Which of the following statements are true? Select all that apply.
A. ∠3 ≅ ∠2 because they are alternate interior angles.
B. m∠1 + m∠3 = 180° because they form a straight angle.
C. ∠3 ≅ ∠6 because they are alternate interior angles.
D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180°.
Answers
The true statement are
2. <1 + <3 = 180 because form a straight angle.
3. ∠3 ≅ ∠6 because they are alternate interior angles.
4. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180°.
What are parallel lines?
Two lines in a plane are said to be parallel if they do not intersect when extended infinitely in both directions.
Two lines cut by a transversal line are parallel if the corresponding angles so formed are equal. In general, the corresponding angles are in relative positions and lie along the same side of the transversal.Two lines cut by a transversal line are parallel if the alternate interior angles so formed are equal. In general, the pairs of the alternate interior are found in the inner side but lie on the opposite sides of the transversal.Two lines cut by a transversal line are parallel if the alternate exterior angles so formed are equal. In general, the pairs of alternate exterior angles are found on the outer side but lie opposite each other.As, from the figure
1. <3 = <2 because of vertically opposite angle.
Hence, it is false
2. <1 + <3 = 180 because form a straight angle.
Hence, it is true.
3. ∠3 ≅ ∠6 because they are alternate interior angles.
Hence, it is true.
4. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180°.
Hence, it is true.
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Related Questions
Solve the following inequality 17 less than or equal to negative 3X +2 less than or equal to 26.. what is the answer
Answers
Answer:
-5 less than or equal to x less than or equal to -8
Step-by-step explanation:
You have to isolate x.
Start with removing +2.
Take 2 away from both sides
15 less than or equal to -3x less than or equal to 24
Then, the only thing you have to isolate after that is -3, you have to remove it from x.
Since -3x is multiplying, you have to divide by -3 on the other sides.
15 divided by -3 is -5
24 divided by -3 is -8
Therefore,
The answer is...
-5 less than or equal to x less than or equal to -8
A dolphin dives down into the ocean and resurfaces along a path that is modeled by x^2- 8x + 4y = 0, where the distances are in feet. How many feet is the dolphin from its starting point along the
water's surface?
8 feet
6 feet
4 feet
O feet
please guys i need help
Answers
Answer:
6ft
Step-by-step explanation:
The Dolphin is 8 feet apart from starting point along the water surface.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Equation: x²- 8x + 4y = 0
Now, solving for variable 'y' we get
y= (8x - x²) /4
y= 2x - x²/4
So, the Dolphin is 8 feet apart from starting point along the water surface.
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Which number is a favor of 12 but not a multiple of 2
Answers
Answer:
3
Step-by-step explanation:
a forrest covers an area of 2400 km^2. if each year the area decreases by 8.5%, what will the area be after 14 years? round answer to nearest square kilometer. (please explain how you get the answer so i can do future questions myself! thank you :) )
Answers
Answer:
1581.62810745 square km
Step-by-step explanation:
P = Initial Area = 2500 square km.
r = rate of decreasing = 8.75%
n = number of years = 5 years
A = 2500 ( 1 - 8.75/100)^5
A = 2500 {(100–8.75)/100}^5
A = 2500 (91.25/100)^5
A = 2500 (0.9125)^5
A = 2500 * 0.63265124298
A = 1581.62810745
House of Mohammed sells packaged lunches, where their finance department has established a
weekly relationship between its Revenue R, in dollars and the number of lunches x, as R=x(82−x)
(a) Write the revenue R, in the form R=ax2+bx+c (b) What is the revenue when 35 lunches are sold? (c) Explain why the graph of R has a maximum.
(d) Write R in the form a(x−h)2+k
(e) How many lunches must be sold for them to achieve their maximum revenue?
(f) State the company's maximum revenue.
(2 marks) (2 marks) (2 marks)
(5 marks)
(2 marks) (2 marks)
(g) Complete the following table of values and graph the Revenue equation using the ordered pairs
(x , R). Label the coordinates of the vertex.
x
10
20
30
40
50
60
70
80
90
R
( 10 marks)
Answers
The revenue function is a quadratic equation and the graph of the function
has the shape of a parabola that is concave downwards.
The correct responses are;
(a) R = -x² + 82·x(b) $1,645(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.(d) R = -1·(x - 41)² + 1,681(e) 41(f) $1,681Reasons:
The given function that gives the weekly revenue is; R = x·(82 - x)
Where;
R = The revenue in dollars
x = The number of lunches
(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;
R = x·(82 - x) = 82·x - x²
Which gives;
R = -x² + 82·xWhere, the constant term, c = 0
(b) When 35 launches are sold, we have;
x = 35
Which by plugging in the value of x = 35, gives;
R = 35 × (82 - 35) = 1,645
The revenue when 35 lunches are sold, R = $1,645
(c) The given function for R is R = x·(82 - x) = -x² + 82·x
Given that the leading coefficient is negative, the shape of graph of the
function R is concave downward, and therefore, the graph has only a
maximum point.
