The weight of an object with a mass of 2 kg would be 6 N on this planet, assuming the direct variation relationship holds.According to the given information, the weight of an object varies directly with its mass.
This implies that there is a constant of proportionality between weight and mass. Let's denote this constant as k.
From the given data, we have:
Mass = 5 kg
Weight = 15 N
Using the direct variation equation, we can write:
Weight = k * Mass
Substituting the given values, we have:
15 N = k * 5 kg
To find the value of k, we divide both sides of the equation by 5 kg:
k = 15 N / 5 kg = 3 N/kg
Now that we know the constant of proportionality, we can find the weight of an object with a mass of 2 kg:
Weight = k * Mass = 3 N/kg * 2 kg = 6 N.
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Find two consecutive positive integers such that the square of the larger integer is 19 more than 9 times the smaller integer define your variables and write an equation HURRY HELP PLEASE SHOW STEPS
Answer:
9 and 10
Step-by-step explanation:
x = 1st positive integer
x+1 = 2nd positive integer
Solve for both x and x+1(x+1) is the next positive integer after x (Ex. 3 aka 2+1 is next integer after 2).
Larger Integer: x+1 ==> being squared
Smaller Integer: x ==> being multipled by 9
9x + 19 = (x+1)^2 ==> the square of (x+1) is 19 more that 9 multiplied by x.
9x + 19 = (x+1)(x+1) ==> simplify
9x + 19 = x(x+1) + 1(x+1) ==> distribute (x+1) to x and 1.
9x + 19 = (x*x + 1*x) + (1*x + 1*1)
9x + 19 = x^2 + x + x + 1 ==> simplify
9x + 19 = x^2 + 2x + 1
19 = x^2 - 7x + 1 ==> subtract 9x on both sides
Make one side of the equation equal to 0 so you can factor the equation:
0 = x^2 - 7x - 18 ==> subtract both sides by 19
0 = x^2 + 2x - 9x - 18 ==> 2x - 9x = -7x and 2 * (-9) = -18
0 = x*x + 2x - 9x - 18
0 = x(x + 2) - 9(x + 2) ==> factor
0 = (x - 9)(x + 2)
x - 9 = 0 x + 2 = 0
x = 9 x = -2
Out of x = 9 and x = -2, only x = 9 is positive.
Hence, x = 9 and x+1=10.
Hence, the answers are 9 and 10.
Christine went shopping and bought each of her ten nephews a gift, either a video costing $14.95 or a CD costin $16.88. She spent $161.08 on the giftsHow many videos and how many CDs did she buy?
Therefore , the solution to the given problem of linear equation comes out to be we bought 6 videos and 3 CDs.
Define a linear equation.The term "linear" refers to any function that has the algebraic form y=mx+b. m is the y-intercept, while B is the slope. The previous sentence contains a two-variable linear equation since both y and y are factors. Equations involving two variables are called bivariate equations. y + z = 2 and 3z - 6 + x = 3 are two of the many applications for linear equations. The equation y=mx+b, where m stands for the slope and b for the y-intercept, is referred to as a linear equation. The formula is Y=mx+b, where m denotes the inclination and b the y-intercept.
Here,
A collection of equations will be constructed.
Let V = the number of videos purchased.
C will stand for the quantity of purchased CDs.
Since there are eight nephews in all, and each nephew received either a video or a CD, the sum of the numbers of movies and CDs is nine.
So V + C = 9.
We are also aware of how much each CD and film cost and how much money was wasted.
So 14.95V + 16.88C = 140.34
Here, let's experiment with substitution.
Let's just solve for V since it doesn't matter whichever variable we do it for. V = 9 - C
Therefore, replace "V" in the second equation with "9-C," and the result will be 134.55 - 14.95C + 16.88C = 140.34 1.93C = 5.79 C = 3
You can add C = 3 straight into either of the original equations, though I believe I know which one is simpler for you.
V + 3 = 9
V = 6
So we bought 3 CDs and 6 videos.
Therefore , the solution to the given problem of equation comes out to be we bought 6 videos and 3 CDs.
