Answer:
It cannot be simplified any further.
The simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15 is (y-4)/(y-5) .
Simplifying the equation(y^2-y+12)/(y^2-2y-15) factor both the numerator and denominator...
(y^2-4y-3y+12)/(y^2-5y+3y-15)
(y(y-4)-3(y-4))/(y(y-5)+3(y-5))
((y-4)(y-3))/((y-5)(y+3)) so the (y+3) and (y-3) cancel leaving
(y-4)/(y-5)
(y-4)/(y-5) the simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15.
To learn more about Simplifying the equation refer:https://brainly.com/question/26779637
#SPJ2
A bag of marbles has 12 red, 7 yellow, 5 blue and 1 white. Find the probability of selecting 4 marbles from the bag where all 4 are red.
There are 25 marbles: (12 red, 7 yellow, 5 blue, 1 white)
The probability of the first marble being red is 12/25 because there are 12 red marbles still available and no marbles are missing
The probability of the second marble being red is 11/24 because only 11 red marbles are available and 1 marble has already been selected from the pile
The probability of the third marble being red is 10/23 because only 10 red marbles are available and 2 marbles have already been selected from the pile
The probability of the fourth marble being red is 9/22 because only 9 red marbles are available and 3 marbles have already been selected from the pile
Since we are interested in all of these events occurring simultaneously, we must multiply the probability of all 4 events, like so:
[tex] \frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} [/tex]
Solving for this we are left with:
[tex] \frac{9}{230} \: \: or \: \: 0.0391[/tex]
An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24π inches . The artist plans to fill the inside of each dot with blue colored glass. What is the area of the blue glass will be needed to fill each butterfly dot?
Answer:
144 π or 452.4 sq inches, for each dot
Step-by-step explanation:
We are given the perimeter of the circle (24π), and we are asked to find the area of the circle basically.
The Circumference of a circle is given by C = 2 * π * r
while its area is given by A = π r²
So, having the circumference, we can isolate r to use it in the area calculation.
C = 2 * π * r
24π = 2 * π * r (now dividing both sides by 2π)
12 = r
The radius is 12 inches.
That means the area of one dot is:
A = π r² = π 12² = 144 π sq inches
The amount of blue glass needed for each dot is 144 π or 452.4 sq inches
Answer: 144
Step-by-step explanation:
Anne has saved 9 dollarsfor a new coat.Tgat is 1/6 as much money as she needs.How much does the coast cost?
The coat will cost $54
PLEASE HELP ME!!!!!!!!!!!!!!!!!!
Answer:
a) 4 - [tex]vt - d = \frac{1}{2} at^{2}[/tex]
b) 1 - [tex]2(vt - d) = at^{2}[/tex]
c) 6 - [tex]\frac{2(vt - d)}{t^{2}} = a[/tex]
Step-by-step explanation:
It simply asks the steps to go from the original displacement formula to isolate a (the acceleration). It's just a matter of moving items around.
We start with:
[tex]d = vt - \frac{1}{2} at^{2}[/tex]
We then move the vt part on the left side, then multiply each side by -1 (to get rid of the negative on the at side and to match answer choice #4):
[tex]vt - d = \frac{1}{2} at^{2}[/tex]
Then we multiply each side by 2 to get rid of the 1/2, answer #1:
[tex]2(vt - d) = at^{2}[/tex]
Finally, we divide each side by t^2 to isolate a (answer #6):
[tex]\frac{2(vt - d)}{t^{2}} = a[/tex]
A bald eagle has a nest in a mountain treetop.
The eagle flies 650 miles east and 150 miles south.
What is the distance of the eagle from his nest?
You can use the Pythagorean theorem to solve.
Distance = √(650^2 + 150^2)
Distance = √(422500 + 22500)
Distance = √(445000)
Distance = 667.08 miles
Rounded to the nearest whole mile = 667 miles.
The calculated distance is approximately 667.08 miles.
Calculating the Distance of the Eagle from Its Nest
To determine the distance of the eagle from its nest after flying 650 miles east and 150 miles south, we can use the Pythagorean theorem, which is applicable for right-angled triangles.
The eagle's eastward flight of 650 miles and southward flight of 150 miles form the two perpendicular sides of a right triangle, while the hypotenuse represents the straight-line distance from the nest.
