Dan uses a compass to draw an arc from Q, as shown. He wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
first chart
Which figure shows the next step to construct a congruent angle at R?
Charts 2 3 4 & 5
Answers
Answer:
Chart 2.
Step-by-step explanation:
In the figure Dan has constructed an angle at point Q.He wants to cinstruct an angle ar point R which is congruent to angle made at point Q.To construct the angle at point R Dan needs to draw an arc at point R .He will put the compass on point R and draw an arc .This is shown in the figure 2.
The figure is added below.
Related Questions
all real cube roots of 27
Answers
Victor Malala has a net income of $1240.00 per month. If he spends $150.00 on food, $244.00 on a car payment, $300.00 on rent, and $ 50.00 on savings, what percent of his net income can he spend on other things?
Answers
Food: F=$150.00
Car payment: C=$244.00
Rent: R=$300.00
Saving: S=$50.00
Other things: O=?
F+C+R+S+O=I
$150.00+$244.00+$300.00+$50.00+O=$1240.00
Solving for O:
$744.00+O=$1240.00
$744.00+O-$744.00=$1240.00-$744.00
O=$496.00
Percent of his net income Victor can spend on other things: P=?
P=(O/I)*100%
P=($496.00/$1240.00)*100%
P=(0.40)*100%
P=40%
Answer: 40% of his net income Victor can spend on other things.
solve for x z= 19+2 (x+y)
Answers
Hope it helps
Jewelry is commonly weight in carats.Five carats are equivalent to one gram.How many grams of gold are contained in 24-carat gold chain
Answers
A right cylinder has a radius r of 19.4 cm and a height h of 48.3 cm. what is the volume of the cylinder in m3
Answers
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A triangle has side lengths of 7, 24, and 26. Is the triangle right, acute, or obtuse? a. right c. obtuse b. acute Please select the best answer from the choices provided A B C
Answers
Answer:
Option C. Obtuse
Step-by-step explanation:
we know that
Applying the Pythagoras Theorem
If [tex]c^{2}=a^{2} +b^{2}[/tex] ----> is a right triangle
If [tex]c^{2}>a^{2} +b^{2}[/tex] ----> is a obtuse triangle
If [tex]c^{2}<a^{2} +b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
Verify
[tex]c^{2}=26^{2}= 676[/tex]
[tex]a^{2} +b^{2}=7^{2} +24^{2}=625[/tex]
therefore
[tex]676>625[/tex]
[tex]c^{2}>a^{2} +b^{2}[/tex] -----> is a obtuse triangle
for triangle cab find the length of a Side a
Answers
the law of cosines establishes that
a²=c²+b²-2*c*b*cos A
in this problem
a=?
b=21
c=32
A=40°
a²=32²+21²-2*32*21*cos 40-----> a²=435.44---------> a=20.87 units
The polar coordinates of a point are given. find the rectangular coordinates of this point.(5, 3pi/4
Answers
Here, x is 5cos 135 deg = 5(-1/sqrt(3))
and y is 5* sin 135 deg = 5*(1/sqrt(3))
Write this point in the form (x,y), using the above values for x and y.
At the grocery store, an 8-inch cherry pie costs $4.39 and a similar 10-inch cherry pie cost $6.15. which is the better deal?
Answers
for the 10 inch pie you are paying about 61 cents per inch
so the 8 inch pie is a better deal
hope this helped
oh and to get those numbers divide 4.39 by 8 and 6.15 by 10
For his phone service, Jason pays a monthly fee of $19, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $75.10.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answers
Given:
monthly fee - $19
additional - $0.05 per minute
charged in a month - $75.10
Req:
number of minutes
Sol:
monthly fee + additional fee ≥ charged in a month
19 + 0.05m ≥ 75.10
0.05m ≥ 56.10
m ≥ 1,122 minutes per month
Jason used his phone service for 1,112 minutes in the span of one month
f(x)=e^(x) where it is translated 1 unit right and 2 units down
Answers
1) It is tanslated 1 unit right:
g(x)=f(x-1)→g(x)=e^(x-1)
2) and 2 units down:
h(x)=g(x)-2→h(x)=e^(x-1)-2
Answer: e^(x-1)-2
A collection of dimes and quarters worth $9.25. There are 46 coins in all. Find how many of each there are. How many dimes are there?
