We can conclude -
m = -A/B → unit rate of change of [y] with respect to [x].c = - C/A → the point where the graph cuts the [y] axis.Equation → y = mx + cWhat is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
Given is a straight line.
The equation of a straight line is written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Now, from this we get -
m = -A/B {Slope}
c = - C/A {y - intercept}
So, the equation will be -
y = mx + c
We can also calculate slope by -
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, we can write -
m = -A/B → unit rate of change of [y] with respect to [x].
c = - C/A → the point where the graph cuts the [y] axis.
Equation → y = mx + c
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The room numbers of two adjacent classrooms are two consecutive odd numbers. If their sum is 708, find the classroom numbers.
Answer: classroom numbers are 353 and 355
Step-by-step explanation:
Let x represent the first no
Then x+2 represents the second number
Turn the question to an equation= x - (x +2) =708
Therefore, 2x + 2= 708
2x= 708-2
2x= 706
x= 353 and x+2= 355
Hope you understand, please mark brainliest.
Answer:
The first number is 353, and the second is 353 + 2, or 355.
Step-by-step explanation:
Represent the first number by n and the next by n + 2.
Then n + (n + 2) = 2n + 2 = sum of the two numbers = 708.
Subtracting 2 from both sides yields 2n = 706. Dividing both sides of this latest result by 2 yields n = 353.
The first number is 353, and the second is 353 + 2, or 355.
Check: do 353 and 355 sum up to 708? YES
What is the Pythagorean Thereom
Answer:
Step-by-step explanation:
The Pythagorean theorem states that for a right triangle, the sum of the square for each of the sides is equal to the square of the hypotenuse.
See attached for graphic and formula
what set of numbers are shaded on the hundred chart.
A: only all the factors of 45
B: only the multiples of 45
C: only all the factors of 90
D: only all the multiples of 90
A: the factors of 45 are the only one shaded on the hundreds chart
The shaded numbers, all are factors of 45. Therefore, option A is the correct answer.
We need to check what set of numbers is shaded on the hundred charts.
What are the factors?In math, a factor is a number that divides another number completely with no remainder. Factors and multiples are a part of our daily life. For example, they are used in arranging items in a box, handling money, finding patterns in numbers, solving ratios, and working with expanding or reducing fractions.
The factor of a number is always less than or equal to the given number.
From the given chart the shaded numbers are 1, 3, 5, 9, 15 and 45.
The shaded numbers, all are factors of 45. Therefore, option A is the correct answer.
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A circle has a diameter of 12cm. What is the area of the circle in square centimeters?
A) 75.36 cm2
B)113.04 cm2
C)452.16 cm2
D)37.68 cm2
Answer:
B. 113.04 cm^2
Step-by-step explanation:
The area of a circle is:
a=[tex]\pi[/tex]r^2
Because we have the diameter, we need to find the radius.
d=2r
12=2r
Divide by 2 on both sides
r=6
Plug 6 in for "r" in the area formula.
a=[tex]\pi[/tex]r^2
a=[tex]\pi[/tex]6^2
a=36[tex]\pi[/tex]
a=36*3.14
a=113.04 cm^2
So the answer is choice B
Hope this helps!
Mar 12: 3
Mar 13: 8
Mar 14: 11
Mar 15: 16
Mar 16: 25
Mar 17: 50
Whats the pattern? Is the pattern linear, quadratic, or exponential? Can you predict the number of cases for march 18, 19 and 20? What about March 25th?
Answer:
Mar 18: 125Mar 19: 318Mar 20: 743Mar 25: 15,070Step-by-step explanation:
The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.
The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...
(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60
where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.
____
The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.
The values for Mar 12 through Mar 25 are ...
3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070
Answer: Mar 18: 125
Mar 19: 318
Mar 20: 743
Mar 25: 15,070
Step-by-step explanation:
The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.
The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...
(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60
where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.
____
The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.
The values for Mar 12 through Mar 25 are ...
3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070
Step-by-step explanation:
.
Meat costs $8.00 per pound at the store. What is the slope and y-intercept?
