Answer:
x=1
Step-by-step explanation:
so just plug 1 in and you wil get it
Answer:
16
Step-by-step explanation:
6(2)+4
6 x 2=12
12+4=16
Which transformation confirms that rectangle ABCD and rectangle EFGH are similar?
A) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.
B) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.
C) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.
D) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.
Answer:
Option D is correct.
Step-by-step explanation:
We are given that,
'Rectangle ABCD is translated to map onto the rectangle EFGH'.
That is, 'Rectangle ABCD is similar to rectangle EFGH'.
So, we see that,
Rectangle ABCD is rotated towards the left and then decreased in size to map onto EFGH.
That is, we have,
Rectangle ABCD is rotated counter-clockwise by 90° about the origin and then dilated by a factor of [tex]\frac{1}{2}[/tex] with the origin as the center of dilation.
Hence, option D is correct.
The polar form of this is?
Answer:
2, 120 degrees
Step-by-step explanation:
The first step in finding the polar form is finding the modulus, r
r= sqrt( x^2 + y^2)
r = sqrt( (-1)^2 + sqrt(3)^2)
r = sqrt(1+3)
r= sqrt(4)
r =2
The next step is finding the angle
theta = arctan (y/x)
theta = arctan (sqrt(3)/-1))
theta = arctan (-sqrt(3))
theta = -60
The point (-1, sqrt(3)) is in the 2nd quadrant, but our angle is in the 4th quadrant, so we add 180 degrees
theta = -60 + 180 = 120
theta = 120 degrees
Tom is 45 and pays $2042 on his mortgage each month while his total take hime pay is $5950 per month. The national average, for those aged 35-64, on housing costs is 35% of income. Compute the percent of Tom's income that he spends on housing.
Answer:
34.32%
Step-by-step explanation:
Tom is 45 years old.
Tom earning = $5950 per month
Mortgage payment = $2042
Percentage of amount paid towards mortgage in his income = (2042/5950)*100
= 34.32%
Tom pays 34.32% of his income towards mortgage.
The national average of his age group pays 35% of income towards housing.
Thank you.
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.
Which equation represents the data in the table?
A) s=4√d
B) s=0.37d+20 NOT B
C) s=13.7log20
D) s= 1/25d²
Please choose one of the answers provided.
Edit: It is not Choice B
Answer:
Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]
Step-by-step explanation:
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.
d s
20 17.89
40 25.30
60 30.98
80 35.78
100 40.00
We will check each option for table.
[tex]s=4\sqrt{d}[/tex]
For d=20, Put d=20 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{20}\approx 17.89[/tex]
For d=40, Put d=40 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{40}\approx 25.30[/tex]
For d=60, Put d=60 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{60}\approx 30.98[/tex]
For d=80, Put d=80 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{80}\approx 35.78[/tex]
For d=100, Put d=100 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{100}\approx 40.00[/tex]
All the value of table satisfy the first equation.
Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]
One integer is 9 less than 5 times another. Their product is 18. Find the integers.
Answer:
x = 3 and x=-6/5
Step-by-step explanation:
x = one integer
y = other integer
One integer is 9 less than 5 times another
x= 5y-9
product is 18
xy = 18
Substitute in for x
(5y-9) *y = 18
Distribute
5y*y -9y = 18
5y^2 - 9y = 18
Subtract 18 from each side.
5y^2 - 9y -18= 18-18
5y^2 - 9y -18 = 0
Using the quadratic formula
-b ± sqrt(b^2 -4ac)
-----------------------
2a
-(-9) ±sqrt(9^2 -4*5*(-18))
--------------------------------------
2(5)
9 ±sqrt(81 +360))
--------------------------------------
10
9 ±sqrt(441)
--------------------------------------
10
9±21
----------
10
x = (9+21)/10 and x = (9-21)/10
x = 30/10 and x = (-12)/10
x = 3 and x=-6/5
Final answer:
The two integers in question are 21 and 6, with 21 being 9 less than 5 times 6, and their product equating to 18.
Explanation:
Finding the Two Integers
The problem states that one integer is 9 less than 5 times another integer, and their product is 18. Let's call the first integer x and the second integer y.
