Answers
The value of x is 20°
According to the question we have been given two parallel lines which is cut by a transversal line. There are total 8 angles and given is the measure of
∠4 = 5x + 35° and ∠7 = 45°.
We need to find the value of x.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
Now using these rules we will solve this problem
Because of corresponding angles , ∠3 = ∠7 = 45°
Also ∠3 and ∠8 make a linear pair and sum of linear pair is 180°.
Therefore , ∠3 + ∠8 = 180°
45° + 5x + 35° = 180°
5x = 180° - 80°
x = 20°
Hence the value of x is 20°
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Related Questions
Edna has spent her whole life traveling. she has been to 4 different continents and to 11 countries on each continent. round to the leading digit to determine approximately how many countries edna has visited.
Answers
Edna has visited 44 countries.
For given question,
Edna has spent her whole life traveling. she has been to 4 different continents and to 11 countries on each continent.
Here each continent has 11 countries.
She visited 4 different continents.
So, the total number of countries she has visited would be given by an expression,
11 × 4
We solve above expression to determine how many countries Edna has visited.
11 × 4 = 44
Therefore, approximately 44 countries Edna has visited.
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a turn consists of rolling a standard die and tossing a fair coin. the game is won when the die shows a $1$ or a $6$ and the coin shows heads. what is the probability the game will be won before the fourth turn? express your answer as a common fraction.
Answers
The probability that the game will be won before the fourth turn is [tex]\frac{91}{216}[/tex].
What is probability?Probability refers to the possibility of the occurrence of an event.
P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]
Now,
Probability of winning the game in first turn = [tex]\frac{1}{3}\frac{1}{2}=\frac{1}{6}[/tex]
Probability of losing the first game but winning the second one = [tex]\frac{5}{6}\frac{1}{6} = \frac{5}{36}[/tex]
Probability of losing the first two games but winning the third one = [tex]\frac{5}{6}(\frac{5}{6})\frac{1}{6} = \frac{25}{216}[/tex]
Thus, the probability of winning the game before fourth turn = [tex]\frac{1}{6}+\frac{5}{36}+\frac{25}{216}=\frac{91}{216}[/tex]
Hence, The probability that the game will be won before the fourth turn is [tex]\frac{91}{216}[/tex].
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When some software companies develop software, they do it with "planned obsolescence"
in mind. This means that they plan on the sale of the software to rise, hit a point of
maximum sales, then drop and eventually stop when they release a newer version of the
software. Suppose a graph of the curve showing the number of sales over time can be
modeled with a parabola and that the company plans on the "life span" of its product to be
6 months, with maximum sales reaching 1.5 million units. Write an equation that models
this situation.
Answers
The equation of the parabola that models the given situation is y = [tex]\frac{-1}{6}(x-3)^{2}[/tex] + 1.5.
Define parabola and its types.A parabola is a roughly U-shaped mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions that all define the same curves.
To represent a parabola algebraically in the coordinate plane, the standard equation of a parabola is used. The general equation of the parabola is given by y = [tex]a(x-h)^{2}[/tex]+ k or x = [tex]a(y-k)^2[/tex] +h, where (h,k) denotes the vertex. A regular parabola's standard equation is [tex]y^2[/tex] = 4ax.
Now, the equation of parabola for the given situation is calculated as:
y = [tex]a(x-3)^2[/tex]+ 1.5
Now, put the value of x = 0 and y = 0.
0 = [tex]a(0-3)^2[/tex]+ 1.5
0 = 9a + 1.5
-9a = 1.5
a = - 1.5/9
a = -1/6
Now, put the value of a in equation y = [tex]a(x-3)^2[/tex]+ 1.5 to obtain:
y = [tex]\frac{-1}{6}(x-3)^{2}[/tex] + 1.5.
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evaluate the expression if a=3/4, b=-8, c=-2, d=3, and g=1/3
Answers
pick a symbol that goes in the blank (pls answer asap i will give brainliest)
3 -1 ___ 1/4
=
<
>
Answers
Answer:
>
Step-by-step explanation:
2 of course greater than quarter
Answer:
Step-by-step explanation:
goo ba i think its gobba
Write a subtraction sentence where the difference is positive use a positive and a negative interference
Answers
The subtraction sentence where the difference is positive which uses a positive and negative integer are written as 5 - (-3) =8.
Integers are all real , rational numbers except the decimals and fractions. There are 3 types of integers : positive negative and zero integers.
Integers include zero, a positive natural number, and a negative integer represented by a minus sign. The negative numbers are the inverse additions of the comparable positive numbers.
