how do you use Congruence and similarity criteria to prove relationships in geometric figures?
Congruence and similarity criteria are used to determine congruence and proportional relationships respectively. That is, congruence criteria is used to establish a relationship of equivalence, and similarity criteria is used to establish a relationship of proportion with a common ratio between the figures.
Determine whether the line that passes through points (-2, 1) and (6, 5) is parallel, perpendicular or neither to a line with a slope of -2.
We have a line with slope -2. A parallel line would have a slope of -2 too, and a line perpendicular to it will have a slope of 1/2.
If line A is perpendicular to B, the slope of B is the inverse multiplicative of the sloe of A. That is why a line perpendicular to the one with slope -2 is 1/2:
[tex]\text{Perpendicular Slope}=-\frac{1}{-2}=\frac{1}{2}[/tex]Now we know the slopes for both cases: parallel and perpendicular. If the slope is different to -2 or 1/2, we can say that is not parallel nor perpendicular to the line given.
Let's evaluate the slope of the line that passes through points (-2, 1) and (6,5).
The slope is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where x₁ and y₁ are the x and y-coordinates of the first point (-2 and 1), and x₂ and y₂ are the x and y coordinates of the second point (6 and 5, respectively).
Replacing values:
[tex]\begin{gathered} m=\frac{5-1}{6-(-2)}=\frac{4}{6+2}=\frac{4}{8} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]The slope of the line passing through the points given is 1/2, then, according to what was said above, that line is perpendicular to a line with slope -2.
Is 91.470 rational or irrational?
The number 91.470 is the rational number.
What is termed as the rational number?Rational numbers are written in the form p/q, in which p and q are any integer and q 0 respectively. The following are the various types of rational numbers.Integers such as -2, 0, 3, and so on are rational numbers.Rational numbers are fractions with integer numerators and denominators, such as 3/7, -6/5, and so on.Ending decimals such as 0.35, 0.7116, 0.9768, and so on are rational numbers.Rational numbers are non-terminating decimals with repeating patterns (just after decimal point), including such 0.333..., 0.141414..., and so on. These are commonly referred to as non-terminating recurring decimals.For the given number.
91.470 can be written in the fraction as;
91470/1000
Or 914/100
As, the form is p/q where q ≠ 0.
Thus, the number 91.470 is the rational number.
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Write a biconditional for the following conditional. Then state the truth value of the statement
If two lines intersect at right angles, then they are perpendicular.
The biconditional for the conditional statement is : Two line intersect each other at right angles . The two lines are perpendicular.
A conditional statements are part of mathematical reasoning, a fundamental ability that enables students to evaluate a given hypothesis without reference to a particular context or meaning.
Simply put, when a scientific research or allegation is studied, the logic is not reliant on an individual's viewpoint. Deductions and evidence must have factual and scientific foundations.Conditionals are programming language instructions used to manage judgments in the field of computer science. They are also referred to as conditional statements, conditional expressions, and conditional constructions.One needs to be capable of logical reasoning and critical thinking in mathematics in order to respond to questions involving mathematical reasoning and conditionals.The truth value for the conditional statement is true as we know that when two lines intersect at 90° then they are said to be perpendicular.
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The student council raises money for the school dance every year through an auction. Each auction ticket costs $125. If the student council needs to raise greater than or equal to $2,000, which inequality represents the number of auction tickets,t, the student council must sell?
The inequality that represents the number of auction tickets,t, the student council must sell is given as 125t ≥ 2000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the total number of tickets be represented by t.
The auction ticket costs $125 and the student council needs to raise greater than or equal t $2,000. This will be 125t ≥ 2000.
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Given the graph below write an equation of the form f(x) = Acos(w(x-c))+D
Amplitude = (Maximum + Minimum)/2 , = (1 + 1.8)/2= (2.8)/2= 1.4
Period = distance for the function to repeat. So, the distance is from -0.5 to 3.5, then it is 4, then it is smaller than 2 times pi number.
C is the distance from the Y axis to the function.
