The set of independent variables of a function called the domain of the function.
Domain is the set of values for which the given function is defined.
The set of all possible values of the dependent variable called the range.
The range of a function refers to all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.
The set of all possible values for the function called the the domain of the function.
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State what additional information is required in order that the triangles are congruent for the reason given.
The additional information is required in order that the triangles are congruent for the SSS congruent theorem is IW = IH
How to determine the additional information?From the question, we have the following parameters that can be used in our computation:
Triangles = IWO, and IHO
Given theorem = SSS
The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent
From the question, we can see that the following corresponding sides on the triangles have the same mark
W O and H O
A O and A O
This implies that these sides are congruent sides
For the triangle to be congruent by SSS, the following sides must also be congruent
IW must be congruent to IH
Hence, the additional information on the congruency of the triangles is IW = IH
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vwe are standing on the top of a 368 feet tall building and launch a small object upward. the object's vertical position, measured in feet, after t seconds is h ( t )
For the given quadratic function, the highest point that the object reaches is (5, 768).
Since we are given with the quadratic function of h(t)=−16t2+160t+368, where Let a = -16, b = 160, and c = 368, so the vertex for the equation will be :t = -b/2a = -(160)/2(-16) = -160/(-32) = 5, so substituting this value in the equation for the value of t is
h(5) = -16(5)2 + 160(5) + 368 = -400 + 800 + 368 = 768
Here the highest point that the object reaches is (5, 768), which means that at a time of 5 seconds, the object reaches the building after being launched at the height of 768 feet
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We are standing on the top of a 368 feet tall building and launching a small object upward. The object's vertical position, measured in feet, after t seconds is
We are standing on the top of a 1200 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is What is the highest point that the object reaches?
Find the point in the first quadrant where the line y = 4 x intersects a circle of radius 5 centered at the origin.
The graph of the point of intersection is given below.
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2πr.
The equation of a circle is x² + y² = r²
We have,
The equation of a circle
x² + y² = r²
r = 5
x² + y² = 25 ______(1)
The line.
y = 4x _____(2)
Now,
The line intersects the circle.
The point of intersection.
x² + (4x)² = 25
x² + 16x² = 25
17x² = 25
x = √(25/17)
x = ± 5/√17
x = 5/√17 and x = -5/√17
Now,
At x = 5/√17,
y = 4 x 5/√17
y = 20/√17
At x = -5/√17,
y = 4 x 5/√17
y = 20/√17
Thus,
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
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PLEASE HELP ASAP
Let m, n, p, and q represent distinct positive numbers. If the equation below is true, which variable represents the greatest number?
1/2m = 1/3n = 1/4p = 1/5q
A. m
B. n
C. p
D. q
E. This cannot be determined with the given information.
The equation illustrates that the variable that represents the greatest number is E. This cannot be determined with the given information.
Which variable represents the greatest number?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
From the information, the variable is given as 1/2m = 1/3n = 1/4p = 1/5q.
It should be noted that the greatest variable cannot be determined based on the information. In conclusion, the correct option is E.
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Given the vector u equal to 7 (cos 330°, sin 330°) and vector v equal to
4 (cos 90°, sin 90°), find the sum u + v and write your answer in magnitude and
direction form with the magnitude rounded to the nearest tenth and the direction
rounded to the nearest degree, 0° ≤0 < 360°.
The magnitude of u + v is 6.08 and the direction of the vector u + v is 4.7°.
What is rounded to the nearest tenth?
To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.
