Answer:
\(x=\frac{33}{7}\)
Step-by-step explanation:
Since ED is parallel to CA, the two triangles in the figure share all 3 angles and therefore must be similar. By definition, the corresponding sides of similar polygons are in a constant proportion.
Therefore, we have:
\(\frac{11}{11+x}=\frac{14}{20},\\14(11+x)=20\cdot 11,\\11+x=\frac{20\cdot 11}{14},\\x=\frac{110}{7}-11=\boxed{\frac{33}{7}}\)
Sam found that is the product of 5 and a number is increased by 8 the result is 10 more than the product of 3 and the number what is the number
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
number = x = ?
Step 02:
x = number
5 * x + 8 = 10 + 3 * x
5x + 8 = 10 + 3x
5x - 3x = 10 - 8
2x = 2
x = 2 / 2 = 1
The answer is:
The number is 1
The table shown lists random points found on a coordinate plane. Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line Which of the two functions created in Part A has the greater rate of change? Show your work.
The second part of the two functions created in Part A has the greater rate of change.
The table given lists the points (2,5), (7,2), and (10,3) on a coordinate plane.
Using these three points, two linear functions can be created.
The first linear function, f(x) = mx + b, is calculated by taking the slope, m, and the y-intercept, b, and then fitting it into the linear equation.
The slope of a line is found by calculating the rise over the run.
Using two points, the slope is calculated using \(m = (y^{2} - y^{1} )/(x^{2} - x^{1} ).\)
Using the two points (2,5) and (7,2), the slope is calculated as
m = (2 - 5)/(7 - 2) = -3/5.
The y-intercept, b, is the point at which the line crosses the y-axis.
This can be found by plugging in the coordinates of any one of the points into the linear equation and solving for b.
For the first linear equation, (2,5) will be used.
The linear equation becomes 5 = -3/5 × 2 + b, which is then solved for b to get b = 9/5.
Therefore, the first linear equation is
f(x) = -3/5x + 9/5.
The second linear equation is calculated in the same way.
Using the points (7,2) and (10,3), the slope is calculated as
m = (3 - 2)/(10 - 7) = 1/3.
Plugging the coordinates of either point into the linear equation and solving for b will give the y-intercept. This time, (7,2) will be used.
The linear equation becomes 2 = 1/3 × 7 + b, which is then solved for b to get b = -13/3.
Therefore, the second linear equation is f(x) = 1/3x - 13/3.
To prove that these lines work exclusively with the three points given, the x-value and y-value of each point should be plugged into both equations.
For the first point, (2,5), the equations become:
f(x) = -3/5x + 9/5 = 5
f(x) = 1/3x - 13/3 = 5
For the second point, (7,2), the equations become:
f(x) = -3/5x + 9/5 = 2
f(x) = 1/3x - 13/3 = 2
And for the third point, (10,3), the equations become:
f(x) = -3/5x + 9/5 = 3
f(x) = 1/3x - 13/3 = 3
The equations all equal the corresponding y-values, proving that these two lines created with the three points are exclusive to these points.
The line with the greater rate of change is the second equation,
f(x) = 1/3x - 13/3.
To find the rate of change, the slope of the line must be found, which is already calculated to be m = 1/3.
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if you flip a coin two times, what is the probability that one toss will come up heads and the other will come up tails?
The probability that one toss will come up heads and the other will come up tails when you flip a coin two times is 50%.
Imagine you've got a coin, and you flip it two times. Once you flip a coin, it can either arrive on heads (the side with a confront) or tails (the side with the hawk, in the event that it's a US quarter).
On the off chance that you flip the coin two times, there are four distinctive conceivable ways the coin can arrive:
heads-heads (HH),
heads-tails (HT),
tails-heads (TH),
and tails-tails (TT).
Presently, out of these four conceivable results, the HT and TH results have one hurl(toss) that comes up heads and the other hurl that comes up tails. So, we're curious about the likelihood of getting either HT or TH.
Since there are four conceivable results and two of them are HT and TH, the likelihood of getting one hurl that comes up heads and the other that comes up tails is 2 out of 4, or 50%.
