The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
Which equation represents the line that is perpendicular to and passes through (-8,-2)?
x = -2
x = -8
y = -6
y = -8
The equation of the line that is perpendicular to y = 1/6 is: B. x = -8.
How to Find the Equation of Perpendicular Lines?Perpendicular lines have slope values that equals -1 when multiplied together, that is, they are negative reciprocals.
Given the equation, y = 1/6, the slope is 0. This means it is a vertical line, therefore, the line that is perpendicular to it would automatically be a vertical line with an undefined slope which passes through (,8, -2).
The line therefore, would intercept the x-axis at -8. The equation would be: x = -8.
Equation of the perpendicular line is therefore: B. x = -8.
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Match the information on the left with the appropriate equation on the right.
m=1, b=-3. x+y=1
m=1, (-1,2) x-y=-1
(-2,3),(-3,4) x-y=-3
x-y=3
The equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1
Equation of a lineA line is the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;
y = mx + b
m is the slope
b is the y-intercept
Given that m=1, b=-3, the required equation will be y = x - 3 or x - y = 3
For the parameter m=1, (-1,2)
y - 2 =1(x+1)
y - 2 = x+1
y =x + 3
Hence the equation of the line for the parameters m=1, (-1,2) is y = x + 3
For the coordinates (-2,3),(-3,4)
Slope = 4-3/-3+2
Slope = -1
For the intercept;
4 =-1(-3) + b
b = 4 - 3
b = 1
Hence the equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1
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Given the graph of g(x), describes the transformation of the parent function f(x)=2^x
Answer:
The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units
Find the slope-intercept form of the line that
passes through the point (-7, 3) and is
parallel to the line 2x+5y = 3.
1
10 ft
Cone 1
2.5 ft
8 ftl
2 ft
Cone 2
the cowboys football team started at the zero yard line.throughout the course of the first quarter the team gained 7 yards, lost 8 yards and then lost 7 more yard. what is the total of these three plays? how many yards did the team gain or lose?
The net number of yards lost by the cowboys football team is; 8 yards.
How many yards did the team gain or lose?It follows from the task content that the number of yards gained or lost by the football team during each of the three plays is; gained 7 yards, lost 8 yards and then lost 7 more yard.
Hence, by polarising yard gain as positive and yard loss as negative; we have;
Net total = 7 - 8 -7 = -8
Hence, the team lost 8 yards in the total game.
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math stuff who ever answers right gets brainlest answer
Answer:
Median is 83
Range: 61
Step-by-step explanation:
The median is the number in the middle. The range is the max. number subtracted from the min number.
the equation of a line is 1.5x2 what are its slope a y intercept
Answer:
1.5 is the slope and 2 is the intercept
Step-by-step explanation:
I am assuming that the equation is y = 1.5x + 2.
What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually over four years?
The total repayment made, including principal and interest is $1262.27
Compound interestThe formula for calculating the compound interest is calculated as shown below;
A = P(1+r)^t
where
P is the principal = $1100
rate = 3.5% = 0.035
time "t" =4 years
Substitute
A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)
A = 1262.27
Hence the total repayment made, including principal and interest is $1262.27
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What is the question of the translated function, g(x), if f(x)=x^2
-Dear lord help
The graph of the parabola g(x) is (x+2)^2 + 3
Translation of functionGiven the following parent function of the parabola expressed as;
f(x) = x^2
The function g(x) shows a horizontal translation to the left by 2 units and vertical translation up by 3 units to have the equation;
g(x) = (x+2)^2 + 3
Hence the graph of the parabola g(x) is (x+2)^2 + 3
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A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 8%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $692.50. How much was the hotel charge in each city before tax?
Step-by-step explanation:
x = hotel charge before tax in 1st city
y = hotel charge before tax in 2nd city
y = x + 1500
x×0.08 + y×0.05 = 692.5
why ?
a% of b = b×a/100
why ?
b = 100%
1% = 100%/100 = b/100
a% = a×1% = a×b/100 = b×a/100
so, e.g. 8% of something is that something multiplied by 8/100 or 0.08
now, we are using the first equation in the second equation :
x×0.08 + (x + 1500)×0.05 = 692.5
x×0.08 + x×0.05 + 1500×0.05 = 692.5
x×0.13 + 75 = 692.5
x×0.13 = 617.5
x = 617.5 / 0.13 = $4,750
y = x + 1500 = 4750 + 1500 = $6,250
the hotel charge before tax in the first city : $4,750
the hotel charge before tax in the second city : $6,250
Your local pizza store sells medium pizzas for $6.79 each, and breadsticks for $2.49 per order.
For a party, you decide to order 4 pizzas and 2 orders of breadsticks. There is a $3 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?
The total bill after tax is $38.44.
