Answer:
Breadth=8
Length=6
OR
breadth = 6
length=8
Step-by-step explanation:
Area of 4 walls = 2(l+b)h
112=2.4(l+b)
112/8=l+b
14=l+b
l=14-b
Area of base or ceiling=l x b
48=(14-b).b
48=14b-b²
b²-14b+48=0
factorize it and we get
(b-6)(b-8)=0
taking b-6=0
b=6
l=14-6
l=8
Look at the image down below
Using the concept of ratios, the constant of proportion between middle school and high school is 3/4
What is ProportionalityProportionality is a fundamental concept in mathematics and physics. It is a relationship between two or more variables where a change in one causes a proportional change in the other. In other words, the ratio between the two remains constant. Proportionality is an important concept in mathematics because it is used to make predictions and solve problems. The constant of proportionality is the ratio between the two variables that remain constant in a proportional relationship.
To determine the constant of proportionality in this relationship, we can write an equation in the form
y = kx
k = constant of proportionOr we can easily use ratio to find the constant of proportion
Number of girls in middle school = 6
Number of girls in high school = 8
The ratio = 6/8 = 3 / 4 = Option B
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Which statements are true about the volume of the triangular pyramid shown? Select two choices. (Recall the formula V = one-third B h.)
A triangular pyramid. The base has a base of 8 feet and height of 2 feet. The pyramid has a height of 6 feet.
[Not drawn to scale]
The value of h in the formula V = one-third B h is 2 ft.
The area of the base, B, is 8 feet squared.
The sum of the areas of the faces can find the volume.
The volume is 16 feet squared.
The expression One-third (8) (2) (6) can be used to find the volume of the pyramid.
The correct statements are,
The area of the base, B, is 8 feet squared.
The expression one-third (8) (2) (6) can be used to find the volume of the pyramid.
What is a triangular pyramid?A tetrahedron is a polyhedron in geometry that has four triangular faces, six straight edges, and four vertex corners. It is often referred to as a triangle pyramid. The tetrahedron is the simplest and only regular convex polyhedron with less than five faces.
Given that a triangular pyramid. The base has a base of 8 feet and a height of 2 feet. The pyramid has a height of 6 feet. The volume of the triangle is calculated as,
The area of the base,
A = 1/2 x b x h
A = 1/2 x 8 x 2
A = 8 feet
The volume will be calculated by the formula,
Volume = 1 / 3 x Base are x h
Volume = 1 / 3 x 8 x 2 x 6
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A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 7 grams and the amount of gold in each necklace is 18 grams. The jeweler made a total of 7 bracelets and necklaces using 82 grams of gold. Determine the number of bracelets made and the number of necklaces made.
The number of bracelets made is 4 and number of necklaces made is 3.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the number of bracelets made and y be the number of bracelets made.
There are total of 7 bracelets and necklaces.
x + y = 7
Amount of gold in each bracelet = 7 grams
Amount of gold in x bracelets = 7x grams
Amount of gold in each necklace = 18 grams
Amount of gold in y necklaces = 18y grams
Total gold used is 82 grams.
7x + 18y = 82
We have two linear equations :
x + y = 7 ⇒ x = 7 - y
7x + 18y = 82
Substituting x = 7 - y in second equation,
7 (7 - y) + 18y = 82
49 - 7y + 18y = 82
11y = 82 - 49
11y = 33
y = 33/11
y = 3
x = 7 - y = 7 - 3 = 4
Hence the number of bracelets and necklaces are 4 and 3 respectively.
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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where × represents the number of years since 2012, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1171.
Regression equation:
Final answer:
The linear regression equation is y = 22.086x + 898.620 and the year for 1171 cases is 2024
How to determine the linear regression equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
Using a graphing calculator, we have the following summary
Sum of X = 15Sum of Y = 5723Mean X = 2.5Mean Y = 953.8333Sum of squares (SSX) = 17.5Sum of products (SP) = 386.5The regression equation is represented as
Regression Equation = ŷ = bX + a
Where
b = SP/SSX = 386.5/17.5 = 22.08571
a = MY - bMX = 953.83 - (22.09*2.5) = 898.61905
So, we have
ŷ = 22.08571X + 898.61905
Approximate
y = 22.086x + 898.620
When the new cases is 1171, we have
22.086x + 898.620 = 1171
This gives
x = 12
i.e. year = 2012 + 12 = 2024
Hence, the year is 2024
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Which graph shows a system of equations with the solution (5, -3)?
Right-hand bottom graph shows a system of equations with the solution (5, -3).
What is Graph?A diagram that depicts the connection between two values, measures, or other objects as a line or curve.