There are two cases;
Case 1;
when modulus of positive integer ≥ modulus of negative integer;
Example; 5 - (-3) = 5 + 3 = 8 (Here, |5| > |-3|)
Case 2;
when modulus of positive integer ≤ modulus of negative integer;
Example; 5 - (-10) = 5 + 10 = 15 (Here, |5| < |-10|)
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Determine the domain of the following graph
Answers
Answer:
5555555555555555555555555555
pay a $12 set up fee for club T-shirts plus $5 per shirt.
The math club had to
Formulate an equation. Let s represent the number of t-shirts and C the cost.
Answers
Answer:
Step-by-step explanation:
c=12+5t?
A cylinder has a radius of 5 centimeters and a height of 8 centimeters. Describe how the following change affects the volume of the cylinder.
d. The dimensions are exchanged.
Answers
Answer:
no d
Radius is changed
Step-by-step explanation:
TRUE OR FALSE? 0.75 is an irrational number
Answers
Answer:
FALSE
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
0.75 has a finite number of digits and can be expressed in a fraction of integers.
0.75=75/100
75/100=3/4
The graph of h is a translation 6 units down and 2 units left of the graph of f(x)=x^2−7x. For each value of x, g(x) is 115% of h(x). Write a rule for g
Answers
The rule for the function g(x) is:
g(x) = 1.15*(x^2 - 3x -16)
How to write a rule for the function g?
First we know that the function f(x) is f(x) = x^2 - 7x
And we know that h(x) is a translation of 6 units down and 2 units to the left of f(x), then:
h(x) = f(x + 2) - 6
Now we know that g(x) is 115% of h(x), then we can write:
g(x) = 1.15*h(x)
Replacing h(x) by the rule above we get:
g(x) = 1.15*(f(x + 2) - 6)
Replacing the actual function there:
g(x) = 1.15*( (x + 2)^2 - 7*(x + 2) - 6)
g(x) = 1.15*( x^2 + 4x + 4 - 7x - 14 - 6)
g(x) = 1.15*(x^2 - 3x -16)
This is the rule for function g(x).
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Which description matches the graph of the inequality y > x + 4?
Answers
The graph of the inequality y > x + 4 matches the description in Option(c)
a shaded region above a dashed boundary line.
How to graph Linear Inequalities?A linear inequality is similar to a linear equation, but instead of a =, it will have an inequality sign like >,<, or ≤,≥.Place "y" on the left and the remaining variables on the right in the equation.Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>).Shade above the line in the graph for a "greater than" (y> or y≥)or below the line in the graph for a "less than" (y< or y≤).Given function: y > x + 4
Let's plot the graph of the given function and then match it with the options to see which is the solution.
So we will Plot y = x + 4 (as a dashed line because y > )
the coordinates will be,
x = 0 , y = 4
x = -1 , y = 3
x = -2 , y = 2
x = 1 , y = 5
x = 2 , y = 6
The purple shaded region satisfies the inequality y > x + 4.
Hence the graph description is a shaded region above a dashed boundary line.
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The complete question is: "Which description matches the graph of the inequality y > x + 4?
a) a shaded region above a solid boundary line
b) a shaded region below a solid boundary line
c) a shaded region above a dashed boundary line
d) a shaded region below a dashed boundary line."
Which equation describes the line with slope -2/3 that crosses the y-axis at the point (0, 4) ?
Answers
Answer:
In slope-intercept form:
[tex]y = - \frac{2}{3} x + 4[/tex]
In a zoo there are zebras and orangutans.
Altogether there are 36 heads and 100 feet.
How many zebras are there?
Answers
Answer:14 zebras 22 orangutans
Step-by-step explanation: 14x4=56 22x2=44 56+44=100
What is the image point of (-6, 1) after a translation left 2 units and down 3 units?
Answers
Answer:
it is either -8,4 or -4,4
Step-by-step explanation:
i think this is it
C. C. A different class is made up of 40â% women and has 20 women in it. What is the total number of students in theâ class?
Answers
Total number of students in a class is 50.
A class has 40% of women.
Total Number of women in a class = 20 equation 1
Let total number of students in a class = x
According to the question a class has 40% of women. Mathematically we can write it as,
Total Number of women in a class = 40 % of x
Total Number of women in a class = ( (40x) / 100 ) equation 2
On equating equation 1 and equation 2, we get
20 = ( (40x) / 100 )
⇒ 40x = 2000
⇒ x = 50
Total number of students in a class is 50.
