Answer:A
Step-by-step explanation:
The vertex of the image L'(6,8) is the greatest distance from the origin.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say the x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.
Since each point is equidistant from the axis of reflection as that of the image of that point. Thus, if we reflect a point (x,y) along the x-axis, then its x abscissa will stay the same but y ordinates will negate. Thus (x,y) turns to (x, -y)
Given that a triangle with vertices L (-2,5), E (1,4), and D (2,-2) is translated 4 units left, 3 units up, and then reflected over the line y=4 to form the image triangle L’E’D'.
If we subtract 4 from each x number and add 3 to each y number and then reflect over the line y=4 so then that would give each distance.
L (-2,5) -- L (-2 - 4,5 - 4 )
L'(6,8)
Resulting that L'(6,8) being the farthest from the origin (0,0)
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Can you please help with this.
Suppose f is a function that takes a real number x and performs the following steps in the order given:
(1) add 1
(2) take the square root
(3) subtract 4
(4) divide into 7
Find an expression for f(x).
f(x) =
X
State the domain of f using interval notation.
Answer:
Expression for f(x) = [tex]\frac{\sqrt{x + 1} - 4}{7}[/tex]
Domain in interval notation: [tex]\:[-1,\:\infty \:)[/tex]
Step-by-step explanation:
[tex]\textrm{Let }f(x)\text{ represent the function}[/tex]
Step 1: Add 1 to [tex]x[/tex] ==> x + 1
Step 2: Take square root ==> [tex]\sqrt{x+1}[/tex]
Step 3: Subtract 4: ==> [tex]\sqrt{x+1} - 4[/tex]
Step 4: Divide by 7 ==> [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]
The expression for f(x) is [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]
The domain of a function is the set of all inputs for which the function is real and defined
[tex]\sqrt{x+1}[/tex] is real only for positive values of the square root
This means
[tex]\sqrt{x+1} \ge 0[/tex]
Squaring both sides we get
[tex]x + 1 \ge 0[/tex]
Subtracting 1 from both sides we get
[tex]x \ge -1[/tex]
This is the lower limit for [tex]x.[/tex] There is no upper limit
The domain of[tex]f(x)[/tex] is therefore
[tex]x \ge -1[/tex]
In interval notation it is expressed as
[tex][-1,\infty)[/tex]
Note the square bracket on the left and parenthesis on the right. This notation means that -1 is part of the domain but [tex]\infty[/tex] is not included since at [tex]\infty[/tex] the function is not defined
Helppp!!!
How am I able to find the 14th term of an arithmetic sequence given a4=14 and a10=16
Answer:
[tex]a_{14}=\dfrac{52}{3}[/tex]
Step-by-step explanation:
General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.Given terms of an arithmetic sequence:
[tex]a_4=14[/tex][tex]a_{10}=16[/tex]Substitute the values into the general formula to create two equations:
[tex]\sf\underline{Equation \:1}\\\begin{aligned}a_4 & = 14\\\implies a+(4-1)d & = 14\\a + 3d & = 14\end{aligned}[/tex]
[tex]\sf\underline{Equation \:2}\\\begin{aligned}a_{10} & = 16\\\implies a+(10-1)d & = 16\\a + 9d & = 16\end{aligned}[/tex]
Subtract Equation 1 from Equation 2 to eliminate a:
[tex]\begin{array}{l r l}& a+9d & = 16\\- & a+3d & = 14\\\cline{2-3}&6d & = \:\:2\end{array}[/tex]
Solve for d:
[tex]\begin{aligned}\implies 6d & = 2\\\dfrac{6d}{6} & = \dfrac{2}{6}\\d & = \dfrac{1}{3} \end{aligned}[/tex]
Substitute the found value of d into one of the equations and solve for a:
[tex]\begin{aligned}a + 3d & = 14\\ \implies a+3 \left(\dfrac{1}{3}\right)&=14\\a+1&=14\\a+1-1&=14-1\\a&=13\end{aligned}[/tex]
Substitute the found values of a and d into the general formula to create an equation for the nth term of the arithmetic sequence.
