Answer:
x = 3
Step-by-step explanation:
8 - 3x = 17
You have to switch the 8 to the other side. To do this, you would have to move it after the 17 and add a minus to it, making it a -8 (this is because when a number is switched to the other side of the '=' sign, the number gets 'mirrored' aka positive numbers become negative and negative numbers become positive).
3x = 17 - 8
3x = 9
Now you have to do the same thing you did with 8 but instead you have to do it with 3. Since 3 has an invisble 'times sign' by it, the number after the equals will be divided by 3 in this case so...
x = 9 ÷ 3
x = 3
Answer: -3
Step-by-step explanation:
8-3x=17
-8 on both side to cancel it out
-3x=9
divide -3 on both sides
which would equal to -3
To check
8-3(-3)=17
8+9=17
17=17
Which of the following equations correctly shows the relationship between the values of x and the values of y?
Answer~ A. y=3x-4
Explanation~ Look at the X column. Start with the first row, which is 5 in the x column and 11 in the y column. Looking back at the equation. As you can see, it has the same variables that are in the table. Replace the x with the 5 from the table.
*Remember to put the 5 in parenthesis; you must always do this when plugging in numbers into your equations*
If done correctly, your equation should now look like this:
y=3(5)-4
Following PEMDAS, the order you solve order of operations, you must first multiply, as Multiplication is before Subtraction. So, you must multiply the 5 and 3. 5×3=15, so, now your equation should look like:
y=15-4
Simply subtract 4 from 15, and you should get 11. Therefore,
y=11
Continue this process down through the table to double check your work.
I hope I helped! Sorry for the dang essay lol
Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of APQR after a counterclockwise rotation of 90° about the origin
Label the image APQ'R'.
Answer:
See explanation
Step-by-step explanation:
A triangle PQR has its vertices at points P(1,-1), Q(3,-2) and R(3,-4).
A counterclockwise rotation by angle of 90° about the origin has the rule
[tex](x,y)\rightarrow (-y,x)[/tex]
Hence,
[tex]P(1,-1)\rightarrow P'(1,1);[/tex][tex]Q(3,-2)\rightarrow Q'(2,3);[/tex][tex]R(3,-4)\rightarrow R'(4,3).[/tex]The image triangle is shown in attached diagram.
4m – 5n + 6p + 2m - 3n – 2p
Use scientific notation to find the product of 7.13 × 10 -3 and 40. Include all of your calculations in your final answer.
Answer: 2.852 × 10-1
Step-by-step explanation:
7.13 x 10^-3 = 0.00713
0.00713 x 40 = 0.2852
0.2852 = 2.852 × 10-1
Answer:
[tex]\large\boxed{2.852\times10^{-1}}[/tex]
Step-by-step explanation:
[tex]\text{The scientific notation:}\\\\a\times10^k,\ 1\leq a<10,\ k\in\mathbb{Z}\\\\(7.13\times10^{-3})\times40=(7.13\times40)\times10^{-3}=285.2\times10^{-3}\\\\\text{Move the decimal point two places to the left,}\\\text{ increasing the exponent of the power of 10 also by 2}\\\\=2.852\times10^{-3+2}=2.852\times10^{-1}[/tex]
Classify the following triangle. Check all that apply
Answer:
Scalene and obtuse
Step-by-step explanation:
obtuse cuz 132 is greater than 90
scalene cuz all three sides have different lengths
give all possible proportions using the numbers 2 5 8 and 20
Answer:
[tex]\frac{2}{5},\frac{1}{4},\frac{1}{10},\frac{5}{2},\frac{5}{8},\frac{4}{1},\frac{8}{5},\frac{10}{1}[/tex]
Step-by-step explanation:
Proportions are fractions that can be created using the numbers given. Let's pair each and reduce if possible.
