The value of x will be 15 and the value of y will be 4.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.
x / ( x + 5 ) = 18 / ( 18 + 6 )
x / ( x + 5 ) = 18 / 24
24x = 18x + 90
6x = 90
x = 15
The value of y will be calculated by considering the two left-hand triangles.
12 / ( 12 + y) = 15 / 20
240 = 180 + 15y
15y = 60
y = 60 / 15
y = 4
Therefore, the value of x will be 15 and the value of y will be 4.
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15. Write the factored form of 9+24 by pulling out the GCF?*
There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.
What is GCF ?In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer
. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.
CalculationGCF by listing factor method :-
Factors of 9: 1, 3, 9
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.
other two methods are attached below .
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The sequence below is arithmetic. Complete parts (a) through (d) below.
- 1, 2, 5, 8, ...
(a) Find the common difference.
The common difference is d= . (Type a whole number.)
(b) Find the eighth term.
The eighth term is ag =
(Type a whole number.)
(c) Find a recursive rule for the nth term.
(Type an equation.)
(d) Find an explicit rule for the nth term.
(Type an equation.)
Answer:
see explanation
Step-by-step explanation:
- 1, 2, 5, 8
(a)
the common difference
d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3
(b)
to find a term in the sequence add d = 3 to the previous term
a₅ = = 8 + 3 = 11
a₆ = 11 + 3 = 14
a₇ = 14 + 3 = 17
a₈ = 17 + 3 = 20
(c)
the recursive rule is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 : a₁ = - 1
(d)
the explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 1 and d = 3 , then
[tex]a_{n}[/tex] = - 1 + 3(n - 1) = - 1 + 3n - 3 = 3n - 4
Monthly charge £16
150 free minutes then 13p per minute
150 free texts then 15p per text
during one month,Jo makes 170 calls and sends 182 texts
work out the total charge for the month
The total charge for the month is £625.36.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given:
Fixed monthly plan - 616
free minutes - 150
Used minutes - 170
Free text - 150
Used text - 182
Charging amount over the free limit - 18p
Number of minutes over the limit - 170 - 150 = 20
Number of text over the limit - 182 - 150 = 32
So the extra amount that will be added to the monthly charge would be -
(20 x 0.18) +(32 x 0.18)
The total charge of the month would be -
C= 616+(20*0.18) +(32*0.18)
C= 616+3.60+5.76
C= 625.36
Therefore, the total charge for the month is £625.36.
The correct question is given below,
Here are the monthly charges for Jo's mobile phone
Monthly charge 616
150 free minutes, then 18p per minute
150 free texts, then 18p per text
During one month, Jo makes 170 minutes of calls and sends 182 texts,
Work out the total charge for the month
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Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: m
The value of angle A and B are 60° and 120° respectively.
How to calculate the angles?It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.
Therefore A = D
B = C
When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:
ABK = 30°
Also, KBC = 90°
Therefore, B = 30° + 90° = 120°
A = D = 180° - 120° = 60°
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Complete question:
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: mA and mB.
I WILL MARK BRANLIEST FOR CORRECT ANSWER! The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who use a mobile device in a traditional class?
23%
37%
46%
72%
The joint relative frequency is 23%. So option (1) is correct.
Joint relative frequency is defined as the ratio of a frequency that is not in the total row or column to the total number of values or observations. The marginal frequency in a two-way frequency table is the entry in the "total" for the column and the "total" for the row.
Given data:
Traditional Online Row totals
Computer: 28 62 90
Mobile device: 46 64 110
Column totals: 74 126 200
The joint relative frequency can be found by the formula:
= (Number of students using a mobile device in traditional class / Total Number of students) x 100%
Number of students using mobile devices in traditional class = 46
Total number of students = 200
= (46 / 200) x 100%
= 0.23 x 100%
= 23 %
Therefore the joint relative frequency of students in traditional classes using a mobile device is 23%.
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What is the converse of the following conditional statement?
"If this month is September, then next month ends in the letter r."
Determine the validity of the converse and give a counterexample if the converse is not valid.
The converse statement is:
"If next month ends in the letter r, then this month is September."
And a counterexample of this is the month of September.
What is the converse of the conditional statement?A conditional statement is of the form:
If P, then Q.
And a converse statement of the above one will be:
if Q, then P.
Here our conditional statement is:
"If this month is September, then next month ends in the letter r."
So we have:
P = this month is September.
Q = The next month ends in the letter r.