Given that vector u is 7 (cos 330°, sin 330°)
Vector v equal to is 4 (cos 90°, sin 90°)
Calculating the value of cos 330° and sin 330°:
cos 330°
= cos (3×90° + 60°)
= sin 60°
= √3/2
sin 330°
= sin (3×90° + 60°)
= -cos 60°
= -1/2
The vector u can be written as 7 (cos 330°, sin 330°) = 7(√3/2, -1/2) =(7√3/2, -7/2) = 7√3/2 i - 7/2j
The vector v can be written as 4 (cos 90°, sin 90°) = 4(0,1) = (0,4) = 0i + 4j
Add vector u and v:
u + v
= 7√3/2 i - 7/2j + 0i + 4j
= 7√3/2 i + 1/2 j
= 6.06 i + 0.5 j
The magnitude of the vector u+v is √( 6.06² + .5²) = 6.08
The angle is
tan θ = y/x
tan θ =0.5/6.06
θ = 4.7°
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Question 10(Multiple Choice Worth 5 points)
(Proportional Relationships LC)
Does the graph represent a proportional relationship?
graph with a line from 0 comma 0 and going through 25 comma 8
No, it is not proportional because the line does not go through (0, 0).
No, it is not proportional because the graph is curved.
Yes, it is proportional because it is a line that goes through (0, 0).
Yes, it is proportional because the x-axis and y-axis are numbered correctly.
Since the graph has a line from 0 comma 0 and going through 25 comma 8, C. Yes, it is proportional because it is a line that goes through (0, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it starts from the origin (0, 0) and as such, it is proportional.
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Evaluate 2xx ÷ 3yy for x = 1 2 and y = 3 5 -show the steps
The value of 2xx ÷ 3yy is 288/1225
What is simplification?In mathematics, simply or simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.
Given that, an expression 2xx ÷ 3yy, where x = 12 and y = 35
2x12x12/3x35x35 = 288/1225
Hence, The value of 2xx ÷ 3yy is 288/1225
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Assume that the game playthrough times for a newly released puzzle game has a mean of 49.8 minutes and a standard deviation of 4.2 minutes. A sample of size n39 playthrough times is randomly selected from a gaming population. What is the probability that the sample.mean is in between 50 minutes and 51 minutes? You may use a calculator or the portion of the z-table given below. Round your answers to three decimal places where appropriate
The probability that the sample mean is in between 50 minutes and 51 minutes is 0.345.
How to calculate probability?
n = sample size = 39
σ = standard deviation =4.2
μ = population mean = 49.8
Probability is the chance that an event can occur, in this case probability is used to measure the chance sample mean is between 50 minutes and 51 minutes. So,
P(50 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])
= P([tex]\frac{50-49.8}{\frac{4.2}{\sqrt{39}}}[/tex] ≤ z ≤ [tex]\frac{51-49.8}{\frac{4.2}{\sqrt{39}}}[/tex])
= P(0.30 ≤ z ≤ 1.78)
= P(z ≤ 1.78) - P(z ≤ 0.3)
using z table and we get,
= 0.9625 - 0.6179
= 0.3446
= 0.345
Thus, the probability is 0.345 for the sample mean is within 50 and 51.
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Jina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $91
and allows unlimited mileage.
Company B has an initial fee of $55
and charges an additional $0.80
for every mile driven. For what mileages will Company A charge less than Company B?
Use m
for the number of miles driven, and solve your inequality for m
Hence for miles greater than 45, the Company A will charge less than Company B.
Given:
Jina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $91 and allows unlimited mileage.Company B has an initial fee of $55 and charges an additional $0.80 for every mile driven.we are asked to find for what mileages will Company A charge less than Company B = ?
from the question we frame the inequality as:
⇒ 91< 55+0.80m
⇒ 36<0.80m
⇒ 45<m
or
m>45
Check answer
55+45(0.8)=91 check
Hence for miles greater than 45, the Company A will charge less than Company B.
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Jeff Ryan bought 200 shares of BUI for $19.50. Eight weeks later he sold the stock for $20.75. Assuming a 3% commission, his bottom line was a gain of:
Multiple Choice
$250.00
$374.50
$8.50
$257.50
His bottom line was a gain from selling and 3% commission is $257.50.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The cost price of 200 shares of BUI is (19.50×200) = $3900.
The selling price of 200 shares of BUI is (20.75×200) = $4150.
