[tex]y=2\frac{2}{3}+16[/tex] is the answer as it passes perpendicular and through point A
40PT! - Mathematical Proofs: Practice Save and Exit
Select the correct answer from each drop-down menu.
Options for first box - transitive property, subtraction property of equality,
segment addition, substitution property of equality
Options for second box - AC does not equal XZ, AC equals XZ, AB equals YZ,
AB does not equal YZ
Thankyou!
The option for the first box is segment addition and the option for the second box is AC does not equal XZ.
What is Congruence of Figures?Two or more figures are congruent if the dimensions of the one figure is equal to the dimension of the other figure.
Proof of the congruence of two lines are given using the contradiction method.
Given that AC ≅ XZ and BC ≅ XY.
It is proving AB ≅ YZ.
We get by following some steps,
AB + BC ≠ YZ + XY
We know that, AB and BC are the segments joining to form the line AC.
AB + BC = AC
Similarly, YZ and XY are the segments joining to form the line XZ.
YZ + XY = XZ
Substituting in AB + BC ≠ YZ + XY, we get AC ≠ XZ.
So here we are using the segment addition to write AC ≠ XZ
Hence applying segment addition to AB + BC ≠ YZ + XY, AC ≠ XZ
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why do we use sampling with replacement instead of sampling without replacement? incorporate the definion of sampling with replacement.
Sampling with replacement is a type of sampling technique in which the same unit can be selected multiple times from the sample population.
This type of sampling is used when the size of the sample population is very large and it is not possible to select a unique unit from the population. The formula for sampling with replacement is nCr, where n is the population size and r is the sample size. For example, if the population size is 10 and the sample size is 3, then the total number of combinations would be 10C3 = 120. This means that 120 possible samples can be selected from the population, with each unit having an equal probability of being selected. Sampling with replacement is often used in statistical analysis to generate a representative sample of the population.
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-3/4 + -5/8 pls help
The addition of the fractions, -3/4 + -5/8 = -11/8.
How to Add Fractions together?To add fractions together, ensure you find the common denominator of the fractions you are adding together.
Given the fractions, -3/4 + -5/8, add the fractions as explained below:
-3/4 - 5/8 (i.e. minus times plus is equal to minus)
The common denominator is 8, therefore:
[2(-3) - 1(5)] / 8
(-6 - 5) / 8
= -11/8
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7 QUESTIONS PAY IS 100 WILL GIVE BRAINLEIST
A maintenance worker needs to wax a restaurant floor shaped like the image shown.
A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet.
If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor?
$1,224.75
$1,569.75
$2,104.50
$2,449.50
Question 2(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?
sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2
Question 3(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.
What is the area of the parallelogram?
four hundred twenty-three and one-half ft2
four hundred twenty-seven and one-half ft2
four hundred thirty-three and one-eighth ft2
four hundred fifty-five and one-eighth ft2
Question 4(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 6.2 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
20.2 m2
43.4 m2
33.4 m2
86.8 m2
Question 5(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
An image of a rhombus is shown.
A rhombus with a base of 16 centimeters and a height of 15.5 centimeters.
What is the area of the rhombus?
15.75 cm2
31.5 cm2
124 cm2
248 cm2
Question 6(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 4 inches. The vertical height between these bases is 2.3 inches. That vertical height intersects the bottom base, leaving 2.5 inches between it and the vertex to the left. The side on the right is the longest at 5.2 inches. There is a horizontal line connecting the vertex of the bottom base to the 5.2-inch side and that line is 3 inches.
Which of the following represents the total area of the figure?
16.425 in2
20.775 in2
24.15 in2
28.5 in2
Question 7(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 43 meters. The height of the figure is 34 meters. The portion from the vertex to the perpendicular height is 22 meters. The portion from a point to a vertical line created by two vertices is 18 meters.
Which of the following represents the total area of the figure?
306 m2
1,836 m2
2,142 m2
3,978 m2
Answer:
Step-by-step explanation:
I got you.
1.
The six-sided figure can be broken down into a rectangular prism with dimensions 35 x 20 x 30 and a right triangular pyramid with base 35 x 15 and height 30.
The rectangular prism has a total floor area of 35 x 20 = 700 square feet.