From the problem, we can write two equations:
x = 5y - 9 (One integer is 9 less than 5 times the other)
xy = 18 (The product of the two integers is 18)
Using substitution from the first equation, in the second equation, we replace x with 5y - 9 and solve for y:
(5y - 9)y = 18
This equation leads to a quadratic equation: 5y^2 - 9y - 18 = 0. Factoring the quadratic equation, we find two pairs of numbers that multiply to give -18 and add up to -9: (-6) and 3.
The factors of the equation are (5y + 3)(y - 6) = 0, giving us y = 6 or y = -³/₅. However, since we are looking for integers, we disregard the fraction and only consider y = 6. Plugging y = 6 back into x = 5y - 9, we get x = 5(6) - 9 which simplifies to x = 21.
Therefore, the two integers are 21 and 6.
Nathan just bought a car. He models the value, V, in dollars, of the car after t years as V(t)=21,000(0.861)^t. Based on this model, by what percent does the value of Nathan car decrease each year?
Answer:
Value of the car is decreasing by 13.9% each year.
Step-by-step explanation:
This equation tells us V(t) is the value of the car after a certain time in years, $21,000 is the initial value of the car. What we need to focus on is on the 0.861 part of this equation. This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time. By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 =1) then we have 100%-86.1%=13.9%. This means that the value of the car is decreasing 13.9% each year.
Please help: this is due in 15 minutes and showing the work is needed
Answer:
4 people
Step-by-step explanation:
You Know that 1/3 of an hour is 20 min, and u find out that 1/4 of an hour is 15 min. So then it takes 45 min for 1 person. 3 1/3 hour= 3 hr 20 min= 200 min. 200/45=4.44...= 4 people
please help me asap!
Answer:
D) [tex](x-5)^2 + (y-2)^2 = 49[/tex]
Step-by-step explanation:
Center is (5,2) and radius = 7
We use center - radius form of equation of circle
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) represents the center
and r is the radius of the circle
We know center is (5,2) so h= 5 and k =2
r= 7
Plug in all the values
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
[tex](x-5)^2 + (y-2)^2 = 7^2[/tex]
[tex](x-5)^2 + (y-2)^2 = 49[/tex]
In rectangle ANHG, whose perimeter is 100, OP, PQ, and QR are congruent and mutually perpendicular and O is the midpoint of AN. If GH = 40 which is PQ?
Answer:
5
Step-by-step explanation:
The sum of adjacent sides of the rectangle is half the perimeter, 50, so ...
... AH = 50-40 = 10
Then ...
... OP +QR = 10 = 2×OP . . . . . QR ≅ OP
... OP = 5 = PQ . . . . . . . . . . . . PQ ≅ OP
Jamie owns a sailboat rental company, which has a large variety of sailboats of different sizes. He observed that the speed of the sailboat (with the wind) largely depends on the length of the sailboat, and is approximately one and a half times the square root of its length. Which of the following options represents the relationship between length and speed of a sailboat?
Answer:C
Step-by-step explanation:
Formula must be S(x) = (1+1/2)√x = 1.5√x, eliminating A and D. Diagram must show that a zero length boat doesn't move, and that boat length four feet goes 1.5×2 = 3 knots. That eliminates B. Check: C says zero feet goes zero knows and 4 feet goes 3 knots.
Answer:
Graph C
Step-by-step explanation:
We know the speed is equal to one and a half times the square root of the length. This means that speed is the dependent variable (y), and length is the independent variable (x).
Since the speed, S(x), is 1.5 times the square root of the length (x), we get the function
S(x) = 1.5√x.
When x = 0, S(x) = 1.5√0 = 1.5(0) = 0. This makes it graph C.
Alex, Bob, and Claudia split 126 cm wire evenly among themselves. They then proceeded to cut their pieces of wire into smaller, equal parts. Alex cut his wire 18 times, and kept 7 pieces. Bob cut his wire 2 times more than Alex did, and kept 9 pieces. While Claudia divided her wire into 13 equal parts, and kept only one piece. Who kept the longest part of the original wire and what was the length of that part?
If Alex cut his wire 18 times, he ended up with 19 equal pieces. He kept 7, so has 7/19 of his 1/3 of the wire.