(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;
(h, k) = The vertex of the equation
a = The leading coefficient
The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;
R = x·(82 - x) = -x² + 82·x
At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;
[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]
Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]
The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681
Which gives;
(h, k) = (41, 1,681)
a = -1 (The coefficient of x² in -x² + 82·x)
The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41
Therefore;
The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681
The maximum revenue of the company is $1,681Learn more about the quadratic function here:
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Sam has 60 toy cars. 20% of the cars are red.
How many cars are red?
A. 12
B. 20
C. 48
D. 40
Answers
Answer:
A
Step-by-step explanation:
20% of 60 is 12
Hope that helps
60 divided by 100 =0.6
0.6 x 20= 12
12
1. A FoodPanda rider believes that his tips from various customers has a slightly right skewness with a mean of RM10 and a standard deviation of RM2.50. a. Calculate the mean and standard deviation of the sampling distribution of this tips for a sample of 25 customers. Describe the shape of its sampling distribution. [4 marks]
Answers
Using the Central Limit Theorem, it is found that:
The sampling distribution is slightly right skewed, with mean of RM 10 and standard deviation of RM 0.5.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, if the sample size is at least 30, the shape is approximately normal, otherwise it still is skewed.In this problem, the mean is of 10 and the standard deviation is of 2.50, hence [tex]\mu = 10, \sigma = 2.5[/tex]
Sample of 25, hence [tex]n = 25, s = \frac{2.5}{\sqrt{25}} = 0.5[/tex]
Since the underlying distribution is skewed and the sample size is less than 30, the shape of the sampling distribution is slightly right skewed.
The sampling distribution is slightly right skewed, with mean of RM 10 and standard deviation of RM 0.5.
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pls help wiht this question ill give you 69 points whoever awnsers
Answers
Answer:
what's thequestion?
Step-by-step explanation:
If the probability that a randomly chosen college student uses a ride sharing app is 0.27, then what is the probability that a randomly chosen college student does not use a ride sharing app?
Give your answer as a decimal.
Answers
Answer:
0.73
Took the quiz
The probability that a randomly chosen college student does not use a ride sharing app is 0.73.
What is the probability?Probability is a stastistical measure that is used to determine who likely it is that event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a randomly chosen college student does not use a ride sharing app = 1 - 0.27 = 0.73
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When Abrams born his parent put $2000 in account that you did 1.2% interest compounded semi annually when he turns 16 in Spain to give him the money to buy a car how much will Abrams you receive on his 16th birthday
Answers
Answer:
$2421.95
Step-by-step explanation:
To calculate the final value from compound interest, we can use the formula
A = P(1+r/n)^(nt), where A represents the final amount, P is the initial amount, r is the rate, n is the number of times compounded per time period, and t is the amount of time.
Here, P is 2000, 1.2% is the rate (to convert to a decimal, we can divide by 100 to get 0.012), n = 2 because it is compounded semi-annually, and 16 is the number of years, or t. Plugging these in, we get
2000(1+0.012/2)^(2*16) = 2421.95
7(2e-1)-3=6+6e pls help and do step by step
Answers
Answer:
e = 2
Step-by-step explanation:
7(2e - 1) - 3 = 6 + 6e
14e - 7 - 3 = 6 + 6e
14e - 10 = 6 + 6e
14e - 6e - 10 = 6
8e - 10 = 6
8e = 6 + 10
8e = 16
8e/8 = 16/8
e = 2
Recheck:
7(2e - 1) - 3 = 6 + 6e
7(2(2) - 1) - 3 = 6 + 6(2)
7(4 - 1) - 3 = 6 + 12
7(3) - 3 = 18
21 - 3 = 18
18 = 18 ✅
Express in the form
1
:
n
.
Give
n
as a decimal.
14
:
7
Answers
Answer:
n is 0.5
Step-by-step explanation:
Answer:
1:0.5
Step-by-step explanation:
Find the perimeter of the rectangle whose: length = 1m, breadth = 75cm
Pls all answer fast PLS
Answers
Answer:
The perimeter of the rectangle is 3.5 m or 350 cm.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Find the volume in cubic feet of a rectangular moving van with length 14 feet, width 7 feet, and height 7 feet
Answers
Answer:
length (l) = 14 feet
breadth (b) = 7 feet
height (h) = 7 feet
so, volume of the
rectangular moving
van = l*b*h
=14feet * 7feet *7feet
= 686 cubic feet
state whether each of the following equations represent growth or decay.