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Which area of the physical activity pyramid can be most easily incorporated into an individual's everyday activities? A. flexibility
Lifestyle is the area of the physical activity of the pyramid that can be most easily incorporated into an individual's everyday activities.
The physical activity pyramid tells us about the Frequency intensity and time formulae also called FIT formulae of different types of physical activity. It is just like the food pyramid where the lowest level contains the most beneficial activities and the highest level the least.
The physical activity pyramid has 7 levels and they are:
Physical Activity.Vigorous Sport and Recreation.Vigorous aerobicsMuscle Exercises.Flexibility Exercises.Balancing EnergyAvoiding inactivityThe physical activity pyramid has 5 areas, they are Flexibility, vigorous sports aerobics anaerobic, and lifestyle. The lifestyle area is the summed up 30-40 mins of self-chosen activities, such as leisure time, occupational or household activity.
Complete question - Which area of the physical activity pyramid can be most easily incorporated into an individual's everyday activities? A. flexibility B. lifestyle C. aerobic D. anaerobic
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√15x² • √10x³ process
Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic equation.
How many techniques exist to identify roots?Divide the given number into its prime factors as the first step. Form similar factor pairs in which both factors are equal. This is step two. Take one factor from the pair in step three. Step 4: Calculate the product of the factors you got by taking one from each pair of factors.
How do you locate an equation's four roots?A number's fourth root is the same as its square root's fourth root. The radical is multiplied by 4 to represent the fourth root, representing it as 4. For instance, 16's fourth root is is 2, i.e. 2 × 2 × 2 × 2 = 16.
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The complete question is " Simply quadratic equation √15x² • √10x³ . "
Graph the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. What are the coordinates of F'?
K = 1/2
The coordinate of the point F' after dilation will be (1, -1). Then the correct option is D.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The coordinate of point F is (2, -2). And the scale factor is 1/2. Then the coordinate of the point F' after dilation will be calculated as,
⇒ (1/2) × (2, -2)
⇒ (1/2 × 2, 1/2 × -2)
⇒ (1, -1)
The coordinate of the point F' after dilation will be (1, -1). Then the correct option is D.
The graph is given below.
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I put RT can someone explain what I did wrong
Step-by-step explanation:
please see attached for explaination
Write the rule to describe the transformation.
C(-2, -1), D(2, 2,), E(-1, -2)
C'(-4, -2), D'(4, 4), E'(-2, -4)
Answer: (x-2, y-1)
Step-by-step explanation:
What are the 3 main viewpoints to look at a 3D object?
The three main viewpoints for looking at a 3D object are the top view, the side view, and the front view.
What is vector?Vector is a physical properties.
The top view, also known as the plan view, is a view of the object from above. This view shows the overall shape of the object, as well as its orientation in space. The side view, also known as the elevation view, is a view of the object from the side. This view shows the details of the object's depth, thickness, and height. The front view, also known as the orthographic view, is a view of the object from the front. This view shows the details of the object's width, length, and height. By looking at the object from each of these three views, one can gain a better understanding of its full three-dimensional nature.
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Is triangle ABC congruent to triangle XYZ?
Therefore , the solution of the given problem of triangle comes out to be ABC is congruent with XYZ.
Describe the triangle.A triangle is a polygon since it has three parts and three vertices. It is a fundamental geometric figure. A triangle with the corners A, B, & C is referred to as triangle ABC. A single planar and triangle are found in geometric shapes when four elements are not collinear. Due of its three sides and top right corner, triangles are classified as polygons.
Here.
ABC is congruent with XYZ, hence
then,
∠A equals ∠X
∠B is equivalent to ∠Y.
∠C equals ∠ Z
and,
xy is equivalent to line ab.
yz is identical to line bc.
xz is equivalent to line ac.
Cpct was used to resolve this.
congruent triangle's matching triangle segments
Therefore , the solution of the given problem of triangle comes out to be ABC is congruent with XYZ.
