Line PQ has endpoints at P (-2,3) and Q (4,1). The center of dilation is (-1,4) and the scale factor is 2. What are the coordinates of the endpoints of P'Q'?
Answers
The trick is to double the distance from the centre of dilation to each point, P and Q to get the point P' and Q'
P' (-3, 2)
Q' (9, -2)
Related Questions
What is the circumference of this circle, in millimeters? use 22/7 for pi
r = 49
Answers
Answer: circumference = 308mm
Step-by-step explanation: the formula for the circumference of a circle is given by
C=2πr
Given that r=49mm
Pi=22/4
C=2*22/7*49
C=44*7=308mm
In geometry, the circumference of a circle is the distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge of a disk, circumference is a special case of perimeter.
Find the missing length.
Answers
a^2+b^2=c^2
12^2+9^2=c^2
144+81= c^2
225=c^2
15=c
Final answer: c=15
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13. 0 1 2
Answers
m∠C = 85°, a= 10, c = 13
From the Law of Sines,
sin(A)/a = sin(C)/c
sin(A) = (a/c)*sin(C)
= (10/13)*sin(85°)
= 0.7663
m∠A = sin⁻¹ 0.7663 = 50°, or 130°
When m∠A = 50°, obtain
m∠B = 180° - (m∠A + m∠C) = 180 - (50+85) = 45°
Again from the Law of Sines, obtain
b = (sinB/sinC)*c = 9.2
When m∠A = 130°, obtain
m∠B = 180° - (130 + 85) = -35° (not possible)
Therefore this triangle does not exist.
Answer:
There is only one possible triangle, with
A=50°, B=45°, C=85°, a=10, b=9.2, c=13.
Final answer:
Correcting for the apparent typo in the question, assuming 'c' refers to an angle and a side length respectively, there can only be one possible triangle formed given the angle and two sides. This is based on geometric principles where a unique triangle can be determined from an angle opposite and its respective side length.
Explanation:
The question presents a probable typo since it mentions two different values for 'c'. Assuming 'c = 85°' refers to an angle, and 'c = 13' refers to the length of a side opposite this angle, the proper interpretation involves finding possible triangles given an angle and two sides. However, the principles of geometry dictate that with one angle and two sides specified, especially in this non-ambiguous manner where one side length and the angle opposite are known, one can determine a unique triangle, assuming the given information leads to a viable geometric figure.
By using the Law of Sines, one might attempt to find the other angles or sides, but since we only have one angle and one side length, we directly know there's no ambiguity - geometrically speaking, there's only one way to construct such a triangle, thus, only one possible triangle can be formed given the corrected assumptions.
How many cans of paint are needed to cover an area of 2,200 square units if one can of paint covers an area of 400 square units? 4 5 6 8?
Answers
Then you just need to divide 2,200 square units with 400 square units.
The equation will be : (2,200 square units / 400 square units) x 1 can= 4.5 cans
After you round up the result it would be 5 cans.
Answer: 5 cans
Simplify 5 − (−1).
a. 6
b. −6
c. 4
d. −4
Answers
Subtracting a negative number is the same as adding a positive.
So instead of
5 - (-1)
We could write
5 + 1
5 + 1 = 6
The answer is 6.
Hope this helps! :)
Answer: it is a
Step-by-step explanation: :) :v :B
Smallville’s town council has records of the town’s budget over a 10-year period. Create a best fit and model for the data. What does the model predict the town’s budget will be in the year 2011?
Answers
If these were the missing choices:
A)$391,000
B)$417,000
C)$404,000
D)$411,000
My answer is D) $411,000 in 2011.
There is an average increase of 4% from the previous budget to arrive at the amount of the current year.
2009 budget $381,700
381,700 * (1.04)² = 381,700 * 1.0816 = 412,846.72 only Choice D. is nearest to the amount
2000 budget $265,100
265,100 * (1.04)¹¹ = 265,100 * 1.540 = 408,254 only Choice D. is nearest to the amount.
Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption? 4:9 ≠ 6:13 4:9 ≠ 6:7 4:13 ≠ 6:9 4:5 ≠ 6:13
Answers
Please see attached file for the triangle’s figure:
Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).
Therefore, the inequality that she will use to contradict the assumption
is 4:9 ≠ 6:13.
To add, a relation that holds
between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.
Inequalities are governed by the following properties:
Transitivity
Converse
Addition and subtraction
Multiplication and division
Additive inverse
Multiplicative inverse
Applying a function to both sides
Answer:
4:9 ≠ 6:13.
Step-by-step explanation:
If BC = 5 and CD = 26, find AC.
Answers
Answer:
[tex]AC=\sqrt{130}[/tex]
Step-by-step explanation:
AC is the geometric mean. Solve it using this proportion:
[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]
Now fill in the values we know:
[tex]\frac{5}{AC}=\frac{AC}{26}[/tex]
Cross multiply to get
[tex](AC)^2=130[/tex]
That means that
AC = [tex]\sqrt{130}[/tex], which, in decimal form is
AC = 11.40175425
The population of a type of local frog can be found using an infinite geometric series where a one equals 84 and the common ratio is one over five find the sum of the infinite series that will be the upper limit of this population. 87,105,425, or this series is divergent
Answers
Since r, the common ratio squared is less than one, the sum will converge to a limit. Rule: if r^2<1 infinite series converges, otherwise it diverges.
Since the sum of any geometric sequence is:
s(n)=a(1-r^n)/(1-r)
And if r^2<1, (1-r^n) becomes 1-0=1 as n approaches infinity.
So whenever r^2<1 the sum of the infinite series is just:
s(n)=a/(1-r)
Since a=84 and r=1/5 this infinite series has a sum of:
s(n)=84/(1-1/5)
s(n)=84/(4/5)
s(n)=5(84)/4
s(n)=105
Point r is located at (3,0). point s is located at (0,-4). what is the equation of the line through these two points
Answers
slope = (-4 - 0) / (0 - 3) = -4/-3 = 4/3
y = mx + b
slope(m) = 4/3
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 4/3(0) + b
-4 = b
so ur equation is : y = 4/3x - 4....or 4x - 3y = 12 <==
4n-3<12 solve and please don't give me the answer just the equation
Answers
So first bring -3 to the right hand side:
4n-3<12 => 4n < 12+3 => 4n < 15
Then divide by 4
4n/4 < 15/4 => n < 15/4
You can't simplify it beyond that.
The circle given by x^2+y^2-4x-10=0 can be written in standard form like this: (x-h)^2+y^2=14. What is the value of h in this equation??
Answers
Answer: H=2
Step-by-step explanation:
we just need to complete the square for the x terms
gropu x terms
x^2-4x
take 1/2 of linear coefient and square it
-4/2=-2, (-2)^2=4
x^2-4x+4
factor
(x-2)^2
h=2
The value of h is 2.
Completing the square for the x terms by grouping x terms
x^2-4x
Taking 1/2 of linear coefficient and squaring it.
-4/2=-2, (-2)^2=4
x^2-4x+4
Factorizing the equation.
(x-2)^2
h=2.
What is an equation?An equation is a mathematical statement this is made of two expressions related with the aid of an identical sign. As instance, 3x – 5 = 16 is an equation. To fix this equation, we get the value of the variable x as x = 7.
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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -(x-4)2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answers
g(x) is f(x) reflected about the about the x-axis and shifted to the right by 4 units.
Since -x^2-5 = 0 implies x = +-sqrt(5)i, there are no x-intercepts
Transformations:
Reflect f(x) in the x-axis,
then vertically shift the result down by 5 units,
to get g(x).
A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^10 and outside the cylinder x+y=1. find the volume.