Replacing that in the converse statement formula we get:
"If next month ends in the letter r, then this month is September."
A counterexample is September, it ends with an r, and the month after it is not September.
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Answer:
If next month ends in the letter r, then this month is September. The converse is invalid; a counterexample is December.
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Answer:
Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.
Step-by-step explanation:
Evaluate 2(x - 3) if x = 15
Answer:
24
Step-by-step explanation:
2(x-3)
2(15-3)
2(12)
24
Hopes this helps please mark brainliest
Answer:
24
Step-by-step explanation:
2(x - 3)
==> plug in x = 15
2(15 - 3)
==> subtract 3 from 15
2(12)
==> multiply 2 and 12
=24
Remember we evaluate using pemdas
Parenthesis
Exponents
Multiplication and Division (going left to right)
Addition and Subtraction (going left to right)
This is the order of operations we use to determine which operation we perform. Here we first used "parenthesis" and did all operations inside of the parenthesis. We then ended with multiplication
A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top. Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
A) What are the dimensions of the square to be cut from each corner?
B) What would the volume be of the open box?
Dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
What is Three dimensional shape?Three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top
Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
Let the cut squares will have side h then h is the height of the box and the two lengths are (25-2h) and (20-2h).
The dimensions of the box are (25-2h) and (20-2h)..
Volume of the box will be V=h(25-2h)(20-2h)
Hence, dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
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Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answer:
See below.
Step-by-step explanation:
Let the price of drinks be x and the price of candies be y.
Condition # 1:9x + 4y = 60 --------------------(1)
Condition # 2:10x + 2y = 57.50 --------------(2)
Multiply Eq. (2) by 22(10x + 2y) = 57.50*2
20x + 4y = 115 --------------(3)
Subtract Eq. (3) from (1)9x + 4y - 20x - 4y = 60 - 115
9x - 20x = -55
-11x = -55
11x = 55
Divide both sides by 11x = 55/11
x = $5Put x = 5 in Eq. (1)
9(5) + 4y = 60
45 + 4y = 60
Subtract 45 to both sides4y = 60 - 45
4y = 15
Divide both sides by 4y = 15/4
y = $3.75So, the cost of one drink is $5 and the cost of one candy is $3.75.
[tex]\rule[225]{225}{2}[/tex]
what is 15.0782 rounded to
the nearest 10
Reason:
The digit in the tens place is 1. Just to the right is 5, which tells us to bump the 15 up to 20.
We can say that 15.0872 is closer to 20, than it is to 10.
Be sure not to mix up "tens place" with "tenths place".
The round-off from the number 15.0782 to the nearest 10 will be 20.
What is rounding off to the number?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.
Given that the number is 15.0782. The round-off to the nearest 10 will be 20 for the number.
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Total revenue is determined by price
multiplied by output. What is the total
revenue for 95 goods each priced at
$8?
A. $760
B. $450
C. $930
Answer:
A. $760
Step-by-step explanation:
Price: $8
Amount of goods; 95
revenue = price x total units
$8 x 95 = $760 revenue
Click the two inequalities represented by the system of inequalities graph below.
The system of inequalities that best represent the shaded feasible region shown on the graph is
y < x + 1y < -x - 2How to determine the inequalities represented inequalities graphinformation gotten from the question include
inequality graph showing shaded regions
some interpretation on the information from the question include
shading below the is less thandotted lines mean the inequality do not have equal toThis interpretation removes the first and the last options since they contain the equal to sign
positive slope moves from bottom left to top right
y < x + 1
negative slope moves from top left to down right
y < -x - 2
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In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 64 degrees, angle QPR is equal to x, angle PRD is equal to 110 degrees.
A) The value of the measure of angle x is; x = 55 degrees.
B) The way we got x is that the Internal angle between 2 parallel lines are equal and also that the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.
What is the measure of the missing angles?A) From the given image attached, we see that the angle RPB can be calculated as;
m∠RPB = 180 - 120 = 60 degrees.
This is because sum of angles on a straight line sums up to 180 degrees.
Now, by definition of alternate angles, we can say that angle BPR is equal to 60 degrees.
Thus, the value of angle x is;
x = 180 - 60 - 65
x = 55 degrees.
B) From the given diagram, we can say that;
m ∠RPB + m < PRD = 180 degrees
This is because Internal angle between 2 parallel lines are equal.
Secondly the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.
