=====================================================
Explanation:
Apply the difference of squares rule
x² - 4y² = 13
x² - (2y)² = 13
(x - 2y)(x + 2y) = 13
Since x and y are positive integers, this means x-2y and x+2y are both integers as well.
The value 13 is prime. Its only factors are 1 and 13
Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:
A) x-2y = 1 and x+2y = 13B) x-2y = 13 and x+2y = 1----------------
Let's consider case A
We have this system of equations
[tex]\begin{cases}x-2y = 1\\x+2y = 13\end{cases}[/tex]
Add the equations straight down
x+x becomes 2x-2y+2y becomes 0y = 0 which goes away1+13 becomes 14Therefore we have 2x = 14 solve to x = 7
From here, plug this into either equation to solve for y
x-2y = 1
7 - 2y = 1
-2y = 1-7
-2y = -6
y = -6/(-2)
y = 3
You should get the same result if you used x+2y = 13
----------------
Since we've found that x = 7 and y = 3, notice how case B is not possible
Example: x-2y = 13 becomes 7-2(3) = 13 which is false.
Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.
-----------------
Let's check those x and y values in the original equation
x² - 4y² = 13
7² - 4*(3)² = 13
49 - 4(9) = 13
49 - 36 = 13
13 = 13
The answer is confirmed.
Determine whether the given sequence could be geometric, arithmetic, or neither. If possible, identify either the common ratio or the common difference. 7, 9, 10, 12, ....
The sequence is neither geometric nor arithmetic
How to determine the sequence type?The sequence is given as:
7, 9, 10, 12, ....
Calculate the common difference to determine if the sequence is arithmetic;
d = 12- 10 = 10 - 9 = 9 - 7
Evaluate
d = 2 = 1 = 2
The above is false because 2 and 1 are not equal.
So, the sequence is not arithmetic
Calculate the common ratio to determine if the sequence is geometric;
r = 12/10 = 10 /9 = 9/7
Evaluate
r = 1.2 = 1.11 = 1.29
The above is false because the numbers are not equal.
So, the sequence is not geometric.
Hence, the sequence is neither geometric nor arithmetic
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An object is pulled up a ramp with a 25° incline. the force required to move the object is 300 pounds. what is the component form of the force vector?
Answer: D, (272,127)
Step-by-step explanation:
sorry it’s late but just took it on edge
The expendlvre on good of a ram is Rs 8000 . If the number of degree of sector food is 40°. Find his total expenditure.
(Please answer urgently)
The total expenditure is Rs 72,000.
What is the total expenditure?
The total expenditure can be determined using this equation:
(total amount spent on a good x total value of circle) / degree of the sector of good
(8000 x 360) / 40 = Rs 72,000
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here are 7 healthy blue fish, 3 unhealthy yellow fish, 8 healthy green fish, and 3 unhealthy blue fish in a tank. what is the probability of catching a healthy blue fish?
Answer: 1/3
Step-by-step explanation:
7/21=1/3
find the sum (3x^2+2x+3)+(x^2+x+1)
Hello !
Answer:
4x² + 3x + 4
Step-by-step explanation:
(3x² + 2x + 3) + (x² + x + 1)
= 3x² + 2x + 3 + x² + x + 1
= 3x² + x² + 2x + x + 3 + 1
= 4x² + 3x + 4
There are 3 yellow fish, 5 blue fish, and 7 green fish in a tank. What is the probability of catching an orange fish?
Answer: there's no orange fish
One angstrom is the tenth billionth part of a meter. express this information in scientific notation
The scientific notation for the given information is 1 × [tex]10^{-10}[/tex]. Thus, one angstrom is written as 1 × [tex]10^{-10}[/tex] and denoted by A°.
How to write in scientific notation?Scientific notation is used to write very large numbers or very small numbers in a simple way that is easy to understand and easy for calculate.
A number is written in scientific notation as follows:
Scientific notation: m × [tex]10^n[/tex]
where m is the absolute value of the number or a decimal number and n is the power and 10 is the base.
Expressing the given information in scientific notation:The given information is,
One Angstrom = ten billionths part of a meter
Since ten billion = [tex]10^{10}[/tex]
So, ten billionth part of a meter = 1 ×1/[tex]10^{10}[/tex] = 1 × [tex]10^{-10}[/tex].
therefore, the scientific notation for one Angstrom is 1 × [tex]10^{-10}[/tex].
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It is estimated that recycling 1 ton of paper saves about 17 trees. About how many trees are saved if 8254 ton of paper are recycled
Answer:
142318 trees
Step-by-step explanation:
8254x17=140318
Solve each triangle. Round answers to the nearest tenth.
