Answers
Answer:
\(\text{ Less than 1}\)Explanation: We can see that the resulting figure which is F'G'H'E' has the Width and height both reduced to half:
\(\begin{gathered} W^{\prime}=\frac{1}{2}W \\ H^{\prime}=\frac{1}{2}H \end{gathered}\)This means that it has the scale factor of:
\(F\mathrm{}S=\frac{1}{2}\)Because all the dimensions are reduced by one half, therefore the answer is:
\(\text{ Less than 1}\)
Related Questions
Consider the experiment of rolling fair six-sided die until a 5 is observed. Let A be the event that a 5 is observed on the first roll. Let B be the event that it takes at least two rolls for the first 5 to be observed. Find the following probabilities. (Round to nearest 4 decimal places)
P(A∩B)
P (A)
P(B)
Answers
Answer:
P(A∩B) = 0
P(A) = 0.1667
P(B) = 0.8333
=================================================
Explanation:
The events
A = a 5 is observed on the first rollB = it takes at least two rolls for the first 5 to be observedare mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.
This allows us to say P(A∩B) = 0
In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.
-----------------------
P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.
------------------------
We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.
Put another way, we have two options:
Option 1: The first roll is "5". The probability is 1/6Option 2: The first roll is NOT "5" (so you'll need to do at least another roll to get "5"). The probability is 5/6.The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.
The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.
7. N.CN.7 Determine the zeroes for the equation below. Select all that apply.
x² - 6x +13=0
A. 1
B. 5
C. 13
D. -3 + 2i
E. 3+2i
F. 3+4i
G. 6 + 4i
H. 3-21
I .6-41
Answers
Answer:
D. -3 + 2i and E. 3+2i are the zeroes for the equation.
Step-by-step explanation:
The ratio of sweaters to dresses that Susan has is 7:2. If Susan has 14 dresses then how many sweaters does she have?
Answers
Answer:
4 sweaters
Step-by-step explanation:
If the ratio is 7:2, then 14//7 = 2
2x2=4
A line passing through the point (0, 4) has a slope of-2. Write the equation of the line in point-slope form.
Answers
Answer:
\(y-4=-2(x-0)\)
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of -2, and contains the point (0,4).
We want to write the equation of the line in point-slope form.
Point-slope form is given as \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.
SolvingSince we are already given the slope, we can immediately plug it into the formula.
Substitute -2 as m.
\(y-y_1=-2(x-x_1)\)
Now, let's label the values of our points to avoid confusion and mistakes.
\(x_1=0\\y_1=4\\\)
Substitute into the formula.
\(y-4=-2(x-0)\)
Topic: point-slope form
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Designer builds and sells small chairs and large chairs. The cost of material is $10 for each small chair and $15 for each large chair. The selling price is $22 for a small chair and $51 for a large chair. The designer spends $305 on material to make chairs. The designer makes eight more small chairs than large chairs. Write a system of equations that can be used to determine s, the number of small chairs and T, the numbers large chairs, the designer makes. How many small chairs did the designer make?
Answers
After solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.
What is meant by the system of equations?
A set of equations with a finite number of solutions is referred to as a system of equations. A system of equations in algebra consists of two or more equations and looks for common answers to the equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.
Given,
Cost of material for small chair = $10
Cost of material for large chair = $15
The selling price for a small chair = $22
The selling price for a large chair = $51
The total money spent on materials = $305
Designer makes 8 more small chairs than large chairs.
If the number of large chairs = t and the number of small chairs = s
Using the given equations, we can write the following system of equations.
10s + 15t = 305
s - t = 8
Now we make the coefficient of s in both equations the same.
Multiply 10 in the second equation.
10s + 15t = 305
10s - 10t = 80
Subtracting,
5t = 225
t = 45
s = 8 + t = 45 + 8 = 53
Therefore after solving the system of equations, we found that the number of small chairs is 53 and the number of large chairs is 45.
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What is the domain for...
y=0.25x-12
Answers
Answer:
Domain: (-infinity,infinity)
Step-by-step explanation:
You're welcome. :)
(I couldn't write the infinity symbol so I wrote infinity.)
solve for the roots in simplest form by completing the square
x^2-12x+20=0
Answers
Answer:
x = 10 or x = 2
Step-by-step explanation:
Solve for x:
x^2 - 12 x + 20 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 20 from both sides:
x^2 - 12 x = -20
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 36 to both sides:
x^2 - 12 x + 36 = 16
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 6)^2 = 16
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 6 = 4 or x - 6 = -4
Hint: | Look at the first equation: Solve for x.
Add 6 to both sides:
x = 10 or x - 6 = -4
Hint: | Look at the second equation: Solve for x.
Add 6 to both sides:
Answer: x = 10 or x = 2
A population, f(x), after x years may be modeled with f(x)=2(3)^x. What is the initial amount , growth rate, domains and range?
