False. The converse of the given conditional statement is "If a polygon has exactly three sides, then it is a triangle."
What are conditional statements?Logic statements that contain both the hypothesis and the conclusion are known as conditional statements. A statement is considered to be true when it is used as the hypothesis, but a statement is considered to be true when it is used as the conclusion. In a conditional statement, the conclusion can only be true if the hypothesis is accurate. For instance, "If it is raining, then the ground is wet" is a conditional statement, with "it is raining" serving as the hypothesis and "the ground is wet" as the conclusion. If the hypothesis is correct, the conclusion must likewise be correct. If the hypothesis is incorrect, the conclusion might be right or false.
How to solve?
The converse of the given conditional is false.
In general, the converse of a conditional statement is not always true.
In the given example, a polygon can have exactly three sides and still not be a triangle (e.g. an equilateral triangle).
Therefore, the converse of the given conditional is false.
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The length (L) of a rectangle of fixed area varies inversely as the width (W). If the
length of the rectangle is 6 feet when the width is 12 feet, find the length of the
rectangle when the width is 4 feet.
Answer:
Length of the rectangle is 18 ft when its width is 4ft
Step-by-step explanation:
Let us assume that the length is represented by l.
Let us assume that the width is represented by w.
As given
The length of the rectangle varies inversely with its width.
Thus
L x 1/w
l=k/w
Where k is the constant of proportionality .
As given
If the
length of the rectangle is 6 feet when the width is 12 feet,
l=6, w=12
putting the values in l = k/w
6 = k/12
k = 12 x 6
k=72
As given
width is 4ft
k= 72, w = 4
Putting the values in, L = k/w
L= 72/4
L=18 ft
Therefore the length of the rectangle is 18 ft when its width is 4ft
Hope this helps You
Pls plss help me on this !!
Answer:
C) is 20
Step-by-step explanation:
3 inches x 5= 15
so we do the same with 4 minutes
4 minutes x 5= 20
Write the expression that completes the equation to represent the
result of transforming y = |x| with the steps listed below.
1: Shift the function 5 units to the left.
2: Shift the function 4 units down.
y = | x + 5 | - 4
You subtract 4 outside the abs val to move the graph down.
You add 5 inside the abs val to move the graph left. (Inside translations are the opposite of what you'd expect.)
11-14 are confusing can anyone help and tell me how to get the written answer
Answer:
11) KF = DB
12) DC=YZ
13) <C = <W
14) <S and <K
Step-by-step explanation:
11) For this question, we want to try and use SSS to prove the triangles are congruent. SSS stands for side-side-side postulate, so all sides have to be equivalent. We already have ED = FB as given, and DF = DF due to reflexive property. From this information, we already have two sides. Additional information that would be needed to figure out the third side is KF = DB, as it's the only side we are missing.
12) For this question, we want to use SAS postulate, which stands for side-angle-side. We already have one side congruent, which is BC=YX. We have one angle congruent which is <C = <Y. With this information, we have one side and one angle. This means that we need to find another side that is congruent. The side that we need to find here is DC=YZ, as it will help us prove the triangles are congruent with SAS.
13) For this question, we want to use AAS, which stands for angle-angle-side. We already have one angle congruent, which is <CDE = WDE. We have one side congruent as well, which is DE = DE due to reflexive property. With this given information, we have one angle and one side. We only need one more angle before the other angle to figure this out. The angles that are needed are <C = <W.
14) For this question, we want to use ASA, which stands for angle-side-angle. The one angle we have already is <KTM = <UTS, which is because of vertical angles are congruent. The one side that we have is ST=TK. With this, we have one angle and one side. We just need one more angle to prove this, which would be <S and <K.
Remember, for triangle congruency postulates, they have to be in order. They cannot just be out of order. For example, in question 14, we have to find the measures in order. First we need an angle, side, and then another angle. The first angle is <S and <K, then the side we have is ST=TK, and then our last angle, <KTM = <UTS.
Concrete tiles are made using buckets of cement,sand and gravel mixed in the ratio 1:4:6
i. How many buckets of gravel are needed for 8 buckets of cement?
ii. If 10 buckets of sand are used, how many buckets of gravel will be needed?
Answer:
48 buckets of gravel
15 buckets of gravel
Step-by-step explanation:
A group of 10 students took tests in math, English, and chemistry.
The scatter plots compare the students’ scores on the tests
Complete the sentences to describe the data.
The math and English scores show
a positive correlation
a negative correlation
no correlation
The math and chemistry scores show
a positive correlation
a negative correlation
no correlation
The correlation of the scatterplots are defined as;
The math and English scores show; A positive correlation.