Using the sum and difference formula to determine the exact value of cos165
Answer:
-0.9659258 is the exact value
What is the absolute value I need help please help me complete this problem
3 887 860 round it to the nearest million
4,000,000
because the hundred thousand place value is the digit 5 or higher, the millions rounds up!! in this case, the 3 in the millions rounds up to 4 and the rest of the digits on the right turn to 0, also remember commas!!!!!
3 887 860 rounded to the nearest million is 4 000 000.
From the given number 3 887 860, stating the place value of each digit
We have 0 ones (or unit), 6 tens, 8 hundreds, 7 thousands, 8 ten thousands, 8 hundred thousands and 3 million.
Hence, the number we are rounding is 3 (since we are asked to round to the nearest million)
To round a number, we either round up or round down.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down; and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Since, the number that follows the digit we are rounding is 8, then we round up. We round up by adding 1 to the digit we are rounding and turn the remaining numbers to zeros.
(3+1 = 4)
Hence, 3 887 860 rounded to the nearest million is 4 000 000.
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Using your math skill add 3/4+1/3
Answer: 9/12 + 4/12 which equals 13/12 or 1 1/12
Explanation: The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator. Keep the denominators the same with the answer then add!
QUESTION 9
Write the expression by using exponents.
2.2.2.2.2.2
moginio
QUESTION 10.
Answer:
2^6
Step-by-step explanation:
2*2*2*2*2*2
There are six 2's multiplied together so the base is 2 and the exponent is 6
2^6
A bag contains 77 orange marbles and 21 green marbles. If a representative sample contains 33 orange marbles, then how many green marbles would you expect it to contain? Explain. 100 points :)
Because the ratio of orange marbles to green marbles is ___ in the population, the expected number of green marbles is ___ times the number of orange marbles in the representative sample. There should be ___ green marbles.
9 green marbles are expected in the representative sample.
The expected number of green marbles is 0.27 times the number of orange marbles in the representative sample.
Step-by-step explanation:
Given that,
A bag contains 77 orange marbles and 21 green marbles.A representative sample contains 33 orange marbles and the green marbles not known.So, the expected number of green marbles can be assumed as 'x'.The ratio of orange marbles to green marbles is in proportion to the ratio of orange marbles to green marbles in the representative sample.
To find the value of x :
The proportions are 77/21 = 33/x
Cross multiplying the denominators and keeping x alone on one side,
x = (33 × 21) ÷ 77
x = 693 ÷ 77
x = 9 green marbles.
Therefore, the number of green marbles expected in the representative sample is 9.
To find the how many times the green marbles is to the number of orange marbles in representative sample = 9/33 = 0.27 times.
The green marbles is 0.27 times to orange marbles in the representative sample.
A pizza shop sold slices of cheese, pepperoni, and sausage pizza during lunch.
• They sold 117 slices of pepperoni.
• They sold 34 more slices of pepperoni than cheese.
• They sold 28 more slices of sausage than cheese.
Problem:
How many slices of sausage pizza were sold during lunch?
A
55
B
123
C
139
D
111
End
Session
I need the value of O and N in the picture (the diagonal lengths)
Answer:
N=15 O=17
Step-by-step explanation:
since we know this is a rectangle and the lines are diagonals we can assume they create right triangles. For line N we set up the Pythagorean Theorem which is a^2 + b^2 = c^2 and to find N we plug in 9 for a and 12 for b. 9^2 + 12^2 = c^2 c^2 = 225 so now we find the square root of c^2 so c or in this case N = 15, now we repeat this same exact sequence for O but N is now our base and 8 is our height of the triangle so we will plug in 8 for a and 15 for b: 8^2 + 15^2 = c^2 c^2 = 289 and the square root of 289 is 17.
Check the picture below.
Is 10 an irrational number
Answer:
yes, it is
hope its helpful ! :)
Could you guys please help
Answer:
t = 2.76
PLEASE VOTE BRAINLIEST
Step-by-step explanation:
Which is the graph of f(x) = √x
Answer:
i just need points
Step-by-step explanation:
The ratio of the number of white shapes to the number of black shapes is 5:11
The ratio of the number of white circles to the number of white squares is 3:7
The ratio of the number of black circles to the number of black squares is 3:8
Work out what fraction of all the shapes are circles.