The net gain is (4150 - 3900) = $250 and with 3% commission it is,
= (103/100)×250.
= $257.50.
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sume of angles of a triangel greater than 180 degrees when teh triange is so large that it extends to cosmological scales
In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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which equation represents the line that passes through the points (- 3, 7) and (9, - 1) ^ prime; which equation represents a line that is parallel to the line y=-3x+4; what is the equation of the line passing through the points (2/5 19/20); what is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?; what method can be used to write the equation of a line in slope-intercept form given two points?; what is the equation of the line that passes through the points (15, 9) and (-2, 9)?; which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?; which can be the first step in finding the equation of the line that passes through the points
1. The equation of the line is:
y=-2x/3 + 5
2. The equation of the line in slope intercept form is:
y=3x+5
1. Given:
we have two points:
(-3,7) = (x₁,y₁)
(9,-1) = (x₂,y₂)
equation of the line is:
y - y₁ = m(x-x₁)
₁first calculate slope m = y₂-y₁/x₂-x₁
m = -1-7/9-(-3)
m = -8/12
m = -2/3
now, y - 7 = -2/3 (x-(-3)
y-7=-2/3(x+3)
y-7=-2x/3-2
y=-2x/3-2+7
y=-2x/3 + 5
hence equation of the line is y=-2x/3 + 5
2. Given two points:
(2, 11) and (4, 17)
(2, 11) = (x₁,y₁)
and (4, 17) = (x₂,y₂)
slope intercept form:
y=mx+c
we need to calculate the m value:
m = 17-11/4-2
m = 6/2
m=3
now substitute in the given form:
y - 11 = 3(x-2)
y-11=3x-6
y=3x-6+11
y=3x+5
Hence we get the required answer.
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Exercise 1
Directions: Describe the end behaviors of the following functions:
1. f(x) = x5 – 19x3 + 48x
2. f(x) = - x4 - 49x2 - 5
3. f(x) = x2 - 10x + 16
4. f(x) = - x (x + 9) (x - 1)
5. f(x) = 4x2 - 2x + 1
On solving the derivatives we got - 6x5-15 , 4x² - 98x , x-5)²-9, -3x²-16x+9 , -2
What is derivative?Differentiation is the rate at which a function changes with regard to a variable in mathematics (in mathematics, the rate of change of a function with respect to a variable). The usage of derivatives is necessary while solving calculus and differential equation problems.
1. f(x) = 6x5-15 DERIVATIVE
2.f(x) = 4x² - 98x DERIVATIVE
3. f(x) = (x-5)²-9
4.f(x)= -3x²-16x+9 DERIVATIVE
5.f(x)=-2 DERIVATIVE
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what is 2 1/6 + 4 3/6 as a fraction
Answer:
6 2/3
Step-by-step explanation:
2 1/6 + 4 3/6
6 4/6
6 2/3
Which of the following is a solution of the equation 2x 3y 3 *?
If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
The formula is 2x + 3y = 3. There are an infinite number of solutions to this equation.
We must first enter any random value for any variable, followed by the matching value for the other variable, in order to find any solution to this equation.
Now, if we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, one of the solutions to this equation is (0,1).
Hence, If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.
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Complete question-
Find the one of the solution of 2x + 3y = 3?
Which of the following are true?
I.
√36 > 5
7 <10
√√17-8>√√17 +8
II.
III.
Answer:
Only I
Step-by-step explanation:
I. √36 > 5
√36 = 6
6 > 5
Its true
II. 7 < √10
√10 = 3.16 approximately
Hence, 7 > √10
But 7 < √10 is wrong
III. √(17 - 8) > √(17 + 8)
√(17 - 8) = √9 = 3
√(17 + 8) = √25 = 5
√(17 - 8) < √(17 + 8)
But, √(17 - 8) > √(17 + 8) is wrong
Answer:
1.) √36 > 5
Step-by-step explanation:
1.) √36 > 5
= 6 > 5( it is true because 6 is greater than 5)
2.) 7 < √10
= 7 < 3.16 ( it is false because 7 is greater than 3.16)
3.)√17–√8 > √17 + √8
= 4.12 – 2.82 > 4.12 + 2.82
= 1.3 > 6.94( it is false because 6.94 is greater than 1.3)
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an escalator has a slope of 3/4 after traveling forward 128 feet, the escalator is 96 feet above the floor. Write this word problem in point slope form
The point slope form of the slope of escalator and distance is y-24 = 3/4(x-32).
