The figure below shows parallel lines cut by a transversal:
A pair of parallel lines is shown, cut by a transversal.
Which statement is true about ∠7 and ∠8?
Answers
For the given parallel ines cut by a transversal line the correct statement is (4). ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.
What types of angles are formed when a transversal cuts paralle lines?The intersections of two parallel lines formed by a transversal form several angles. These are referred to as transversal angles. Here are some examples of transversal angles:
Corresponding anglesAlternate Interior AnglesAlternate Exterior AnglesCo-interior AnglesAngles are said to be supplementary to each other when two adjacent angles are formed at a point on a line so that the sum of their measures is 180°.
∠7 and ∠8 are supplementary in the attached figure since they represent a pair of adjacent angles which constitute a straight line.
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The correct question:
Please Help! The figure below shows parallel lines cut by a transversal:
Which statement is true about ∠7 and ∠8?
1. ∠7 and ∠8 are supplementary because they are a pair of corresponding angles.
2. ∠7 and ∠8 are complementary because they are a pair of adjacent angles on a straight line.
3. ∠7 and ∠8 are congruent because they are a pair of adjacent angles on a straight line.
4. ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.
Related Questions
Is the following relation linear, quadratic, or cubic? If it is linear, find the equation. Explain your reasoning and include all of your work in your final answer.
p = {( x, y ) : (1, 0), (2, 4), (3, 8), (4, 12), . . . }
Answers
Since the rate of change is constant, the relation is linear, and is modeled by:
y = 4x - 4.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that when x changes by 1, y always changes by 4, hence we have a linear relation with a slope of 4, given as follows:
y = 4x + b
When x = 1, y = 0, hence we use it to find b as follows:
0 = 4 + b
b = -4.
Hence the relation is:
y = 4x - 4.
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Black or Orange? There are 46 children going to a party. 18 will wear black costumes, 12 will wear orange costumes and some will wear both black and orange. Half of the guests will go in costumes that are neither black nor orange. How many children will wear both orange and black?
Answers
The number of children wearing both black and orange costumes is 7.
Let P denote the universal set, the number of children going to a party.
Then n(P) = 46
Let B denote the number of children wearing black costumes to the party.
Then n(B) = 18
Let O denote the number of children wearing orange costumes to the party.
Then n(O) = 12
We are asked to find how many children will wear both orange and black. That is to find n(B ∩ O).
We are also given that half of the guests are wearing costumes that are neither black nor orange.
Then n(B ∪ O)' = n(P)/2 = 46/2 = 23, where n(B U O)' denotes the complement of n(B U O).
We also know that n(B ∪ O) = n(P) - n(B U O)' = 46 - 23 = 23
⇒ n(B U O) = n(B) + n(O) - n(B ∩ O)
⇒ 23 = 18 + 12 - n(B ∩ O)
⇒ 23 = 30 - n(B ∩ O)
⇒ n(B ∩ O) = 30 - 23 = 7
⇒ n(B ∩ O) = 7.
Therefore, the number of children wearing both black and orange costumes is 7.
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1/2 of the candles on Claire's birthday cake are pink. 2/10 of the candles are green. The rest are red. What fraction of the candles is red?
Answers
Answer:
Step-by-step explanation:
10 would be the total, since 2/10 are green. 1/2 of 10 is 5, so 5 candles are pink. 5+2=7. 10-7=red candles (3), there is ultimately 3 candles that are red.
What is the reciprocal of the divisor 5 1/5 divided by 1/10
Answers
The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.
The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.
The reciprocal of the divisor 5 1/5 divided by 1/10
To the reciprocal of the divisor.
Equation: 5 1/5 divided by 1/10
1st: Flip the 1/10 to become 10/1
2nd: Change division to multiplication
New equation: 5.1/5.10/1
⇒ 50/5
⇒ 10.
The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.
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After examining the functions f(x)
ove
In(x + 2) and g(x) = et-1,
the interval (-2,3], Lexi determined that the correct number of
solutions to the equation f(x) = g(x) is
(1) 1
(3) 3
(2) 2
(4) 0
Answers
The number of f(x) = g(x) solutions is an option (2) The right answer is 2, thus.
What exactly is a function graph?A graph is a diagram or visual representation that organizes the presentation of facts or values. The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph.
For the predicament,
f(x) = In(x + 2) and g(x) = e(x - 1) throughout the range [(-2,3].
In the graph below,
plot the two functions f(x) and g(x).
These two functions cross at two locations in the range [(-2,3]).
The function's solution is revealed at the intersection point.
Consequently, we might say that the number of solutions.
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-1.4,1 1/25,1.25 least to greatest
Answers
Answer: -1.4,1 1/25,1.25
Step-by-step explanation:
-1.4,1 1/25,1.25
1 1/25=
1+0.04=1.04
Order: -1.4, 1.04, 1.25 ==> -1.4,1 1/25,1.25
Without solving, determine whether the solution of 1/3x=21 is
greater than
or less than 21. Explain.
Answers
is the value of the digit 5 in 0.5is 1/10 times as much as the value in 0.05
Answers
Answer:
No
Step-by-step explanation:
1/10 = 0.1
0.05 x 0.1 = 0.005
Eve bought 28.37 pounds of peanuts and 30.36 pounds of raisins. How many pounds of snacks did she buy in all?
Answers
Answer:58.73
Step-by-step explanation:
28.37+30.36=58.73
Solve the formula for the variable c.
x/a=b/c
Answers
Answer:
(d) c = ab/x
Step-by-step explanation:
You want to solve the proportion x/a = b/c for the variable c.
SolutionThe usual method recommended for solving almost any kind of proportion is to first clear the fractions. You do this by multiplying both sides by the product of the denominators. This has the appearance of "cross multiplication."
[tex]\dfrac{x}{a}=\dfrac{b}{c}\qquad\text{given}\\\\\\\dfrac{x}{a}\cdot ac=\dfrac{b}{c}\cdot ac\qquad\text{multiply by $ac$}\\\\xc=ba\qquad\text{simplify; each numerator times the opposite denominator}[/tex]
At this point, it is a "one-step" linear equation in c, so is solved by dividing by the coefficient of c, which is x.
[tex]\dfrac{xc}{x}=\dfrac{ab}{x}\\\\\boxed{c=\dfrac{ab}{x}}[/tex]
∠A and \angle B∠B are vertical angles. If m\angle A=(7x+26)^{\circ}∠A=(7x+26)
∘
and m\angle B=(4x+29)^{\circ}∠B=(4x+29)
∘
, then find the value of x.
Answers
Because the angles are vertical angles, the value of x is 1
How to determine the value of x?The angles are given as
A = 7x + 26
B = 4x + 29
The angles are vertical angles
So, we have
A = B
This gives
7x + 26 = 4x + 29
Evaluate the like terms
3x = 3
Divide by 3
x = 1
Hence, the value of x is 1
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The length of a rectangle is 2 times its width.
The area of the rectangle is 32 in.². What is
the length of the rectangle?
Answers
Pa answer please, need lang for grade 11 students
Answers
Juan is paid 1575 pesos, 1800 pesos, 2137.5 pesos
It is given that Juan Dela Cruz is paid 45 peso for every hour he works for up to 40 hours and 1.5 times i.e. 67.5 pesos for every hour after 40 hours.
The first part asks for Juan's earning if he works 35 hours
Therefore , according to the function,
Juan's pay = 35 x 45 = 1575 pesos
The second part asks for Juan's earning for 40 hours
Therefore, according to the function,
Juan's pay for 40 hours = 40 x 45 =1800 pesos
The third part asks for Juan's earning for 45 hours
Juan's pay for 45 hours according to the function=
67.5h-900 = 67.5 x 45 -900 = 2137.5 pesos
Hence, Juan is paid 1575 pesos, 1800 pesos, 2137.5 pesos
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Locate the value of the constant π on a number line using rational numbers.
