Answer:
Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3
Step-by-step explanation:
i) the pre-image co-ordinates is Y(6, -12)
ii) the coordinates of the image is Y' (2, -4)
iii) therefore we can clearly see that if we divide the coordinates of the pre-image (6,-12) by 3 then we get the coordinates of the image(2,4).
Therefore this is a dilation with scale factor of 1/3.
Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3
Final answer:
The transformation from the pre-image point Y(6, -12) to the image point Y'(2, -4) is a dilation with a scale factor of 1/3.
Explanation:
Given an image point Y'(2, -4) of a transformation and the pre-image point Y(6, -12), we can determine the type of transformation and the scale factor. The transformation is a type of change that affects the position, size, or shape of a figure. To find out the type of transformation and the scale factor, we compare coordinates.
Since the x-coordinate changed from 6 to 2, it has been reduced by a factor of 3 (6 divided by 3 equals 2). The y-coordinate changed from -12 to -4, which also has been reduced by a factor of 3 (-12 divided by 3 equals -4). This consistent reduction indicates that the transformation is a dilation. The objects are shrunk uniformly in both dimensions by the scale factor.
The correct answer is therefore dilation with scale factor 1/3.
A cantaloupe weighs 1/2. A watermelon weighs four times as much as the cantaloupe, how much does the watermelon weighs?
Answer:2
Step-by-step explanation: 1/2=0.5 0.5x4=2
Find the final price on a $1,049 television
that is on sale for 12% off of the sales tax is
4.5%
Answer:
$883.40
Step-by-step explanation:
Calculate the amount of money needed to pay after the discount.n
$1049 × 88% = $923.12
Calculate the amount of money needed to pay after the tax.
$923.12 × 104.5% = $883.3684210526
=$883.40(rounded off to nearest cents)
hope this helps
To find the final price of the television on sale, calculate the discount amount, subtract it from the original price, and then add the sales tax amount.
Explanation:To find the final price of the television, we first need to find the discount amount by multiplying the original price ($1,049) by the discount percentage (12%).
Discount amount = $1,049 × 0.12 = $125.88
Next, subtract the discount amount from the original price to get the sale price:
Sale price = $1,049 - $125.88 = $923.12
Finally, add the amount of sales tax to the sale price. To find the sales tax amount, multiply the sale price by the sales tax rate (4.5%):
Sales tax amount = $923.12 × 0.045 = $41.54
Final price = Sale price + Sales tax amount = $923.12 + $41.54 = $964.66
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Buying a Car Math Quiz
QUESTION 2 of 10: According to AAA the average monthly maintenance cost on a used car is 75 per month. You are looking to pay cash for
the exact same Jeep at two different dealers. Dealer "A' wants $4.995.00. Dealer "B" wants 55,595.00 with free maintenance coverage for
one year. Which is the best deal?
Answer:
Dealer B
Step-by-step explanation:
Maintenance cost per year = 75$
Dealer "A' wants $4.995.00.
Dealer "B" wants 55,595.00 with free maintenance cover for a year.
It is obvious that the best deal is what dealer B is offering, with free maintenance cover per year. for example, if i pick dealer A, calculate the maintenance cover for 3years = $2700
whereas for dealer B, a whole year maintenance cost is free, it implies that one will start paying the next coming year i.e a year lesser than dealer A. by that time the one who picked dealer A must have paid $3600 for maintenance while the one who picked dealer B will about to pay $1800.
The best deal is what dealer B is offering coupled with the free maintenance cover for 1year.
Final answer:
After calculating the total costs for one year, Dealer B offers a better deal on the Jeep by saving $300, as it includes free maintenance, contrasting with Dealer A which results in higher overall costs after adding maintenance payments.
Explanation:
To determine which car deal from the dealers is the better option, we need to calculate the total cost of each option over the course of one year, including the average monthly maintenance cost on a used car. According to AAA, this cost is $75 per month.