What is the total bill?The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14
Now, determine the total cost after delivery fee has been added : $3 + $32.14 = $35.14
Now determine the total cost after tax : (1.094) x $35.14 = $38.44
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The total bill after tax of 9.4% is $38.44.
It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price
total cost of 4 pizzas= $6.79 *4
total cost of 4 pizzas=$27.16
total cost of 2 orders of breadsticks=$2.49*2
total cost of 2 orders of breadsticks=$4.98
total cost of purchase prior to adding delivery cost=$27.16+$4.98
total cost of purchase prior to adding delivery cost=$32.14
total cost of purchase after delivery cost=$32.14+$3
total cost of purchase after delivery cost=$35.14
total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)
total cost inclusive of 9.4% sales tax=$35.14*1.094
total cost inclusive of 9.4% sales tax=$38.44
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2) (x+3)
2) Correct the error:
There is an error in the students' work shown below:
Question: Simplify (x-3)(x-7)
Solution: (x-3)(x-7)
x-x-3(x)-7(x) - 21
x²-10x-21
What is the error? Explain how to solve the problem.
The expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.
Simplifying factorsQuadratic equations are equations that has a leading degree of 2. The standard quadratic equation is given as;
f(x) = ax^2+bx+c
Given the product of the expression below;
f(x) = (x-3)(x-7)
Expand
f(x) = x(x) - 7x - 3x -3(-7)
f(x) = x^2 - 7x - 3x + 21
f(x) = x^2 - 10x + 21
Hence the expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.
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Which graph represents the solutions to the inequality |2x − 6| < 4? (5 points) number line with a closed circle on 1, shading to the left and a closed circle on 5, shading to the right number line with a closed circle on 1, shading to the right and a closed circle on 5, shading to the left number line with an open circle on 1, shading to the left and an open circle on 5, shading to the right number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left
The graph that represents the inequality is:
Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.
What is the inequality?The inequality is:
|2x - 6| < 4
Which means that the distance of 2x - 6 to the origin is less than 4, hence:
-4 < 2x - 6 < 4.
The solution is:
2x - 6 > -4
2x > 2
x > 1
2x - 6 < 4
2x < 10
x < 5
The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:
Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.
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A music store sells music equipment at a 35%
markup. It a piece of equipment costs $150.00
what will the selling price be? I
The selling price of an equipment costing $150.00 with 35% markup is $202.50
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given that the mark up is 35%, hence:
Markup = [(selling price - cost price)/cost price] * 100%
Substituting:
$202.50
Selling price = $202.50
The selling price of an equipment costing $150.00 with 35% markup is $202.50
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Part A Your presentation should make a convincing argument that human activity is the major cause of climate change. Your presentation should answer some of these questions: What is climate? How is Earth’s climate changing? What are the natural and human factors that affect climate? How do scientists know that human activity is the major force behind climate change? What evidence do scientists have that climate is changing? Write down two additional questions you have about climate change that will help you make this argument in your presentation. 12pt
Climate is the long-term weather pattern that can be seen in an area over a period of years.
How to explain the climate?Earth’s climate changing as the Earth's atmosphere heats up, it collects, retains, and drops more water, thereby changing weather patterns and making wet areas wetter and dry areas drier.
The factors that affect climate includ deforestation, desertification, urbanization, etc.
Scientists know that recent climate change is largely caused by human activities from an understanding of basic physics by comparing observations with models, and then fingerprinting the detailed patterns of climate change caused by different human and natural influences
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A road sign has the shape of an equilateral triangle with a side length of 48 inches. What is the height of the sign? The road sign is about 38.2 inches tall The road sign is about 38.2 inches tall The road sign is about 23.5 inches tall The road sign is about 23.5 inches tall The road sign is about 41.6 inches tall The road sign is about 41.6 inches tall The road sign is about 43.7 inches tall
The height of the equilateral triangle is 41. 6 inches. Option C
How to determine the height
The formula for finding the height of an equilateral triangle is given as;
h = (a√3)/2
we have a = 48 inches
Let's substitute the value
Height, h = [tex]\frac{48\sqrt{3} }{2}[/tex]
Height = [tex]\frac{48 * 1. 732}{2}[/tex]
Height = [tex]\frac{83. 14}{2}[/tex]
Height = [tex]41. 6[/tex] Inches
Thus, the height of the equilateral triangle is 41. 6 inches. Option C
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find x and y
plssss help
90 + 6x = 180
-90
6x = 90
÷6
x = 15
5y + 4y + 90 + (6x15) =360
9y + 90 + 90 = 360
9y + 180 = 360
- 180
9y = 180
÷9
y = 20
Hope this helps!
Type the correct answer in the box.
Net of a triangular prism includes 3 same-sized rectangles that coincide along their width. Each rectangle has length labeled 10 centimeters and width labeled 15 centimeters. Isosceles triangle is placed above and below of second rectangle.
The surface area of the three-dimensional figure is
square centimeters.