So, in the event that you flip a coin two times, there's a 50-50 chance that you'll get one hurl that comes up heads and the other that comes up tails
Hence, the likelihood that one hurl will come up heads and the other will come up tails after you flip a coin two times is 2 out of 4, or 50%.
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30 POINTS ANSWER ASAP
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 is the equation in slope intercept form.
slope = -2/3
y intercept = 490
allso, can u mark brainlist
each student desk holds 6 textbooks. if there are 12 desks in a room. How many textbooks can they hold altogether.
Answer:
72
Step-by-step explanation:
just times 6 by 12 to get the answer
im very lost amd i just want a quick answer.
An angle bisector is a line that divides an angle into two equal parts
From the figure attached, we will observe that Line RU bisects Angle TRP into two parts (TRU & PRU)
Hence, the corect answer is a. (RU)
Anna is reading a 300-page book. She can read a page in two minutes. If she has finished reading 75 percent of the pages, how many minutes of reading does she have left
Answer:
150 minutes
Step-by-step explanation:
If Anna read 75% of her 300-page book, then she has already read:
300 × 75%
= 300×0.75
= 225
225 pages.
If Anna has already read 225 pages, then she has:
300 - 225 = 75
75 pages left still to read.
If Anna reads 2 minutes per page, then she has
75 × 2 = 150 minutes.
She has 150 minutes of reading left to finish her book.
By the way, it's weird to say you have 150 minutes of something to do. In real life 150 minutes = 2 1/2 hours. jfyi. Have a great day!
Combine like terms to simplify the expression below.
5y - 8x - y + 12x
Answer:
-6y+4x
Step-by-step explanation:
ccombine the like terms
Answer:
4y + 4x
Step-by-step explanation:
Combine like terms
5y - 8x - y + 12x
4y-8x+12x
Combine like terms
4y-8x+12x
4y+4x
Rearrange terms
4y+4x
4x+4y
Find the geometric mean of 6 and 48
Answer:
48+6= 54
54/2= 27
Answer is 27
Step-by-step explanation:
which of the following is the most widely used method for rating attributes?
The most widely used method for rating attributes is the Likert scale.
The Likert scale is a popular method for measuring attitudes, opinions, and perceptions of individuals towards a particular attribute or construct.
It consists of a series of statements or items that respondents are asked to rate on a scale typically ranging from "Strongly Disagree" to "Strongly Agree" or from "Very Unsatisfied" to "Very Satisfied."
The scale can vary in the number of response options, but it usually has five or seven points.
The Likert scale provides a way to quantify subjective responses and allows researchers to gather data on people's preferences, opinions, and perceptions.
It is widely used in various fields such as psychology, social sciences, market research, and customer satisfaction surveys.
Therefore, the Likert scale is the most widely used method for rating attributes.
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in a class of 150 students the ratio of boys to girls is 3 2 how many more boys than girls are in the class
The number of boys and girls in a class of 150 students is 90 and 60 respectively.
RATIO:
Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.
i.e., it shows how many times a number contains another.
Total number of students = 150
ratio of boys to girls = 3 : 2
B:G = 3 : 2
now
3x + 2x = 150
5x = 150
x = 30
the number of boys = 3x = 3 X 30 = 90 boys.
the number of girls = 2x = 2 X 30 = 60 girls.
The number of boys and girls in a class of 150 students is 90 and 60 respectively.
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Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $2,500 for their reception. If the reception hall charges a $60 cleanup fee plus $39 per person, find the greatest number of people that they may invite and still stay within their budget.
Answer:
62 personsStep-by-step explanation:
Step one:
given data
total budget=$2500
we are told that the hall charges $60 for cleanup, the amount is a fix charge
and per person is $39
let the number of persons be x
The model for the situation is described by y=mx+c
Step two:
2500=39x+60
solve for x
2500-60=39x
2440=39x
divide both sides by 39 we have
x=2440/39
x=62.56
The greatest number of people that they may invite and still stay within their budget. is 62
Which description could set up the
following system of equations
A. Drinks cost $2 and Hamburgers cost
$4.50. You bought 8 more drinks than
hamburgers and spent $23.50
B. Student tickets cost $2 and Adult cost
$4.50. After 8 tickets were sold, the
amount of money collected was $23.50
C. A rental car company charges $2 per
day plus $4.50 for each mile driven. What
is the # of miles driven if $23.50 was
collected after 8 days of driving
D. Books cost $2 and CDs cost $4.50 A
total of $23.50 was collected and the
books outnumbered the CDs by a total of 8
Answer:
B. Student tickets cost $2 and Adult cost
$4.50. After 8 tickets were sold, the
amount of money collected was $23.50
Step-by-step explanation:
x+y = 8 means we have 8 things
2*x + 4.50y = 23.50
The first item costs 2 dollars each and the second item costs 4.50 each and the total costs for all items bought is 23.50
In the formula A = r², find A when ris
14 centimeters.
