Answer:
• Equations
[tex]y=x+2[/tex][tex]y=x^2[/tex]• Solutions (2, 4) and (–1, 1)
Explanation
System of equations
• Linear equation
[tex]y=x+2[/tex]• Quadratic equation
[tex]y=x^2[/tex]We have to set both equations to 0 and equalize them:
• 1. Setting them to 0:
[tex]0=x+2[/tex][tex]0=x^2[/tex]• 2. Equalizing them:
[tex]x+2=x^2[/tex]To solve the system using the General Quadratic Formula, we have to set the equation in the form ax² + bx+ c = 0:
[tex]x^2-x-2=0[/tex]Thus, in this case a = 1, b = -1 and c = -2. Using the formula:
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-2)}}{2(1)}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{1+8}}{2}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{9}}{2}[/tex]Finding both solutions:
[tex]x_1=\frac{1+3}{2}=\frac{4}{2}=2[/tex][tex]x_2=\frac{1-3}{2}=\frac{-2}{2}=-1[/tex]Finally, replacing these values in the linear equation to find y:
[tex]y_1=2+2=4[/tex][tex]y_2=-1+2=1[/tex]Therefore, the solutions are (2, 4) and (–1, 1).
91.276-4.319
to the nearest whole number
Answer:
that's a good question
Step-by-step explanation:
given six people how many combinations of three are possible if the order does NOT matter
Answer:
20 Combos
Step-by-step explanation:
6C3 = 6! / ( 3! * 3!) = 20 COMBOS
Given the equation 6(8g + 2) + 45 = 153, write a scenario similar to Parts A and B that could be represented by the equation. Solve for g and explain what each number in the equation represents, including the solution.
The value for g is 2, meaning that each family bowled 2 games.
How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.
Given, the equation is 6(8g + 2) + 45 = 153
Following the steps in the available literature, we have the equation as:
6(8g + 2) + 45 = 153 ⇒ 48g + 12 + 45 = 153 ⇒ 48g = 153 - 45 - 12 = 96
⇒ g = 96/48 ⇒ g = 2
Thus, g as suggested will determine number of times each family bowled.
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45 is divisible by which of the following numbers? (1 point) 1, 5, 8 1, 2, 3 1, 2, 5 1, 3, 5, 9
Answer:
1,3,9,5
Step-by-step explanation:
Answer:
9, 5, 1, 3
Step-by-step explanation:
i forgot my vocabulary
But i still know decent engrish
GEOMETRY HELP ASAP
F (x,y) = (...,...)
1. y or -x
2. -x or y
The function which can be the reflection along y-axis will be F(-x, y).
A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. Reflection may be defined as the changes which occur on a graph for a given curve. If reflection of a point occurs along x axis, then there will be change in the y coordinate and if reflection along y axis, then there will be change in the x coordinate. We have a function F(x, y) and we need to find reflection along y axis so there will be change in the x coordinate, so new function will be F(-x, y).
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a line passes through the point (1,6) and has a slope of 7. Write an equation in point-slope form for this line.
Please answer quickly.
Answer:
[tex]y-6=7(x-1)[/tex]
Step-by-step explanation:
The equation of a line with slope [tex]m[/tex] and that passes through [tex](x_1, y_1)[/tex] in point-slope form is [tex]y-y_1=m(x-x_1)[/tex].
what is the equivalent ratios of 500:10?
Step-by-step explanation:
1. Transform by dividing both sides by Highest common factor which is 10 in this case.
2. Final answer is 50:1
what is the answer to this? :(5x^4)^3
Answer:
it is 25 or 35
Step-by-step explanation:
auto pistons at wenming chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
The value of the mean is 155.96mm
Calculation of the mean is:
n=5
Mean= [tex]\frac{\sum fx}{n}[/tex]
Mean=[tex]\frac{156.9+153.2+153.6+157.5+158.6}{5}[/tex]
Mean=779.8/5
Mean=155.96mm
The question was incomplete, the complete question is given below:
Auto pistons at Wenming Chung's plant in shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
Day Mean X(mm) Range R (mm)
1 156.9 4.2
2 153.2 4.6
3 153.6 4.1
4 157.5 4.8
5 158.6 4.7
What is the value of mean in mm, (round your response to 2 decimal places)
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Jake has 30 fish in his aquarium. Emi has 1/3 the number of fish that Jake has and 1/2 the number of fish that Tobin has.
If the three students combined all their fish in the school's new aquarium, how many fish would there be?
Using Linear equation, The total number of fishes in the aquarium is found to be 50.
What is an linear equation in one variable?Linear equation is an equation containing one unknown variable with power one and constants.
The standard form of an linear equation in one variable x is :
ax + b = 0 , where a, b are constants
x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting, multiplying, dividing same number to both sides.
Given that number of fishes jake has in the aquarium = 30
And that number of fishes Emi has is 1/3 the number of fish that jake has .
Therefore, Number of fishes that Emi has = 1/3 (30) = 10
Also given that Emi has 1/2 the number of fish that Tobin has .
Let Tobin has x fishes
⇒ 1/2(x) = Number of fishes Emi has
⇒ (1/2)x = 10, this is an linear equation in x
Multiplying both sides by 2, We get:
⇒ 2× (1/2)x = 2 ×10
⇒ x = 20
∴ Tobin has 20 fishes
If the three students combined all their fish in the school's aquarium,
the Total number of fishes = 30+20+10 = 50
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Rewrite 72.3 + (-39.1) by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.
72.3 - 39.1 = 4 tens - 7 ones - 2 tens is the correct order after rewriting.
Given the formula 72.3 + (-39.1)
removing the parentheses:
= 72.3 + (-39.1) (-39.1)
= 72.3 - 39.1
converting decimal numbers to place values
72.3 = 7tens plus 2units plus 3tenths
72.3 = 7(10) (10)
+2(1)+3(1/10)
72.3 =70+2+0.3
Similarly, 39.1
39.1 = 3tens plus 9units plus 1tenth
39.1 = 3(10)+9(1)+1(1/10)
39.1 =30+9+0.1
72.3 - 39.1 = 70+2+0.3 - (30+9+0.1)
72.3 - 39.1 = 70+2+0.3 - 30-9-0.1
72.3 - 39.1 = 70-30+2-9+0.3-0.1
72.3 - 39.1 = 40 - 7 +0.2
Hence after rewriting we get 72.3 - 39.1 = 4 tens - 7 ones - 2 tens
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Is the graph of f(x) = (4/5)^(x) Increasing or Decreasing?
The graph of the function f(x) = (4/5)^(x) is decreasing.
We are given a graph.The graph shows the function f(x).The function f(x) equals (4/5)^(x).We need to check whether the given function f(x) is increasing or decreasing.f(x) = (4/5)^(x)f(x) = (0.8)^(x)We can see that 0.8 lies between 0 and 1.We know that if a number lies between 0 and 1, it becomes more and more small as it is raised to a higher power.Even from the given graph, we can see that the function is always decreasing as we go from left to right.The function f(x) is an exponentially decreasing function.To learn more about functions, visit :
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an amusement park sells child and adult tickets at a ratio of 8:1. on saturday they sold 147 more child tickets than adult tickets. how many tickets did the amusment park sell on saturday?
Beth owns a coffee shop. She uses half a litre of mayonnaise each day. Mayonnaise costs £2.35 for a 1 litre jar and £4.65 for a 2 litre jar. Beth buys enough mayonnaise to last for 14 days. What is the lowest price Beth can buy this mayonnaise for? Show your working.
Answer:
£16.30
Step-by-step explanation:
0.5*14=7 litres for 2 weeks
The total cost to buy 7 litres = 7 × 2.35 = 16.45
The cost of 7 litres with the 1 litre jars is £16.45
The total cost to buy 7 litres = (4.65 × 3) + 2.35 = 16.30
The cost of 7 litres with the 2 and 1 litre jars is £16.30
16.45-16.30=15p
The lowest price Beth can buy this mayonnaise for £16.30.
What are arithmetic operations?The study of numbers and their operations, which are crucial to all other fields of mathematics, is included in the field of arithmetic operations. Addition, subtraction, multiplication, and division are the four basic operations of these systems.
It is given that, A coffee business is owned by Beth. Every day, she consumes half a litre of mayonnaise. A 1-litre jar of mayonnaise costs £2.35, and a 2-litre container costs £4.65. Beth purchases 14 days' worth of mayonnaise.
We have to find the cheapest price Beth can get this mayo for,
0.5*14=7 litres for 2 weeks
The total cost to buy 7 litres is,
= 7 × 2.35
= 16.45
The cost of 7 litres with the 1-litre jars is £16.45
The total cost to buy 7 litres is,
= (4.65 × 3) + 2.35
= 16.30
Thus, the cheapest price Beth can buy this mayonnaise for £16.30.
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Mark has downloaded four times as many songs on his music player as Chloe. If Mark has 40 songs, how many songs does Chloe have?
Answer:
Chloe has 10 songs.
Step-by-step explanation:
40 ÷ 4 = 10
Mrs. Walter wanted to plant one daffodil for every 3 tulips in her garden. If she planted 20 daffodils, how many tulips did she plant?