Answer:
the fractions of all the shapes are circles can be obtained would be computed as:
[tex]\frac{450}{1600}=\frac{9}{32}[/tex]
Step-by-step explanation:
The fraction of the number of white shapes to the number of black shapes is 5/11.
Let us consider that there are:
500 white shapes1100 black shapesAs the fraction of the number of white circles to the number of white squares is 3:7
It means out of 10 total parts, 3/10 are white circles and 7/10 are white squares.
Calculating Number of white circles:
[tex]\frac{3}{{10}} \times 500=150[/tex]
Calculating Number of white squares:
[tex]\frac{7}{{10}} \times 500=350[/tex]
As the fraction of the number of black circles to the number of black squares is 3:8.
Calculating Number of black circles:
[tex]\frac{3}{{11}} \times 1100=300[/tex]
Calculating Number of black squares:
[tex]\frac{8}{{11}} \times 1100=800[/tex]
As
the total number of circles is 150 + 300 = 450, and the total number of shapes is 500 + 1100 = 1600Therefore, the fractions of all the shapes are circles can be obtained would be computed as:
[tex]\frac{450}{1600}=\frac{9}{32}[/tex]
In below diagram, line AB is parallel to CB.
i.e. AB∥CD
∠EGB = 57°
Find ∠EHD.
In the given diagram, line AB is parallel to CB. i.e. AB∥CD ∠EGB = 57°
then the value of ∠EHD = 57°
In this diagram, since AB is parallel to CD, we can infer that ∠EGB and ∠EHD are corresponding angles, and corresponding angles are congruent when a pair of parallel lines are intersected by a transversal. Given that ∠EGB = 57°, we conclude that ∠EHD is also 57° based on the properties of corresponding angles. Thus, ∠EHD = 57°.
When two parallel lines are intersected by a transversal, the corresponding angles formed on either side of the transversal are congruent. In this case, we are given that line AB is parallel to line CD, which implies that ∠EGB and ∠EHD are corresponding angles.
Given: ∠EGB = 57° (Given in the diagram)
Since AB || CD, ∠EGB ≅ ∠EHD (corresponding angles are congruent).
Therefore, ∠EHD = ∠EGB = 57°.
Hence, ∠EHD is also 57° based on the properties of corresponding angles.
In mathematical terms, we use the property of corresponding angles formed by a transversal intersecting two parallel lines to establish the congruence between ∠EGB and ∠EHD. This property is a fundamental aspect of geometry dealing with angles and parallel lines.
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2(11x-6)-18 is equal to 22x-30
Answer: Yes they are equal
Step-by-step explanation: First you have to solve 2(11x-6)-18:
2(11x-6)-18
22x - 12 - 18
22x - 30
They equal!
Answer:
0
THE RIGHT HAND SIDE IS EQUAL TO THE LEFT HAND SIDE.
Step-by-step explanation:
2(11x-6)-18 is equal to 22x-30
the above question can as well be expressed as
2(11x-6) - 18 = 22x -30
the next thing is to apply the BODMAS(BRACKET, OF, DIVISION, MULTIPLICATION, ADDITION , SUBTRACTION.) rule by first opening the bracket
22x - 12 -18 = 22x -30
We will proceed to collect the like terms
22x -22x = -30+12+18
0 = -30 +30
0=0
the answer is = 0
THEREFORE THE RIGHT HAND SIDE IS EQUAL TO THE LEFT HAND SIDE.
Order from least to greatest 3/6,3/4,2/8
Answer: 2/8; 3/6 and 3/5
Step-by-step explanation:
3/6 = 1/2 = 0.5
3/4= 0.75
2/8= 1/4 = 0.25
To arrange in the order of least to greatest= 2/8; 3/6 and 3/5
Susan's cat loses 1 1/4 pounds. then then it loses another 1/8 pound. what what is the total change in the cat's weight?