Step-by-step explanation:
A = r², find A when r is 14 centimeters.
A = (14)²
A = 196 cm²
Terrence gets a loan with a $50 processing fee. The loan is for $700 with an interest rate of 8% for one
year.
The interest on the loan is
The APR on this loan is
Answer:
15.14%
Step-by-step explanation:
The formula for APR is stated thus:
APR=fees+interest/principal/n*365*100
principal is the loan amount of $700
fees is the processing fees on the loan which is $50
interest amount=principal*interest %=$700*8%=$56
n is the number of days of the loan which is a year i.e 365 days
APR=($50+$56)/$700/365*365*100
APR=$106/$700/365*365*100
APR=0.151428571 /365*365*100
APR=0.151428571 *100=15.14%
The annual percentage rate on the loan is 15.14% which represents the actual cost on the loan not just the interest cost of 8% annually
Does anybody know what (20x30)+10 to the second power is?
Answer:
372,100.............
Answer:
\(372100\)
Step-by-step explanation:
A number to the \(x\) power represents \(x\) amount of times the number is multiplied by itself. To the second power means that the number is multiplied by itself twice.
\([(20\times30)+10]^2 = 610^2\) (first work on terms inside parentheses)
\(= 372100\) (\(610^2 = 610\times 610\))
Hope this helps :)
please help ill give 20 points!!!
Answer:
H
Step-by-step explanation:
As you can see the more shirt's that were bought the lower the price becomes per shirt.
There are a adults at the fair. There are 20 more kids than adults. Choose the expression that shows how many kids there are.
The expression that represents the number of kids in the fair is 20 + a
How to determine the expression for the number of kids?From the question, the given parameters are:
Adults = a
Kids = 20 more kids than adults
The above can be represented as
Kids = 20 + Adults
Substitute Adults = a in the equation Kids = 20 + Adults
So, we have the following equation
Kids = 20 + a
Remove the variable "kids"
So, we have the following expression
20 + a
Hence, the expression is 20 + a
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Use the given information to write an equation to represent the linear relationship in point-slope form.
A polar bear gained 0.4 kilogram each week after it was born. After 3 weeks, it weighed 1.7 kilograms.
The polar bear has a birth weight of 0.5 kilogram.
The linear equation is y = x + 0.4t
Given,
The weight gained by polar bear each week after it was born = 0.4 kg
The weight of polar bear after 3 weeks = 1.7 kilo grams
We have to write an linear equation to represent this ;
Here,
y be the weight of polar bear
x be the initial weight
t be the number of week.
So,
the equation be like;
y = x + 0.4t
Then,
1.7 = x + 0.4 x 3
x = 1.7 - 1.2 = 0.5
The polar bear has a birth weight of 0.5 kilogram.
The linear equation is y = x + 0.4t
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Please help me! Will actually mark Brainliest!!!!
Answer:
B
Step-by-step explanation:
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has vertices P′(4, 0), Q′(3, 1), and R′(−1, −2).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/2
(B) Coordinates of Δ P"Q"R"
P" (-4,0)
Q"(-3,1)
R"(1,-2)
(C) Triangles PQR and P"Q"R" are not congruent.