Answers
Growth rate: 3
Domain: all real numbers
Range: all positive real numbers.
2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and range of the function is all positive real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is:
f(x) = 2(3)ˣ
To find the initial amount, we need to find f(0):
f(0) = 2(3)⁰ = 2(1) = 2
So the initial amount is 2.
To find the growth rate, we can use the formula:
growth rate = (f(x) - f(0)) / f(0) × 100%
= (2(3)ˣ - 2) / 2 × 100%
= (3ˣ - 1) × 100%
So the growth rate is (3ˣ - 1)×100%.
The domain of the function is all real numbers because the function is defined for all values of x.
The range of the function is all positive real numbers because the function is always positive for any value of x.
Specifically, the range of the function is (0, infinity).
Hence, 2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and range of the function is all positive real numbers
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209.69 rounded to 2 Dp
Answers
Answer:
209.70
Step-by-step explanation:
209.70 to 2decimal places
Rate of change In gallons of gas per year from 1995 to 1997???!?
Answers
The rate of change In gallons of gas per year from 1995 to 1997 is: C. Δg/Δt = 4 gal/year.
How to calculate the rate of change?In Geometry, the rate of change of the data in this table can be calculated by using this mathematical equation;
Rate of change (slope), m = (Change in y-axis, Δg)/(Change in x-axis, Δt)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (1995, 1997).Points on the y-coordinate = (530, 538).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), Δg/Δt = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), Δg/Δt = (538 - 530)/(1997 - 1995)
Rate of change (slope), Δg/Δt = 8/2
Rate of change (slope), Δg/Δt = 4 gallon/year.
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The volume of a large aquarium is 210 ft it is 3 3/5ft wide and 2 4/5 ft high what is the length of the aquarium
Answers
Answer:
21 ft
Step-by-step explanation:
HELPPP PLSSS
Find the value of x in the figure:
Answers
Answer:
4
Step-by-step explanation:
ΔADE ~ ΔABC, so
AD : AB = (x + 1) : (4x - 6)
Note AB = 2 AD, so
4x - 6 = 2(x + 1)
4x - 6 = 2x + 2
2x = 8
x = 4
1.25y-0.35y=585
Solve for y
Answers
Answer:
y = 650
Step-by-step explanation:
0.9y = 585
y = 650
Answer:
\(y = 650\)
Step-by-step explanation:
\(1.25y-0.35y=585\)
\(0.9y=585\)
\(y = \frac{585}{0.9}\)
\(y = 650\)
Find the volume of the figure. Round to the nearest hundredth when necessary. I got 257.2288 I if this is correct, I am not sure how to round it to the nearest hundredth. or if to leave it this way.
Answers
ok
Volume of a cylinder = Area of the base x height
= pi*r^2 * h
= 3.14* 3.2^2*8
= 3.14*10.24*8
= 257.23 km^3
We got the same result, you just need to round to the nearest hundred.
pi = 3.14
r = 3.2 km
h = 8 km
Which of the scenarios below are considered seller-based discounts? options are in the picture
Answers
The scenarios that can be considered a seller-based discount are:
A. The offer by Wire and Cable
B. Carfna's Fine Foods
C. Mouser Electronics offer
E. Carchex Car Maintenance
What is a seller-based discount?A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.
The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.
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Find the length of x??
Answers
Answer:
8 meters.
Step-by-step explanation:
the formula for the hypotenuse of a right triangle is: \(a^2 + b^2 = c^2\). Where C= hypotenuse and a and b = other sides. We can sub in a and c to get \(6^2 + x^2 = 10^2\\\). Simplify to \(36+x^2=100\). Subtract 36 from both sides to get x^2 = 64. \(\sqrt{64} =8\)
math math math math math math math
Answers
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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Consider the triangles below. Which statement is true?
Answers
Answer:
B
Step-by-step explanation:
I just need part B answered. and also, if part A is wrong, please correct it.I need it done ASAP
Answers
We have the following:
A.
\(\begin{gathered} 2y=-3x+16 \\ \frac{2}{2}y=-\frac{3}{2}x+\frac{16}{2} \\ y=-\frac{3}{2}x+8 \end{gathered}\)\(\begin{gathered} y=-\frac{3}{2}\cdot0+8 \\ y=8 \end{gathered}\)A solution to this equation (0, 8)
B.
