The systems have a unique solution if k ≠ 6.
The given equations are:
kx+ 2y=5
3x + y =1
Concept used:
If [tex]\frac{a_{1} }{a_{2} }[/tex] ≠ [tex]\frac{b_{1} }{b_{2} }[/tex] , then the system of equations [tex]a_{1}x + b_{1}y + c_{1} = 0[/tex] [tex]a_{2}x + b_{2}y + c_{2} = 0[/tex] has a unique solution.
Calculation,
kx+ 2y-5=0
[tex]a_{1}=k, b_{1}=2 , c_{1} = -5[/tex]
3x + y -1=0
[tex]a_{2}=3, b_{2}=1 , c_{2} = -1[/tex]
according to the question,
[tex]\frac{a_{1} }{a_{2} }[/tex] ≠ [tex]\frac{b_{1} }{b_{2} }[/tex]
⇒[tex](\frac{k}{3})[/tex] ≠ [tex](\frac{2}{1} )[/tex]
⇒ k ≠ 6
∴ The systems have a unique solution if k ≠ 6.
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solve for the point of the intersection using substitution
4x+2y=10
2x=26+2y
First, solve the equation for one of the variables in the pair of equations to be solved using substitution method x = 2/13, y = 52
What is the approach to substitution?The substitution method is one algebraic approach to solving a linear system. By substituting one y-value for another, the substitution method works. We will illustrate this with an example. Since y = y, we can use y in the first equation instead of the second one.
How to find the calculation?4x+2y=10⋅2x=26+2y
Take the first equation, for example. For a result of 20, multiply 10 by 2.
4x+2y=20x
20 x both sides should be subtracted.
4x+2y−20x=0
Get 16x by combining 4x and 20x.
−16x+2y=0
The second equation is an example. For a result of 20, multiply 10 by 2.
20x=26+2y
From both sides, subtract 2y.
20x−2y=26
First, solve the equation for one of the variables in the pair of equations to be solved using substitution. Replacing that variable in the other equation with the result follows.
−16x+2y=0, 20x−2y=26
By placing x on the left side of the equal sign, isolate x from one of the equations and solve it for x.
−16x+2y=0
In the equation, deduct 2y from both sides.
−16x=−2y
Subtract 16 from both sides.
x= − 16/ 1(−2)y
16 divided by 2y is the answer.
x= 8 / 1 y
The second equation, 20x2y=26, should now read 8 y instead of x.
20×( 8 /1 )y−2y=26
multiply 20 times 8 y.
2 / 5 y−2y=26
Boost 2y by 2.5 years.
2 /1 y=26
2 times both sides will give you y=52.
In the formula x = 81y, change y to 52. You can solve for x directly because the resulting equation only has one variable.
x= 8 /1 ×52
52 x 8 /1 is the multiplication.
x= 2 /13
The system has now been resolved substitution equation are
x = 2/13, y=52
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5
r
−
8.35
s
when
r
=
12
and
s
=
4
?
Answer:
26.40
Step-by-step explanation:
r=12
s=4
5r − 8.35s =
5(12) - 8.35(4) = ==> plug in 12 for r and 4 for s
60 - 33.40 = ==> simplify
60.00 - 33.40 =
60 - 33 + 0.00 - 0.40 =
27 - 0.40 = 26.40
Pleaseeee helppp need this by tonight
Answer:
the domain is x ≥ -4
Step-by-step explanation:
on the x-axis, the graph does not extend below -4. the point on the graph is filled in, which makes the domain greater than or equal to -4.
hope this helped, good luck!
Wbić is the od one out
The odd one out is the furthest to the right. the Nickels.
The first square is 25 cents. The second square is 25 cents. The third square is 15 cents.
I hope this helps you :D
What is the nature of roots of quadratic equation 9x2 12x +4?.
The nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.
The nature of the roots of a quadratic equation is determined by its discriminant (b2 – 4ac). The discriminant of the given equation 9x2 12x + 4 is (12)2 – 4(9)(4) = 144 – 144 = 0.
Since the discriminant is equal to zero, the equation has two equal (or identical) roots. This indicates that the equation has one root since its roots are equal. We may apply the quadratic formula to get the equation's root.
The quadratic formula states that the roots of a quadratic equation can be found by solving the equation:
x = (-b ± √(b2 – 4ac))/2a
When we apply the formula to the given equation, we get:
x= (-12 ± √(0))/2(9)
Since the discriminant is equal to zero, the equation has one root. The root of the equation is x = -4.
