y = -2x is line parallel to given line.
What is line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that are endlessly stretched in the opposing directions.
Main body:
The slope-intercept form is
y=mx+b, where
m is the slope and b is the y-intercept.
y=mx+b
Using the slope-intercept form, the slope is −2.
m=−2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope −2 and a given point (0,0) to substitute for
x₁ and y₁ in the point-slope form
y−y₁=m(x−x₁)
, which is derived from the slope equation
m=(y₂−y₁)/(x₂−x₁).
y−(0)=−2*(x−(0))
Simplify the equation and keep it in point-slope form.
y+0=−2⋅(x+0)
Solve for y.
y=−2x
Hence y = -2x is line parallel to given line.
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Given: m//n
Prove: angle 1 and angel 4 are supplementary
⇒ Supplementary angles are angles that add up to 180°
⇒ ∠1+∠2=180°(angles on a straight line)
∠2=∠4( Corresponding angles are equal m||n)
⇒*NOTE THE FOLLOWING STATEMENT IS TO MAKE YOU UNDERSTAND,IT MUST NOT BE INCLUDED IN YOUR ANSWERBOOK)
If ∠2=∠4
in the place of ∠2 in the equation ∠1+∠2=180° we can substitute ∠4 since the two angles (∠2 and ∠4) are equal by corresponding angles
______________________________________________________
⇒You may include this step now as you now know how ∠4 came up.
∴∠1+(∠4)=180°
∠1+∠4=180°
Now from the above equation we can see that ∠1 and ∠4 are supplementary angles as they both add up to 180°
Solve The Problem
All the students in grades
and are going on a field trip to Coney Island
Each grade has 125 students. The cafeteria needs to pack lunches. About how
many students are going on the trip? Represent the exact amount of students
in all three grades using an array, How many students are there altogether? Please help me thank you
The total number of students going on a trip is 375 students.
Given that,
The entire third through fifth graders are taking a field trip to Coney Island. There are 125 pupils each grade. The cafeteria should provide lunches.
We have to find how many students will be travelling on the trip.
So,
In Grade 3 we have 125 students.
In Grade 4 we have 125 students.
In Grade 5 we have 125 students.
So,
Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5
= 125 + 125 + 125 = 375.
Therefore, The total number of students going on a trip is 375 students.
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It is estimated that only around 200,000 Americans have central heterochromia (two different eye colors in the same eye). If the population of the United States
was 327,750,000 people at the time of this report, what percent of Americans had central heterochromia?
0.0061%
0.00061%
0.61%
0.061%
The percent of Americans that had central heterochromia is A. 0061%.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States
was 327,750,000 people.
The percent of Americans that had central heterochromia will be:
= Those with the disease / Total population × 100
= 200,000 / 327,750,000 × 100
= 0.0061%
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There are 212 parks in the city of Indianapolis and the city has a population of 870,000. What is the number of parks per capita in the city of Indianapolis? Round to 6 decimal places.
The number of parks per capita when there is the total population of 870,000 people and there are 212 parks is 4,103.77358.
What is per captia?
“Per capita” is a Latin term that means “per head.” This term is used to express the average per person, the term “per capita” is occasionally used in statistics instead of “per person.”
On a given case, the per capita parks for population can be calculated by dividing total population by total parks.
According to the given illustration,
Total population of city = 870,000
Total Parks= 212
Calculation of parks per capita in the city of Indianapolis:
Per capita shops = Total population/ Total shops
Per capita shops =870,000/212
Per capita shops = 4,103.77358
Therefore, the number of parks per capita is 4,103.77358.
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what’s the x intercept of a table with 22,27,32
The x-intercept of the table of values is 12 or (12, 0).
How to Find the X-Intercept of a Table?To find the x-intercept of a table that represents a linear relationship between x and y, first write the equation that models the table.