According to the inquiry,
Due to the fact that the two lines meet at the position where they do, the graph on the bottom right depicts a system of equations with the answers (5, -3) (5, -3).
Therefore, the proper answers to the problem are represented by the bottom right.
Right-hand bottom graph has the proper equations and their answers (5,-3).
Right-hand bottom graph shows a system of equations with the solution (5, -3).
The complete question is
Which graph shows a system of equations with the solution (5, -3)?
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Find the sales tax selling price 20$ rate of sales tax 3%
In the triangle below, what is the side adjacent?? HELP
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
The following equations are equivalent:
2 + x = 5
x + (negative 4) = 7
Negative 5 + x = negative 2
All of these three equations are equivalent because they all represent the same mathematical relationship between x and other numbers. The variable x is the same in each equation. We can see this by applying the same operation on both sides of the equations, and the variable x will cancel out and the two sides will be equal.
True or False? If false, state the correct solution.
Answer:
TRUE
Step-by-step explanation:
(2x^2-5x-3)/(x-3) = (2x+1)
(2x^2)/(x-3) - (5x)/(x-3) - 3/(x-3) = (2x+1)
[separated each term on the left side]
(2x^2)- (5x) - 3 = (2x+1)(x-3)
2x^2- 5x - 3 = (2x+1)(x-3)
(2x+1)*(x-3) = (2x+1)(x-3)
Both sides are the same. The equation is TRUE.
why is there a limit
Term limits have been approved almost everywhere they’ve been on the ballot.
Are term limits helpful?
However, the evidence suggests that at the margin, term limits are helpful to the cause of individual liberty. Elhauge’s report showed that term limits lessen the influence of seniority. His research demonstrated that long-term lawmakers from both major parties vote for more bureaucracy than do lawmakers who have been in office for shorter times.
Therefore, term limits have been approved almost everywhere they’ve been on the ballot
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How do you find the coordinates of a midpoint example?
To find the coordinates of the midpoint of two points in a plane, you can use the midpoint formula. The midpoint formula is:
(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and (x,y) are the coordinates of the midpoint.
For example, if you have two points (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:
(x,y) = ((3 + 7) / 2, (4 + 10) / 2)
(x,y) = (5, 7)
The midpoint of points (3,4) and (7,10) is (5,7).
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e.
d.
C.
b.
a.
12
Original
Fractions
47 35 59 23 14207956 5238
Common
Denominator
35
Equivalent Fractions
> or <
+11
4
7
9
5
12
3.5
름
5
6
3.8
ble to help you rewrite the problems with common denominators. Then solve.
The fractions with the common denominators are given as follows:
4/7 = 36/63.5/9 = 35/63.The inequality relating the fractions is given as follows:
4/7 > 5/9.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y, as follows:
Fraction = x/y.
The terms are classified as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.The fractions for this problem are given as follows:
4/7.5/9.The denominators are given as follows:
7 and 9.
The least common multiple of 7 and 9 is given as follows:
7 x 9 = 63.
Hence the equivalent fractions are given as follows:
4/7 = 36/63. (63/7 = 9, hence both the numerator and denominator are multiplied by 9).5/9 = 35/63 (63/9 = 7, hence both the numerator and denominator are multiplied by 7).The equivalent fractions have the same denominator, while the equivalent fraction to 4/7 has the greater numerator, hence the inequality is given as follows:
4/7 > 5/9.
Missing InformationThe problem is given by the image presented at the end of the answer.
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2x+3y=3,2y+3z=4,2x+2z=8
Answer:
x=6/5
y=1/5
z=14/5
i think i not 100% sure
What is the measure of 23 if clld?
Answer:
i tink im doing this complete wrong but 1.380649×10−23 J
Step-by-step explanation:
How many square meters are in 280 square centimeters
We can perform a change of units to see that 280 square centimeters is equivalent to 0.028 square meters.
How many square meters are in 280 square centimeters?We want to perform a change of units between square centimeters and meters.
Remember the relation:
100cm = 1m
Now we can square both sides of that equation, then we will get:
(100 cm)^2 = (1m)^2
10,000 cm^2 = 1m^2
Then if we have a measure in square centimeters, to transform it into square meters we need to divide that measure by 10,000.
Then:
280 cm^2 = (280/10,000) m^2 = 0.028 m^2
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How do you write 10x10x10x10 in exponential form?
Answer:
10^4
Step-by-step explanation:
10= 10^1
10x10 = 10^2 (2 10s)
10x10x10=10^3 (3 10s)
10x10x10x10=10^4 (4 10s)
basically the number of 10s you are multiplying will be the number of exponents you will use in this case.
A cubical tank full of water is emptied in a cylindrical tank. If the edge of cubical tank is 77cm, find the height to which the water rises in the cylinder whose bbase diameter 1.4m.
