution:
Given that isosceles triangle has an angle that measures 40 degrees.
If a triangle is isosceles then it has 2 identical angles and the third different one.
Let the two identical angles be "a"
We know that sum of angles in a triangle is 180 degree
a + a+ 40 = 180
2a + 40 = 180
2a = 180-40
a = 70
Thus the two identical angles are 70 degree and 70 degree
Now let the identical two angles be "40" and the third angle be "a"
Now sum of angles = 180 degree
40 + 40 + a = 180
80 + a = 180
a = 100
Thus the third angle in this case is 100
70 and 100 are other angles could be in that isosceles triangle
Answer:
70, 40, and 100
Step-by-step explanation:
I am taking the IXL and wanted to know what t was and i got it wrong because someone answered it was only 70 and 100 when it is actually 40 100, and 70. Trust me i just got it wrong and IXL gave me the right answers.
You rotate a triangle 90° counterclockwise about the origin. Then you translate its image 1 unit left and 2 units down. The vertices of the final image are (-5,0),(-2,2) and (-2,-1) . What are the vertices of the original triangle?
Answer:
The coordinates of the original triangle are (2,4). (4,1) and (1,1)
Step-by-step explanation:
About the origin, I have to rotate a triangle 90° counterclockwise. Then I translate its image 1 unit left and 2 units down.
The vertices of the final image are (-5,0), (-2,2), and (-2,-1).
We need to get the vertices of the original triangle.
So, start from a triangle with vertices (-5,0), (-2,2), and (-2,-1) and do the reverse to get the original triangle.
So, we will translate the image triangle by 1 unit right and 2 units up and we will get the triangle with vertices (-5 + 1, 0 + 2), (- 2 + 1, 2 + 2) and (- 2 +1, - 1 + 2) ≡ (-4,2), (-1, 4) and (-1,1).
Now, we have to rotate this intermediate triangle by 90° clockwise.
Therefore, the coordinates of the original triangle are (2,4). (4,1) and (1,1) (Answer)
{Since, for 90° rotation the coordinates of all the vertices will interchange their location (i.e. x-value to y-value and y-value to x-value) and a negative sign will be added to the y-coordinate of the interchanged coordinates}