Answer:
To solve a system of equations by graphing, you need to graph each equation on the same coordinate system and find the point where the two lines intersect. If the equations are in slope-intercept form, you can identify the slope and y-intercept and graph them. If one of the equations is in slope-intercept form, you can rewrite the other one in that form and graph them. If both equations are in other forms, you can find the x- and y-intercepts and graph them.
In this case, we have two equations:
y = x + 5
y = -2x - 1
To graph these equations, we can start by finding their intercepts:
y = x + 5
0 = x + 5
x = -5
So the intercept for y = x + 5 is (-5, 0). Similarly,
y = -2x - 1
0 = -2x - 1
x = -1/2
So the intercept for y = -2x - 1 is (-1/2, 0). Now we can plot these points on a coordinate plane and draw a line through each point. The point where these two lines intersect is our solution.
Therefore, the solution to this system of equations is (-3, 2).
Step-by-step explanation:
the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?
11. Triangles can be classified by their side lengths or by their angle measures. Sometimes triangles are classified using both classifications (side length and angle measure) but these can be redundant and unnecessary. Give an example of a classification based on both side length and angle measure that is unnecessary and explain why.
By answering the presented question, we may conclude that As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.
An isosceles triangle has two sides of equal length, but a right triangle has one angle that measures 90 degrees. As a result, an isosceles right triangle is one with two equal-length sides and one 90-degree angle.
The Pythagorean theorem states that in any right triangle, the two legs (the sides next to the right angle) are always of equal length. Hence, if we know that a triangle has one 90-degree angle and two equal-length sides, we already know that it is a right triangle and that the two legs are equal. As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.
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The function g(x) is a transformation of the cube root parent function,
�
(
�
)
=
�
3
f(x)=
3
x
. What function is g(x)?
The function g(x) is a cubic function, which is a transformation of the cube root parent function, f(x) = 3√x. The equation for g(x) is g(x) = 3x3, where a = 3, b = 0, c = 0, and d = 0.
What is function?Function is a set of instructions or commands that can be used to perform a specific task. It is a reusable code that can be used over and over again to perform a similar task. Functions are used to structure programs, making them easier to read, understand, and debug. Functions are also used to divide a large program into smaller, more manageable parts.
The function g(x) is a cubic function, which is a transformation of the cube root parent function, f(x) = 3√x. A cubic function is a polynomial of degree 3, where the highest exponent of the variable is 3. The general equation for a cubic function is y = ax3 + bx2 + cx + d, where a, b, c, and d are constants. This equation can be rearranged to express the function in terms of x, as follows:
g(x) = ax3 + bx2 + cx + d
By plugging in the values for f(x), we can determine the values of a, b, c, and d. We can start by setting f(x) equal to g(x).
3√x = ax3 + bx2 + cx + d
By taking the cube root of both sides, we can determine the value of a:
a = 3
Next, we can substitute this value into the equation for g(x):
g(x) = 3x3 + bx2 + cx + d
From this, we can see that b = 0, c = 0, and d = 0. Therefore, the function g(x) is a cubic function with equation g(x) = 3x3.
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$2000 are invested in a bank account at an interest rate of 5 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
Find the amount in the bank after 7 years if interest is compounded quaterly.
Find the amount in the bank after 7 years if interest is compounded monthly.
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Simple interest calculation.
Using the formula A = P(1 + r/n)^(nt), where:
A = the amount in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
a) If interest is compounded annually:
A = 2000(1 + 0.05/1)^(1*7) = $2,835.08
b) If interest is compounded quarterly:
A = 2000(1 + 0.05/4)^(4*7) = $2,888.95
c) If interest is compounded monthly:
A = 2000(1 + 0.05/12)^(12*7) = $2,905.03
d) If interest is compounded continuously:
A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
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Factor completely. 5x ^2-5y ^2
In this expression, the GCF is 5. Therefore, we can factor out a 5 to get 5(x² - y²).
What is difference of squares formula?The difference of squares formula states that the difference of two squares can be factored into the product of two terms, one of which is the sum of the terms and the other is the difference of the terms.
When factoring polynomials, it is important to factor out the greatest common factor (GCF).
In this expression, the GCF is 5.
Therefore, we can factor out a 5 to get 5(x² - y²).
Now, we can expand the parentheses and factor out the remaining terms. Since both terms are perfect squares, we can factor them using the difference of squares formula:
5(x² - y²) = 5(x + y)(x - y)
In this case, the terms are x and y, resulting in the factorization of 5(x² - y²) into 5(x + y)(x - y).
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Point B(5,-2) is translated 4 units right and 2 units down and then dilated by a factor of 2 using the origin as the center of dilation what is the resultant point?
the the coordinates of the resulting point are (18, -8). of the resulting point are (18, -8).
What is center of dilation?
