The statement that best describes the relationship between the two triangles is the option;
The triangles are not similar; all the corresponding sides are not proportionalWhat are the conditions for the similarity of two triangles?Two triangles are similar if they satisfy the following conditions.
Two angles of one triangle are congruent to two angles in the other triangle (AA, Angle-Angle similarity postulate)Two sides of one triangle are proportional to two sides of the other triangle and the included angle of the two sides in each triangle are congruent (SAS, Side-Angle-Side similarity postulate)The three sides of one triangle are proportional to the three sides of the other triangle (SSS, Side-Side-Side, similarity postulate)The length of the sides of the triangles are;
First triangle, a₁ = 3, b₁ = 5. c₁ = 15
Second triangle. a₂ = 9, b₂ = 6, c₂ = 18
The ratio of the corresponding sides is therefore;
[tex]\dfrac{a_1}{a_2} = \dfrac{3}{9} =\dfrac{1}{3}[/tex]
[tex]\dfrac{b_1}{b_2} = \dfrac{5}{6}[/tex]
[tex]\dfrac{c_1}{c_2} = \dfrac{15}{18} =\dfrac{5}{6}[/tex]
The ratio of the three corresponding sides of the triangles are not the same such that the corresponding sides of the triangles are not constantly proportional.
Therefore the two triangles are not similar because all the corresponding sides are not proportional.
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Whats the answer to this?
The required image of points (-4, 6) is (-6, -4) as per the given condition,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
As the image of the point (5, -1) is mapped as, (1, 5),
Which implies a function that (x, y) mapped as (-y , x)
So for (-4, 6) mapped as (-6, -4)
Thus, the required image of points (-4, 6) is (-6, -4) as per the given condition,
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a regular deck of playing cards is shuffled what would probability of not drawing an ace
Answer:44/52
Step-by-step explanation:There are four aces in a deck of 52 cards, so the probability of not drawing an ace is 44/52 =
Juan has a sandbox and wants to double the length, width and height. If the original box holds 1 cubic foot of sand, how many more feet of sand must be added to fill up the new box.
Juan must add a volume of 7 cubic feet for the enlarged sandbox.
How much sand must we add to an enlarged sandbox?
The volume occupied by the sandbox (V), in cubic feet, is represented by the volume formula for a parallelpiped:
V = w · l · h
Where:
w - Width, in feetl - Length, in feeth - Height, in feetJuan wants to know the additional amount of sand required for the enlarged sandbox. If we know that the initial volume is equal to a cubic foot and each length is double, then we find that the resulting volume for sandbox is:
V' = (2 · w) · (2 · l) · (2 · h)
V' = 8 · (w · l · h)
V' = 8 · V
V = 8 ft³
The addition of sand is found by the following subtraction:
ΔV = V' - V
ΔV = 8 ft³ - 1 ft³
ΔV = 7 ft³
An additional volume of 7 cubic feet is needed for the sandbox.
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8x - 6 = 2(4x-3)
Does the equation have one
none, or infinite solutions?
Explain why.
The given linear equation has only one solution i.e. x = 3/4
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A linear equation in one variable has
(a) Only one solution
(b) Two solutions
(c) More than two solutions
(d) No solution
Here,
On solving we have 8x - 6 = 0 or x = 3/4. The above linear equation is only true if x = 3/4 and
Hence, the given linear equation has only one solution i.e. x = 3/4.
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HELP 50 POINT MATH QUESTION MIDDLE SCHOOL
In the proportional relationship table, x would represent distance and y, weight.
The complete table is given in the explanation below.
What is a Proportional Relationship?If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.
x represents distance (cm)
y represents weight (newtons).
Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:
k = y/x = 28/20
k = 1.4
The equation would be y = 1.4x.
Use the equation to complete the table by substituting the value of each missing variables:
Row 2, when x = 55:
y = 1.4(55)
y = 77
Row 3, when y = 140:
140 = 1.4x
140/1.4 = x
100 = x
x = 100
Row 4, when x = 1:
y = 1.4(1)
y = 1.4
The table would be:
Distance (cm) Weight (newtons)
Row 1 20 28
Row 2 55 77
Row 3 100 140
Row 4 1 1.4
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The function a ( b relates the area of a trapezoid with a given height of 12 and one base length of 9 with the length of its other base.it takes as input the other base value and returns as output the area of the trapezoid
A (b)=12. B+9/2 which equation represents the inverse function b ( a which takes the trapezoids areas and put and returns as output the length of the other base
Answer:
B(a) = a/6 - 9
Step-by-step explanation:
The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.
What is the area of a trapezoid?
If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as
= [(a + b)h]/2
Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.
Therefore, 'b' is the parallel side of the base.
The given function that represents the area of the trapezoid is:
A(b) = [12(b + 9)]/2
Let, A(b) = a.