The right triangular pyramid has a base area of 0.5 x 35 x 15 = 262.5 square feet and a total floor area of 262.5 + 700 = 962.5 square feet.
So the total floor area of the six-sided figure is 962.5 square feet.
To find the cost to cover the floor with wax, we multiply the floor area by the cost per square foot:
962.5 * $1.38 = $1322.35
So the wax will cost $1322.35 to cover the floor.
2.
The shape for the quilt block can be divided into two right triangles and a rectangle. The rectangle has a length of 13 inches and a width of 5.18 inches, so its area is 13 * 5.18 = 67.34 square inches. The two right triangles each have a base of 5 inches and a height of 6 inches, so their area is 0.5 * 5 * 6 = 15 square inches each. The total area of the two right triangles is 15 * 2 = 30 square inches. The total area of the quilt block is 30 + 67.34 = 97.34 square inches.
So the area of the shape for the quilt block is 97.34 square inches.
3.
The area of a parallelogram is given by the formula: Area = base * height.
So the area of this parallelogram is:
22.5 feet * 19.25 feet = 432.0625 ft^2
So the area of the parallelogram is 432.0625 square feet or approximately 432 and 6/16 square feet.
4.
An isosceles trapezoid has two equal sides that are parallel to each other. In this case, the two equal sides are perpendicular to the height and are equal to 4 + 7 = 11 meters each. The average of the two parallel sides is the formula for the top base of a trapezoid, so the top base is (3 + 11)/2 = 7 meters.
The area of a trapezoid is given by the formula: Area = (bottom base + top base) * height / 2.
So the area of this trapezoid is:
(3 + 7) * 6.2 / 2 = 33.4 m^2
So the area of the trapezoid is 33.4 square meters.
5.
The area of a rhombus is given by the formula: Area = (diagonal 1 * diagonal 2) / 2.
In this case, the base of the rhombus is equal to one of its diagonals, and the height is equal to the other diagonal. So the area of this rhombus is:
(16 * 15.5) / 2 = 124 cm^2
So the area of the rhombus is 124 square centimeters.
6.
he total area of the figure can be found by dividing it into two parts: a parallelogram and a triangle.
The parallelogram can be found by using the formula for the area of a parallelogram: Area = base * height. In this case, the base is 4 inches and the height is 2.3 inches, so the area of the parallelogram is: 4 * 2.3 = 9.2 square inches.
The triangle can be found by using the formula for the area of a triangle: Area = (base * height) / 2. In this case, the base is 2.5 inches and the height is 3 inches, so the area of the triangle is: (2.5 * 3) / 2 = 3.75 square inches.
The total area of the figure is the sum of the areas of the parallelogram and triangle: 9.2 + 3.75 = 12.95 square inches.
So the total area of the figure is approximately 12.95 square inches.
7.
The figure can be broken down into two triangles and a rectangle. The area of one triangle is (1/2)bh = (1/2)(22)(34) = 308. To find the area of the other triangle, use the Pythagorean theorem to find the length of the remaining side. The two remaining sides are 43 and 18, and the hypotenuse is the side connecting the two vertices, so we have:
a^2 + b^2 = c^2
43^2 + 18^2 = c^2
1,849 + 324 = c^2
2,173 = c^2
c = 46.7
The area of this triangle is (1/2)bh = (1/2)(46.7)(34) = 786.2
The rectangle has a base of 43 and a height of 34, so its area is 43 * 34 = 1,462
The total area of the figure is 308 + 786.2 + 1,462 = 2,556.2 square meters.
So the answer is 2,556.2 m2.
Find the value of x.
Answer:
Step-by-step explanation:
9.5 678 then ada 9.76
Patty is using a cylinder shape container to hold 48 in³ of liquid. The height of the container is 6 inches tall. What is the best approximation for the radius of the container? Responses 1.6 in. 1.6 in. 2.5 in. 2.5 in. 3.2 in. 3.2 in. 4.0 in.
The radius of the cylinder will be 1.6 inches. Then the correct option is A.
What is the volume of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be given as,
V = π r²h cubic units
Patty is using a cylinder shape container to hold 48 in³ of liquid. The height of container is 6 inches tall. Then the radius of the circle is given as,
V = π r²h
48 = 3.14 x r² x 6
r² = 2.5477
r = 1.596
r ≈ 1.6 inches
The radius of the cylinder will be 1.6 inches. Then the correct option is A.