[tex]\implies a_n=13+(n-1)\dfrac{1}{3}[/tex]
[tex]\implies a_n=13+\dfrac{1}{3}(n-1)[/tex]
To find the 14th term, simply substitute n = 14 into the equation:
[tex]\begin{aligned}a_n & = 13+\dfrac{1}{3}(n-1)\\\implies a_{14}& = 13+\dfrac{1}{3}(14-1)\\&=13+\dfrac{1}{3}(13)\\ & = \dfrac{39}{3}+\dfrac{13}{3}\\&=\dfrac{52}{3}\end{aligned}[/tex]
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32006 in standard form
Answer:
the answer is 3.456 × 108
Simplify the expression
Solution:
Substitute the value of the variable into the expression, then simplify.
Answer: -8
_________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Answer:
2x/y = -8
Step-by-step explanation:
The values are,
→ x = 12
→ y = -3
Given expression,
→ 2x/y
Simplifying the expression,
→ 2x/y
→ (2 × 12)/(-3)
→ (24)/(-3)
→ -(24/3) = -8
Hence, the answer is -8.
Jill and Frank decided to take a long weekend in New York. City Hotel has a special getaway weekend for $79.95. The price is per
person per night, based on double occupancy. The hotel has a minimum two-night stay. For this price, Jill and Frank will receive $50
credit toward their dinners at City's Skylight Restaurant. Also included in the package is a $3.99 credit per person toward breakfast for
two each morning.
Since Jill and Frank do not own a car, they plan to rent a car. The car rental agency charges $19.95 a day with an additional charge of
$.22 a mile and $1.19 per gallon of gas used. The gas tank holds 24 gallons.
From the following facts, calculate the total expenses of Jill and Frank (round all answers to nearest hundredth or cent as appropriate).
Assume no taxes.
Answer:
$560.33
Step-by-step explanation:
Hotel: 79.95*2*2=$319.8
Dinner: 182-50=$132
Breakfast:
24.17+26.88=$51.0551.05-3.99*4=$35.09Rental:
19.95*2=$39.94940-4820=120 120*0.22=$26.41/2=2/4 3/4-2/4=1/4 ---> so they used 1/4 of the tank which is 1/4*24=6 6*1.19=$7.1439.9+26.4+7.14=$73.44Hotel+dinner+breakfast+rental: 319.8+132+35.09+73.44=$560.33
Which of the following does not describe a rigid motion transformation?
Option 2. The description of the rigid motion transformation would be the dilation of the figure by the scale factor of 1/2.
What is meant by the term rigid motion transformation?The term rigid motion transformation has to do with the fact that when an object is moved the size and the shape of the object would still have to stay the same. This is different for the non rigid motion. This because the size and the shape would have to increase in this case.
When the object is moved from one area to the other and it remains the same then we would have to say that the rigid transformation has occurred.
Hence we would have to say that Option 2. The description of the rigid motion transformation would be the dilation of the figure by the scale factor of 1/2.
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Find the value of x in each case
Answer:
x=18
Step-by-step explanation:
m(<BCD) = 2x alternative Z
c=2x d=8x
m(<CD) =180 U
180/10x
x=18
a angle measures 10.8 more than the measure of its complementary angle what is the measure of each angle
Calculate the distance between the points P=(1, -1) and N=(5, -8) in the coordinate plane.
Round your answer to the nearest hundredth.
PLEASE PLEASE HELP ME
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06[/tex]
Suppose you need 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m to tow a car How would you calculate theme of this much chain
The mass of the tow chain will be equal to 12.96 kg.
What is an expression?The mathematical expression is the combination of 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 be used to denote the logical syntax's operation order and other properties.