The value of the missing triangle sides and angles are XY = 20.9, YZ = 12.4 and ∠Y = 119°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule is used to show the relationship between the sides and angles of a triangle.
In the triangle XYZ:
∠X + ∠Y + ∠Z = 180° (sine rule)
22 + 39 + ∠Y = 180
∠Y = 119°
Using sine rule:
XY / sinZ = XZ / sinY
XY / sin(39) = 29 / sin(119)
XY = 20.9
Also:
YZ / sinX = XZ / sinY
YZ / sin(22) = 29 / sin(119)
YZ = 12.4
The value of the missing triangle sides and angles are XY = 20.9, YZ = 12.4 and ∠Y = 119°
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Help please I will mark brainliest
Answer:
are we supposed to solve the graph
Step-by-step explanation:
Compare the linear relationships.
Linear equation A: y=3x
Linear equation B is partially represented by the points in this table.
x y
5 20
7 28
9 36
Which linear equation has the greater slope? Why?
Select the option that correctly answers both questions.
Equation A has the greater slope. It has a slope of 4, and equation B has a slope of 3, which is smaller.
Equation A has the greater slope. It has a slope of 4 textsf comma and equation B has a slope of 3 textsf comma which is smaller.
Equation B has the greater slope. It has a slope of 8, and equation A has a slope of 3, which is smaller.
Equation B has the greater slope. It has a slope of 8 textsf comma and equation A has a slope of 3 textsf comma which is smaller.
Equation B has the greater slope. It has a slope of 4, and equation A has a slope of 3, which is smaller.
Equation B has the greater slope. It has a slope of 4 textsf comma and equation A has a slope of 3 textsf comma which is smaller.
Equation A has the greater slope. It has a slope of 8, and equation B has a slope of 3, which is smaller.
Answer:
1: Slope intercept form is y=mx+b, where m is slope and b is the y-intercept. We can use this form of a linear equation to draw the graph of that equation on the x-y coordinate plane.
2: We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal. If we subtract the same number from both sides of an equation, both sides will remain equal.
A: For example: If you pay 30 dollars a month for your cell phone and 10 cents per minute of usage the monthly cost of using your cell phone would be a linear equation of a function, C, the monthly cost based on the number of minutes you use monthly.
Answer:
Option 3 is the correct answer :)
Step-by-step explanation:
A college student takes the same number of credits each semester. Before beginning college, the student had some credits earned while in high school. After 3 semesters, the student had 41 credits, and after 6 semesters, the student had 68 credits. If C(t), is the number of credits after t semesters, write the equation that correctly models this situation.
Answer:
C(t) = 9t + 14
Step-by-step explanation:
write two equations with the given information
x + 6y = 68
x + 3y = 41
(x and y are just random variables, with x being the number of credits from high school and y being the number of credits earned each semester)
subtract (x+3y=41) from (x+6y=68) to get 3y=27
y = 9
then plug back in to one of the equations to find x
x + 3(9) = 41
x + 27 = 41
x = 14
then write the equation for C(t)
C(t) = 9t + 14
because you start with 14 credits from high school then add 9 credits for each semester taken
36. Salma has a salary of 6.2 x 10 to the power of 4 dollars per year. Carter has a salary of
1.2 x 10to the power of 6 dollars per year. How much larger is Carter's salary than
Salma's?
5.2 x 10²
5 x 10to the power of-2
7.4 x 10 to the power of 10
1.138 x 10to the power of6
Carter's salary is $1.1138⁶ more than Salma's salary.
How much larger is Carter's salary than Salma's?To perform the difference, we need to be able to take a common factor.
We know that Salma's salary is $6.2×10⁴
While Carter's salary is $1.2×10⁶
To get the same common factor, 10⁴, we can divide and multiply Carter's salary by 100, so we get:
[tex]1.2*10^6*\frac{100}{100} = (1.2*100)*(10^6/100) = 120*10^4[/tex]
Then Carter's salary is $120*10⁴
The difference between Carter's and Salma's salaries is:
$120*10⁴ - $6.2×10⁴ = $113.8*10⁴
If we return to the scientific notation, we get:
$113.8*10⁴ = $1.1138⁶
This means that Carter's salary is $1.1138⁶ more than Salma's salary.
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Write the answer of p/q form 7.6 bar
7.6 expressed in p/q form is 7 3/5.
What is 7.6 in p/q form?
7.6 is in decimal. The decimal is a number that consists of integers and non integer. The integers are to the left of the decimal point and the non-integers are to the right of the decimal point.
In order to convert 7.6 to a fraction, note that 7 is the whole number while 0.6 is the non integer.