The general point slope form is given by the equation -
y - y1 = m (x - x1)
Now we are given the slope as 3/4. So, keeping the values of y1 and x1 in the equation. Let us assume the points as (32, 24). As per the points, 32 is x1 and 24 is y1.
y - 24 = 3/4(x - 32)
y - 24 = 3x/4 - 3/4×32
Performing division on Right Hand Side of the equation
y - 24 = 3x/4 - 3×8
y - 24 = 3x/4 - 24
Rewriting the equation
y - 3x/4 = - 24 + 24
Solving the equation on Right Hand Side of the equation
y - 3x/4 = 0
y = 3x/4
Thus, the equation is y - 24 = 3/4(x - 32).
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Which set of ordered pairs does not represent a function? a.{(3, 7), (–1, 9), (–5, 11)} b.{(9, –5), (4, –5), (–1, 7)} c.{(–2, 1), (3, –4), (–2, –6)}
From the given question, relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} does not represent the function.
What is a function?
In mathematics, a connection between one variable (the independent variable, x) and another variable is defined as an expression (the dependent variable, y).For example - f(x) = 4x + 6
The collection of ordered pairs from the question is presented.
It is evident that the relation set exists.
{(9, 1), (6,2), (3, 3), (6,4), (9,5)}
It not accurately depict the function since for x = 6, [y] has two potential values, none of which is possible.
so that's why relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} can not represent a function.
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nora has $640 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $418.55. she buys 2 bicycle reflectors for $19.39 each and a pair of bike gloves for $27.23. she plans to spend some or all of the money she has left to buy new biking outfits for $38.86 each. use the drop-down menu below to write an inequality representing oo, the number of outfits she can buy while staying within her budget.
Layla should by not more than 4 outfits in order not to exceed her budget
The inequality expression is n ≤ 4
price of a new bicycles = $418.55
2 bicycle reflectors = $19.39
a pair of bike gloves = $27.23
new biking outfits = $38.86 each
Nora's total money to spend at a bicycle store = $38.86
How to write the required inequalityLayla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items
We write the expression as;
$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86
where n represents the number of the new biking outfits
$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86
( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) / $38.86≥ n
( $640 - $484.56 ) / $38.86 ≥ n
( $155.44) / $38.86 ≥ n
4 ≥ n
Layla should by not more than 4 outfits in order not to exceed her budget
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Given A(1,4), B(-2,5)and C(3, 4), which coordinate pair will make AB perpendicular to CD ?
The coordinate pair of D that will make AB perpendicular to CD is ( 4,7)
How are lines perpendicular in a coordinate?The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1.
The slope of a line is given as ( y1-y2)/(x1-x2)
for AB and CD to be perpendicular
( y2-y1)/(x2-x1) × ( y4-y3)/(x4-x3) = -1
therefore (5-4)/-2-1 = ( y4-y3)/(x4-x3)
1/-3 ×(y4-4)/(x4-3) = -1
(y4-4)/(x4-3) = 3/1
therefore 3= y4-4 and 1 = x4-3
therefore y4 = 3+4= 7
and x4 = 1+3= 4
therefore the coordinate of D = (x4,y4) for AB perpendicular to CD = (4,7)
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hese are curves obtained by the intersection of right circular cone and a plane.
a. Parabola
b. Ellipse
c. Hyperbola
d. Conic sections
Answer: conic sections
Step-by-step explanation: the other options are a part of conic sections that are named depending on the angle of the plane relative to the cone, and the intersection.
