All the correct expressions are,
Slope of BC = - 2/5
Slope of CD = 5/2
Slope of DE = - 3/5
Slope of EB = 3
Length of BC = √ 29
Length of CD = √ 29
Length of DE = √34
Length of EB = √40
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Coordinate of B = (- 9, 1)
Coordinate of C = (- 4, - 1)
Coordinate of D = (- 2, 4)
Coordinate of E = (- 7, 7)
Now, We know that;
The slope of line passing through the points (x₁ , y₁) and (x₂, y₂) is,
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Thus, Slope of BC is,
⇒ m = (- 1 - 1) / (- 4 - (-9))
⇒ m = - 2/5
Slope of CD is,
⇒ m = (4 - (-1)) / (- 2 - (-4))
⇒ m = 5/2
Slope of DE is,
⇒ m = (7 - 4) / (- 7 - (-2))
⇒ m = 3/- 5
⇒ m = - 3/5
Slope of EB is,
⇒ m = (1 - 7) / (- 9 - (-7))
⇒ m = - 6/-2
⇒ m = 3
Length of CD is,
⇒ CD = √ (- 2 - (-4))² + (4 - (- 1))²
= √4 + 25
= √ 29
Length of BC is,
⇒ BC = √ (- 4 - (-9))² + (- 1 - 1)²
= √25 + 4
= √ 29
Length of DE is,
⇒ DE = √ (- 2 - (-7))² + (4 - 7)²
= √25 + 9
= √ 34
Length of EB is,
⇒ EB = √ (- 7 - (-9))² + (7 - 1)²
= √4 + 36
= √ 40
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alex earns a $35,000 salary in the first year of his career. each year, he gets a 3% percent raise. which expression gives the total amount alex has earned in his first n years of his career?
After n years Alex will earn salary which can be expressed as $(1 + 0.03)^n * 35,000.
The total amount Alex has earned in his first year of his career is $35,000.
In the second year of his career, he gets a 3% raise, which is an increase of 3/100 * $35,000 = $1,050.
So his salary for the second year is $35,000 + $1,050 = $36,050.
In the third year of his career, he again gets a 3% raise, which is 3/100 * $36,050 = $1,081.50
So his salary for the third year is $36,050 + $1,081.50 = $37,131.50
We can see that for each year, his salary is increasing by a fixed percentage of the previous year's salary.
This pattern can be represented by the expression:
(1 + 0.03)^n * 35,000
Where n is the number of years since the start of his career. This expression gives the total amount Alex has earned in his first n years of his career.
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In ΔXYZ, y = 500 inches, m∠Y=117° and m∠Z=10°. Find the length of z, to the nearest inch.
Answer:
97 inches
Step-by-step explanation:
Using law of sines, we know that y/sin∠Y = z/sin∠Z.
Solve:
[tex]\frac{500}{sin117}[/tex] = [tex]\frac{z}{sin10}[/tex]
Therefore, z = (500/sin117)(sin10)
Enter this into a calculator to get:
z = 97.44495296, which rounds to 97 inches.
I hope this helps! :D
John goes to a restaurant and has a bill of 32.57. He uses a 10% off coupon on the cost of the meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied. how much does he spend?
The total amount spent by John is $37.78.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that John goes to a restaurant and has a bill of 32.57. He uses a 10% off coupon on the cost of the meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied.
Amount left as a tip -
{t} = 18% of 32.57
{t} = 18/100 x 32.57
{t} = 5.87
Amount included in tax -
8% of 32.57
8/100 x 32.57
2.61
Billed amount after coupan is applied -
10% of 32.57
10/100 x 32.57
$3.26
Amount spend -
(32.56 - 3.26) + 2.61 + 5.87
$37.78
Therefore, the total amount spent by John is $37.78.
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which graph shows different numbers of tickets that ellena can sell to raise more than 180$
Which of the reasons to network is most important for recent culinary program graduates?
A. Developing friendships that may lead to business referrals
B. Learning best practices from experienced professionals
C. Recommending extensive contacts that can help others
D. Sharing their favorite recipes and stories from their program
Answer:
C. gaining confidence
Mary ran 1 3/5 miles on Monday and 7 1/5 miles on Tuesday. How many times her Monday’s distance was her Tuesday’s distance?
Mary's Tuesday distance is 1/8 times her Monday distance
How to calculate the number of Mary's Tuesday distance that is her Monday's distance?
