Rectangles are similar figures, thus if scaled copies of each other then the ratios of corresponding sides must be equal
compare ratios of lengths and widths
rectangles A and B
k = [tex]\frac{12}{15}[/tex] = [tex]\frac{4}{5}[/tex] ← ratio of lengths
k = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex] ← ratio of widths
scale factors are equivalent, hence rectangle A is a scaled copy of B
rectangles C and B
k = [tex]\frac{15}{30}[/tex] = [tex]\frac{1}{2}[/tex] ← ratio of lengths
k = [tex]\frac{10}{15}[/tex] = [tex]\frac{2}{3}[/tex] ← ratio of width
scale factors (k ) are not equal, hence C is not a scaled copy of B
rectangles A and C
k = [tex]\frac{30}{12}[/tex] = [tex]\frac{5}{2}[/tex] ← ratio of lengths
k = [tex]\frac{15}{8}[/tex] ← ratio of widths
the scale factors are not equal hence A is not a scaled copy of C
For two rectangles, one of length L and width W, and other of length L' and width W', the second is a rescale of the first one only if exists a real number k such that:
L' = k*L
W' = k*W
Here we know:
Rectangle A: length = 12, width = 8Rectangle B: length = 15, width = 10Rectangle C: length = 30, width = 15Let's see if rectangle A is a scaled copy of rectangle B.
To see this, we just must see if the quotients between the lengths and between the widths are equal:
15/12 = 1.25
10/8 = 1.25
Then yes, rectangle A is a rescaled copy of rectangle B, and the scale factor is k = 1.25
Is rectangle B a rescaled copy of rectangle A?
Obviously yes. The scale factor will be the inverse of the previous one, we will get:
k = 1/1.25 = 0.8
How we do know that rectangle C is not a scaled copy of rectangle B?
Because the length of C is twice the length of B, but the width of C is not twice the width of B.
Is rectangle A a scaled copy of rectangle C?
No, as we already see that rectangle C is not a rescaled copy of rectangle B, and we know that rectangle A is a rescaled copy of rectangle B.
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What percentage increase is this?
225 to 255
13 .3333... = 13 [tex]\frac{1}{3}[/tex] %
percentage increase is calculated as [tex]\frac{increase}{original}[/tex] × 100%
increase = 255 - 225 = 30 and original = 225
[tex]\frac{30}{225}[/tex] × 100% = 13.33.... % = 13 [tex]\frac{1}{3}[/tex] %
Tom paid $245.97 for a laptop. This was 3/5 of the original price. What was the original price?
Let's make the mysterious, original price not-so-mysterious by calling it x. 245.97 is 3/5 of x.
We can equation this.
245.97 = 3/5x
x = 245.97 / (3/5)
x = 409.95
The answer, I believe, is $409.95. Hope this helps!
The original price of the laptop that Tom bought is calculated using the formula for the value of a part. This leads us to an equation, $245.97 / 0.6, resulting in the original price of the laptop being $409.95.
Explanation:The subject of this question is basic mathematics, predominantly fraction and ratio. The problem states that Tom paid $245.97, which was 3/5 of the original price of the laptop. To find the original price, we can apply the formula for the value of a part, which states that the whole is equal to the part divided by the ratio representing the part. In this case, this gives us the equation $245.97 / (3/5) = Original Price.
To make this easier, we can convert the fraction 3/5 to its decimal form, which is 0.6. So, we will then have $245.97 / 0.6 = Original Price, which should give us the original price of the laptop. Completing the math, we find that the original price of the laptop is $409.95.
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Q # 16..please help me
Direct variation is a relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).
Given the equation [tex]2x-4y=0,[/tex] you can see that
[tex]4y=2x,\\\\y=\dfrac{2}{4}x=\dfrac{1}{2}x.[/tex]
Then the constant [tex]k=\dfrac{1}{2}.[/tex]
Answer: correct choice is C.
A cell phone company sold 450 cell phones in three hours. This was 30% of the number of phones sold that day. How many cell phones did the cell phone company sell that day?
A cell phone company sold 450 cell phones in three hour
450 is 30% of the number of phones sold that day
30% of number of phones = 450
We need to find the number of phones for 100%
Let x be the number of cell phones sold that day
30% of x is 450
[tex]\frac{30}{100} * x= 450[/tex]
multiply by 100 on both sides
30 * x = 45000
Divide by 30
x = 1500
So 1500 cell phones are sold that day
To find the total number of cell phones sold by the company in a day, set up a proportion using the given information and solve for the total number of cell phones sold. In this case, the company sold 15,000 cell phones that day.