Answers
0.10d +0.25(46 -d) = 9.25
-0.15d = 9.25 -(0.25*46) = -2.25 . . . . simplify, subtract .25*46
d = 2.25/.15 = 15 . . . . . . . . . . . . . . . . . divide by the coefficient of d
There are 15 dimes.
Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. John's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for John to have 25 acres of tangerine trees and 15 acres of grapefruit trees?
No, because 50(25) + 75(15) ≠ 1500 No, because (50 + 75)(20 + 15) ≠ 1500 Yes, because 50(25) + 75(15) ≥ 1500 Yes, because 50 + 75 + 25 + 15 ≤ 1500
Answers
Total pounds of trees = 50x + 75y
For x = 25 acres and y = 15 acres
Total weight of trees = 50*25 + 75*15 = 2,375 pounds
This exceeds the maximum weight of fruits (that is, 1,500 pounds) possible from this farm. Therefore, John cannot have 25 acres of Tangerine trees and 15 acres of grapefruit trees.
using the quadratic formula to solve 7x^2-x=7, what are the values of x?
Answers
[tex]a x^{2} +bx+c=0[/tex]
So, to make this true subtract 7 from each side.
The equation is now 7[tex] x^{2} [/tex] - x - 7 = 0
Values for a, b, and c: a = 7, b = -1, c = -7
Plug these variables into the quadratic equation.
[tex] x= \frac{1 {\pm} \sqrt{ -1^{2}-4*7*-7}}{2*-7} [/tex]
Square -1 to get 1 and multiply -4 x 7 x -7 to get 196.
[tex]x= \frac{1 {\pm} \sqrt{1+196}}{2*-7}[/tex]
Multiply 2 x -7 to get -14, the denominator, and add 1 to 196.
[tex]x= \frac{1 {\pm} \sqrt{197}}{-14}[/tex]
Since 197 is not a square number, and I don't know if you want to leave it in radical form or not, I will just because it's easier to understand.
Hope this helps!
The average score on a standardized test is 750 points with a standard deviation of 50 points. What is the probability that a student scored more than 850 on the standardized test ?
Answers
z=(x-μ)/σ
where:
x=850
μ=750
σ=50
thus
z=(850-750)/50
z=2
thus
P(x>850)=1-P(x<850)=1-P(z<2)=1-0.9772=0.0228
Answer: P(x>850)=0.0228
Answer:
2%
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
What are the different types of solutions that you can get when you solve a system of linear equations? Describe the graphs of these different types of systems.
Answers
Answer:
there are no solutions (lines do not intersect)there is one solution (lines intersect at one point)there are an infinite number of solutions (lines overlap—are the same line)Step-by-step explanation:
"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.
A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.
The geometry of lines on a plane comes into play with regard to solutions.
The lines may be parallel, hence never intersect. (No points will be on all the lines.)The lines may intersect at one point.The lines may be the same line, overlapping, identical, coincident, consisting of all the same points, an infinite number.in the sport competition France won more gold medals than Italy, who won more good medals than Korea. if the total number of gold medals won by the consecutive intergers whose sum is 36. find the number of gold medals won by each.
Answers
10+11+12 =33 so the numbers are correct.
France 16
Italy 15
Korea 14
HELP FAST ILL MAKE BRAINIEST Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following colored data tables. Purple: Weight of elk antler pairs at Mount St Helens NVM: {34, 34, 30, 30, 30, 28, 28, 26} Red: Weight of elk antler pairs at Rocky Mountain NP: {40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the following for each set of data: a. Purple Mean: b. Red Mean: c. Purple Median: d. Red Median: e. Purple MAD: f. Red MAD:
(c) Calculate the means-to-MAD ratio for the two areas of collection. (
d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain. Answer:
Answers
The diagram is shown in figure 1.
a.2 Weight of elk antler pairs at Rocky Mountain NP
The diagram is shown in figure 2.
b. Calculate the following for each set of data:
We can found the mean (µ) of a set of data points by adding them up and dividing by the number of data points.
