AJ is the bisector of ∠HJI. Determine the value of x.Question options:A) 22.5 B) 10 C) 12 D) 2.5
Answers
From the Angle bisector Theorem we have:
\(\frac{A}{B}=\frac{X}{Y}\)Substituting the given values, we have:
\(\begin{gathered} \frac{15}{8}=\frac{3x}{4} \\ \\ 4\times15=8\times3x\to60=24x \\ x=\frac{60}{24}=2.5 \end{gathered}\)Answer is:
D) 2.5
Related Questions
In 3 to 5 sentences how can I describe weather or not files should be deleted from your computer. “quick I’m being timed”
Answers
For a variety of reasons, files on your computer shouldn't be destroyed. One, you might have to keep them since your work is crucial. Two, I should have them just in case.
Describe a computer.A computers is a piece of electrical equipment used to manipulate data or information. It has the ability to store, retrieve, and process data.You may already be aware of the fact you are able to use a computers to surf the Internet, send emails, type documents, and play games.
What makes it a computer?Modern computers are given their names after the jobs that they replaced. The term "computer" was first used in the English language in the 17th century to refer to a person who performed mathematical computations. It made its first mention of a calculator in 1897. The "human" computer is now outdated in the age of the "machine."
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You have a bag of marbles that has 3 blue marbles and 4 red ones. What is the chance that you pick a blue OR a red marble?
Answers
Answer:
7/7
Step-by-step explanation:
Add up the amount of the marbles in total and read what color the marble they ask for the chances of. The color of marble should go first then the total of the marbles. (they could ask for more than one color so just add up both the colors given.)
The Boolean expression
A >= B
is equivalent to which of the following expressions?
(A) !(A < B)
(B) !(B >= A)
(C) !(A <= B)
(D) A != B
(E) B >= A
Answers
The Boolean expression A >= B is equivalent to !(A < B) (option A)
To simplify a Boolean expression, use De Morgan's Law.
De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.
The principle is:
NOT (A AND B) is equivalent to (NOT A) OR (NOT B)
NOT (A OR B) is equivalent to (NOT A) AND (NOT B)
When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.
! is the symbol of negation or NOT.
Hence,
! (>) becomes <=
! (<) becomes >=
Here are some examples:
!(A > B) is equivalent to (A <= B)
!(A <= B) is equivalent to (A > B)
!(A >= B) is equivalent to (A < B)
!(A == B) is equivalent to (A != B)
!(A != B) is equivalent to (A == B)
!(A < B) is equivalent to (A >= B)
From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)
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Find the product
3(z+4)(x-5)
Answers
Answer:
3zx-15z+12x-60
Step-by-step explanation:
first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20
then distribute the 3 to get the answer
Question 3:
Hank is throwing a party. The party costs $20 per person. Answer the questions below to describe the relationship between the cost of the party and the number of friends attending.
The independent variable is .
The dependent variable is .
The equation that can be used to represent this relationship:
If 50 people attended, what would be Hank's cost?
(Only input numeric values, no commas, decimal points, or symbols.)
Answers
Answer:
$1000
Step-by-step explanation:
It would be $1000 in total of all the people attending the party. This is because, you need to multiply, 50 and 20! The answer will be 1000.
Raphael paid 1120 for a camera during a 30% off sale what was the camera regular price ?
Answers
the regular price was "x", which is the 100%.
we also know that Raphael paid 1120 for it and that that is 30% off, namely 100% - 30% = 70%, so 1120 is really the 70% from the original price, so.
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 1120&70 \end{array}\implies \cfrac{x}{1120}=\cfrac{100}{70}\implies \cfrac{x}{1120}=\cfrac{10}{7} \\\\\\ 7x=11200\implies x=\cfrac{11200}{7}\implies x=1600\)
circles of radii , and are mutually externally tangent, where and are relatively prime positive integers. find
Answers
The ratio of the areas of the two circles equals the square of the ratio of their radii: = 1/4
Let O1 be the center of the larger circle and O2 be the center of the smaller circle. T is the tangent point between the two circles.
The distance between their centers, O1O2, is equal to the sum of their radii, i.e., r1 + r2.
The Pythagorean theorem gives us:
(O1O2)^2 = r1^2 + r2^2
By substituting r1, r2, and O1O2 values, we obtain:
(r1 + r2)^2 = r1^2 + r2^2
By broadening and simplifying, we get:
2r1r2 = r2^2
When both sides are divided by r22, we get:
2r1/r2 = 1
So, r1/r2 = 1/2. r2 = 2r1.
The ratio of the areas of the two circles equals the square of the ratio of their radii:
A1/A2 = (r1/r2)^2 = 1/4
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A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4
What is the sample space for this compound event?