Starting with 2:
2/5
2/8 = 1/4
2/20 = 1/10
Then 5:
5/2
5/8
5/20 = 1/4
Then 8:
8/2 = 4/1
8/5
8/20 = 2/5
Lastly 20:
20/2 = 10/1
20/5 = 4
20/8 = 5/2
So, we can see some are repeating, hence the unique proportions are:
2/5, 1/4, 1/10, 5/2, 5/8, 4/1, 8/5, 10/1
The possible proportions using the numbers 2 5 8 and 20 are:
1. 2:5 = 8:20
2. 2:8 = 5:20
3. 5:20 = 2:8
4. 8:2 = 20:5
5. 20:5 = 8:2
6. 5:2 = 20:8
To create all possible proportions using the numbers 2, 5, 8, and 20, you can set up ratios and see how you can pair these numbers.
A proportion is essentially an equation that states two ratios are equal.
Here are some possible proportions you can create:
1. 2:5 = 8:20
(This is a direct proportion where both ratios reduce to 2:5.)
2. 2:8 = 5:20
(Again, this is a direct proportion where both ratios reduce to 1:4.)
3. 5:20 = 2:8
(This is just another way to write the second proportion.)
4. 8:2 = 20:5
(This is an inverse proportion where the first ratio is the reciprocal of the second.)
5. 20:5 = 8:2
(This is just another way to write the fourth proportion.)
6. 5:2 = 20:8
(This is an inverse proportion where the first ratio is the reciprocal of the second.)
7. 20:8 = 5:2
These are all the possible proportions you can create using the numbers 2, 5, 8, and 20. Note that in each proportion, you can switch the positions of the numbers (e.g., 2:5 = 8:20 is the same as 5:2 = 20:8), but the ratios remain the same.
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r+10<-3(2r-3)+6(r+3)
Answer:
r<17
Step-by-step explanation:
Distribute -3 through parentheses --> r + 10 < 6r+9+6 (r + 3)
Take out the oppisities --> r + 10 < 9 + 18
Move constant to the right and change the sign r < 27 -10
Subtract --> r < 17
An outdoor spa (hot tub) draws 1487 watts to keep the water warm. If the utility company charges $0.13 per kilowatt-hour, how much does it cost to operate the spa for four months during the winter (24 hours per day)? Assume each month has 30 days.
Answer:$556.73
Step-by-step explanation:
Watts (1487) multiplied by the hours used daily (24) =35688
Divided by 1000 = 35.68
multiply 35.68 times the number of days (120) = $556.73
Another example:
wattage x hours used ÷ 1000 x price per kWh = $$
1487 x 2880 ÷ 1000 x $0.13 = $556.73
Answer:
$556.7328 is total cost of operating hot tub for 4 months in an outdoor spa.
Step-by-step explanation:
Power drawn by hot tub = 1487 Watts = 1.487 kiloWatt
1 Watt = 0.001 kiloWatt
Utility charges charged by the company = $0.13 / (kiloWatt hour)
Charges in 1 day or 24 hours : (1 day = 24 hours)
$0.13 / (kiloWatt hour) × 1.487 kiloWatt × 24 hours = $4.63944
4 months = 4 × 30 = 120 days (1 month = 30 days)
Total charge for operating hot tub for 4 months or 120 days:
$4.63944 × 120 = $556.7328
Subtract using the number line.
−1 1/3−1/6
A number line ranging from negative two to two with an arrow on both ends and tick marks every one sixth
−1 5/6
−1 1/2
−1 1/6
1 1/2
Answer:
−1 1/2
Step-by-step explanation:
i took the test <3
The subtraction of the given expression by the number line is -3/2.
The given expression is:
[tex]-1 \dfrac{1}{3} - \dfrac{1}{6}[/tex]
The improper fraction of [tex]-1 \dfrac{1}{3} =- \dfrac{4}{3}[/tex]
So, the given expression can be written as:
[tex]-\dfrac{4}{3} - \dfrac{1}{6}[/tex]
Since LCM of (3, 6) = 2
[tex]-\dfrac{4}{3} - \dfrac{1}{6} =\dfrac{-2\times 4 - 1}{6}\\\\ -\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{9}{6}\\\\ -\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{3}{2}\\\\[/tex]
Now according to the number
This subtraction will be done, if we add 1/6 toward the left side of the number line.
Hence,
The subtraction:
[tex]-\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{3}{2}\\\\[/tex]
The procedure by number line is attached below.
