m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°;
Bisector BD bisects ∠ABC.
∠ABD= (8x+35)°, ∠CBD= (11x+23)°.
As given, bisector BD bisects the angle ABC so this means, the angle ABC is divided into two halves.
So,
angle ABD= angle CBD.
and ∠ABD= (8x + 35)° (i)
∠CBD= (11x + 23)° (ii)
So,
(8x + 35)° = (11x + 23)°
On solving the above equation, we have
3x= 12
x= 4.
Putting x=4 in (i) we have,
∠ABD= 8(4) + 35
∠ABD= 67°
As ∠ABD = ∠CBD, we have
∠CBD= 67°
Now,
∠ABC= ∠ABD + ∠CBD
∠ABC= 67° + 67°
∠ABC= 134°.
Hence, m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.
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3z+6+4z+9+8u combine like terms
Answer:
8u + 7z + 15
Step-by-step explanation:
Let's solve the problem,
→ 3z + 6 + 4z + 9 + 8u
→ 8u + (3z + 4z) + (6 + 9)
→ 8u + 7z + 15
Thus, solution is 8u + 7z + 15.
Answer:
8u±7z±15
Step-by-step explanation:
3z±6±4z±9±8u
8u±3z±4z±9±6
8u±7z±15
Hope its helpful for you
The length of a rectangle is 6 meters shorter than 4 times its width. The area of the rectangle is 238 square meters. How long and wide is the rectangle?
The width and length of the rectangle given its area is 8.5 meters and 28 meters respectively.
Area of rectangleLength of the rectangle = (4w - 6) metersWidth of the rectangle = wArea of rectangle = 238 square metersArea of a rectangle = Length × width
Substitute the parameters238 = (4w - 6) × w
238 = 4w² - 6w
Change to quadratic equation4w² - 6w - 238 = 0
Using quadratic formulaa = 4
b = -6
c = -238
w = -b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(4)(-238) / 2(4)
= 6 ± √36 - (-3808) / 8
= 6 ± √36 + 3808 / 8
= 6 ± √3844 / 8
= 6 ± 62 / 8
= 68/8 or -56/8
w = 8.5 or -7
The value of w can not be negativeSo,
w = 8.5 meters
Recall,
Length of the rectangle = (4w - 6) meters
= 4(8.5) - 6
= 34 - 6
= 28 meters
Therefore, the width and length of the rectangle given its area is 8.5 meters and 28 meters respectively.
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2(2x - 5) = 3x + x - 2x What is the solution of the equation? X =
Answer:
Step-by-step explanation:
2(2x-5)=3x+x-2x
4x-10=3x+x-2x
4x-10=2x
4x-10+10=2x+10
4x=2x+10
2x=10
2/2
10/2=5
x=5
The solution to the equation 2(2x-5) = 3x + x - 2x is x = 5
Given data:
To solve the equation 2(2x - 5) = 3x + x - 2x, we will simplify and solve for x.
Step 1: Distribute the 2 to the terms inside the parentheses:
4x - 10 = 3x + x - 2x
Step 2: Combine like terms on both sides of the equation:
4x - 10 = 2x
Step 3: Subtract 2x from both sides to isolate the variable x:
4x - 2x - 10 = 0
Simplifying:
2x - 10 = 0
Step 4: Add 10 to both sides to eliminate the -10 term on the left side:
2x - 10 + 10 = 0 + 10
Simplifying:
2x = 10
Step 5: Divide both sides by 2 to solve for x:
(2x)/2 = 10/2
Simplifying:
x = 5
Hence, the solution is x = 5.
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According to the bar chart, Alphabet's revenue in 2011 was 37,905 million dollars. Write Alphabet's 2011
revenue in ordinary notation.
thirty-seven billion nine hundred five million
Answer:
hskekndndndokn jskjskiwijsnjskjskiwijsn kkskskskjd kdkdkdndndn
Step-by-step explanation:
Thunder from a bolt of lightning travels 1/10 mile in 1/2 second. At this rate, how many miles can it travel in one second?
Answer:
1/5 mile
Step-by-step explanation:
1/10 mile in 1/2 second
This can be written as a ratio:
1/10 mile : 1/2 second
We need the ratio in terms of 1 second, so multiply both numbers in the ratio be 2.
2 × 1/10 mile : 2 × 1/2 second =
= 2/10 mile : 1 second
= 1/5 mile : 1 second
Answer: 1/5 mile
Write a rule to describe each transformation.
Transfomation using X and Y co-odrinate points
K(-3,2) , L(-4,3), M(-3,3), N(-1,2) → K'(0,2) , L'(-1,3) , M'(0,3), N'(2,2)
What is a transformation ?
