Kelvin should fasten each piece of wood approximately 7.1 from the corner.
What is the Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
a² + b² = c²
a = b
So,
2a² = c²
a² = 100/2
a = [tex]\sqrt{50}[/tex]
a = 7.1
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:: 3x + 3 = 2(x + 7)
Answer: x= 11
Step-by-step explanation:
Answer:
x=11
Step-by-step explanation:
im assuming u r trying to find x
you need to solve the bracket first (2×x =2x , 7×2= 14)
After that move numbers with x to ur left, to make life easier
3x-2x= x
14-3 = 11
x=11
Evaluate.
15÷(3+13)^2
Responses:
1 7/20
1 7/9
4 1/2
5 1/9
PLEASE HELP
Answer:
explain 15/256
PLEASEEEE HELPPP!!!!
If BC= 6x+6 , AB= 8x+9 , and AC=142 find BC
The value of BC is 60.6.
What exactly is the segment addition property?According to the segment addition postulate, if we have two locations on a line segment, A and C, a third point B lies on the line segment AC if and only if the lengths between the points match the requirements of the equation AB + BC = AC.
Given:
BC = 6x+6
AB = 8x+9
AC = 142
We need to find BC.
As AB and BC combine to form AC, we add them together and equate them with the value of AC to determine the value of x.
Using the property of segment addition,
AB + BC = AC
8x + 9 + 6x + 6 = 142
Combine the variable terms and constants together,
14x + 15 = 142
14x = 142 - 15 (Subtracting both sides by 15)
14x = 127
x = 9.1
Hence the value of BC is,
BC = 6x + 6 = 6(9.1) + 6 = 60.6
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What are the sum of all the factors of 50 which are between 1 and 50. A. 42B. 2550C. 92D. 15
Factors of 50 are the numbers which on dividing 50 leave no remainder. 50 is a composite number, therefore, it has more than 2 factors.
We can get the factors of 50 by Prime Factorization. We can draw a factor tree to get the prime factors of 50 as shown below:
Therefore, the prime factors are:
[tex]2,5,5[/tex]Hence, the other factors are:
[tex]\begin{gathered} 2\times5=10 \\ 5\times5=25 \end{gathered}[/tex]Therefore, the factors of 50, including 1 and 50, are:
[tex]1,2,5,10,25,50[/tex]The question asks to sum all the factors between 1 and 50. This means that 1 and 50 are not included in the sum.
Therefore, the sum will be:
[tex]\Rightarrow2+5+10+25=42[/tex]The correct option is OPTION A.
Ben orders t-shirts for $8.00 per t-shirt. There is a $6.00 flat fee for shipping. He only has $50.00 to spend. How many t-shirts can he
buy?
PLEASE PLEASE HELP RN 20 POINTS ADDED
Answer: The answer is 5 shirts
Step-by-step explanation:
8x + 6 = 50
subtract 6 from each side:
8x +6 (-6) = 50 (-6)
8x=44
divide by 8:
8x/8=44/8
x=5.5
round to single shirts:
x=5 shirts
Answer:
Step-by-step explanation: you have to divide 50 by 8 then get your answer of 6.25, but you also have to consider two things; the extra $6.00 flat fee, and you cant buy 6.25 shirts, so what we do is multiply 8 times 6 to get 48, but we have to consider the extra $6.00, so you take away 8 which gives you 5 shirts, plus the shipping fee so in all he can buy 5 shirts.
Change 36 inches into feet given the fact that 1 foot = 12 inches.
===============================================
Work Shown:
1 foot = 12 inches
3*1 foot = 3*12 inches
3 feet = 36 inches
I multiplied both sides by 3 so that the "12" turns into "36".
Answer:3 feet
36/12=3
3x12=36
so 36 inches= 3 feet
hope it helps
how many ways can you make a 5 digit password that can be any number (including zero) or letter (not case sensitive)? 916132832
These work out to 60,466,176 case insensitive combinations of letters.
There are 10 digits 0–9.
The are 26 letters in the modern alphabets.
However, you didn’t specify whether capital and lowercase letters count as the same letter or separate. In the former case, there are 26 letters, in the latter, there are 52.
There is also such a thing as lowercase numbers, but since they aren’t in common standard usage, I won’t count those.
You also didn’t specify that characters couldn’t be repeated, so I am going to assume that the same character can appear multiple times in a 5 character combination.