For Dealer A, the cost of the car is $4,995 with no free maintenance, so the total cost after one year is the price of the car plus 12 months of maintenance:
Cost of the car: $4,995
12 months of maintenance: 12 * $75 = $900
Total cost for Dealer A after one year: $4,995 + $900 = $5,895
For Dealer B, the car costs $5,595 but comes with free maintenance for one year, which means:
Total cost for Dealer B after one year: $5,595
Comparing these totals, we see that Dealer B offers the better deal, with the overall savings being:
Savings: $5,895 - $5,595 = $300
(5x+17)+(2x+50) What does x equal?
Answer:
Step-by-step explanation:
(5x+17)+(2x+50)
5x+2x + 17+50
7x+67
IF 7x+67 = 0
7x = -67
x = - 67/7 OR x = -9.57
Solve for the variable 8x+7=-9
Answer:
-2
Step-by-step explanation:
8x+7=-9
8x=-9-7
8x=-16
x=-16/8
x=-2
Can you help solve this please
50 points for all questions
9) Volume of the cone: [tex]9152 mm^3[/tex]
10) New volume of the cone: [tex]339 mm^3[/tex]
11) The volume of the cone shrinks by a factor of [tex]3^3=27[/tex]
12) Volume of the composite figure: [tex]15 ft^3[/tex]
Step-by-step explanation:
9)
The volume of a cone is given by the equation
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
where
[tex]\pi r^2[/tex] is the area of the base, where
r is the radius of the cone
h is the height of the cone
For the cone in this problem, we have:
r = 18 mm (radius)
h = 27 mm (height)
Therefore, the volume of this cone is
[tex]V=\frac{1}{3}\pi (18)^2 (27)=9152 mm^3[/tex]
10)
In this second exercise, the radius and the height of the cone are divided by 3. Therefore we have:
[tex]r'=\frac{r}{3}=\frac{18}{3}=6 mm[/tex] is the new radius of the cone
[tex]h'=\frac{27}{3}=9 mm[/tex] is the new height of the cone
Therefore, the new volume of the cone is
[tex]V=\frac{1}{3}\pi r'^2 h'[/tex]
And substituting, we find
[tex]V=\frac{1}{3}\pi (6)^2 (9)=339 mm^3[/tex]
11)
We can understand what happened to the volume of the cone after dividing its dimensions by 3 by calculating the ratio of the original volume to the new volume:
[tex]\frac{V}{V'}=\frac{9152}{339}=27[/tex]
This means that the new volume of the cone is 27 times smaller than the original volume.
We see that this "factor of shrinking" corresponds to the total factor of shrinking ofits dimensions, to the power of 3. In fact:
- Each the radius and the height of the cone has shrunk by a factor of 3
- However, the cone is a figure in 3 dimensions, so the total factor of shrinking of its volume is [tex]3^3 = 27[/tex]
12)
The composite figure consists of a squared pyramid + a parallelepiped.
The volume of the square pyramid is given by:
[tex]V_1 = \frac{1}{3}Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 6 ft is the height of the pyramid
Substituting,
[tex]V_1 = \frac{1}{3}(5)(1)(6)=10 ft^3[/tex]
The volume of the parallelepiped is given by
[tex]V_2=Lwh[/tex]
where
L = 5 ft is the length of the base
w = 1 ft is the width of the base
h = 1 ft is the height
Substituting,
[tex]V_2 = (5)(1)(1)=5 ft^3[/tex]
So, the total volume of the composite figure is
[tex]V=V_1+V_2=10+5=15 ft^3[/tex]
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Answer:
9) Volume of the cone: 9152 mm^3
10) New volume of the cone: 339 mm^3
11) The volume of the cone shrinks by a factor of 3^3=27
12) Volume of the composite figure: 15 ft^3
Step-by-step explanation:
Again stuck why because our teacher got fired so we are stuck with substitute teacher
Q: 7>-20+b
Simply
Answer:
27 > b
Step-by-step explanation:
7 > -20 + b
7 + 20 > -20 + 20 + b
27 > b
please could someone help me?
if you have a scientific calculator type in y=4/3x+4
and you should find your answer
I need help with this please!
Answer:
If two parallel lines [tex]p[/tex] and [tex]q[/tex] are cut by a transversal, then the alternate interior angles are congruent.
Below is the prove of this.
Step-by-step explanation:
As we know that Alternate interior angles are two angles that are on the interior of [tex]p[/tex] and [tex]q[/tex], but on opposite sides of the transversal.
In other words, If two parallel lines [tex]p[/tex] and [tex]q[/tex] are cut by a transversal, then the alternate interior angles are congruent.
Lets prove this.
Given: p ║ q
Prove: ∠1 ≅ ∠2
Statement Reasons
1. p ║ q 1. Given
2. ∠1 ≅ ∠3 2. Corresponding Angles Postulate
3. ∠3 ≅ ∠2 3. Vertical Angles Congruence Theorem
4. ∠1 ≅ ∠2 4. Transitive Property of Congruence
Hahn passes the 0 point running 5 meters per second to the right. where will he be 6 seconds later
Answer:
30 meters away
Step-by-step explanation:
each second is equal to 5 meters, hence meters per second
Tell whether x and y show direct variation
1. y - x = 4
2. x - y = 0
3. 8 = xy
4. What expression represents the sum of (2x-5y) and (x+y)?
5. What expression is equivalent to (7x-5) - (3x-2)?
Answer:
i) this does not show direct variation.
ii) this shows direct variation
iii) this shows direct variation
iv) (2x-5y) + (x+y) = 3x - 4y
v) (7x-5) - (3x-2) = 4x - 3
Step-by-step explanation:
i.) y - x = 4 this does not show direct variation.
ii) x - y = 0 [tex]\Rightarrow[/tex] x = y this shows direct variation
iii) 8 = xy [tex]\Rightarrow[/tex] 8/x = y this shows direct variation
iv) the sum of (2x-5y) and (x+y) [tex]\Rightarrow[/tex] (2x-5y) + (x+y) = 3x - 4y
v) expression that is equivalent to (7x-5) - (3x-2)
[tex]\Rightarrow[/tex] (7x-5) - (3x-2) = 4x - 5 + 2 = 4x - 3
Find 987 divided by 47 using the most efficient strategy you can. Show your work
The quotient of 987 divided by 47 is found to be 21 using estimation and step-by-step long division.
Explanation:The question asks to find 987 divided by 47 using an efficient strategy and show the work. To solve this, we can perform long division.
First, we see how many times 47 goes into 987. Since 47 is close to 50 and we know that 50 times 20 is 1000, which is just above 987, we can start by estimating around 20.20 times 47 is 940. We subtract this from 987 to get a remainder of 47.Since we see that 47 goes into 47 exactly once more, we add this to our previous quotient of 20.The final answer is 21 because 47 goes into 987 exactly 21 times. The most efficient strategy here was to use estimation and subtraction to find the quotient step-by-step.
Jennie has 177 more songs downloaded on her mp3 player than Diamond. Together, they have 895 songs downloaded. How many do each of them have?
Answer:jennie has 536 songs and diamond has 359
Step-by-step explanation:
What ratio is equivalent to 2:9
Answer:
8:36
Step-by-step explanation:
Factors: 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36
GCF: 4
8 ÷ 4 = 2 36 ÷ 4 = 9
how do you do linear models?
Answer:
Identify the input and output values.
convert the data to do coordinate pairs.
find the slope.
write the linear model.
use the model to make a prediction by evaluating the function at the given x-value.
use the model to identify an x value that results in a given y value.
What’s 3 5/8 as a fraction
If you divide any number by itself , what is the result?
Answer:
it the same number.
Step-by-step explanation:
If five 4 liter bottles of soda are split evenly among 40 people how many liters of soda will each person get?