On Monday Mary ran 1 3/5 miles
= 8/5
On Tuesday Mary ran 1/5 miles
Therefore the number of times her Tuesday distance was her Monday distance can be calculated as follows
1/5 ÷ 8/5
= 1/5 ×5/8
= 1/8
Hence her Tuesday distance was 1/8 times her Monday distance
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a shade allows light to pass through from a lamp, but reduces the intensity of the light. the intensity of the light is reduced by 15% if the fabric is 1mm thick. each additional millimetre of fabric reduces the intensity by another 15%
a) write an expression that gives percent P, of light which penetrates x mm of fabric. b) use the equation to determine the percentage of light that will pass through a cloth, that is 2.75mm thick
a) The exponential function that gives the percent P is: P = (0.85)^x.
b) The percentage of light that will pass through a cloth that is 2.75mm thick is given as follows: 63.96%.
How to define the exponential function?A decaying exponential function is defined as follows:
y = a(1 - r)^x.
In which the parameters are given as follows:
a is the initial value.r is the decay rate, as a decimal.The parameter values for this problem are given as follows:
a = 1, r = 0.15.
Hence the function is:
y = (0.85)^x.
The percentage passing through a cloth that is 2.75 mm thick is given as follows:
y = (0.85)^2.75
y = 0.6396.
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Determine whether the variable is qualitative or quantitative Weight Is the variable qualitative or quantitative? A. The variable is qualitative because it is a numerical measure B. The variable is quantitative because it is an attribute characteristic. C. The variable is quantitative because it is a numerical measure. D. The variable is qualitative because it is an attribute characteristic.
A. The variable is qualitative because it is a numerical measure is correct answer.
Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. for instance: Eye color (variables include: blue, green, brown, hazel).
In statistics, qualitative variables are given nominal scales since they cannot be ordered on a numerical scale. Qualitative variables are exactly what the word "nominal" means: names. No ordering is either conceivable or inferred on a nominal scale (except for alphabetical ordering like New York, Washington, West Virginia or Chelsea, Edinburgh, London). In other words, data are classified according to a category on the nominal scale.
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PLEASE HELP I WILL GIVE BRAINLIEST
For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E
The coordinates of vertices after dilation by scale factor of 1.5 with center of dilation is D'(3,-3), E'(6,-3) and F'(1.5,-6).
What is the vertices after dilation?A dilation is just a transformation which enlarges or contracts the size of a figure. This means that the preimage and image are similar and are scaled up or down using a factor.
The vertices of the triangle are D(2,-2), E(4,-2), F(1,-4).
The origin-centered dilation with a scale factor of k is defined as,
(x,y) → (kx,ky)
As a result, dilation with a scale factor of 1.5 centered at the origin is defined as,
(x,y) → (1.5x,1.5y)
The image's vertices are
D(2,-2) → D'(3,-3)
E(4,-2) → E'(6,-3)
F(1,-4) → F'(1.5,-6)
Therefore the coordinates of vertices after the dilation by the given scale factor 1.5 is D'(3,-3), E'(6,-3) and F'(1.5,-6).
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There are 10 girls and 16 boys in a class. The teacher has sticks with each student's name on them in a bag. What is the probability of selecting sticks with a boy's
name and then a girl's name if the first stick is not replaced?
40
A
169
(B)
16
65
45
128
26
51
The probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.
Now, According to the question:
Formula to find the probability of an event:
"P(A) = n(A) / n(S)
where, n(A) is the number of favorable outcomes of an event A
n(S) is the total number of outcomes for an experiment"
"Information available from the question"
Total number of students are,
n(S) = 10 + 16
n(S) = 26
Let event A: selecting first stick with a boy name
n(A) = 16
So, the probability of a boy is,
P(A) = n(A)/n(S)
P(A) = 16/26
P(A) = 8/13
if the first stick is not replaced, then n(S) would be,
26 - 1 = 25
Let event A: selecting first stick with a boy name
n(B) = 10
So, the probability of a boy is,
P(B) = n(B)/n(S)
P(B) = 10/25
P(B) = 2/5
Therefore, the probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.
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I’m kinda slow can someone help
Answer:
60
Step-by-step explanation:
You're not slow.
