justina needs to dilate traiangle ABC using a scale factor of 1.5
Answers
Using the rule for a dilation, it is found that:
1. The table with the coordinates is given by the first image.
2. The graph of the dilated triangle is given by the second image.
3. The rule is: (x,y) -> (1.5x, 1.5y).
What is the effect of a dilation of a figure?When a figure is dilated by an scale factor of a, each vertex of the figure is multiplied by the scale factor of a, hence the rule is given by the following vector:
(x,y) -> (ax, ay).
The coordinates of the vertices of the pre-image are given as follows:
A(-2, -2), B(2,2), C(4, -2).
The dilation has a scale factor of 1.5, hence the rule for the calculation of each vertex of the image, considering the pre-image, is given as follows:
(x,y) -> (1.5x, 1.5y).
Then the vertices of the image will be given as follows:
A'(-3, -3), B'(3,3), C'(6, -3).
Each coordinate of A, B and C was simply multiplied by 1/2, and the triangle with these vertices is given by the second image at the end of the answer.
What is the missing information?The problem is incomplete, and is given by the first image at the end of the answer.
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Related Questions
Find the orthocenter of AABC.
A(3,5), B(6,5), C(5,3)
Answers
Answer:
(5, 4)
Step-by-step explanation:
What is Orthocenter?
A point where the altitudes of the triangle meet is known as the point of concurrency or simply the orthocenter of the triangle
Expand and simplify the expression using properties of operations. 8(3x−7)
Answers
The expression 8 ( 3x - 7 ) when expanded gives 24xx - 56.
The cornerstone of mathematics is the theory of operations; we use it to compute and remember fundamental truths. The subsequent three characteristics are applied to addition and multiplication: Commutative Property, Associative Property, and Distributive Property.
The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
Consider the expression 8( 3x - 7 ),
Let's say y is equal to 8( 3x - 7 ).
By using the distributive property:
y = 8 × 3x - 8 × 7
y = 24x - 56
Therefore,
8( 3x - 7 ) = 24x - 56
Therefore, when the expression 8( 3x - 7 ) is expanded we obtain the expression 24x - 56.
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The figure shows the design of a rectangular windowpane. The four horizontal lines are parallel. The measure of angle 6 is 53 degrees. What is the measure of angle 12? Write and solve an equation to find the answer.
Answers
∠6 and ∠12 are supplementary angles. That means, they add up to 180°
[tex]\angle6+\angle12=180\degree[/tex]Substitute ∠6 by 53° to find ∠12.
[tex]53+\angle12=180[/tex]Subtract 53 from both sides to find ∠12.
[tex]\begin{gathered} 53+\angle12-53=180-53 \\ \angle12=127\degree \end{gathered}[/tex]Answer: ∠12 = 127°.
4. Find “a” so that the parabola y = ax² + 3x + 11 goes through the point (3,2).
Answers
Answer:
a = - 2
Step-by-step explanation:
since the point (3, 2 ) lies on the parabola, then it makes the equation true.
substitute x = 3, y = 2 into the equation and solve for a
y = ax² + 3x + 11
2 = a(3)² + 3(3) + 11
2 = 9a + 9 + 11
2 = 9a + 20 ( subtract 20 from both sides )
- 18 = 9a ( divide both sides by 9 )
- 2 = a
Answer:
a = -2
Step-by-step explanation:
Given quadratic equation:
[tex]y=ax^2+3x+11[/tex]
In order to find "a", substitute the given point on the curve (3, 2) into the equation and solve for a:
[tex]\begin{aligned}y&=ax^2+3x+11\\\textsf{Substitute $(3,2)$} \implies 2&=a(3)^2+3(3)+11\\2&=9a+9+11\\2&=9a+20\\2-20&=9a+20-20\\-18&=9a\\9a&=-18\\\dfrac{9a}{9}&=\dfrac{-18}{9}\\\implies a&=-2 \end{aligned}[/tex]
Therefore, the value of "a" so that parabola y = ax² + 3x + 11 goes through the point (3, 2) is:
[tex]\large \boxed{a=-2}[/tex]
Factor out the GCF -27z^3-9z^4+18z^6
Answers
The simplified expression for -27z^3-9z^4+18z^6, using the greatest common factor, is given as follows:
9z³(-3 - z + 2z³).