7.6 = 7 + 6/10
7 3/5
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[tex]\boxed{\bf{Help\;please}}[/tex]
____________________
[tex]\boxed{\bf{Answer\;Requirements-:}}[/tex]
No spam
No absurd answers
[tex]\bf{Only[/tex]
People who are good at trig
[tex]\bf{should\;answer}[/tex]
Answer:
-8m
Step-by-step explanation:
This question only requires to to substitute t = 0 and t = 1 into the equation to find the displacement.
Lets find the displacement at t = 0.
[tex]x(0)=4sin(\pi (0)+\frac{\pi }{2} )\\=4sin(\frac{\pi }{2} )\\= 4m[/tex]
Lets find the displacement at t = 1.
[tex]x(1) = 4sin(\pi (1)+\frac{\pi }{2} )\\=4sin(\pi +\frac{\pi }{2} )\\=-4m[/tex]
Total displacement = Final Position - Initial Position
= x(1)-x(0)
= -4m - 4m
= -8m
On a coordinate plane, triangle K J L is shown. Line segment G H goes from side J K to J L. Point K is at (0, 0), point G is at (e, f), point J is at (2 e, 2 f), point H is at (e + d, f), and point L is at (2 d, 0).
To prove part of the triangle midsegment theorem using the diagram, which statement must be shown?
The length of JK equals the length of JL.
The length of GH is half the length of KL.
The slope of JK equals the slope of JL.
The slope of GH is half the slope of KL.
Based on the triangle midpoint theorem, the statement which must be shown is that: B. the length of GH is half the length of KL.
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.
Based on the triangle midpoint theorem, we can infer and logically deduce that the statement which must be shown is that the length of GH is half the length of KL.
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Answer: B. The length of GH is half the length of KL.
Step-by-step explanation: TRUST ME! The answer is correct on Edge. :)
Can someone help with this question?
A cubic function is known as a function whose graph is in the shape of a horizontal S.
The graph that meets these requirements is the graph D.
A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing (in m/min)
Answer:
Let R be the radius of the tank, H(t) the height of the water at time t, and V(t) the volume of the water. The quantities V(t), R and H(t) are related by the equation
V(t) = πR²H(t) ___(1)
The rate of increase of the volume is the derivative with respect to time,
dV/dt
and the rate of increase of the height is
dH/dt
We can therefore restate the given and the unknown as follows
Given:
dV/dt = 4m³/min
Unknown:
dH/dt
Now we take derivative of each side of (1) with respect to t:
dV/dt = πR²dH/dt
So
dH/dt = 1/πR²dV/dt
Substituting R = 3 m and dV/dt = 4m³/min we have
dH/dt = 1/π(3)² ⋅ 4 = 4/9π
Answer: the height of the water increasing at a rate of
dH/dt = 4/9π²
≈ 0.14 m/minKeep the triangle that you created in part A. You will now copy the triangle to a different location on the grid using three of its sides:
In a different place on the grid, draw a new line segment that is parallel to and has the same length as AB. Label this segment DE.
Next, copy AC and BC . A reliable way to do this is to draw a circle centered on each endpoint of your new line segment. Make the radius of each circle equal to each of the lengths of the two remaining line segments on the original triangle. One of the intersection points of the two circles marks the third vertex of your new triangle. Place a point on the intersection, and label the point F.
Finish copying the triangle by drawing a polygon through the three points that you've established.
You should now have two triangles on the grid. What do you notice about the two triangles in terms of their size and shape?
The thing that I notice about the two triangles in terms of their size and shape is that they that is the triangles tend to appear to be of the same size and shape.
What are Congruent triangles?Congruent triangles are known to be triangles that are said to have both the same shape and also of the same size for the two triangles.
Note that in the case above, we need to understand that the factors of a triangle are composed of 3 angles and the 3 facets and when you put the three together following the description given, a Congruent triangle will be formed.
Therefore, The thing that I notice about the two triangles in terms of their size and shape is that they that is the triangles tend to appear to be of the same size and shape.
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reflect the points p(4,-3) and q(7,2) on the line which passes through the origin and point (4,4).state the coordinate of image p and q
Answer:
P' (- 3, 4 ) , Q' (2, 7 )
Step-by-step explanation:
the line passing through the origin and (4, 4 ) has equation
y = x
a point reflected in the line y = x
(x, y ) → (y, x ) , then
P (4, - 3 ) → P' (- 3, 4 )
Q (7, 2 ) → Q' (2, 7 )
Warm-Up
Recognizing a Function
Determine the graph that represents a function.
Answer:
The 2nd one.
Step-by-step explanation:
The 2nd one is a quadratic function as it is a parabola.