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-5|x+3|+3=-17 what’s the answer
Answer:
x=−7,1
Step-by-step explanation:
1 Subtract 33 from both sides.
-5|x+3|=-17-3−5∣x+3∣=−17−3
2 Simplify -17-3−17−3 to -20−20.
-5|x+3|=-20−5∣x+3∣=−20
3 Divide both sides by -5−5.
|x+3|=\frac{-20}{-5}∣x+3∣=
−5
−20
4 Two negatives make a positive.
|x+3|=\frac{20}{5}∣x+3∣=
5
20
5 Simplify \frac{20}{5}
5
20
to 44.
|x+3|=4∣x+3∣=4
6 Break down the problem into these 2 equations.
x+3=4x+3=4
-(x+3)=4−(x+3)=4
7 Solve the 1st equation: x+3=4x+3=4.
x=1x=1
8 Solve the 2nd equation: -(x+3)=4−(x+3)=4.
x=-7x=−7
9 Collect all solutions.
x=-7,1x=−7,1
Label each angle as acute, obtuse, right, or straight and estimate the measure in degrees.
Answer:
7) Obtuse, I didn't use a protractor, so I'm estimating about 130 degrees.
8) Straight, all straight lines are equal to 180 degrees.
9) Acute, I estimated about 30-40 degrees, again, no protractor used.
Step-by-step explanation:
If x = 4y + 21y and y = 14 + 5, what is 3x × 7? No need to show your work.
y = 19
x = 4(19) + 21(19) = 76 + 399 = 475
3(475) × 7
1425 × 7
9975 <--- answer.
Hope this helped!
Nate
Answer:
the answer is 39
Step-by-step explanation:
what is the first need to solve (2/5) x -6=-16
Answer:
x = -25
Step-by-step explanation:
Solve for x:
(2 x)/5 - 6 = -16
Hint: | Put the fractions in (2 x)/5 - 6 over a common denominator.
Put each term in (2 x)/5 - 6 over the common denominator 5: (2 x)/5 - 6 = (2 x)/5 - 30/5:
(2 x)/5 - 30/5 = -16
Hint: | Combine (2 x)/5 - 30/5 into a single fraction.
(2 x)/5 - 30/5 = (2 x - 30)/5:
(2 x - 30)/5 = -16
Hint: | Multiply both sides by a constant to simplify the equation.
Multiply both sides of (2 x - 30)/5 = -16 by 5:
(5 (2 x - 30))/5 = -16×5
Hint: | Cancel common terms in the numerator and denominator of (5 (2 x - 30))/5.
(5 (2 x - 30))/5 = 5/5×(2 x - 30) = 2 x - 30:
2 x - 30 = -16×5
Hint: | Multiply 5 and -16 together.
5 (-16) = -80:
2 x - 30 = -80
Hint: | Isolate terms with x to the left hand side.
Add 30 to both sides:
2 x + (30 - 30) = 30 - 80
Hint: | Look for the difference of two identical terms.
30 - 30 = 0:
2 x = 30 - 80
Hint: | Evaluate 30 - 80.
30 - 80 = -50:
2 x = -50
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 2 x = -50 by 2:
(2 x)/2 = (-50)/2
Hint: | Any nonzero number divided by itself is one.
2/2 = 1:
x = (-50)/2
Hint: | Reduce (-50)/2 to lowest terms. Start by finding the GCD of -50 and 2.
The gcd of -50 and 2 is 2, so (-50)/2 = (2 (-25))/(2×1) = 2/2×-25 = -25:
Answer: x = -25
Answer:
x = -25
Step-by-step explanation:
(2/5)x - 6= -16 (add 6 to both sides)
(2/5) x = -16 + 6
(2/5) x = -10 (multiply both sides by 5)
2x = -10 (5)
2x = -50 (divide both sides by 2)
x = -50 / 2
x = -25
If John has pairs 5 different colors pairs of socks, how many orders can he wear them in over five days? Repetition is allowed because John is alright with wearing dirty socks.
55
25
5!
125
Answer:
25
Step-by-step explanation:
The number of orders in which John can wear socks is 5⁵, the correct option is A.
What is Permutation and Combination?Permutation is the method of arranging all the elements of the set in order, Combination is the selection of elements from the set such that the order of selection does not matter.