\(\begin{gathered} y=-\frac{3}{2}\cdot28+8=-3\cdot14+8 \\ y=-42+8 \\ y=-34 \end{gathered}\)The point is (28, -34)
solve {6x-5y=21 2x+5y=-5 with elimination please help fast :(
Answers
Answer:
19
Step-by-step explanation:
In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answers
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
2(x-3)=x-5+x plz help
Answers
Answer:
x is undefined
Step-by-step explanation:
Simplify the expression, we get
2x-6=2x-5
This will not work
There are no solutions
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Answers
Answer:
4x + 3y = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
• Parallel lines have equal slopes
calculate the slope of the line using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = \(\frac{-1-3}{3-0}\) = \(\frac{-4}{3}\) = - \(\frac{4}{3}\) , then
y = - \(\frac{4}{3}\) x + c ← is the partial equation
to find c substitute (- 3, 2 ) into the partial equation
2 = 4 + c ⇒ c = 2 - 4 = - 2
y = - \(\frac{4}{3}\) x - 2 ← equation in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 4x - 6 ( add 4x to both sides )
4x + 3y = - 6 ← in standard form
50 = 5x - 2 + 6x-3
Solve for x
Answers
Answer:
The answer would be X=5
what is the variable "d" equal to in the equation 2d + 13
Answers
Answer:
d=-6.5
Step-by-step explanation:
2d+13=0
2d=-13
d= -13/2
d=-6.5
Fill in the boxes to add the expressions.
(5.19+4m)+(4.18+3.95m) = (4m+_)+(5.19+_)=_
Answers
Using common factor method, sum of the given expressions is 17.14m + 9.37
what is common factor ?
In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.
In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.
According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:
(5.19 + 4.18) + (4m + 3.95m)
9.37 + 7.95m
So, the sum of the expressions is:
(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m
Now, we can use the distributive property to factor out a common factor of m from 7.95m:
9.37 + 7.95m = 4m + (5.19 + 7.95)m
We can factor out a common factor of 1 from (5.19 + 7.95)m:
4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m
Adding the coefficients, we get:
4 + 5.19 + 7.95 = 17.14
Therefore, the sum of the expressions is:
(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.
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A fence is to be installed around a rectangular field. The field's perimeter is 208 feet. Find the dimensions of the field if the length of the
field is 4 feet more than the width, as shown in the figure to the right (use P=2L+2W)
Answers
Width is 50 on each side and length.
Find the dimensions of the field if the length ?
To use this length and width of a rectangle given the perimeter calculator, we need to input the perimeter and the value of one side. Let's look at this example: The perimeter of a rectangle is 10 inches, and the width is 3 inches. Substitute in the known values: L = 10 / 2 - 3.In the same way, if the perimeter and the width are known, the length can be calculated using the formula: Length(L) = P/2 - w. Where P = perimeter of the rectangle; and w = width of the rectangle.To calculate the length and width of a rectangle first, calculate the value of width 'w' by using the area of rectangle formula that is, 'w = A/l'. Then substitute the value of width in the formula of the perimeter of a rectangle and simplify the value of length 'l', that is, P = 2 (l + A/I).To learn more about perimeter refers to:
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What is the first step to solving the division problem below?
Divide 15 into 82 to get 5.
Divide 15 into 82 to get 6.
Multiply 15 by 5 to get 75.
Multiply 15 by 6 to get 80.
Answers
Answer:
divide 15 into 82 to get 5 is the first step
Step-by-step explanation:
Answer:
The answer is A, ¨Divide 15 into 82 to get 5.¨
Step-by-step explanation:
Please make as brainliest! Thanks and i hope it is right!!! Pls say if wrong. Bye
Suppose that ƒ is a function given as f(x) = 4x² + 5x + 3.
Simplify the expression f(x + h).
f(x + h)
Simplify the difference quotient,
ƒ(x + h) − ƒ(x)
h
=
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The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(x+h)-f(x)
f'(x) =lim
h→0
h
ƒ(x + h) − f(x)
h
=
Answers
Answer:
f(x +h) = 4x² +4h² +8xh +5x +5h +3
(f(x+h) -f(x))/h = 4h +8x +5
f'(x) = 8x +5
Step-by-step explanation:
For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.
F(x+h)Put (x+h) where h is in the function, and simplify:
f(x+h) = 4(x+h)² +5(x+h) +3
= 4(x² +2xh +h²) +5x +5h +3
f(x +h) = 4x² +4h² +8xh +5x +5h +3
Difference quotientThe difference quotient is ...
(f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h
= (4h² +8xh +5h)/h
(f(x+h) -f(x))/h = 4h +8x +5
LimitWhen h=0, the value of this is ...
f'(x) = 4·0 +8x +5
f'(x) = 8x +5
__
Additional comment
Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.
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Solving Systems Using Inverses
Solve the system:
4x - 5y + z = 9
6X + 8y - Z=27
3x – 2y + 5z = 40
([?], [ ], [ ])
Answers
Answer:
12x the second -12x -16
Step-by-step explanation:
Solving systems of equations with 3 variables is very similar
Answer:
[3,2,7]
Step-by-step explanation: