The solution is Option A.
Substitution is the second strategy for solving a system of equations
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
ax + by = c be equation (1)
Let the second equation be represented as B
dx + ey = f be equation (2)
On adding or subtracting both the equations , we can eliminate one of the variables from the system of equations
And , to calculate the other variable , substitute the value of the variable in either of the equations to solve the system of equations
So , we will get the value of the variable x and y
Hence , the system of equations can be solved by substitution
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A line passes through the points (–6,5) and (8,–2). What is its equation in point-slope form?
Answer:
y - (-2 ) = 1\2 ( x- 8)
Step-by-step explanation:
The point slope form equation is y-y₁=m(x-x₁)
( -6 , 5 ) ( 8 , -2 )
( x , y ) (x1 , y1 )
Firstly we need to find the slope
y1 - y -2 - 5
we can find the slope by this equation : ------------- = --------------
x1 - x 8 - (-6)
The slope is 1\2
Help me please and thank you
A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red? Express your answer as a common fraction.
The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
What is conditional probability?The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.
Suppose you choose a red/black card:
The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].
Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].
Suppose you choose a red/red card:
The probability of choosing red and red card is 2/6.
Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .
Considering we see a single side of the card we have the following probability:
[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]
The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].
The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].
So, the conditional probability of both red sides is given as:
[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]
Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
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Cory is hiking up a hill with a constant slope the double number line shows that after Cory hikes 3 km his elevation is 120 m
Cory is hiking up a hill with a constant slope the double number line shows that after Cory hikes 3 km his elevation is 120 m. Select the double number line that correctly labels is option 'A'.
What do you meant by hiking?From brief half-day programs to extensive itineraries lasting more than 20 days, the activity's duration varies. The majority of the time, it is an activity that accepts groups of various sizes.
A long stroll, especially one undertaken for the sake of recreation or exercise; see also hike; an increase, particularly in quantity or amount. While it is entirely up to each hiker to assign whatever classification they see fit to their experience, I have found that the vast majority of hikers fall into one of the three most common categories: peak-bagging, long-distance hiking, or day hiking.
Because it is a constant slope and Cory hikes 3 km his elevation is 120 m.
slpoe = 120m/3km = 40m/1km
So, Cory's elevation after he hikes 1 km, his elevation is 40 m.
Cory's elevation after he hikes 2 km, his elevation is (2*40 m) 80 m.
Cory's elevation after he hikes 4 km, his elevation is (4*40 m) 160 m.
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The complete question is:
Cory is hiking up a hill with a constant slope. The double number line shows that after Cory hikes 3 km his elevation is 120m. Select the double number line that correctly labels Cory's elevation after he hikes 1, 2, and 4 km. Choose 1 answer:
Isaac's father is 49 years old. He is four years older than three times Isaac's age. How old is Isaac
If Isaac's father is four years older than three times of Isaac's age and the age of father is 49 years old. So, Isaac age will be 15 years old.
How old is Isaac?According to online myth, there is a mathematical equation that regulates the lower bound for a possible dating partner's socially acceptable age: half your age plus 7, or, in mathematical words, if x is your age, the bottom barrier is [tex]f(x) = x/2 + 7[/tex].
Consider Isaac is L
Let us suppose L is x years old.
3 times the age of L = 3x
3 times L’s age plus 4 years = 3x + 4
Furthermore, L’s father’s age is 49 years older than L’s age.
Therefore,
[tex](3x + 4) = (49) (49)\\(3x + 4) -4 = (49) – 4\\3x = 45\\3x/3 = 45/3\\X = 15[/tex]
L’s age is 15 years since we expected L’s age = x (and x=15).
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QUESTION 3
A woman weighs 145 pounds. She gains 12 pounds one
month and 6 pounds the next month. What is her new
weight?
148 pounds
151 pounds
P
O 157 pounds
+
O 163 pounds
Answer:
163 pounds
Step-by-step explanation:
you would use 145 and add 12 to it for the first month, then add 6 for the next month, which will give you a new weight of 163 pounds
what is the distance of the cookie?
A., 10 inches.
Hope this helps!
Sue has 20 biscuits in a tin.
There are: 12 plain biscuits
5 chocolate biscuits
3 currant biscuits
Sue takes two random biscuits from the tin.
Work out the probability that they are not the same type.
Answer:
The probability that the two biscuits were not the same type is 58.4%.
How much is the probability that the two biscuits were not the same type?
The probability that they are different is the opposite of the probability that they are the same.
The probability that they are the same is:
⇒ P(plain, plain) = (12/20) (11/19) = 132 / 380
⇒ P(chocolate, chocolate) = (5/20) (4/19) = 20 / 380
⇒ P(currant, currant) = (3/20) (2/19) = 6 / 380
⇒ P(same) = 132/380 + 20/380 + 6/380
⇒ P(same) = 158/380
⇒ P(same) = 79/190
Therefore, the probability that they are different is:
⇒ P(different) = 1 − 79/190
⇒ P(different) = 111/190
⇒ P(different) ≈ 58.4%
What does probability mean?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
How do you prove irrational rational and irrational?