The formula for the Pythagorean theorem is:
a² + b² = c²
Where:
a = 650 miles
b = 150 miles
c = the distance from the nest
Therefore, the distance of the eagle from his nest is approximately 667.08 miles.
A vendor sells three types of watches. Of the watches in stock 20% are mens watches, 40% are ladies watches and the rest are childrens watches. There are 250 all together how many childrens watches are there math
Answer:
100.
Step-by-step explanation:
The percentage of children's watches = 100 - 20 - 40 = 100-60
= 40%.
40% = 0.40 as a decimal fraction.
So the number of children's watches
= 0.40 * 250
= 100.
the price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD
A. 7/5m
B. 0.79m
C. 0.21m
D. 2/5m
Final answer:
The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD is 2/5m.
Explanation:
The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD can be calculated as follows:
Let's assume m is the amount needed to manufacture the CD.To find the price that sells for 21% more than m, we need to add 21% of m to m.The expression that represents the price is therefore: m + 0.21m.Combining like terms, we get 1.21m.Therefore, the correct answer is D. 2/5m.
Is the given sequence arithmetic? If so, identify the common difference. −34, −28, −22, −16, . . .
yes, −6
yes, 6
yes, −4
no
Answer:
yes, 6
Step-by-step explanation:
The given sequence is −34, −28, −22, −16, . . .
We check to see if there is a constant difference among the terms.
[tex]d=-28--34=-22--28=-16--22=6[/tex]
Since there is a constant difference of 6 among the consecutive terms, the sequence is arithmetic.
The correct choice is yes, 6
Please please help me
Answer:
169 : 289
Step-by-step explanation:
Since the figures are similar then
linear ratio of sides = a : b, then
ratio of areas = a² : b²
ratio of sides = 52 : 68 = 13 : 17
ratio of areas = 13² : 17² = 169 : 289
Find the greatest common factor of 8m 3 and 6m 4
The greatest common factor of 8m^3 and 6m^4 is 2m^3. This is found by determining the highest number or term that can divide both terms exactly, considering both the coefficients and the power of the variable.
Explanation:The question asks for the greatest common factor of the terms 8m3 and 6m4. The greatest common factor (GCF) is the highest number or term that divides both numbers exactly. Ignoring the coefficients (8 and 6), we can easily see that these terms both contain the variable 'm', raised to the powers 3 and 4, respectively.
The rule for dealing with variables when finding the GCF is to take the variable to the power which is the lesser of the two. In this case, that would be m3. Now, looking at the coefficients (8 and 6), the highest number that can divide them both exactly is 2. Therefore, the greatest common factor of 8m3 and 6m4 is 2m3.
Learn more about Greatest Common Factor here:https://brainly.com/question/29584814
#SPJ3
The greatest common factor of 8m³ and 6m⁴ is 2m³, which is found by identifying the shared prime factors and the lowest power of 'm' present in both terms.
To find the greatest common factor (GCF) of 8m³ and 6m³, we need to find the highest power of each prime number and the variable that is contained in both terms. The prime factorization of 8 is 23, and for 6, it is 2 × 3. Since both have at least one factor of 2, we'll use that in our GCF. Additionally, since the lowest power of 'm' that appears in both terms is m3, we will also use that.
The GCF is the product of these shared factors. So, we have:
2 (the common prime factor)
m3 (the lowest power of 'm' in both terms)
Therefore, the GCF of 8m³ and 6m⁴ is 2m³.
The table show whether a bus pass is a child’s or adult’s pass and whether it is a daily or monthly pass
(it’s a lot of different answers, like 50.8% or 60% or 60.8%)
do anybody have a for sure answer?
Answer:
50.8%
Step-by-step explanation:
That is the one my friend and I chose. It is 31/61 when all the stuff is added together and that is put to 50.8 as a percentage..
question 66
true or false
Answer:
True
Step-by-step explanation:
we know that
sin(-360°)=sin(360°)=0
therefore
y=sin(-360°)=0
Scores on a standardized test are normally distributed with a mean of 228 and a standard deviation of 18. Students who score at least 2.3 standard deviations above the mean receive a certificate.
What is the minimum score required to receive the certificate?
