A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.
How to show the proof?In the given figure, AB||DC. AD is the transversal, such that:
∠A + ∠D = 180-degrees.
The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.
From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.
From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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A) 16/12
B) 12/20
C) 12/16
D) 16/20
Answer:
COA opposite/ adjacent
16/12
A
The three dot plots together are the scores of teenagers in three samples from this population. Which of the three samples is most representative of the population? Explain how you know.
The sample that is most representative of the population is: sample 3.
What is a Representative Sample of a Population?A representative sample of a population can be defined as a subset of that particular population that reflects almost or same characteristics of the main population such as the shape, center, and spread.
From the three dot plots given, the one that has almost same pattern and characteristics is sample 3 considering it has almost similar spread and shape.
Thus, the most representative sample is: sample 3.
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Y
5
What is the equation of the graphed line written in
standard form?
4
3
2
1
O 2x + 3y = -6
O 2x + 3y = 6
O y=-{x-2
O y=x-2
5-4-3-2 12
1 2 3 4 5
x
2
-3
The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex] and for line 2x + 3y = 6 will be,[tex]\rm y = \frac{-2}{3}x+2[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
a) 2x + 3y = -6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2[/tex]
To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.
b) 2x + 3y = 6
The line in which the standard form is found as;
Ax + By + C = 0
The typical form of a slope intercept is
y = mx+c
where m denotes the slope and b the line's y-intercept.
[tex]\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2[/tex]
Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex]
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What is the equation of the graphed line written in standard form?
2x + 3y = -6, 2x + 3y = 6
Summary:
a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.
b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.
Factor out the GCF from the given polynomial.
14x-2
Answer:
2(7x-1)
Step-by-step explanation:
14 & 2 gcf 2 factor and wal lah!
What is the value of
(1/8)^-1/3
PLEASE I NEED THE AWNSER QUICK PLEASE AND TY
Answer:
2.66666666667
Step-by-step explanation:
(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.
9.80 x 10^-3 + 1.60 x 10^-4
Answer:
0.00016098
Step-by-step explanation:
First multiply 9.8 by 10^-3 which equals 0.0098
Then add 0.0098 to 1.6 which equals 1.6098
Then multiply 1.6098 by 10^-4 which equals 0.00016098
Therefore, 0.00016098 is your answer
vertex of y = −2(x−4)2 + 3
and identify it as a minimum or a maximum.
An equation is formed of two equal expressions. The vertex of the equation y=-2(x-4)²+3 will lie at (4,3).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
If we plot the graph of y=-2(x-4)²+3, then the vertex of the graph will lie at (4,3).
Hence, the vertex of the equation y=-2(x-4)²+3 will lie at (4,3).
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please help will give branliest
This proof was correctly started by both eric and maggie.
The next step in the proof is to set the right side of the equations equal.
This would be done by the transitive property of equality.
What is a Mathematical Proof?This refers to the use of inference to make an argument to show the logical conclusion to a set of assumptions.
Based on the given diagram that shows Triangle XYZ and the mathematical proof that both Eric and Maggie are trying to prove, they both give the correct proof and the next step was to make the right side of the equations equal.
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Answer:
1: both
2: set the right side
3: transitive property
Step-by-step explanation:
got it right on plato :)
What is the solution to the trigonometric inequality sin^2(x) > cos(x) over the interval 0<= x <= 2pi radians?
The solutions to the trigonometric inequality in the interval is given by:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex], or [tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
What is the trigonometric inequality?It is given by:
[tex]\sin^{2}{x} > \cos{x}[/tex]
We have the following identity:
[tex]\sin^2{x} = 2\sin{x}\cos{x}[/tex]
Hence:
[tex]2\sin{x}\cos{x} > \cos{x}[/tex]
[tex]2\sin{x} > 1[/tex]
[tex]\sin{x} > \frac{1}{2}[/tex]
Between the first and second quadrant, the solution is:
[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex]
Between the third and fourth quadrants, the solution is:
[tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]
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Which graph represents f(x)= | x+3|
The graph of the function looks like V. And the vertex of the function will be at (-3, 0).
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = |x + 3|
Then the graph of the function looks like V. And the vertex of the function will be at (-3, 0).
The graph of the function is given below.
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even numbers less than 9
Answer:
2, 4, 6, 8
Step-by-step explanation:
even numbers are numbers that can be equally split in half.
Example:
2 ⇒ 1 - 14 ⇒ 2 - 26 ⇒ 3 - 38 ⇒ 4 - 4Slopes of parallel \perpendicular lines
Hello, the answer should be [tex]m=\frac{6}{5}= 1,2[/tex].
First, let's edit the given function as [tex]y[/tex] parameter leave alone.