Bob cut his wire 20 times, so ended up with 21 pieces, of which he kept 9. So he has 9/21 = 3/7 of his 1/3 of the wire.
Claudia kept 1/13 of her 1/3 of the wire, so has the smallest piece.
Bob kept (3/7)·(1/3)·126 cm = 18 cm.
Alex kept (7/19)·(1/3)·126 cm ≈ 15.47 cm.
Bob kept the longest part of the original wire.
The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln (9t + 4), where y is the number of mowers sold. How many mowers will be sold 6 years after a model is introduced?
Answer:
22,332
Step-by-step explanation:
Put 6 where t is in the equation and do the arithmetic.
... y = 5500 ln(9·6 +4) = 5500 ln(58) ≈ 22,332
Answer:
The answer is: 22,332 mowers will be sold 6 years after a model is introduced.
Step-by-step explanation:
Given that y = 5500 ln (9t + 4)
In order to calculate the number of mowers (y) that will be sold after 6 years, substitute t = 6 (years):
y = 5500 ln (9 × 6 + 4) = 5500 In 58
In 58 = natural logarithm of 58 = 4.0604
Therefore, y = 5500 In 58 = 5500 × 4.0604 = 22,332.44 = 22,332 mowers.
How many hours are in a decade
Answer:
87600
Step-by-step explanation:
Answer:
87600 hours
Step-by-step explanation:
1 decade = 10 years
1 year = 365 days
1 day = 24 hours
1 decade * 10 years/ 1 decade * 365 days/ 1 year * 24 hours / 1 day
87600 hours
Identify negative angle measure. Select all angles that have a negative measure.
see attachments below
Step-by-step explanation:In Algebra, angles are measured counterclockwise (CCW), generally using the +x axis as a reference. Thus any angle with an arrow shown in the CW direction will have a negative measure.
Know that clockwise measured angles are negative and anticlockwise measured angles are positive in sign.
Thus,
In first figure first angle is positive, second is negative.In second figure first angle is negative, second is positive.In third figure, first angle is positive, second angle is negative, third angle is positive.How does rotation measure specifies sign of angles?
It is a standard convention used in mathematics that if you measure an angle clockwise(like the clock's hand moves), then the measured angle will be written with negative sign.
If the angle is measured anticlockwise, then the measured angle is written with positive sign.
Thus, by these conclusions, we have:
Thus, In first figure first angle is positive, second is negative.In second figure first angle is negative, second is positive.In third figure, first angle is positive, second angle is negative, third angle is positive.Learn more about sign of angles here:
https://brainly.com/question/11043027
please show work with answer
∠A ≅ ∠T . . . . given
AX ≅ TX . . . . given
∠AXM ≅ ∠TXH . . . . vertical angles are congruent
ΔAXM ≅ ΔTXH . . . . ASA theorem
MX ≅ HX . . . . CPCTC
___
15.The acronyms that invoke theorems based on two or three sides being congruent are inapplicable in this case.
SSS
SAS
A gumball machine has 420 red gumballs. If the red gumballs are 75% of the total number of gumballs, how many gumballs are in the gumball machine?
Answer:
The answer is 560
Step-by-step explanation:
multiply 420 by .75 for 75%
(420).75=560
how do i find a median?
Final answer:
The median is found by arranging a data set in ascending order and locating the middle value for an odd number of values or averaging the two middle values for an even number. Quartiles divide the data into sections and are related to the median. The median offers a measure of the center that is not skewed by outliers.
Explanation:
To find the median of a data set, start by arranging the data in ascending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, calculate the median by taking the average of the two middle values.
For example, for the ordered data set 3, 4, 8, 8, ... 44, 44, 47, which has 40 values, the median is between the 20th value (24) and the 21st value (24). In this case, since they are the same number, the median is 24. However, if the two numbers were different, you would add them together and divide by two to find the median.
When considering a data set like 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, with an even number of values (14), the median is the average of the 7th and 8th values, in this case, (6.8+7.2)/2 = 7. The quartiles can also be determined: Q1 is the median of the lower half, and Q3 is the median of the upper half of the data set.
Measures of the center of the data, like mean, median, and mode, offer different ways to represent the data set's central tendency. The median is particularly useful in data sets with outliers, as it is not as affected by extreme values as the mean.
