Answers
Answer:
a) y = -2x + 3
b) y = -3x + 7
c) y = -1/2x + 4
d) y = 2
Step-by-step explanation:
Gradient is also known as slope
a) y = mx + b
3 = (-2)0 + b
b = 3
y = -2x + 3
b) y = mx + b
1 = (-3)(2) + b
1 = -6 + b
b = 7
y = -3x + 7
c) Slope m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(4 - 2) = -1/2
y = mx + b
3 = -1/2(2) + b
3 = -1 + b
b = 4
y = -1/2x + 4
d) The x‐axis or any line parallel to the x‐axis has a slope of 0.
y = mx + b
2 = -3(0) + b
b = 2
y = 2
Answer:
a) The equation of this line is y = -2x + 3
b) The equation of this line is y = -3x + 7
c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4
d) The equation of this line is y = 2
Step-by-step explanation:
The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.
a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:
y - 3 = -2(x - 0)
Simplifying the right-hand side gives:
y - 3 = -2x
Adding 3 to both sides gives the final equation:
y = -2x + 3
b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:
y - 1 = -3(x - 2)
Simplifying the right-hand side gives:
y - 1 = -3x + 6
Adding 1 to both sides gives the final equation:
y = -3x + 7
c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:
m = (y2 - y1)/(x2 - x1)
Substituting the coordinates of the two points, we get:
m = (2 - 3)/(4 - 2) = -1/2 or -0.5
Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:
y - 3 = (-1/2)(x - 2)
Simplifying the right-hand side gives:
y - 3 = (-1/2)x + 1
Adding 3 to both sides gives the final equation:
y = (-1/2)x + 4 or y = -0.5x + 4
d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.
Related Questions
What is the sum of the interior angle
measures of a regular hexagon? Show
or explain how you can use the sum
of the interior angles of a triangle to
determine the answer.
Answers
Answer:
The sum of the interior angle measures of a regular hexagon is 720°.
Step-by-step explanation:
To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:
Sum of interior angles = (n - 2) × 180°
In the case of a hexagon, n = 6. So, we can plug this value into the formula:
Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°
The sum of the interior angle measures of a regular hexagon is 720°.
To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:
Sum of interior angles of hexagon = 4 × 180° = 720°
The sum of the interior angle measures of a regular hexagon is 720°.
Please answer the question
Answers
Answer: $105
Step-by-step explanation:
I would take 5+2=7 then take 7×15=105
Answer is $105 to ship.
What is the lowest price a dozen eggs could reach before Farmer Johnson would be forced to shut down in the short run? (Please enter your answer without a dollar sign, for values less than 1.00, you must put a 0 before the decimal)
Answers
If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.
To determine the lowest price a dozen eggs could reach before Farmer Johnson would be forced to shut down in the short run, we need to know his minimum average variable cost (AVC) of producing eggs.
The average variable cost is the variable cost per unit of output, and it includes costs that vary with the level of production, such as labour, feed, and utilities.
If the price of a dozen eggs falls below the minimum AVC, Farmer Johnson will not be able to cover his variable costs and will incur losses. In the short run, he may continue to produce as long as he can cover his variable costs, but he will eventually be forced to shut down if he cannot cover his fixed costs as well.
Without information on Farmer Johnson's specific costs, we cannot determine the exact minimum AVC or the lowest price at which he would shut down. However, we can say that the lowest price a dozen eggs could reach before he would be forced to shut down is equal to his minimum AVC.
If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.
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Find the area of the triangle.
3).
Answers
Answer:
86.60254
Step-by-step explanation:
30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)
What is the approximate value of this logarithmic expression? log8 24
Answers
Answer: 1.5283
Step-by-step explanation:
When saying something like log base 8 of 24, we know that this means 8 to the power of what is equal to 24. The answer is 1.5283. If you would like to round sine it is the approximate value, do it.
Please, say thanks, rate, and please please please, give brainlist.
1. Sketch a graph of a system generated by a linear equation and a quadratic equation that has no solution. Explain how the possibility occurs.
2. Sketch a graph of a system generated by a linear equation and a quadratic equation that has exactly one solution. Explain how the possibility occurs.
3. Sketch a graph of a system generated by a linear equation and a quadratic equation that has exactly two solutions. Explain how the possibility occurs. (You do not need to write any equations.
Just provide a simple sketch and explanation please, no equations are necessary.
Answers
Answer:
Sure give me a sec
Step-by-step explanation:
1) A system of equations has no solution if the graphs of the equations do not intersect. 2) A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point. 3) A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points.