{H, T, 1, 2, 3, 4}
{H1, T1, H4, T4}
{HT1, HT2, HT3, HT4}
{H1, T1, H2, T2, H3, T3, H4, T4}
Answers
Answer:
The answer is the longest one <3
Step-by-step explanation:
I took the test:
If the coin is tossed and a card is chosen from 1 to 4, then the total sample will be 8. Then the correct option is D.
What is a sample?A sample is a collection of well-defined elements. A sample is represented by a capital letter symbol and the number of elements in the finite set is shown as a curly bracket {..}.
A student tosses a coin and then draws a card from a stack of 4 cards labeled 1 through 4.
Then the total number of the sample will be
Total sample = 2 × 4
Total sample = 8
Then the sample is given below.
\(\rm Sample = \begin{Bmatrix}(H,1) & (H,2) & (H,3) & (H,4) \\\\(T,1) & (T,2) & (T,3) & (T,4) \\\end{Bmatrix}\)
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Need Help You Can Get 35 point!!!
The width of a rectangular field is represented by x meters. The length of the field is 10 more than twice its width . The area of the field is 5500m^2
Part A
Write an equation that can be used to determine the dimensions, in meters, of the field.
Part B
What is the width, in meters, of the field?
The width is ( ) meters.
Answers
Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x
Part B: width is 50 meters.
How to determine the valueThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that the variables are expressed as;
A is the areal is the lengthw is the widthWe then have that;
l = 2x + 10
Substitute the values
5500 = (2x + 10)(x)
expand the bracket
5500 = 2x² + 10x
2x² + 10x - 5500
x² + 5x - 2750
x² + 55x - 50x - 2750
x(x + 55) - 50(x + 55)
x = 50 meters
Length = 2(50) + 10
Length = 100 + 10 = 110 meters
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A local dry-cleaning company bought new equipment and its estimated useful life is 4 years. Using the straight-line depreciation method, what is the rate of depreciation each year?
Answers
Answer:
$2,500 or 25%
Step-by-step explanation:
Let's use the same example:
Cost of Equipment = $10,000
Useful Life = 4 years
Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100
Annual Depreciation = Cost of Equipment / Useful Life
Annual Depreciation = $10,000 / 4 years
Annual Depreciation = $2,500
Depreciation Rate = ($2,500 / $10,000) * 100
Depreciation Rate = 0.25 * 100
Depreciation Rate = 25%
The diagram represents two statements: p and q.
Which represents region B?
р v q
p —> q
p ^ q
q —> p
Answers
Answer:
p v q
Step-by-step explanation:
Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?
Answers
Answer:
4b mod 12 = 4
Step-by-step explanation:
Since b mod 12 = 7, it implies that there is an integer, m such that
b = 12m + 7.
We desire to find 4b mod 12
So, multiplying b by 4, we have
4b = 4(12m + 7)
4b = 4 × 12 m + 4 × 7
4b = 4 × 12 m + 28
4b = 4 × 12 m + 24 + 4
4b = 4 × 12 m + 12 × 2 + 4
Factorizing 12 out, we have
4b = 12(4m + 2) + 4
Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.
comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,
q = 4m + 2 and r = 4
So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.
In this exercise we have to calculate the value of the unknown, so we have:
the value is 4
we know that the equation will be given as:
\(b = 12m + 7\\\)
we need to multiply both sides by 4 to become another known equation, like this:
\(4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4\)
So factoring this equation we will find that:
\(4b = 12(4m + 2) + 4\)
Thus, when making a comparison between the two equations, we have that:
\(4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4\)
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orthogonal projection onto plane 1 point possible (graded) find an expression for the orthogonal projection of a point onto a plane that is characterized by and . write your answer in terms of , and . (enter theta 0 for the offset . enter norm(theta) for the norm of a vector . use * to denote the dot product of two vectors, e.g. enter v*w for the dot product of the vectors and . )
Answers
This is the expression for the orthogonal projection of v onto the plane P characterized by θ and θ_0 is, proj_P(v) = [v₁ - (v₁ cos(θ) + v₂ sin(θ)) cos(θ), v₂ - (v₁ cos(θ) + v₂ sin(θ)) sin(θ)]
Let's assume that the plane P is given by the normal vector n = [cos(θ), sin(θ)], and a point on the plane is given by r = [cos(θ_0), sin(θ_0)].
To find the orthogonal projection of a point v onto P, we need to find the component of v that lies in the direction of the normal vector n, and then subtract that component from v. This can be done using the dot product of v and n:
proj_n(v) = (v · n) / ||n||^2 × n
where · denotes the dot product, ||n|| is the length of n, and proj_n(v) is the projection of v onto n.