Also, since the combinations are an alphanumeric string of characters rather than a number, I will assume that leading zeroes are allowed.
So, there are either 36 (10 digits and 26 letters).
To find the number of combinations you multiply the number of possibilities for each character;
36 x 36 x 36 x 36 x 36
These work out to 60,466,176 case insensitive combinations of letters.
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SSS stands for ___ Congruence Postulate ( will mark Brainliest )
Answer:
I believe it stands for Side, Side, Side
Step-by-step explanation:
When two triangles with all three sides are equal they're SSS
using a calculator,find the value of each mathematical statement.
PLSSS HELP
The exponents are solved below\
What are exponents?
Exponentiation is a mathematical process denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, more succinctly, "b to nth." In other words, when a base raised to one exponent is multiplied by the same base raised to another exponent, the exponents accumulate.
The exponents are solved as follows
(10⁻²)⁹ = 10⁻¹⁸ = 1/10¹⁸
10⁻³ - 10⁻⁸ = 1/10³ - 1/10⁸ = (10⁵ - 10⁸)/10⁸ = 9.9999x10⁻⁴
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mark has 5 pants and 7 shirts in his closet. he wants to wear a different pant/shirt combination each day without buying new clothes for as long as he can. how many weeks can he do this for?
Mark has 35 unique combinations to choose from, so can he co go 5 weeks with this set of clothes
Number of pants in Mark's closet = 5
Number of shirts in Mark's closet = 7
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
He can choose amongst the pants in 5 ways, similarly, he can choose among the shirts in 7 ways
Total number of combinations = 5*7 = 35 unique combinations
So, if he wears one combination each day he can last 35 days or 5 weeks, without buying new clothes
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Write a two-column proof
The angles ∠4 and ∠6 are found to be supplement angles.
What are termed as the supplement angles?Supplementary angles are the ones that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°. Complementary angles, on the other hand, add up to 90 degrees. When the 2 supplementary angles are joined together, they create both a straight line and an angle.It should be noted, however, that the two supplementary angles are not required to be adjacent to each other. As a result, any two angles could be supplementary if their total amount is equal to 180°.For the given question;
∠5 ≅ ∠6 ( both are congruent means equal)
As, ∠4 and ∠5 are forming on the straight line. Thus,
∠4 + ∠5 = 180 (linear pair)
But, ∠5 ≅ ∠6 , replacing ∠5 with ∠6 .
∠4 + ∠6 = 180 supplement angles.
Thus, ∠4 and ∠6 are found to be supplement angles.
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Identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutiveinterior, vertical, or adjacent. Explain step-by-step
Given: Pair of parallel lines and a transversal with angles x and y.
Required: To determine which type of angles are formed by x and y.
Explanation: Consider the following figure below showing a pair of parallel lines and a transversal
In the figure, line l is parallel to line m, and line n is the transversal.
Further alternate angles are the pair:
[tex](\angle1&\angle8),(\angle2&\angle7),(\angle3&\angle6),(\angle4&\angle5)_[/tex]The angles lying inside the parallel lines are alternate interior, while the angles lying outside the parallel lines are the alternate exterior.
While the corresponding angles are the pair:
[tex](\angle2&\angle6),(\angle1&\angle5),(\angle3&\angle7),(\angle4&\angle8)[/tex]Finally, the consecutive interior angles are the pair of non-adjacent angles that lie on the same side of the transversal. In the figure above, the consecutive interior angles are:
[tex](\angle4&\angle6),(\angle3&\angle5)[/tex]Hence the given pair of angles x and y are consecutive interior angles.
Final Answer: Option D is correct.
Terms from two sequences are given in tables below. Which of the following statements are true? Select all that apply.
As per the terms from the two sequences given in tables as attachment hereby along with the question statement, the following statements from the provided options are true.
(i) [(a₁) > (g₂)]
(iv) Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ).
As per the question statement and the reference tables attached thereby along with the question, we are provided with terms from the two sequences in table format, and five statements based on the sequences.
We are required to determine which statements among the five, are true.
To solve this question, we will use the trial-and-error method, where we will consider individual statement and assess it's honesty.
First statement is [(a₁) > (g₂)], which is true. As we can see from the table, that, [(a₁) = 10] and [(g₂) = 4], i.e., (10 > 4), or, [(a₁) > (g₂)].