John has 5 pairs of different colour socks
The ways in which he can wear the socks if repetition is allowed is 5⁵.
He has 5 choices on day 1, day 2, day 3, day 4 and day 5.
The correct option is
5^5
25
5!
125
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Diego moves the shape down, turns it 90 degrees clockwise, then moves the shape to the right. Draw the location of the shape after each move.HELP!!!
The shape moves from its original position, point A, to a point down from A, point B, after the first move. Even after a 90-degree clockwise rotation, because we are considering the shape as a point, it will still be at point B. The final move to the right places the shape at point C. The final position of the shape is at point C.
Explanation:For the purpose of illustrating this problem, let's assume that the original placement of the shape is at point A. Now, based on the movements described, here are the steps:
Move the shape down: This results in a downward shift from point A, let's say to point B. Turn it 90 degrees clockwise: The direction of a shape after a 90-degree clockwise rotation changes, but if we consider the shape as a simple point, its location would still be at point B. Move the shape to the right: From point B, if we move the shape rightwards, it will now be at a new location, let's say point C.
The final location of the shape will be at point C, which is down and to the right of the initial position, point A, after a clockwise rotation.
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Some wire is used to make 3 rectangles: A, B, and C. Rectangle B’s dimensions are 3/5 cm larger than Rectangle A’s dimensions, and Rectangle C’s dimensions are 3/5 cm larger than Rectangle B’s dimensions. Rectangle A is 2 cm by 3 1/5 cm.
a. What is the total area of all three rectangles?
b. If a 40-cm coil of wire was used to form the rectangles, how much wire is left?
Answer:
a. [tex]30.36\ cm^2[/tex]
b. [tex]1.6\ cm[/tex]
Step-by-step explanation:
a. You know that the dimensions of Rectangle A are [tex]2\ cm* 3\frac{1}{5}\ cm=2\ cm* 3.2 cm[/tex]
Since Rectangle B’s dimensions are [tex]\frac{3}{5}\ cm[/tex] (which is 0.6 cm) larger than Rectangle A’s dimensions, then the dimensions of Rectangle B are:
[tex](2\ cm+0.6\ cm)( 3.2\ cm+0.6\ cm)=2.6\ cm*3.8\ cm[/tex]
Since Rectangle C’s dimensions are [tex]\frac{3}{5}\ cm[/tex] (which is 0.6 cm) larger than Rectangle B's dimensions, then the dimensions of Rectangle C are:
[tex](2.6\ cm+0.6\ cm)( 3.8\ cm+0.6\ cm)=3.2\ cm*4.4\ cm[/tex]
The find the total area of all three rectangles you must add the products obtained when you multiply their dimensions. Then:
[tex]A_t=(2\ cm* 3.2 cm)+(2.6\ cm*3.8\ cm)+(3.2\ cm*4.4\ cm)\\\\A_t=30.36\ cm^2[/tex]
b. The perimeter of a rectangle can be calculated with this formula:
[tex]P=2l+2w[/tex]
Where "l" is the lenght and "w" is the width.
Knowing the dimensions of each rectangleg, you can calculate the total perimeter as follows:
[tex]P_t=(2)[(2\ cm+ 3.2 cm)+(2.6\ cm+3.8\ cm)+(3.2\ cm+4.4\ cm)]\\\\P_t=38.4\ cm[/tex]
Then, if a 40-cm coil of wire was used to form the rectangles, the amount of wire that is left is:
[tex]40\ cm-38.4\ cm=1.6\ cm[/tex]
A publisher prints 1,512 copies of a book in each print run. If they print 305 runs, how many books will be printed?
Answer: 461,160 books will be printed.
Step-by-step explanation:
1,512×305=461,160
Answer: [tex]461,160\ books[/tex]
Step-by-step explanation:
According to the exercise, the number of copies of a book printed in each run is:
[tex]1,512\ copies\ per\ run[/tex]
Then, let be "x" the number of the number of books that will be printed in 305 runs.
In order to calculate the value of "x", you must multiply 1,512 (which is the number of copies of a book printed in each print run) by 305.