How to factor an expression by GCF?To find a symbolic expression by the greatest common factor, we have to:
Find the greatest common factor of the numeric coefficients.Find the greatest common factor of the exponents.Then we multiply these GCFs.
For this problem, the numeric coefficients are given as follows:
27, 9 and 18, hence the GCF is of 9.
The exponents are given as follows:
z³, z^4 and z^6, hence the GCF is of z³, which is the expression with the lowest exponent.
Then the GCF of the expression is given as follows:
9z³.
To simplify the expression, each term of the expression is divided by 9z³, hence the factored expression is:
9z³(-3 - z + 2z³).
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A man's taxable income is $3.060 If tax is paid at 12%. How much is the man's net income
Answers
A man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27
The taxable income = $3060
The tax percentage = 12%
Income tax is the a type of tax impose on income generated by businesses and individuals by the government
Consider the net income as x
Then,
12% of the income = x×(12/100)
Therefore the equation will be
x - x×(12/100) = 3060
x(1-(12/100) = 3060
x(1-0.12) = 3060
0.88x = 3060
x = 3060/0.88
x = $3477.27
Hence, a man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27
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25.42 marked down by 33%
Answers
25.42 marked down by 33 % is 17.0314.
This is a question of percentages.
Percentage
A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentages have no dimension. Hence it is called a dimensionless number.
33 % of 25.42 is given by:-
(33/100)*(25.42) = (33*25.42)/100 = 838.86/100 = 8.3886
25.42 marked down by 33 % = 25.42 - 8.3886 = 17.0314.
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fill in the blank question. julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. calculate the amount of sales tax julia will pay on the purchase. round to the nearest cent if necessary.
Answers
julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. then Julia have to pay $2.57 as sales tax on purchase of headphones.
Given,
The cost of headphones which Julia wants to purchase on sale = $ 42.79
The sales tax in Julia's country = 6%
We have to calculate the amount of sales tax Julia will pay on the purchase:
That is,
Sales Tax Value = Percentage of sales tax × Price of headphones
Sales Tax Value = (6 / 100) × 42.79
Sales Tax Value = 0.06 × 42.79
Sales Tax Value = 2.5674
Sales Tax Value ≈ 2.57
Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.
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2x-5 > -11 or -10x - 6 ≥ 44
Answers
The solution of given inequalities are x > -3 and x ≤ 5.
How do you solve an inequality?When resolving an inequality, you can do one of the following: add the same amount to each side; deduct the same amount from each side; multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.
Given inequalities are 2x - 5 > -11 and -10x - 6 ≥ 44.
To solve the first inequality,
2x - 5 > -11
Adding 5 on both sides,
2x - 5 + 5 > -11 + 5
2x > -6
Divide both sides by 2,
x > -3
To solve the second inequality,
-10x - 6 ≥ 44
Adding 6 on both sides,
-10x - 6 + 6 ≥ 44 + 6
-10x ≥ 50
Divide both sides by -10, and change the inequality sign
x ≤ 5
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If a car has 80-liter petrol and after one hour driving the car use 6-liter petrol, how
much petrol will remain after x-hours driving?
Answers
Answer:
13.3 liters of petrol left
Step-by-step explanation:
80 ÷ 6 = 13.3
please help. I will do anything.
Answers
Answer:
216 miles
Step-by-step explanation:
so the base fee is 18.99, subtract the total (219.87) by 18.99.