Therefore, the nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.
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an eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground, how far from the building is the base of the ladder?
The distance between the building and the base of the ladder is 4 feet.
What are trigonometric functions?The trigonometric functions are functions that can be applied to determined the side or measure of internal angle of a given triangle. Given that some required properties are given.
Given that the ladder is 8 feet long, let the distance between the building and the base of ladder be represented by t.
So that;
Cos θ = adjacent/ hypotenuse
Cos 60 = x/ 8
x = 8*Cos 60
= 8*0.5
x = 4
Thus, the building is 4 feet far to the base of the ladder.
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4 less than the product of 1 and x
4 less than the product of 1 and x is x - 4.
How to represent word expression in algebraic expression?An algebraic expression is a variable expression described using its terms, and operations on the terms.
In other words, algebraic expression are mathematical expressions where variables and constant are combined using operations such as subtraction, addition, multiplication etc.
Therefore, let's express the word expression in algebraic expression,
Hence, 4 less than the product of 1 and x is represented as follows:
(1 × x) - 4
x - 4
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I need help on this!
One must first divide a compound inequality into two other inequalities before solving it.
Compound inequalities: how to solve them?One must first divide a compound inequality into two other inequalities before solving it. Choose between a union of sets ("or") and an intersection of sets for the solution ("and"). the graph and the inequalities should then be solved.Inequalities that include the words "and" or "or" connecting them are referred to as compound inequalities. Examples include It must be larger than -2 and less than or equal to 5. "x 3" or "is more than or equal to 3 or less than -4" are equivalent expressions. Take note of the two inequality indications that each of these disparities has.One must first divide a compound inequality into two other inequalities before solving it.To learn more about compound inequality refer to:
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Jayden owns 32 rabbits. If 12 of his rabbits are male, what percentage of Jayden's rabbits are male
Answer:
37.5%
Step-by-step explanation:
We take
12 divided by 32, then times 100% = 37.5%
So, 37.5% of Jayden's rabbits are male
Is a triangle possible with length of the sides as 10. 2 cm 6. 8 cm and 4. 6 cm?.
Yes, it is possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(4.6cm + 6.8cm) =10.2cm
11.4cm = 10.2cm
LHS>RHS
A triangle is possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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A peron in a wheelchair exert a force of 25 n to go up a ramp that i 10 m long. The weight of the peron and wheelchair i 60 n and the height of the ramp i 3 m
To determine the amount of work done by the person in the wheelchair going up the ramp, you can use the formula for work:
work = force x distance x cos(theta)
where force is the force exerted by the person (25 N), distance is the distance traveled (10 m), and theta is the angle between the force and the displacement.
The angle between the force and the displacement is 90 degrees because the force is perpendicular to the displacement.
The force exerted by the person is to overcome the force of gravity on the person and wheelchair weight (60 N).
work = force x distance x cos(90)
work = (25 N + 60 N) x 10 m x cos(90)
work = 85 N x 10 m x 0
work = 0 J
It's impossible to do work when the angle between the force and the displacement is 90 degrees because the force and the displacement are perpendicular to each other.
The height of the ramp (3 m) is not used in this calculation, as it is not related to the force or distance.
The work done by the person in the wheelchair is 0 J because the force exerted by the person is perpendicular to the displacement. However, the person will be expending energy to overcome the force of gravity and move the wheelchair up the ramp.
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What is the value of the expression below when
�
=
3
x=3?
7
�
2
+
9
�
−
3
7x
2
+9x−3
Answer:
The value of the expression when x=3 is:
7^(3/2) + 9x - 3
We can simplify it as:
49 + 9*3 - 3
= 49 + 27 -3
= 73
So the final value of the expression is 73.
Given expression y=7x²+9x-3
Given value of x=3
We want to find the value of y.
Substitute the value of x=3 in y expression
y=7(3²)+9(3)-3
y=7*9+9*3-3
y=63+27-3
y=87
Therefore, the value of given expression is 87
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Complete question
What is the value of the expression below when x=3,
y=7x²+9x-3
please help!!!! asap!!!! piecewise functions
Answer:
undefined
Step-by-step explanation:
You want the value of f(-1), given the piecewise defined function f(x).
DomainThe function is defined for values of x greater than 1. The value x=-1 is not part of the domain of the function:
f(-1) = "undefined"
third root of 27x ^ 9
Answer: 3x^4*sqrt(3x) is the answer
Step-by-step explanation:
Factor 27 into its prime factors
27 = 33
To simplify a square root, You take the square factors, or factors that are raised to an even exponent.