Second statement is that, "The constant difference for (aₙ) is 10" which is False. We can clearly see from the table that, (a₁ = 10), (a₂ = 15), (a₃ = 20), (a₄ = 25) and so on, and [(25 - 20) = (20 - 15) = (15 - 10) = 5], i.e.,
[(a₄ - a₃) = (a₃ - a₂) = (a₂ - a₁) = 5]. Hence, the common difference for (aₙ) is 5, and not 10.
Third statement is that, "(aₙ) can be modelled by a linear function, and (gₙ) can be modelled by an exponential function" which is true for the first part, but false for the second, making the complete statement false as whole.
From the left hand side table, we can see that, (a₂ = 15) and (a₁ = 10),
Or, [a₂ = (10 + 5)]
Or, [a₂ = (a₁ + 5)]
Similarly, (a₃ = 20),
Or, [a₃ = (15 + 5)]
Or, [a₃ = (a₂ + 5)]
That is, we can generalise (aₙ) as
[aₙ = {(aₙ₋₁) + 5}] where, (n = 2, 3, 4, 5...) and (a₁ = 10).
Hence, (aₙ) can be modelled by a linear function.
But from the right hand side table, we can see that, (g₂ = 4) and (g₁ = 2),
Or, [g₂ = (2 * 2)]
Or, [g₂ = 2g₁]
Similarly, (g₃ = 8),
Or, [g3 = (2 * 4)]
Or, [g₃ = 2g₂], it goes on for (gₙ).
Therefore, we can generalise (gₙ) as
[gₙ = 2*(gₙ₋₁)] where, (n = 2, 3, 4, 5...) and (g₁ = 2).
Here, (gₙ) can also modelled as a linear function and not as a exponential function (which goes in the form of "xⁿ").
Coming to the fourth statement, "Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ)" is true, as from both the tables,
For (n = 5), [aₙ = a₅ = (a₄ + 5) = (25 + 5) = 30],
And [gₙ = g₅ = (2 * g₄) = (2 * 16) = 32], which is greater than 30,
Or, [(g₅) > (a₅)].
Similarly, for (n = 6), (a₆ = 35) while (g₆ = 64), i.e., [(g₆) > (a₆)], and it continues for greater values of "n".
Coming to the last statement, that [a₁₀ > g₆], is false. As we can observe from the both the tables and their sequence,
For (n = 5), (aₙ = 50), for (n = 6), (aₙ = 35), for (n = 7), (aₙ = 40), for (n = 8), (aₙ = 45), for (n = 9), (aₙ = 50) and for (n = 10), (aₙ = 55),
While on the other hand, for (n = 5), (gₙ = 32) and for (n = 6), (gₙ = 64).
Since (64 > 55), therefore, [(g₆) > (a₁₀)].
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The nurse is assessing a client’s lymphatic system. For which enlarged node should the nurse suspect that the client has a blockage within the right lymphatic duct?.
The enlarged node that the nurse should suspect that the client has a blockage within the right lymphatic duct is the right cervical node
What is the lymphatic system?A network of tissues, blood arteries, and organs called the lymphatic system collaborates to transport lymph, a colorless, watery fluid, back into your circulatory system. Every day, your body's arteries, smaller arteriole blood vessels, and capillaries circulate about 20 liters of plasma.
The right lymphatic duct receives drainage from the right cervical node. The thoracic duct receives drainage from the superficial popliteal, superficial inguinal, and lumbar nodes. The sides and back of the neck include the cervical lymph nodes.
Typically, these glands are incredibly tiny. A lymph node, however, is swollen if its diameter is higher than 1 centimeter. Deep inside the neck, the cervical lymph nodes are located.
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Is the following statement true or false? The cube root of zero is zero.
The statement that The cube root of zero is zero is true .
What is cube root ?The number that results in the original number after being multiplied three times is known as the cube root of a number.[tex]\sqrt[3]{}[/tex] The sign is used to represent a number's cube root in radical form.
The cube root of 0 will be calculated and explained here. First, observe that the mathematical symbol for the cube root of O is as follows:
[tex]\sqrt[3]{0}[/tex]
The number (n), which you can multiply twice by itself to get the number zero, is the cube root of zero. Alternatively, n×n×n should equal 0. Consequently, the following equation can be used to address the issue:
[tex]n^{3}[/tex] = 0
The answer to the cube root of 0 is as follows when the aforementioned equation is solved:
[tex]\sqrt[3]{0}[/tex]= 0
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2/5 y 6/15 son equivalentes?