Answer:
.5 or l/2 liter
Step-by-step explanation
4 liters x 5= 20 liters / 40 people =.5 or 1/2 liter
Which Fraction is less than 3/5 3/10 3/4 2/3 or 5/3
Answer:
The fraction less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Given fractions are
[tex]\frac{3}{5} ,\frac{3}{10} ,\frac{3}{4}, \frac{2}{3}, \frac{5}{3}[/tex]
[tex]\frac{3}{5} =0.6\\\\\frac{3}{10}= 0.3\\\\\frac{3}{4} =0.75\\\\\frac{2}{3}=0.66 \\\\\frac{5}{3}=1.66[/tex]
Arranging the fraction in increasing order of their value
[tex]\frac{3}{10}= 0.3<\frac{3}{5} =0.6<\frac{2}{3}=0.66<\frac{3}{4} =0.75<\frac{5}{3}=1.66[/tex]
So,the fractions less than [tex]\frac{3}{5}[/tex] is [tex]\frac{3}{10}[/tex]
3 1/2, 3 5/6, 4 2/12, ………………, 4 5/6
What is the missing term?
What rule can you create for this pattern?
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
The sequence is [tex]3\frac{1}{2}, 3\frac{5}{6}, 4\frac{2}{12}, .... , 4\frac{5}{6}[/tex].
So, we have to find the missing term.
The sequence can be written in improper fraction as [tex]\frac{7}{2}, \frac{23}{6}, \frac{25}{6}, ... , \frac{29}{6}[/tex].
Therefore, the sequence is in A.P. as the consecutive numbers in the sequence are increasing by [tex]\frac{1}{3}[/tex].
As, [tex](\frac{23}{6} - \frac{7}{2}) = \frac{1}{3} = (\frac{25}{6} - \frac{23}{6})[/tex].
Therefore, the missing number is [tex](\frac{25}{6} + \frac{1}{3}) = \frac{27}{6} = \frac{9}{2} = 4\frac{1}{2}[/tex]. (Answer)
What place is the 4 at in the number 562,347
Answer: tenth place
Step-by-step explanation:
Answer:
The tens place.
Step-by-step explanation:
In order, the numbers would go as follows:
7 would be in the ones place.
4 would be in the tens place.
3 is in the hundreds place.
2 is in the thousands place.
6 is in the hundred thousands place.
5 is in the millions place.
How do I solve for Log(x+3)+log2=3 ?
Answer: x = 995
Step-by-step explanation:
In this equation our log doesn't have a base so it is given the default base of 10. This makes our equation really.
[tex]log_{10}(x+3) + log_{10}(2) = 3[/tex]
Now we put every equation as the exponent of our base 10 looks like this:
[tex]10^{log_{10} (x+3)} + 10^{log_{10} (2)} = 10^{3}[/tex]
Now we cancel out the log base 10 and the 10. We are left with:
(x+3) + (2) = 10^3
Lastly solve for x
x + 5 = 1000
x = 995
A farmer had a total of 995 horses and cows. After selling some of the horses and cows, he had 510 horses and 390 cows left. How many horses and cows did he sell altogether?
Answer: 95 sold
Step-by-step explanation:
995 horses and cows - 510 horses and 390 cows left = 95 sold
Answer:
95
Step-by-step explanation:
add 510 + 390 to find out the total number of horses and cows he has left. this equals 900
then you subtract the total of horses and cows he started with by what he has left to find out how many he sold
995-900=95
23
Select the correct answer.
What happens to an electric current produced from an electromagnet when the direction of the magnetic field changes?
A.
The current stops.
B. The current increases.
C.
The direction of the electric current changes.
D.
The current decreases.
E.
The direction of the electric current stays the same.
Reset
Next
Answer:
For plato users: Option C.
Step-by-step explanation:
there are 5 pink shirts and 9 green shirts. If there are 27 green shirts,how many pink shirts are there?
Answer:
Step-by-step explanation:
5 pinks =9 greens
x pinks = 27 greens
Cross multiply
5pinks × 27 greens =x pinks × 9greens
Divide both side by 9green
5 pinks × 27 greens / 9greens =x pinks
Then green cancel greens
x pink = 15 pinks
Then, 27 greens implies 15 pinks
Sara is reading a 280-page book. If
she has read 129 pages, what percent
of the book has she not read? im
Answer:
30%?