Therefore, you get that the number of books that will printed in 305 runs is:
[tex]x=(1,512)(305)\\\\x=461,160\ books[/tex]
If the perimeter of a square is 32 inches, what is the area
Final answer:
To find the area of a square when given its perimeter, divide the perimeter by 4 to find the side length and then square this length. Thus, a square with a perimeter of 32 inches has an area of 64 square inches.
Explanation:
If the perimeter of a square is 32 inches, we can calculate the length of one side by dividing the perimeter by 4, because a square has 4 equal sides. So each side is 32 inches ÷ 4, which equals 8 inches.
Once we have the side length, we can calculate the area of the square. The area of a square is determined by squaring its side length (side length × side length). In this case, the area would be 8 inches × 8 inches, which equals 64 square inches.
Therefore, the area of the square with a perimeter of 32 inches is 64 square inches.
What is the slope of the line that passes through the points (−3,1) and (7,−14)? Write your answer in simplest form.
Answer is provided in the image attached.
Using the slope formula, the slope, in simplest form, of the line that goes through (-3, 1) and (7, -14) is: [tex]\mathbf{-\frac{3}{2}}[/tex]
Recall:
Slope of a line that passes through any two points is found using the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Given the two points that the line passes through are: (-3, 1) and (7, -14)
Let,[tex](-3, 1) = (x_1, y_1)\\\\(7, -14) = (x_2, y_2)[/tex]
Substitute[tex]m = \frac{-14 - 1}{7 - (-3)} = \frac{-15}{10} \\\\m = -\frac{3}{2}[/tex]
Therefore, using the slope formula, the slope, in simplest form, of the line that goes through (-3, 1) and (7, -14) is: [tex]-\frac{3}{2}[/tex]
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Suppose the price of a certain item increases by 3.8% a total of 5 times, and then decreases by 1.4%
a total of 2 times. By what overall percent did the price increase?
Answer:
The price was increased by 17.15%
Step-by-step explanation:
step 1
we have that
[tex]100\%+3.8\%=103.8\%=103.8/100=1.038[/tex]
Let
x -----> the price of a certain item
we know that
If a price increases by 3.8% a total of 5 times
then
The new price will be equal to multiply the original price by 5 times 1.038
so
[tex]x(1.038)(1.038)(1.038)(1.038)(1.038)=x(1.038)^5[/tex]
step 2
we have that
[tex]100\%-1.4\%=98.6\%=98.6/100=0.986[/tex]
we know that
If a price decreases by 1.4% a total of 2 times
then
The new price will be equal to multiply the actual price by 2 times 0.986
The actual price is [tex]x(1.038)^5[/tex]
so
[tex]x(1.038)^5(0.986)(0.986)=x(1.038)^5(0.986)^2=1.1715x[/tex]
[tex]1.1715-1=0.1715[/tex]
convert to percentage
[tex]0.1715*100=17.15\%[/tex]
therefore
The price was increased by 17.15%
Answer: The price increased by 17.149618%.
Step-by-step explanation:
Given that the price of a certain item increases by 3.8% = 0.038 a total of 5 times.
So every time the price was (1 + 0.038) = 1.038 times the original price.
So after 5 times the price is = [tex]1.038^5=1.205[/tex] times the original price.
Then it decreased by 1.4% twice. So the new price is = [tex]1.205\cdot\left(1-0.014\right)^{2}=1.17149618[/tex] times the original price.
So the percentage increase is = [tex]\left(1.17149618-1\right)\cdot100 \%=17.149618 \%[/tex]
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What is the equation of the following line (4,-3) (0,0)
Answer:
y=5/4x
Step-by-step explanation:
The original price of a mountain bike was reduced by $125.
If p = the mountain bike's original price in dollars, which algebraic expression
represents the reduced price?
A. 125+ p
B. 125p
c. p-125
D. 125 - P
Courtney works for a company that hand builds furniture. She works forty-two and a half hours a week and is paid $14.42 per hour. Work each of the following problems in decimal form.
1.How much does Courtney make a week before taxes are taken out of her paycheck?
2.If 18 percent of Courtney’s paycheck is withheld for taxes, how much money is left for Courtney?
3.After Courtney pays her taxes, she also puts $38.25 into savings each week. Now, how much money is left for Courtney to spend each week?