So given was the formula for perimeter
12x + 1/2 - 4x - 8.5 + 2x + 8
They want you to find perimeter is x = 6, so this is a matter of plug and play. so everywhere you see an x, you'll replace it with the number 6
And we will start simplifying what we can
P = 12(6) + 1/2 - 4(6) - 8.5 + 2(6) + 8
P = 72 + 0.5 - 24 - 8.5 + 12 + 8
P = 72 - 24 - 8 + 12 + 8
P = 72 - 12
P = 60
(WILL MARK BRAINLIEST)
John plans to practice piano at least 2 1/2 hours this weekend.
If he practices 1 1/6 hours on Saturday and 1 1/4 hours on Sunday, will he meet his goal?
John will be able to meet the goal of practicing piano for mentioned time on Saturday and Sunday.
Required amount of practice = [tex]2 \frac{1}{2} [/tex] hours
Required amount of practice = (2×2)+1/2
Required amount of practice = 5/2 hours
Required amount of practice = 2.5 hours
Practice performed on Saturday = [tex]1 \frac{1}{6} [/tex]
Practice performed on Saturday = (6×1)+1/6
Practice performed on Saturday = 7/6 hours
Practice performed on Sunday = [tex]1 \frac{1}{4} [/tex]
Practice performed on Sunday = (4×1)+1/4
Practice performed on Sunday = 5/4 hours
Combined practice performed = 7/6 + 5/4
Combined practice performed = 1.2 + 1.3
Performing addition
Combined practice performed = 2.5 hours
The performed practice is equal to the goal and hence he will meet the goal.
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we have 20 cards including 10 a, 5 b and 5 c. we randomly take a card. if it is not a, what is the probability that it is b?
We randomly take a card, if it is not a, then the probability that it is b, is 1/4.
We have to find the the probability that it is a card of b, if it is not a.
We have total number of cards = 20
The cards of a = 10
The cards of b = 5
The cards of c = 5
We don't select the card a, then;
The probability of choosing card b = The total number of card b/total number of cards
The probability of choosing card b = 5/20
The probability of choosing card b = 1/4
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Which is a correct solution for the following system of Inequalities
The correct solution for the following system of Inequalities is (-1, 1) because it is on the darker region.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the x axis and let y represent the y axis.
The solution to the system of linear equalities is the intersection of both inequalities which is the darker region.
The point that satisfies both inequalities as shown on the graph is (-1, 1) because it is on the darker region.
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geometry - i need help with this problem and it’s pretty easy. i’m just curious on how i would round the square root of 95 within the problem
Step-by-step explanation:
I am not sure what you mean. you don't round the intermediate numbers and results. only the final result.
you keep the irrational terms (like square root) like variable terms as they are and apply operations on them without actually expressing them as numbers.
only at the very last moment (when the final result is calculated) would you express them as actual number. and then you round the final result.
so, this is solved via Pythagoras :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
in our case we have
BP² = BN² + NP² = 7² + sqrt(95)² = 49 + 95 = 144
you see ?
no need ever to bring the actual result of sqrt(95) into the picture. just keep it at sqrt(95) and do with it, what you would do with any actual number.
BP² = 144
BP = sqrt(144) = 12
so, we never had to deal with the actual irrational number.
we know how it is created, so we keep using that term to represent it.
Please help someone with this additional gcse maths 'surds and indices' question :)
The simplest form of the expression is given as 12 + 6√3.
What is the simplest form of the expression?
We know that when we are asked to simplify in mathematics, they are asking us to write the expression in the simplest form that the expression can be in. In this case, we are to simplify 6/2 - √3.
Then we would now have to multiply the numerator and the denominator by the conjugate of the denominator such that we have;
6/2 - √3 * 2 + √3/2 + √3
12 + 6√3/4 +2√3 - 2√3 - 3
12 + 6√3/1
12 + 6√3
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Angela wants to learn how to rock climb. The Rocky Climbing gym has a special where 5 climbs cost $52.50.
Select the equation that represents the total cost, t, of c climbs. Assume the relationship is proportional.
Answer: t = 10.50c
Step-by-step explanation: The relationship between the number of climbs, c, and the total cost, t, is proportional. This means that the ratio of t to c is constant. One way to represent this relationship is through an equation of the form:
t = kc
where k is a constant of proportionality. In this case, we know that 5 climbs cost $52.50, so we can use this information to find the value of k:
52.50 = k(5)
k = 52.50/5 = 10.50
So the equation that represents the total cost, t, of c climbs is:
t = 10.50c
Where t is the total cost, c is the number of climbs and 10.50 is the constant of proportionality.