Therefore, a = [12(b + 9)]/2
⇒ 2a = 12(b + 9)
⇒ a = 6(b + 9)
⇒ a = 6b + 54
⇒ 6b = a - 54
⇒ b = (a - 54)/6
⇒ b = a/6 - 9
If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:
B(a) = a/6 - 9
KT's Restaurant has contracted with the Vidalia Times for
5,000 column inches in daily newspapers and 10,000
column inches in the Saturday newspaper. Daily column
inches are $27.55, and Saturday rates are $29.35 per
column inch. How much should KT's Restaurant budget for
newspaper advertising for the coming year?
The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500
Given,
The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000
The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000
The cost of daily column = $27.55 per column inch
The cost of Saturdays = $29.35 per column inch
We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;
Here,
There are approximately 53 Saturdays in a year.
So,
365 - 53 = 312
Then,
The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000
The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500
Therefore,
The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500
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step by step solution
x+1≥ 3or4/3x<-8
Answer:
Step-by-step explanation:
The answer for this can be an inequality or an interval notation or a graph
* Subtraction of (1) in both sides of the inequality
* Let's call part A: [tex]X+1\geq 3[/tex]
* Let's call part B: [tex]\frac{4}{3} X < -8[/tex]
* Solve part A first:
Do the subtraction of (1) on both sides of the inequality.
X ≥ 3 −1
X ≥ 2
Subtract
* Solve part B now:
Multiply for 3/4 both sides of the inequality to eliminate the [tex]\frac{4}{3}[/tex]
[tex]\frac{4}{3} X (\frac{3}{4} < -8 (\frac{3}{4})[/tex])
X < -24/4
X < -6
Answer
Inequality Form:
x < −6 or x ≥ 2
Interval Notation:
( − ∞,−6)∪[2,∞)
In Graph:
See the attach
Select the two values of x that are roots of this equation. 2x^2 + 7x + 6 = 0  A. x = –2  B.   C. x = –4  D. x = –3
The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.
How to find the roots of an equation?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
The equation to find the roots, is a quadratic equation.
Hence,
2x² + 7x + 6
2x² + 3x + 4x + 6
x(2x + 3) + 2(2x + 3)
Hence,
(x + 2)(2x + 3) = 0
Therefore,
x + 2 = 0 or 2x + 3 = 0
x = -2 or x = -3 / 2
The roots of the equation is x = -2 and x = -3 / 2
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he box is 3 inches by 4 inches by 5 inches. A second box is
4 inches by 4 inches by 4 inches. Explain how to decide
which box holds more.
Answer:
4x4x4
Step-by-step explanation:
3x4x5= 60
4x4x4= 64
64 is a higher volume than 60
Answer:
In order to find out which box can hold more, we can find the respective volumes of the boxes.
Volume of first box
= 3 inches × 4 inches × 5 inches
= 60 inches³
Volume of second box
= 4 inches × 4 inches × 4 inches
= 64 inches³
∴Since the second box has a greater volume than the first box, the former can hence hold more than the latter.
The pH of solution measures its acidity and can be determined using the formula pH= -log(base of 10 )C, where is the concentration of hydronium ions in the solution. measured in moles per litre .A lower pH indicates a more acidic solution.
The concentration of Hydronium ions type of coffes is 1.3 x 10above-5 moles per liter .
Calculate the pH of the coffee.
The value of pH of the coffee is 4.89
How to determine the pH of the coffee?pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution
Given: The formula pH= -log₁₀ C,
where is the concentration of hydronium ions in the solution measured in moles per litre
The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter
To calculate the pH, we will substitute the value of the concentration (C) into the given formula:
pH= -log₁₀ C (C = 1.3 x 10⁻⁵ moles per liter)
pH = -log₁₀(1.3 x 10⁻⁵) = 4.89
Therefore, the pH of the coffee is 4.89
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Use the difference of two squares to find each product.
17•7
The product of 17×7 using the difference of two squares is 119.
= 17×7
=(12+5)(12-5)
=12(12-5)+5(12-5)
=12×12-12×5+5×12-5×5
=12²-5²
=144-25
=119
The difference between two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the sum of the square roots and the other one is the difference of the square root.
I hope this answer helps.
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What other congruence is needed to prove that △QRP≅△QFP by ASA?
QR≅QF
∠R≅∠F
∠QPR≅∠QPF
PR≅PF
Can an equation of a line in standard form be written in a way where A, B, or C are either negative or positive? It’s hard to explain… for example
-x+y=-2
Can that be a way to do it? Or would the correct way be like
x-y=2?
Or what about
2x-2y=4? Can I divide by 2 on both sides to rewrite it as
x-y=2? I’m just wondering….