Answer:
60 tulips
Step-by-step explanation:
1 daffodils : 3 tulips
Since she planted 20 daffodils
20 × 3 = 60 tulips
i am less then 10. i am not a multiple of 2. i am a composite number what am i?
Answer:
9
Composite numbers under 10:
4,6,8, and 9.
The only one of those 4 that is not a multiple of 2 is 9
Step-by-step explanation:
Hope it helps! =D
In an isosceles triangle ABC, the measure of vertex angle C is 30° more than the measure of each base angle. Find the measure of each angle of the triangle
Answer:
30 + x + x + x = 180
so, 30 + 3x = 180
sub 30 on both sides
3x = 150
divide 3 on both sides
x = 50
an acorn is falling from 13 feet in the air if it descends 4.8 feet every second write and solve the equation to determine how long it will take for the acorn to be 1 foot above the ground
It will take 6 seconds for the acorn to be 1 foot above the ground.
What is linear equation?A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A typical form linear equation is, for instance, 2x+3y=5. When an equation is provided in this format, finding both intercepts is rather simple (x and y).
Given:
acorn is falling from 13 feet
Every seconds it descends = 4.8 feet
let us assume that the equation for the distance between the acorn from the ground is
x =13 - 4.8 y
where is y is time in seconds and x is the distance
if x = 1 foot
1 = 13 -4.8y
-12 = -4.8y
y = -12 / -4.8
y = 2.5 seconds
Hence, it will take 6 seconds for the acorn to be 1 foot above the ground.
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select graph for solution of open sentence click until correct graph appears [×]=2
Given:
[tex]|x|=-2[/tex]Let's graph the the absolute value equation.
From the equation let's solve for x.
Since |x| = -2, there is no possible value of x that can satisfy this equation. This is because an absolute value can never be a negative number.
Therefore, we can say there is no solution.
This absolute value equation can not be graphed.
ANSWER:
No solution
4.17. for a standard normal random variable z, compute (a) p(z ≥ 0.99) (b) p(z ≤ −0.99) (c) p(z < 0.99) (d) p(|z| > 0.99) (e) p(z < 10.0) (f) p(z > 10.0) (g) with probability 0.9, variable z is less than what?
Answer: 1.28
Step-by-step explanation:
1. P(Z > 0.99) = 1 -Ф (0.99) = 1-0.8389 = 0.1611
2.P(Z <-0.99) = Ф(-0.99) = 0.161 (known that from [a] by symmetry)
3.P(Z <0.99) = Ф(0.99) = 0.8389
4. P(Z >0.99) = P(Z <-0.99) + P(Z > 0.99) = 2(0.1611) = 0.3222
The value z = 10.0 is out because it is too large. On comparing with the largest value, z = 3.99,
we get
5. P(Z < 10.0) > P(Z <3.99) = 1.0
6.P(Z > 10.0)<P(Z > 3.99) =10.0
7. On solving the equation
Ф(Z) = 0.9
for Z.
In Table A4, find the value of z corresponding to the probability 0.9. The nearest value is Ф(1.28) = 0.8997. Therefore, z ≈ 1.28
Select the equation of the line that goes through point (4,−2) and is parallel to the equation 2x+5y=15.
A. -2/5x + y= -18/5
B. -5/2x + y= -12
C. 2/5x + y= -2/5
D. 5/2x + y= 8
Kamryn’s doctor recommended that she drink 64 fluid ounces of water every day. There are about 30 milliliters in 1 fluid ounce. Which measurement represents the number of milliliters in 64 fluid ounces?
help please
64 fluid ounces is equivalent to 1920 milliliters in measurement.
What is Unit conversion?Conversion of units means to convert between different units of measurement for the same quantity. Their are many different units that can be used to represent the same quantity. Some examples of units are m, cm, litre etc.
Given is Kamryn’s whose doctor recommended that she drink 64 fluid ounces of water every day and are about 30 milliliters in 1 fluid ounce.
A fluid ounce is a unit of capacity equal to one twentieth of a pint (approximately 0.028 litre)
In one fluid ounces → 30 milliliters.
Then, in 64 fluid ounces there will be → 64 x 30 = 1920 milliliters.
Therefore, 64 fluid ounces is equivalent to 1920 milliliters in measurement.
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Please help!
Find the value of x and y
We can conclude that the value of angle y is 70° and x is 35°.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.So, a measure of 'x':
We can see that ∠BAC = ∠DAE (Inversely opposite angles)
∠BAC = ∠DAE = 40°We can observe that △DAE is an isosceles triangle with ∠2x and ∠y being equal.Let 2x be y for instance:
y + y + 40 = 1802y = 180 - 402y = 140y = 140/2y = 70°Now, we know that y = 70 and similarly 2x = 70.