A cell phone company sold 450 cell phones in three hours, which was 30% of the phones sold that day. To find the total number of cell phones sold that day, we can set up a proportion:
Let x be the total number of cell phones sold that day.
450/3 = x/100
450 × 100 = 3x
45000 = 3x
x = 15000
Therefore, the cell phone company sold 15,000 cell phones that day.
what is the equation of the line in standard form? please help me I am really having a hard time with this
Answer:
-4 - 2
m= --------- (over)
-1 - 2
Step-by-step explanation:
2x - y = 2
obtain the equation of the line in slope-intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (- 1, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{-1-2}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2
the line crosses the y-axis at (0, - 2 ) ⇒ c = - 2
y = 2x - 2 ← in point-slope form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange y = 2x - 2 into this form
subtract y from both sides
0 = 2x - y - 2 ( add 2 to both sides )
2x - y = 2 ← in standard form
Wanchen makes limeade using 3 5 cup water per 1 3 cup lime juice. Find the unit rates of water (cups) per lime juice (cups).
Answer:
Unit rate is 2.69 cups of water for 1 cup of lime juice.
Step-by-step explanation:
Rate of water (cups) per lime juice (cups) means how much water (cups) is added to 1 cup of lime juice to make limeade.
This can be calculated as,
Unit rate = Number of water (cups) / Number of lime juice (cups)
Unit rate = [tex]\frac{35}{13}[/tex]
Unit rate = 2.69 cups of water for 1 cup of lime juice.
What is the remainder when the polynomial 6x^2+11x−3 is divided by x + 2?
PLEASE HELP
remainder = - 1
6x² + 11x - 3 ÷ (x + 2 ) = 6x - 1 - [tex]\frac{1}{x+2}[/tex]
Answer: The required remainder is 1.
Step-by-step explanation: We are given to find the remainder when the following polynomial is divided by (x + 2) :
[tex]p(x)=6x^2+11x-3.[/tex]
Remainder Theorem : If a polynomial f(x) is divided by (x - a), then the remainder is f(a).
So, for the given polynomial p(x), the remainder will be equal to p(-2).
We have
[tex]p(-2)\\\\=6(-2)^2+11(-2)-3\\\\=24-22-3\\\\=-1.[/tex]
Thus, the required remainder is -1.
Need help lease!!!!!!!
(11)
the equation of a line in point- slope form is
y = mx + c ( m is the slope and c the y-intercept
thus y = 4x + 3 ← in slope-intercept form
the equation of a line in point- slope form is
y - b = m(x - a ) ( m is slope and (a, b ) a point on the line )
thus y - 3 = 4 ( x - 0 ) or y - 3 = 4x ← in point- slope form
the equation of a line in standard form is
Ax + By = C ( a is a positive integer and B, C are integers
rearrange y - 3 = 4x into this form
4x - y = - 3 ← in standard form
(12)
y = - 2x - 1 ← in slope-intercept form
y + 1 = - 2x ← in point- slope form
2x + y = - 1 ← in standard form
what is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?
x³ - 3x² + 4x - 2
complex roots occur in conjugate pairs
1 + i is a root then so is 1 - i
the factors of the polynomial are therefore
f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))
= (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )
= x³ - 3x² + 4x - 2
Answer:
f(x) = x3 – 3x2 + 4x – 2
Step-by-step explanation:
David wants to install a fence around his garden. The garden is rectangular and has an area of 240 square feet. One side of the garden is along the street and is 12 feet long. For this side of the garden, David will use fencing that costs $18 per linear foot. For the other three sides of the garden, David will use fencing that costs $15 per linear foot. What is the total cost of fencing? $756 $996 $1,032
Answer:
$996
Step-by-step explanation:
The rectangular plot has an area that is the product of its length and width. We are given the width as 12 feet, and the area as 240 ft², so we can find the length from ...
... A = L×W
... 240 ft² = L×(12 ft)
... 240 ft²/(12 ft) = L = 20 ft
Opposite sides of the rectangle are the same length, so the cost of fence for a side of a given length will be the sum of the costs of the opposites sides.
The 12 ft side has one segment that is $18 per foot, and one that is $15 per foot. For the 20 ft sides, both are $15 per foot. Then the total cost can be figured from ...