Factors which will be taken are:
9 = 32
Factors which will remain inside the root are:
3 = 3
To finish this we take the square root of the factors that were taken out. This can be done by dividing their exponents by 2 :
3 = 3
I hope this helps!
What is the plane by 3 points?.
Three points can define the two distinct vectors AB and AC (A, B, and C). The two vectors' cross product, which they both lie on, may be utilized as the plane's normal.
It is logical to assume that this is the case since a plane contains precisely two linearly independent vectors since it has a dimension of two. If the three points were collinear, there wouldn't be two linearly independent vectors; instead, the origin and tips of the two vectors are the three points.
The three points that make up a plane in a three-dimensional space can be used to define it as long as they are not on the same line. On a plane, there exist at least three non-collinear points. A line that connects any two locations in a plane is also considered to be a part of the plane. A line is created at the place of intersection when two planes clash.
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What is the product of 45?.
The product of 4 x 5 is 20.
The term product in math is defined as product of two numbers is the result you get when you multiply them together.
Here we need to identify the product of 4 x 5.
As per the definition we all know that the product also known as multiplication is the process of multiplying it by another number.
Here we all know that the multiplication table is used for this onw,
So, here we have to write the multiplication table, that is
=> 4 x 1 = 4
=> 4 x 2 = 8
=> 4 x 3 = 12
=> 4 x 4 = 16
And then the value of
=> 4 x 5 = 20.
Complete Question:
What is the product of 4 x 5?
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Polynomial from Description
Use the information below to answer the questions.
Find the value of a,b,c and d.
The polynomial function is obtained to be h(x) = -2 (x - 4)(x - 1)²(x + 2), with the values a = -2, b = -4, c = -1 and d = 2.
What is a polynomial?
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
The characteristics of the polynomial are -
The zeros are located at 4, 1 (multiplicity of 2) and-2
The end behavior is as follows -
As x reaches negative infinity, f(x) reaches negative infinity.
As x reaches infinity, f(x) reaches negative infinity.
The y-intercept of the function is (0, 16)
The equation of h(x) can be written as -
h(x) = a(x+b)(x+c)²(x+d)
The zeroes of the polynomial can be written as -
x = 4 ⇒ (x - 4)
x = 1 ⇒ (x - 1)
x = 1 ⇒ (x - 1)....Since the multiplicity is 2 so write it two times.
x = -2 ⇒ (x + 2)
So, the equation will be -
y = a (x - 4)(x - 1)(x - 1)(x + 2)
The y-intercept is given as (0,16).
So, substitute the values of x and y with 0 and 16 respectively.
y = a (x - 4)(x - 1)(x - 1)(x + 2)
16 = a (0 - 4)(0 - 1)(0 - 1)(0 + 2)
16 = 2a(-4)(-1)(-1)
16 = 2a × -4
16 = -8a
a = -2
Hence, the equation becomes y = -2 (x - 4)(x - 1)(x - 1)(x + 2).
On graphing the equation it can be seen that -
As x → -∞, f(x) x → -∞
As x x → ∞, f(x) x → -∞
Therefore, the polynomial equation is h(x) = -2 (x - 4)(x - 1)²(x + 2).
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9. - Laura, Raúl y Miguel compraron un terreno de 900 metros cuadrados con valor de 540,000 pesos.
Laura puso 300,000 mil pesos, Raúl puso 200,000 mil pesos y Miguel 40,000 mil pesos. ¿Qué cantidad
de terreno le debe tocar a Laura?
a) 600 m2
b) 24 m2 c) 500 m2 d) 30 m2
The amount of yard that has to be given to Laura is c) 500 m2
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information:
Total of money = 540 000
Laura's money = 300 000
Lets represent the amount of money Laura gave:
Laura's % = (300 000 / 540 000) * 100
Laura's % = 30/54 * 100
Laura's % = 5/9 * 100
Laura's % = 55.56%
The amount of yard should be for Laura is:
Laura's yard = Total yards area * Laura's %
Laura's yard = 900 m^2 * 55.56%
Laura's yard = 500 m^2
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How do you write radicals in simplest form?.
Factor the radicand: If the radicand is not already in the form of a perfect square, you can factor it into its prime factors and pull out any perfect squares from the radicand.
For example, √(36) can be simplified to √(49) = √4 * √9 = 23.