The math and chemistry scores show; A negative correlation
What is the correlation of the scatterplot?In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.
A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.
A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
No correlation means there is no relationship between the two variables.
Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.
Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.
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Ninth grade math and I need help.
Answer:
Step-by-step explanation: By using the verticle line test, because the line has passed more than one point, it is NOT A FUNCTION.
PLEASE HELP The definition states that a glide reflection is the composition of a translation and a reflection. Explain why these can occur in either order. (1 pt)
In particular, despite the language overlap, a glide reflection is not a reflection and a (ordinary) reflection is not a glide reflection.
There are many intriguing accounts of what occurs when you mix two of them together. Here are a few instances:
Each isometry may be classified as belonging to one of the five classes listed below.
a consideration,an interpretationthe rotationa reflection of a glide,The map of identity.The identity is the combination of two reflections along the same line.
Translation is the combination of two reflections in dissimilar but related directions. Rotation is the result of two reflections in non-parallel lines.
A gliding reflection is made up of a reflection over a line plus a translation along a non-perpendicular line (and not a reflection).
A reflection is made up of a translation along a perpendicular line and a reflection across a line (and not a glide reflection).
There are fascinating things to say about what occurs when you combine two isometries dependent on the types of the isometries that you combine, but it does not change the fact that the five types are all distinct from one another. I could go on, but I think you get the point now.
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If an antelope eats 7kg of vegetation in 2 days how many killograms of vegetation does it eat per day
Antelope eats 3.5kg of vegetation per day .
What are fractions?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given :
antelope eats 7kg of vegetation in 2 days
Thus , vegetation eated per day = 7 / 2 = 3.5 kg
Hence , antelope eats 3.5kg of vegetation per day .
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A standard television screen has a 4:3 aspect ratio between the width and the height of the viewable screen. What would be the height of Television that is 16 inches wide?
The standard height of the television is 12 inches.
What are ratios?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other.
The given ratio is 4:3. Let us take a variable 'x' such that 4x=16 and 3x=height.
We find x from 4x=16
x=4
Now putting the value of x in 3x, we get 12 inches.
Therefore, the height of the television is 12 inches.
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The standard height of the television is 12 inches.
The aspect ratio of a screen is the ratio of the width to the height. In the case of a television screen with a 4:3 aspect ratio, the width is 4 units and the height is 3 units.
If we let "h" represent the height of the television screen, we can set up the following equation:
4:3 = 16:h
To solve for "h", we can cross-multiply to get:
4h = 48
Dividing both sides by 4, we get:
h = 12
So the height of a television screen that is 16 inches wide and has a 4:3 aspect ratio is 12 inches.
what is aspect ratio?
The aspect ratio of a screen is the ratio of the width to the height of the viewable area of the screen. It is usually expressed as two numbers separated by a colon, such as 16:9 or 4:3.
Aspect ratios are used in a variety of applications, including television screens, computer monitors, and movie theaters. Different aspect ratios are used for different types of content, and some screens can be adjusted to display content in different aspect ratios.
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Find the area of $\triangle ABC$ with vertices $A\left(2,\ -2\right)$ , $B\left(4,\ -2\right)$ , and $C\left(6,\ -11\right)$ .
The area of $\triangle ABC$ is
square units.
The area of the triangle from the vertices is 27 square units
How to determine the area of the triangle?From the question, we have the following parameters that can be used in our computation:
$A\left(2,\ -2\right)$ , $B\left(4,\ -2\right)$ , and $C\left(6,\ -11\right)$ .
Represent the vertices properly
So, we have
A = (2, -2)
B = (4, -2)
C = (6, -11)
The area of the triangle is calculated using
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
Substitute the known values in the above equation, so, we have the following representation
Area = 0.5 * |2 * (-2 + 11) + 4 * (-2 + 11) + 6 * (-2 + 2)|
Evaluate the sum of products
Area = 0.5 * |54|
Remove the absolute bracket
Area = 0.5 * 54
Evaluate
Area = 27
Hence, the area of ABC with vertices is 27 square units
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Waterworks is a company that manufactures and sells paddleboards. Its profit P, in hundreds of dollars earned, is a function of the number of paddleboards sold x, measured in thousands. Profit is modeled by the function [tex]p(x)=-3x^{3}+45x^{2} -132x[/tex]. What do the zeros of the function tell you about the number of paddleboards that Waterworks should produce?
In order to make a profit, Waterworks must produce more than ___ and fewer than ____ paddleboards.
Waterworks must produce more than 4 and fewer than 11 paddleboards.
What do you mean by polynomial?
A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and trinomial.