[tex]15x+18y=270\\\\18y=270-15x\\\\y=\frac{270-15x}{18}\\ \\y=\frac{270}{18}-\frac{15x}{18}[/tex]
IMPORTANT!If the given equation looks like;
[tex]y=f(x)\\\\y=ax+b[/tex]
then, the slope of the equation is the coefficient of [tex]x[/tex] parameter ([tex]a[/tex])
The slope(m);
[tex]m=\frac{-15}{18}=\frac{-5}{6}[/tex]
The product of the slopes of two perpendicular lines must be [tex]-1[/tex]. By that way, the slope of a line perpendicular to the given line is below:
[tex]m_{expected}=\frac{-1}{m_{given}} \\\\m_{expected}=\frac{-1}{\frac{-5}{6} }=\frac{6}{5}[/tex]
Good luck. If you have any questions, then feel free to ask in comments!
Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram.
Circle C and P overlap. Circle C contains 10, circle P contains 8, and the intersection contains 4. Number 3 is outside of the circles.
Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie?
The probability that a customer likes cake and pie is 0.16.
What is the probability?Probability is used to determine the odd that a random event would happen. The odds that the event happens usually lie between 0 and 1.
The probability that a customer likes cake and pie = total number of customers who like cake and pie / total number of customers
4/25 = 0.16
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find the solution set. 7x^2-5x-2=0
Answer:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
, we get that
x
=
−
2
,
0.6
Explanation:
Rearrange the equation so that it becomes:
5
x
2
+
7
x
−
6
=
0
The quadratic formula is:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
In our equation above,
a
=
5
b
=
7
c
=
−
6
Plugging these values into the quadratic equation gives:
x
=
−
7
±
√
7
2
−
4
(
5
)
(
−
6
)
2
(
5
)
x
=
−
7
±
√
49
+
120
10
x
=
−
7
±
√
169
10
x
=
−
7
±
13
10
x
=
−
2
,
0.6
what is a conditional statement that correctly and accurately represents the statement all people who vote in US elections must be 18 or older
A conditional statement to demonstrate the situation presented would be: If a person can vote -> Then they are over 18 years old. An alternative to this would be: If a person is 18 years or older -> Then they can vote in the United States elections.
What is a conditional statement?A conditional statement is a type of structure to express the relationship between two dependent variables. Its structure is as follows:
If P, then Q...
According to the above, two conditional statements about voting in the United States would be:
If a person can vote -> Then he is over 18 years old. If a person is 18 years old or older -> Then they can vote in the United States elections.Learn more about conditional statement in: https://brainly.com/question/18152035
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write down the equation for the following expression and then solve it.
The product of 3 and 4 less than a number is 12.
Answer:
x = 24
Step-by-step explanation:
x - (3 · 4) = 12
x - 12 = 12
+ 12 + 12
x = 24
Please answer correctly!
Answer:
I. Evaluate the largest angle when x = 15
Explanation:
First, solve for x:
x + 8x + x + 30 = 180
10x = 180 - 30
10x = 150
x = 15
Here in the question, his friend wants to find the largest angle in triangle.
So, input x = 15 in the largest angle.
Which is, 8x = 8(15) = 120° <--- largest angle in the triangle.
1. IDENTIFY THE DIFFERENT PARTS OF THE THERMOMETER 100 20 10 30 AN 000
How many hours must Miguel worked to receive $10,000 in total pay?
Using the linear equation, Miguel must work for 160 hours to receive $10,000 in total pay
Complete Question:Miguel works as a technician in a company. If his hourly rate and flat pay are $50 and $2000, how many hours must Miguel worked to receive $10,000 in total pay?
How to determine the number of hours?Let the number of hours be x and the total pay be y.
The equation that represents the total pay is represented as:
y = Rate * x + Base pay
From the question, we have:
Base pay = 2000
rate = 50.
So, we have:
10000 = 50 * x + 2000
Subtract 2000 from both sides
8000 = 50x
Divide both sides by 50
x = 160
Hence, Miguel must work for 160 hours
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Find the value of cos (2pie/3)
Answer:
-1/2 or - 0.5
Step-by-step explanation:
[tex]cos (\frac{2\pi }{3}) = cos 120^{o} = -\frac{1}{2}[/tex]
A grocery wants to make two kinds of coffee. One consoles for $1.40 pound, and the other cells for $2.95 a pound. He wants to makes a total of 21 pounds and sell it for $2.60 per pound. How many pounds of each kind should he use in the new mix? (round off the answers to the nearest hundredth)
Step-by-step explanation:
a lot of typos in the problem description.