Simplify the exponent: If the radical has an exponent (such as cube root), divide the exponent by the index of the radical. Example ∛64 = ∛(4^3) = ∛4 * ∛4 * ∛4 = 4 *4 *4 =4
Combine like factors: If there are any factors in the radicand that match the exponent, you can combine them and simplify the radical further. For example, √(2235) = √(2^235) = 2√(35) = 2√15 = 2*3 = 6.
It is important to note that not all radicals can be simplified to a whole number or a fraction. In some cases, the radical will be in its simplest form when it is left as an irrational number.
For Example, √2 cannot be simplified further.
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For what value of k pair of linear equations has infinitely many solutions KX 4y K 8 0 4x KY 4 0?.
The pair of the linear equations Kx + 4y + (μ+8) = 0 and 4x + ky + 4 = 0 has infinitely many solutions for k = ± 4.
Given lines are
kx + 4y + (μ+8) = 0
4x + ky + 4= 0
for lines to have infinite solutions
a₁/a₂ = b₁/b₂ = c₁/c₂ [a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0]
∴k/4 = 4/k = (μ+8)/4
∴k/4 = 4/k
⇒k² = 16
⇒k = ±4
We have, 4/k = (μ+8)/4
For, k = +4
⇒4/4 = (μ+8)/4
⇒μ = −4
For, k=−4
⇒4/-4 = (μ+8)/4
⇒μ = −12
∴ for k = ±4, the line has infinite solutions.
--The given question is incomplete; the complete question is
"For what value of K, the following pair of the linear equation has infinitely many solutions
Kx + 4y = (μ+8) = 0
4x + ky + 4 = 0"--
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grams per cubic centimeter to kilograms per cubic meter
Grams per cubic centimeter to kilograms per cubic meter is 1000.
1 g/cm³ = 1000 1 kg/m³
How to convert from g/cm³ to kg/m³?The conversion value:
1 gram = 1/1000 kg1 cm³ = 1/1000000 m³Find the conversion from grams per cubic centimeter to kilograms per cubic meter!
Grams per cubic centimeter = g/cm³Kilograms per cubic meter = kg/m³Multiply the number with the each conversion value!
See that the cubic centimeter is as a denominator. So, we reverse the fractional value.
1 g/cm³
= 1 × 1/1000 × 1000000/1 kg/m³
= 1000 kg/m³
Hence, the conversion value from grams per cubic centimeter to kilograms per cubic meter is 1000.
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Classify the system and give the number of solutions.
Please explain too
The system formed by linear equations - 8 · x + 8 · y = 1 and - 32 · x + 32 · y = - 5 has no solution.
How to classify a system of linear equations
In this problem we find a system formed by two linear equations with two variables. There are three kinds of systems of linear equations:
One solutionInfinite solutions - When a equation is a multiple of the other one.No solution - When an absurdity exists between independent coefficients.First, write the system of linear equations:
- 8 · x + 8 · y = 1
- 32 · x + 32 · y = - 5
Second, multiply the first equation by 4:
- 32 · x + 32 · y = 4
Third, use transitive property:
4 = - 5 (CRASH!)
The system of linear equations has no solution.
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A contruction ite in the hape of a quare i urrounded by a wooden wall 2m high. If tge length of one ide of the wall i 45m. Find the area of the contruction ite
The construction site area is 2025 square meters, calculated by finding the area of a square with side length 45m.
What is square ?
A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle where all sides are equal in length and opposite sides are parallel. It can also be defined as a polygon with four sides and four angles, all of which are right angles.
The construction site is in the shape of a square and the wooden wall surrounding it is 2m high and has a length of 45m.
Since the wall encloses a square, the length of one side of the square is equal to the length of the wall (45m).
Therefore, the area of the construction site can be calculated by finding the area of a square with side length 45m.
The formula for the area of a square is side length squared (s^2).
area = 45m x 45m = 2025 square meters.
So , The construction site area is 2025 square meters, calculated by finding the area of a square with side length 45m.
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How will you describe the nature of roots of 2x² 4x 7?.
Therefore, the real and unequal roots of the quadratic equation. The roots are uneven and real when the discriminant is bigger than zero. The roots are equal and real when discriminant is equal to zero.
When are the real and unequal quadratic equation roots?When a, b, and c are real integers and the discriminant is bigger than zero (b2 - 4ac > 0), the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.
Which quadratic equation's roots are rational and unequal?In this situation, we say that the roots are hypothetical. Ax2 + bx + c = 0 has real, rational, and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.
D=b \s2 \s −4ac=42 \s −4×2×(−7)=16+56=72>0.