Systems with no solution
A system of equations has no solution if the graphs of the equations do not intersect. This can happen if the graphs are parallel, or if one graph is completely contained within the other graph.
For example, the graph of a linear equation is a line, and the graph of a quadratic equation is a parabola. If the line and the parabola are parallel, then they will never intersect, and the system will have no solution.
Another way for a system to have no solution is if one graph is completely contained within the other graph. For example, the graph of the equation y = x is completely contained within the graph of the equation y = [tex]x^2[/tex]. This means that there are no points that satisfy both equations, and the system will have no solution.
Systems with exactly one solution
A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point. This can happen if the graphs are intersecting lines, or if the graphs are intersecting parabolas.
For example, the graph of the equations y = x and y = [tex]x^2[/tex] intersect at exactly one point, which is the point (0,0). This is because the two graphs intersect when x = 0, and there is no other point where they intersect.
Systems with exactly two solutions
A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points. This can happen if the graphs are intersecting parabolas that have different slopes.
For example, the graph of the equations y = [tex]x^2[/tex] and y = 2[tex]x^2[/tex] intersect at exactly two points, which are the points (0,0) and (1,1). This is because the two graphs intersect when x = 0 and when x = 1, and there are no other points where they intersect.
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Which of the following is the graph of the function shown below?
W.
X.
Y.
Z.
A.
X
B.
Y
C.
W
Answers
Answer:
Cannot be drawn directly.
Step-by-step explanation:
The graph of every function w = f (x, y, z) will be a surface in R 4, though it can't be drawn directly; however, slicing horizontally by w = c produces relations c = f (x, y, z) in x, y, and z whose graphs will be surfaces in 3-space which can be drawn. Therefore, the graph of the function shown above cannot be drawn directly.
can you help me with this?
Answers
Answer:
8 cm³
Step-by-step explanation:
You want the volume of Prism B similar to Prism A, where the volume of Prism A is 216 cm³, its height is 9 cm, and the height of Prism B is 3 cm.
Volume ratioThe ratio of volumes is the cube of the ratio of heights:
(Prism B volume)/(Prism A volume) = ((Prism B height)/(Prism A height))³
(Prism B volume)/(216 cm³) = ((3 cm/(9 cm))³ = 1/27
Prism B volume = (216 cm³)·(1/27) = 8 cm³
The volume is 8 cubic centimeters.
The masses of 4 samples of baking soda are measured to perform an
experiment
in science class.
2
2/1/2
3
31/1/201
4
4
112
5
What is the total number of grams of baking soda in all 4 samples?
Answers
The total number of grams of baking soda in all 4 samples is given as follows:
B. 16 grams.
How to obtain the number of grams?The total number of grams of baking soda in all 4 samples is obtained as the sum of the amounts for each sample.
The dot plot shows the number of samples with each amount, hence:
One sample has 2.5 grams.One sample has 3.5 grams.Two samples have 5 grams.Hence the total amount is given as follows:
2.5 + 3.5 + 2 x 5 = 16 grams.
Missing InformationThe problem is given by the image presented at the end of the answer.
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please help
P (-∞ < z < ∞) =
Answers
The entire area is under the standard normal distribution curve, which is 1 by definition.
In other words, a typical normal random variable has a 100% chance of landing anywhere within its range of potential values (-∞ to +∞).
This makes sense since the area under the standard normal distribution curve, which is a continuous probability distribution, shows the likelihood that the random variable will take on any value within its range. Since the entire area under the curve is 1, the likelihood that any potential value for the random variable will occur is 1, or 100%.
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Which expression is equivalent to 7m+5.5(2+m)
?
Answers
Pour développer il faut appliquer la distributivité de la multiplication :
7m + 5.5(2+m) = 7m + 5.5 x 2 + 5.5m
= 7m + 11 + 5.5m
Il faut combiner les termes contenant m :
= 7m + 5.5m + 11
= (7 + 5.5)m + 11
= 12.5m + 11
You want to purchase a new car
In 9 years and expected the car to cost $15,000. Your bank offers a plan a guaranteed APR of 6.5% .
If you make regular deposits.
How much should you deposit each month to end up $15,000 in 9 years ? 
Answers
The approximate amount to be deposited each month at a guaranteed APR of 6.5% that will accrue to $15,000 in 9 years is $97.57.