Which functions are decreasing? Select all answers that are correct. Responses The function consists of four sections. Section 1 is a line from begin ordered pair negative 3 comma 4 end ordered pair to begin ordered pair negative 1 comma 4 end ordered pair. Section 2 is a line from begin ordered pair negative 1 comma 4 end ordered pair to begin ordered pair 1 comma 0 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 0 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma negative 2 end ordered pair. Image with alt text: The function consists of four sections. Section 1 is a line from begin ordered pair negative 3 comma 4 end ordered pair to begin ordered pair negative 1 comma 4 end ordered pair. Section 2 is a line from begin ordered pair negative 1 comma 4 end ordered pair to begin ordered pair 1 comma 0 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 0 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma negative 2 end ordered pair. The function goes through begin ordered pair negative 4 comma negative 2.5 end ordered pair, begin ordered pair negative 3 comma negative 5 end ordered pair, begin ordered pair negative 2 comma negative 2 end ordered pair, begin ordered pair 0 comma 5 end ordered pair, begin ordered pair 2 comma negative 2 end ordered pair, begin ordered pair 3 comma negative 5 end ordered pair and begin ordered pair 4 comma negative 2.5 end ordered pair. Image with alt text: The function goes through begin ordered pair negative 4 comma negative 2.5 end ordered pair, begin ordered pair negative 3 comma negative 5 end ordered pair, begin ordered pair negative 2 comma negative 2 end ordered pair, begin ordered pair 0 comma 5 end ordered pair, begin ordered pair 2 comma negative 2 end ordered pair, begin ordered pair 3 comma negativ
The sections of the function that are decreasing, defined by the ordered pairs are;
Section 2; (-1, 4) to (1, 0)
Section 4; (3, 2), to (5, -2)
The part of the second function that is decreasing is; (2, -2) to (3, -5)
What is a function?A function is a definition of the mapping of the set of input variables unto the set of the output variables.
The points in the specified functions are;
Section 1 line ; (-3, 4) to (-1, 4)
Section 2 line ; (-1, 4) to (1, 0)
Section 3 line ; (1, 0) to (3, 2)
Section 4 line ; (3, 2) to (5, -2)
The points through which the function goes through are; (-4, -2.5), (3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, 2.5) and (5, -2)
A function is decreasing when the positive increase in the x-value of the function is accompanied by a decrease in the y-value.
The sections of the functions that are decreasing are;
Section 2 line ; (-1, 4) to (1, 0),
Section 4; (3, 2) to (5, -2)
Parts of the function that is decreasing is; (2, -2), (3, -5)
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What is the Herfindahl-Hirschman Index for a market with two firms, one having 99.5 percent of the market and the other having 0.5 percent?
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
What is 47 = 2(k+3) +3(k-3) ? This is my missing work from being absent so pleas help me.
Answer: K=10
Step-by-step explanation:
To begin, you should multiply out the terms in front of the parentheses. This results in: 47=2k+6+3k-9
Next, we can combine like terms: 47=5k-3
Add 3 to both sides: 50=5k
Divide both sides by 5: 10=k
k=10
Silicone implant augmentation rhinoplasty is used to correct congenital nose
deformities. The success of the procedure depends on various biomechanical
properties of the human nasal periosteum and fascia. The article "Biomechnics in
Augmentation Rhinoplasty" reported that for a sample of 15 (newly deceased)
adults, the mean failure strain (%) was 25.0, and the standard deviation was 3.5.
(p. 277 #35)
a. Assuming a normal distribution for failure strain, estimate true average strain in
a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about
precision and reliability. How does the prediction compare to the estimate
calculated in part (a)?
A true average strain in a way that converys information about precision and reliability (23.0616, 26.9384)
In this question we have been given:
sample size n = 15
the mean failure strain x(bar) = 25.0
the standard deviation s = 3.5
Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.