Given that 6.0m of Grade 70 bow chain, which has a diameter of 3/8" and weighs 2.16 kg/m.
The mass of 1 m chain = 2.16 kg
Mass of 6-meter chain = 2.16 x 6
Mass of 6-meter chain = 12.96 kg
Therefore, the mass of the tow chain will be equal to 12.96 kg.
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Write each binary number as a base-ten number. 111110
The quotient of 4 and the difference of 7 and a number? You do not need to simplify.
For a body falling freely from rest (disregarding air resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 192 feet high and hits the ground in 8 seconds, how far did it fall in the first 4 seconds?
The distance covered by the falling freely body from rest will be 48 feet.
What is kinematics?The study of motion without considering the mass and the cause of the motion.
When a body falls freely from rest, the distance it travels straight changes as the square of the time (air resistance excluded). If something is dropped 192 feet from the summit of a tower, it lands on the ground in 8 seconds.
We know that the acceleration is due to gravity (g = 32 ft/s²).
d ∝ t²
d/t² = constant
Then the distance covered by the falling freely body from rest will be given as,
d / 4² = 192 / 8²
d / 16 = 192 / 64
d = 16 x 192 / 64
d = 48 feet
The distance covered by the falling freely body from rest will be 48 feet.
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Solve the inequality and express your answer in interval notation. x^2+10x+6 <0
The interval where the function is negative is:
(-5 - √19 , -5 + √19)
That is the solution set of the inequality.
How to solve the inequality?Here we have the following inequality:
x^2 + 10x + 5 < 0
So we want to find the values of x for which the quadratic function is negative.
To do so, we can solve:
x^2 + 10x + 5 = 0
The solutions are given by the quadratic formula:
x = (-10 ± √(10^2 - 4*6))/(2*1)
x = (-5 ± √19)
notice that the quadratic has positive leading coefficient, so it open upwards, then the function is below zero between the two roots, on the interval:
-5 - √19 < x < -5 + √19
Then the correct option is D.
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solve the quadratic equation
Make sure the equations equal 0
4w^2 - 42w + 20 = 0
PLEASE SHOW YOUR WORK!
Answer:
hello! it's all explained in the photo :)
Step-by-step explanation:
If 25 is 30% of a number, what is 130% of that
number?
(a) 83.3
(b) 89.3
(c) 102.3
(d) 108.3
(e) 110.3
Answer:
d
Step-by-step explanation:
Let the number be 'x'.
First find x and then find 130% of x.
30% of x = 25
[tex]\sf \dfrac{30}{100}*x = 25[/tex]
[tex]\sf x = 25*\dfrac{100}{30}\\\\ x = \dfrac{250}{3}\\\\[/tex]
Now, find 130% of x
130% of x = [tex]\sf \dfrac{130}{100}*\dfrac{250}{3}\\\\[/tex]
[tex]\sf = \dfrac{325}{3}\\\\ = 108.3[/tex]
LaVonne estimated 38% of 63 by rounding 38% up to 40%, rounding 63 up to 70, and then multiplying 70 by 0.4 to get 28. Is her estimate reasonable?
No, because she should have rounded 38% down to 30%.
No, because she should have rounded 63 down to 60.
Yes, because she correctly rounded 38% up to 40%.
Yes, because she correctly rounded 63 up to 70.
the correct option is the second one:
"No, because she should have rounded 63 down to 60"
In that case, her estimation would have been 24.
Is her estimate reasonable?First, we need to understand how rounding works. When we want to round to a given digit, we need to look at the digit that its located at its right.
If it is 5 or more, we round up.If it is 4 or less, we round down.In this case, LaVonne estimated 38% of 63, and the roundings that she did are:
38% up to 40%. This is correct, because the second digit is 8, so we round up here.
63 to 70. This is incorrect, because the second digit is 3 (smaller than 4) then here she should have round down to 60 instead of up to 70.