To find the projection of v onto P, we need to subtract the projection of v onto n from v:
proj_P(v) = v - proj_n(v)
= v - (v · n) / ||n||^2 × n
Substituting the expressions for n and θ, we get:
proj_P(v) = v - (v · [cos(θ), sin(θ)]) / (cos^2(θ) + sin^2(θ)) × [cos(θ), sin(θ)]
= v - (v₁ cos(θ) + v₂ sin(θ)) / (cos^2(θ) + sin^2(θ)) × [cos(θ), sin(θ)]
= v - (v₁ cos(θ) + v₂ sin(θ)) / 1 × [cos(θ), sin(θ)]
= [v₁ - (v₁ cos(θ) + v₂ sin(θ)) cos(θ), v₂ - (v₁ cos(θ) + v₂ sin(θ)) sin(θ)]
where v₁ and v₂ are the components of v in the x and y directions, respectively. This is the expression for the orthogonal projection of v onto the plane P characterized by θ and θ_0.
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The given question is incomplete, the complete question is:
Find an expression for the orthogonal projection of a point v onto a plane P that is characterized by θ and θ_0. Write your answer in terms of v, θ and θ_0
a. In the diagram above, angles ABCABC and CBDCBD are
, and their measures sum to
degrees.
b. The measure of \angle ABC∠ABC is
degrees.
Show your work in the box below.
Answers
Answer:
Step-by-step explanation:
..
los conjuntos numericos se relacionan entre si, los irracionales son caso aparte de los conjuntos numericos, cual sera la razon por lo que esto sucede?
Answers
Answer:
Los conjuntos numéricos que se relacionan entre sí son:
Naturales, enteros y racionales.
Los números naturales son aquellos números que se pueden escribir como sumas de 1.
Los números enteros son todos los números naturales, y agregamos el número cero y los números negativos.
Los números racionales son aquellos números que se escriben como cociente de dos números enteros. Acá también podés notar que:
7 = 7/1
entonces todo número entero se puede escribir como el cociente de dos enteros, lo que implica que el conjunto de los números racionales también engloba al conjunto de los enteros.
Entonces si N es el conjunto de los números naturales, Z es el conjunto de los números enteros, y Q es el conjunto de los números racionales, tenemos que:
N ⊂ Z ⊂ Q.
Ahora por otro lado, el conjunto de los números irracionales es aquel que no se puede escribir como cociente de dos números enteros. Con esto ya podemos concluir que no existe ningún elemento compartido entre ninguno de los conjuntos anteriores y este conjunto, y esto se debe a la definición de número irracional, como no se puede construir como el cociente de números enteros, entonces no hay forma de relacionarlo con ninguno de los otros conjuntos.
A figure has been dilated from center O by a scale factor of r = 3/10 scale factor would magnify the dilated figure back to the original size?
Answers
Answer: The new scale factor needs to be 10/3
Explanation:
Consider a line segment that is 10 units long. Apply the scale factor 3/10 to it, and now it's 3 units long because (3/10)*10 = 3.
To get it back to 10 units, we multiply by the scale factor 10/3 which is the reciprocal of the original scale factor. Note that (3/10)*(10/3) = 1. Those two scale factors multiply to 1 to indicate no change has been made overall.
A park has grass and sand. Find the area of the part with grass.
(Sides meet at right angles.)
Answers
Answer:
area of park with grass is 19cm^2
Step-by-step explanation:
area of park
= 5 ✖ 5
= 25cm^2
area of part with sand
= 2 ✖ 3
= 6cm^2
area of park with grass
= 25 - 6
= 19cm^2
Given m| n, find the value of x.
Answers
Answer:
45°
Step-by-step explanation:
x° = (180 - 135)°
= 45°
Hope this helps
With interior alternate angles and adjacent angles concept, the value of x from the given parallel lines is 45°.
Given that, straight line m parallel to straight line n and t is the transversal.
When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.
Here, y=135° (Interior alternate angles are equal)
Now, y°+x°=180° (Adjacent angles on straight line)
135°+x°=180°
x°=45°
Therefore, the value of x from the given parallel lines is 45°.
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A motor oil retailer needs to fill 40 one quart bottles, and he has two tanks: one that contains 12 gallons of oil and one that contains 2 gallons of oil. Which will he need to fill the bottles?
Answers
Answer:12 gallons
Step-by-step explanation: It is enough to fill 40
The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
A motor oil retailer needs to fill 40 one-quart bottles.
We know that in 1 gallon, there are 4 quarts. Then the number of gallons in 40 quarts will be given as,
⇒ 40 / 4
⇒ 10 gallons
The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.
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Calculo de ángulos y valor de x
(240)
(4x-10)
(х410)
Answers
Answer:
240
Step-by-step explanation:
The number of muffins that a baker makes each day is 40% of the total number of muffins she makes
Answers
Answer:
A) 90 muffins were baked Monday
B) 24 blue berry muffins were made Tuesday.
Step-by-step explanation:
A
40% for what number is 36
.4x = 36 Divide both sides by .4
x = 90
B
40% of 60 is what number?
.4 x 60 = 24
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Note: figure not drawn to scale.
Clay's oat barn has an air vent in the shape of a rectangular prism lengthwise through the barn. Clay is able to use the entire volume of the barn, except for the air vent, to store oats. He has decided to fill the barn to capacity to be prepared for the upcoming winter and planting season.
Clay called the Farmers CO-OP and ordered
cubic feet of oats.
Answers
The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
The actual dimensions of the patio are 20 feet by 16 feet.
The scale factor is 1 inch to 4 feet,
This means that 1 inch on the scale drawing represents 4 feet in reality.
So the dimensions of the scale drawing are:
20 feet x (1/4) = 5 inches (length on scale drawing)
16 feet x (1/4) = 4 inches (width on scale drawing)
The area of the actual patio is:
= 20 feet x 16 feet
= 320 square feet
The area of the scale drawing is:
= 5 inches x 4 inches
= 20 square inches
The ratio of the area of the scaled drawing to the actual area of the patio is: 20 square inches : 320 square feet
To simplify this ratio, we need to convert both values to the same units.
Converting the area of the scale drawing to square feet:
= 20 square inches x (1/144) square feet/square inch
= 0.1389 square feet
So the ratio of the area of the scaled drawing to the actual area of the patio is:
0.1389 square feet : 320 square feet
Or, in simplified form:
1 : 2306.56
Thus,
The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56
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please find the answer
Answers
Answer:
I hope this is correct but 8.5 or 8 1/2 Units
Answer:
i think it is 8 1/2.
Step-by-step explanation:
my reasoning is that because v=lwh. the length is 4 and hw is 2 1/8. so i multiplied those together.
Consider this function.
(r) = -3r + 3
Which graph represents the inverse of function ?
Answers
9514 1404 393
Answer:
C. graph Y
Step-by-step explanation:
Starting with f(r) = -3r +3, the inverse function can be found from ...
r = f(y)
r = -3y +3
r -3 = -3y
(r -3)/-3 = y
y = -1/3r +1
The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.
Walk 3 miles per hour to school which is 1 mile away.
Answers
Answer:1/3 hours
Step-by-step explanation:
3h=1
h=1/3
Answer:
20 minutes
Step-by-step explanation:
If you walk 3 miles per hour to a school that is 1 mile away you are getting there in 1/3 of an hour which is equivalent to 20 minutes.
A wire is 71cm long . you wish to cut it into two pieces. One piece is bent into shape of triangle with legs of equal length .The piece is to be bent into shape of circle .
Answers
To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)
The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)
The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)
Solving for\(\(x\),\) we divide both sides of the equation by 3:
\(\(x = \frac{71}{3}\).\)
Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.
The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:
\(\(x = 2\pi r\).\)
Substituting the value of x we found earlier, we have:
\(\(\frac{71}{3} = 2\pi r\).\)
Solving for r, we divide both sides of the equation by \(\(2\pi\):\)
\(\(r = \frac{71}{6\pi}\).\)
Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.
In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.
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What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction? m = –4 m = –2 m = 2 m = 4
Answers
The solution to the equation is mathematically given as
m=-2
This is further explained below.
What is the solution to the equation?Generally, the equation is mathematically given as
\(\frac{m}{m+4}+\frac{1}{4-m}=\frac{m^2}{m^2-16}\)
Where
The LCM of the denominators are
m^2-16=(m+4)(m-4)
Hence
\((m+4)(m-4)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=(m+4)(m-4) \cdot \frac{m^2}{m^2-16} \\\)
m(m-4)-4(m+4)=m^2
m^2-4 m-4 m-16=m^2
8 m=-16
m=-2
In conclusion, the solution to the equation is
m=-2
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Answer:m=-2
Step-by-step explanation:
just answered
-2 1/2 x -1 2/3 please add step by step
Answers
Hey there!
\(Answer: \boxed{4\frac{1}{6}}\)
\(Explanation:\)
Simplify to solve.
\(\boxed{4\frac{1}{6}\text{ is your answer.}}\)
Hope this helps!
\(\text{-TestedHyperr}\)
All six digits in the number are even one digit is used twice all other digits are used once the ones digit is 4 times the hundreds digit the tens digit id the difference of the ones digit and hundreds digit the same digit is in the tens place and hundreds thousands place the thousands digit is not zero
Answers
Answer:
rffrefr
Step-by-step explanation:
Cuánto es 35 entre 3
Answers
Forma exacta:
35/3
Forma decimal:
11.6¯
Forma de número mixto:
11 2/3