What is the solution set of {x | x < -5} ∩ {x | x > 5}?
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Math Torture!
Adam is constructing an equilateral triangle. He has already constructed the line segment and arcs shown.
What should Adam do for his next step?
A. Place the point of the compass on point X and draw an arc, using a width for the opening of the compass that is greater than 12XR.
B. Place the point of the compass on point X and draw an arc, using XR as the width for the opening of the compass.
C. Use the straightedge to draw XR←→ and XS←→.
D. Use the straightedge to extend RS¯¯¯¯¯ in both directions.
Answer:
C. Use the straightedge to draw XR←→ and XS←→.
Step-by-step explanation:
Adam has drawn the arcs by using RS distance as the radius of the circle and mid points as R and S.
So the point X is the same distance from R and S.
So now Adam has to use the straightedge to draw XR←→ and XS←→.
Then, XR = XS = RS
So it is an equilateral triangle.
Therefore, the correct answer is C.
Adam should do for his next step to use the straightedge to draw [tex]\( XR \)[/tex] and [tex]\( XS \).[/tex] The option (C) is correct.
The construction process for the equilateral triangle:
To construct an equilateral triangle using a straightedge and compass:
Construct [tex]\( XR \)[/tex]: Adam has already constructed segment [tex]\( XR \).[/tex]
Draw [tex]\( XS \)[/tex]: Using the straightedge, Adam should draw a line segment [tex]\( XS \)[/tex] from point [tex]\( X \)[/tex] to another point [tex]\( S \)[/tex] such that [tex]\( XS = XR \)[/tex]. This ensures that two sides of the equilateral triangle are equal in length.
Draw [tex]\( RS \)[/tex]: After drawing [tex]\( XS \)[/tex], Adam should use the straightedge to draw segment [tex]\( RS \)[/tex], completing the equilateral triangle [tex]\( \triangle XRS \).[/tex]
This method aligns with the steps typically used in geometric constructions to form an equilateral triangle: ensuring that all three sides are equal in length by first establishing two sides of equal length and then completing the triangle.
Therefore, upon reconsideration, option (C) is indeed the correct next step for Adam to construct his equilateral triangle.
I need help someone explain?????
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $30 per foot, and the fencing for the east and west sides costs $15 per foot. If I have a budget of $120 for the project, what are the dimensions of the garden with the largest area I can enclose?
The largest rectangular orchid garden that can be enclosed within a $120 budget, considering the given costs of fencing, has dimensions of 2 feet by 2 feet, resulting in an area of 4 square feet.
You wish to create a rectangular orchid garden with the house forming the northern boundary, and you're working with a budget of $120 for fencing. The cost per foot for the southern boundary is $30, and for the east and west sides, it's $15 each. We need to determine the dimensions that maximize the area.
Let's denote the width of the garden (east and west sides) as w feet, and the length (only the southern side, as the northern side is the house) as l feet. The total cost of fencing is therefore the sum of the costs for all three sides: Cost = $30l + 2($15w), which simplifies to Cost = $30l + $30w. Since your budget is $120, we can write the equation $30l + $30w = $120, which simplifies further to l + w = 4.
To find the dimensions that give you the largest area, we need to maximize the area A of the rectangle, which is A = l imes w. Substituting w with 4 - l (from our previous equation), we get A = l imes (4 - l). To find the maximum area, take the derivative of A with respect to l and set it to zero, solving for l. This gives us l = 2 feet. Substituting back, we find w = 2 feet as well.
The dimensions for the garden that will give you the largest enclosed area within a $120 budget are 2 feet in width by 2 feet in length, resulting in an area of 4 square feet.
Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Answer:
Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Step-by-step explanation:
It is called the inverse or reciprocal function of f to another function f − 1 that fulfills that:
If f (a) = b, then f − 1 (b) = a.
The inverse of a function when it exists is unique, so that neither "X" nor "Y" can be repeated.
If we analyze the possibilities, in the case of b, c, and d, the value 4 of the "Y" is repeated twice; in the case of a, that does not happen, therefore the answer is: a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2) }
A four person relay team completed a race in 72.4 seconds. On average what was each runner's time?
Answer:
i believe it's 18.1
Step-by-step explanation:
Henry is making a corn grits recipe that calls for 14 cup of corn grits for every 12 cup of water. How much water will he need if he uses 112 cups of corn grits? Enter the number in the box
at 1:00 pm you have 24 megabytes of a movie. at 1:15 pm you have 96 megabytes what is the download rate in megabytes per minute
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1: to find the radius of the circle.)
Mara ran 3 km north and then 4 km east. She will finish her run by running directly home. What was the total distance of her run?
The total distance of her run is 12 Km and this can be determined by using the Pythagorean theorem.
Given :
Mara ran 3 km north and then 4 km east.Mara will finish her run by running directly home.The following steps can be used in order to determine the total distance of Mara run:
Step 1 - The Pythagorean theorem can be used in order to determine the total distance of her run.
