2. Use the areas of the two identical squares to explain why 5² + 12² = 13² without
doing any calculations.
Answers
The equation can be proved by taking Pythagorean Triplets into consideration, therefore 5^{2} + 12^{2} = 13^{2}
What are Pythagorean Triplets?
The "Pythagorean Triple" is a collection of three positive numbers, a, b, and c, that satisfy the following rule:
a^{2} + b^{2} = c^{2}
From the figure two in the attached image it can be very well observed that 5,12 and 13 are making a pythagorean triplets, therefore it can be said 5^{2} + 12^{2} = 13^{2}
Hence Proved.
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Related Questions
Can someone please help
Answers
Answer:
The measure of angle 1=52
The measure of angle 2=58
The measure of angle 3=31
Step-by-step explanation:
The measure of angle 1 is 52 because the angle out of the triangle is 128. The measure of angle 1 plus 128 equals 180. Using this info you could do 180-128, which equals 52. The measure of angle 1 equals 52.
The measure of angle 2 is 58 because I already know 2 of the values of the triangle, in which Angle 2 is also in. One triangle adds up to 180. The values of the other 2 angles are 52 and 70. Using this information I can use the equation 52+70+x=180, which you then simplify to 122+x=180. X equals 58. The measure of angle 2 equals 58
The measure of angle 3 is 31 because the angle out of the triangle is 70. The missing angle plus 70 equals 180. Using this info I could do 180-70. The missing angle is 110. There is already one given angle, and I have figured out the other, using this info I can now finally find the measure of angle 3. I can find this out by using the equation 110+39+x=180. You would then simplify the equation to 149+x=180. X equals 31. The measure of angle 3 equals 31.
Evaluate the expression when a = -6 and y=4. y-9a
(can someone help? I'm not used to how this is formatted.)
Answers
Answer: 58
Step-by-step explanation:
First you substitute the values, so
4-9*-6
Then you solve using order of operations
Answer:
58
Step-by-step explanation:
y-9a
Let a = -6 and y=4
Substitute the values in
4 -9(-6)
Multiply first
4 + 54
Add
58
Question 10(Multiple Choice Worth 2 points)
(Adding and Subtracting with Scientific Notation MC)
Simplify (3.7 x 10-9) - (8.2 x 10-8). Write the final answer in scientific notation.
O-7.83 x 10-8
-7.83 x 10-9
O-4.5 x 10¹
O-4.5 x 10-¹
Answers
The simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.
We will solve the given expression using laws of exponents.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
(3.7 x 10^-9) - (8.2 x 10^-8)
= (3.7 x 10^(-1 -9)) - (8.2 x 10^-8)
= (3.7 x 10^-1 x 10^-8) - (8.2 x 10^-8)
= (0.37 x 10^-8) - (8.2 x 10^-8)
= (0.37 - 8.2) x 10^-8
= - 7.83 x 10^-8
So, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) is - 7.83 x 10^-8.
Thus, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.
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Which of the following is the solution of
the system of equations shown?
A. (2, 2)
B. (-2, 2)
C. (2,-2)
D. (-2,-2)
(The answer isn’t B. I already tried that)
Answers
(-2,-2)
If you buy an AED 50 meal with a 5% tax.
The tax amount to be paid is AED
Answers
Answer:
2.5 dhs
Step-by-step explanation:
5% of AED50
50x5/100=250/100
=AED2.5
(2,-2) and (0,-1)
what is the linear equation
Answers
The linear equation of the given points (2, -2) and (0, -1) is y = (-1/2)x - 1
The first point = (2, -2)
The second point = (0, -1)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (-1 - -2) / (0 - 2)
= -1+2 / -2
= 1 / -2
= - 1/2
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values in the equation
y - -2 = (-1/2) (x-2)
y + 2 = -1/2 x + 1
y = (-1/2)x + 1 -2
y = (-1/2)x - 1
Hence, the linear equation of the given points (2, -2) and (0, -1) is y = (-1/2)x - 1
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how many thousandths are in one hundredth
Answers
Answer:
ten thousands
Step-by-step explanation:
Ten thousandths are in one hundredth.
What is fraction?
Fractions represent parts of a whole. In mathematics, fractions are represented as numbers that define part of a whole. A fraction can be a part or subset of any quantity of a whole, and a whole can be any number, value, or thing.
All fractions consist of a numerator and a denominator, separated by horizontal bars called fraction bars.
The denominator indicates the number of parts into which the whole is divided. Placed at the bottom of the break below the break bar. The
counter indicates how many sections of the fraction are displayed or selected. Placed at the top of the break above the break bar.