Future value for an annuityIn order to find out how much you should deposit each month to end up with $15,000 in 9 years, we can use the future value formula for an annuity:
FV = PMT * [(1 + r)^n - 1] / r
where:
FV is the future valuePMT is the deposit amountr is the monthly interest raten is the total number of deposits (in months).The total number of deposits, n, is the number of months in 9 years:
n = 9 * 12 = 108
The monthly interest rate from the annual percentage rate (APR):
r = (1 + 0.065/12) - 1 = 0.0054166667
Let's substitute the values and solve for PMT:
15,000 = PMT * [(1 + 0.0054166667)^108 - 1] / 0.0054166667PMT = 15,000 / [(1 + 0.0054166667)^108 - 1] * 0.0054166667PMT ≈ $97.57Therefore, you should deposit approximately $97.57 each month to end up with $15,000 in 9 years, assuming a guaranteed APR of 6.5%.
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Jeremy has a fish tank that has a 30 cm by 90 cm rectangular base. The water is 25 cm deep. When he drops rocks in
the tank, the water goes up by 2 cm. What is the volume in liters of the rocks?
The volume of the rocks is ____ L
Answers
The volume of water displaced can be calculated by finding the volume of the rectangular prism that is formed by the portion of the rocks that is submerged in the water. The length and width of the prism are the same as the base of the tank (30 cm by 90 cm), and the height is 2 cm (since the water level rises by 2 cm when the rocks are added). Therefore, the volume of water displaced by the rocks is:
V_water = 30 cm x 90 cm x 2 cm = 5400 cm^3
To convert the volume to liters, we divide by 1000:
V_water = 5400 cm^3 ÷ 1000 = 5.4 L
Therefore, the volume of the rocks is 5.4 L.
∫1/^2+4+25 by partial of integration
Answers
The integral of 1/(2+4x²+25x²) using partial integration is (1/2) arctan(10x) + C, where C is the constant of integration.
To solve this integral, we will use the technique of partial integration. This technique is also known as integration by parts and is used to find the integral of a product of two functions. The formula for integration by parts is as follows:
∫u dv = uv - ∫v du
where u and v are functions, and du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.
Let's apply this formula to our integral:
∫1/(2+4x²+25x²) dx
We need to choose two functions, u and dv, such that when we differentiate u, we get a simpler function, and when we integrate dv, we get a simpler function. In this case, we can choose:
u = 1, and dv = 1/(2+4x²+25x²) dx
Now, let's find du/dx and v:
du/dx = 0 (since u is a constant)
To find v, we need to integrate dv. We can use the substitution method to evaluate the integral:
Let u = 5x
du/dx = 5
dv = 1/(2+4x²+25x²) dx
Substituting u and dv:
v = ∫ dv/dx du = ∫1/(2+4u²) du
v = (1/2) arctan(2u)
v = (1/2) arctan(2(5x))
v = (1/2) arctan(10x)
Now, we can apply the formula for integration by parts:
∫1/(2+4x²+25x²) dx = uv - ∫vdu
∫1/(2+4x²+25x²) dx = (1) x (1/2) arctan(10x) - ∫(1/2) arctan(10x) x 0 dx
∫1/(2+4x²+25x²) dx = (1/2) arctan(10x) + C
where C is the constant of integration.
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Find the total surface area of this composite figure.
Answers
In the given diagram, the total surface area of the composite figure is 361.28 square yards
Calculating the total surface area of a composite figureFrom the question, we are to calculate the total surface area of the given composite shape
In the composite shape, we have a cone and a hemisphere
The total surface area of the composite figure = Surface area of the hemisphere + Curved surface area of the cone
Surface area of the hemisphere = 2πr²
Where r is the radius
Curved surface area of a cone = πrl
Where r is the radius
and l is the slant height
In the given diagram,
Using the Pythagorean theorem,
l² = 12² + 5²
l² = 144 + 25
l² = 169
l = √169
l = 13 yd
Radius of cone and hemisphere = 5 yd
Total surface area of the composite figure = 2πr² + πrl
Substituting the parameters
Total surface area of the composite figure = 2π(5)² + π(5)(13)
Total surface area of the composite figure = 50π + 65π
Total surface area of the composite figure = 115π
Total surface area of the composite figure = 361.28 yd²
Hence,
The total surface area is 361.28 square yards
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26). Is Δ EFG ≅ Δ HIJ?
27). What is the scale factor of Δ EFG to Δ HIJ?
28). What is the ratio of their perimeters?
29). What is the ratio of their areas?
Answers
The triangles are not congruent.