4.In decimal form, what percent of Courtney’s paycheck is left after she pays her taxes and puts money into savings?
5.There is on average 4.35 weeks in a month. How much does Courtney make a month after taxes?
1. 612.85
14.42 x 42.5 = $612.85
2. 110.313
612.85 x .18 = $110.313
3. $72.063
110.313 - 38.25 = $72.063
4. %11.75
72.063 / 612.85 = 0.11758
0.11758 x 100 = %11.75
5. 479.861
110.313 x 4.35 = 479.861
Courtney's weekly earnings before taxes are $612.85. After an 18% tax, her earnings are $502.54, which becomes $464.29 after saving $38.25. The paycheck's remaining percentage is 75.76%, and her monthly earnings after taxes average $2,186.05.
Courtney earns $14.42 per hour and works 42.5 hours a week. To calculate her weekly earnings before taxes:
Weekly earnings = Hourly wage times Hours worked per week
Weekly earnings = $14.42 times 42.5
Weekly earnings = $612.85
To find out how much she makes after an 18% tax deduction:
Taxed amount = Weekly earnings times Tax rate
Taxed amount = $612.85 times 0.18
Taxed amount = $110.31
Earnings after tax = Weekly earnings - Taxed amount
Earnings after tax = $612.85 - $110.31
Earnings after tax = $502.54
After Courtney saves $38.25, her disposable weekly income is:
Money left to spend = Earnings after tax - Savings
Money left to spend = $502.54 - $38.25
Money left to spend = $464.29
Now, to calculate the percentage of paycheck left after taxes and savings:
Percentage left = (Money left to spend / Weekly earnings) times 100
Percentage left = ($464.29 / $612.85) times 100
Percentage left = 75.76%
For her monthly earnings after taxes, considering an average of 4.35 weeks per month:
Monthly earnings after taxes = Earnings after tax times Average weeks per month
Monthly earnings after taxes = $502.54 times 4.35
Monthly earnings after taxes = $2,186.05
6. The box plot displays the temperature
of saunas in degrees Fahrenheit. What is
the median?
110 112 114 116 118 120 122 124 126
degrees (Fahrenheit)
The median of the given data is 118.
It is required to find the median.
What is median?The median is the middle value in a set of data .The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.
Given:
The given date are arranged in ascending order
110 112 114 116 118 120 122 124 126 °F
Total number of the data is 9 which is odd ,so the median is
n+1/2
Where n=number of values in data set
According to given question we have,
Median=n+1/2
Median=9+1/2
Median=5
The 5th term of the number is median of the given data i.e 118.
Therefore, the median of the given data is 118.
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It was reported that approximately 15.5 million telephone votes were cast. Each vote was for
either Laine or Alejandro. If the ratio of "Laine votes" to "Alejandro votes” was 29:21, how
many votes did Alejandro receive? What percent of the votes did Laine receive?
Answer:
Alejandro received 6.51 million of votes
Laine received 58% of votes
Step-by-step explanation:
If the ratio of "Laine votes" to "Alejandro votes” was 29:21, then the number of "Laine votes" was 29x and the number of "Alejandro votes” was 21x. In total, 15.5 million votes were cast. So
29x + 21x = 15.5 million
50x = 15.5 million
x = 0.31 million
Then
the number of "Laine votes" [tex]=29\cdot 0.31=8.99[/tex] million
number of "Alejandro votes” [tex]=21\cdot 0.31=6.51[/tex] million
Laine received
[tex]\dfrac{8.99}{15.5}\cdot 100\%=58\%[/tex]
What is the reciprocal of 3x+5/8x−2?
Answer:
[tex]\frac{3x+5}{8x-2}[/tex]
Explanation:
The reciprocal of a fraction is when you just "turn it upsidedown". Which means, you take the numerator and the denominator and swap their places. So instead of having the [tex]\frac{numerator}{denominator} you would change it to \frac{denominator}{numerator}[/tex]
Answer:
(8x - 2) / (3x + 5).
Step-by-step explanation:
Just invert the fraction:
= (8x - 2) / (3x + 5).
30 POINTS + BRAINLIEST! Please if you can, help! I'm on a timer!
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has vertices P'(1, 0), Q'(0, −1), and R'(−2, −1).