Answers
The value of the constant π is located between 3 and 4 on a number line
How to locate the value of the constant π on a number line using rational numbers?The value is given as
Value = π
As a general rule, the value of π is
π = 22/7
So, we have
Value = 22/7
Evaluate the quotient of 22/7
So, we have
Value = 3.143
The number 3.143 is greater than 3 but less than 4
This means that, 3.143 is between 3 and 4
In other words, the value of the constant π is located between 3 and 4 on a number line
Hence, the value of the constant π is located between 3 and 4 on a number line
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The point (-3,-5) is on the graph of a function. Which equation mus O f(-3) -5 f(-3,-5) = -8 O f(-5) = -3 f(-5, -3) = -2
Answers
So the correct answer is a. f(-3)=-5.
Solution :
Cartesian coordinate system
A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
Cartesian Plane:
A plane consists of axes and quadrants. Thus, we call the plane the Cartesian Plane, or the Coordinate Plane, or the x-y plane. The axes are called the coordinate axes.
Abscissa and Ordinate
The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis and it is known as Abscissa.
The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis and it is known as the Ordinate.
So,
the point (-3, -5) corresponds to the graph of the function.
A point on a graph in the Cartesian coordinate system then that point consists of coordinates (x, y).
In, y=f(x) and x so (x, f(x))
x is a x-coordinate and y=f(x) is y-coordinate.
So if we have a point (-3, -5) the corresponding coordinates are x=-3 and
y=f(x)=-5. So it must be true that y=f(-3)=-5.
So the correct answer is a. f(-3)=-5.
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0.000345 standard form
Answers
Answer:
0.000345 in standard form would be:
3.45 times 10 to the -4 power
Step-by-step explanation:
The number tells use that we have to divide by 10 and we are working with a negativenumber equal to the power of 4.
Answer:
3.45 × 10^-4
Step-by-step explanation:
Move from the decimal point till you you get to after the first number.
Then you put the decimal point there and because it's starts with 0. i.e it is not up to one
You put minus in front of it when raising it to the power of 10
A(5,0) and B(0,8)are two vertices of triangle OAB.
What is the equation of the bisector of angle 0AB
If E is the point of intersection of this bisector
and the line through A and B, find the co-ordinate:
of E. Hence show that OA:OB= AE:EB
Answers
The equation of the bisector of angle OAB is y=x
If E is the point of intersection of this bisector and line through A and B then the co-ordinates of E is (40/3,40/3)
Since E is the point of intersection of the bisector of angle OAB and line A and B hence we can say OA:OB=AE:EB
Since point O is the origin hence we can say the co-ordinates of point O are (0,0) and the angle bisector of the angle OAB makes and angle of 45 degree from x axis, So by the formula of Line passing through origin (y= mx )
where ,
∅=angle made by the bisector the angle OAB to the x axis(i.e. 45 degree)
m=tan∅
now using substitution method ,
m=tan45
m=1
the equation of the bisector of angle OAB is y=x
Now, the equation of the line passing through point A(5,0) and point B(0,8) by formula,
(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)
here , y1=0, x1=5, y2=8, x2=0
again by substitution method,
(y-0)={(8-0)/(0-5)}*(x-5)
y={8/-5}*(x-5)
8x - 5y = 40
point E is the intersection of 8x - 5y = 40 and y=x the solving these two equations by substitution method we get;
x=40/3
y=40/3
the co-ordinates of point E are (40/3,40/3)
E is the intersection point of the bisector of the angle OAB and the line through point A and B ,
on comparing triangle OEA and triangle OEB we can say that,
OA:OB= AE:EB
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Lynn wants to multiply
44
×
305
. She says that all she has to do is find
4
×
305
and then double that number.
Which explains whether or not Lynn's method will give her the correct answer?
Answers
Statement (C) "Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 8, not by 44" is the correct explanation of the above-given situation.
What are mathematical operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.So, 4 × 305 = 1220
Double of 1220: 1220 + 1220 = 2440Which is equal to: 8 × 305 = 2440and not equal to 44 × 305 = 13420Therefore, statement (C) "Lynn's method will not yield the correct result. Multiplying by 4 and then doubling the result is equivalent to multiplying by 8, not 44 "is the correct explanation for the situation described above.