Rational and Irrational numbers can be depicted as the number that can be communicated as p/q are reasonable and which can't be communicated are called Unreasonable Numbers.
Rational Numbers are characterized as a number that can be addressed as p/q where q isn't equivalent to zero.
We can likewise, say that the part where the denominator and the numerator are whole numbers and the denominator isn't equivalent to zero is called Reasonable Numbers.
For Instance: 2/3, 3/9, addresses Rational numbers.
Irrational Numbers are characterized as genuine numbers that can't be communicated as a proportion of whole numbers.
For Instance: [tex]\sqrt{2}[/tex], [tex]\sqrt{3}[/tex] addresses an Irrational number.
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Find the values of x and y.
-2x+y=-35
L
to
||
2x°
(y + 10)°
yᵒ
Answer:
x = 60 , y = 85
Step-by-step explanation:
assuming the figure is a trapezoid
• each lower base angle is supplementary to the upper base angle on the same side.
x + 2x = 180
3x = 180 ( divide both sides by 3 )
x = 60
and
y + y + 10 = 180
2y + 10 = 180 ( subtract 10 from both sides )
2y = 170 ( divide both sides by 2 )
y = 85
Identify an irrational number between 7 and 8
What is the solution to the system of equations below x y 7 and x 2y 11?
The solution to the system of equations is x = 3 and y = 4.
this question is related to system of equations ,
the equations are,
x + y = 7 .......[1]
x + 2y = 11
x= 11 - 2y
now, place the value of x in equation 1,
(11 - 2y) + y = 7
11 - 2y +y = 7
11 - y = 7
- y = 7 - 11
- y = - 4
y = 4
now to find the value of x, place the value of y in equation 1
x + 4 = 7
x = 7 - 4
x = 3.
so, the value of x and y is 3 and 4.
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Determine which of the two acute angles has a cosine of 3/4. Eliminate the other acute angle.
Answer:
Both <y and <w have a cosine of 3/4
a salesman goes to Murano and buys three dozen vases paying €16.25 each. During transport if they break me 9. How much did each remaining vase sell for if he earned €360
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
what is unitary method ?
The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)
given
A salesperson purchases three dozen vases (12 * 3 = 36),
at a cost of 36 * €16.25 (or $585),
with seventeen remaining.
The cost of selling each remaining vase is € 585 / 17
= € 34.41.
The vase sells for € 34.41, and he made €360 during a break on the ninth transfer.
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Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers $2\frac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella
Since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
To determine this:
We can start by using the information given to find out how long it takes Bella and Ella to meet.
Since Ella rides 5 times faster than Bella walks, we can use the following equation to find out how long it takes each of them to cover the 2-mile distance:
Time (Ella) = Time (Bella) / 5
We can also use the distance formula to find out how long it takes Bella to cover the 2-mile distance:
Distance = Speed x Time
We know that Bella's speed is [tex]$2\frac{1}{2}$[/tex] feet per step, and the distance between their houses is 10,560 feet. So:
10,560 feet = [tex]$2\frac{1}{2}$[/tex] feet/step x Time (Bella)
Solving for Time (Bella), we get:
Time (Bella) = 10,560 feet / [tex]$2\frac{1}{2}$[/tex] feet/step = 4,224 steps
Now we can use this information to find out how long it takes Ella to meet Bella:
Time (Ella) = Time (Bella) / 5 = 4,224 steps / 5 = 844.8 steps
And since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
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Is a 45 45 triangle isosceles?
Yes, a 45 45 triangle is an isosceles triangle, meaning that two of its sides are equal in length.
A 45 45 triangle is a triangle in which two of its angles are 45 degrees. This type of triangle is also known as an isosceles triangle because it has two sides of equal length. To determine whether a triangle is isosceles, we need to measure the lengths of its sides. In a 45 45 triangle, both sides are equal in length as the angles are equal. Therefore, a 45 45 triangle is an isosceles triangle. The triangle also has two acute angles (less than 90 degrees) and one obtuse angle (greater than 90 degrees). This type of triangle is a special type of triangle and is often used in geometry and trigonometry.
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thank you guys for helping me but i still need help -^-
Answer:
x = 25
Step-by-step explanation:
(4x - 17) + 36 + 61 = 180
(4x - 17) + 97 = 180
4x - 17 = 83
4x = 100
x = 25
Have a nice day!
Answer:
x = 25
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
4x - 17 + 61 + 36 = 180
4x + 80 = 180 ( subtract 80 from both sides )
4x = 100 ( divide both sides by 4 )
x = 25
HELP ASAP PLEASE
i dont underatand this
Answer:
IST x-2= 2
Step-by-step explanation:
Answer: -2x-3 = x
Step-by-step explanation:
You have 2 -x's and 3 -1's in the first balance thing. In the second, you have 1 x.