The center of dilation is a fixed point in the plane.
Starting with point B(5, -2), if we move it 4 units to the right and 2 units down, we get:
B'(9, -4)
Next, we need to dilate the point by a factor of 2, using the origin as the center of dilation. This means we need to multiply both the x-coordinate and y-coordinate of B' by 2.
So, doubling the x-coordinate of B' gives:
2 × 9 = 18
And doubling the y-coordinate of B' gives:
2 × (-4) = -8
Therefore, the coordinates of the resulting point are (18, -8).
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Is 40, –40, 16, or –16 the solution of the equation 28=d−12?
Answer:
To check whether 40, -40, 16, or -16 is the solution of the equation 28 = d - 12, we can substitute each value into the equation and see if it results in a true statement.
When we substitute 40 into the equation, we get:
28 = 40 - 12
Simplifying, we get:
28 = 28
This is a true statement, so 40 is a solution of the equation.
When we substitute -40 into the equation, we get:
28 = -40 - 12
Simplifying, we get:
28 = -52
This is not a true statement, so -40 is not a solution of the equation.
When we substitute 16 into the equation, we get:
28 = 16 - 12
Simplifying, we get:
28 = 4
This is not a true statement, so 16 is not a solution of the equation.
When we substitute -16 into the equation, we get:
28 = -16 - 12
Simplifying, we get:
28 = -28
This is not a true statement, so -16 is not a solution of the equation.
Therefore, the only solution of the equation 28 = d - 12 is d = 40.
Find tan(Q).
A 1
3 9
"5
135°
P
para os a
was a s
Save and Exit
Next
Submit
Answer:
tanQ = 1
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ OPQ is an exterior angle of the triangle , then
∠ R + ∠ Q = 135°
90° + ∠ Q = 135° ( subtract 90° from both sides )
∠ Q = 45°
Then
tanQ = tan45° = 1
Determine if the function below is continuous.
A. not continuous at x = 5
B. not continuous at x = 0
C. continuous
D. not continuous x = -2
Is the function above continuous: B. not continuous at x = 0.
What is a continuous function?In Mathematics and Geometry, a continuous function can be defined as a type of function in which there is no discontinuities or breaks between the intervals for the points plotted on a graph.
What is a discrete function?In Mathematics and Geometry, a discrete function can be defined as a type of function in which the ordered pair of values on the x-axis and y-axis are separate from each other and unconnected.
By critically observing the graph shown above, we can reasonably infer and logically conclude that it represents a discrete function because it is not continuous at x is equal to 0 i.e x = 0.
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I need help in like 5 minutes please
Answer: 3/2 or 1 1/2 or 1.5
Step-by-step explanation:
9/8 times 2 is 2.25 or 9/4
9/4-6/8= 3/2 or 1 1/2 or 1.5
A rectangle has an area of 108 square
centimeters. Its width is 9 centimeters.
What is the perimeter of the
rectangle?
Therefore, the perimeter of the rectangle is 42 centimeters.
What is area?The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.
Here,
To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.
We can use the formula for the area of a rectangle:
Area of rectangle = length x width
Plugging in the values we have:
108cm² = length x 9cm
Solving for the length, we can divide both sides by 9cm:
length = 108cm² / 9cm
length = 12cm
So, the length of the rectangle is 12 centimeters.
To find the perimeter of the rectangle, we can use the formula:
Perimeter of rectangle = 2 x (length + width)
Plugging in the values we have:
Perimeter of rectangle = 2 x (12cm + 9cm)
Perimeter of rectangle = 2 x 21cm
Perimeter of rectangle = 42cm
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.
What is the circle's equation when its centre is on the x-axis?The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.
Circle's standard equation is written as:
x²+y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is : x²+y²-2x-8=0
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This demonstrates circle's centre is on the x-axis.
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The circle has a radius of three units.
For the circle x²+y²=9, radius is expressed as:
r² = 9
r = 3 units
As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.
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(h+3)2 find the square. Simplify your answer.
(h+3)² simplified is:(h+3)² = h² + 6h + 9
What is binomial?
Binomial refers to a type of probability distribution that describes the number of successes in a fixed number of independent trials.
The expression (h+3)² is a binomial squared. When we square a binomial, we use the formula:
(a+b)² = a² + 2ab + b²
where a and b are any numbers or variables. In this case, our binomial is (h+3), so we can use the formula with a=h and b=3:
(h+3)² = h² + 2h3 + 3²
The first term, h², comes from squaring the h in the binomial. The second term, 2h3, comes from multiplying the two terms in the binomial together and then doubling the result. Finally, the third term, 3^2, comes from squaring the 3 in the binomial.
Simplifying the expression, we can combine like terms. We have h² as the first term, 23h as the second term, and 3^2 as the third term. 23h is equal to 6h, so we can rewrite it as:
(h+3)² = h² + 6h + 9
And that is the simplified form of the expression (h+3)².