Given that, two triangles, EFG and HIJ are similar,
So,
Since, the triangles are similar, but according to the definition of similarity, two objects that are similar are not necessarily congruent,
so the Δ EFG is not congruent to Δ HIJ.
Cos 30° = HI / HJ
√3/2 = 3/HI
HI = 3.5
Therefore, the scale factor Δ EFG to Δ HIJ = EF / HI = 10/3.5 = 2/0.7
The ratio of perimeter of similar objects are same as the scale factor,
so, the ratio of their perimeters = 2/0.7
The ratio of the areas of the similar objects are the ratios of the squares of the scale factor.
So, the ratio of their areas = 4/0.49
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John has 6 different flags that he wants to hang on the wall. How many different ways can the flags be arranged in a row?
Answers
There are 6 different ways can the flags be arranged in a row.
We have,
Total number of flags = 6
So, to find the number of ways to arranged n object = n!
Then, the number of ways to arrange the flag
= 6!
= 6 x 5 x 4 x 3 x 2 x 1
=120 x 6
= 720 ways
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how can a formula help me find perimeter?
Answers
- The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
- The perimeter of a square is given by the formula: P = 4s, where P is the perimeter and s is the length of one side.
- The perimeter of a triangle is given by the formula: P = a + b + c, where P is the perimeter and a, b, and c are the lengths of the sides.
By using these formulas, you can calculate the perimeter of a shape given its dimensions. For example, if you know the length and width of a rectangle, you can use the formula P = 2l + 2w to find its perimeter. If you know the length of one side of a square, you can use the formula P = 4s to find its perimeter. If you know the lengths of the sides of a triangle, you can use the formula P = a + b + c to find its perimeter.
Polygon D has been dilated to create polygon D′.
Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 6.4 and left and right sides labeled 7.6.
Determine the scale factor used to create the image.
Scale factor of 0.6
Scale factor of 0.8
Scale factor of 1.2
Scale factor of 1.6
Answers
Answer: The scale factor used to create the image is 0.8
Step-by-step explanation: To determine the scale factor used to create the image, we can divide the corresponding side lengths of the dilated polygon D' by the corresponding side lengths of the original polygon D.
For example, the top and bottom sides of polygon D have a length of 8, while the corresponding sides of polygon D' have a length of 6.4.
So, the scale factor used to create the image is:
6.4 / 8 = 0.8
Therefore, the scale factor used to create the image is 0.8.
The height and radius of a cone are each multiplied by 3.
What effect does this have on the volume of the cone?
The volume of the cone is multiplied by
Answers
If both the height and radius of a cone are multiplied by 3, the new radius and height will be 3r and 3h, respectively.
We can substitute these values into the volume formula for the new cone:
V = (1/3)π(3r)^2(3h)
Simplifying the expression gives:
V = (1/3)π(27r^2h)
V = 9πr^2h
So, the volume of the new cone is 9 times larger than the volume of the original cone.
Therefore, if both the height and radius of a cone are each multiplied by 3, the volume of the cone is multiplied by 9
The face of a clock has a circumference of 14 in.What is the area?Use 3.14 for
Answers
The area of the face of a clock with a circumference of 14 inches is approximately 15.6 square inches. This is calculated using the formula for the area of a circle, which is πr², where r is the radius of the circle.
To find the area of the face of the clock, we need to use the formula for the area of a circle, which is
A = πr²
where A is the area of the circle, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.
Since the circumference of the clock is 14 inches, we can use the formula for the circumference of a circle to find the radius
C = 2πr
14 = 2πr
r = 14 / (2π)
r = 2.227 in (approx)
Now that we know the radius, we can use the formula for the area of a circle
A = πr²
A = 3.14 x (2.227)²
A = 15.6 sq in (approx)
Therefore, the area of the face of the clock is approximately 15.6 square inches.
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Two similar octagons have areas of 4 ft2 and 16 ft2. Find their similarity ratio.
1:4
1:2
1:16
1:8
Answers
The similarity ratio between the two octagons is 1:2 (Option b).
To begin, we need to know that similar figures have the same shape, but they may differ in size. For instance, we can have two octagons with different areas but the same shape. In this case, we are given that the two octagons are similar, and we are given the areas of the two octagons.
Let the similarity ratio between the two octagons be "x". For areas, we know that the ratio of the areas of two similar figures is the square of their similarity ratio. Therefore, we can set up the following equation:
x² = (Area of smaller octagon) / (Area of larger octagon)
Substituting the given areas, we get:
x² = 4 / 16
x² = 0.25
Taking the square root of both sides, we get:
x = √0.25
x = 0.5
Therefore, the similarity ratio between the two octagons is 1:2 (Option b).