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the sugar sweet company will choose from two companies to transport its sugar to market. The first company charges $2804 to rent trucks plus an additional fee of $100.25 for each ton of sugar. The second company does not charge to rent trucks but charges $225.75 for each ton of sugar.
A. For 22.3 tons of sugar, the two companies would charge the same.
B. The cost, when the two companies charge the same, would be $5040.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A. To find the amount of sugar for which the two companies charge the same, we can set the cost for each company equal to each other and solve for the amount of sugar.
The equation for the first company would be:
2804 + 100.25x (where x is the number of tons of sugar)
The equation for the second company would be:
225.75x
Setting these two expressions equal to each other and solving for x, we get:
2804 + 100.25x = 225.75x
x = 22.3
So, for 22.3 tons of sugar, the two companies would charge the same.
B. To find the cost when the two companies charge the same, we can plug 22.3 tons of sugar into either of the two equations:
2804 + 100.25 × 22.3 = $5039.57
or
225.75 × 22.3 = $5039.57
So, the cost when the two companies charge the same would be $5040.
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The question seems incomplete, the missing part has been below:
The sugar-sweet company will choose from two companies to transport its sugar to market. The first company charges $2804 to rent trucks plus an additional fee of $100.25 for each ton of sugar. The second company does not charge to rent trucks but charges $225.75 for each ton of sugar.
A. For what amount of sugar do two companies charge the same?
B. What is the cost when two companies charge the same?
pleaseeeeeeeeee i need help fast
Answer:Ariel
Step-by-step explanation: because if you divide 300 by 2 and then times it by 5 equals 750
81 is what percent of 3600?
Answer:
2.25%
Step-by-step explanation:
hope dis help
Answer:
2.25%
Step-by-step explanation:
The arc length of a circle intercepted by a central angle of 41.9° is 9.9 inches, what is the radius of the circle? Round to the nearest 10th of an inch.
Answer:
Radius = 13.8 inches
Step-by-step explanation:
The relationship between arc length, s , the radius r and central angle θ in radians is given by the formula
s = rθ where r = radius, θ is central angle in radians
Or,
r = s/θ
Given s = 9.9 in and θ = 41.4° we get
θ in radians = (θ in degrees) x π/180 radians
So 41° = 41 x π/180 radians = 0.7156 radians
r = s/θ
r = 9.9/0.7156
r = 13.835 inches
Rounded to the nearest tenth:
r = 13.8 inches
Which pair of values for x and y will not satisfy the following system?
Number 2
The point (1, 1) does not satisfy the given inequality system.
What is an inequality? What are algebraic expressions?An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > cIn mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the inequality system as -
y < 2x - 1
y > x - 1
Refer to the graph of the inequalities attached. The points in the shaded region represents the solution coordinates for the given system of equations. The point (1, 1) lies on the dotted line. So, this does not satisfy the given inequality system.
Therefore, the point (1, 1) does not satisfy the given inequality system.
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A teacher has 60 students in her class.she wants to form equal groups for project,what different groups she can make
A teacher has 60 students in her class and wants to form equal groups for a project. To determine the different groups she can form, we need to find the divisors of 60. The divisors of 60 are the numbers that divide evenly into 60.
The divisors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
These divisors represent the different numbers of students the teacher can form into groups. For example, she could form 60 students into 1 group, 30 students into 2 groups, 20 students into 3 groups, 15 students into 4 groups, and so on.
The teacher could also form more unusual groupings, such as 10 students into 6 groups, 12 students into 5 groups, or 6 students into 10 groups. The important factor is that the number of students must be divisible by the number of groups to ensure that each group has an equal number of students.
In conclusion, a teacher with 60 students in her class can form groups with the following number of students: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. These groupings allow her to balance the workload and provide equal opportunities for students to participate in the project. The choice of grouping size will depend on the specific requirements of the project and the teacher's preferences.