Answer:
270
Step-by-step explanation:
The mean is 228 and the standard deviation is 18.
2.3 standard deviations above the mean is:
228 + 2.3×18
228 + 41.4
269.4
Since scores are usually integers, we round up to 270.
Chase plays the piano and the cello. For every 2 hours he practices the piano, he practices the cello for 3 hours. If he practiced the piano for 5 hours last week, how many hours did he spend practicing the cello?
He would have played the cello for 7 hours and 30 minutes because 4 hours would be 6 hours of the cello and then he only did one more hour so you split 3 in half and that makes it an hour and a half. So the answer is 7 hours 30 minutes
Given that the ratio of piano practice to cello practice for Chase is 2:3, if he practiced the piano for 5 hours, he would have practiced the cello for 7.5 hours.
Explanation:To find out how many hours Chase spent practicing the cello, we first need to assess the ratio of piano to cello practice. The problem tells us that for every 2 hours practicing the piano, Chase spends 3 hours practicing the cello. So, the ratio of piano to cello practice is 2:3.
If he practiced the piano for 5 hours, the equivalent time spent practicing the cello can be found by setting up a proportion like: (2 hours piano / 3 hours cello) = (5 hours piano / x hours cello), where x is the number of cello practicing hours. Solving this proportion for x gives us x = (5 * 3) / 2 = 7.5 hours.
An interpretation of this result is that for every hour Chase spends practicing the piano, he spends 1.5 hours practicing the cello. Therefore, Chase spent 7.5 hours practicing the cello last week, given that he practiced the piano for 5 hours.
Learn more about Ratio and Proportion here:https://brainly.com/question/26974513
#SPJ3
Drag each statement to show whether it is true, based on the graph.
Boxes are
True, Not True, Cannot Be Determined
- There is suppose to be 5 answers there is only 4 to go in each box...
the 5th answer box is - Almonds cost $0.65 per one pound
Answer:
Step-by-step explanation:
The first and fourth answer choices are the correct one: $2.20/0.65 lb, $2.20 for 0.65 lb of almonds.
Answer:
i) True
ii) Not True
iii) Cannot be Determined
iv) True
Step-by-step explanation:
From the given graph, we infer the following information.
Cost of 0.65 Almonds is $2.2
Therefore,
i) The price per one pound of almonds equals [tex]\frac{2.20}{0.65lb}[/tex]---TRUE
ii) 2.2 pounds of almonds cost $0.65 ---------> Not True.
iii) Each bag of almonds weighs 2.2 pounds -----> Cannot be Determined (Because we don't have any information about bag)
iv) 0.65 pound of almonds costs $2.20 -----------> True
A roller coaster starts from a deck at an elevation of 20 feet above the ground. On the first hill it climbs 78 feet and then drops 85 feet. On the second hill the coaster climbs 103 feet and then drops 110 feet. How far below or above the deck is the coaster after the completion of the two hills?
Answer:
14 feet below. the deck.
Step-by-step explanation:
That would be (20 + 78 - 85 +103 - 110 ) feet above the ground
= 6 feet above the ground.
That is 20 - 6 = 14 feet below the deck.
the volume of the figure below is 496.21 ft^3
True or False
Answer:
First option: True.
Step-by-step explanation:
To know if the volume of this cylinder is 496.21 ft³, you need to use the formula for calculate the volume of a cylinder:
[tex]V=\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
You can observe in the figure that the radius of the cylinder is 4.5 feet and the height is 7.8 feet.
Then, knowing this, you can substitute these values into the formula.
Therefore, the volume of this cylinder is:
[tex]V=\pi (4.5ft)^2(7.8ft)\\V=496.21ft^3[/tex]
Then the answer is: True.
please help thank you.
first answer choices: 18 20 37 48
second answer choices: 38 38.5 42 72
third answer choices: 26 and 32, 28 and 42.5, 29 and 42.5, 38.5 and 43
fourth answer choices: 9 13.5 26 38
fifth answer choices: interquartile range, median, lower and upper quartiles, range
Answer:
range= 20 median= 38 lower quartile and upper quartile= 29 and 42.5
interquartile range= 13.5
Step-by-step explanation:
range= you take the biggest number and subract it from the smallest number.
median= you set the numbers to smallest to biggest then go in from the left and right moving both fingures at once till you get to the middle.