The surface area of this three-dimensional figure is equal to 536.6 square centimeters.
How to determine the surface area?First of all, we would determine the total area of the three rectangles by using this formula:
Total area = 3 × Length × Width
Total area = 3 × 15 × 10
Total area = 450 cm².
Next, we would determine the total area of the two triangles by using this formula:
Total area = 2 × (1/2 × b × h)
Total area = b × h
Total area = 8.66 × 10
Total area = 86.6 cm².
Surface area = 450 + 86.6
Surface area = 536.6 cm².
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We know for a fact that the equation:
[tex]|z+z'| \leqslant |z|+|z'|[/tex]
holds for any 2 complex numbers
I came up with the conclusion that:
[tex]|z+z'|=|z|+|z'|[/tex]only holds when z and z' are pure imaginary or pure real numbers of the SAME sign.
How can i prove this algebraically/geometrically?
Note: Irrelevant answers will be reported
They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].
Let [tex]z=z'=a+bi[/tex]. Then
[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]
[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]
so [tex]|z+z'|=|z|+|z'|[/tex].
The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].
I need answers please help me
Answer:
the ansqer is g(x) = 4^x-4 + 2
Blue Ocean Realty Co. pays weekly salaries of $33,300 for a six-day workweek (Monday through Saturday).
help with this question please !
Answer:
angle 8 is congruent to angles 3, 6, and 1
Step-by-step explanation:
If n and q are parallel then corresponding and vertical angles would be congruent. So: angle 8 is congruent to angles 3, 6, and 1.
a store marks up the wholesale price of a skateboard by 112%. The retail price is $35. What is the wholesale price of the skateboard?
Find the y-intercept of the line.
y=0.2x-6.9
y-intercept:
Answer:
0.2
Step-by-step explanation:
y = mx + b The slope is the number before the x.
Use the slope-intercept form to estimate the slope and y-intercept.
Slope: 0.2
y-intercept: (0,−6.9)
What is slope-intercept form?The slope intercept form in math exists as one of the forms utilized to estimate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.
The slope-intercept form exists y = mx + b, where m exists the slope and b exists the y-intercept.
y = mx + b
Use the slope-intercept form to estimate the slope and y-intercept.
Slope: 0.2
y-intercept: (0,−6.9)
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Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3. Include
your work in your final answer. Type your answer in the box provided to submit your solution.
Answer:
y= 2x -6
Step-by-step explanation:
The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
To find the equation of a line, two information are needed:
Slope (given/ calculated)A pair of coordinatedGiven that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:
y= 2x +c
Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.
2x -3y= 6
When x= 3,
2(3) -3y= 6
6- 3y= 6
3y= 6 -6
3y= 0
Divide both sides by 3:
y= 0
Coordinate that lies on the graph is (3, 0).
Substitute the point into the equation and solve for c:
y= 2x +c
When x= 3, y= 0,
0= 2(3) +c
0= 6 +c
c= -6
Substitute the value of c back into the equation:
Thus, the equation of the line in slope-intercept form is y= 2x -6.
Additional:
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40 Points!
Will give brainliest to whoever answers
The calculation of the trigonometry illustrates that:
sin 45° = 1/✓2
cos45/tan 45 =
cos 45 sin 45 = 1/2
How to illustrate the trigonometry?Opposite = 1
Adjacent = 1
Hypothenuse = ✓2
Tan 45 = opposite/adjacent = 1
Sin 45 = opposite/hypothenuse = 1/✓2
Cos 45 = adjacent/hypothenuse = 1/✓2
cos45/tan 45 = (1/✓2) / 1 = 1/✓2
Cos 45 sin 45 = 1/✓2 × 1/✓2 = 1/2
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A recipe for a cake instructs you to bake it at 220° C for 45 minutes. How many degrees Fahrenheit is this?
This is an exercise on Thermometric scales.
We have as data:
T = 220 °CT = °F ??We apply the following formula:
[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\ ^{\circ}C+32 \end{gathered}$}[/tex]
We substitute data in the formula:
[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\times220+32 \end{gathered}$}[/tex]
First multiply 9 x 220, then the result of this division is divided by 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf =396+32 \ \ \to \ \ [Add] \end{gathered}$}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf =428 \ ^{\circ}F \end{gathered}$}}[/tex]
Therefore the cake recipe that should be baked at 220 °C for 45 minutes, on the Fahrenteir scale is 428 °F. Which indicates that it will be very hot.
PLEASE IF ANYONE CAN HELP
ME SOLVE THESE ILL GIVE YOU BRAINLEAEST THANK YOU
Answer:
You must graph the two equations and find the point of intersection (x,y)
Point of intersection: (-4, -3)
Step-by-step explanation:
I can not provide a picture, but if you know how to graph these linear functions on the graph properly, you will find a point where the linear functions intersect at (x,y).