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If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
Answers
The value of angle m< EBF is determined as 56⁰.
What is the sum of angles in a straight line?
The sum of angles in a straight line is 180 degrees. The value of angle EBF can be determine using the concept of sum of angles in a straight line as shown below.
m< EBC + m< ABE = 180
3y + 10 + 2y - 20 = 180
5y - 10 = 180
5y = 180 + 10
5y = 190
y = 190/5
y = 38
The value of m< EBF is calculated as follows;
Assuming equal division, m< EBF = m< ABE
m< EBF = 2y - 20
m< EBF = 2(38) - 20
m< EBF = 56⁰
Thus, the value of angle m< EBF is determined as 56⁰.
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8. Which number is a solution of the
inequality 8-b≥ 27?
A -76
B-80
(C) -86
D-140
Answers
Answer:
All of the options.
Step-by-step explanation:
We first subtract 8 from both sides. We now divide both sides by -1. However, something to keep in mind, is when you multiply/divide by a negative number, you just flip the sign. In this case, we need to divide both sides of the equation by -1, to get b and our answer. So now, we need to find an answer from our answer choices that is smaller than -19. I think all of them would be right in this case, as they fit the equation. So all of them should be right (: As if you plug in the values, you get answers that could be solutions to the equation!
I hope this helps, have a blessed day!
Jeffrey caught 8 worms in his backyard. 4 worms had a length of 3 inches. The other 4 worms were all the same size. The total length of all the worms combined is 32 inches. Which equation below represents the lengths of all the worms?
A 4x + 3x = 324x + 3x = 32
B 4(x + 3) = 324(x + 3) = 32
C 4x + 3 = 324x + 3 = 32
D 3(x + 4) = 32
Answers
Option (B) 4 ( x + 3 ) = 32 is the equation that represents the lengths of all the worms.
We are given that:
Jeffrey has 8 worms
The 4 worms in it has the length of 3 inches.
The expression would become:
Length = 4 × 3
Also, we are given that the rest 4 worms are of equal length.
Let that equal length be x
The expression becomes:
Length = 4 × x = 4 x
Also, we are given that the total length of the worms = 32 inches.
The equation becomes:
32 = 3 × 4 + 4 × x
4 ( x + 3 ) = 32
Therefore, option (B) 4 ( x + 3 ) = 32 is the equation that represents the lengths of all the worms.
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Round 0.687 to the nearest hundredth
Answers
Answer:
0.69
Step-by-step explanation:
The 8 is in the hundredths place.
0.687 becomes 0.680, but since the leftmost digit dropped is a 7, the 8 goes up 1 to 9.
Answer: 0.69
Answer:
0.69
Step-by-step explanation:
Help with problems 17 and 18 please and thank you
Answers
Answer: 17. Domain: x is all real numbers
Range: y>=0
18. r=2
Step-by-step explanation:
17. f(x)=|x-2|
|x-2|>=0
x-2>=0
x>=2
x-2=<0
x=<2
x can be less than, equal to, or greater than 2. Hence,
Domain: x is all real numbers
|x-2|>=0 ==> f(x)>=0
Hence, the range is:
Range: y>=0
18. m=(y2-y1)/(x2-x1)
2=(9-3)/(5-r)
2=6/(5-r)
2(5-r)=6
5-r=3
r=2
In am writing this because the app says the answer is to short :)))
Describe the meaning of a reflection. Select the two correct answers. A reflection can be done on a point, shape, or object. b A reflection is a perpendicular turn around a point. A reflection can change the measures of the angles of a figure. c A reflection flips a shape across a line. d A reflection changes the length of line segments.
Answers
Answer:
A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage.A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
Step-by-step explanation:
It took clare 100 minutes to walk the east side of garden at a constant speed. if the total distance of the east side is 2,500 feet, at what speed was she walking? feet per minute
Answers
Answer: 25 ft per min.
Step-by-step explanation:
Time= 100 min.
Distance= 2500 ft.
Speed= 2500/100 = 25 ft per min.
Which expression of signed decimal numbers has a positive quotient?
Group of answer choices:
2.5 divided by negative 9.56
Negative 1.7 divided by negative 10.06
Negative 9.34 divided by 0.55
Negative 0.3 divided by 9.44
Answers
The quotient of an expression of signs decimal numbers is positive:
= 0.16.
The correct option is B.
Briefing:There is one key notion when dividing any negative integer by another: the negative signs cancel out. This is unique to this situation. A positive number divided by such a negative number equals a negative number. As a result, you can't divide any two numbers as well as expect a positive result. In general, negative and positive numbers behave differently.