Now, solve for 'x' as follows:
2x = 70x = 70/2x = 35°Therefore, we can conclude that the value of angle y is 70° and x is 35°.
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What is the average rate of change of the equation g(x)=−x2+2x−4 from x = 2 to x = 5
The average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .
The average of change of the function f(x) from x=a to x=b is given by the formula
Average rate of change = (f(b)-f(a))/(b-a)
In the question ,
it is given that
the function is g(x) =−x²+2x−4
we need to find g(2) and g(5) .
g(2) = −(2)²+2(2)−4
= -4 + 4 -4
= -4
g(5) = −(5)²+2(5)−4
= -25 +10 -4
= -15 -4
= -19
So , Average rate of change = (g(5) - g(2))/(5-2)
Substituting the values , we get
Average rate of change = (-19 - (-4))/3
= (-19+4)/3
= -15/3
= -5
Therefore , the average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .
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what are the answer to these questions
( 1 ) The y-intercept for the first graph is 50. The correct option is B.
( 2 ) The y-intercept for the second graph is 12. The correct option is C.
( 3 ) The y-intercept for the third graph is 0. The correct option is C.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
The y-intercept of the first graph:-
y = mx + c
m= ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 350 - 50 ) / ( 4 ) = 75
y = mx + c
50 = 75 x 0 + c
c = 50
The y-intercept of the second graph:-
y = mx + c
m= ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 30 - 12 ) / ( 4 ) = 4.5
y = mx + c
12 = 4.5 x 0 + c
c = 12
The y-intercept of the third graph:-
y = mx + c
m= ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 6 - 3 ) / ( ( 8 - 4 ) = 3 / 4
y = mx + c
3 = ( 3 / 4) x 4 + c
c = 0
Therefore, the y-intercept of all the graphs is calculated above.
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Ms. Yoto is putting together bags of fruit that contain 1 pear for every 2 apples. How many apples are there in a bag if there is a total of nine pieces of fruit (using algebraic formulas).
The number of apples in the bag are 6
What are algebraic equations?
Algebraic equation are the equation containing coefficients and variable Which can be solved by various method like substitution and elimination.
We are given that, Ms. Yoto is putting together bags of fruit that contain 1 pear for every 2 apples.
Also the total number of fruits in the bag are 9
Now mr. Yoto is putting 3 fruit at a time and the bag contains total of 9 fruits that means 3 such sets were put
in each set there were 2 apples and 1 pear
Hence there were 6 apples and 3 pear
Hence the number of apples in the bag is 6
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Eric has 130 coins consisting of Nickels and quarters. The coins combined value comes to $15.90. Find out how many of each coins Eric has.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the two coins
Let N represents Nickels
Let Q represents quarters
STEP 2: Get the first equation
Equation 1: Eric has 130 coins consisting of quarters and nickels. This is given as:
[tex]N+Q=130------Equation\text{ 1}[/tex]STEP 3: Get the second equation
The total value of all of the coins is $15.90. Each quarter represents .25 and each nickel represents .05, then the second equation is:
[tex]0.25Q+0.05N=15.90------Equation\text{ 2}[/tex]STEP 4: Multiply Equation 2 by 100 to remove the decimals
[tex]\begin{gathered} Equatio\text{ 2}\times100\text{ will give:} \\ 25Q+5N=1590----Equation\text{ 3} \end{gathered}[/tex]STEP 5: Make N the subject of Equation 1
[tex]undefined[/tex]Expand and simplify 3(2x-1) + 2(2x + 5)
Use the distributive property to expand the binomials.
3(2x - 1) = 6x - 3
2(2x + 5) = 4x + 10
6x - 3 + 4x + 10
Combine like terms.
6x + 4x + 10 - 3
10x + 7
Step-by-step explanation:
3(2x-1)+2(2x+5)
6x-3+4x+10
6x+4x+10-3
10x+7
Which answer is an equation in point-slope form for the given point and slope?
Point: (5, 9); Slope: 2
Responses
y−9=2(x−5)
y−5=2(x+9)
y−9=2(x+5)
y+9=2(x−5)
The equation which forms the correct slope-point form equation is
y - 9 = 2( x - 5). Thus, option (1) is the answer.
The point-slope form is a method that uses the slope of the line and a random coordinate on any point of the line to create an equation of that line.
The equation in the point-slope form is written in the format: [tex]y-y_{1}=m(x-x_{1})[/tex] , where m is the slope and [tex]x_{1}[/tex] and [tex]y_{1}[/tex]are the coordinates of the point on the line.
The given slope is 2, the x-coordinate is 5, and the y-coordinate is 9. There will be no addition symbol in the equation. There is only a subtraction of the coordinates in the equation form. Since options 2, 3, and 4 have addition signs, they do not show the correct equation.
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