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The complete question is given below:
Lynn wants to multiply 44 × 305 44×305. She says that all she has to do is find 4 × 305 4×305 and then double that number. Which explains whether or not Lynn's method will give her the correct answer?
A. Lynn's method will give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 44.
B. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 6, not by 44.
C. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 8, not by 44.
D. Lynn's method will not give her the correct answer. Multiplying by 4 and then doubling the product is the same as multiplying by 16, not by 44.
A rental car company charges $53.46 per day to rent a car and $0.13 for every mile driven. Mei Mei wants to rent a car, knowing that:
She plans to drive 350 miles.
She has at most $260 to spend.
Which inequality can be used to determine dd, the maximum number of days Mei Mei can afford to rent for while staying within her budget?
Answers
The correct inequality will be 53.46d + 45.5 ≤ 260
What does a math inequality look like?
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Given That:
She plan to drive 350 miles and each mile cost $0.13 which is total $45.5
and she have to pay $53.46 for each day
So the correct inequality will be 53.46d + 45.5 ≤ 260
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Tv sells at 60 percent off retail what percent is wholesale price
Answers
The wholesale price of the TV will be 0.40 x where x represents the retail price.
Percentage :
In mathematics, it is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Let the retail price of TV be x
Now, we are given that it is sold off at 60 percent discount.
Whole sale price = x - 60 % of x
Whole sale price = x - 60 / 100 x
Whole sale price = x - 0.60 x
Whole sale price = 0.40 x.
Therefore, the wholesale price of the TV will be 0.40 x where x represents the retail price of the TV.
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Find the value of x. Round the length to the nearest tenth.
Answers
Answer:
done it step by step
Step-by-step explanation:
The cost of 6 gallons of gas at one gas station costs Julian $13.50. The cost of 8 gallons of gas at a different gas station cost Dorian
$18.80.
Answers
Answer:
$5.30 for two gallons
Step-by-step explanation:
Challenge Yossi used to have a square garage with 230 ft2 of floor space. He recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
Answers
with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.
We are given that Yossi has a garage of area = 230 feet²
We know that area of square is:
A = side²
230 = s²
s = √ 230
s = 15.17 feet
Now area is increased by 50 %
New area = 230 + 50% of 230
A' = 230 + 115
A' = 345 feet²
s² = 345
s = √ 345
s = 18.57 feet
Percent increase in length = 18.57 - 15.17 / 15.17 × 100
Percent increase in length = 22.41 %
Therefore, with the original length as 15.17 feet and the new length as 18.57 feet, there is an increase of 22.41 % in the length of the garage.
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Solve the following inequality algebraically. |x−5∣>10
Answers
Answer:
The answer to the inequality is
x < -5
x > 15
Are test scores a good predictor of the overall grade for a course? A random sample of student grades in an
introductory statistics class was taken. The data are shown.
Test 54 56 36 87 71 69 61 38 72 40
Final 60 60 29 94 76 80 54 26 77 52
The two variables have summary statistics -58.4, -60.8, s. 16.87 and s, -21.89. The formula for the
contribution tor for the first data point is (frac{x (1)-\bar(x)}{s_{x}}) (\frac{y_{1)-\bar(y)s (yl) The value for
y, is
X
Answers
The contribution of the first data point, (54, 60) to correlation is given by the option with the equation equation;
[tex] \displaystyle{\left( \frac{54 - 58.4 }{16.87}\right)\cdot \left( \frac{60 - 60.8}{21.89 }\right)}[/tex]What is the formula the correlation coefficient?The correlation coefficient is given by the formula;
[tex]r = \frac{1}{n - 1} \times \sum( \frac{x - \bar{x}}{s_{x} })( \frac{y - \bar{y}}{s_{y} })[/tex]
Where;
(x, y) are the coordinates of a data point.