Lower quartile= exclude the medain and average the 4 numbers
Upper quartile= exclude the medain and average the 4 numbers
interquartile range= subract 29 from 42.5
range (i think)
Pls help me...........
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
sin²x = 1 - cos²x
sinx = [tex]\sqrt{1-cos^2x}[/tex]
note that cosΘ = [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex]
sinΘ = [tex]\sqrt{1-(3/5)^2}[/tex]
= [tex]\sqrt{1-\frac{9}{25} }[/tex]
= [tex]\sqrt{\frac{16}{25} }[/tex] = [tex]\frac{4}{5}[/tex]
Which choice is equivalent to the quotient shown here when x is greater than or equal to 0?
Answer: OPTION C
Step-by-step explanation:
Remember that:
[tex]\sqrt[n]{a^n}=a[/tex]
And the Product of powers property establishes that:
[tex]a^m*a^n=a^{(mn)}[/tex]
Rewrite the expression:
[tex]\frac{\sqrt{18x} }{\sqrt{32} }[/tex]
Descompose 18 and 32 into their prime factors:
[tex]18=2*3*3=2*3^2\\32=2*2*2*2*2=2^5=2^4*2[/tex]
Substitute into the expression, then:
[tex]\frac{\sqrt{(2*3^2)x} }{\sqrt{2^4*2} }[/tex]
Finally,simplifying, you get:
[tex]\frac{3\sqrt{(2)x} }{2^2\sqrt{2} }=\frac{3\sqrt{2x}}{4\sqrt{2}}=\frac{(3)(\sqrt{x})(\sqrt{2})}{(4)(\sqrt{2})}= \frac{3\sqrt{x}}{4}[/tex]
Please help asap!!!!
Answer:
11
Step-by-step explanation:
There is a rather simple method to this.
The factor given is ( x - 2 ) and the dividend is ( 2x⁵ - 7x³ - x² + 4x - 1)
To find the remainder, we will take it as x - 2 = 0
We will get x as 2
Now, substitute the value.
2 ( 2 )⁵ - 7 ( 2 )³ - ( x )² + 4 ( 2 ) - 1
2 ( 32 ) - 7 ( 8 ) - ( 4 ) + 8 - 1
64 - 56 - 4 + 8 - 1
8 - 4 + 8 - 1
16 - 4 - 1
16 - 5
11
Hence, the remainder is 11.
At Wonderful Water park, the water trough ride cost $2.75 per ride. If you have $15. then how many times could you ride?
Answer:
The maximum number of rides is 5
Step-by-step explanation:
Let
x----> the number of rides
we know that
The inequality that represent this situation is
[tex]2.75x\leq 15[/tex]
Solve for x
Divide by 2.75 both sides
[tex]x\leq 15/2.75[/tex]
[tex]x\leq 5.45[/tex]
Round down
The maximum number of rides is 5
Answer:
The maximum number of rides is 5
answer is 5 i took the test
Which choice is equivalent to the expression below when x is greater than or equal to 0?
Answer:
Choice A is the correct answer
Step-by-step explanation:
[tex]2x\sqrt{2x}[/tex]
Find the attachment below for the explanation
For this case we must indicate an expression equivalent to:
[tex]\sqrt {18x ^ 3} - \sqrt {9x ^ 3} +3 \sqrt {x ^ 3} - \sqrt {2x ^ 3}[/tex]
So, rewriting the terms within the roots we have:
[tex]18x ^ 3 = (3x) ^ 2 * (2x)\\9x ^ 3 = (3x) ^ 2 * (x)\\x ^ 3 = x ^ 2 * x\\2x ^ 3 = (2x) * x ^ 2[/tex]
So:
[tex]\sqrt {(3x) ^ 2 * (2x)} - \sqrt {(3x) ^ 2 * (x)} + 3 \sqrt {x ^ 2 * x} - \sqrt {(2x) * x ^ 2} =[/tex]
Removing the terms of the radical:
[tex]3x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} -x \sqrt {2x} =[/tex]
We simplify adding terms:
[tex]3x \sqrt {2x} -x \sqrt {2x} -3x \sqrt {x} + 3x \sqrt {x} =\\2x \sqrt {2x} + 0 =\\2x \sqrt {2x}[/tex]
Answer:
Option A
What is the value of x if 2 + 4x = 10?