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Please help me i will pay you
Answer: -x+5/(x-1)(x+3)
Step-by-step explanation:
Subtract 3/(x-1)-4(x+3)
3(x+3)/(x-1)(x+3)-4(x-1)/(x+3)(x-1)
= 3x+9/(x-1)(x+3)-4x+4/(x+3)(x-1)
= -x+5/(x-1)(x+3)
how to find total surface area of a triangular prism
Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh
Now, According to the question:
The surface area of a triangular prism is also known as the total surface area. Therefore, it is calculated using the formula, Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh; where:
b is the bottom edge of the base triangle,h is the height of the base triangle,L is the length of the prism andS1, S2, and S3 are the three edges (sides) of the base triangle(bh) is the combined area of the two triangular faces [2 × (1/2 × bh)] = bhLearn more about Surface area of a triangular prism at:
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Sum of Geometric Series (Sigma Notation)
The answer is 387.97
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....
Given here: To find the sum of the geometric series from n=2 to n=34
we know To find the sum of a finite geometric series, use the formula, Sn=a1(1−rⁿ)/1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio
S₃₂= 400 (1-0.93³²) /0.93
= 430.12×(1-0.098)
= 387.97
Hence, The answer is 387.97
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Rick builds new homes for Eastover Construction Company. Yesterday, Rick installed a horizontal support beam parallel to the base of a triangular roof. Then, Rick installed a vertical support beam between the top and base of the roof, perpendicular to the horizontal beam and the base of the roof. Along the vertical beam, the distance from the top of the roof to the horizontal beam is 28 feet, and the distance from the horizontal beam to the base of the roof is 42 feet. The base of the roof is 90 feet long.
what is the length of the horizontal beam
Answer:
90 feet.
Step-by-step explanation:
The horizontal beam is parallel to the base of a triangular roof, and the vertical beam is perpendicular to the horizontal beam and the base of the roof. So the length of the horizontal beam is the same as the base of the roof which is 90 feet.
The area of a trapezium is 90m². If the sum of the parallel sides is 30m. Find the perpendicular height of the trapezium
The perpendicular height of the trapezium is given as follows:
h = 6 m.
How to obtain the area of the trapezium?The area of a trapezium with parallel sides a and b, and height h, is given by the equation presented as follows:
A = 0.5h(a + b).
The sum of the parallel sides is 30m, hence:
a + b = 30.
The area is of 90m², hence the height of the trapezium is obtained as follows:
15h = 90
h = 90/15
h = 6 m.
(as a + b = 30, hence 0.5(a + b) = 15).
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We know
Area =1/2(Sum of parallel sides)×height
90=1/2(30)h15h=90h=6m'I decided to add 8.6 to my number then multiply the result by 3, After that I subtracted 1.9 then doubled the result. The answer is 59.2'
What number was Savannah first thinking of?
Answer:
The number was 1.9------------------------------------------
Let the number be x.
Set up equation to reflect all the operations:
((x + 8.6)*3 - 1.9)*2 = 59.2Solve it in below steps:
((x + 8.6)*3 - 1.9)*2 = 59.2(x + 8.6)*3 - 1.9 = 59.2/2 (x + 8.6)*3 - 1.9 = 29.6(x + 8.6)*3 = 29.6 + 1.9 (x + 8.6)*3 = 31.5x + 8.6 = 31.5/3 x + 8.6 = 10.5x = 10.5 - 8.6 x = 1.9k/6+8=5
show work
solve k
Answer: K = -18
Step-by-step explanation:
Given equation: K/6+8=5
Let's subtract 8 from both sides of the equation
K/6 = -3
Multiply both sides by 6
K = -18
What is the formula of midpoint Class 10?
As follows is the Midpoint Formula: [tex](x,y) = [\frac{(x_{1} +x_{2}) }{2} , \frac{(y{1} +y_{2}) }{2} ][/tex]
A mathematical equation called the midpoint formula is used to determine where two data points meet midway. Its ability to compute percentage changes based on the difference between starting and ending values is this equation's defining feature.
How to Calculate the Midpoint:
Using this midpoint formula, we can determine the coordinates of the terminus of the given line and use them to determine the midpoint of the straight line on the graph.
Suppose the endpoints of the line is (x₁,y₁) and (x₂,y₂) then the midpoint is given as:
The Midpoint Formula is given as,
[tex](x,y) = [\frac{(x_{1} +x_{2}) }{2} , \frac{(y{1} +y_{2}) }{2} ][/tex]
Where x₁ and x₂ are the coordinates of the x-axis. y₁ and y₂ are the coordinates of the y-axis.