Answer:
2x-2y=4 that is the best way u can write it
Write in vertex form and state the vertex of the graph:
f(x)=20x+9+5[tex]x^{2}[/tex]
The vertex is (-2, 11), then the vertex form of the quadratic is:
f(x) = 5*(x + 2)^2 - 11
How to write the quadratic equation in vertex form?A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:
y = a*(x - h)^2 + k
And for a quadratic equation of the form:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
In this case, our equation is:
f(x) =5x^2 + 20x + 9
Then:
h = -20/2*5 = -2
Evaluating in x = -2 we get:
f(-2) = 5*(-2)^2 + 20*-2 + 9
f(-2) = 5*4 - 40 + 9
f(-2) = 20 - 40 + 9 = -20 + 9 = -11
The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:
f(x) = 5*(x + 2)^2 - 11
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PLEASE HELP DUE RIGHT NOW
WILL MARK BRAINLIEST IF YOU HELP
please actually help though dont just comment for points, or put links i will report you
Answer: : (4 – 5) – (13 – 18 + 2).
Step-by-step explanation:
hoped dat helped
1. Classify the figure in as many ways as possible. (1 wwwwww www Orectangle; square; quadrilateral; parallelogram; Orectangle; square; parallelogram Orhombus; quadrilateral; square MI
The figure given can be classified into; rhombus, quadrilateral, square.
The correct answer option is option c
How to classify a figure?Quadrilateral: This is a polygon with four sides.
Rhombus: This is a parallelogram having all sides of equal length.
Rectangle: A quadrilateral having opposing sides parallel and four right angles.
Square: A polygon with four sides of equal length and four right angle.
Parallelogram: This is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.
In conclusion, the figure can be classified into quadrilateral, rhombus and square.
Complete question:
The complete question is in the attached image.
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If x = 2 and t = 4, what is the value of 1/8(x^3− 4)(t² + 8)?
Answer:
64
Step-by-step explanation:
you need to plug the number in subtract and add then multiply the number from the first pair of parenthesis into the main number and after multiply the second pair into it.
2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
Answer:
$ 1.38
Step-by-step explanation:
5.50 ÷ 4 = 1.375. rounded to 2 dp: 1.38
Find(f-g)(x)if f(x)=/4x and g(x)=/16x
The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = √4x and g(x) = √16x
Evaluate the square roots in the above equations
This gives
f(x) = 2√x and g(x) = 4√x
To find the composition (f - g)(x), we make use of
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation So, we have the following equation
(f - g)(x) = 2√x - 4√x
Evaluate the like terms
This gives
(f - g)(x) = -2√x
Hence, the value of the composition is (c) (f - g)(x) = -2√x
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4. If there were 6183 total votes, how many yes votes were there?
The number of yes votes on whether to raise property taxes, using proportions, was of 3345, considering that 6183 total votes.
What is a proportion?A proportion is a fraction of a total amount, and equations are built with these fractions and the rates in the context of a problem to find the desired measures in the problem using basic arithmetic operations such as multiplication and division.
One application of proportions is for ratio problems, as one ratio between two amounts a and b is given by the division of a by b, and over the total, these rates are:
Fraction of a: a/(a + b).Fraction of b: b/(a + b).The ratio of yes votes to no votes was 5 to 4, hence the fraction of yes votes is given as follows:
5/(5 + 4) = 5/9.
The total number of votes was of 6183, hence the number of yes votes is calculated as follows:
5/9 x 6183 = 3435 total yes votes.
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In their October 2003 issue, Consumer Reports evaluated the price and performance of 23
models of cordless phones. Computer output gives these summaries for the prices:
a. Were any of the prices outliers? Explain how you made your decision.
b. One of the manufacturers advertises a cordless phone “economy-priced at only $31.95”.
Would you consider that to be a very low price? Explain.
Considering the five number summary of the data-set, we have that:
a. None of the prices were outliers, as all the prices are within 1.5 IQR of the quartiles.
b. That is not a very low price, as it is above the first quartile, while very low prices have to be 1.5 IQR below the first quartile.
How to identify outliers on the five number summary?The outliers, considering the five number summary of a data-set, are the values that are more than 1.5 Interquartile Ranges from the quartiles, that is, either:
1.5 IQR below the first quartile, which is a low outlier.1.5 IQR above the third quartile, which is a higher outlier.The interquartile range of a data-set is the difference between the third quartile and the first quartile, hence, for the given data-set:
IQR = Q3 - Q1 = 110 - 30 = 80.
Hence the bounds for outliers are given as follows:
Low outliers: 30 - 1.5 x 80 = -90. (there will be no low outliers).High outliers: 110 + 1.5 x 80 = 230.Since the maximum value of 200 is less than 230, there are no outliers in the data-set.
Missing InformationThe five number summary is given by the image at the end of the answer.