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Answer both of um I'll mark you brainliest
Answer:
1) 71.83
2) 43
3) 41
4) 755.66
5) 458
6) 1757.12
7) 123 meters
The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 side touching. What is the total number of white cubes that were used to build the prism?
Answer:34?
Step-by-step explanation: not too sure but yeah
-2(7+3m) +6m>3 (3m-5)
Answer:
1/9 > m
Step-by-step explanation:
-2(7+3m)+6m>3(3m-5)
Distribute.
-14-6m+6m>9m-15
Combine like terms.
-14>9m-15
1>9m
Get m to be alone.
1/9>m
-2(7+3m) + 6m > 3(3m-5)
-2(3m+7) + 6m > 3(3m-5)
The final answer is m < 1/9
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Evaluate 3 (2x - 1).
Answer:
6x - 3
Step-by-step explanation:
3 ( 2x - 1 )
= 3 ( 2x ) - 3 ( 1 )
= 6x - 3
Answer:
x=1/2 or 0.5 or just 6x-3
Step-by-step explanation:
3(2x-1)
distribute.
6x-3
get 6x alone
6x=3
divide
x=3/6
x=1/2 or 0.5
-5(x + 1) - 9 = 2
help me this is algebra and i dont not look like dream *half moon emoji*
Answer:
-3.2
Step-by-step explanation:
-5(x+1)-9=2
first simplify by distributiom
-5(x)-5(1)-9=2
simplify the multiplication
-5x-5-9=2
add the numbers
-5x-14=2
now to get x by itself on one side we undo in reverse order and move the -14 over to the other side so add 14 to both sides to cancel the -14
-5x=2+14
simplify
-5x=16
now divide both sides by -5 to get x by itself
-5x/-5=16/-5
simplify
x=-3.2 or as a fraction, [tex]-\frac{16}{5}[/tex]
if he uses upper and lower control limits of 520 and 480 hours, what is the probability that a sample mean is out of control?( assuming the process standard deviation is known to be 20 hours)
0.0456 is the probability that a sample mean is out of control.
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.UCL = 520
LCL = 480
Mean (X ) = 500
Standard Deviation of sample (Sn) = 11.55
Z (for UCL) = (UCL - Mean)/Sn
Z (for UCL) = (520-500)/10
Z (for UCL) = 2
Z (for LCL) = (LCL - Mean)/Sn
Z (for LCL) = (480 - 500)/10
Z (for LCL) = -2
*Use Z table to find confidence level between Z value of -2 and 2.
Confidence level = 0.4772 + 0.4772
Confidence level = 0.9544
Risk (α ) = 1 - confidence level
Risk (α) = 1 - 0.9544
Risk (α) = 0.0456
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Mark and Janet together have 10 pairs of jeans.
Janet has 6 more pairs of jeans than John.
How many pairs of jeans does John have?
Answer:
John has 4 pair of jeans.
Hope this helps : )
Step-by-step explanation:
Together they 10, so if Janet has 6 more, we have to subtract.
10 - 6 = 4
Check:
6 + 4 = 10 ✔
Complete the function table. Function: p = 1⁄2w + 5
If y=8 when x=4, write the direct variation equation and find y when x=5
HELPP
A recipe calls for 6 ounces of raisins. How many milligrams of raisins is this? (1 ounce = 28.35 grams and 1 gram = 1,000 milligrams) 170.1 milligrams 1,701 milligrams 17,010 milligrams 170,100 milligrams
The measurement of a quantity requires units to be defined. The 6 ounce of raisins is equal to 171100 milligrams of it.
What is Measurement unit ?A measurement unit is unit to measure different quantities such as mass, length and time.
The measurement unit of one quantity can be converted into the other by multiplying it with a certain number.
Given that,
The amount of raisins is 6 ounces.
Since One ounce is equal to 23.85 grams,
6 ounce converted in grams equals 6 × 28.35 = 171. 10 grams
Now, 1 gram = 1000 milligrams.
Therefore, 171. 10 grams = 171.10 × 1000 milligrams
= 171100 milligrams.
Hence, 6 ounces of raisins is equivalent to 171100 milligrams.
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Answer:
A recipe calls for 170,100 milligrams of raisins.
Step-by-step explanation:
I took the exam and got it right
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located
1,-1), and Monique's desk is located at (-4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
O√7 feet
O√14 feet
√85 feet
O√61 feet
√14 feet, A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
What is coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of numbers, or coordinates, which are written as ((x,y)).