To write the equation, first find the slope (m) using two pairs of values, say, (22, 36) and (27, 54)
Slope (m) = (54 - 36)/(27 - 22)
Slope (m) = 18/5
Write the equation that represents the table of values by substituting (a, b) = (22, 36) and m = 18/5 into y - b = m(x - a):
y - 36 = 18/5(x - 22)
To find the x-intercept, substitute y = 0 into the equation, y - 36 = 18/5(x - 22) to find the value of x:
0 - 36 = 18/5(x - 22)
-36 = 18/5(x - 22)
5(-36) = 18(x - 22)
-180 = 18(x - 22)
-180/18 = x - 22
-10 = x - 22
-10 + 22 = x
12 = x
x = 12
The x-intercept is 12 or (12, 0).
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Use the equation below to find v, if u = 18, a = 6, and t = 4
v = u + at
The value of v from the given equation v=u+at is 42
What is an equation?An equation is a mathematical expression that contains an equals symbol
From the given equation v=u+at
u=18
a=6
t=4
Substituting for u,a and t in the equation
v=18+6(4)
expanding the bracket
v=18+24
v=42
Hence, the the v in the equation v=u+at is 42
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Madison needs to order some new supplies for the restaurant where she works. The restaurant needs at least 474 spoons. There are currently 246 spoons. If each set on sale contains 6 spoons, use the drop-down menu below to write an inequality representing s, the number of sets of spoons Madison should buy.
38 sets
474 - 246 = 228
228 ÷ 6 = 38
Is 4.5 greater, less than, or equal to 4 and 1/2
Answer:
equal to
Step-by-step explanation:
4 + 1/2= 4+ 0.5= 4.5
4.5=4.5
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
Answer:cap
Step-by-step explanation:C A P
Emma learned in science class that fruit fly populations can increase by about 30% each day. She found 7 fruit flies on a rotten banana today, and she is curious how many fruit flies could be on the banana in a few days. You can use a function to approximate the number of fruit flies on the banana after x days.
The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.
What is an exponential function?An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.
Exponential functions must always contain an exponent, which is an integer raised to some power.
When the exponent is positive, it implies the function is increasing in value and vice versa.
Percentage increase per day = 30%
The number of fruit flies found = 7
The number of days = x days
Let the number of flies after x days = y
y = 7 x 1.3ˣ
Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.
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A middle school principal is signing the diplomas of the school's graduating eighth graders. She previously signed 37 diplomas. Now, she is signing more diplomas at a rate of 0.5 per second.
Write an equation that shows how the total number of diplomas signed, y, depends on the number of seconds the principal spends signing them, x.
y=
An equation that shows how the total number of diplomas signed depends on the number of seconds the principal spends signing them is y = 37 + 0.5x.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, let x be number of seconds the principal spends signing them. The principal already signed 37 diplomas. Th equation to illustrate this is 37 + 0.5x.
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“on the following checking account record, enter the figures and add or subtract them to keep the running total correct”
will mark brainliest and 100 points :))
The running total is $95.27.
There are two types of records, Active and Inactive. There are also two major classifications, Vital and Important.
Why is record keeping important?In order to create reliable financial statements, you need good records. These consist of balance sheets and income (profit and loss) statements. These statements might assist you in managing your business and dealing with your bank or creditors.He opened the account with $299.88. He subsequently wrote many cheques, from which you deduct the sum of 299,88.
He deposited a check, thus 299.88-90.48= 209.40, 209.40 - 65.00= 144.40, and then he added $381.33 to 144.40 to get 525.73.
then you need to deduct more since he wrote more checks.
Consequently, 525.73-54.47=471.26, and 471.26-375.99=95.27, giving him a balance of $95.27.
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The current total is $95.27. Active and Inactive records are the two types of records. There are two major classifications as well: Vital and Important.
Why is record keeping important?Good records are required to create reliable financial statements. Balance sheets and income (profit and loss) statements are included. These statements may help you manage your company and deal with your bank or creditors.
Good Records are documents that contain recorded data that demonstrate the effectiveness of the quality management system, regardless of format or feature.
Given,
He deposited into the account = $299.88
He then wrote a number of cheques, from which you deduct = $299,88.
He deposited a check, thus 299.88 - 90.48
= 209.40, 209.40 - 65.00
= 144.40
and then he added $381.33 to 144.40 to get 525.73.
then you need to deduct more since he wrote more checks.