... (12 ft)·($18/ft + $15/ft) + (20 ft)·($15/ft +$15/ft) = 12·$33 +20·$30 = $996
A ferryboat makes four trips to an island each day.The ferry can hold 88 people.If the ferry is full on each trip,how many passengers are carried by the ferry each day?
Multiplication was invented to reduce the work involved in repeated addition.
... 88 + 88 + 88 + 88 = 4×88 = 352
352 passengers are carried to the island each day.
_____
Some questions must be answered before we can give a definite answer.
1. If the same person rides twice, are they counted twice?
2. Are passengers on the return trips (from the island) counted?
3. If return trip passengers are counted, is the ferry full on those trips?
4. Does every passenger to the island return the same day?
5. Does any passenger go to the island more than once per day?
What are the domain and range for the exponential function f(x)=ab^x , where b is a positive real number not equal to 1 and a > 0? Help please!
O domain: ( -∞,∞) ; range: (-∞,0)
O domain: (-∞,0] ; range: (-∞,∞)
O domain (-∞,∞) ; range: (0,∞)
O domain (0,∞) ; range: (-∞,∞)
Answer: Domain (-∞,∞) ; range: (0,∞)
Step-by-step explanation:
1. The exponential functions with the form [tex]f(x)=ab^{x}[/tex] has domain of all real numbers, becaure there is no values in the set of real number for which the value of [tex]x[/tex] is not define. When [tex]x[/tex] approches to ∞, the function approches to ∞.
2. When [tex]x[/tex] approches to -∞, the function approches to 0 but never touches it. This means that [tex]y[/tex] is always greater than zero ([tex]y>0[/tex]). Therefore, the range of the function is (0,∞).
Answer:
Lesson 1 unit 5 exponential, logarithmic, pricewise functions
Step-by-step explanation:
1. A and D
2. C
3. B
4.c
What is it called when transformation of the plane which reflects each point and then translates it called
The figures in a plane can be reflected, rotated, translated or dilated to produce new figures or images.
A transformation that moves all points to the same distance and in the same direction. The final figure looks the same, just moved over. It does not flip or gets rotated. It also does not change size.This type of translation is called glide reflection. Its the summation of translation and reflection.
Answer:
Glide Reflection
Step-by-step explanation:
Simplify. 7√50x^15y^21 Assume x and y are nonnegative.
A.5x7y102xy−−−√B.35x7y102xy2−−−−√C.35x7y10xy−−√D.35x7y102xy−−−√
Given expression is [tex]7 \sqrt{50x^{15}y^{21}}[/tex] where x and y are non negative.
Now we have to simplify this to find the correct matching choice.
[tex]7 \sqrt{50x^{15}y^{21}}[/tex]
[tex]=7 \sqrt{25*2x^{15}y^{21}}[/tex]
[tex]=7 \sqrt{25*2x^{14}*xy^{20}*y}[/tex]
[tex]=7*5x^{7}y^{10} \sqrt{2*x*y}[/tex]
[tex]=35x^{7}y^{10} \sqrt{2xy}[/tex]
Which best matches with choice D.
Hence final answer is [tex]35x^{7}y^{10} \sqrt{2xy}[/tex] .
Answer:
B
Step-by-step explanation:
I also got 35x^7y^10√2xy
:)
Please Help Soon!
Find (1.6 x 108)(5.8 x 106) (4 x 106) , expressed in scientific notation
A) 1.05 * 10^8
B) 2.32 * 10^8
C) 2.32 * 10^9
D) 9.28 * 10^8
we are given
[tex]\frac{(1.6\times 10^{8})(5.8\times 10^{6})}{(4\times 10^{6})}[/tex]
Since, we have to write this in scientific form
so, we will make all 10^x terms together
and all other terms together
so, we get
[tex]=\frac{(1.6\times 5.8) (10^{8}\times 10^{6})}{(4\times 10^{6})}[/tex]
we can multiply terms
[tex]=\frac{(9.28) (10^{8+6})}{(4\times 10^{6})}[/tex]
[tex]=\frac{(9.28) }{4} \times 10^{8+6-6}[/tex]
[tex]=2.32 \times 10^{8}[/tex]
so, option-B...........Answer
Answer:
2.32 x 10^8
Step-by-step explanation:
2.32 x 108
108 + 6 - 6 = 108
and
(1.6)(5.8)
(4)
=
9.28
4
= 2.32
thus,
2.32 x 108
Factor the quadratic expression completely. 15xˆ2-4x-4
Answer:
(3x-2)(5x+2)
Step-by-step explanation:
we have to multiply 15 and 4.
then find the factors of this product.
we get,
15 x 4=60
Now, factors of 60 which make 4 are 6 and 10
because 6-10=-4
So,
[tex]15 x^{2}-4x-4\\ =15x^{2} -10x+6x-4\\[/tex]
Now, we have to take common factor pairwise.