A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the probability that a leg bone is less than 62 inches
Answer:
The probability of a leg bone measuring less than 62 inches is about 75% (74.86%).
Step-by-step explanation:
To answer this question we can calculate the z-score, then use a table to look up a corresponding percentile using z tables.
The length is a random variable with mean = 60 in and standard deviation of 3 in and we are looking at a particular sample that 62 in long. That sample has the following z value:
[tex]z = \frac{62 - \mu}{\sigma}=\frac{62-60}{3}=\frac{2}{3}\approx0.67[/tex]
The area under the normal distribution curve that corresponds to the z value of 0.67 (using a z table - available on line) is 0.7486. This is the probability that a random sample of a fossil leg length is less that our particular value 62 inches. Roughly speaking, the probability of a leg bone less than 62 in is about 75% (aka 75-th percentile).
what is the solution to the following equation x2 - 10x + 24 =0
Answer:
x=6 x=4
Step-by-step explanation:
x^2 - 10x + 24 =0
We need to factor this equation
What numbers multiply together to give us 24 and add together to give us -10
-6* -4 = 24 and -6+-4 = -10
(x-6) (x-4) = 0
Using the zero product property
x-6 = 0 x-4=0
x=6 x=4
Answer:
1.)C
2.)A
3.)B
Step-by-step explanation:
edge 2024
What is the slope of a line that is parallel to a line with slope of m=-6/5.What is the slope of the line that is perpendicular to a line with a slope of m=6/5.Explain how you know
Answer:
a) m = -6/5
b) m = -5/6
Step-by-step explanation:
The slopes of parallel lines are the same. The parallel line will have a slope equal to that of the line it is parallel to, -6/5.
__
The slopes of perpendicular lines are the opposite of the reciprocal of one another. The perpendicular line will have a slope that is the negative reciprocal of the slope of the one it is perpendicular to: -1/m = -1/(6/5) = -5/6.
if u=(1+i√3) and v=(1-i√3), what is uv?
Answer:
4
Step-by-step explanation:
You may recognize these as factors of the difference of two squares:
... a² -b² = (a+b)(a-b)
where a=1 and b=i√3.
Then the product is ...
... 1² -(i√3)² = 1 - 3i² = 1 +3 = 4
_____
Of course, i = √-1, so i² = -1.
Answer: 4
Step-by-step explanation:
u=(1+i√3) =2 v=(1-i√3)=2 Uv = (2)(2)=4
Select the correct answer. Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets?
A: The mean study time of students in Class A is less than students in Class B.
B: The mean study time of students in Class B is less than students in Class A.
C: The median study time of students in Class B is greater than students in Class A.
D: The range of study time of students in Class A is less than students in Class B. E: The mean and median study time of students in Class A and Class B is equal.
Answer:
B: The mean study time of students in Class B is less than students in Class A.
Step-by-step explanation:
To find out why answer B is the right answer, I will give you facts from each option.
Option A is false. The mean study time in Class A is 4.8. Meanwhile in Class B it is 4. For Class A, sum up the 20 study times which is 96 and divide them by 20, you will get 4.8 hours of mean study time. For Class B, the sum of the 20 study times is 80, which divided by 20 will be 4.
Option B is True. See previous explanation.
Option C is False. The median study time in Class B is 4. The median study time in Class A is 4.8,
Option D is False. The range in Class A is from 2 to 8. The range in Class B is from 2 to 7.
Option E is False: The mean and median study time of these classes is different.
Answer:
B: The mean study time of students in Class B is less than students in Class A.
Step-by-step explanation:
Which triangle is similar to triangle SRT?
Answer:
Triangle PQR
Step-by-step explanation:
PQR I am just adding extra words so I have a higher word count so it accepts my answer :)
Please Help If You Know How To Do Simple Interest ;3
Worth 15 points each (I think cause I put 30 points)
Answer:
$5875
Step-by-step explanation:
The simple interest formula for the ending balance is ...
... A = P(1 +rt)
You have principal amount P=5000, interest rate r=0.05, and time t=3.5, so the amount (A) is ...
... A = $5000(1 +0.05·3.5) = $5000·1.175
... A = $5875
Diana invests $25,000 in a bank at the beginning of the year. She will receive 7% interest at the end of the year, but she will have to pay a 16% tax on the interest received.