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88x + 281 = −27.00
Show work
Which points are reflections of each other across both axes?(–2, 8) and (2, –8)(–7, –1) and (–7, 1)(5, –6) and (–5, –6)(4, –3) and (–3, 4)
The points (–2, 8) and (2, –8) are reflections of each other across both axes. This can be seen by taking their coordinates and plugging them into the reflection formula, which is (x, y) → (–x, –y).
When we plug in the coordinates for the first point, we get (–2, 8) → (–(–2), –(8)) = (2, –8). This is the coordinates of the second point, so they are reflections of each other.
The points (–7, –1) and (–7, 1) are also reflections of each other across both axes. Using the same reflection formula, we get (–7, –1) → (–(–7), –(–1)) = (7, 1), which are the coordinates of the second point.
The points (5, –6) and (–5, –6) are reflections of each other across both axes. Applying the reflection formula, we get (5, –6) → (–(5), –(–6)) = (–5, 6), which are the coordinates of the second point.
Finally, the points (4, –3) and (–3, 4) are reflections of each other across both axes. Using the reflection formula, we get (4, –3) → (–(4), –(–3)) = (–4, 3), which are the coordinates of the second point.
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Please help me answer this math question
According to the information, we can infer that she is going to pay $108 as total for the photos; but every photo has a different price from $12 to $0.75
How to calculate the price of each photo?To calculate the price of each photo we have to take into account how many photos fits in a sheet of pictures. Then we have to divide the total price of each sheet in the number of photos she is going to get from each sheet.
Picture for her parentsMeasures: 8 * 10Quantity: 1Price: 1 * $12 = $12Pictures for her grandparentsMeasures: 5 * 7Quantity: 8Price of sheets: 4 * $12 = $48Price of each photo: $12 / 2 = $6Pictures for her aunts and unclesMeasure 3 * 5Quantity: 5Price of sheets: 2 * $12 = $24Price of each photo: $12 / 3 = $4Pictures for her friendsMeasure: Wallet SizeQuantity: 32Price of sheets: 2 * $12 = $24Price of each photo: $12 / 16 = $0.75Then she is going to use 9 sheets, so she is going to pay $108 in total.
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Which quantity is proportional to 35⁄80?
Check all that are true.
26⁄52
7⁄16
14⁄36
3⁄5
21⁄48
The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The fraction number is given below.
⇒ 35 / 80
⇒ 7 / 16
⇒ 21 / 48
The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.
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Which expression is equivalent to -8(10x-3)
A: -80x+24
B: -80x-24
C: -80x-3
D: -80x+3
Is 3 included in the solution set of x>3 Explain.
3 is not included in the solution set of x>3
What is an inequality?
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used
Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa
If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.
From the question,
x>3 (x should be greater than 3) means the the value of x is more or greater than 3, that is, x is 4,5,6,...
Hence, 3 will not be included in the values of x>3
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How do you find the vertex of a quadratic function in intercept form?
The intercept form of a quadratic equation is y = a ( x − p ) ( x − q ) , where is the same value as in standard form, and and are the intercepts
What is quadratic function in intercept form?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepness's," but they all share the same fundamental "U" shape. Y = a (x p) (x q) is a quadratic equation's intercept form, where and are the intercepts, and and are the same value as in standard form.It is referred to as being in standard form when the quadratic function f(x) = a(x - h)2 + k is not equal to zero. The graph opens either upward or downward depending on whether an is positive or negative. The vertex is the point, while the vertical line x = h is the line of symmetry (h,k).To learn more about quadratic function refer to:
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A fair 6 sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?.
Answer: each time you roll a 6-sided die is 1/6 percent to get any number
Step-by-step explanation:
Where is 0 latitude and 0 longitude?
0 degree latitude and 0 degree longitude is at equator
Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.
Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.
What is the uses of latitude?
Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.
The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.
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Select the correct answer from each drop-down menu. two triangles abc and def are represented. segment ac and segment de has single tick mark. angle c and angle d has double tick marks on arc. if , then ∆abc and ∆efd are congruent by the asa criterion. if , then ∆abc and ∆efd are congruent by the sas criterion.