Answer:
decrease of 1 3/8 lbs (= 11/8 lbs)
Step-by-step explanation:
given that the cat loses 1 1/4 lbs and 1/8 lbs
1 1/4 can be expressed as an improper fraction 5/4
hence the total weight loss
= 1 1/4 + 1/8
= 5/4 + 1/8
= 10/8 + 1/8
= 11/8
= 1 3/8
Answer:
1 3/8
Step-by-step explanation:
change 1/4 into /8 which is 2/8 then add together which is 3/8 the add the one so 1 3/8
In the figure BC || DE . Angles__________
CAF and EFA
GAC and DFE
CAF and EFH
GAB and EFA
are congruent______________________________________
By linear pair theorem
because they are corresponding angles of parallel lines cut by a transversal
by vertical angles theorem
by the transistive property of congruence
∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal. ∠AFE ≅ ∠HFD by the Vertical Angles Theorem. ∠GAC ≅ ∠HFD by the_______________ Property of Congruence.
addition
subtraction
substitution
transistive
CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal. ∠GAC ≅ ∠HFD by the transitive Property of Congruence.
What are congruent angles?Angles that are of the same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of the same measure,
then
[tex]m\angle A = m\angle B[/tex]
is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
We write the congruency between them as;
[tex]\angle A \cong \angle B[/tex]
In the figure BC || DE .
Angles
CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal.
GAC and DFE are not congruent
CAF and EFH are not congruent
GAB and EFA are not congruent
∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal.
∠AFE ≅ ∠HFD by the Vertical Angles Theorem.
Therefore, ∠GAC ≅ ∠HFD by the transitive Property of Congruence.
∠AFD = ∠AFE
Two angles that are equal to the same angle must themselves be equal.
( By Transitive property of equality)
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A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, which takes the ball back to the starting point. What angles are formed by these tosses. Step by Step explanation.. Please
angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.
Step-by-step explanation:
Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.
The Law of Cosines (also called the Cosine Rule) says:
[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]
Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:
⇒ [tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]
⇒ [tex]c^2 -a^2 - b^2 = -2ab (cosx)[/tex]
⇒ [tex](cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}[/tex]
⇒ [tex](cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}[/tex]
⇒ [tex](cosx) =0.18310[/tex]
⇒ [tex]cos^{-1}(cosx) = cos^{-1}(0.18310)[/tex]
⇒ [tex]x = 79.45[/tex]
The Law of Sines (or Sine Rule) is very useful for solving triangles:
[tex]\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}[/tex]
We can now find another angle using the sine rule:
⇒[tex]\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}[/tex]
⇒[tex]sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}[/tex]
⇒[tex]Y = 59.02 degrees[/tex]
So, the third angle =[tex]180 - 79.45 - 59.02 = 41.53 degrees.[/tex]
Therefore, angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.
a triangle has sides that measure 6m,8m,12m. is it a right triangle?
Answer:
no
because it should be 99
Write a proportion for: a train can travel 126 miles in 3 hours. How many miles can the train travel in 5 hours?
Answer:
210
Step-by-step explanation:
126 / 3 = 42
42 x 5 = 210
therefore the train can traval 210 miles in 5 hours.
hope this helps
~angilina
Great a word problem for x+2=3x-8
what is unusual about the arrangement of the fossils in the diagram
Answer:
The oldest fossil is closer to the surface.
Step-by-step explanation:
Usually, the closer to the core of the Earth, the older the fossils. However, in this image, the oldest fossil is closer to the surface.
Answer:
The younger fossil is in the bottom layer, while the older fossil is in the top layer. These locations are opposite to the principle of superposition.
Step-by-step explanation:
Plato
i just don’t understand. help
Answer:
I'm so sorry you don't know this. Here!
Step-by-step explanation:
You divide 1,060 with 30%
1,060 - 30% (30) = 742!
Val scored 742 points!
A circle with a radius of 5 has a sector with a central angle of 9/10pi radians what is the area of the sector
Answer:
11.25pi units² or 35.3 units² (3 sf)
Step-by-step explanation:
½×r²×theta
½ × 5² × 0.9pi
11.25pi units²
Or, 35.3 units² (3 sf)