A.) How much interest will Diana earn after she pays the tax?
B.) What percent of Diana's investment is the interest after paying the tax?
Answer:
A) $1470
B) 5,88%
Step-by-step explanation:
B) Diana will end up with 100% -16% = 84% of the interest she earns, so her effective interest rate is ...
... 7% × 84% = 5.88%
A) Diana's investment earns ...
... 0.0588 × $25000 = $1470
After paying a 16% tax on the interest, Diana will earn $1,470 in interest. This represents 5.88% of her original $25,000 investment.
Diana invests $25,000 in a bank at 7% interest, which she will receive at the end of the year. However, she must pay taxes at a rate of 16% on the interest earned.
First, we calculate the total interest Diana would earn without taxes:
Total Interest = Principal imes Interest Rate
Total Interest = $25,000 imes 0.07 = $1,750.
Next, we calculate the tax on the interest:
Tax on Interest = Interest Earned imes Tax Rate
Tax on Interest = $1,750 imes 0.16 = $280.
Now, we subtract the tax from the total interest to find the interest after taxes:
Interest After Taxes = Total Interest - Tax on Interest
Interest After Taxes = $1,750 - $280 = $1,470.
We find the percentage of the original investment that the interest after taxes represents:
Percent of Investment = (Interest After Taxes / Principal) imes 100
Percent of Investment = ($1,470 / $25,000) imes 100 = 5.88%.
HELP PLEASE ON 13- A, B, C
Can anyone tell me if the ones I did are right
adam spent 13.10 on supplies for school. book covers cost 1.50 and boxes of mechanical pencils were each 2.80. if he bought seven items total, then how many of each did he buy
5 book covers and 2 boxes of pencils
Step-by-step explanation:If all 7 were book covers, the cost would be 10.50. The cost is 2.60 more than that. Each box of mechanical pencils costs 1.30 more than a book cover, so there must be 2.60/1.30 = 2 boxes of mechanical pencils (and 5 book covers).
_____
If you want an equation, let p represent the number of pencil boxes. Then 7-p is the number of book covers.
... 1.50(7-p) +2.80p = 13.10
... 1.30p = 13.10 -10.50 . . . . . subtract 10.50, collect terms
... p = 2.60/1.30 = 2 . . . . pencil boxes
... 7-2 = 5 . . . . . book covers
Question: Graph the line defined the equation 8x + 8y = 24
Choose: A,B,C or D!!!
Answer:
B
Step-by-step explanation:
8x + 8y = 24
-8x on both sides
8y = -8x + 24
Divide by 8 on both
y = -x + 3
Answer:
B
Step-by-step explanation:
(÷8)8x + 8y = 24(÷8)
x + y = 3
y = - x + 3
If x is negative, then the function is decreasing.
y = - x + 3
When x = 0
y = - 0 + 3
y = 3
(0,3)
When y = 0
- x + 3 = 0
- x = - 3
x = 3
(3,0)
Alternative B
I hope I helped you.
what are the apparent zeros of the function graphed above. (-0.7, -2,7)
Answer:
x ∈ {-2, 1, 4}
Step-by-step explanation:
The graph shows y = 0 when x = -2 or 1 or 4. Hence these values of x are the zeros of the function.
How do I write Domain and Range in inequality notation?
Answer:
Domain: (-infinity, infinity) Range: (-infinity, infinity)
Step-by-step explanation:
They are parabolas, therefore you can assume that they go on infinitely. To find range, you must look at your y values. Look for your lowest point. Because the line goes done forever, your beginning mark would be (-infinity.
To find the other part, you look at your positive y values. Look for the highest value. Because this goes on infinitely, the completed version of your notation would be (-infinity, infinity). Be sure to use the infinity symbol though, which looks like an 8 rotated 90 degrees.
To find domain, look at your x values. To begin, look at your left-most values, which would be the negative numbers. Because the line goes on forever to the left, your notation would be (-infinity. To find the other part of domain, look at your positive x values. Because this line goes on infinitely as well, the completed version of your notation would be (-infinity, infinity). Infinity is never bracketed, it is always in parenthesis.