D is the horizontal line that passes through the middle of the distance between the maximum and minimum point, which is in that case the same one as the period has to use
Then, the formula is:
[tex]\begin{gathered} f(x)=Acos(w(x\text{ -c\rparen + D A is amplitude, C is horzontal distance and D}midpoint \\ \\ f(x)=1.4cos(4(x\text{ - 1.7\rparen+\lparen-0.4\rparen} \\ f(x)=1.4cos(4x\text{ - }6.8)\text{ - }0.4 \end{gathered}[/tex]If a bug can flap its wings at a rate of 69 times in 4 seconds, how manytimes do they flap their wings in 1.476 minutes? Round to 1 decimal.w
First, we need to change 1.476 minute to seconds
1.476 minutes = 1.476 x 60= 88.56 seconds
Let the number of times they flap there wings in 1.476 minute be X
69 times = 4 seconds
X = 88.56 seconds
cross-multiply
4X = 69(88.56)
4X= 6110.64
Divide both-side of the equation by 4
X = 1 527.66 ≈ 1 528 times
HURRY!!!
What is the value of |243| + |−23| − |−16|?
Answer:
250
Step-by-step explanation:
everything u need is in the picture
please answer asap im begging
Answer:
y = 3x + 3 :D
Step-by-step explanation:
Equation of line: y = mx + b :)
b: Y intercept
m: Slope
Now lets solve :)
Lets find M first :)
We need 2 points so lets use (0,3) and (1,6) :)
We fist need to subtract :)
6 - 3 = 3
1 - 0 = 1
Now we divide :)
3/1 = 3
Lets put that into our equation :)
y = 3x + b
Now lets find B :)
To find b, we need to see where the line intercepts the y axis! This will be at point (0,3)!
The y intercept will be 3 :)
The final equation will be y = 3x + 3 :)
Have an amazing day!!
Please rate!
1. Solve the Systemy = 2x - 6y = -6x - 14
x = -1
Explanation:The given equations:
y = 2x - 6
y = -6x - 14
Since both equations are equal to y, we will equate the right hand side of both equations.
y = y
2x - 6 = -6x - 14
collect like terms:
2x + 6x = -14 + 6
8x = -8
divide both sides by 8:
8x/8 = -8/8
x = -1
Julia sells subs for $6 each. How many subs will she need to sell to break even each month based on the costs listed below?
Labor costs (management & workers) = $11,000
Insurance = $400
Rent = $1300
Utilities = $300
Average cost of ingredients/packaging for each sub = $1.32
Answer:
2777.7777... subs
Step-by-step explanation:
11000+400+1300+300=13000
6-1.32=4.68
13,000/4.68
=2777.777777...
Function Notation - Transformationsill send a picture of the question
Let's see how two points on the left are mapped to their corresponding points on the right:
Point A has a corresponding point at A'. We have:
f(A) = A'
f(-6, -3) = (2, 4)
Point B has a corresponding point at B'. We have:
f(B) = B'
f(-4, -1) = (4, 6)
Now, notice that:
2 = -6 + 8
4 = -3 + 7
So, for (x, y) = (-6, -3), we have:
f(x, y) = (2, 4) = (x + 8, y + 7)
Notice that the same happens to the mapping of the other point:
4 = -4 + 8
6 = -1 + 7
So, for (x, y) = (-4, -1), we have:
f(x, y) = (4, 6) = (x + 8, y + 7)
Therefore, the rule for the transformation is
f(x, y) = (x + 8, y + 7)
Please help with #9 i’m on please help with angles
We know that two angles shown have to add to a right angle, which measures 90°, then we have the equation:
[tex]\begin{gathered} x+5x=90 \\ 6x=90 \\ x=\frac{90}{6} \\ x=15 \end{gathered}[/tex]Hence, the value of x is 15°; which means that:
[tex]\begin{gathered} x=15 \\ 5x=75 \end{gathered}[/tex]Therefore, the angles are 75° and 15°
solve for x: 3/2+1/2x=2x
Here we will try to solve an equation involving a variable ( x ) given as follows:
[tex]\frac{3}{2}\text{ + }\frac{1}{2}\cdot x\text{ = 2x}[/tex]We use the following basic mathematical operations when solving any equation:
[tex]\text{Multiplication, Division, Addition, Subtraction}[/tex]We will first try to isolate our vairable ( x ) on either side of the " = " sign. We will try to isolate ( x ) on the right hand side of " = " sign. To do this we will employ the mathematical operation of " Subtraction ".