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A flower garden is composed of 1/2 tulips and 3/10 of the tulips are pick.
How many pink tulips are in the garden? Type your answer like this: 1/2
Answers
There are 3/20 pink tulips
How to calculate the number of tulips that are pink ?
A flower garden is composed of 1/2 tulips
3/10 of this amount are the pink tulips
Therefore the number of pink tulips can be calculated as follows
= 1/2 × 3/10
= 3/20
Hence 3/20 of the tulips in the garden are pink
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Given the following stock quotation, find the symbol for the stock.
Boeing
BA
80.12
81.09
79.20
81.00
1.22 153 3.41 6.237
Answers
The symbol for the stock boeing is BA.
We are given that;
Quotation 80.12 81.09 79.20 81.00
Now,
It is the first item in the quotation after the company name. The other items are the previous close price, the open price, the low and high prices of the day, the current price, the change in percentage, the volume in millions, the dividend yield and the P/E ratio.
Therefore, by the equation the answer will be BE.
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If M is a subset of N and N is a subset of P, then, M is a subset of P that is?
Answers
This is correct. If M is a subset of N and N is a subset of P, then, M is a subset of P.
How to explain the subsetsThis follows from the transitivity of the subset relation. In set theory, the transitive property states that if a relation applies between elements A and B, and between elements B and C, then it also applies between elements A and C.
For the subset relation, if M is a subset of N (M ⊆ N), this means that every element in M is also an element of N. Similarly, if N is a subset of P (N ⊆ P), every element in N is also an element of P.
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A ladder of length (2x+6) feet is positioned x feet from a wall. If the ladder reaches a height of (2x+4) feet along the wall. Find the longest leg.
A. 10ft
B. 24ft
C. 26ft
D. 13cm
Answers
Using the Pythagoras theorem, the longest leg has the length of 24 feet.
Given that,
A ladder of length (2x+6) feet is positioned x feet from a wall.
Height of the ladder = (2x + 6) feet
Distance of ladder from the wall = x feet
Height of the wall that the ladder is placed = (2x + 4) feet
These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.
Longest leg is (2x + 4) feet
Using the Pythagoras theorem,
(2x + 6)² = (2x + 4)² + x²
4x² + 24x + 36 = 4x² + 16x + 16 + x²
4x² + 24x + 36 = 5x² + 16x + 16
x² - 8x - 20 = 0
(x - 10) (x + 2) = 0
x = 10 or x = -2
x = 2 is not possible.
So x = 10
Longest leg = 2x + 4 = 20 + 4 = 24 feet
Hence the length of the longest leg is 24 feet.
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At what values of x does f(x)=0?
Answers
Answer:
f(x) = 0 at x = -2, 1, 3
A, B, and D are the correct choices.
AOC and BOD are diameters of a circle, centre O.
Prove that triangle ABD and triangle DCA are congruent by RHS.
Answers
If AOC and BOD are diameters of a circle, centre O, we can prove that triangle ABD and triangle DCA are congruent by RHS.
First, we can observe that angle AOB and angle COD are both right angles since they are angles subtended by diameters of the circle.
Since AO and BO are equal radii of the circle, they have the same length. Similarly, CO and DO are equal radii of the circle and have the same length. Thus, we have:
AO = BO = CO = DO
Now, consider triangle ABD and triangle DCA. We have:
AB = DC (both are diameters of the circle, hence have the same length)
AD = AD (common side)
∠ADB = ∠CDA = 90° (both are right angles)
Therefore, by the RHS (Right Angle-Hypotenuse-Side) congruence criterion, we can conclude that triangle ABD and triangle DCA are congruent.
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FLOWER Delfina photographed a triangular flower for a photo contest. The flower was approximately regular and had
side lengths measuring about 4 centimeters. What is the area of the flower? Round your answer to the nearest
tenth.
Answers
Answer:
8 centimeters squared.
Step-by-step explanation
This is just me assuming flower was flat???
The triangle was regular, so it measured 4 by 4 by 4. Triangle formula is 1/2bh.
1/2bh
1/2*4*4
2*4
8
Y=(0,3) slope=4
What’s the equation
Answers
An equation of the line in slope-intercept form include the following: y = 4x + 3.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (0, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 4(x - 0)
y - 3 = 4x
y = 4x + 3
Read more on point-slope here: brainly.com/question/24907633
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