How to plot the function-2x+1 on a graph
Answer:
Start at 1 on y-intercept and go down 2 units and right 1 unit
Step-by-step explanation:
First you have to graph your y-intercept (1) *which is the red dot in the graph I made for you*
Then you must use your slope (-2) to graph the rest
Since your slope is negative you have to go down from your y-intercept. In your case you are going down 2 units from your intercept. And since your slope is a whole number instead of a fraction you just go to the right 1 unit to make the coordinate (1,-1).
That is how you graph your equation.
I hope this helped!
y=6 in graph form please!!!
Answer:
It will be straight line on x equal zero and y equal 6 horizontal straight line
what is the volume? please please PLEASE help T0T
The volume of the cuboid is 16 cubic yards.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
A cuboid with height 2 yards, length 2 yards and width 4 yards.
The volume of the cuboid,
= length x width x height
= 4 x 2 x 2
= 16 cubic yards.
Therefore, the volume is 16 cubic yards.
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Use substitution to solve the system
4x+3y = 2
x-2y = -5
X=
Y=
The solution for linear equations given will be x=-1 and y=2 using substitution method.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now
Given 4x+3y=2 -->1
x-2y=-5 --->2
Using substitution method, In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation.
From 2, x=2y-5
Put x=2y-5 in 1
4(2y-5)+3y=2
11y-20=2
y=22/11
y=2
Hence,
x=2*2-5
x= -1
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Triangle congruence proof
Given the information, the triangle congruence prove is explained below.
Properties of congruent triangles?If the corresponding sides or measure of angles of two or more triangles have common properties, then the triangles are said to be congruent. Such that on comparing their sides and internal angles, some have equal values.
With the given information in the question, the prove is explained below:
STATEMENTS REASONS
1. AB ≅ CD Given
2. <ABD ≅<CDB Given
3. AD ≅ BC Equal sides of a parallelogram
4. <ADB ≅ <CBD Alternate angle theorem
5. <A ≅ <C Opposite property of a parallelogram
Therefore, it can be deduced that;
ΔABD ≅ ΔCDB
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jamal plans to buy a new laptop which is currently priced at $859. ON saturday the store is giving a 25% discount off all laptops =. he will need to pay 8.5% sales tax on the final purchase. how much will the final cost of the laptop be if jamal buys it on saturday.
The final cost of the laptop be if jamal buys it on saturday is $695.79
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
The new laptop is currently priced at $859
On saturday the store is giving a 25% discount off all laptops
Sales tax on final purchase=8.5%
Now, the final value on saturday be x
x*100/859=25
x=25*859/100
x=214.75
The value will be 859-214.75=644.25
8% of 644.25
x*100/644.25=8
x=8*644.25/100
x=51.54
Final cost= 644.25+51.54
=695.79
Therefore, the final cost after 8 percent sales tax will be $695.79
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Can u solve and show me the steps pls
Answer:
[tex]\dfrac{-8y}{y-3}[/tex]
Step-by-step explanation:
[tex]\sf \dfrac{49 - y^2}{6y^2 +42y}=\dfrac{7^2-y^3}{6y^2 +6*7y}\\\\[/tex]
[tex]\sf =\dfrac{(7+y)(7-y)}{6y(y + 7)}=\dfrac{(7+y)(7-y)}{6y(7+y)}\\\\\\=\dfrac{7-y}{6y}[/tex]
y² - 10y + 21
sum = -10
Product = 21
Factors = (-7) , (-3) {(-7)*(-3) = 21 & (-7)+ (-3) = -10}
y² - 10y + 21 = y² - 7y - 3y + 21
= y(y - 7) - 3(y - 7)
= (y - 7) ( y - 3)
[tex]\sf \dfrac{49 -y^2}{6y^2 + 42y}*\dfrac{48y^3}{y^2 - 10y + 21}=\dfrac{7-y}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\[/tex]
[tex]\sf = \dfrac{(-1)(y-7)}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\=\dfrac{(-1)*8y^2}{y-3}\\\\\\=\dfrac{-8y^}{y-3}[/tex]
what is the value of x in 12 ( x + 10 ) = 24
also explain
Answer: x = -8
Step-by-step explanation:
12 ( x + 10 ) = 24
First we divide the two sides of the exercise by 12.