219.87-18.99=200.88
200.88 divided by 0.93 (charge for each mile driven)
200.88/0.93=216
thats a lot of miles.
please answer this question with method
Answers
Answer:
see explanation
Step-by-step explanation:
the volume (V) of the container is
V = 10 × 4 × 5 = 200 m³
change the dimensions of the box to m , to be same as container
l = 50 cm = 0.5 m , b = 40 cm = 0.4 m , h = 20 cm = 0.2 m
then
volume of box = 0.5 × 0.4 × 0.2 = 0.04 m³
Number of boxes that can be stored in container is
200 ÷ 0.04 = 5000
thus no more than 5000 boxes can be placed in the container
cos^4x - sin^4x +1 = 2cos^2x
prove
Answers
Proved [tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x
We will use the Pythagorean Theorem:
Sin²x + Cos²x = 1
from which we can get:
Sin²x = 1 - Cos²x
Also, note that the difference in the similarity of squares can be written:
A² - B² = (A - B)
We can use this with A = Sin²x and B = Cos²x as follows:
[tex]Sin^{4}x - Cos^{4}x[/tex]
= (Sin²x)² - (Cos²x)²
= (Sin²x - Cos²x) (Sin²x + Cos²x)
= Sin²x - Cos²x
= (1 - Cos²x) - Cos²x
= 1 - 2Cos²x
Now move the 1 and negative symbols to the left.
[tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x
The trigonometric ratios are related to each other by equations called trigonometric identities.
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f(n) = n - 7
f(-9k) =
Answers
Answer:
[tex]-9k-7[/tex]
Step-by-step explanation:
Replace n with -9k.
The length of a violin string varies inversely as the frequency of its vibrations. A violin string 14 inches long vibrates at a frequency of 450 cycles per second. Find the frequency of a 10-inch violin string.
Answers
The frequency of the 10 inch violin string will be 630 cycles per second or Hertz if the violin string 14 inches long vibrates at a frequency of 450 cycles per second.
As per the question statement, A violin string 14 inches long vibrates at a frequency of 450 cycles per second and we are supposed to find out the frequency of a 10-inch violin string.
We should be knowing that the length of a violin string varies inversely as the frequency of its vibrations.
f = m/l, where "f" is the frequency and "l" is the length and "m" is the constant number
450 = m / 14
m = 6300
Therefore New frequency = 6300 / 10 = 630 cycles per second
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What is the converse of the following conditional statement?
"If a person is a teenager, then the person is 13 years old or older."
Determine the validity of the converse and give a counterexample if the converse is not valid.
If a person is not a teenager, then the person is not 13 years old or older. The converse is invalid; a counterexample is a person who is 12 years old.
If a person is 13 years old or older, then the person is a teenager. The converse is invalid; a counterexample is a person who is 20 years old.
If a person is a teenager, then the person is 13 years old or older. The converse is valid.
If a person is 13 years old or older, then the person is a teenager. The converse is valid.
Answers
The converse statement is "If a person is 13 years old or older, then the person is a teenager. The converse is valid" . Option D
What is a converse statement?The converse of a conditional statement is defined as a statement that is formed when the hypothesis and conclusion of a sentence are both reversed or interchanged.
If the conditional statement is expressed as a → b
The converse statement is referred to as b → a
It is important to note that the original statement must be a conditional statement for a converse statement to derived from it.
Given the conditional statement:
"If a person is a teenager, then the person is 13 years old or older."
The converse statement would be written as;
If a person is 13 years old or older, then the person is a teenager.
We can see that the converse statement is valid because anyone that is 13 or older is a teenager
Hence, the converse statement is valid. Option D
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A spinner with 8 equally sized slices has 2 red slices, 3 blue slices, and 3 yellow slices. What is the probability of stopping on a red or blue slice?
Answers
Answer:
The probability is 5/8
Step-by-step explanation:
The table shows a country’s average fuel consumption for light duty vehicles for several years. Let XP the number of years since 1985 so that executes five cents for 1990 and so forth. Find the linear regression model for the status. What does slope and regression model represent
Answers
Using linear function concepts, it is found that:
The slope is of 0.172 means that the fuel economy increases by 0.172 mpg each year.The intercept of 17.04 means that the fuel economy was of 17.04 mpg in 1985.What do the slope and the intercept of a linear function represent?The slope-intercept representation of a linear function is:
y = mx + b.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we will use a calculator from the points on the table to build a linear function of best-fit. The points are given as follows:
(5, 17.9), (10, 18.7), (15, 19.7), (20, 20.5), (25, 21.3).