If you put those together into an equation, you get -2x-3 = x (since in this balance, the two sides are equal).
Then you solve the equation to find x:
-2x-3 = x
-3 = 3x
x = -1
Find the product (8×+9y) (8×-9y)
Answer:64x^2-81y^2
Step-by-step explanation:
difference of the squares
Please help ASAP this is for a final test
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answer: I'm sorry bro i don't know
Step-by-step explanation:
Which equation shows a way to find 3075/15. A 30/15+75=2+5 B 30/15x75=2x5 C 3000/15+75=200+5 D 3000/15x75=200x5. I need the answer quick please its for a test!!!!!!! HURRY!
Answer:
C. 3,000÷15+75÷15=200+5
Step-by-step explanation:
I got this because 3075 ÷ 15 = 205. That whole equation is equal to 200+5. 200+5=205.
Hope it's correct cause I have the same question on a quiz !
Answer:30/15+75=2+5 B 30/15x75=2x5
Step-by-step explanation: Because i am a teacher so i know the answer
What is the solution set for 10 - 4x < -22?
Answer:
x>8
Step-by-step explanation:
make the equation equal to -22 and get 8 and see if if it is less than or greater than
What is the surface area? in Square Inches
Answer:
24
Step-by-step explanation:
How do you find height of a triangle when base is given to you?
The height of a triangle can be found using the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Therefore, the height of a triangle can be found by rearranging the formula to height = (2 * area) / base.
To find the height of a triangle when the base is given, first use the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Next, rearrange the formula to height = (2 * area) / base so that the height can be found by dividing the area by the given base. Once the area is known, the height can be found by plugging the area and base into the rearranged formula. For example, if the base of a triangle is 8 and the area is 12, then the height of the triangle can be found by dividing 12 by 8, which is equal to 1.5. Therefore, the height of the triangle is 1.5.
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What is the value of x
Answer:
12
Step-by-step explanation:
Tell algebra to stop looking for his x an just watch her 24/7
Answer:
value of x is 12
hope it helps.
Find the area of the rhombus. AB=7 ft. Round to the nearest tenth.
Answer:
7 x 7 = 49
49 divided by 2 ( x 1/2) = 24.5
Formula:
D1 x D2 x 1/2
In this case D1 and D2 are both 7
and 1/2 is just 1/2 so multiply them.
please give a step by step explanation please
The radius of a sphere whose surface area is 324*pi cm² is:
R = 9 cm.
What is the radius of the sphere in the image?We know that the surface of a sphere of radius R is given by:
S = 4*pi*R^2
Where pi = 3.14
Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:
S = 324*pi cm² = 4*pi*R^2
We can divide both sides by pi, so we get:
324 cm^2 = 4*R^2
Now we can solve that equation for R, we will get:
R^2= (324 cm^2)/4 = 81cm^2
R = √(81 cm^2)
R = 9cm
The radius of the sphere is 9cm.
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hey! please help i’ll give brainliest
Answer:
all of these
Step-by-step explanation:
Answer:
All of these
Step-by-step explanation:
Am = ex. I am playing tennis
Is = ex. She is playing tennis
Are = ex. We are playing tennis
Hope this helps :)
Consider the division of 8y2 - 12y + 4 by 4y.
What are the values of a and b?
=a+b++
O a = 2y and b = 3
O a= { and b = -3y
O a= 2y and b = -3
O a = ? and b = 3y
Mark this and return
Save and Exit
Next
Sub
By solving the given Algebraic expression, the correct answer is Option (C) ,a = 2y and b = –.
What is an Algebraic Expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.
Assume that 8y2 - 12y + 4 has terms with a=8y² , b=-12y, c=4
Now, to divide 8y2 - 12y + 4 by the monomial (single term) 4y,
The easy way is divide each term of the dividend by the monomial:
8y2 - 12y + 4 /4y
=(8y²-12y+4)/4y
=(8y²/4y)-(12y/4y)+(4/4y)
=2y-3+1/y
After performing the division we get that now a = 2y and b = –3
We can conclude that the correct answer is a = 2y and b = –3
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7. Mai and Tyler are selling items to earn money for their elementary school. The school
earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai
sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10
wreaths and 7 potted plants and the school earns $62.50.
This situation is represented by this system of equations:
[ 14w + 3p = 70.50
10w+7p = 62.50
Explain why it makes sense in this situation that the solution of this system is also a
solution to 4w + (-4p) = 8.00.
On solving the provided question we can say that - her in the equation 14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex]14w + 3p = 70.50 \\[/tex]
10w+7p = 62.50 ,
[tex]w = 12\\[/tex]
p = 18
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