So what she should have gotten is:
0.4*60 = 24
That is a better estimation, were the actual value of the 38% of 63 is:
0.38*63 = 23.94
You can see that when rounding down, the estimation is much closer to the actual value.
So, the correct option is the second one:
"No, because she should have rounded 63 down to 60"
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Solve for x.
x^2 = a
a>0
Answer:
x<0; x>0
Step-by-step explanation:
Basically, anything but zero, depending on what a is.
Answer:
x = ± [tex]\sqrt{a}[/tex]
Step-by-step explanation:
x² = a ( take square root of both sides )
x = ± [tex]\sqrt{a}[/tex]
Husain would like to divide £ 68000 in the ratio 2:3 for his 2 brothers Ali and Hassan. How much money each will get?
2:3=5
Ali=2÷5×£68000
Ali=£40800
Hassan=3÷5×£68000
Hassan=£27200
90 items to ship full case and 8 items per case
Answer:
That means you would only be able to fit 11 cases since 8 × 11 = 88. Any more cases would exceed 90 items.
Step-by-step explanation:
The stemplot displays 26 students’ scores on a 90-point statistics test.
A stemplot titled Test scores has values 43, 45, 46, 51, 52, 53, 55, 57, 60, 63, 63, 65, 66, 67, 67, 69, 69, 71, 71, 72, 74, 76, 77, 79, 84, 85.
Which of the following best describes the center and variability of the distribution?
The scores on the test are centered around 63 and vary from 45 to 85.
The scores on the test are centered around 66 and vary from 43 to 85.
The scores on the test are centered around 66 and vary from 40 to 80.
The scores on the test are centered around 69 and vary from 45 to 85.
Answer:
The answer is B
Step-by-step explanation:
Just look at the numbers, that is the only one with the correct range.
The scores on the test are centered around 66 and vary from 43 to 85. Therefore, the correct option is option B.
What is mathematical distribution?
Distributions are objects that generalise the traditional idea of functions used for mathematical analysis. They are often referred to as Schwartz distributions or generalised functions. Functions with no classically defined derivatives can be distinguished using distributions.
In the theory of partial differential equations, distributions are frequently utilised because it may be simpler to prove the existence of distributional solutions (weak solutions) rather classical solutions or because there may not be any suitable classical solutions. The scores on the test are centered around 66 and vary from 43 to 85.
Therefore, the correct option is option B.
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x+[tex]\sqrt{x}[/tex]x=90
Answer:
x=3 and her is right
Answer whyyyy
Step-by-step explanation:
Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 3 square feet. How many bags of sand are needed? Use 3.14 for pi. Round bags up.
Number of bags of sand needed to cover the area of circular pool is 51 bags.
What is a circle?A circle is a round-shaped figure that has no corners or edges.
Now it is given that,
Diameter of pool, D = 14 feet
So, Area of pool = π(D/2)²
⇒ Area of pool = π(14/2)²
⇒ Area of pool = π(7)²
⇒ Area of pool = 153.86 square feet
Now given Area of 1 bag = 3 square feet
So, number of bags required = Area of pool / Area of 1 bag
⇒ number of bags required = 153.86/ 3
⇒ number of bags required = 51.28
⇒ number of bags required ≈ 51
Thus, Number of bags of sand needed to cover the area of circular pool is 51 bags.
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Michael is grocey shopping. Before adding fruit to the bag, it weighed 5/9 pounds. Michael added 2/15 pounds of fruit to the bag. How much does it weigh now?
Answer:
31/45 lb
Step-by-step explanation:
You want to know the weight of a 5/9 lb bag after 2/15 lb of fruit are added to it.
Sum of fractionsFractions can be added when they have a common denominator. Here, the denominator will need to have factors of 3² = 9 and 3·5 = 15. It can be ...