Taking 5x as common factor from first pair and 2 from second pair,
we get
[tex]15x^{2} -10x+6x-4\\=5x(3x-2)+2(3x-2)\\=(3x-2)(5x+2)[/tex]
(3x - 2 )(5x + 2 )
consider the factors of the product 15 × - 4 = - 60
which sum to give the coefficient of the middle term ( - 4 )
the factors required are - 10 and + 6
split the x- term using these factors
15x² - 10x + 6x - 4 ( factor by grouping )
= 5x(3x - 2) + 2(3x - 2)
Take out the common factor (3x - 2)
= (3x - 2)(5x + 2)
Complete the synthetic division problem below. -1|2 8 6What is the quotient in polynomial form?
A 2x + 6 is the quotient
Answer:
The quotient in polynomial form is 2x+6
Step-by-step explanation:
use the synthetic division
---------------------------
-1 2 8 6
0 -2 -6
-------------------------------------
2 6 0
Now we use the quotient we got.
quotient is 2 and 6. Remainder is 0
In quotient we have only two numbers
So we write it as 2x+6
The quotient in polynomial form is 2x+6
PLEASE HELP What is the range of this function? -1, -4, 4, 1, 8, 7, 18, 15
B
the range of the function are the values that the domain map to
here range { - 4, 1, 7 , 15 }
The range is the output values (also known as the y values)
-4, 1, 7 ,15 or letter B
The boys at Academy camp are working on math problems to prepare for a math competition. The camp leader has put a problem on the board for the students to work on. Paolo does the following problem incorrectly. Explain the error and redo the problem showing the correct answer
Paolo's answer -0.43-0.2 = -0.23
We don't actually know what the problem originally was, so we don't know what the error was or what the correct answer should be.
If the numbers on the left are given, and the problem is to find the number on the right, then ...
Paolo added 0.2 instead of subtracting it.
-0.43 -0.2 = -0.63 . . . . . correct answer
_____
If the left and right numbers are given and the problem is to find the one in the middle, then ...
Paolo incorrectly calculated 0.43 -0.23, getting -0.2 instead of +0.2.
-0.43 +0.2 = -0.23 . . . . correct answer
_____
If the problem is to find the term on the left, then ...
Paolo incorrectly added 0.2 and -0.23, getting -0.43 instead of -0.03.
-0.03 -0.2 = -0.23 . . . . correct answer
Solve x for the equation 2x^2-5x+1=3
Steps:
subtract 3 from both sides:
2x²-5x+1 - 3 = 3 - 3
Simplify:
2x² - 5x - 2 = 0
Solve with the quadratic formula :
for a = 2 , b = - 5 , c = - 2
x₁ = - ( - 5 ) +√ ( -5 )² - 4 * 2 ( - 2 ) / 2 * 2 =
x₁ = 5 + √ 41 / 4
x₂ = - ( - 5 ) - √ ( -5 )² - 4 * 2 ( - 2 ) / 2 * 2
x₂ = 5 - √ 41 / 4
What is the value of (a + b) in the system of equations below?
8(a + b) + 3z = −9
a + b + z = 2
Select one:
A. -5
B. -4
C. -3
D. -2
C
given the 2 equations
8(a + b) + 3z = - 9 → (1)
(a + b) + z = 2 → (2)
multiply (2) by 3 so that the coefficients of z are equal
3(a + b) + 3z = 6 → (3)
subtract (1) - (3) to eliminate term in z
5(a + b) = - 15 ( divide both sides by 5 )
(a + b) = - 3 → C
Which number line represents the solutions to |x + 4| = 2?
the first number line
given | x + 4 | = 2
removing the bars from the absolute value gives
x + 4 = 2 or x + 4 = - 2
x = 2 - 4 or x = - 2 - 4
x = - 2 and x = - 6 ← solutions
these are indicated on the number line by a solid circle at - 2, - 6
Answer:
The solution is represented by the first number line, wich has the solutions x=-6 and x=-2.