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URGENT! PLease AUTOMOTIVE
Note that the tools are matched against the alphabet are given as follows:
A. Drill index - Box that drill bits are stored in
B. Fender cover - Used to protect the vehicle's finish
C. Impact driver - Hand tool that is used to loosen fasteners that are very tight
D. Speed handle - Fits between a socket and a ratchet
F. Flare nut wrench - Tool used to loosen and tighten fuel line fittings
J. Stubby screwdriver - What a very short screwdriver is called
K. 6-point socket - Can be used on a 6-point fastener head
L. 12-point socket - Used on square drive fastener heads
N. Impact driver - An air-powered tool used to remove fasteners
O. Impact socket - Used with air tools
P. Slide hammer - Puller that uses a heavy weight that is slid against its handle
Q. Bearing separator - Used with a puller to pull a bearing from a shaft
R. Torque wrench - Measures the turning effort applied to a fastener
S. Chisel - Hand tool used for quickness when assembling parts
T. Dead blow hammer - A soft-faced hammer that has metal shot in its head
U. Creeper - Used to move around under vehicles
V. Hex wrench/ViseGrips - Commonly called Allen wrenches/Pliers that can be locked to a part
W. Safety goggles - Worn whenever working in the shop
X. Crowfoot wrench/Extension - Wrench used with a ratchet
Y. Coarse tooth hacksaw blade - Hacksaw blade that is the best choice for cutting thick steel
Z. Fine tooth hacksaw blade - Hacksaw blade that is the best choice for cutting Sheet Metal.
How can the above tools be classified?The above tools can be classified as hand tools and power tools used in various mechanical and automotive applications.
Their importance lies in their ability to make repair and maintenance tasks efficient and precise, ensuring the proper functioning of machinery and vehicles.
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Solve the following logarithmic equation. Write your answer in exact form.
Answer:
x is undefined
Step-by-step explanation:
[tex]\ln[/tex] is the Natural Logarithm.
The natural log of a negative number is undefined.
Help! Please :D Thank you btw!!! I need help on this question
The true statements for the expression 5 / 8m = 10 are,
A) The equation can be the same as 1 / 8m = 2.
C) The equation can be solved by dividing both sides by 5 / 8.
D) The equation can be solved by multiplying both sides by 8 / 5.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is 5 / 8m = 10.
The true statements are:-
A) The equation can be the same as 1 / 8m = 2.
5 / 8m = 10
m= 16
1 / 8m = 2
m = 8 x 2 = 16
C) The equation can be solved by dividing both sides by 5 / 8.
5 / 8m / 5 / 8= 10 / ( 5 / 8 )
m = 8 x 2 = 16
D) The equation can be solved by multiplying both sides by 8 / 5.
5 / 8m x 8 / 5 = 10 x 8 / 5
m = 16
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Lauren has a coin collection. She keeps 3 of the coins in her box, which is 4% of the collection. How many total coins are in her collection?
The total number of coins is equal to 35
How to determine the total number of coins?We have the following parameters that can be used in our computation:
Given that She keeps 3 of the coins in her box, which is 4% of the collection.
Number of coins in the box = 7
Proportion of coins in the box = 20%
These parameters mean that the Number of coins in the box = Proportion of coins in the box x Total number of coins
Substitute the known values in the equation, so, we have the following representation
7 = 20% x Total number of coins
Then Divide both sides by 18%
Total number of coins = 35
Hence, the total number of coins is; 35
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If you were to make a quadrilateral by rotating triangle RST 180 degrees about U, which type of quadrilateral would form
If you were to make a quadrilateral by rotating triangle RST 180 degrees about U, a Rhombus would form.
A Rhombus is a type of quadrilateral that is defined by its unique properties. The most distinctive characteristic of a Rhombus is the presence of two pairs of congruent and adjacent sides. These sides create a symmetrical figure that is easily recognizable. The other key property of a Rhombus is the presence of two pairs of equal, opposite angles. When a triangle, such as RST, is rotated 180 degrees about a central point, such as U, it creates a Rhombus. The sides of the triangle become the sides of the Rhombus, while the rotation creates the diagonal lines that connect the vertices. This rotation also ensures that the Rhombus has the desired properties of two pairs of congruent sides and two pairs of equal, opposite angles.