Answers
For this case, we use
the cylindrical coordinates:
x² + y² = r²
dV = r dz dr dθ
The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞
θ = 0 to 2π
Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ
V = ∫ [0 to 2π] 1/18 dθ
V = θ/18 |[0 to 2π]
V = π/9
The volume of the volcano is an illustration of definite integral
The volume of the volcano is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
The graphs are given as:
[tex]\mathbf{z = 0}[/tex] and [tex]\mathbf{z = \frac{1}{(x^2 + y^2)^{10}}}[/tex]
The cylinder is:
[tex]\mathbf{x + y =1}[/tex]
For cylindrical coordinates, we have:
[tex]\mathbf{r^2 =x^2 + y^2}[/tex]
So, we have:
[tex]\mathbf{z = \frac{1}{(r^2)^{10}}}[/tex]
[tex]\mathbf{z = \frac{1}{r^{20}}}[/tex]
Where:
[tex]\mathbf{r = 1 \to \infty}[/tex]
[tex]\mathbf{\theta = 0 \to 2\pi}[/tex]
So, the integral is:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{20}}} \, r\ dr } \, d\theta }[/tex]
Cancel out r
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{19}}} \, dr } \, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {r^{-19}} \, dr } \, d\theta }[/tex]
Integrate
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}r^{-18}}} |\limits^{\infty}_1 \, d\theta }[/tex]
Expand
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(\infty^{-18} -1^{-18}) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(0 -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}( -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{\frac{1}{18} }} , d\theta }[/tex]
Integrate
[tex]\mathbf{V = \frac{1}{18}(\theta)|\limits^{2\pi}_0}[/tex]
Expand
[tex]\mathbf{V = \frac{1}{18}(2\pi - 0)}[/tex]
[tex]\mathbf{V = \frac{1}{18}(2\pi )}[/tex]
Cancel out 2
[tex]\mathbf{V = \frac{1}{9}\pi}[/tex]
Hence, the volume is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
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What percent of 210 is 70?
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 210&100\\ 70&x \end{array}\implies \cfrac{210}{70}=\cfrac{100}{x}\implies x=\cfrac{70\cdot 100}{210}[/tex]
so x%=x/100
'of' means multiply
so
what percent of 210 is 70 translates to
x/100 times 210=70
210x/100=70
21x/10=70
times 10 both sides
21x=700
divide both sides by 21
x=33.333333
33.33333333% of 210 is 70
Match the perfect square trinomials with their factors 4a2 + 4a + 1 (2 + a)(2 + a) 4a2 − 4a + 1 (2a + 1)(2a + 1) 4 − 4a + a2 (2a − 1)(2a − 1) 4 − 4a − a2 (2 − a)(2 − a) 4 + 4a + a2
Answers
4 − 4a + a2 = (2 - a)^2 = (2 − a)(2 − a)
4a2 − 4a + 1 = (2a -1)^2 = (2a − 1)(2a − 1)
4 + 4a + a2 = (2 + a)^2 = (2 + a)(2 + a)
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 6
A =
37.68 sq. units
113.04 sq. units
226.08 sq. units
Answers
Area of a circle = [tex] \pi r^{2} [/tex] = [tex]3.14 * 6 * 6 = 3.14 * 36 = 113.04 [/tex] sq. units.
Hence, the answer is B.
Answer: 113.04 sq. units
The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?
Answers
When 332 college students are randomly selected and surveyed, it is found that 113 own a car. find a 99% confidence interval for the true proportion of all college students who own a car?
Answers
n = 332, sample size
p = 113/332 = 0.3404, sample proportion
99% confidence interval
The confidence interval for the population is calculated from
[tex]p \pm z^{*} \sqrt{ \frac{p(1-p)}{n} } [/tex]
where z* = 2.58 for the 99% confidence level (from tables)..
[tex]2.58 \sqrt{ \frac{0.3404(1-0.3404)}{332} } =0.0671[/tex]
Therefore the 99% confidence interval is
(0.3404 - 0.0671, 0.3404 + 0.0671) = (0.2733, 0.4075)
Answer:
The 99% confidence interval is (0.273, 0.408) or (27%, 41%).
That is, between 27% and 41% of the students own cars.
Find the area under the standard normal curve between z = -1.5 and z = 2.5
Answers
To area under the standard normal curve between z = -1.5 and z = 2.5 is 0.927
Explanation:A standard normal curve, also known as the standard normal distribution, is a bell-shaped, symmetrical probability distribution with a mean of 0 and a standard deviation of 1. It serves as a reference for many statistical analyses and is often denoted as the Z-distribution.
To find the area under the standard normal curve between z = -1.5 and z = 2.5, we need to use the z-table. The z-score of -1.5 corresponds to an area of 0.0668 and the z-score of 2.5 corresponds to an area of 0.9938. To find the area between these two z-scores, we subtract the smaller area from the larger area:
= 0.9938 - 0.0668
= 0.927
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The area between these z-scores is 0.9270.
The area under the standard normal curve between z = -1.5 and z = 2.5 can be found using the z-table.
First, find the area to the left of
z = -1.5, which is 0.0668.
Next, find the area to the left of
z = 2.5, which is 0.9938.
Subtract these two values to get the area between z = -1.5 and z = 2.5 :
0.9938 - 0.0668
= 0.9270.