Answers
Answer:
answer below
Step-by-step explanation:
f(x) = a* bˣ
if a>0 and b>1 : growth
if a>0 and 0<b<1 : decay
5) 7) 9) : growth
6) 8) 10) : decay
When analyzing whether an equation represents growth or decay, we examine the relationship between the variables involved. If an equation shows a positive relationship, it represents growth, while a negative relationship indicates decay.
When determining whether an equation represents growth or decay, we need to examine the relationship between the variables involved. 1. If the equation represents a positive relationship, where as one variable increases, the other variable also increases, then it represents growth. 2. On the other hand, if the equation represents a negative relationship, where as one variable increases, the other variable decreases, then it represents decay.
Let's look at some examples to illustrate this: Example 1: y = 2x In this equation, as x increases, y also increases. Therefore, it represents growth. Example 2: y = -3x In this equation, as x increases, y decreases. Therefore, it represents decay. Example 3: y = -0.5x + 3 Here, as x increases, y decreases. So, this equation represents decay. Example 4: y = 4.5x + 2 As x increases, y also increases. Hence, this equation represents growth. In summary, when analyzing whether an equation represents growth or decay, we examine the relationship between the variables involved. If an equation shows a positive relationship, it represents growth, while a negative relationship indicates decay.
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x+3<9 answer pls 2x+5<12
Answers
Answer:
first one: x<9 second: x<3.5 or 7/2
Step-by-step explanation:
first: substract 3 from both sides
second: substract 5 and then divide by 2
If y= cos x, what x-value corresponds to a y-value of 1/2 between pi and 2 pi
Answers
Answer:
pi/3, 5pi/3
Step-by-step explanation:
We can see that when cosine is at 1/2, the angle measures are pi/3 degrees and 5pi/3 degrees. You can use a unit circle to find this. You can also find arccos(1/2), but that will only give you the value pi/3, not 5pi/3.
We can plug these in to find that they are indeed equal to 1/2.
The x-value that corresponds to a y-value of 1/2 between π and 2π is π/3.
Here, we have,
To find the x-value that corresponds to a y-value of 1/2 between π and 2π for the equation y = cos(x), we can use the inverse cosine function (also known as arccosine or cos⁻¹).
The inverse cosine function will give us the angle whose cosine is a specific value.
In this case, we want to find the angle whose cosine is 1/2.
Using the inverse cosine function, we can write the equation as:
x = arccos(1/2)
To solve this equation, we need to evaluate the inverse cosine of 1/2. In general, the inverse cosine of a value returns an angle between 0 and π (180 degrees). In this case, we are interested in finding an angle between π and 2π.
The value of arccos(1/2) is π/3.
Therefore, the x-value that corresponds to a y-value of 1/2 between π and 2π is π/3.
It's important to mention that the cosine function is periodic, so there are multiple x-values that can correspond to a y-value of 1/2. In this case, we have chosen the x-value that lies between π and 2π.
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five men can repair a stretch of road in 8 hrs. how many men would be needed to repair the same road in 3 1/3 hrs
also tell if its direct or inverse proportion
i just wanna check my answer, whether its correct or not
Answers
Answer: 12 men would be needed to repair the same road in 3 1/3 hrs. Inverse proportion because usually in work,food and time its inversly proportional.
8 hours --> 5 men
1 hour --> 5*8 = 40 men
3 1/3 hours --> 40/ (3 1/3) men
--> 12 men
Let f(x)=5(3)x−4. Evaluate f(6).
Answers
5(3)(6)-4
15(6)-4
90-4
86
hope it helps
Given that:
f(x) = 5(3)x-4
f(6) = 5(3)(6) - 4 ⇛15(6) - 4 ⇛90-4 ⇛86Ans.
what is the rate of change for these data?
Answers
Answer:
-2 gallons per minute
Step-by-step explanation:
As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.
So, the rate of change is -30 gallons per 15 minutes
However, we can simplify this ratio by dividing both sides by 15, so we get
-2 gallons per minute
Help me please i really need it
Answers
=======================================================
Explanation:
The ratio we want is in the format green:red:total which means we list the number of green first, then the number of red next, then the number total last. The order is very important. This is because we'll simply list the numbers without saying the color name or "total". So the reader will imply what the numbers refer to, based on this order mentioned.
We have:
50 red70 green42 yellow50+70+42 = 120+42 = 162 totalThe ratio of green to red to total is 70:50:162
To reduce the ratio, we divide all three parts of that ratio by the GCF 2
70/2 = 3550/2 = 25162/2 = 81The ratio 70:50:162 fully reduces to 35:25:81 which is the final answer.
This says that for every 35 green marbles, we have 25 red marbles and 81 total marbles.
Pls help I’ll brainlest ASAP
Answers
Rise/Run
How much each point rises should be divided by how much is slides left or right.
So your answer is 7/5x
Type the correct answer in each box.
Quadrilateral EBCD is an isosceles trapezoid with m∠EDC = 110°, m∠ABC = 133°, and m∠DEA = 114°.
m∠DEB = __°
m∠BCD= __°
m∠EAB= __°
Answers
Answer:
m∠DEB = _70_°
m∠BCD= _110_°
m∠EAB= _73_°
Step-by-step explanation:
To find ∠DEB:
Take the angle of ∠EDC, which is 110°. We know the total degree in a triangle is 180°. So, we do 180° - 110° to get 70°.
To find ∠BCD:
Because EBCD is an isosceles trapezoid, this means that ∠D and ∠C both have the congruent angles. Since we know ∠EDC is 110°, this means that ∠C is also 110°.
To find ∠EAB:
We know that m∠ABC is 133° and ∠DEA is 114°. However, both angles count both the triangle and trapezoid. Previously we figured out that ∠DEB is 70°. We'll take the angle of ∠DEA and subtract the angle of ∠DEB from it, which gets us 44°. To figure out the angle of ∠B, we take the angle of ∠ABC and subtract 70° or the angle of ∠DEB, which gets us 63°. Now we take the total degree of a triangle, 180° and minus both 44° and 63° from it, which is 73°.
- 2021 Edmentum
The quotient of a number and negative eight is five-eighths. Find the number.
Answers
Answer:
-64/5
Step-by-step explanation:
Basically, the word "quotient" means the answer to a division problem. Therefore, its a division problem, so you have to work backwards with multiplication. -8 times a number is 5/8, so the other number is going to be negative.
The number is -64/5
Answer:
n = -5
Step-by-step explanation:
Form this quotient, representing the number by n: n / (-8) = 5/8.
Solve this equation for n by multiplying both sides by 8: -n = 5. Then n = -5
A city park is in the shape of a triangle where
the sides have lengths 170 m, 162 m, and
177 m. If a fence was built around the
perimeter of the park, how long would the
fence need to be?
Answers
Answer:
solution here
length
c=170
a=162
b=177
perimeter=?
now,
perimeter of triangle = a+b+c
=170+162+177
=511
perimeter=511 cm
perimeter = length of fence
therefore,the fence should be 511 cm long.
The length of the fence needed would be 509 meters.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.The sum of the angles of the triangle is equal to 180 degrees.Given is that a city park is in the shape of a triangle where the sides have lengths 170 m, 162 m, and 177 m.
The length of the fence needed would be the perimeter of the triangle. We can write the perimeter of the triangle as -
P = sum of the side lengths
P = 170 + 162 + 177
P = 509 meters
Therefore, the length of the fence needed would be 509 meters.
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The candy store is selling Twizzlers. They have a sale of four Twizzlers for $6.00. Which equation below represents this proportional relationship?
A. y=1.5x C. y= x 2/3 B. x= 4y D. x= 6y
Answers
Answer:A. y=1.5x
Step-by-step explanation:
x represents the number of twizzlers
1.5 represents the the price that you have to pay for each Twizzlers
And y represents the total cost
Find the values of the variables.
Answers
Answer:
x = 50
y = 65
Step-by-step explanation:
The marked sides show you that the triangle is isosceles. That means the base angles, y° and 65°, are congruent.
y = 65
__
The sum of the angles in a triangle is 180°.
65° +65° +x° = 180°
x° = 180° -130° = 50° . . . . . . subtract 130°
x = 50
A student has a savings account with $475 in it.
She deposits $125 of her paycheck into the account
every week. Her goal is to save $7,000 for college.
How long will it be before she has $1350?
Answers
Answer: 7 weeks
Step-by-step explanation:
Let x represent number of weeks
Let y represent the total amount
Amount = Paycheck deposited * number of weeks + Initial amount
y = 125x + 475
Number of weeks until she has $1350
1350 = 125x + 475
125x+475-475=1350-475
125x=875
x=7
Therefore, the student will have $1350 in her bank account after 7 weeks
I Hope This Helps
Which expression is equivalent to 6(7x - 9)?
Answers
Answer:
42x - 54 I think
Step-by-step explanation:
Just simplify it
Find the value of x
Answers
Answer:
6.93
Step-by-step explanation:
hope this helps