Therefore, (h+3)² simplified is:(h+3)² = h² + 6h + 9
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The length of the altitude of an equilateral triangle is 4 square root of 3 . Find the length of a side of the triangle.
[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{3} \end{cases}\implies 4\sqrt{3}=\cfrac{s\sqrt{3}}{2} \\\\\\ 8\sqrt{3}=s\sqrt{3}\implies \cfrac{8\sqrt{3}}{\sqrt{3}}=s\implies 8=s[/tex]
I'LL MARK THE BRAINLIEST TO THE USER THAT GETS IT RIGHT!
A} 38
B} -7
C} -18
D} 11
Answer:
the answer will be A
Step-by-step explanation:
for the explanation the picture will do the best
mark me branliest as you promised
Part of the proceeds from a garage sale was $290 worth of $5 and $20 bills. If there were 8 more $5 bills than $20 bills, find the number of each denomination.
Answer:
18 5-dollar bills
10 20-dollar bills
A conic has vertices at (0,8) and (0,-8) and foci at F(0, √48) and F(0,-√48). (a) Write the standard form of the equation of this conic.
The standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
What is conic?It is a type of curve with a curved line in the middle and two straight lines on the sides. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The standard form of the equation of a conic is
Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.
In this case, the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
To derive this equation, we'll use the distance formula to calculate the distance between the vertices and the foci. The distance between the vertices and the foci is given by
d = √((x_1 - x_2)² + (y_1 - y_2)²)
where (x_1, y_1) is the coordinates of the first vertex and (x_2, y_2) is the coordinates of the first foci.
For the first vertex, (x_1, y_1) = (0, 8). For the first foci, (x_2, y_2) = (0, √48). Thus, the distance between the two points is
d = √((0 - 0)² + (8 - √48)² )
= √(0 + (-8 - √48)² )
= √(-16 - 2√48 + 48)
= √(32 -2√48)
= 2√(16 - √48)
= 2√(16 - 6.9)
= 2√(9)
= 2(3)
= 6
So, the distance between the vertices and the foci is 6.
The equation of the conic can then be written as x² + y² - 16x - 16y - (-8)² = 0, which simplifies to x² + y² - 16x - 16y - 192 = 0.
Thus, the standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
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Angel made a table runner that has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width. What are the dimensions of the table runner?
the dimensions of the table runner are [tex]20[/tex] inches in length and [tex]4[/tex] inches in width.
What are the dimensions?Let's denote the width of the table runner as "w" inches. Since the length is 5 times greater than the width, the length would be 5w inches.
The area of a rectangle is calculated by multiplying its length by its width. Given that the area of the table runner is 80 square inches, we can set up the following equation:
Length × Width = Area
[tex](5w) \imes w = 80[/tex]
Simplifying further:
[tex]5w^2 = 80[/tex]
Dividing both sides by 5:
[tex]w^2 = 16[/tex]
Taking the square root of both sides:
w = ±4
Since the width cannot be negative in this context, we discard the negative value. Therefore, the width (w) of the table runner is [tex]4[/tex] inches.
Substituting this value back into the equation for length:
Length [tex]= 5w = 5 \times 4 = 20[/tex] inches
So, the dimensions of the table runner are [tex]20[/tex] inches in length and 4 inches in width.
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Please help me, I am confused on how to do this problem.
Find the exact value, cos(-pi/12). Use the half angle strategy.
Using the half angle formula, cos(-π/12) = ±√[2 + √3]/4]
What is the half angle formula?The half angle formula for cosine is cosФ/2 = ±√[(1 + cosФ)/2]
Since we want to find the value of cos(-pi/12) using the half angle formula, we have that cosФ/2 = cos(-π/12)
⇒ Ф/2 = -π/12
⇒ Ф = -π/12 × 2
⇒ Ф = -π/6
So, substituting this into the equation, we have
cosФ/2 = ±√[(1 + cosФ)/2]
cos(-π/6)/2 = ±√[(1 + cos(-π/6))/2]
= ±√[(1 + cos(π/6))/2]
Now, we know that cos(π/6) = √3/2
So, substituting this into the equation, we have that
cos(-π/6)/2 = ±√[(1 + cos(π/6))/2]
cos(-π/12 = ±√[(1 + cos(π/6))/2]
= ±√[(1 + √3/2)/2]
= ±√[[2 + √3]/2)/2]
= ±√[[2 + √3]/2 × 2]
= ±√[2 + √3]/4]
So, cos(-π/12) = ±√[2 + √3]/4]
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Différenciation implicit function containing product and quotient. d/dx (2y/5x)
Answer:
To differentiate the given expression, we will need to use both the product rule and the quotient rule.