b.1 Purple Mean:
Set: [tex]\{34, 34, 30, 30, 30, 28, 28, 26\} \rightarrow \frac{34+34+30+30+30+28+28+26}{8} \rightarrow \boxed{\mu=30}[/tex]
b2. Red Mean:
Set: [tex]\{40, 38, 36, 36, 36, 36, 34, 32\} \rightarrow \frac{40+38+36+36+36+36+34+32}{8} \rightarrow \boxed{\mu=36}[/tex]
b.3 Red Median
The Median is the middle of a sorted list of numbers. The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest. So, arranging the red set we have:
[tex]\{32, 34, 36, 36, 36, 36, 38, 40\}[/tex]
Given that the number of elements is pair, the median can be solved as follows:
[tex]\overline{x}=\frac{x_{(n/2)}+ x_{((n/2)+1)}}{2}[/tex]
∴ [tex]n=8[/tex]
∴ [tex]x_{(n/2)}=x_{(4)}=36[/tex]
∴ [tex]x_{((n/2)+1)}=x_{(5)}=36[/tex]
Then:
[tex]\overline{x}=\frac{36+36}{2}=36[/tex]
b.4 Purple MAD
The Mean Absolute Deviation (MAD) is when you find the distance of each data point from the mean and then find the mean of those distances. So:
[tex]\{34, 34, 30, 30, 30, 28, 28, 26\}[/tex] has [tex]\mu=30[/tex]
[tex]distances=\{4, 4, 0, 0, 0, 2, 2, 4\} \rightarrow \frac{4+4+0+0+0+2+2+4}{8}= \boxed{MAD=2}[/tex]
b.5 Red MAD
[tex]\{40, 38, 36, 36, 36, 36, 34, 32\}[/tex] has [tex]\mu=36[/tex]
[tex]distances=\{4, 2, 0, 0, 0, 0, 2, 4\} \rightarrow \frac{4+2+0+0+0+0+2+4}{8}= \boxed{MAD=1.5}[/tex]
c. Calculate the means-to-MAD ratio for the two areas of collection
c.1 Purple set:
The ratio is the relationship between the mean and the MAD indicating how many times the first number contains the second, so:
[tex]\frac{\mu}{MAD}= \frac{30}{2}=\boxed{15}[/tex]
c.2 Red set:
[tex]\frac{\mu}{MAD}= \frac{36}{1.5}=\boxed{24}[/tex]
d. What inference can be made about the areas in regard to weight of dropped elk antlers?
MAD tells us how far, on average, all values are from the middle. So, in the example weight of elk antler pairs at Mount St Helens NVM are, on average, 2 away from the middle. On the other hand, weight of elk antler pairs at Rocky Mountain NP are, on average, 1.5 away from the middle. So, we can assure that elk antler pairs at Rocky Mountain NP weighs more than elk antler pairs at Mount St Helens NVM.
Which quadratic equation equation is equivalent to (x^2-1)^2 -11(^2-1) +24=0
Answers
Use substitution: [tex]x^2-1=t[/tex]
[tex]t^2-11t+24=0\\\\t^2-8t-3t+24=0\\\\t(t-8)-3(t-8)=0\\\\(t-8)(t-3)=0\iff t-8=0\ \vee\ t-3=0\\\\t=8\ \vee\ t=3[/tex]
we're going back to substitution:
[tex]x^2-1=8\ \vee\ x^2-1=3\ \ \ \ |add\ 1\ to\ both\ sides\ of\ the\ equations\\\\x^2=9\ \vee\ x^2=4[/tex]
therefore
[tex]x=\pm\sqrt9\ \vee\ x=\pm\sqrt4\\\\\boxed{x=-3\ \vee\ x=3\ \vee\ x=-2\ \vee\ x=2}[/tex]
Answer:
x = ± 3 and ± 2
Step-by-step explanation:
The given quadratic equation is
[tex](x^{2}-1)^{2}-11(x^{2}-1)+24=0[/tex]
To make this question easier we will consume ( x² -1 ) = a
a² - 11a + 24 = 0
Now we can factorize this equation easily
a²- 8a - 3a + 24 = 0
a (a-8) - 3 ( a-8) = 0
( a-3 ) ( a-8 ) = 0
Therefore, a - 3 = 0 ⇒ a = 3
or a - 8 = 0 ⇒ a = 8
Now we put the value a
when a = 3 (x² - 1) = 3
x² = 3 + 1 = 4
x = √4
= ± 2
when a = 8 (x² - 1) = 8
x² = 9
x = √9
= ± 3
Therefore, x = ± 3 and ± 2 will be the answer.
If f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, how small can f(8) possibly be?
Answers
f'(x) can only be 2 and not less so then f(x) would increase by 2 for every x increasing by 1 all the way to x=8.
So then smallest possible f(8) would be f(8) = f(3) + 2 + 2 + 2 + 2 + 2 = f(3) + 2(8-3) = 21
Hope this helps.