I assume the price of the mix is 1:1 related to the prices of the individual types of coffee.
so, from what I understood we can define
x = pounds of the first type of coffee.
y = pounds of the second type of coffee.
x + y = 21 pounds
1.4x + 2.95y = 2.6(x + y) = 2.6×21 = $54.60
in the second equation we have to bring the given "$2.60 per pound" to the total price, which is $2.60 times the total amount of pounds (which is 21).
from the first equation we get
x = 21 - y
and that we use in the second equation
1.4×(21 - y) + 2.95y = 54.6
29.4 - 1.4y + 2.95y = 54.6
1.55y = 25.2
y = 25.2 / 1.55 = 16.25806452... ≈ 16.26 pounds
x = 21 - y = 4.741935484... ≈ 4.74 pounds
so, he should mix 4.74 pounds of the first (cheaper) type and 16.26 pounds of the second (expensive) type.
In a school,The ratio of the number of boys to the number of girls is 8:5. One quarter of the boys and 1/15 of the girls wear glasses. When another 48 students who wear glasses join the school,the total number of students becomes 216. How many boys wore glasses at first?
Answer:
hi look here https://www.louisianabelieves.com/docs/default-source/assessment/grade-6-answer-key.pdf?sfvrsn=293b981f_2
Step-by-step explanation:
Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?
A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).
The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.
What do these functions have in common?
Here we have the functions:
[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]
f(x) is quadratic, and g(x) is exponential.
Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards. So first and second options are false.
Also, g(x) never intersects the x-axis, so third option is false.
Finally, the y-intercepts of the given functions are:
[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]
So the y-intercepts are equal, meaning that the correct option is D.
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Answer:
Both f(x) and g(x) have the same y-intercept of (0, 1).
Step-by-step explanation:
I got it right on the test.
What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?
The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
How to determine the equation of the directrix?The parabola equation is given as:
[tex]\frac 14(y + 3) = (x -2)^2[/tex]
A parabola is represented as:
[tex]4p(y - k) =(x -h)^2[/tex]
By comparing both equations, we have:
4p = 1/4 ==> p = 1/16
-k= 3 ==> k = -3
The directrix is represented as:
y = k - p
So, we have:
[tex]y = -3 - \frac 1{16}[/tex]
Take the LCM
[tex]y = \frac {-16 * 3- 1}{16}[/tex]
Evaluate
[tex]y = \frac {-49}{16}[/tex]
Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
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Find slope and intercept of the line 3x - 2y - 7 = 0
The slope and intercept of the line 3x - 2y - 7 = 0 are -1.5 and -3.5 respectively
How to determine the slope and the intercept?The equation of the line is given as:
3x- 2y - 7 = 0
Add 7 to both sides
3x - 2y = 7
Subtract 3x from both sides
-2y = -3x + 7
Divide both sides by -2
y = -1.5x -3.5
A linear equation is represented as:
y = mx + c
Where m represents slope and c represents the intercept
By comparison;
m = -1.5 and c = -3.5
Hence, the slope and intercept of the line 3x - 2y - 7 = 0 are -1.5 and -3.5 respectively
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Drag the tiles to the correct boxes to complete the pairs.
Match the systems of equations with their solution sets.
y + 12 = 1² + s
s+y = 3
y - 17 = 12 -9r
- + y = 1
Solution Set
(2,3) and (8,9)
(-2,3) and (7-6)
(-2,5) and (3,-5)
(-5,8) and (3,0)
y-15 = -12 + 4s
=+y=1
y + 5 = 1²-3r
2s + y = 1
Linear-Quadratic System of Equations
Answer:
y+12=1+s = (-5,8)(3,0)
y-17=12-9r = (2,3)(8,9)
y-15=-12+4x = (-2,3)(7,-6)
y+5=x-3x = (-2,5)(3,-5)
If I have $1,050 dollars, and I want to buy something 6 times for $45 dollars, how much times can I buy it until I run out of money?
Answer:
140
Step-by-step explanation:
here,
You have 1050
now
$1050(45×6)
=140 items
I need help to find the coordinates
Dean Field is a bookkeeper for a retail shop. He is super excited about his upcoming two-week vacation to Hawaii. His flight leaves to Honolulu at 7pm on Friday. At 4:45pm on Friday he realizes the company’s trial balance is a mess and it does not balance. He places random numbers in the General Ledger system to make it balance and leaves the office to catch his flight. He knows he can correct the situation when he returns from his vacation. What are your thoughts about this case?
The fact that Dean Field places random numbers in the general ledger system to make it balance and leaves the office to catch his flight is wrong.
What is a ledger?It should be noted that a ledger simply means a record of the balance of each of the accounts of a business.
In this case, when he realizes the company’s trial balance is a mess and it does not balance, he should have waited and ensured that he re calculated it and made it balance.
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39. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 5 exterior angles and equate to 360
5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is
23x + 15 = 360 ( subtract 15 from both sides )
23x = 345 ( divide both sides by 23 )
x = 15