Then the function is:
y = 0.172x + 17.04.
Then:
The slope is of m = 0.172, meaning that each year, the fuel economy increases by 0.172 mpg.The intercept of b = 17.04 was the fuel economy in 1985.What is the missing information?The table is missing, and is given by the image at the end of the answer.
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Jillian and Nikki each filled their cars with gasoline. The graphs below show the amount of gas in each car and the miles driven since filling the tank. A graph titled Jillian's Car has miles driven on the x-axis, and gallons of gas left on the y-axis. A line goes through (0, 22) and (100, 16). A graph titled Nikki's Car has miles driven on the x-axis and gallons of gas left on the y-axis. A line goes through points (0, 20) and (100, 16). Which statement is supported by the graphs? Jillian’s car holds more gasoline and gets better gas mileage. Nikki’s car holds more gasoline and gets better gas mileage. Jillian’s car holds more gasoline, but Nikki’s car gets better gas mileage. Nikki’s car holds more gasoline, but Jillian’s car gets better gas mileage.
Answers
The statement that is best supported by the graph is; Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.
How to Interpret Linear Graphs?The total amount of gasoline each car tank can hold is shown on the left of each graph on the y-axis.
Jillian's car holds 22 gallons.
Nikki's car holds 20 gallons.
Jillian's car holds more gasoline.
Now we need to see which car gets better gas mileage. Getting better gas mileage means you can go farther with each gallon of gas.
With Jillian's car, after using 22 gallons of gas, you have gone 350 miles, and the gas tank is empty.
350 miles with 22 gallons is 350/22 = 15.9 miles per gallon.
With Nikki's car, you start with only 20 gallons. By the time you drive 350 miles, you still have some gas left. Not only did you start with less gas, 20 gal vs. 22 gal, but after driving the same distance, 350 miles, there is still some gas left in the tank, 6 gallons.
That means Nikki's car used 20 - 6 = 14 gallons to drive 350 miles. 350/14 = 25 miles per gallon.
The more miles per gallon you get, the better the mileage. Thus;
25 miles per gallon is better mileage than 15.9 miles per gallon.
Nikki's car has a smaller gas tank, but it gets better mileage.
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is 10,000,000,001 prime? explain your reasoning
Answers
Answer:
Answer down below!
Step-by-step explanation:
It is not prime!!
10,000,000,001 is an odd eleven-digits composite number following 10000000000 and preceding 10000000002. In scientific notation, it is written as 1.0000000001 × 10^10. The sum of its digits is 2. It has a total of 3 prime factors and 8 positive divisors. There are 9,897,840,000 positive integers (up to 10000000001) that are relatively prime to 10000000001.
What is 3™+a= a+r, for m
Answers
Answer: m = (3/2)r
Step-by-step explanation:
2/3m+a=a+r, for m
----
(2/3)m + a = a + r
---
(2/3)m = r
Write an equation for the line that is parallel to the given line y=3/4x + 7 and that passes through the given point G(8,3)
Answers
The equation for the line that is parallel to the given line y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.
As given in the question,
Equation of the given line :
y=3/4x + 7
Slope of the given line = (3/4)
Equation of line with slope (3/4) & passing through point (8, 3) is given by:
y - 3 = [tex]\frac{3}{4}[/tex] (x - 8)
⇒ 4 (y - 3) = 3 (x - 8)
⇒ 4y - 12 = 3 x - 24
⇒ 4 y = 3 x - 24 + 12
⇒ 4 y = 3 x - 12
⇒ y = (3/4)x - 3
Therefore, the equation for the line that is parallel to the given line
y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.
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Mark reads 42 pages of a book every 3/4hour wright a quation that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads
Answers
Equation is y= 56x that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads.
What is rate of change?The term rate of change (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.