As we know ,
one hundredth is 1/100
one thosandth is 1/1000
But now , 10 × 1/1000 = 1/100
This means that there are 10 thousandths in one hundredth.
Hence, ten thousandths are in one hundredth.
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10 A factory produces lemon-scented widgets. Each widget is cheaper, the more that are produced, but costs will go up if too many widgets are produced, due to storage requirements. The accountant for the factory says that the costs for producing x thousands of units a day can be approximated by the formula C = 0.04x2 - 8.504x + 25302. Find the daily production level that will minimize the costs. Be sure to show your work and include units of measurement.
Answers
The daily production level that will minimize the costs is 106300 units.
How to calculate the production level?From the information, the function is given as C = 0.04x² - 8.504x + 25302.
c = cost
From the function, the following can be deduced:
a = 0.04
b = 8.504
c = 25302
Then, -b/(2a) will be:
= -8.504 / (2 × 0.04)
= 106.300
Note that production level will minimize the cost in thousands.
The production level will now be:
= 106.300 × 1000
= 106300 units
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In the picture, you see 1 paper cup and 5 paper cups that are stacked together. The table shows the heights of stacks with different numbers of cups.
Which function rule gives the height of a stack of cups in terms of the number of cups in a stack?
Answers
The function rule that gives the height of a stack of cups is h(c) = 8+ 2(c)
How to determine the function rule that gives the height of a stack of cups?
Looking at the image, 1 paper cup has a body height of 8cm (total height = 10cm) and the height of the cups increases by 2cm for each cup added.
If you add three cups, for example, the height increases by 6cm (3 x 2cm). If you add n cups the height will increase by 2n and the total height will be 8+2n
Number of cups, c >>>>> Process >>>>> Height of stack, h(cm)
c 8+ 2(c) h
h(c) = 8+ 2(c)
Note: It is h(c) because c is the input and h is the output
Therefore, the function rule that gives the height of a stack of cups in terms of the number of cups in a stack is h(c) = 8+ 2(c)
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Evaluate n(x) = -1 - x + 4 when x = -2,0, and 5
Answers
x = -2, n(-2) = -1 - (-2) + 4 = 5
x = 0, n(0) = -1 - 0 + 4 = 3
x = 5, n(5) = -1 - 5 + 4 = -2
Of the 250 sheep in a flock, 34% are white. What is the total number of white sheep in the flock?
Answers
85 total white sheep are in the flock
A train travels at 80 miles per hour. An equation can be written that compared that the time(t) with the distance(d). What is the domaine and range?
Answers
The equation that compares the time (t) with the distance (d) would be; 80 (t) = d
What is an equation?
An expression that depicts the relationship between two or more numbers and variables is called an equation. Two or more equations that can be solved to get a singular result are referred to as a system of equations. The equation's power must be in one degree.
Given that A train travels at 80 miles per hour. We need to find the equation that compares the time (t) with the distance (d)
where t means time so if the train travels 2 hours then it will travel;
80 × 2 = 160 miles
Therefore, the equation that compares the time (t) with the distance (d) would be; d = 80t.
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Alexa has $4.75 worth of dimes and quarters. She has 2 more dimes than quarters. Determine the number of dimes and the number of quarters that Alexa has.
Answers
Answer:
Alexa has 13 quarters and 15 dimes.
Step-by-step explanation:
First, we should set up a system of equations using the given information. We can use q to represent the number of quarters and d to represent the number of dimes.
Since quarters are $0.25, dimes are $0.10, and the total is $4.75 we know 0.25q + 0.1d = 4.75
The problem tells us that there are 2 more dimes than quarters, so d = q + 2
To solve for the number of quarters, we can substitute the second equation into the first equation.
0.25q + 0.1 (q + 2) = 4.75
0.25q + 0.1q + 0.2 = 4.75
0.35q = 4.55
q = 13
Then, to solve for the number of dimes, we can substitute q into the second equation.
d = q + 2
d = 13 + 2
d = 15
A farmer estimates that he will harvest 7250 bushels of wheat. The weather is perfect during the growing season, so he harvests 1 more bushels of wheat than expected. How many bushels of wheat does the farmer harvest?