Given the derivative f '(x) ≥ 2, the function f(x) increases by at least 2 units for every increase in 'x' from 3 to 8. Therefore, the smallest possible value of f(8) is reached when the increase is exactly 2 per 'x', giving us a result of 21.
Explanation:
The question is about calculus, specifically related to the concept of derivatives and their role in function interval analysis. Given the information that f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, we are asked to find the smallest possible value of f(8).
The derivative, f '(x), represents the rate of change of the function f(x). It is mentioned that f '(x) ≥ 2, which means that the function f(x) is increasing at a rate not less than 2 units per increase in 'x' from 3 to 8.
This suggests that the smallest possible value of f(8) could be achieved by assuming that f(x) increases exactly by 2 units for every increase in 'x'. So, from x = 3 to x = 8 is a change of 5 units in 'x'. Multiply this by the rate of change 2 to obtain the total change in f(x), which is 5 * 2 = 10. Added to the initial value f(3) = 11, we get the smallest possible value for f(8) is 11 + 10 = 21.
Learn more about Derivatives here:https://brainly.com/question/32963989
#SPJ2
hey can you please help me posted picture of question
Answers
The solution is shown below:
(8 - 3i)(6 + 5i)
= 8(6 +5i) - 3i(6 + 5i)
= 48 + 40i - 18i - 15i²
= 22i + 48 - 15(-1)
= 22i + 48 + 15
= 22i + 63
= 63 + 22i
Q9 Q11.) Complete the first and second equations of the system of equations.
Answers
See picture below for the answer. Let me know if you have questions about the answer.
You have $25 in your bank account. You make $7 per hour babysitting. How many hours must you babysit to have a total of $165 in your account?
Answers
You start with 25 dollars, you make 7 an hour:
7x + 25
Set this to 165:
7x + 25 = 165
Now subtract 25 from both sides:
7x = 140
Divide both sides by 7:
x = 20
So, you must babysit 20 hours.
Hope this helps!
25 + 7h = 165
h is the total number of hours you spend babysitting.
Solve for h to find how many hours you need to babysit to have a total of $165 in your bank account.
25 + 7h = 165
Subtract 25 from both sides.
7h = 140
Divide both sides by 7.
h = 20
You must spend 20 hours babysitting to have $165 in your bank account.
The circle graph shows the different types of books that Yubo enjoys reading
Which two types of books does Yubo spend a total of of her time reading?
Choose exactly two answers that are correct.
A.
Fiction
B.
Mystery
C.
Poetry
D.
History
Answers
History=0.4~40%
Poetry=0.3~30%
hence we can conclude that the answer is:
C. Poetry
D. History
Answer:
its really History and Mystery hope i hlaaaaaaaaaaaaaaaaped
The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9. what is the sample standard deviation?
Answers
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9
to get the standard deviation we use the formula for variance given by:
σ²=[Σ(x-μ)²]/(n-1)
σ² is the variance
μ is the mean
The mean of the data will be:
μ=(8+8+8+5+9+8+7+6+6+7+7+7+7+9+9)/15=7.4
The variance will be found as follows:
σ²=[(8-7.4)²×4+(5-7.4)²+3×(9-7.4)²+5×(7-7.4)²+2×(6-7.4)²]/(15-1)
σ²=1.4
thus
σ=√1.4=1.1183
Hence, the sample standard deviation is:
1.1832
Step-by-step explanation:The data is given by:
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9.
The mean of these data points is given by:
[tex]Mean(x')=\dfrac{8+8+8+5+9+8+7+6+6+7+7+7+7+9+9}{15}\\\\i.e.\\\\Mean(x')=\dfrac{111}{15}\\\\i.e.\\\\Mean(x')=7.4[/tex]
Now,
x x-x' (x-x')²
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
5 5-7.4= -2.4 5.76
9 9-7.4=1.6 2.56
8 8-7.4=0.6 0.36
7 7-7.4= -0.4 0.16
6 6-7.4= -1.4 1.96
6 6-7.4= -1.4 1.96
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
9 9-7.4=1.6 2.56
9 9-7.4=1.6 2.56
∑(x-x')²=19.69
Now the variance of the sample population is given by:
[tex]Variance=\dfrac{\sum (x-x')^2}{n-1}[/tex]
where n is the number of data points.
Here n= 15
Hence, n-1=14
Hence, we get:
[tex]Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4[/tex]
We know that the standard deviation is the square root of the variance.
i.e.