We will subtract ( 1 / 2 x ) from both sides of " = " sign:
[tex]\begin{gathered} \frac{3}{2}\text{ + }\frac{1}{2}\cdot x\text{ - }\frac{1}{2}\cdot x\text{ = 2x - }\frac{1}{2}\cdot x \\ \\ \frac{3}{2}\text{ = x}\cdot\text{ (}\frac{4\text{ - 1}}{2}) \\ \\ \frac{3}{2}\text{ = }\frac{3}{2}\cdot x \end{gathered}[/tex]The next mathematical operation we will apply is " Division ". We will divide the left hand side of the equation with right hand side constant as follows:
[tex]\begin{gathered} x\text{ = }\frac{\frac{3}{2}}{\frac{3}{2}} \\ \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1}} \end{gathered}[/tex]The solution to the given equation is as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1 }}[/tex]QUESTION ATTACHED
PLEASE HELp
Answer:
yh no question....thanks for the points tho :)
Jack borrows $2,700 at a rate of 8.2% per year. How much total will he pay if it takes 3 months to repay the loan?
well, a year has a total of 12 months, so 3 months is really 3/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2700\\ r=rate\to 8.2\%\to \frac{8.2}{100}\dotfill &0.082\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ A=2700[1+(0.082)(\frac{1}{4})] \implies A = 2700(1.0205)\implies A=2755.35[/tex]
solve for k 8/7=12/k
Answer:
[tex]k=\frac{21}{2}[/tex]Explanation:
Given the equation:
[tex]\frac{8}{7}=\frac{12}{k}[/tex]To solve for k, let us take the reciprocal of both sides, so that k is a numerator.
[tex]\frac{7}{8}=\frac{k}{12}[/tex]Multiply both sides by 12
[tex]\begin{gathered} k=\frac{7}{8}\times12 \\ \\ =\frac{7\times12}{8} \\ \\ =\frac{84}{8} \\ \\ =\frac{21}{2} \end{gathered}[/tex]The mean amount of gasoline charged by Key Refining Co.'s customers is $70 per month. The distribution of amount spent is approximately normal with a standard deviation of $10. Compute the probability (area under the curve) of selecting a customer who spent between $57 and $83 per month.
The probability (area under the curve) of picking a client who spends between $57 and $83 per month is 0.4032.
Given,
Mean, μ = $70
Standard Deviation, σ = $10
z = (x-μ) ÷ σ
P(The consumer was charged from around $70 and $83),
P(70 ≤ x ≤ 83) = P((70 - 70) ÷ 10)) ≤ z ≤ ((83-70) ÷ 10)) = P(0 ≤ z ≤ 1.3)
=P(z ≤ 1.3) - P(z ≤ 0)
=0.9032 - 0.500 = 0.4032 = 40.32%
P(70 ≤ x ≤ 83) = 40.32%
Customers with Key Refining Company loans typically spend an average of $70 monthly on gasoline and servicing. With either a standard deviation of $10, the expenditure distribution is about normal. For z = 1.3, the area under the curve is 0.4032.
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The lengths of the sides of a triangle are 5,6, and 7. If the perimeter of a similar triangle is 36, what is the length of the shortest side of the similar friangle? A) 5 B) 10 C) 4 D) 6
The length of the sides of a triangle are 5, 6 and 7.