Answers
The number of bushels of wheat does the farmer harvest is 7251 bushels of wheat
The farmer's estimated number of bushels of wheat in the harvest = 7250 bushels
The weather is perfect during the growing season
The number of additional bushels of wheats harvested = 1 bushels
The number of bushels of wheat does the farmer harvest = The farmer's estimated number of bushels of wheat in the harvest + The number of additional bushels of wheats harvested
Substitute the values in the equation
The number of bushels of wheat does the farmer harvest = 7250 + 1
Here we haver to use the addition
Add the terms
= 7251 bushels of wheat
Hence, the number of bushels of wheat does the farmer harvest is 7251 bushels of wheat
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Factor -1/2 out of 1/2x+6
Answers
Answer:
-x-12
Step-by-step explanation:
1/2x+6
first divide by -1/2 or multiply by -2(its the reciprocal)
-2(1/2x+6)
-2*1/2x+6*-2
-x-12
Select the correct answer.
Which number best represents the slope of the graphed line?
A. -5
B.-1/5
C. 1/5
D.5
Answers
Answer:
A. -5
Step-by-step explanation:
You want the slope of a graphed line that crosses grid points (0, 2) and (1, -3).
SlopeThe sign of the slope is positive if the line goes up to the right. This line goes down to the right, so the sign of its slope is negative. (Eliminates choices C and D)
The magnitude of the slope is the ratio of vertical distance to horizontal distance between two points. This line drops 5 vertical squares for each square to the right, so its slope is ...
rise/run = -5/1 = -5
The slope is best represented by -5.
__
Additional comment
From a point on the line that is a crossing of grid lines, if the line crosses the next vertical grid line before it crosses the next horizontal grid line, the magnitude of its slope is less than 1.
Here, the line crosses several horizontal grid lines before it crosses another vertical grid line, so its slope has a magnitude greater than 1. When the choice is between -5 and -1/5, the larger magnitude number is -5.
From two points on the line, you can find the slope using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-3 -2)/(1 -0) = -5/1 = -5 . . . . . . using points (0, 2) and (1, -3)
Sparx homework
I really need help on how to solve this!
Answers
Answer:
a] 5 dogs
b] 16 dogs
Step-by-step explanation:
The minimum number of dogs that could have a mass of more than 26 kg is 5. This is because dogs with a mass of 30 ≤ x ≤ 40 have a frequency of 5. The dogs in the 20 ≤ x ≤ 30 range could be more than 26 kg, but they could also be less than 26 kg, so these are not included in the minimum.
The maximum number of dogs that could have a mass of 26 kg is 16 because both dogs in the 30 ≤ x ≤ 40 range (5) and 20 ≤ x ≤ 30 range (11) could weigh more than 26 kg. 11 + 5 = 16, giving us our answer for the maximum.
the dimensions of col a and nul a add up to the number of columns in a.
a. true
b. false
Answers
Using Rank theorem , the dimensions of col A and Null A add up to the number of colmns in A. It is true statement.
The rank of matrix A denoted as rank(A) is the dimension of the column space Col(A).
The nullity of matrix A written as nullity(A) is the dimension of the null space Nul(A)
Rank Theorem:
If A is a matrix with n columns, then
Rank (A) + nullity (A) = n
In other words we can say that
dim (Col(A) ) in column space + dim (Nul(A)) in empty space = total number of columns in A
The rank theorem is really important theorem.
It is gives a strong relationship between the Null space ( all possible vector x such that Ax = 0) and the column space (the set of vectors b matching Ax=b) explain the two main objectives. The more freedom we have for choosing x, the less freedom we have for choosing b, and vice versa.
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Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement. Daya's employer also contributes a set percentage, which will increase her total by $161,531.00. What is the percent increase between the total without Daya's employer contribution and the total with? Round to the nearest whole percent.
94%
79%
52%
48%
Answers
The percent increase between the total without Daya's employer contribution and the total with is A. 94%.
How to calculate the percentage?From the information, Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement and her employer also contributes a set percentage, which will increase her total by $161,531.00.
Therefore, the percentage increase will be:
= Increase in amount / Original amount × 100
= 161,531/172486 × 100
= 94%
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Given the equation y=2-(x-3)^2
Find the cordinates of the vertex of the curve it describes
Find the x intercept
Find the y intercept
Answers
Answer:
Y= -7
X= 4.4
Step-by-step explanation:
Y= 2 - ( x-3)^2
When x= 0
Y= 2- ( 0-3)^2
Y will equals -7
When y = 0
(x-3)= √2
X = 4.4
What is the value of x? Show your work. 20x⁰ 8x° 17x
PLEASE I NEED HELP
Answers
Answer:
x = 8
Step-by-step explanation:
the exterior angles of a triangle sum to 360° , that is
20x + 8x + 17x = 360
45x = 360 ( divide both sides by 45 )
x = 8
Adding two negatives makes a bigger number? Is this true or false? Explain.