Transformations of co-ordinates can be calculated by taking reference from the original figure to the transformed figure by adding or subtrating the point values depending upon where they have transformed in X and Y co-ordinate.
In the given figure there are 4 points K,L,M,N and they have been transformed to K', L',M',N' each point having X and Y co-ordinate values.
K has moved 3 units right so 0
L has moved 3 units right so -1
M has moved 3 units right so 0
N has moved 3 units right so 2
K(-3,2) , L(-4,3), M(-3,3), N(-1,2) → K'(0,2) , L'(-1,3) , M'(0,3), N'(2,2)
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f is the function (x)-2x+5.
(a) Find (3)
(6) Express the inverse function f' in the form f'(x)-
g is the function g(x)-²-25.
(c) Find g(-3).
(d) (1) Find gfx)
r'(x)-
Give your answer as simply as possible.
(ii) Solve g(x)-0.
gf(x) -
(1)
8
e
(5)
The given functions can be solved using composition functions.
What is a composition function?Function composition is a mathematical procedure where two functions, f and g, are taken and a function, h = g f, is produced such that h(x) = g(f(x)). The function g is applied in this operation on the outcome of applying the function f to x.
function (x)-2x+5.
(a) f(3) = 2(3) + 5
= 11
(b) f'(x)
y = 2x + 5
y - 5 = 2x
x = y - 5 / 2
f'(x) = x - 5 / 2
g is the function g(x)-²-25.
(c) g(x)-²-25
g(-3) = (-3)² - 25
g(-3) = -16
(d) g(f(x)) = g(2x + 5)² - 25
= 4x² + 25 + 20x - 25
⇒ 4x² + 20x
r'(x) = 2x + 5
(ii) g(x) - 0
⇒ g(x)
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need an answer asap please
Answer:
the answer is A
that is 828263
The temperature fell 12 degrees over 4 hours. What was the average change in temperature per hour?
Expression:
Answer:
The average change is 3 degrees per hour.
To calculate the average of any data we have to divide the change by the time taken for that change.
let us suppose there is a data 4,5,6,7 and 8.
Average of the data will be the sum of data divided by the number of terms.
Average=[tex]\frac{4+5+6+7+8}{5}[/tex]
=[tex]\frac{30}{5}[/tex]
= 6
So now we will calculate the average change in temperature per hour,
Given that there is a fall of 12 degrees in 4 hours.
Average change per hour=[tex]\frac{12}{4}[/tex]
= 3 degrees per hour
So, the required change is 3 degrees per hour.
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what is the value of 10 to the power of -16 written as a fraction
Answer: 1e-16
Step-by-step explanation:
Steps
(x)n = (10)-16
=
1
10 x 10 x .... x 10
=
1
10000000000000000
= 1e-16
Camilo uses 32 ounces of filling to make empanadas de queso. He puts 8 empanadas on each of 3 trays. Write a fraction to show how many ounces of filling Camilo uses in each empanada.
Answer: The fraction that will show the number of ounces of filling Camilo uses is x = 32 ounces
Step-by-step explanation:
Calculation by using fractions method :
The number of ounces used is x = 32
The number of trays = 3
Number of empanadas on each tray = 8
Therefore, the total number of empanadas on the 3 trays
= 3×8
= 24
If x = empanadas
32 ounce = x
Therefore, the fraction that shows number of ounces of filling Camilo uses in each empanada is x = 32 ounces
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Which operations can be applied to a matrix in the process of Gaussian elimination?
a. replacing a row with the absolute values of that row
b. replacing a row with three times another row
c. replacing a row with twice that row
d. replacing a row with the sum of that row and another row.
e. swapping rows
(multiple answer are correct)
The following operations can be applied to a matrix during the Gauss Jordan elimination process:
(C) Replacing a row with twice the number of rows.(D) Substituting a row for the sum of that row and another row.(E) Row swapping.What is Gauss Jordan's elimination?Gaussian elimination, also known as row reduction in mathematics, is a method for solving systems of linear equations. It is made up of a series of operations performed on the corresponding coefficient matrix. This method can also be used to compute a matrix's rank, determinant of a square matrix, and inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777-1855), though some special cases of the method were known to Chinese mathematicians as early as 179 AD, albeit without proof.During the Gauss Jordan elimination process, the following operations can be applied to a matrix:
Replacing a row with twice the number of rowsSubstituting a row for the sum of that row and another row.Row swappingTherefore, the following operations can be applied to a matrix during the Gauss Jordan elimination process:
(C) Replacing a row with twice the number of rows.(D) Substituting a row for the sum of that row and another row.(E) Row swapping.Know more about Gauss Jordan's elimination here:
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what is the angle of depression zipline
Answer and Explanation:
The problem provides the following information:
Hypotenuse
=
h
y
p
=
5129
ft
Vertical drop
=
o
p
p
=
1275
ft
To find the angle of depression, the best trigonometric ratio to use is the sine ratio. After equating it with the ratio of the opposite side over the hypotenuse, get the inverse of the sine ratio as shown:
sin
θ
=
o
p
p
h
y
p
θ
=
sin
−
1
(
o
p
p
h
y
p
)
θ
=
sin
−
1
(
1275
ft
5129
ft
)
θ
=
sin
−
1
(
0.2485864691
)
θ
=
14.3938824691
≈
14.4
∘
The angle of depression is
14.4
Use the following information to write an equation in terms of X. Then solve the equation and find RS and RT.