Step 2 - The Pythagorean theorem is given below:
[tex]\rm H^2 = P^2+B^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 3 - Now, substitute the values of the known terms in the above expression.
[tex]\rm H^2 = (3)^2+(4)^2[/tex]
H = 5 Km
Step 4 - So, the total distance of Mara run is given below:
Total distance = 5 + 4 + 3 = 12 Km
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At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply.
joe is using his allowance money to download songs from the internet. he can download them at a rate of eight songs every 10 minutes. Jasmine, who is downloading songs with the money she made from her part time job, can download at a rate of 12 songs every 15 minutes. Who is downloading songs faster?
Joe: 8 songs in 10 minutes = 8/10 = 0.8 songs per minute
Jasmine: 12 songs in 15 minutes = 12/15 = 0.8 songs per minute
they are downloading at the same speed
What is 32,020.20 rounded to the nearest square mile
A dealer dealt the following cards from a shuffled deck: 3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6 4 , 5 , K , 2 , 7 , 6 , A , J , J , A What was the experimental probability of dealing a black card?
Answer:
Total number of cards in shuffled deck=3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6, 4 , 5 , K , 2 , 7 , 6 , A , J , J , A .
Total number of cards in a deck of card = 52 cards, out of which 26 are black cards and 26 are red card.
As, it is not given that out of the 20 cards dealt by dealer is either red card or black card.
A=3=2B +1 R or 1 B + 2 R
2=4=2 R +2 B
3=1=1 R or 1 B
4=1=1R or 1 B
5=2=2 R or 2 B
6=2=2 R or 2 B
7=1=1 R or 1 B
8=0
9=0
10=0
J=2= 2 R or 2 B
K=3= 2 R + 1 B or 1 R +2 B
Q=1=1 R or 1 B
If you count total number of black cards among the number of cards dealt by dealer, the possibilities of black card drawn is either 15 or 16 from 20 cards drawn.
As, Experimental probability is the probability obtained through experiment which is different from theoretical Probability.
Total number of cards =52
So, Probability of dealing with black cards by dealer which is either 15 or 16 in number is given by
[tex]=\frac{\text{total favorable outcome}}{\text{total possible outcome}}\\\\\frac{15}{52} {\text{or}} \frac{16}{52}=\frac{4}{13}.[/tex]
40%
Step-by-step explanation:There are 20 cards in total.
8 are black: 3,2,K,5,6,4,A,J
12 are red: 2,A,K,Q,2,5,K,2,7,6,J,A
so that means 8 of the 20 are black or 8/20
and 8/20 is 40% which is your answer.
Harvey invested $6000 for 2 years in a savings account paying simple interest with a yearly interest rate of 5.5%. How much simple interest did he earn.
Harvey earned a simple interest of $660 over 2 years on his $6000 investment.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, We know that;
Simple interest is calculated using the formula:
I = P r t
Where: I = Interest earned P = Principal amount (amount invested) r = Annual interest rate t = Time period (in years)
Now, In this case,
Harvey invested $6000 for 2 years at an annual interest rate of 5.5%.
So, using the formula:
I = 6000 x 0.055 x 2
I = $660
Therefore, Harvey earned a simple interest of $660 over 2 years on his $6000 investment.
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For the number 4768.325, what is the sum of the tens digit and the tenths digit
Which of the following is a measurement of the space between two objects? A. Area B. Pounds C. Circumference D. Miles
Final answer:
The space between two objects is measured as distance or length, with miles being the correct unit of measurement among the given options.
Explanation:
The measurement of the space between two objects is referred to as length or distance. If we look at the options provided: A. Area, B. Pounds, C. Circumference, D. Miles, it is clear that miles is a unit of measurement that describes distance. Area measures the size of a surface, pounds measure weight or mass, and circumference measures the distance around a circle. When considering distances, especially those that are long such as between two cities, miles is an appropriate unit to use. For example, the distance between your house and school would best be measured in kilometers or miles, rather than in smaller units like inches or centimeters, or in unrelated units like pounds or areas.
Figure ABCDE is the result of a 180° rotation of Figure LMNOP about the point. Which angle in the pre-image corresponds to ∠B in the image? Enter your answer in the box.
Figure L M N O P is rotated 180 degrees about a point resulting in image A B C D E.
Answer: ∠M in the pre-image corresponds to ∠B in the image.
Step-by-step explanation:
When we look at the figures , we can see that the three vertices B , C , D are one side as vertices to M , N ,O .
Clearly , vertex C corresponds to vertex N ( presents in the middle )
Also, point B is at the right from point C .
In Figure L M N O P , vertex M is at the right from vertex N .
Thus , vertex M corresponds the vertex B.
It means ∠M in the pre-image corresponds to ∠B in the image.
Daniel ate 1/3 of the left over pizza. If there were 2 1/2 pizzas left, how much did Daniel eat?