To know if 2/5 and 6/15 are equivalent, we do a multiplication, then,
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times2}{5\times2}=\frac{4}{10} \ \ \longmapsto \ Not \ the \ result } \end{gathered}$} }[/tex]
Since if we try it with number 1, the result would be the same, then we continue with 2 being closer, then we continue with number 3, successively, until we reach the expected answer.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times3}{5\times3}=\frac{6}{15} } \end{gathered}$} }[/tex]
2/5 and 6/15 are equivalent?, The two fractions are equivalent, (True).can someone please help me solve this math problem with solution too?? TYY!!
Answer: 2080
Step-by-step explanation:
62² −42²
3844−42²
3844−1764
2080
PLS HELP ASAP THIS QUESTION IS REALLY EASY
Answer:
x = -1, y = -1
Step-by-step explanation:
[tex]4x + 3 = - 8x - 9[/tex]
[tex]12x + 3 = - 9[/tex]
[tex]12x = - 12[/tex]
[tex]x = - 1[/tex]
[tex]y = 4( - 1) + 3 = - 4 + 3 = - 1[/tex]
3 1/8 times 3 1/2 times 4/5
Answer: 8.75
Step-by-step explanation:
3 1/8 into a decimal is 3.125
3 1/2 into a decimal in 3.5 or 3.50
4/5 into a decimal is 0.8 or .8
Then just multiply 3.125 and 3.5 and you get 10.9375
Next, multiply 10.9375 by 0.8 and you get 8.75
Therefore your answer is 8.75
For questions 1-2, find the distance and midpoint of the segments given the endpoints. 1. AB with A(3, 4) and B(-1, 10) Midpoint
Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]then, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(3,4)=A \\ (x_2,y_2)=(-1,10)=B \\ \Rightarrow d(A,B)=\sqrt[]{(-1-3)^2+(10-4)^2}=\sqrt[]{4^2+6^2}=\sqrt[]{16+36}=\sqrt[]{52} \\ =\sqrt[]{4\cdot13}=2\cdot\sqrt[]{13} \\ d(A,B)=2\cdot\sqrt[]{13} \end{gathered}[/tex]Given equal probabilities of the birth of a xy or xx, what is the probability that a group of four siblings includes all xy? all xx? all xy or all xx?.
The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).
Let us first know how do chromosomes work?
Long DNA molecules called chromosomes contain all or a portion of an organism's genetic code. Males receive one X and one Y chromosome from each parent, whereas females receive two X chromosomes from each parent.
For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probaility of receiving one X chromosome and one Y chromosome is similarly 1/2.
Therefore, the probability that all XY siblings are present in a group of 4 siblings is:
[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]
Also the probability that a family of four siblings or offspring includes all XX is
[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]
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The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).
For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probability of receiving one X chromosome and one Y chromosome is similarly 1/2.
Therefore, the probability that all XY siblings are present in a group of 4 siblings is:
1/2*1/2*1/2*1/2=1/16
Also the probability that a family of four siblings or offspring includes all XX is
1/2*1/2*1/2*1/2=1/16
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A cyclists speed is 1.5 times faster than a walkers speed. they simultaneously start moving in the same direction from the same point and, after 1.5 hours, the distance between them is 12.5 miles. what are their speeds?
Answer:
The biker's pace is 25 miles per hour and the walker's speed is 50/3 miles per hour.
Answer:The speed of the walker is 16.67 miles per hour.
The speed of the cyclist is 25 miles per hour.
How to calculate the value?
Let the speed of a walker = x
Biker's speed = 1.5x
Their relative speed will be:
= 1.5x - x = 0.5x
Distance between them = 12.5 miles
Time taken = 1.5 hours.
It should be noted that distance will be:
= Speed × Time
12.5 = 1.5 × 0.5x
Divide through to get x
12.5 = 0.75x
x = 16.67 miles per hour.
Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.
let x denote the number of times harry potter manages to irritate professor snape in one day. let y denote the number of times ron weasley manages to irritate professor snape in one day. and let the joint probability mass function for (x, y) be given as
the probability that Ron will get in trouble with Professor Snape at least two times in one day is 0.7
We are given
X 0 1 2 3 4
P(X) 0.15 0.20 0.20 0.30 0.15
we want Ron Weasley to get in trouble at least two time in one day
that mean X 2
P(X 2) = P(X=2) + P(X=3) + P(X=4)
= 0.20+0.30+0.15
= 0.65= 0.7 (rounded to nearest tenth)
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4. last year nina invested $6,000. she put some of it in a cd the paid 4% simple interest, and she put the rest of it in a savings account that earned 2.5% simple interest. at the end of the year she earned a total of $204 interest. how much did she invest in each account? assume there were no other deposits or withdrawals.
She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
Here, we want to know the amount of money invested in each account
Let the amount invested in the 4% simple interest account be $x ----> (a)
While the amount invested in the 2.5% account be $y -------->(b)
So mathematically;
Both the interests are added to get total interest
x + y = 6,000 ••••••(i)
Let’s now evaluate the interest
for the 4% account , interest = 4/100 * x = 4x/100
For the 2.5% account, interest = 2.5/100 * y= 2.5y/100
The addition of both interests gives the total simple interest;
4x/100 + 2.5y/100 = 204
Multiply through by 100
4x + 2.5y = 20,400 •••••••(ii)
From i, x = 6,000 - y
Putting this into equation ii
4(6,000-y) + 2.5y = 20,400
24,000 - 4y + 2.5y = 20,400
24,000-20,400 = 4y - 2.5y
1.5y = 3,600
y = 3,600/1.5
y = $2,400
Recalling it again,
x = 6000 - y
x = 6,000 - 2,400
x = $3,600
Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
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Quadratic equation whose roots are -6 and 2 and whose leading coefficient is 2
Answer:
x² + 4x - 12
Step-by-step explanation:
Roots: -6 and 2
Leading coefficient: x²
(x + 6)(x - 2)
x(x - 2) + 6(x - 2)
x² - 2x + 6x - 12
x² + 4x - 12
I hope this helps!
Can anyone help me with this?
Answer:
13 sec
Step-by-step explanation:
Prius' acceleration
60 mi/hr = 88 ft s
accel = change in v / change in time = 88 f/s / 10.3 s = 8.54 ft / s^2
F = ma = 2903 * 8.54 = 24802 lb ft/s^2
Now increase the mass to 4903 by adding a 2000 lb trailer (which, by the way is way past the towing capacity of an anemic Prius !)
F = ma
24802 = 4903 a shows a = 5.06 ft/s^2
45 mi/hr = 66 ft/s
a = change in v / change in time
5.06 = 66 / 5.06 = 13 sec
Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece
of poster board and then folding up the sides. The volume V(x) in cubic inches of the
open-top box is a function of the side length x in inches of the square cutouts.
Write an expression for V(x).
what is the volume of the box when x=6
The expression for volume is (28-2x)(22-2x)x and when x=6, the volume is 840 inch^3.
What is volume?
A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. It means that the amount of space a closed form can occupy in three dimensions depends on its volume. Volume is a gauge of a thing's potential. For instance, a cup is said to have a 100 ml capacity if the brim can hold 100 ml of water. Another way to measure volume is the amount of space a three-dimensional item takes up.
According to question,
Let x be the height of the cubic box
Length = (28-2x)
Breadth = (22-2x)
Volume = x(28-x)(22-x)
When x =6
Volume = 6(28-6×2)(22-6×2)
=6(10)(14)
=840 inch^3
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what is an equation of the line that passes through the points (-4, 5) and (-4, -2)
Answer: no equation can pass through those points
Step-by-step explanation:
the x value -4 has two y values, 5 and -2. a function needs at most 1 y value to be considered a function.
can you help me with this? i got it wrong
1) Let's sketch this out so that we can better understand it
2) Reminding ourselves of the metric relations of a right triangle we can write out the following:
[tex]\begin{gathered} h^2=m\cdot n \\ YO^2=26\cdot12 \\ YO=\sqrt[]{312} \\ OZ=\sqrt[]{26.12} \\ OZ=\sqrt[]{312} \\ YZ=\sqrt[]{312}+\sqrt[]{312} \\ YZ=2\sqrt[]{312} \\ YZ=35.3 \end{gathered}[/tex]Note that the radius intersects that chord with a 90º angle so it bisects that chord.