Plot triangles PQR and P'Q'R' on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)
(There is no image provided.)
See the attached picture for the answers:
Final answer:
The scale factor of the dilation that transforms triangle PQR to triangle P'Q'R' does not exist. The coordinates for the reflected triangle P''Q''R'' are P''(-1, 0), Q''(0, -1), and R''(2, -1). Triangle PQR and triangle P''Q''R'' are not congruent.
Explanation:
To find the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R', we can compare the lengths of corresponding sides in the two triangles. The distance between P(4, 0) and P'(1, 0) is 3, the distance between Q(0, -4) and Q'(0, -1) is 3, and the distance between R(-8, -4) and R'(-2, -1) is 6.
Since the lengths of corresponding sides are not equal, the triangles are not similar and there is no scale factor that transforms triangle PQR to triangle P'Q'R'.
To reflect triangle P'Q'R' about the y-axis, we simply change the sign of the x-coordinate for each vertex. The coordinates for the reflected triangle P''Q''R'' are P''(-1, 0), Q''(0, -1), and R''(2, -1).
Triangle PQR and triangle P''Q''R'' are not congruent because their corresponding sides have different lengths.
Un triángulo rectángulo tiene un área de 84 pies2 y una hipotenusa de 25 pies de largo. ¿Cuáles son las longitudes de sus otros dos lados?
Answer:
7 feet and 24 feet
Step-by-step explanation:
In the right triangle, the hypotenuse is 25 feet long. The area of this triangle is 84 square feet.
Let x feet and y feet be the lengths of triangle's legs.
By the Pythagorean theorem,
[tex]x^2+y^2=25^2\\ \\x^2+y^2=625[/tex]
The area of the right triangle is half the product of its legs, thus
[tex]84=\dfrac{1}{2}xy\\ \\xy=168[/tex]
Solve the system of two equations:
[tex]\left\{\begin{array}{l}x^2+y^2=625\\ \\xy=168\end{array}\right.[/tex]
From the second equation:
[tex]x=\dfrac{168}{y}[/tex]
Substitute it into the first equation:
[tex]\left(\dfrac{168}{y}\right)^2+y^2=625\\ \\168^2+y^4=625y^2\\ \\y^4-625y^2+168^2=0\\ \\D=(-625)^2-4\cdot 168^2=(625-2\cdot 168)(625+2\cdot 168)=289\cdot 961=17^2\cdot 31\\ \\\sqrt{D}=17\cdot 31=527\\ \\y^2_{1,2}=\dfrac{-(-625)\pm 527}{2}=49,\ 576\\ \\y_1=7,\ y_2=-7,\ y_3=24,\ y_4=-24[/tex]
The length of the leg cannot be negative, so
[tex]y_1=7\Rightarrow x_1=\dfrac{168}{7}=24\\ \\y_2=24\Rightarrow x_2=\dfrac{168}{24}=7[/tex]
What is the volume of a rectangular prism with the dimensions: base 3 1 2 cm, height 1 1 2 cm, and length 5 1 2 cm? A) 30 1 2 cm3 B) 28 7 8 cm3 C) 15 1 2 cm3 D) 14 7 16 cm3
Answer:
1.78913×107
Step-by-step explanation:
312·112·512≈1.78913×107
Answer:
b
Step-by-step explanation:
What is 5 divided by 3/7
Final answer:
To divide 5 by 3/7, we multiply 5 by the reciprocal of 3/7 which is 7/3, resulting in 35/3 or 11 2/3.
Explanation:
To calculate 5 divided by 3/7, we invert the fraction 3/7 and multiply by 5. It’s the same as multiplying 5 by the reciprocal of 3/7. The reciprocal of 3/7 is 7/3. Therefore:
5 × 7/3 = 5 × (7 ÷ 3)
5 × 7/3 = (5 × 7) ÷ 3
5 × 7/3 = 35/3
5 × 7/3 is 11 with 2 left over or, in other words, it is 11 2/3.
Remember, when you divide by a fraction, you are essentially calculating how many times that fraction goes into the number. So here, 5 divided by 3/7 is asking how many groups of 3/7 there are in 5, which is why we multiply by the reciprocal.