[tex]\boldsymbol{\sf{x+10=\dfrac{24}{12} }}[/tex]
We divide 24 by 12..
x + 10 = 2
Subtract 10 from both sides.
x = 2 - 10
Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.
x = -8
Answer:
[tex] \sf \: x = - 8[/tex]
Step-by-step explanation:
Given equation,
→ 12(x + 10) = 24
Now the value of x will be,
→ 12(x + 10) = 24
→ 12(x) + 12(10) = 24
→ 12x + 120 = 24
→ 12x = 24 - 120
→ 12x = -96
→ x = -96 ÷ 12
→ [ x = -8 ]
Hence, the value of x is -8.
EASY STATISTICS QUESTION--- PLEASE HELP!!!
The required mean of the table is 32.71.
How can I calculate the probability distribution's mean and standard deviation?Mean: The formula is E(X)=μ=∑xP(x). where x represents the value of the random variable X, P(x) represents the corresponding probability, and the symbol Σ represents the sum of all products xP(x). Here we use the symbol μ for mean, since it is a parameter. Represents the population mean.
Mean=Total of household/Total number of dogs
⇒ [tex]\frac{(323+176+87+51+32+8+10)}{(0+1+2+3+4+5+6)}[/tex]=[tex]\frac{687}{21}[/tex]=32.71
Standard Deviation: Standard deviation is calculated as the square root of variance by determining the deviation of each data point from the mean. If the data points are far from the mean, there will be more variation within the data set. Therefore, the wider the data, the higher the standard deviation.
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Pls help me on this homework question
The graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24 .
What is trend line?A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.
a graph line indicating the general path that a collection of points appears to take.
When plotting predictions, trendlines, also referred to as lines of best fit or regression lines, are frequently used to graphically represent trends in data series. Typically, a trendline is a line or curve that crosses or links two or more points in a series to indicate a trend.
From the graph that passes through the points (4,16) and (6,12) , the equation of trend line is K = -2J + 24.
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Bicycles in the late 1800s looked very different than they do today.
60ft 9ft
a. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.
Note that where the diameter of the bicycles are 60 inches and 9 inches respectively, the rotation of each tire after traveling 600 feet would be:
Small Tire (9in Diameter ) = 188.4 Rotations.
Big Tire (60 in Diameter) = 3.2 rotations
Note that the above were arrived at using the knowledge of Circumference.
What is the circumference of a circle?Note that the circumference in geometry is the perimeter of a circle or ellipse.
This is calculated using the formula:
C = 2πr
or
C = πD
Where C = Circumference
R = radius
D = Diameter which is 2r
π = 3.14
To arrive at how many rotations each tire did, we'd have to divide the distance traveled by the circumference of each tire.
For the Small Tire, the diameter is 9 feet.
Thus, the circumference of Small Tire = 3.14 * 9
= 28.26 feet
Thus, the rotations by the small tire is:
600/28.26
= 21.2314225053
[tex]\approx[/tex] 21.2feet
Applying the same process to the big tire, we have:
C = 3.14 * 60
C = 188.4
The rotations by the big tire =
600/188.4
= 3.1847133758
[tex]\approx[/tex] 3.2 feet.
Thus, the rotations by each tire over 600ft is given as:
Big Tire = 3.2
Small Tire = 188.4 .
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Full Question:
See attached image.
which of the following is not true of a good hypothesis? a) it includes a null hypothesis b) it is experimentally testable c) it is phrased as an if, then statement d) it must contradict previous theories e) it could explain an unexpected observation.
False claims do not have to engage with previous theories in order to be effective. So it must contradict previous theories. So the option d is correct.
A tentative, verifiable explanation for a natural world phenomenon is what is known as a scientific hypothesis. The scientific method's foundational element is it.
It's sometimes referred to as a "informed guess" that was made using past knowledge and observation. Despite the fact that this is true, a hypothesis is a better guess.
Creating a hypothesis calls for active observation and background research, in contrast to making a "informed guess," which implies a random prediction based on one's expertise. A hypothesis is predicated on the fundamental tenet that no outcome is predetermined.
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What is the distance between PQ?
P: (1,6)
Q: (7,2)
The distance between PQ : 7
Given points P: (1,6)
Q : (7,2)
distance between two points formula is : √(x2-x1)^2 + (y2-y1)^2
(x1,y1)= (1,6)
(x2,y2) = (7,2)
therefore
= √(7-1)^2 +(2-6)^2
= √36+16
= √52
= 7.211