RS = 2x - 8
ST = 11
RT = x + 10
equation:?
x=?
RS=
RT=
We get the values of RS and RT as 6 and 17 respectively after solving the equations.
We are given the equations:
RS = 2x - 8
ST = 11
RT = x + 10
Now, we know that:
RS + ST = RT.
Substituting the values, we get that:
2 x - 8 + 11 = x + 10
2 x + 3 = x + 10
2 x - x = 10 - 3
x = 7
Now substituting it to find RS and RT:
RS = 2 x - 8
RS = 2 ( 7 ) - 8
RS = 14 - 8
RS = 6
RT = x + 10
RT = 7 + 10
RT = 17
Therefore, we get the values of RS and RT as 6 and 17 respectively after solving the equations.
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3x + 6y = 9 solve for x
Answer:
x= -2y+3
Step-by-step explanation:
First move the variable to the right: 3x= 9-6y
Next divide both sides of the equation by 3: x=3-2y
Lastly reorder the numbers, the variable should be placed first: x= -2y+3
Simplify the given expression. Write your answer with positive exponents.
(x^-4/ y^3)^-7
Step-by-step explanation:
(x^-4 / y³)^-7 = x²⁸ / y^-21 = x²⁸ / 1/y²¹ = x²⁸y²¹
1.) (3+x)2-(3+x)=12
2.) 4x2+3(x+6)=0
3.) 2a(6a-8)+4=39
Answer:1. X=9
2. x
=
Step-by-step explanation:
Oliver threw the discus 43.82 feet. Jason threw the discus 50.02 feet. What is the difference between the two distances?
A 6 feet
B 6.2 feet
C 13.8 feet
D 16.02 feet
The difference between the distances thrown by Oliver and Jason while discus throwing is 6.2 feet.
The correct answer is Option B.
Given data:
Oliver threw the discus 43.82 feet.
Jason threw the discus 50.02 feet.
Oliver threw the discus a distance of 43.82 feet, while Jason's throw reached a distance of 50.02 feet. The difference is calculated by subtracting the shorter distance from the longer distance, resulting in 6.2 feet.
Difference = Longer distance - Shorter distance
Difference = 50.02 feet - 43.82 feet
On simplifying the equation:
Difference = 6.2 feet
This represents the variation in their performances, with Jason achieving a greater distance by 6.2 feet compared to Oliver's throw.
Hence, the difference is 6.2 feet.
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What is an equation of the line that passes through the points (6, -1) and (1, 4)?
Calculate (6.25×109) - (3.44 × 108)
Answer: 309.73
Step-by-step explanation:
decreasing order 67,567
Answer:
n2jnsjsns. sisjnenws jsjsjjejsnsbss
5.
Audrey gives each of her 6 closest friends a $20 gift card to their favorite store alono
with a small amount of cash during the holiday season. She spends the same amount of
money on each of her friends. If she spends $360 each year on holiday gifts for her
6 closest friends, how much cash does she give each friend?
1.
Define the variable.
3. Solve the equation.
Date
Period,
2. Write an equation that can be used to answer the question.
Explain the meaning of the solution.
Does the solution make sense for the problem? Why or why not?
Answer:
She gives 40 dollars to each friend.
The variable that you are trying to find is the amount of cash she gives to each friend. In the below equation, I call it x.
The equation is x = (360/6) - 20.
Step-by-step explanation:
1. Let the variable be x be the amount of cash Audrey gives to each friend.
2. The equation is 6x + 20 = 360.
3. The solutions is x = 57.
4. Audrey gives each friend $57 in cash along with a $20 gift card to their favorite store during the holiday season.
5. The solution does not entirely make sense for the problem because we cannot give fractional amounts of cash.
The solution should be rounded to the nearest dollar, making it $57 per friend.
We have,
1.
Let's define the variable "x" as the amount of cash Audrey gives to each of her 6 closest friends.
2.