Answer:
Step-by-step explanation:
H=456,533/pier^2
H=456533×7/22×7×7*. Here 7 as radius
H=29.645cm
Solving systems of equations by substitution worksheet
1. y = 6x-11
-2x-3y = -7
2. 2x-3y = -1
y = x-1
1. steps to find the value of x
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate y:
-6x+y= -11 | times -3| becomes 18x-3y=33
18x-3y=33
-2x-3y = -7
y in the equation can be eliminated to become:
20x=40
x=40/20
x=2
steps to find the value of y:
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate x:
-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21
-6x+y= -11
-6x-9y=-21
x in the equation can be eliminated to become:
10y=10
y=-10/10
y=1
2.
1. steps to find the value of x
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate y:
-x+y=-1| times -3| to 3x-3y=3
-2x-3y = -1
3x-3y=3
y in the equation can be eliminated to become:
-5x=-4
x=4/5
Steps to find the value of y:
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate x:
-x+y=-1| multiplied by 2| becomes -2x+2y=-2
-2x-3y = -1
-2x+2y=-2
x in the equation can be eliminated to become:
-5y=1
y=-1/5
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Rewrite 5 square root 3^4 as an expression with a rational exponent. Then mark this number on the graph of f (x) = 3^x. Explain how you know where to place it.
Step-by-step explanation:
the nth root of something can be expressed as 1/n as exponent.
e.g. sqrt(2) = 2^(1/2).
so, the 5th root of 3⁴ = 3^(4/5)
for f(x) = 3^x
that means that x = 4/5 = 0.8.
so, I go on the x-axis to the right to 0.8, and from there straight up to the actual curve.
that is the desired point.
The boatbill is present in a density of at least one pair per 20 acres at the same time that two different types of plants are dominant. What are these plants?.
The two types that the boatbill will dominate are grasses and shrubs according to the attached table.
What is density?The density of an item is defined as its mass divided by its volume. Density is commonly expressed in grams per cubic centimeter (g/cm3). Remember that grams are a unit of mass and cubic centimeters are a unit of volume (the same volume as 1 milliliter). “Density = mass divided by volume.” Density is a compound metric that tells us about an object's mass in proportion to its volume. The density of a substance is the measure of how densely it is packed together. It is expressed as mass per unit volume. Density Symbol: D or ρ Density Formula: = m/V, where is the density, m is the object's mass, and V is its volume.
Here,
According to the accompanying data, the boatbill will predominate among grasses and bushes.
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The equation and the tables represent two different functions. Use the equation b = 6a - 10 and the table to answer the questions. This table represents c as a function of a.
Answer:
[tex]A. \;\;b \;is \;greater[/tex]
[tex]B.\;\;a = 1, b = -4[/tex]
[tex]C.\;\;a = 6, c = 20[/tex]
Step-by-step explanation:
Part A
We have the relationship
[tex]b = 6a - 10[/tex]
When [tex]a[/tex] is [tex]-2[/tex], the value of [tex]b[/tex] is
[tex]b = 6(-2) -10 = -12 -10 = -22[/tex]
The corresponding value of [tex]c[/tex] for [tex]a = - 2[/tex] is -[tex]21[/tex]
[tex]-21[/tex] is greater than [tex]-22[/tex] so answer is : [tex]b[/tex] is greater
Part B
When [tex]c[/tex] is [tex]6[/tex], we see that the value of [tex]a[/tex] from the table is [tex]1[/tex]
The corresponding value of b is:
[tex]b = 6(1) - 10 = 6 - 10 = -4[/tex]
Part C
When [tex]b = 26[/tex], plugging this into the equation[tex]b = 6a - 10[/tex] we get
[tex]26 = 6a - 10\\\\26 + 10 = 6a\\\\36 = 6a\\\\[/tex]
or
[tex]6a = 36[/tex] giving [tex]a = 36/6 = 6[/tex]
For [tex]a = 6[/tex], from the table we see that the corresponding value of [tex]c = 20[/tex](ANS)
The sum of all interior angles in a polygon is 9 degrees. How many sides does the polygon have? Please show your working.
How do I olve thi ytem of equation uing the elimination method. (I don't jut want the anwer, I want an explanation on how to get the anwer. )
y=3x13
2x=y-9
Answer:
-4
Step-by-step explanation:
y=3x13
2x=y-9
2x=3x+13-9
2x=3x+13-9
2x=3x+4
-3 -3
-x=4
-x/ -x/
x=-4
(You said "3x13" so i'm going to guess you meant to say "3x+13").
(If you meant "3x-13" I can also help you with that too)!
11
1 point
Which is the slope of the proportional relationship?