[tex] \bar{x}[/tex] = The mean for the x-values
[tex]S_{x}[/tex] = The standard deviation of the x-values
[tex] \bar{y}[/tex] = The mean of the y-values
[tex]S_{y}[/tex] = The standard deviation of the y-values
The given parameters are;
[tex] \bar{x}[/tex] = 58.4
[tex]S_{x}[/tex] = 16.87
[tex] \bar{y}[/tex] = 60.8
[tex]S_{y}[/tex] = 21.89
The formula for the contribution of the first data point, (54, 60) to correlation, r, is therefore;
[tex] \displaystyle{\left( \frac{54 - 58.4 }{16.87}\right)\cdot \left( \frac{60 - 60.8}{21.89 }\right)}[/tex]
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Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'.
Question 1 options:
(14,3)
(9,3)
(-6,10)
(-8,6)
(-6,2)
Answers
The correct options are (a) , (14,3) , (d), (-8,6) and (e) , (-6,2)
By concept of translation, the coordinates of new triangle A'B'C' are given as follows:
A' (14, 3), B' (-6,2), C (-8, 6).
What is a translation?A translation can be define or represented by a change in the graph of a function, which are done by the means of operations such as multiplication, addition or subtraction either in it’s range(i.e. the values of y) or in it’s domain(i.e. the values of x). Examples are compression of points or shifting left right or bottom up, stretching and reflections over the axis that is the x-axis or the y-axis, or rotations around the origin.
For the given question, the translation rule is given as follows:
(x , y) -> (2x, y-3).
Applying the rule to each point of triangle, we have that:
A': (2(7), 6-3) = (14, 3).
B': (2(-3), 5-3) = (-6, 2).
C': (2(-4), 9-3) = (-8, 6).
Thus, the coordinates of triangle formed i.e. A'B'C' are given as follows:
A' (14, 3), B' (-6,2), C' (-8, 6).
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The complete question is:
Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'.
Question 1 options:
a. (14,3)
b. (9,3)
c. (-6,10)
d. (-8,6)
e. (-6,2)
The triangle has side lengths l,m, and n. Find the length of each side and the perimeter of the triangle. (PLEASE SHOW WORK)
Answers
The measure of the sides is 27, 23 and 16 and the perimeter is 56 respectively
The perimeter of a triangleThe triangle is a 2 dimensional shape that has 2 sides.
Given the following sides
l = m + n - 12
n = m - 7
m = l - 1/4n
l = m + 1/4n
Substitute
m + 1/4n = m + m - 7 - 12
m + 1/4(m-7) = 2m - 19
m + 1/4m - 7/4 = 2m - 19
-m + 1/4m = -19 + 7/4
-3/4m = -19(4)+7/4
-3/4m = -69/4
-3m = -69
m = 23
Hence the value of m from the given expression is 23
n = 23 - 7
n = 16
l = 23 + 16 -12
l = 39 - 12
l = 27
n = 23 - 7
n = 16
Hence the measure of the sides is 27, 23 and 16 respectively
Perimeter = 27+23+16
Perimeter = 56
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Which model shows the sum of 0.19 and 0.8?
Answers
Explanation: it’s obvious
15 points for the answer.
3^x=27÷x+3x
Answers
Answer:
x = 2.638
Step-by-step explanation:
Answer
Unless you need a different version of this answer?
Step-by-step explanation:
(27in(3)
x=___4_______ True
In(3)
An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $190 and the lower-priced speaker dock sells for $80. Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $3,870. How many lower-priced speaker docks did it sell?
Answers
Using a system of equations, it is found that it sold 27 lower-priced speaker docks.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Amount of the lower-priced speaker sold.Variable y: Amount of the higher-priced speaker sold.Last week the store sold three times as many lower-priced speaker docks as higher-priced speaker docks, hence:
x = 3y -> y = x/3.
Combined sales totaled $3,870, hence, considering the price of each speaker:
80x + 190y = 3870.
Since x = 3y:
240y + 190y = 3870.
430y = 3870
y = 3870/430
y = 9.
Hence:
x = 3y = 3 x 9 = 27.
It sold 27 lower-priced speaker docks.
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