Find the missing numbers 85,95, _ ,100,105, _
Trygg has 3/4 package of marigold seeds. He plants 1/6 of those seeds in his garden and divides the rest equally into 10 flower pots. What fraction of a packege of seeds is planted in each flower pot? Show your work.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
We are given that
Trygg has package of marigold seeds=[tex]\frac{3}{4}[/tex]
He plants seeds in garden=[tex]\frac{1}{6}\times \frac{3}{4}=\frac{1}{8}[/tex]
Remaining seeds=[tex]\frac{3}{4}-\frac{1}{8}=\frac{5}{8}[/tex]
He divide remaining seeds equally into 10 flower pots.
We have to determine the fraction of a package of seeds is planted in each flower pot.
Seeds in each pot=[tex]\frac{\frac{5}{8}}{10}=\frac{1}{16}[/tex]
Hence, seeds planted in each pot=[tex]\frac{1}{16}[/tex]
Rajendra has 14 4/5 pounds of trail mix. He is putting them into bags that hold 1 1/2 pounds each. Does he have enough trail mix to completely fill 8 bags?
Answer: Yes , Rajendra has enough trail mix to completely fill 8 bags.
Step-by-step explanation:
Given : Total trail mix Rajendra has = [tex]14\dfrac{4}{5}[/tex] pounds
Convert [tex]14\dfrac{4}{5}[/tex] into improper fraction.
[tex]14\dfrac{4}{5}=\dfrac{(14)(5)+4}{5}=\dfrac{74}{5}[/tex]
Amount of mix in each bag = [tex]1\dfrac{1}{2}[/tex] pounds.
[tex]=\dfrac{1(2)+1}{2}=\dfrac{3}{2}[/tex] pounds
Then, the total number of bags can be filled by the trail mix Rajendra has
= Total trail mix ÷ Amount of mix in each bag
[tex]=\dfrac{74}{5}\div\dfrac{3}{2}[/tex]
[tex]=\dfrac{74}{5}\times\dfrac{2}{3}=\dfrac{148}{15}=9.86666666667\approx9[/tex]
It means Rajendra has enough trail mix to fill 9 bags.
Since 9 > 8
Therefore , Rajendra has enough trail mix to completely fill 8 bags.
Answers matching "The combined average weight of an okapi and a llama is 450 kilograms. The average weight of 3 llamas is 190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?"
Let us say that:
x = weight of llamas
y = weight of okapi
From the problem, we can create the equations:
x + y = 450 --> 1
3 x = y + 190 --> 2
Rewriting equation 1:
x = 450 – y
From equation 2:
3 (450 – y) = y + 190
1350 – 3 y = y + 190
4 y = 1160
y = 290
From equation 1:
x = 450 – 290
x = 160
Therefore a llama weighs 160 kilograms while okapi weigh 290 kilograms on average.
Given the function f(x) = −2x2 + 4x − 7, find f(−4). −55 −7 9 25
Answer:
Option (a) is correct.
The value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55
Step-by-step explanation:
Given : [tex]f(x) = -2x^2 + 4x- 7[/tex]
We have to find the value at f(-4) and choose the correct option from the given options.
Consider the given function [tex]f(x) = -2x^2 + 4x- 7[/tex]
Since, we have to find the value of f(-4) that is value of f(x) at x = -4
Substitute, value of x = -4 in given function, we have,
[tex]f(-4) = -2(-4)^2 + 4(-4)- 7[/tex]
Simplify, we have,
[tex]f(-4) = -55[/tex]
Thus, the value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55
Option (a) is correct.
Write a user-defined function that determines the polar y coordinates of a point from the cartesian coordinates in a two-dimensional plane.
What is the rate of change of y with respect to x for this function?
HELP FOR BRAINLYEST
what is the answer 4(6/10−1/5)+0.4=
Or in shorter answers 2
Monique Fournier deposited $12,500 into a savings account paying 6.5% annual interest compounded monthly. What amount will she have in her account after 3 years? How much compound interest will she have earned?
Explaining the calculation of the amount in the account after 3 years and the compound interest earned.
Amount in the account after 3 years:
Calculate the monthly interest rate: 6.5% annual interest divided by 12 (months) = 0.0054167
Calculate the total amount using the compound interest formula: $12,500 * (1 + 0.0054167)^36 = $15,183.41
Compound interest earned:
Subtract the initial deposit from the total amount: $15,183.41 - $12,500 = $2,683.41
Carmen is making 5 parts strawberry juice to 3 parts water. Carmen would like to make 64 fluid ounces of the strawberry drink. How many fluid ounces of strawberry juice and water does Carmen need?
Ok so if she needs 64 floz, If u add 5+3 you get 8. 64/8 = 8
Now You multiply your parts of water and juice by 8.
5*8= 40 <---- Answer
3*8 =24 <----Answer
To check your answer you would add up the parts of each. 40+24= 64
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