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The range for the eight numbers shown is 40. Find the two possible values of the missing number. 42 13 19 5 ? 11 27 33
The missing value to make the set of numbers to have a range of 40 is the number 2.
What is the range?In mathematics, the range can be defined as the difference between the greatest and lowest values in a set of numbers. Due to this, the range can be found by using subtraction.
What is the current range?In this case, the current range is 37 which is a result of 42 (greatest value) -5 (lowest value). However, the required range is 40. Let's calculate the missing value:
42-40 = 2
Based on this, the missing value is 2.
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30 points. Given f(x)=4(x−2)3+2, classify each statement about f−1(x) as true or false.
se
The point of symmetry on f−1(x) is (2,2).
The domain of f−1(x) is (−∞,4).
The graphs of f−1(x) and f(x) are reflections across the line y = x.
f−1(x) is not a function.
The classification of the statements are
The point of symmetry on f−1(x) is (2,2): TrueThe domain of f−1(x) is (−∞,4): FalseThe graphs of f−1(x) and f(x) are reflections across the line y = x: Falsef−1(x) is not a function: FalsHow to classify the statementsFrom the question, we have the following parameters that can be used in our computation:
f(x) = 4(x - 2)³ + 2
First, we calculate the inverse
So, we have
x = 4(y - 2)³ + 2
This gives
4(y - 2)³ = x - 2
Divide by 4
y - 2 = (x - 2)/4
Take the cube roots and add 2
f-1(x) = 2 + ∛[(x - 2)/4]
It is true that the point of symmetry of the function is (2, 2)However, the domain is not (−∞,4); the domain is all set of real valuesThe graphs of f−1(x) and f(x) are not reflections across the line y = x.Lastly, f−1(x) is a function.Read more about inverse functions at
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Please help. I need the answer asap.
Answer:
Option 4
Explained below
Step-by-step explanation:
A relationship is a function if and only if one value of the input does not result in more than one value of the output
In other words, for a function f(x), for a value of x there should only be one value for y
Looking at the figure, we see that in option 4 for the value 2 there are two resultant mappings, A and B
Hence the relation in option 4 is NOT a function
how to calculate interest if ra te and amount are only given?.
If only rate and amount are given, interest can be calculated by multiplying the amount and the rate.
How to find interest ?Interest can be found by the formula :
= Interest rate x Amount
This means that finding the interest simply requires multiplying the given interest rate by the amount in question.
For instance:
If you have $100 as the principal, an interest rate of 5% (or 0.05 as a decimal), and a time period of 1 year, the interest would be calculated as follows:
= 100 x 5 %
= $ 5
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WILL GIVE BRAINELIST
Answer:
Step-by-step explanation:
Distribute.
8x + 32
pt2. is A.
Si la hipotenusa de un triángulo rectángulo mide 2 cm y uno de sus lados mide 1 cm ¿ cuánto mide el otro lado ?
Answer:
Step-by-step explanation:
a^2+b^2=c^2
c^2-b^2=a^2
2^2-1^2=c^2
c^2=3
c=[tex]\sqrt{3}[/tex]
espero que esto te ayude, pero no se si esta correcto lo siento
Andrea has half as many model cars as ridhi. Eleni has three fewer model cars that Andrei. write an expression for E.the number of model cars Eleni has, in terms of R, the number of model cars ridhi has.
The number of model of cars Eleni has in terms of R is E = R / 2 - 3.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let us suppose the model of cars with Ridhi = R.
Andrea thus has:
A = R / 2
Eleni has three fewer model cars that Andrei. Thus,
E = R / 2 - 3
Hence, the number of model of cars Eleni has in terms of R is E = R / 2 - 3.
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The following ordered pairs are solutions to an exponential equation: (0,1), (1,3), (2,9), (3,27). Write the equation
The equation y = 3^x represents the relationship between two variables, x and y, where y is equal to 3 raised to the power of x. The value of y is determined by the value of x.
The equation that represents these ordered pairs is likely to be of the form y = a * b^x, where a and b are constants. To determine the values of a and b, we can use the given ordered pairs:
(0,1): 1 = a * b^0 => a = 1
(1,3): 3 = a * b^1 => b = 3
So, the equation is y = 1 * 3^x.
This can also be written as y = 3^x.