Given
ΔPQR is transformed into ΔP'Q'R'
Coordinates of P, Q, R are
P (8,0),
Q(6,2)
R(-2,-4)
Coordinates of P'Q'R' are
P′(4, 0)
Q′(3, 1)
R′(−1, −2)
(A) By Distance formula we can find the distance between P Q and P'Q'
Distance formula = \(D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Where D = Distance between two points
from distance formula we can write that
PQ = \(\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}\)
Similarly
P'Q'= √2
PQ /P'Q' = 2
hence the scale factor of dilation is 1/2 (Compression)
(B )The Coordinates of Reflection about y axis can be written for a point
(x,y) as (-x,y)
So the Coordinated of Δ P"Q"R" can be written as
P" (-4,0)
Q"(-3,1)
R"(1,-2)
(C) ΔPQR and ΔP"Q"R" are similar triangles but they are not congruent because their sides are not equal in size.
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4. Triangle ABC is similar to triangle DEF. Which proportion must be true?
The similar triangles in the question, with proportional sides indicates;
4. The proportion that must be true is the option G
G. 4/6 = 7/x
What are similar triangles?Similar triangles are triangles are triangles that have the same shape but may have different sizes.
The possible triangles in the question includes two triangles with specified side lengths AB = 6 inches, AC = 7 inches, DE = 4 inches, DF = x inches
The definition of similar triangles indicates that we get;
DE/AB = EF/BC
DF/AC = DE/AB
DF/AC = EF/BC
Therefore;
(x/7) = 4/6
The correct option which indicates the proportion that must be true, therefore is option G
G. 4/6 = x/7
Part of the question includes two triangles, please see attached diagram created with MS Excel
The possible proportions, from which to select the proportion that must be true are;
F (7/x) = (4/6)
G 4/6 = x/7
H 6/4 = x/7
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Consider the equation of a circle given by (x+8)² + (y+4)² = 256. What is the diameter of the circle?
The diameter of the circle with the circle equation (x+8)² + (y+4)² = 256 is 32 units
How to determine the diameter?The equation of the circle is given as:
(x+8)² + (y+4)² = 256
As a general rule, a circle equation is represented as:
(x - a)² + (y - b)² = r²
Where r is the radius.
By comparing both equations, we have:
r² = 256
Take the square roots of both sides
r = 16
Multiply by 2 to get the diameter
d = 32
Hence, the diameter of the circle is 32 units
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an urn contains 5 blue balls and 6 orange balls. in how many ways can we select 1 blue balls and 2 orange balls from the urn? a) 17 b) 75 c) 35 d) 149 e) 30 f) none of the above.
Using the formula of combination and probability theorem , The answer is b) 75.
What do you mean by combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
What is the formula of combination?The formula for combination is:
\(C(n,r) = \frac {n!}{r!(n-r)!}\)
selecting 1 blue ball from 5 blue balls = C(5,1)
=5
selecting 2 orange balls from 6 balls = C(6,2)
=15
Total ways of selection = 5*15=75
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What is the area in square millimeters of the yellow triangle outlined on the origami figure at the right (b = 3cm h= 1.76)
Answer:
2.64
Step-by-step explanation:
b*h=5.28
5.28/2=2.64
Drag and drop to the correct line.
y=-0.5+1 y=0.5+1 y=-2x-1 y=2x-1 y=-2x+1 y=2x+1
Answer:
the point is at 0,1 because it just isn't easy to tell where the stuff is qt it's a graph it's k-3 grade stuff bro
can the tangent constraint be applied between a line and an arc?
Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.
In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.
This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.
In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.
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A circle has an area of 1256.637061. What is the diameter? (round to the nearest whole number)
Answer:
The diameter is 40
Step-by-step explanation:
the cost of a bag of apples is based on the cost of one apple and the total number of apples in the bag
The number of apples in the bag is 18.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Cost of a bag of apples = $36
Cost of one apple = $2
Now,
The number of apples in the bag.
= 36 ÷ 2
= 18
Thus,
The number of apples in the bag is 18.
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The complete question.
The cost of a bag of apples is $36 based on the cost of one apple which is $2 .
Find the total number of apples in the bag?
Select all the statements that describe the expression 5 + 2x
A.The expression represents 5 plus 2 plus x.
B.The expression represents 5 plus 2 times x.
C.The expression represents 5 plus x plus 2
D.The expression represents the product of 2 and X plus 5.
E.The expression represents the sum of 5 and 2x.
F.The expression represents the product of 5 and 2x.