Answer:
x = 2
Step-by-step explanation:
2 + 4x = 10
4x = 10 - 2
x = 8
x = 8 ÷ 4
x = 2
In a contest, players have to pick marbles from a bag. The bag contains 30 blue marbles, 20 yellow marbles, 10 red marbles, and 40 green marbles. A player wins $7 on picking a green marble, loses $5 on picking a blue marble, loses $3 on picking a yellow marble, and wins $2 on picking a red marble.
How will you simulate this game without actually having 100 marbles in a bag?
A.
Use the numbers 1–10 to represent different marbles based on their probabilities.
B.
Use the numbers 1–25 to represent different marbles based on their probabilities.
C.
Use the numbers 1–17 to represent different marbles based on their probabilities.
D.
Use the numbers 1–4 to represent different marbles based on their probabilities.
Answer:
D
Step-by-step explanation:
There are 4 colors to choose from, so use numbers 1-4 to represent each color.
I want to paint all three walls of the kitchen. One wall is half a cylinder. I want to paint the walls only, not the ceiling. The walls are 9' high. How many square feet will I be painting? Round to the nearest tenth.
Answer:
335.5 sq ft.
Step-by-step explanation:
Let's start with the 2 straight 10-feet long walls, it's easier.
Each of those two wall sections are 10 feet long by 9 feet high... They're rectangles, so their area is their base (10) by their height (9).
Wall 1 = 10 x 9 = 90 sq ft
Wall 2 = 10 x 9 = 90 sq ft
Now the half-circle portion.
The trick here is to calculate half of the circumference. The circumference of a circle is given by C = 2 π r, but we only want half of it... so C/2 = π r
We have the radius (r = 5.5 ft).
So, the half circle has a (half) perimeter of: 5.5 π r = 17.28 ft
Then we multiply this by the height of 9 feet: 17.28 = 155.52 sq ft
Then we add the two other walls:
Total area = 90 + 90 + 155.52 = 335.52, which we round down to 335.5 sq ft.
Please please help me
Answer:
151.4496 cm²
Step-by-step explanation:
The area of a trapezoid is found using the formula ...
A = (1/2)(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases and h is the distance between them. Fill in the numbers and do the arithmetic.
A = (1/2)(22.2 cm + 8.52 cm)(9.86 cm) = 151.4496 cm²
select the angle that correctly completes the law of cosines for this triangle
Answer:
Option 'B'
Step-by-step explanation:
The law of cosines states that given a triangle with sides a, b, c, then:
[tex]c^{2} =a^{2}+b^{2} -2abcos(y)[/tex] where 'y' is the opposite angle to the side 'c'.
In this case, given that the equation is: [tex]15^{2} =8^{2} + 17^{2} -2(8)(17)cos(y)[/tex] we can clearly see that c=15, and the opposite angle to 'c' is 62 degrees.
The correct option is Option 'B'
ANSWER
B. 62°
EXPLANATION
The cosine rule is given by:
[tex] {b}^{2} + {c}^{2} - 2(bc) \cos(A) = {a}^{2} [/tex]
where A is the angle that is direct opposite to the side length which is 'a' units.
The given relation is:
[tex]8^{2} + {17}^{2} - 2(8)(17) \cos( - ) = {15}^{2}[/tex]
The missing angle should be the angle directly opposite to the side length measuring 15 units.
From the diagram the missing angle is 62°
Consider a triangle with side lengths of 10 ft, 17.32 ft, and 20 ft. By examining the side lengths, what can you conclude about the measurement of the angles? Explain your reasoning. A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3 . B) The angles are 60-60-60. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3. C) The angles are 45-45-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3. D) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 2.
Answer:
A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.
Step-by-step explanation:
The answer choice speaks for itself.
The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.
The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.
Clearly, the given leg lengths match the second set of ratios more closely:
10 : 17.32 : 20 ≈ 1 : √3 : 2.
Please please help me
Answer:
(x - 5)² + (y + 3)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (5, - 3) and r = 4, thus
(x - 5)² + (y - (- 3))² = 4², that is
(x - 5)² + (y + 3)² = 16 ← equation of circle