For example, when x = 0, y = 3^0 = 1. When x = 1, y = 3^1 = 3. When x = 2, y = 3^2 = 9. And so on. The ordered pairs (0,1), (1,3), (2,9), (3,27) are solutions to this exponential equation because they satisfy the equation. For each ordered pair, the x value is plugged into the equation, and the corresponding y value is obtained. The obtained y values match the y values in the ordered pairs, which means that the equation is a correct representation of the relationship between x and y.
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5+3y=(2+y)
Show work and steps
Answer: y= -3/2
Step 1: Move the terms
Step 2: Collect like terms and Calculate
Step 3: Divide both sides
The steps with the problem is on the png below.
Jane was shopping at the Shoe Palace. She buys 5 pairs of shoes. Including tax, 27. 75, she spends a total of 227. 75. How much did each shoe cost?
Each shoe costs 20 dollars.
Let us assume that the cost of each pair of shoe is m dollars.
Jane buys five pairs of shoes.
so, the cost of five pairs of shoes would be 5 × m = 5m dollars
Let us assume that S represents the total amount of money she spend on the shoes and C be the total cost
C = S + tax
227.75 = S + 27.75
S = 227.75 - 27.75
S = 200 dollars
The cost of 5 pairs of shoes (without tax) = $200
Using unitary method the cost of each pair of shoes would be,
m = 200/5
m = 40 dollars
This means that the cost of a pair of shoes is 40 dollars
Thus, the cost of each shoe = 40/2
= 20 dollars
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Write 3 situations where you would use the number -5
We can use the number -5 as:
1. Temperature: If a temperature is measured below 0 degrees Celsius (the freezing point of water), it can be expressed as a negative number. For example, if the temperature is -5 degrees Celsius, it means that it is 5 degrees below the freezing point.
The temperature of 82 degrees above zero is a positive number, and we write it as 82, whereas the temperature of 5 degrees below zero is a negative number, and we write it as -5.
2. Money: In transactions of money, a negative number can be used to represent a debt, or an amount owed. For example, if someone's account balance is -$5, it means they owe $5.
3. Coordinate System: In coordinate system, a point can be located using two numbers, representing its x and y coordinates. If the point has an x coordinate of -5, it means that it is 5 units to the left of the origin (0,0).
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In a survey of men in a certain country (ages 20 - 29), the mean height was 64.7 inches with a standard deviation of 2.9 inches. (a) What height represents the 90th percentile? (b) What height represents the first quartile?
Answer:
Step-by-step explanation:
(a) To find the height that represents the 90th percentile, we would need to use a standard normal distribution table and a Z-score. We need to first find the Z-score corresponding to the 90th percentile by solving for Z using the formula:
Z = (x - μ) / σ
Where x is the height at the 90th percentile, μ is the mean height (64.7 inches), and σ is the standard deviation (2.9 inches).
Z = (x - 64.7) / 2.9
Since the 90th percentile corresponds to a Z-score of 1.28, we can use the above formula to find x:
x = μ + Zσ
x = 64.7 + (1.28)(2.9)
x = 68.9 inches
So, the height that represents the 90th percentile is 68.9 inches.
(b) To find the first quartile (25th percentile), we would use a Z-score of -0.67.
x = μ + Zσ
x = 64.7 + (-0.67)(2.9)
x = 62.3 inches
So, the height that represents the first quartile is 62.3 inches.
jeff is 3 years older than four times the age of adam. if the sum of their ages is 63, what is the age of adam.
By making and solving the respective equation x + 4x + 3 = 63, we can conclude that the age of Adam is 12 years.
What are equations?According to a mathematical equation, two amounts or values are equivalent to a meaningful term, for example, 6 x 4 = 12 x 2.
When two or more factors must be taken into account together in order to comprehend or describe the entire situation, an equation is used.
So, we know that:
Jeff is 3 years older than four times of Adam.
Now, let Adam be x and Jeff be 4x + 3.
Then, the equation will be:
x + 4x + 3 = 63
5x + 3 = 63
5x = 63 - 3
5x = 60
x = 60/5
x = 12
Adam: = x = 12 years
Therefore, by making and solving the respective equation x + 4x + 3 = 63, we can conclude that the age of Adam is 12 years.
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