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Productive Investments Limited provided the
returns for Laska stocks for 2017 to 2021. Use the
information supplied to answer the questions below.
Year
2017
2018
2019
2020
2021
Laska return
-2.2%
-3.4%
12.5%
-0.8%
8.6%
a) Calculate the range of the market returns. (2
Marks)
b) Calculate the mean market return for 2022 (2
Marks).
c) Calculate the variance of the market returns (6
Marks).
d) Calculate the standard deviation of the market
returns (2 Marks).
e) Comment on your results (4 Marks).
The range of market return is 15.9% and the mean of market return is 2.94%
Productive Investments Limited provided the returns for Laska stocks for 2017 to 2021.
Year Laska return
2017 -2.2%
2018 -3.4%
2019 12.5%
2020 -0.8%
2021 8.6%
The range of market return = Highest return - lowest return
= 12.5 - (-3.4)
= 15.9%
mean market return = (-2.2 +(-3.4) + 12.5 +(-0.8) + 8.6)/5
mean market return = 2.94%
Therefore, the range of market return is 15.9% and the mean of market return is 2.94%
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The dimensions of a rectangle are 6x-7 and 3x-1. what is the area in square feet?
please help fast!!
The area of the rectangle is given by the formula below:
A = 18x^2 - 27x + 7
What is the area of the rectangle?For a rectangle of width W and length L, the area is given by the formula:
A = W*L
Here we know that the dimensions of a rectangle are 6x-7 and 3x-1, then we can define:
L = 6x - 7
W = 3x - 1
Replacing that in the area formula above we will get:
A = (6x - 7)*(3x - 1)
Now we can expand that product:
A = (6x)*(3x) + (6x)*(-1) + (-7)*(3x) + (-7)*(-1)
A = 18x^2 - 6x - 21x + 7
A = 18x^2 - 27x + 7
That is the formula for the area in terms of x.
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A school is arranging a field trip to the zoo. The school spends 862.68 dollars on passes for 40 students and 2 teachers. The school also spends 345.20 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
0.150985
Step-by-step explanation:
You add the two decimals together which gives you 120788.
Then, you move the decimal 4 places which is 12.0788.
Then you divide 12.0788 by 2 which gives you 6.0394.
Finally, you divide 6.0394 by 40 which gives you 0.150985.
a coin is tossed 5 times. find the probability that none are tails
Answer:
[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]
Step-by-step explanation:
The probability of "not a tail" is 1/2. The five tosses are independent, so the probability of "not a tail" 5 times in succession is
[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]
Find the equation of a line perpendicular to -5x + y = 9 that passes through the
point (0, -9)
The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]
How to find the equation of a line?The equation of the line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptPerpendicular lines follows the following rules as follows:
m₁ m₂ = -1
Let's find the slope of -5x + y = 9 .
y = 5x + 9
Hence,
slope = 5
Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to -5x + y = 9 .
5m₂ = -1
m₂ = -1 / 5
m₂ = - 1 / 5
Therefore, let's find the y-intercept of the line using (0, -9)
-9 = - 1 / 5(0) + b
b = -9
Therefore, the equation of the line is y = - 1 / 5 x - 9
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A park found him spray 20 gallons of water in one half an hour then was turned off for a while when it was turned back on it's break 30 gallons and 347 hours explain how you think I found and sprayed water at the same rate both times it was on
The rate of spray at both times is 40 gallons/hour and it is the same.
What is the rate of change?
How quickly something changes over time is referred to as its rate of change, or ROC. Thus, it is the acceleration or deceleration of changes (i.e., the rate) rather than the magnitude of individual changes.
We have,
spray 20 gallons of water in 1/2 hour.
30 gallons and 3/4 hours (it's not 347 hours).
We simply calculate the rate for one hour:
1/2 hour = 20 gallons
3/4 hours = 30 gallons
Then for 1 hour,
1 hour = 20 * 2 = 40 gallons
1 hour = 30 * 4/3 = 40 gallons
Hence, the rate of spray at both times is 40 gallons/hour and it is the same.
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create an x and y table of all 5 points in the picture (graphing)
The x and y table of all 5 points in this graph include the following:
x y
1 1
2 2
3 3
4 4
5 5
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Additionally, the graph of any proportional relationship is always modeled by a straight line with the data points passing through the origin (0, 0).
In this scenario, we can reasonably and logically deduce that all of the data points in this graph are represented by the red symbols.
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what is 954 divided by 70 using long division and with a remainder
Answer:
13 Remainder 44
Step-by-step explanation:
The solution after divide is, 13 and remainder = 44
We have to given that;
954 divided by 70 by using long division and with a remainder.
Now, We can divide as,
⇒ 954 divided by 70
70 ) 954 ( 13
-70
----------
254
- 210
----------
44
Therefore, The solution is, 13 and remainder = 44
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