[tex]Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832[/tex]
What is the inverse function of f(x)=5x-3
Answers
The inverse function of f(x) = 5x - 3 is found by switching x and y to solve for x, resulting in the inverse function f⁻¹(x) = (x + 3) / 5. This process is part of understanding function transformations that change a function's graph.
Finding the Inverse Function
Find the inverse function of f(x) = 5x - 3. To find the inverse, we need to switch the roles of x and y. So we first write y = 5x - 3. We then solve this equation for x to get x as a function of y. Performing the steps:
Add 3 to both sides: y + 3 = 5x.
Divide both sides by 5: (y + 3) / 5 = x.
This new equation x = (y + 3) / 5 represents the inverse function. To use the proper notation, we replace y with f⁻¹(x) and x with y, giving us f⁻¹(x) = (x + 3) / 5.
Understanding Function Transformations
When considering transformations such as f(-x) or f(2x), these changes to the independent variable result in specific alterations to the graph of the function, such as reflections across the y-axis or horizontal shrinkage by half.
The poplution of Las vegas, Nevada has been increasing at an annual rate of 7.0%. If the poplution of las vegas was 478,434 in the year 1999, predict its population in 2010.
Answers
p(x) = 478,434*1.07^x
For x=11, this is
p(11) = 478,434*1.07^11 ≈ 1,007,033
The relation predicts the Las Vegas population in 2010 to be 1,007,033.
Which of these points does not change its location when it is reflected across the y-axis? (2, 0) (0, 6) (3, 3) (–5, 5)
Answers
Answer:
-5,5
Step-by-step explanation:
A taxi driver estimates that his earnings are $240 on a fine day and $320 on a wet day. What are his expected earnings on a day with probability of rain of 0.45?
Answers
Probability of not raining=1-0.45=0.55
The expected earning will be given by:
E(x)=240(0.55)+320(0.45)
E(x)=132+144
E(x)=276
Answer: $276
A person in a balloon which is 2,000 feet above the airport finds that the angle of depression to a ship out at sea is 21°. Find the horizontal distance between the balloon and the ship.
Answers
The horizontal distance between the balloon and the ship can be calculated using the tangent function is 1639 feet.
To find the horizontal distance between the balloon and the ship, we can use the tangent function in trigonometry. Let's denote the horizontal distance as x, and the distance between the balloon and the ship along the ground as y.
We have the angle of depression (21°) and the altitude of the balloon (2,000 feet). We can set up the equation:
tan(21°) = y / (2,000 + y)
Now, we need to solve for y:
tan(21°) * (2,000 + y) = y
y * tan(21°) = 2,000 * tan(21°) - y * tan(21°)
y * (1 - tan(21°)) = 2,000 * tan(21°)
y = (2,000 * tan(21°)) / (1 - tan(21°))
Now, calculate the value:
y ≈ (2,000 * 0.364) / (1 - 0.364)
y ≈ 728 / 0.636
y ≈ 1,148.17
Now that we have the value of y, we can find the horizontal distance x using the Pythagorean theorem:
[tex]x^2 + y^2 = (2,000)^2\\x^2 + (1,148.17)^2 = 4,000,000\\x^2 = 4,000,000 - 1,319,441.98\\x^2 = 2,680,558.02\\x = 1,638.84 (rounded)[/tex]
The horizontal distance between the balloon and the ship is approximately 1,639 feet.
Horizontal distance = height of balloon / tangent(angle of depression) = 2000 / tan(21°) ≈ 5243.87 feet.
To find the horizontal distance between the balloon and the ship, we can use trigonometry, specifically the tangent function.
Let's denote:
- [tex]\( h \)[/tex] as the height of the balloon above the ground (2,000 feet in this case).
- [tex]\( \theta \)[/tex] as the angle of depression (the angle formed between the line of sight from the balloon to the ship and the horizontal ground).
Given that the angle of depression [tex]\( \theta \)[/tex] is 21°, we can use the tangent function:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
In this case, the opposite side is the height of the balloon above the ground (2,000 feet), and we want to find the adjacent side, which represents the horizontal distance between the balloon and the ship.
So, we have:
[tex]\[ \tan(21°) = \frac{2000}{\text{horizontal distance}} \][/tex]
To find the horizontal distance, we rearrange the equation:
[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \][/tex]
Now, we can calculate this:
[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \approx \frac{2000}{0.381} \approx 5243.87 \text{ feet} \][/tex]
So, the horizontal distance between the balloon and the ship is approximately 5243.87 feet.