If the perimeter of a similar triangle is 36
Perimeter of a triangle = a + b+ c
The perimeter of the first triangle is
P = 5 + 6 + 7
P = 11 + 7
P = 18
To find the smallest lengths
18 / 36 = 5 / x
Introduce cross multiplication
36 x 5 = 18 * x
180 = 18x
Divide both sides by 18
180/18 = 18x/18
x = 180/18
x = 10
The answer is 10
The circumference of a circle is 16 M what is the diameter of the circle
Given
Circumference, C = 16m
Find
diameter
Explanation
We know Circumference of a circle
[tex]\begin{gathered} C=2\pi r \\ 16=2\times\frac{22}{7}\times r \\ \frac{16\times7}{2\times22}=r \\ \frac{4\times7}{11}=r \\ \frac{28}{11}=r \end{gathered}[/tex]diameter = 2r
[tex]undefined[/tex]
You are the manager of a rental car company. A customer, Sandy Furrow, has asked you for an estimate of charges for a nine day rental of an SUV. She expects to drive 670 miles. If the company charges $55.50 per day plus 15 1/2 cents
per mile for this category of vehicle, what would be the total rental charge (in $) for Sandy's trip?
The total cost of her trip will be of $159.7.
What is equation?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. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.
given:
Cost of 16 cents per mile= 16/100 = 0.16
Cost of $52.50 per day =52.50
linear function for the charge y in function of the number of miles x is:
y(x) = 0.16x + 52.50
The cost of driving 670 miles
So, y(670) = 0.16 x 670 + 52.50
y(670) = 107.2 + 52.50
y(670) = 159.7
Hence, The total cost of her trip will be of $159.7.
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hello can you explain to me how I should write this out please
Here, we want to calculate the interquartile range
Mathematically, this is the difference between the lower quartile (1st quartile or 25th percentile) and the upper quartile (3rd quartile or 75th percentile)
We already have the numbers arranged from top to bottom
The count of numbers is 9 numbers
We have the first quartile as;
[tex]\frac{(n+1)}{4}\text{ = }\frac{10}{4}\text{ = 2.5th which is 3rd term}[/tex]The third term here is the weight of baby Selena
The 3rd quartile can be calculated as;
[tex]\frac{3(n+1)}{4}\text{ = }\frac{3(9+1)}{4}\text{ = 7.5 which is 8th term}[/tex]The 8th term is the weight of baby Me
The difference between these weights give the interquartile range as follows;
[tex]\text{Interquartile range =Q}_3-Q_1\text{ = 8 lbs 2 oz - 6 lbs 1 oz = 2 lbs 1 oz}[/tex]Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50dollar per T-shirt ordered.
As Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
To ascertain the maximum or lowest values of a scenario with many restrictions, a system of linear inequalities is frequently utilized. Inequalities reflect a limit of what is permitted or achievable rather than a precise quantity.
It is given that Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50 dollar per T-shirt ordered.
We have to find the maximum number of T-shirts she can buy,
⇒ $280 / $9.50
⇒ 29.47 ≅29
Thus, Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
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Karma has 110 pounds of rice to sell. A vendor offers her $0.01 per 5 grams for her rice. How much money will karma make if she sells her rice to this vendor
Karma will make $99.78 if she sells 110 pounds of rice to the vendor
Quantity of rice available with Karma = 110 pounds
A pound is a unit of weight that is mostly used in the United States, Great Britain, and other English-speaking nations. A pound is approximately 0.454 kilos. A quantity of something is said to weigh one pound if it weighs that much.
The conversion rate of pounds to grams:
1 pound = 453.59 grams
So, 110 pounds will be equal to:
110*453.59
=49894.9 grams
Selling price for 5 grams = $0.01
Selling price for 1 gram:
The selling price of 5 grams/ Price for 5 grams
0.01/5
=$0.002
Selling price for 49894.9 grams = 49894.9*0.002
= $99.78
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help me pls I don't understand what I'm supposed to put here
The feedback loops in each situation are classified as follows:
a) Positive.
b) Negative.
What are positive and negative feedback loops?A positive feedback loop is when there is an amplification or growth of the output signal.A negative feedback loop is when there is a damping of the output signal, which is equivalent to a reduction in it's effect.In the context of this problem, in item a, there is a continuous amplification of the output signal, which is the surface temperatures, as they keep increasing, the three effects listed contribute to the increase of temperature, then the system go back to the beginning still with increasing temperatures, hence it is a positive feedback loop.
In item b, we have a loop with changes in the temperature, it increases and then it decreases, and so on, hence it is a negative feedback loop.