3·3·9 = 45
Using this denominator, the fractions are ...
bag weight = 5/9 lb = 25/45 lb
fruit weight = 2/15 lb = 6/45 lb
The total weight of the fruit and the bag is ...
total weight = 25/45 lb + 6/45 lb = 31/45 lb
With the fruit, the bag weighs 31/45 pounds.
-6(2x+4)+1/2(8+3x)=-20
Based on the table below, evaluate f(2)
From the given table, we can see that the value of f(2) is 4
Input and output values in a tableThe input values in a function table are the dependent variables while the output values in a function table are the dependent variables.
Let the function of the table be represented as y = f(x), this shows that the variable x is independent while f(x) is dependent.
In order to determine the value of f(2), we need the output value, when the input value is 2. From the given table, we can see that the value of f(2) is 4
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Question 4 of 10
Assume that AGHI ALMN. Which of the following congruence statements
are correct? Check all that apply.
Π.A. LNG ΔΗ
B. IG LM
C. ME ZH
D. LG
E. GH = LM
F. TH= NM
Answer:
C. ME ZH
B. IG LM
F. TH= NM
Step-by-step explanation:
The correct congruence statements are A, B, and C such that ∠N = ∠I, GH = LM, and ∠M= ∠H are true for similar triangles.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
To determine which congruence statements are correct, we need to identify the corresponding sides and angles of the triangles.
The corresponding sides and angles are those that are in the same position in each triangle.
Using this information, we can check each statement:
A. ∠N = ∠I: This statement is true because ∠N and ∠I are corresponding angles in the congruent triangles.
B. GH = LM: This statement is true because GH and LM are corresponding sides in the congruent triangles.
C. ∠M= ∠H: This statement is true because ∠M and ∠H are corresponding angles in the congruent triangles.
D. IG = LM: This statement is false because IG and LM are not corresponding sides in the congruent triangles.
E. IH = NM: This statement is false because IH and NM are not corresponding sides in the congruent triangles.
F. ∠L = ∠I: This statement is false because ∠L and ∠I are not corresponding angles in the congruent triangles.
Therefore, the correct congruence statements are A, B, and C.
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Mark is y years old. In five years' time, Jack will be twice as old as Mark and Daniel will be 2 years younger than Jack is now. Write an expression in y for the sum of their 3 ages now.
Answer:
5y + 3 is the sum of the three ages
Step-by-step explanation:
Let y=Mark, d=Daniel j=Jack, and s=The sum
Mark is y years old. In five years jack will be twice as old as Mark
j + 5 = 2(y+5)
j + 5 = 2y + 10
j = 2y + 10 - 5
j = 2y + 5
Daniel will be two years younger than jack is now
d + 5 = j - 2
d = j - 2 - 5
d = j - 7
Replace j with (2y+5)
d = (2y+5) - 7
d = 2y - 2
Expression in terms of y for the sum of the 3 ages now
s = y + j + d
replace j and d with expressions we came up with above
s = y + (2y+5) + (2y-2)
s = y + 4y + 3
s = 5y + 3 is the sum of the three ages
15. The weight of a trout varies jointly as its length and the square of its girth. One angler
caught a trout that weighed 10.5 pounds and measured 26 inches long with an 18-inch
girth. Find the weight of a trout that is 22 inches long with a 15-inch girth. (Girth is the
distance around the body of a fish.)
The weight of the trout is 6.17 pounds.
How to find the weight of the trout?
We know that the weight of a trout varies jointly as its length and the square of its girth.
If W is the weight, x is the length and y is the girth, then:
W = k*x*y^2
Where k is a constant.
We know that one trout with:
x = 26 in
y = 18in
Has a weight of 10.5, then we can write:
10.5 = k*(26)*(18)^2 = k*8,424
Solving for k we get:
10.5/8,424 = k
Then the equation is:
W = (10.5/8,424)*x*y^2
Now, our trout has:
x = 22 in
y = 15 in
Then the weight is:
W = (10.5/8,424)*22*15^2 = 6.17
The weight of the trout is 6.17 pounds.
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