Step-by-step explanation:
We have an absolute value function for the equation. This means that we should have two differents solution in the real number line. As the equation is
[tex]|x+4|=2[/tex]
when we clear out the absolute value, we will have two possible solutions:
[tex]x+4=2[/tex]
and
[tex]-(x+4)=2[/tex]
now we clear x from both equations
[tex]x+4=2 \Leftrightarrow x=2-4 \Leftrightarrow x=-2[/tex]
[tex]-(x+4)=2 \Leftrightarrow -x-4=2 \Leftrightarrow -2-4=x \Leftrightarrow x=-6[/tex]
Then, we have that x=-2 and x=-4 are the solutions for the equation, and therefore the number line that represents the solution is the first one, where the points -6 and -2 are highlighted.
Write an expression that equals (x-13). It must have atleast 2 sets of parentheses and one minus sign. Verify that it is equal to (x-13).
Last Saturday,the MoviePlex theater sold 1,456 tickets.The theater sold 6 times as many regular price tickets as it sold discount tickets.Earl says that the expression 1,456 divided by 6 gives the correct number of discounted tickets.Is Earl correct?show your work
Earl is incorrect
let x be the number of discount tickets sold
then the number of regular tickets sold is 6x
the total tickets sold is 1456, thus
x + 6x = 1456
7x = 1456 ( divide both sides by 7 )
x = 208
number of discount tickets sold = 208
[tex]\frac{1456}{6}[/tex] ≠ 208
but [tex]\frac{1456}{7}[/tex] = 208
Earl is incorrect , dividing by 7 gives the amount sold
what is the correct solution to the equation 5 - 2x = -9?
5 - 2x = -9
[tex] \: \: \: \: \: \: \: \: \: \: \: \bold{ - 2x = - 9 - 5}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ - 2x = - 14}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = \cfrac{ - 14}{ - 2}} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = \cfrac{14}{2} }[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 7}[/tex]
Note: For a problem like this, we must first subtract the number that is 5, then we must know that two negatives make a positive and that we must add 9 and 5 to give us 14, then we must put it as a fraction since it makes it easier for us to finish the problem, next it is known that two negative signs make a positive thus eliminating the less Parentheses and finally we divide so that we get a result of[tex]\bold{ x = 7}[/tex]
In one version of a trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix there are 4.5 cups of peanuts mixed with 3 cups of raisins are these ratios equivalent? explain your reasoning.
Ask google if you still can't get the answer.
Please help me!
Which number equals (3)-3?
Answer:
1/27
Step-by-step explanation:
Its 1/27 because you have to multiply (3)-3,
3 times 3 times 3
that will give you positive 27 so if your on usatestprep its positive 1/27
The number (3)⁻³ equals 1/27, which is the result of taking the reciprocal of 3 raised to the third power.
The question asks which number equals (3)⁻³. The notation (3)-3 indicates that we are dealing with an exponentiation operation, specifically raising the number 3 to the power of -3. To solve this, we'll use the rule that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent. Therefore, (3)⁻³ is equal to 1/(3³).
Now we'll calculate the exponent 3³, which is 3 multiplied by itself three times: 3 x 3 x 3 = 27. So, 1/(3³) is 1/27.
The final answer is therefore (3)⁻³ = 1/27.
Can u plz help me ASAP.I REALLY NEED HELP I DONT UNFERSTAND AT ALL.
The solution follows the sequence ...
eliminate parenthesescollect termselminate decimal fractionsisolate the variable on one side and the constant on the otherdivide by the coefficient of the variable.The problem is in the first step, where parentheses are eliminated. One of the multiplications is done incorrectly, and the error is propagated through the rest of the solution.
0.15(y -0.2) = 0.15y - 0.03 . . . . not 0.15y - 0.3
If you carry forward the value 0.03 instead of 0.30, you find the answer is
... -153/35 = y
______
Some of the other steps should be ...
.15y -.03 = 2 - .5 + .5y
15y -3 = 150 +50y
-153 = 35y
What is the solution of the system
every hour on mondays, the bakers make 75 pies. They make an equal number of pies in each of three flavors: apple, cherry, and lemon. If the bakers work 8 hours on mondays, how many do they make that day?
If they're making 75 pies an hour, and working 8 hours a day, you would multiply 8 by 75. 8x75=600. Hope this helps!