A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.
c = 0.95 or 95%
In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.
Here, the degree of freedom :
df = n - 1
df = 15 - 1
df = 14
and the column with α =(1-c)/2
=0.025
To find the t-value:
t_(α/2) = 2.145
Therefore, the error margin is:
E = t_(α/2) × s/√n
E = 2.145× 3.5/√15
E ≈1.9384
The confidence interval's outer limits are thus:
x{bar} - E = 25.0 - 1.9384
= 23.0616
x{bar} + E = 25.0 + 1.9384
= 26.9384
Therefore, the confidence interval is: (23.0616, 26.9384)
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Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by SAS.
Answer:
Mark the sides BC and DF as congruent---------------------------------------------------
We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS.
SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.
The missing bit is the other side of the marked angle B and D:
sides BC or DF.You have $16 to buy apples for an apple crisp recipe. Apples cost $2 each. Write and solve an inequality that represents the numbers of apples you can buy.
The inequality to buy an apple can be given as 2x ≤ 16
The number of apples we can buy is 8
What is an inequality?
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
We are given that we have only$16 dollar to buy apples and each costs $2
Let the number of apples we can buy be x
Hence the inequality can be given as
2x ≤ 16
Now dividing both sides by 2 we get,
x ≤ 8
Hence we can buy at most 8 apples
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Bob the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 3 clients who did Plan A and 8 who did Plan B. On Tuesday there were 5 clients who did Plan A and 2 who did Plan B. Bob trained his Monday clients for a total of 15 hours and his Tuesday clients for a total of 8 hours. How long does each of the workout plans last?
The number of hours that plan A last is 1 hour and the number of hours that plan B last is 1 1/2 hours.
How long does each workout last?The first step is to form a system of equations using the information in the question:
3a + 8b = 15 equation 1
5a + 2b = 8 equation 2
Where:
a = length of plan A b = length of plan BThe elimination method would be used to determine the required values
In order to determine the value of a, multiply equation 2 by 4
20a + 8b = 32 equation 3
Subtract equation 1 from equation 3 :
17a = 17
Divide both sides of the equation by 17
a = 17/17
a = 1 hour
Substitute for a in equation 1 :
3(1) + 8b = 15
3 + 8b = 15
8b = 15 - 3
8b = 12
b = 12 / 8
b = 1 4/8 = 1 1/2 hours
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Which one is not a polynomial? (a) 4x² + 2x-1 (b) x²-1
(c) y² + 5y + 1
So option b. x² -1 is the correct option of the given statement Because option b satisfy the requirement of not a polynomial.
In mathematics, what does a polynomial mean?An expression for a polynomial can be generated using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables (also known as indeterminates) and coefficients make up a polynomial.
What makes a polynomial unique?It is possible to identify the polynomials by seeing which formulae only include the operations addition, subtraction, multiplication, and non-negative integer exponents. Expressions that include extra operations are regarded as non-polynomial expressions. Specify the grounds for the expressions' non-polynomial status.
Which regulations apply to polynomials?Any function in an equation that uses only positive integer exponents or non-negative integer powers of a variable is known as a polynomial function. These equations include, for instance, the cubic equation, the quadratic equation, and others. A polynomial with an exponent of 1 is, for instance, 2x+5.
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Casual sneaker sales represent 4.5% and athletic shoe sales represent 3.2%
of total store sales. If the total store sales are $900,000, what are the dollar
sales for each department?
Answer: Casual sneaker sales = $40,500 & Athletic shoe sales = $28,800
Step-by-step explanation:
If the total store sales are $900,000 and you already have the percentages of the casual sneaker sales and athletic shoe sales, then you move the decimal point in each percentage two digits to the left, or simply multiply the percentage by .01, then take that number and multiply it by the total, $900,000
Ex:
4.5%(0.01) = .045
3.2%(0.01) = .032
.045(900,000) = 40,500
.032(900,000) = 28,800