A coordinate can be expressed in one of three ways. a coordinate with an integer for degrees, a real number for minutes, and an integer for seconds (DMS). a coordinate that contains minutes (a real number) and degrees (an integer) (MinDec). a coordinate that merely contains degrees (real number).
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Point A is graphed on the coordinate plane. What ordered pair represents point A?
Answer:
-7,7
Step-by-step explanation:
a mixture of 3% disinfectant solution is to be made from 5% and 2% disinfectant solutions. how much of each solution should be used if 21 gallons of 3% solution are needed?
To make 21 gallons of 3% disinfectant solution, 7 gallons of 5% solution are used, and 14 gallons of 2% solution are used.
21 gallons of the 3% solution is required.
Therefore, the amount of disinfectant in the solution
= 3/100 X 21 gallons
= 0.63 gallons
Let the amount of 5% disinfectant solution used be x
Therefore,
the amount of 2% disinfectant solution used is (21 - x)
Now, the amount of disinfectant added through these solutions must be equal to the amount of disinfectant in the solution.
Hence,
5/100 X x + 2/100 X (21 - x) = 0.63
or, 5x/100 + (42 - 2x) / 100 = 0.63
or, 0.05x + 0.42 - 0.02x = 0.63
or, 0.03x = 0.63 - 0.42
or, 0.03x = 0.21
or, x = 0.21 / 0.03
or, x = 7
Therefore 21 - x = 14
Hence 7 gallons of 5% solution is used and 14 gallons of 2% solution is used.
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After raining for 3/4 of an hour, a rain gauge is of 2/5 the way full. If it continues to rain at the same rate for 15 more minutes, what fraction of the rain gauge will be filled?
Answer:
8/15
Step-by-step explanation:
You want the fraction of a rain gauge filled after 15 more minutes when the rain rate is 2/5 of the gauge in 3/4 of an hour.
Proportion15 minutes is 1/4 hour, so 15 more minutes brings the total time to 1 hour. The fraction (x) of the gauge that is filled will be ...
x/1 = (2/5)/(3/4)
x = (2/5)(4/3) = 8/15
After a total of 1 hour, the rain gauge will be 8/15 of the way full.
f(x) = (1 + =)",
k, n EN,
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x),
(a) prove that n = 6k + 2.
Given also that the coefficients of x4 and x5 are equal and non-zero,
(b) form another equation in n and k and hence show that k = 2 and n = 14.
Using these values of k and n,
(c) expand f(x) in ascending powers of x, up to and including the term in x5.
Give each coefficient as an exact fraction in its lowest terms
n>2
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x)
(a) It is proved that n = 6k + 2
(b)k = 2 and n=14
(c) After expansion, the equation is
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
What is the binomial theorem?
The algebraic expansion of a binomial's powers is described by the binomial theorem (also known as binomial expansion) in elementary algebra.
The theorem states that the polynomial (x + y)n can be expanded into a sum including terms of the form axbyc, where the exponents b and c are nonnegative integers and b + c = n, and the coefficient an of each term is a particular positive integer dependent on n and b.
Solution Explained:
f(x)= (1+x/k)^n
Given that the coefficient of x^3 is twice the coefficient of x^2 in the binomial expansion of f(x)
a)
Coeff of x^3 = 1/6[n(n-1)(n-2)/k3]
Coeff of x^2 = 1/2[n(n-1)/k2]
1/6[n(n-1)(n-2)/k3] = 2* 1/2[n(n-1)/k2]
Canceling on both sides gives:
(n-2)/(6k) = 1
n = 6k+2 Hence proved
Given also that the coefficients of x^4 and x^5 are equal and non-zero,
b)
Coeff x^4 = 1/24 [n(n-1)(n-2)(n-3)/k4
Coeff x^5 = 1/120 [n(n-1)(n-2)(n-3)(n-4)/k5
1/120 [n(n-1)(n-2)(n-3)(n-4)/k5 = 1/24 [n(n-1)(n-2)(n-3)/k4
Canceling gives:
(n-4)/(120k) = 1/24
n = 5k+4
From previous:
n = 6k+2 = 5k+4
k = 2
n=14
Using these values of k and n,
c)
Give each coefficient as an exact fraction in its lowest terms
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
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2. On which plane does the point (0,-1,5) lie? (1 point)
O the xy-plane
O the xz-plane
O the yz-plane
O the xyz-plane
( 0 , -1 , 5) point lies on xyz plane .
What is xyz plane ?The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.
To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.
Calculationthis given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .
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