∆ABC and ∆EFD are congruent by the ASA criterion as segment AC and segment DE has single tick mark, angle A and angle E has single tick marks on arc and angle C and angle D has double tick marks on arc.
The ASA (Angle-Side-Angle) criterion states that if two triangles have two angles and the included side congruent (identical), then the two triangles are congruent.
In this case, both triangles ABC and DEF have two angles congruent (angle A and angle E, and angle C and angle D), and the included side (segment AC and segment DE) congruent. Therefore, by the ASA criterion, the two triangles ABC and DEF are congruent.
To be more precise Angle A and angle E has single tick marks on arc which means both angles are congruent and angle C and angle D has double tick marks on arc which means both angles are congruent. As we know, if two triangles have corresponding parts congruent, the two triangles are congruent.
If segment BC equals to segment FD we can prove that the triangles, ∆ABC and ∆EFD are congruent by the SAS criterion.
--The question is incomplete, answering to the question below--
"Two triangles ABC and DEF are represented. Segment AC and segment DE has single tick mark. Angle A and angle E has single tick marks on arc. Angle C and angle D has double tick marks on arc. If , then ∆ABC and ∆EFD are congruent by the ASA criterion. If , then ∆ABC and ∆EFD are congruent by the SAS criterion."
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What is the table of 15 to 20?
Therefore , the solution of the given problem of table comes out to be 15 to 20 table are given as follows : 15,30,45,60,75,90,105,120,135 and 150.
Describe a table.A statistical list is a collection of numbers that shows the outcomes of a computation with numerous inputs. Data is made up of descriptions and numbers and is arranged in rows and columns. The table and indeed the pattern of 10 are easily recalled. In numerical order, the numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, then 20. Value mapping is used to show how multiple data pieces are related to one another. Any science class can benefit from including the values table.
Here,
Given :
=> 15,30,45,60,75,90,105,120,135 and 150
=> 16,32,48,64,80,96,112,128,144 and 160
=> 17,34,51,68,85,102,119,136,153 and 170
=> 18 , 36 ,54,72,90,108,126,144,162 and 180
=> 19,38,57,76,95,114,133,152,171and 190
=>20,40,60,80,100,120,140,160,180 and 200
Therefore , the solution of the given problem of tables comes out to be 15 to 20 table are given as follows : 15,30,45,60,75,90,105,120,135 and 150.
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p(x)=2x+2(x+4) to determine the perimeter of the flower box based on the width x in feet
Answer: The perimeter of the flower box can be determined by adding up the lengths of all four sides. In this case, we can see that the width of the flower box is represented by the variable x in feet, and the height is given as 2(x+4). To find the perimeter, we need to add up the lengths of the top and bottom (2x) and the left and right sides (2(x+4)). So, the perimeter P(x) can be expressed as:
P(x) = 2x + 2(x+4)
Simplifying this expression:
P(x) = 2x + 2x + 8
P(x) = 4x + 8
So the perimeter of the flower box is 4x+8 feet, based on the width x in feet.
Step-by-step explanation:
Imagine you are walking along a forest path. Which of the following is not an action-reaction pair in this situation?a. the gravitational force between you and Earth; the gravitational force between Earth and you.b. your shoe pushing back on Earth; Earth pushing forward on your shoec. your foot pushing back on the inside of your shoe; your shoe pushing forward on your footd. you pushing down on Earth; Earth pushing you forward 1
When we are walking along the forest, the action-reaction pair that will not occur is d) you pushing down on earth and earth pushing you forward.
According to Newton's third law of motion, two bodies exert equal and opposite forces on each other in every interaction. These forces form action-reaction pairs.
Examples of action-reaction combinations/pairs include: pushing the ball with the gun - the ball pushes the gun back (recoil), or the player applies hand force to the ball and throws the ball forward - the ball pushes back with the hand. The properties of action-reaction pairs are: They must arise from the same interaction. The acting force and the reaction force are equal. Action and reaction forces are directed in opposite directions. The forces act on different bodies and are therefore unbalanced.
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