Let's first rewrite the expression using the reciprocal identity for x:
2y/5x = 2y * (5x)^(-1)
Now we can use the product rule and the quotient rule to find the derivative with respect to x:
d/dx [2y * (5x)^(-1)] = 2y * d/dx[(5x)^(-1)] + (5x)^(-1) * d/dx[2y]
Using the chain rule, we can find the derivative of (5x)^(-1) with respect to x:
d/dx[(5x)^(-1)] = -1/(5x)^2 * 5 * (dx/dx)
d/dx[(5x)^(-1)] = -1/(5x)^2
Using the chain rule again, we can find the derivative of 2y with respect to x:
d/dx[2y] = 2 * (dy/dx)
Substituting these expressions back into the original equation, we get:
d/dx [2y/5x] = 2y * (-1/(5x)^2) + (5x)^(-1) * 2 * (dy/dx)
Simplifying this expression, we get:
d/dx [2y/5x] = -2y/(5x)^2 + 2/(5x) * (dy/dx)
Therefore, the derivative of 2y/5x with respect to x is -2y/(5x)^2 + 2/(5x) * (dy/dx).
PLEASE HELEPEPPEE QUICKKK ILL GIVE U
Answer:
21, 22, 23 or
-23, -22 , -21
Step-by-step explanation:
The 3 consecutive integers are x, x + 1, and x + 2
Sum of the squares of the 3 consecutive integers:
x² + (x+1)² + (x+2)² = 1454 Expand this equation
x² + x² + 2x + 1 + x² + 4x + 4 = 1454 Combine like terms
3x² + 6x + 5 = 1454
3x² + 6x + 5 - 1454= 0
3x² + 6x - 1449 = 0
Use quadratic equation to solve for the roots of x: (a = 3, b = 6,
c= -1449)
x = 21, -23
The consecutive numbers are: x, (x + 1), (x + 2)
21, 22, 23
-23, -22 , -21
Identify the range of this relation
The range of this relation include the following: D. {-2, 3, 5}.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.
Based on the information provided in this scenario, the domain and range of this relation in interval notation are as follows:
Domain = {3, 6, 8}
Range = {-2, 3, 5}.
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Continue the equivalent Pattern 1/2 2/4.........
Answer:
3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18, 10/20, etc...
Step-by-step explanation:
The left digit it always half of the one on the right, increasing by one every time.
1/2 ===> 2/4 ===> 3/6 ===> 4/8...
Miss Wu's class made 36
paper flowers. One half of the
flowers were red. One third of
the flowers were yellow. The
rest were blue. What fraction
of the flowers were blue?
Answer:
1/6 of flowers were blue
positive.
an remove
3√5a-8√/35a2
multiply the equations: 1: (3√p-5)(√p+5√5) ? 2: (3√2-8)(3√2+8) *show explanation please*
Based on the information, the product of the first equation is 9p-75, and the product of the second equation is -47.
How to calculate the product of equations?We can use the formula:
(a - b)(a + b) = a² - b²Where a and b can be any expressions. Substituting the first expression into the formula:
(3√p-5)(√p+5√5)(3√p - 5)(√p + 5√5) = (3√p)^2 - (5√5)^2= 9p - 75Substituting the second equation into the formula:
(3√2 - 8)(3√2 + 8) = (3√2)^2 - (8)^2= 9(2) - 64= -47Therefore, the product of the first equation is 9p-75 and the product of the second equation is -47.
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helpppppppp plsssssssss
I think it might be:
Between 1754 and 1885 European imperialism was global. Nations like Britain, France, and Spain grew their Empires in the Americas, on the continent of Africa, and in parts of Asia. Their colonies created power and wealth for European businesses and governments. Eventually, many European countries held a meeting to decide how to divide up the world to avoid wars and conflict between themselves. This meeting was called the Conference.
One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other, 4
Golf, 7
Soccer. 11.
Baseball, 14
Football,39
Basketball, 22
Total percentage of adults who preferred soccer or baseball: is 25%
what is percentage ?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100, or 50/100 as a fraction.
In the given question,
The circle graph shows the percentage of adults who preferred each sport. To find the percentage of adults who preferred soccer or baseball, we need to add the percentages for soccer and baseball.
Soccer: 11%
Baseball: 14%
Total percentage of adults who preferred soccer or baseball: 11% + 14% = 25%
Therefore, 25% of adults preferred soccer or baseball.
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The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 8 centimeters and its depth is 4 centimeters. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.
Step-by-step explanation:
A package is weighed at 11 kg to the nearest kg. Find the largest possible weight for the package.
Answer:11.4999...
Step-by-step explanation:
Any number when rounding that starts with 1, 2, 3 4 will be rounded down. All numbers above will be rounded up. Therefore, you find the largest number that will still round down.