Consequently,
525.73 - 54.47
=471.26
and 471.26-375.99
= 95.27
As a result, The gives him a balance of $95.27.
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A club with fourteen members is to choose three officers: president, vice-president, and secretary-treasurer. If each
office is to be held by one person and no person can hold more than one office, in how many ways can those offices
be filled?
ways
There can be 2184 ways in which three posts can be selected using permutation.
What is permutation?
An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.
Main Body:
Total members =14
total posts =3
As one person can not hold more than 1 post ,
total ways are = ¹⁴P₃
Therefore total ways = 14!/11!
= (14*13*12*11!)/11!
= 14*13*12
= 2184 ways
Hence answer is 2184 ways to select 3 members out of 14.
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What is the solution to the system graphed below? PLS ANSWER WILL MARK BRAINLIST
The solution to the system graphed is (2, 0).
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that changes over time is represented by a line graph.
Given:
From the graph we have two line red and purple.
The intersecting point for both line is (2, 0).
Hence, the solution to the system graphed is (2, 0).
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Which equations shows a proportional relationship between x and y.
y=6x
y= x - 5
The equation that shows a proportional relationship between x and y is y=6x
How to determine the equation?The options represent the given parameters
As a general rule
A proportional relationship is represented as y = kx
Where k represents the constant of proportionality
So, we check the options for equations that has the same form as y = kx
We have
y = 6x
The above equation is a linear equation
In fact, it is a linear equation that shows a proportional relationship
Note that all linear equations have a constant rate of change
So, the proportional relationship is given as
y = 6x
Where the constant of proportion is 6
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Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
What are the slope and vertical intercept of 5x+7y=10
Answer:
-5/7, 10/7
Step-by-step explanation:
The slope of an equation in standard form is -a/b
so -5/7
Set x to 0 to find the vertical intercept
5(0)+7y=10
7y=10
y=10/7
Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?
|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7
Answer:
Answer is b
Step-by-step explanation:
Because
|x-7|=15--->x=15+7, x=22can y’all help me please
Answer:
The slope of this line is undefined.
Two numbers have these properties.
Both numbers are greater than 6.
Their highest common factor (HCF) is 6.
Their lowest common
multiple (LCM) is 60.
Find the two numbers, writing your
answers on one line in the form,
The two numbers are .
and .. .
12 and 30 are the two numbers are greater than 6 with HCF 6 and LCM 60.
What is Highest common factor and Least Common Multiple?
Least Common Multiple is the entire name of LCM in mathematics, whereas Highest Common Factor is the full name of HCF. When two or more numbers are given, the HCF identifies the largest factor present, while the LCM defines the least number that is exactly divisible by two or more numbers.
Assume that the two numbers with HCF of 6 are 6a and 6b, where a and b are co-prime and a, b > 1.
HCF x LCM = Product of the numbers.
6 x 60 = 6a x 6b
10 = a x b
10 can be written as, 1 x 10 and 2 x 5.
But a and b > 1.
So, 10 = 2 x 5
a = 2, b = 5
Therefore, the two numbers are,
6a = 6(2) = 12 and
6b = 6(5) = 30
Hence, the two numbers with HCF 6 and LCM 60 are 12 and 30.
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How could you find a all the factors pairs of 30 using a set of 30 pennies
The factor pairs of 30 are (1, 30), (2, 15), (3, 10), (5, 6), (6, 5), (10, 3), (15, 2) and (30, 1)
The number is 30
The factors pair of a number is the numbers that when we multiply them together we will get the number
Here the number is 30
The factors of 30 are
1, 2, 3, 5, 6, 10, 15, 30
The factor pairs of 30 are
1 × 30 = 30
2 × 15 = 30
3 × 10 = 30
5 × 6 = 30
6 × 5 = 30
10 × 3 = 30
15 × 2 = 30
30 × 1 = 30
Hence, the factor pairs of 30 are (1, 30), (2, 15), (3, 10), (5, 6), (6, 5), (10, 3), (15, 2) and (30, 1)
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three sides of quadrilateral are the same length,g q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. write and equation that represents the situation.