Redo, Answers please?
Answers
10) ?=13
14) ?=13
11+15+13 = 39
39 - 27 = 12
so
answer
? = 12
10)
18 - 11 + 13 = 20
33 - 20 = 13
so
answer
? = 13
14)
16+17+12=45
45 - 27 = 18
answer
? = 18
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is
a-36
b-18
c-288
d-5
Answers
One student can paint a wall in 10 minutes. another student can paint the same wall in 15 minutes. working together, how long will it take for them to paint the wall?
Answers
One student can paint a wall in 10 minutes
another student can paint the same wall in 15 minutes.
If they paint together the wall, the result time will be
15mn - 10mn = 5 mn
proof:
let / = minute
student 1: / / / / / / / / / /
student2: / / / / / / / / / / / / / / /
x----------------------------------------x
already done
the remain time is / / / / / = five minutes
Answer:
6 days
Step-by-step explanation:
Given that one student can paint a wall in 10 minute and another student in 15 minutes.
Since if number of persons increase, painting time decreases, this is a question of inverse proportion
Hence if they work together they can paint in one day
[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work
i.e. work completed in 1 day when they work together
=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]
Hence in 6 days they can together complete the full work
HOW DO YOU MOVE A VARIABLE FROM ONE SIDE OF AN EQUATION TO ANOTHER? I need to know as I'm reviewing module 7 algebra and i want to know please
Answers
For example in the equation 5+a=7, subtract a from both sides to get 5=7-a.
If the initial equation was 5-a=7, add from both sides (5=a+7).
Basically, if the initial value is negative, add its value to cancel to zero.
Do the opposite if the initial value is positive.
A given line has the equation 10x + 2y = −2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
Answers
Step 1
Find the slope of the given line
we have
[tex]10x+2y=-2[/tex]
Isolate the variable y
Subtract [tex]10x[/tex] both sides
[tex]2y=-10x-2[/tex]
Divide by [tex]2[/tex] both sides
[tex]y=-5x-1[/tex]
The slope of the given line is
[tex]m=-5[/tex]
Step 2
Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]
we know that
If two lines are parallel. then their slope are equal
In this problem we have
[tex]m=-5[/tex]
[tex](0, 12)[/tex]
The equation of the line into slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]12=-5*0+b[/tex]
[tex]b=12[/tex]
the equation of the line is
[tex]y=-5x+12[/tex]
therefore
the answer is
[tex]y=-5x+12[/tex]
enter an equation in slope-intercept form that describes a line that contains the points (4,1) and (4,2)
Answers
so... the slope is undefined, the graph of it is just a vertical line, check the picture below, and that's the equation.
now... you can't quite put it in y = mx + b, or slope-intercept form, since it has no defined slope and it doesn't have an y-intercept either.
Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x^5 + 9x^4 + 5x^3 + 3
Answers
In this case because the highest order term is -3x^5, as x approaches -oo, y approaches +oo. And as x approaches +oo, y approaches -oo.
Divide 35b^5 +20ab^3 +20a^2b^2 by 5b^2
Answers
So 35b^5 / b^2 = 35b^3, 30ab^3 / b^2 = 30ab, and 20a^2b^2 / b^2 = 20a^2.
So your final answer is 35b^3 + 30ab + 20a^2.
A club decides to sell T-Shirts for 15$ as a fund-raiser. It cost $20 plus $9 per T-Shirt to make them. How many T-Shirts need to be made to make a profit of at least $150?
Answers
The expression for total price of selling the T-shirts is 15T
Profit = Total cost of selling - Total cost of buying
Profit = 15T - (20+9T)
Profit = 15T - 20 - 9T
Profit = 6T - 20
To make profit ≥150
6T - 20 ≥ 150
6T ≥ 170
T ≥ 170/6
T ≥ 28.3
The minimum number of T-shirts needed is 29 T-shirts
A square garden plot has an area of 75 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot..
Answers
The area of a square is calculated by the formula:
A = l²
As A = 75 ft², we have:
75 = l²
l = √75
Now, note that: 75 = 3 . 25 = 3 . 5²
So:
l = √(3 . 5²) = √3 . √(5²)
l = 5√3 ft
Now, we can assume √3 = 1.73
l ≈ 5 * 1.732
l ≈ 8,7 ft (Note that I have already put it in the nearest tenth)
OK :)