Since Audrey spends the same amount of money on each friend, the equation can be written as:
6x + 20 = 360
3.
Solve the equation:
Subtract 20 from both sides to isolate the term with "x":
6x = 360 - 20
6x = 340
Now, divide both sides by 6 to solve for "x":
x = 340 / 6
x = 56.67 (rounded to two decimal places)
4.
The solution, x = 56.67, means that Audrey gives each of her 6 closest friends approximately $56.67 in cash along with a $20 gift card to their favorite store during the holiday season.
5.
The solution does not entirely make sense for the problem because we cannot give fractional amounts of cash.
In real-life situations, the cash given should be a whole dollar amount, not a fractional value like 56.67.
Therefore, the solution should be rounded to the nearest dollar, making it $57 per friend.
Thus,
1. Let the variable be x be the amount of cash Audrey gives to each friend.
2. The equation is 6x + 20 = 360.
3. The solutions is x = 57.
4. Audrey gives each friend $57 in cash along with a $20 gift card to their favorite store during the holiday season.
5. The solution does not entirely make sense for the problem because we cannot give fractional amounts of cash.
The solution should be rounded to the nearest dollar, making it $57 per friend.
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Ryan has nine 14-ounce bags of popcorn
to repackage and
sell at the school fair.
A small bag holds 3 ounces. How many
small bags can he make?
group of 280 elementary school students and 40 adults are going on a field trip. They are planning to use two different types of buses to get to the destination. The first type of bus holds 50 people and the second type of bus holds 56 people.
Andre says that 3 of the first type of bus and 3 of the second type of bus will hold all of the students and adults going on the field trip.
Is Andre correct?
Answer:
yes!!! because the first 3 types of bus can hold 50 people and the other 3 types of bus can hold 56 people so the total will be 320 people
If 4/15 of the candies in a bag of Skittles are red and 3/10 are yellow, what fraction of the bag are red and yellow?
The fraction of the bag that are red and yellow are [tex]\frac{17}{30}[/tex].
A fraction is a portion of a whole or, more roughly, any number of equal pieces. The word fraction comes from the Latin word fractus, which meaning "broken." When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size. Below (or after) that line, there is a non-zero denominator and a common, vulgar, or simple fraction. Uncommon fractions that use numerators and denominators include difficult fractions, compound fractions, and mixed numeral fractions.To calculate the total fraction of red and yellow candies in the bag of skittles we add the two fractions together.
To add the two fractions together but first rewrite the fractions with a common denominator;
[tex]\frac{4}{15} =\frac{8}{30}[/tex]
[tex]\frac{3}{10} =\frac{9}{30}[/tex]
[tex]\therefore\frac{8}{30} +\frac{9}{30} \\\\=\frac{17}{30}[/tex]
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Find least number which must subtracted from the following to make them perfect square
42029
Answer:
[tex] \sqrt[3 \\ ]8 + \sqrt{114} {?} [/tex]
A function, fx), represents the height of a plant x months after being planted. Students measure and record the height on a monthly basis.
Select the appropriate domain for this situation.
OA
the set of all integers
OB. the set of all positive real numbers
OC. the set of all positive integers.
OD. the set of all real numbers
Answer:
C. the set of all positive integers
Step-by-step explanation:
You want to know the appropriate domain of the function f(x) where x is months after a plant was planted, and f(x) is the height of the plant.
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. In this case, the independent variable is x, the number of months after the plant was planted. Months are counted using the natural numbers, the set of all positive integers.
The appropriate domain is the set of all positive integers.
__
Additional comment
As a practical matter, the domain will have an upper limit, so will not actually be all positive integers.
The range of function values is likely the set of positive real numbers, though it might be integers if the measurements are recorded as integer values (mm or cm or in, for example).
Evaluate the expression a•b for a =24 and b=8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{a\times b}}[/tex]
[tex]\mathsf{= 24\times8}[/tex]
[tex]\mathsf{= 192}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{192}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
1. Which is the first step in solving
x 4 = 4
Subtract 4 from both sides.
Add 4 to both sides.
Add 4 to the left side.
Subtract 4 from the left side.
Answer:
I think to solve for X you have to place like terms on the other side like:
x4 = 4
x=4 - 4 (4 becomes negative)
x=0
how many zeros will be in the product of 5 x 105 the 105 is the 10 of the power of 5
Answer: this equation has 5 zeroes.
Step-by-step explanation:
The number of zeroes in any number can be found by,
we have expression as
[tex]5*10^{5}[/tex]
now ;
10*10 has 2 zeroes;
10*10*10 has 3 zeroes;
similarly ;
this equation has 5 zeroes.
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Answer:
none
Step-by-step explanation: 105×5=525