It is given that Waterworks is a company that manufactures and sells paddleboards. Its profit P, in hundreds of dollars earned, is a function of the number of paddleboards sold x, measured in thousands. Profit is modeled by the function
[tex]p(x) = -3x^{3}+45x^{2} -132x[/tex]
zeroes of the p(x) will show the quantity at which profit = 0 i.e. breakeven
Let p(x) = 0
[tex]-3x^{3} +45x^{2} -132x =0[/tex]
-3x ([tex]x^{2} -15x+44[/tex]) = 0
-3x ([tex]x^{2} -11x-4x+44[/tex] ) = 0
-3x (x(x-11) - 4(x-11)) = 0
-3x (x-11) (x-4) = 0
-3x = 0 or x-11 = 0 or x-4=0
x = 0,11,4
So,profit is obtained when 4<x<11.
Therefore, Waterworks must produce more than 4 and fewer than 11 paddleboards.
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THE DIFFERENCE OF TWO NUMBERS IS 10 IF THE GREATER NUMBER IS 32, FIND THE SMALLER ONE. (STEP BY STEP)
Answer:
22
Step-by-step explanation:
we can set this up and make the unknown number X
32-x=10
Subtract 32 from both sides
32-x=10
-32. -32
-x= -22
Divide both sides by -1
-x=-22
/-1. /-1
x=22
Hopes this helps
The area of a triangle is 474. Two of the side lengths are 87 and 19 and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.
Answer:
Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.
The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:
$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$
$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$
Substituting this expression for $h$ into the formula for the area of the triangle, we get
$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$
Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.
Step-by-step explanation:
Write whether each is an example of commutative, associative, or distributive properties.
15. commulative
16. distributive, distributing the 3 to the 'a' and 'b' within the parentheses.
17. distributive, distributing the w to the variables inside of the parentheses.
a graphic is printed on a circular banner that has a diameter of 4 feet. the same graphic undergoes a dilation with a scale factor of 1/6 to be printed on circular stickers. the diameter of the dilated graphic is _[blank]_ inches.
The required diameter of the dilated graphic is 8 inches.
Explain scale factor.
Scale factor is the ratio of comparing sides on two comparative figures. In math, scale factor is utilized to decide how often bigger or more modest one item or figure is to another.
According to question:We have,
diameter of circular banner = 4 feet
scale factor = 1/6
Then, the diameter of circular sticker = 4(1/6) = 4/6 feet.
In inches, we know
1 foot = 12 inches
4/6 feet = 12(4/6) = 8 inches
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Simplify 2/3(6x-1/9)-x+3/6
Answer:
Step-by-step explanation:
3x+23/54
what is the equation in slope intersept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2
The line that goes through the point (2,-2) and is perpendicular to the line shown by y=2/5x +2 will have the slope intercept equation 5x+3y=6.
What is equation of line?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
Slope of the line given=2/5
Slope of the line perpendicular=-5/2
coordinates=(2,-2)
y=mx+b
-2=-5/2*2+b
b=3
y=-5/2x+3
3y=-5x+6
5x+3y=6
The equation in slope intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2 will be 5x+3y=6.
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A taxi ride costs $4, plus an additional $3 per mile. Graph the line relating taxi ride costs to distance (in miles).
The required equation of line in slope intercept form is
y = 3x + 4
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Let the taxi is driven x miles and the total cost is $y
A taxi ride costs $4, plus an additional $3 per mile
Total cost = 4 + 3x
By the problem,
y = 4 + 3x
This is the required equation of line which represents the above situation.
The graph has been attached here.
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--7x-7y= 28
2x - 7y = 1
please solve this systems of eqautions
After solving the equation the linear equation is x = 27/5 , y = 7/5.
What do you mean by linear equation?
Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.
A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".
Given system of equation:
7x - 7y = 28 ..........(1)
2x - 7y = 1 .............(2)
Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)
7x - 7y = 28
7x - 28 =7y .............(3)
Substitute this value in equation (2)
2x - (7x - 28) = 1
2x - 7x + 28 = 1
-5x + 28 = 1
5x = 28 - 1
5x = 27
x = 27/5
Substitute this value in equation (3)
7y = 7(27/5) - 28
7y = 189/5 - 28
7y = 49/5
y = 7/5
Therefore, x = 27/5 , y = 7/5
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s 1}} 10of 0.9. E Juliet is incorrect because 90 is 1}} 10of 9.
For the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that the expression is,10of 0.9, and its simplification is obtained as 90.
We have to find out why Juliet is incorrect.
Juliet is incorrect because when any decimal value is multiplied by 10 the obtained value is increased by its one's place,
=10 × 0.9
=9
Thus, for the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.