The situation can be represented using the equation 3g + 7 = 40
How to determine the equation that represents the situation?From the question, we have the following parameters that can be used in our computation:
Length of three sides = g
Length of the fourth side = 7
Perimeter = 40
The perimeter of a quadrilateral is the sum of the sides of the shape
This means that
P = sum of the 4 sides
So, we have
P = g + g + g + 7
Evaluate
P = 3g + 7
Rewrite as
3g + 7 = 40
Hence. the equation that represents the situation is 3g + 7 = 40
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X+6=3x we just learned how to do this math today I need help
Answer:
x=3
Step-by-step explanation:
Answer: x=3
Step-by-step explanation:
First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!
-----------------------
So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!
HELP ME PLEASE GRAPH
Answer:
see attached (red)
Step-by-step explanation:
You want the graph of the transformed triangle defined by the lines y=x, x=6, y=-1/3x+4 after rotation 270° and reflection across the y-axis.
TriangleA graph of the lines shows the vertices of the triangle are ...
A(3, 3), B(6, 6), C(6,2)
TransformationsRotation 270° is described by the transformation ...
(x, y) ⇒ (y, -x)
Reflection across the y-axis is described by ...
(x, y) ⇒ (-x, y)
Then the composition of these transformations is ...
(x, y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection over y=-x
ApplicationApplying this composition to the triangle vertices, we find its final location to be ...
A(3, 3) ⇒ A''(-3, -3)
B(6, 6) ⇒ B''(-6, -6)
C(6,2) ⇒ C''(-2, -6)
The triangle with these vertices is shown in red in the attachment.
Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters. How long are the other two sides? What is the perimeter of the garden?
The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.
According to the question,
We have the following information:
Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.
We know that the following formula is used to find the area of rectangle:
Length*width = 18
Length*3 = 18
Length = 18/3
Length of the rectangular garden = 6 meters
Now, perimeter of the rectangular garden:
2(length+width)
2(6+3)
2*9
18 meters
Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.
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Seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary. Find the measures of these three angles.
The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.
How to find angles of a decagon?A decagon simony means a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.
Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.
Therefore,
1440 - 1220 = 220
Let the angles be a, b and c.
Therefore,
a + b + c =220
a + b = 90
b + c = 180
Hence,
a = 220 - 180
a = 40°
b = 90 - 40
b = 50°
c = 180 - 50
c = 130°
The angles are 40°, 50° and 130°.
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The digit 7 appears twice in
the product.
Answer:
The numbers in which 7 appears are. 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97, 107. So, counting all. ∴ Number of times 7 appears = 21
find the smallest value of an expression
(without using a calculator)
[tex]\bf\sqrt{(x-8)^2+(y+4)^2} +|y+3x|[/tex]
Step-by-step explanation:
to eliminate the always positive absolute value at the end let's set y = -3x
that makes the absolute value term = 0 in all cases.
then we have
sqrt((x - 8)² + (-3x + 4)²)
the x-value that makes this a minimum result also makes
(x - 8)² + (-3x + 4)²
a minimum.
x² - 16x + 64 + 9x² - 24x + 16
10x² - 40x + 80
the x that makes this a minimum, also makes
x² - 4x + 8
a minimum.
we get the extreme value as zero of the first derivative :
0 = 2x - 4
4 = 2x
x = 2
so, we get the minimum of all these expressions for x = 2.
as y = -3x, we get y = -3×2 = -6.
the minimum value for the expression is with
x = 2
y = -6
so, the minimum value is
sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =
= sqrt((-6)² + (-2)²) + |-6 + 6| =
= sqrt(36 + 4) + 0 =
= sqrt(40) = 6.32455532...
Simplify to one trigonometric expression.
4 sin
()2 cos()
Answer:
Step-by-step explanation:
the answer is 4
Help pls I will give brainliest!!
Answer:
C. -16
Step-by-step explanation:
Hope this helps you! :))
16
Step-by-step explanation:
the answer is c
just took a test and I got it right