According to the given data:For
a. 2.5 / -9.56
dividing the numbers we get:
= -0.26
For
b. -1.7 / -10.06
dividing the numbers we get:
= 0.16
For
c. -0.3 / 9.44
dividing the numbers we get:
= -0.03
For
d. -9.34 / 0.55
dividing the numbers we get:
= -16.98
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I understand that the question you are looking for is:
Which expression of signed decimal numbers has a positive quotient?
a. 2.5 / -9.56
b. -1.7 / -10.06
c. -0.3 / 9.44
d. -9.34 / 0.55
At a sale, soccer cleats were sold for
$59.50. If the original price was :
$70, what
percentage of its original price were soccer
cleats sold for?
Answers
The percentage of its original price is -17.65%
How to determine the percentage of its original price?The given parameters are
Selling price = $59.50
Original price = $70
The percentage of the original price is calculated as
Percentage = (Selling price - Original price)/Original price * 100%
Substitute the known values in the above equation
So, we have
Percentage = (59.50 - 70)/59.50 * 100%
Evaluate the difference in the above equation
So, we have
Percentage = -10.5/59.50 * 100%
Evaluate the quotient in the above equation
So, we have
Percentage = -0.1765 * 100%
Evaluate the product in the above equation
So, we have
Percentage = -17.65%
Hence, the percentage of its original price is -17.65%
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washer and a dryer cost $618 combined. the washer costs $82 less than the dryer. what is the cost of the dryer?
Answers
Answer:
$227 = washing machine cost
$391 = dryer cost
Step-by-step explanation:
$618 divided by 2 = 309
309 - 82 = 227 = cost of washing machine
618 - 227 = 391 = cost of dryer
You can double-check by,
391 + 227
= 618
$227 = washing machine cost
$391 = dryer cost
Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
a. Prove that given a person's target heart rate, you can calculate his or her age using the formula a=220- T/0.75.
Answers
If the American Heart Association suggests a target heart rate of T=0.75(220-a), Proving that given a person's target heart rate, you can calculate his or her age using the formula a=220- /0.75. His/her age is 16 years.
Target heart ratea. Given:
T=0.75(220-a)
where
T =a person's target heart rate
a= his or her age
Prove:
Hence:
T=0.75(220-a)
T/0.75=220-a
T/0.75-220=a
-T/0.75+220=a
a=-T/0.75+220
a=220-T/0.75
b. How old is she:
a=220-T/0.75
where:
T=153
Substitution
a=220-153/0.75
a=220-204
a=16 years
Therefore proving that given a person's target heart rate, you can calculate his or her age using the formula a=220- /0.75. His/her age is 16 years.
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The complete question is:
Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
a. Prove that given a person's target heart rate, you can calculate his or her age using the formula a=220- T/0.75.
b. If Mai-Lin’s target heart rate is 153, then how old is she? What property justifies your calculation?
The graph of the function f is shown. Find f(4).
-2 -1
S
4
w
2
1
-1
-2
-3
A
1
-2
B 0
C 2
D 5
2
4 5 6
Answers
The value of f(4) on the graph is 2
How to determine the value of f(4)?The figure (i.e. graph) represents the given parameter
The expression f(1) implies that we determine the value of f(x) when x = 1
On the graph, we have the following value:
When x = 4, f(x) = 2
This means that
f(4) = 2
Hence, the value of f(4) on the graph is 2
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Cheyenne is going to the store with $20.she wants buy as many bags of takis as she can. if takis are $1.50 per bag, what is the maximum number she can buy?
Answers
$20/$1.50 = 13.3333
You can’t have 0.3 of a bag, so you round down to 13.
Cheyenne can buy a maximum of 13 bags of Takis.
We have,
To find the maximum number of bags of Takis Cheyenne can buy with $20, we need to divide the total amount of money she has by the cost per bag of Takis.
Cost per bag of Takis = $1.50
Total money Cheyenne has = $20
Maximum number of bags of Takis = Total money / Cost per bag
Maximum number of bags of Takis = $20 / $1.50
Maximum number of bags of Takis = 13.33
Since Cheyenne cannot buy a fraction of a bag, the maximum number of bags of Takis she can buy is 13.
Thus,
Cheyenne can buy a maximum of 13 bags of Takis.
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how to find prime factorization.
find the prime factorization of 1530
Answers
Answer:
Factors: 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530
Prime Factors of 1530 : 2 * 3 * 3 * 5 * 17