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10mm
5mm
13mm
Trapezium
The area of the trapezium will be = 90[tex]mm^{2}[/tex]
According to the figure of the trapezium =
Let us consider the length of base a = 5mm
length of base b = 13mm
height h of the trapezium = 10mm
According to the formula of the area of trapezium
= (1/2) x h x (a + b)
= (1/2) x 10 x (13 + 5)
= 5 x 18
= 90[tex]mm^{2}[/tex]
Therefore, the area of the trapezium will be = 90[tex]mm^{2}[/tex]
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The complete question here could be- Find the area of the trapezium given base a= 5mm, base b= 13mm and height h= 10mm
If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
The point of intersection of f(x) and [tex]f^{-1}[/tex](x) is (3, 3)
What is a function?"It defines a relation between input and output values."
"In function, for each input there is exactly one output."
What is inverse function?"The inverse function of x = f(m) is m =[tex]f^{-1}[/tex] , where x, m are real values"
For given question,
A function f(x) and its inverse function [tex]f^{-1}(x)[/tex], are both plotted on the same coordinate plane.
We know that the inverse function [tex]f^{-1}(x)[/tex] is the mirror image of the function f(x.)
This means, both the functions must be symmetric about the line y = x.
The curve of inverse function [tex]f^{-1} (x)[/tex] would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)
And both the functions intersect each other only on y = x
The point which satisfy the line y = x is (3, 3)
Therefore, the point of intersection of f(x) and[tex]f^{-1} (x)[/tex] is (3, 3)
The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
A.(0, –2)
B.(1, –1)
C.(2, 0)
D.(3, 3)
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(b) if the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
By probability ,181753 are ways are there to distribute the coupons so that at least one woman receives a coupon.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:
= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men
= ( 20 10 ) - ( 15 10 ) = 184756 - 3003
= 181753
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The complete question is -
10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.
(a) If the coupons are identical, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
By probability ,181753 are ways are there to distribute the coupons so that at least one woman receives a coupon.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:
= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men
= ( 20 10 ) - ( 15 10 ) = 184756 - 3003
= 181753
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Hello please perform indicated operation with steps please
Answer:
x^3-2x^2+6x+1
Step-by-step explanation:
x^3+2x-1-2x^2-4x+2
collect like terms
x^3-2x^2+2x+4x-1+2
x^3-2x^2+6x+1
An step by step explanation of all of them would be great .
Btw I did 1 to 5 and they all worked
Solution of x is 1± 5√2 for the given quadratic equation.
What is quadratic equation?
Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.
Main body;
11)
x² = 2x +48
The given is an quadratic equation:
solution of this can be found out using quadratic formula:
x =(-b ±[tex]\sqrt{b^{2} -4ac}[/tex])/2a
for this ,
x² -2x -48 = 0
a = 1
b= -2
c = -48
x =( 2±√ (4- 4*1*-48))/2
x = (2±√200)/2
x = 1± 5√2
Hence solution of x is 1± 5√2.
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Currently my bank balance is R2 000. What will the new balance be if I withdraw R600 from the account in each of the next 3 months?
Answer:
R200
Step-by-step explanation:
R200
solve for x. Express your answer as a proper or improper fraction in simplest terms,
-1/2= 4/9x+5/6
x=
Answer: x=-3
Step-by-step explanation:
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
A bag contains three blue marbles, five red marbles, and four green marbles.
Part A: What is the probability of selecting three marbles where one is blue and two are green?
Part B: What is the probability of selecting one blue marble and then selecting three red marbles?
Part C: In your own words, write a short paragraph that explains your work for Parts A and B.
a) The probability of selecting three marbles where one is blue and two are green is of: 0.0818 = 8.18%.
b) The probability of selecting one blue marble and then selecting three red marbles is of: 0.0152 = 1.52%.
c) The probabilities were obtained dividing the number of desired outcomes by the number of total outcomes, and all the possible combinations were considered.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
The outcomes with one blue and two green are given as follows:
Blue (3/12 probability) then two green, with 4/11 and 3/10 probabilities.Green then blue then green.Green, green then blue.Hence a multiplication for 3 is used for the probability, as follows:
p = 3 x 3/12 x 4/11 x 3/10 = 0.0818 = 8.18%.
For blue then three red, the outcomes are given as follows:
Blue (3/12 probability).Red: 5/11.Red: 4/10.Red: 3/9.Thus the probability is of:
p = 3/12 x 5/11 x 4/10 x 3/9 = 0.0152 = 1.52%.
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What are the domain and range of this graph? f(x)=x^5+x^2
Therefore ,the domain and range of this graph f(x)=x^5+x^2
Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
what is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The domain is all values of x that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
The Range is all values of y that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
Therefore ,the domain and range of this graph f(x)=x^5+x^2 Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
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