Given Data
The hours are indicated by = x
The calculation for the number of pages is =y
Read 42 pages every [tex]\frac{3}{4}[/tex] hour
You can model the equation as follows:
y = mx +b
Rate of change = [tex]\frac{change in y}{change in x}[/tex]
Rate of change = 42 ÷[tex]\frac{3}{4}[/tex]
Rate of change = 42 ×[tex]\frac{4}{3}[/tex]
Rate of change = 56
Equation y= 56x
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Enter the correct answer in the box.
What are the solutions of this quadratic equation?
x² = 16x - 65
Substitute the values of a and b to complete the solutions.
x = a + bi
x = a - bi
Answers
The solutions of the quadratic equation x² = 16x - 65 are:
x = 1/2 + 1/32i
x = 1/2 - 1/32i
What is the solution?We know that a quadratic equation is an equation that is of the sort ax^2 + bx + c = 0. Hence, the equation would be solved and it could have a complex root. By this I mean that the root of the equation could be a complex number as we have in the case of the equation here.
x² = 16x - 65 = 0
x² - 16x + 65 = 0
When we solve by the formula method;
x = -b ±√b^2 - 4ac/2a
x = -(-16) ±√(-16)^2 - 4 (1) (65)/2(16)
x = 16 ±√256 - 260/32
x = 16/32 ±√-4/32
x = 1/2 ± 1/32i
Thus
a = 1/2
b = 1/32
We then obtain;
x = 1/2 + 1/32i
x = 1/2 - 1/32i
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Given the diagram above and bd= 12 and ac= x+ 23, find ac
Answers
The value of AC when BD= 12 and AC = x+ 23 is 28
What is a line segment?A line segment can be defined as the part of a straight line that is being bounded by two different end points, and also contains all the points on the line between its endpoints.
From the information given, we have that line AD is a line with segments, line AB, line BC, line CD with B and C as the midpoints.
Given the points as;
AC = x + 23BD = 12BC = 14 + xAD = 26 + xWe have that;
AC + BC = AD
But line BD = 14 + x, we have;
Line AC = x + 23 - 14 + x
Line AC = 2x + 9
substitute the values into the equation
2x + 9 +12 = 26 + x
collect like terms
2x - x = 26 - 21
Add or subtract like terms
x = 5
But, we have that;
Line AC = x + 23
Line AC = 5 + 23
Add the values
Line AC = 28
Hence, the value is 28
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2/3 times the quantity n plus 16
(n+16)
O(2n+16)
O(n-16)
O(16-n)
Answers
Answer:
24
Step-by-step explanation:
it just is, I don't know how I get this. I just did.
[tex]\frac{2n+48}{3}[/tex]
5.45 divided by 65
If rounding show answer.
Answers
Step-by-step explanation:
1) 5.45 ÷ 65
2) 109/20 x 1/65=
3) 109/1300 or 0.08384615
can anyone decompose 240 - 135 = 105 ?
need new calculation after decomposing? help
Answers
The decomposition of 240 - 135 = 105 will be 15(16 - 9) = 15(7) = 105
What is decomposition?It should be noted that decomposition simply means breaking down of the numbers that are given or illustrated.
It should be noted that the numbers 240 - 135 = 105 all have a common factor of 15. This will be broken down as:
240 - 135 = 105
15(16 - 9)
= 15(7)
= 105
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What is 903 Divided by 72 In Fraction form
Answers
Answer: The answer would be 12 39/72
Step-by-step explanation:
903 divided by 72, you'd get 12.5417. You could also express 903/72 as a mixed fraction: 12 39/72.
Change 23 out of 25 to a percentage
Answers
This how we change 23 out of 25 to a percentage
The numerator of a question is the number that appears above the bar; in this case, the numerator is 23.
The denominator is the number beneath the bar, and in this question, it is 25.
To calculate the value of a fraction, divide the numerator by the denominator.
Therefore, we must divide 23 by 25.
23/25 = 0.92
To determine the percentage, multiply the outcome by 100.
The percentage value will be obtained by multiplying 0.92 by 100.
0.92 x 100 = 92%
As a result, 92% is the answer to the question.
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