3/4
2
1/2
4/3
X3456
Y
3 6
69
8
5 10
6 12
Answer:
The number line that represents the inequality 6x - 12 > -6 is (D)
How to determine the number line?
The inequality is given as:
6x - 12 > -6
Add 12 to both sides
6x > 12 - 6
Evaluate the difference
6x > 6
Divide both sides by 6
x > 1
The number line that represents the above inequality is (D)
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Solving a Mixed-Degree
Consider the following system of equations:
10 + y = 5x + x2
5x + y = 1
The first equation is an equation of a
The second equation is an equation of a
What are the solutions of the system?
Answer:
The solutions are:
(1,-4), and (-11,56)
Step-by-step explanation:
10 + y = 5x + x^2
5x + y = 1
Rearrange both equations to isolate y:
y = x^2 + 5x - 10
y = -5x+1
Since y=y, we set set the right sides of both equations equal to each other:
-5x+1 = x^2 + 5x - 10
Rearrange
-x^2 - 10x + 11 = 0
x^2 +10x - 11 = 0
Factor
(x+11)(x-1) = 0
x = -11 and 1
Use these two values of x to find y. We'll use the simpler equation of
y = -5x+1.
x _y
1 -4 (1,-4)
-11 56 (-11,56)
See the attached graph for proof.
What is section formula and midpoint formula?
The section formula helps to find out the coordinates of points that divide the line in the m:n ratio whereas the midpoint formula helps us to find the midpoint of a line.
The section formula is used in geometry to find out centroid, incenters, etc. It is of two types: Internal division and external division. These types depend on the position of point P.For a point P(x,y) dividing line a(a,b) and B(c,d) in ratio m:n, The
Internal division section formulae is- P(x)=(c.m +a.n)/m+n , P(y)=(d.m+b.n)/m+nExternal division section formulae is- P(x)=(c.m - a.n)/m-n , P(y)=(d.m-b.n)/m-nThe midpoint formula is used to find the center of a line or a figure. It is a mathematical equation used in geometry and economics. On a line from point (x1,y1) to (x2,y2) the midpoint P= (x1+y1)/2 , (x2+y2)/2. It divides the line in 1:1 ratio.
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Perform the following composition of transformation for point P (6, -4.)
T (-1,2) o R (180)
So, on solving the provided question we can say that coordinates are -
(6, -4.) and T (-1,2) y-y1 = m(x - x1) => 2x - y -16 =0
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
here,
coordinates are -
(6, -4.) and T (-1,2)
y-y1 = m(x - x1)
y +4 = 2(x -6)
y+ 4 = 2x - 12
2x - y -16 =0
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Two Places P and q have thesame Longitude. Their Latitude are 15°N and 36°s, Draw diagrams and calculate the great circle distance q
Therefore , the solution of the given problem circle comes out to be
straight line distance from Sydney to Capetown ≈11139 km
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is axis of rotation equal about the center at every angle. Every set of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetrical about the center at every angle.
Here,
The distance between Sydney and Cape Town's longitudes is 151.13° and 18.22°, respectively, for the little circle, which equals 533.669 km. Sydney to Capetown distance in a straight line is
151.13∘−18.22∘=132.91∘
Straight line distance from Sydney to Capetown
d= √53372+53372−2×5337×5337× cos132.91∘
= 9785 km
θ=cos⁻¹ (6400²+6400²−9785² / 2 x 6400×6400)=99.72∘
Great Circle route from Sydney to Cape Town
=>πR / 180∘ ×θ
=> 6400π180∘×99.72∘
=> 11138.831…≈11139 km
Therefore , the solution of the given problem circle comes out to be
straight line distance from Sydney to Capetown ≈11139 km
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Which equation represents a line perpendicular to the line with equation 2x + 3y = 12?.
The equation of the line perpendicular to 2x + 3y = 12 will be y = 3x/2 + c where c ∈ R.
The equation of the line given here is 2x + 3y = 12
Now rearranging it to the slope-intercept form we get
3y = -2x + 12
or, y = -2x/3 + 4
Now any 2 lines are perpendicular when the product of their slopes results in -1.
Hence, let the equation of the line perpendicular to the given line be
y = mx + c, where m is the slope of the line and c is the intercept.
Hence,
-2m/3 = -1
or, m = 3/2
Hence the equation of the line will be
y = 3x/2 + c where c ∈ R
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Translate this sentence into a equation
38 is the product of Dellas score and 2.
Use the variable d to represent Della’s score
The required translation of the given statement into an equation is given as 38 = 2d.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
38 is the product of Della's score and 2.
Let the variable d to represent Della’s score,
2 × d = 38
2d = 38
Thus, the required translation of the given statement into an equation is given as 38 = 2d.
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