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Full Question = What will be the nature of roots of quadratic equation 2x 2 +4x−7=0?
Are all right triangles 30 60 90 triangles?.
No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.
No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.
A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.
For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.
Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.
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20 POINTS PLEASE SOLVE I NEED TO HAVE THIS SUBMITTED!
Interpret the notation that defines the reflection. Show your work and explain the steps
you used to solve.
Therefore , we can conclude from the answer to the above problem that the equation for a reflection from across y-axis is - (x,y) -> (x,y).
Describe the y-axis.The x-axis and y-axis are the coordinate plane two crucial axes. In contrast to the x-axis, which is a horizontally number line, the y-axis is vertical. Its two orthogonal axes make up a coordinate plane. The ordinate refers to the y-axis, whereas the abscissa refers to the x-axis.
Here,
The Y-axis is the line that runs vertically along the graph from bottom to top. The measurement coordinates are parallel to the this axis.
The numbers on the y-axis are known as y-coordinates.
When expressing following result, the x-coordinate and y-coordinate go in parentheses in that order.
(x, y).
A' ( -1, 1 ) => A"(-1, -1) (-1, -1)
B' (-2, 2) => B"(-2, -2) (-2, -2)
C' (-2, 3) => C"(-2, -3) (-2, -3)
and D' (-1, 4) => D " (-1, -4)
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A group of friends went to lunch. The bill, before sales tax and tip, was 37.50. A sales tax of 8% was added..The group then tipped 18% on the amount after the sales tax was added.What was the amount in dollars of the sales tax?
what was the total amount the group paid,including tax and tip?
The amount of sales tax is $3,
The total amount the group paid, including tax and tip is $47.79.
What is the percentage?A percentage is a figure or ratio that can be stated as a fraction of 100.
If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given The bill, before sales tax and tip,
amount of the bill before sales tax and tip = $37.50
sales tax is 8% on bill
sales tax = 8% of 37.50
sales tax = 37.50*8/100
sales tax = 37.50*0.08
sales tax = $3
amount after sales tax = $37.50 + $3
amount after sales tax = $40.5
the tip is 18% of the amount after the sales tax
tip = 18% of 40.5
tip = 40.5*18/100
tip = 40.5*0.18
tip = $7.29
total bill amount = $37.50 + $3 + $7.29
total bill amount = $47.79
Hence the sales tax is of $3 and the total amount is $47.79.
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Danny wants to hang a mirror that is 12 3/4 inches wide in the center of a wall that is 25 inches wide.How much wall space should be left on each side of the mirror?
The width that is left on each side of the mirror is 13 1/4 inches.
How to Hang a Heavy Mirror?Mirrors, due to their size, weight, and combination of robustness and fragility present a challenge for drywall and plaster walls.
The mounting gear for most new mirrors is already included, but it is important to take great consideration when choosing the anchors, screws, and bolts that will connect the mirror to the wall.
Use the following guidance on how to hang a heavy mirror safely so you may update your space while safeguarding your walls and decor after deciding what kind of wall you have and selecting the appropriate materials.
25 - 12 3/4 = 13 1/4
5 1/8 inches broad on each side of the mirror when 13 1/4 are split by two.
5 1/8 + 5 1/8 + 14 3/4 = 25.
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hi please help thanks
The letter on the number line that represents the given number is B.
What is a number line?A number line is a straight line which extends from -∞ to -∞, on which the position or location of all directed numbers can be identified.
Directed numbers are numbers which have either a negative or positive sign. Examples include; -4, -1 2/3. 9 etc. Therefore all numbers can be located on a number line.
Considering the given question, to locate the position of 1 85/100. The whole number make us to understand that its position falls between 1 and 2. And the fraction part shows that the number is closer to 2 more than 1.
Therefore, the letter on the number line that represents 1 85/100 is B.
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Meena i ordering a taxi from an online taxi ervice. The taxi charge $3. 50 jut for the pickup and then an additional $1. 75 per mile driven. How much would a taxi ride cot if Meena i riding for 6 mile? How much would a taxi ride cot that i m m mile long?
The cab ride will cost you $14.
Cost is the quantity of money spent by a business or work to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.
as stated in the inquiry, Meena I'm using an online taxi service to order a taxi.
The cab bills $3.50 for the pickup alone, plus an extra $1.75 for each subsequent mile driven.
The original taxi fare plus the number of kilometres multiplied by the 1.75-cent-per-kilometer cost of the additional drive equals 3.50 + 6 (1.75), which equals $14.
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