Answers
Answer: False, adding two negatives does not make a bigger number. I know this because when adding the two negatives, the absolute value will get bigger. However, the value of the number gets smaller.
the normal model n(58,21) describes the distribution of weights of chicken eggs in grams. suppose that the weight of a randomly selected chicken egg has a z-score of -1.41. what is the weight of this egg in grams? round to the nearest hundredth of a gram.
Answers
By using normal distribution, it is obtained that weight of a randomly selected chicken egg is 28.39 grams
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is
[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]
where, z = [tex]\frac{x - \mu}{\sigma}[/tex]
[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
In case of normal distribution
Formula for z = [tex]\frac{x - \mu}{\sigma}[/tex]
[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
Let the weight of the egg be x grams
Here, z = -1.41, [tex]\mu[/tex] = 58 and [tex]\sigma[/tex] = 21
[tex]-1.41 = \frac{x - 58}{21}\\[/tex]
x = -1.41 [tex]\times[/tex] 21 + 58
x = 28.39 grams
Weight of a randomly selected chicken egg is 28.39 grams
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PLEASE HELP WILL GIVE 100 POINTS AND BRAINLEST ANSWER BOTH QUESTIONS TWO ANSWERS FOR EACH!!
Answers
Circumcenter is equidistant from the vertices, perpendicular bisectors will cross. Incentre is equidistant from the sides. Where the angle bisector cross incenter
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We have to choose the properties of circumcenter.
Circumcenter is equidistant from the vertices.
It is equidistant from the three vertices of the triangle, and thus you can construct a circle centered at the circumcenter and circumscribing the triangle.
and perpendicular bisectors will cross.
We have to choose the properties of incenter.
Incentre is equidistant from the sides.
Where the angle bisector cross incenter
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If there are 20 boxes of bicycles/tricycles total and 48 wheels total how many tricycles were ordered?
write and graph a system of linear equations to model the situation
Answers
The system of equations is:
x + y = 20
2x + 3y = 48
And its graph can be seen in the image at the end.
How to write and solve the system of equations?Let's define the variables:
x = number of boxes with a bicycley = number of boxes with a tricycle.Each bicycle has 2 wheels, each tricycle has 3 weels, and we know that there are 20 boxes and 48 wheels, then the system of equations is:
x + y = 20
2x + 3y = 48
To solve the system graphically we just need to graph both lines on the same coordinate axis and see at which point do the lines intersect, the graph is below.
The solution is x = 12, y = 8.
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(-8,-4), (-1, -3), and (0, -2).
How do I graph this ?
Answers
Answer:
Refer to photo for drawing
Step-by-step explanation:
1. Draw the x y plane
2. Identify -8, -1, 0 on x plane
3. Identify -4, -3, -2 on y plane
4. Mark the intersection point (-8,-4) with x
5. Mark the intersection point (-1,-3) with x
6. Mark the intersection point (0,-2) with x
7. Draw a straight line through the x mark
I need help with this please.
(50 POINTS)
Answers
Answer: ( -2, -3 )
Step-by-step explanation:
PLEASE HELP ASAP!! PLEAZE 20 PIINTS
Answers
a^2-2ab+b^2=(a-b)^2
what is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time?
Answers
Using the concepts of probability, we got that 0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time
We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.
Here, we are rolling a 6-faced dice.
Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.
So, every number has equal probability to come on the top face, therefore the probability of getting 3 on the top face of dice is (1/6)
Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.
Now, picking one marble from 17 marble is can be done in [tex]^1^7C_1[/tex] ways, similarly choosing 1 blue marble from 6 marble can be done in [tex]^6C_1[/tex] ways.
So, probability of picking 1 blue marble randomly=6/17
Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063
Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063
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During a race, all members of a rowing team should keep the oars parallel to produce maximum speed. Let m∠1 = 6x + 18 and m∠2 = 9x +12, and x = 10.
What type of angle pair are angles 1 and 2? (3 points)
Find the measure of angles 1 and 2. Show your steps. (4 points)
Are the oars parallel? Which theorem would be used to prove that the oars are parallel? (3 points)
Answers
∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.
What are consecutive angles?A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.
Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and
m∠2 = 9x+12, and x = 10.
Putting the value of x, we get,
m∠1 = 6x + 18 = 6*10 + 18 = 78°
m∠2 = 9x+12 = 9*10 + 12 = 102°
m∠1 + m∠2 = 180°
Therefore, ∠1 and ∠2 are consecutive angles pairs.
We can prove that oars are parallel by converse of consecutive angles theorem.
Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel
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