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Peter's farm has 160 meters of fencing, and he wants to fence a rectangular field thatborders a straight river. He needs no fence along the river side. Find the largest areaof Peter's farm that can be fenced.
ANSWER
3200 m²
EXPLANATION
Peter wants to build a fence around a rectangular field, except for one side because the river is there,
So, the total perimeter of the fence is,
[tex]P=W+W+L=2W+L[/tex]And this is equal to 160 m. Solving for L,
[tex]160=2W+L\text{ }\Rightarrow\text{ }L=160-2W[/tex]The area of this field is,
[tex]A=WL[/tex]Replace L with the expression we found from the perimeter,
[tex]A=W(160-2W)=160W-2W^2[/tex]The area is given by a quadratic function whose leading coefficient is negative, which means that the graph is a downward parabola and, therefore, the vertex is the maximum value of the area.
The x-coordinate of the vertex is given by,
[tex]f(x)=ax^2+bx+c\text{ }\Rightarrow\text{ }x_{vertex}=\frac{-b}{2a}[/tex]In this case, x is W, a = -2, and b = 160, so the width of the field for the maximum area is,
[tex]W_{vertex}=\frac{-160}{2(-2)}=\frac{160}{4}=40m[/tex]And the length when W = 40 is,
[tex]L=160-2W=160-2\cdot40=160-80=80m[/tex]And the area is,
[tex]A=WL=40m\cdot80m=3200m^2[/tex]Hence, the largest area of Peter's farm that can be fenced is 3200 square meters.
I need help with this homework assignment it’s due by mid night
step 1
see the attached figure to better understand the problem'
step 2
Hypotenuse is AB
Opposite side is BC
Adjacent side is AC
because, the opposite side is the side opposite to the given angle (35 degrees)
adjacent side is the side adjacent to the given angle (35 degrees) and the hypotenuse is the greater side of a right triangle (is the opposite side to the angle of 90 degrees)
step 3
To find out the value of L
we use
cos(35)=40/L -----> adjacent side divided by the hypotenuse
step 4
solve for L
L=40/cos(35)
step 5
L=48.83 ft
step 6
the length of the ladder must be greater than 48.83 ft
step 7
A 50 ft ladder long is enought
because 50 > 48.83
HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 50 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answer:
6 units13 units5 unitsStep-by-step explanation:
You want the lengths of the unknown sides in the given trapezoid figure, knowing that the perimeter is 18 units.
1.The side AB is a vertical line segment, so its length can be found by finding the difference of y-coordinates of its end points.
AB = (2) -(-4) = 2+4 = 6
The length of AB is 6 units.
2.The sum of the lengths of vertical and horizontal segments is ...
AB +BC +CD = 6 +4 +3 = 13
The total distance from A to D along vertical and horizontal segments is 13 units.
3.The perimeter is the sum of the lengths of all sides.
perimeter = AB +BC +CD +AD
18 = 13 + AD . . . . . . substitute known values
5 = AD . . . . . . . . . subtract 13
The length of segment AD is 5 units.
__
Additional comment
Finding the length of a vertical or horizontal line is no different than finding the distance between two points on a number line.
The price of the TV, which cost € 1,260, was reduced by € 189. Calculate the percentage of this TV.
Initial TV price, $1,260
price reduction, $189
percentages:
reduction percentage or discount = 189/1260 = 0.15 = 15%
The above indicates the percentage by which the price was reduced or the discount obtained
percentage paid = (1260-189) / 1260 = 0.85 = 85%
This indicates that we paid 85% of the initial price.
Janna is measuring the dimensions of her bedroom to determine how much paint she should buy for the walls. If her measuring tape has increments of 0.01 meter, which of the following could be the length of one wall with the correct number of significant digits?A)2.51 meters B)2.5 metersC)2.513 metersD)3 meters
The option that can be the length of one wall with the correct number of the significant digit is A)2.51 meters.
How to illustrate the information?From the information given, Janna is measuring the dimensions of her bedroom to determine how much paint she should buy for the walls was stated that the measurements have increments of 0.01 meter.
It's important to note that there are 2 decimal places.
In this case, the appropriate option is 2.51 meters.
In conclusion, the correct option is A.
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