Step-by-step explanation:
im not really sure but 30 percent of 280 is 84 and i couldnt find anything else
since 280-129=88 i thought 84/30% was closest
cual es factor de 8
Answer:
ocho es 8
Step-by-step explanation:
si quieres a saver mas solo necesitas a preguntar ;)
solo estoy jugando no mi mesajas yo no te quiero solo estoy jugando otra ves si te quiero como un amigo
At 10 percent interest, how long does it take to quadruple your money?
Group of answer choices
15.36 years
14.33 years
15.11 years
14.55 years
15.56 years
It takes about 14.55 years for quadruple your money
Solution:
Given that,
At 10 percent interest, how long does it take to quadruple your money
Rule of 144:
The Rule of 144 will tell you how long it will take an investment to quadruple
Here,
Rate of interest = 10 %
Therefore, number of years to quadruple your money is obtained by dividing 144 by 10
Rule of 144 Formula:
[tex]N = \frac{144}{R}[/tex]
Where:
N = Number of many years times.
144 = Is the constant variable.
R = Rate of interest.
[tex]\rightarrow N = \frac{144}{10} = 14.4[/tex]
Thus it takes about 14.4 years for quadruple your money.
Another method:
If initial amount is $ 1 and it if quadruples it should be $ 4
We have to find the number of years if rate of interest is 10 %
Let "n" be the number of years
Then we can say,
[tex]Amount = Principal(1+\frac{R}{100})^n[/tex]
[tex]4 = 1(1+\frac{10}{100})^n[/tex]
[tex]4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55[/tex]
Thus Option D 14.55 years is correct
1.
What is the unit price of shampoo if a
15-ounce bottle costs $2.79?
Answer:
$2.79 per bottle$0.186 per ounceStep-by-step explanation:
When you talk about "unit price," you need to define the unit of interest. Unit prices on grocery store shelves don't always use the same unit, even for like items. Here it might be convenient to use any of the following as the "unit":
1 bottle1 ounce1 pint (16 ounces)1 cup (8 ounces)The "unit price" is computed as ...
unit price = (price for some number of units)/(the number of units)
The "number of units" may be larger, smaller, or equal to 1.
Then the price per cup (8 ounces) would be ...
unit price = (price for 15 oz)/(15/8 cups) = ($2.79)(8/15)
= $1.488 per cup
__
The price per ounce would be ...
unit price = ($2.79)/(15 oz) = $0.186/oz
__
We assume that the unit of interest is probably 1 ounce, but it could be something else. Your grader may expect the value to be rounded to the nearest cent, $0.19 per ounce.
The unit price of shampoo is approximately $0.186 per ounce.
Explanation:To find the unit price of shampoo, divide the cost of the bottle by the number of ounces it contains. In this case, the cost is $2.79 and the bottle is 15 ounces. So, the unit price can be calculated as $2.79 divided by 15 ounces, which gives us approximately $0.186 unit price per ounce.
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jake made some tarts. He sold 3/5 of them and gave 1/4 of the remainder to his friends. If he had 150 tarts left, how many did he sell?
Answer: 90 tarts
Step by Step: 150/5 = 30
30 multiplied times 3 = 90
Final answer:
Jake initially had 750 tarts, sold 450 of them, and had 150 tarts remaining after giving some to his friends.
Explanation:
Jake initially had a total number of tarts. He sold 3/5 of them and then gave 1/4 of the remainder to his friends. If he had 150 tarts left, we need to calculate the number he sold. Let's denote the total number of tarts as T. After selling 3/5 of T, Jake would have 2/5T left. Then, he gives away 1/4 of 2/5T, which means he's giving away 1/4 * 2/5T = 1/10T. So, he is left with 2/5T - 1/10T = 1/5T. We know that 1/5T equals 150, so T equals 150 * 5 = 750. Jake sold 3/5 of these, which is 3/5 * 750 = 450 tarts.