Answer:
[tex]1.\ x^2+y^2=5^2.\\2.\ y^2=9-x.\\3.\ y=2x-2.[/tex]
Owen made 60% of the shots he attempted during his hockey practice. He made 18 shots. How many shots did Owen attempt during his hockey practice?
Answer:
he attempted 30 shots
Step-by-step explanation:
60 percent of 30 is 18 and 40 percent of 30 is 12 so you at 12 plus 18 and get 30
Find the product of √4(√8+3).
O 4√2+6√3
O 2√3+6
O 8√2+6√3
O 4√2+6
Answer:
Step-by-step explanation:
hello :
√4=2 and √8=2√2
√4(√8+3). =2(2√2+3)=4√2+6
Answer:
4√2 +6
Step by step explanation:
To find the product of the the above question, we open bracket.
The question is in surd form.√4(√8+3)
removing brackets.
√4×√8 + √4×3
2√8 + 2×3
2× √4×√2 + 6
2× 2 √2 + 6
4√2 + 6
Find the value of n, if 25.003 = (2x 10) + (5x1)+(3xn)
Answer:
[tex]n=0.001[/tex]
Step-by-step explanation:
[tex](2\times10)+(5\times1)+(3\times n)=25.003\\\\\implies 20 + 5 + 3n = 25.003\\\\\implies 3n+25=25.003\\\\\implies 3n+25-25=25.003-25\\\\\implies 3n = 0.003\\\\\implies n=0.001[/tex]
Ten women sit in 10 seats in a line. All of the 10 get up and then reseat themselves using all 10 seats, each sitting in the seat she was in before or a seat next to the one she occupied before. In how many ways can the women be reseated
Women can be seated in 89 ways.
Let Sn be the number of possible seating arrangements with n women. Consider n≥3 and focus on the rightmost woman. If she goes back to her seat, then there are Sn−1 ways to seat the remaining n−1 women. If he is sitting in the penultimate seat, then the woman who was sitting there before must now sit in the rightmost seat.
This gives us Sn−2 ways to seat another n−2 woman, so we get the recursion Sn=Sn−1+Sn−2. Starting with S1=1 and S2=2 we can calculate S10=89.
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Write the rule for the table, use x for the input.
The linear function that gives the rule for the table is: y = -8x + 2.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, when x = 0, y = 2, hence the y-intercept is of b = 2. When x increases by 1, y decreases by -8, hence the slope is of m = -8, and the rule is given by:
y = -8x + 2.
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How many grams of protein are needed per day by a male non-athlete, weighing 87 kilograms?.
70 grams of protein are needed per day by a male non-athlete, weighing 87 kilograms.
87 kg x 0.8 g protein/kg/day
= 69.6 g protein/day,
Rounded up to 70 g/day.
Maximum American adults eat approximately a hundred grams of protein consistent with a day or roughly two times the advocated amount. Even on a vegan weight-reduction plan people can effortlessly get 60 to eighty grams of protein for the duration of the day from foods like beans, legumes, nuts, broccoli, and entire grains.
The encouraged Dietary Allowance (RDA), which is the minimal amount you want to be healthy, is 0.8 grams in line with a kilogram (zero.36 grams consistent with pound) of body weight in keeping with day 46 grams for a median woman.
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HELPP,what’s the answer?
[tex]\rm y\ \le2x+1[/tex] , [tex]\rm y\le-x+3[/tex] , Option B represents the the graph given .
What is an Inequality ?An Inequality is a statement that connects two algebraic expression by an inequality operator.
To determine the solution of the inequalities , the common area that comes under the inequality will be found
The graph plotted using
y ≥ 2x +1 and y ≥ - x+3
it doesn't represent the solution as given in the question graph , graph no.1
The graph given in the question is the solution of the set of inequalities
This can be understood by Graph 2
[tex]\rm y\ \le2x+1[/tex]
[tex]\rm y\le-x+3[/tex]
As all the inequalities of all the options were plotted and the solution to the system of inequality is represented by the graph
Therefore Option B is the correct answer.
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Find the surface area.
Answer: 30506.49303
Step-by-step explanation:
If a translation maps ∠I onto ∠K, which of the following statements is true?
IMPORTANT!!!!!
The statement which is true is ΔGHI ~ ΔGJK.
What is Translation?This is commonly used in geometry to describe a function which moves object at distances.
This therefore means that translation of ∠I onto ∠K means shifting of point I to point K.
The triangles given are HGI and JGK.
Translation in this scenario therefore means that the triangles are similar only if other angles are mapped to their corresponding angles.
It confirms that ΔGHI ~ ΔGJK thereby making it the most appropriate choice.
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Answer:
ΔGHI ~ ΔGJK
Step-by-step explanation: