The sum of two numbers is 26. When the second number is subtracted from the first number, the difference is 10. Find the two numbers.
how many 16s go into 57
What is the value of p in the equation x2 = 12y?
A student is training for the track team during the first three months of the year by running for 30 minutes every day while averaging 5 miles each day. Select the graph that correctly shows the total miles ran during the time of his training program.
Answer:
Graph 2 :)
Step-by-step explanation:
You have 10 fish, 5 drown, 3 come
back to life. How many fish do you have? ...?
The gift shop at manatee mall was having a clearance sale. everything was marked down 30%. the original price of a manatee hat was $18. what is the clearance price?
Answer
Find out the what is the clearance price .
To prove
As given
The gift shop at manatee mall was having a clearance sale.
everything was marked down 30%.
The original price of a manatee hat was $18.
30% is written in the decimal form
[tex]= \frac{30}{100}[/tex]
= 0.30
Than
The clearance price = 18 - 0.30 × 18
= 18 - 5.4
= $12.6
Therefore the clearance price be $12.6 .
Which of the following is the expansion of (3c + d2)6?
A) 729c6 + 1,458c5d2 + 1,215c4d4 + 540c3d6 + 135c2d8 + 18cd10 + d12
B) 729c6 + 1,458c5d + 1,215c4d2 + 540c3d3 + 135c2d4 + 18cd5 + d6
C) 729c6 + 1,215c5d2 + 810c4d4 + 270c3d6 + 90c2d8 + 15cd10 + d12
D) 729c6 + 243c5d2 + 81c4d4 + 27c3d6 + 9c2d8 + 3cd10 + d12
E) c6 + 6c5d2 + 15c4d4 + 20c3d6 + 15c2d8 + 6cd10 + d12
Answer: Option A) [tex]729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}[/tex] is the correct expansion.
Explanation:
on applying binomial theorem, [tex](a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r[/tex]
Here a=3c, [tex]b=d^2[/tex] and n=6,
Thus, [tex](3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r[/tex]
⇒ [tex](3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6[/tex]
⇒[tex](3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}[/tex]
⇒[tex](3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}[/tex]
⇒[tex](3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}[/tex]
Answer:
Option (a) is correct.
[tex](3c+d^2)^6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^{10}+d^{12}[/tex]
Step-by-step explanation:
Given : [tex]\left(3c+d^2\right)^6[/tex]
We have to expand the given expression and choose the correct from the given options.
Consider the given expression [tex]\left(3c+d^2\right)^6[/tex]
Using binomial theorem ,
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
We have [tex]a=3c,\:\:b=d^2[/tex]
[tex]=\sum _{i=0}^6\binom{6}{i}\left(3c\right)^{\left(6-i\right)}\left(d^2\right)^i[/tex]
also, [tex]\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}[/tex]
for i = 0 , we have,
[tex]\frac{6!}{0!\left(6-0\right)!}\left(3c\right)^6d^2^0=729c^6[/tex]
for i = 1 , we have,
[tex]\frac{6!}{1!\left(6-1\right)!}\left(3c\right)^5d^2^1=1458c^5d^2[/tex]
for i = 2 , we have,
[tex]\frac{6!}{2!\left(6-2\right)!}\left(3c\right)^4d^2^2=1215c^4d^4[/tex]
for i = 3 , we have,
[tex]\frac{6!}{3!\left(6-3\right)!}\left(3c\right)^3d^2^3=540c^3d^6[/tex]
for i = 4 , we have,
[tex]\frac{6!}{4!\left(6-4\right)!}\left(3c\right)^2d^2^4=135c^2d^8[/tex]
for i = 5 , we have,
[tex]\frac{6!}{4!\left(6-4\right)!}\left(3c\right)^2d^2^4=18cd^{10}[/tex]
for i = 6 , we have,
[tex]\frac{6!}{6!\left(6-6\right)!}\left(3c\right)^0d^2^6=d^{12}[/tex]
Thus, adding all term together, we have,
[tex](3c+d^2)^6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^{10}+d^{12}[/tex]
Thus, Option (a) is correct.
Donte simplified the expression below.
4(1 + 3i) – (8 – 5i) = –4 + 8i
What mistake did Donte make?
A.He did not apply the distributive property correctly for 4(1 + 3i).
B.He did not distribute the subtraction sign correctly for 8 – 5i.
C.He added the real number and coefficient of i in 4(1 + 3i).
D.He added the two complex numbers instead of subtracted.
Intr un oras sunt 235 de blocuri cu 8 etaje si cu 177 mai multe blocuri cu 4 etaje.Formuleaza intrebarea pentru a rezolva problema astfel
Which algebraic expression represents “the product of a number and five”?
Answer:
5n
Step-by-step explanation:
group of answer chances below
A. n - 5
B. 5n
C. 5 + n
D. 5/n
*Need Help??!!
Which table is a probability distribution table?
Photo is attached.
Answer: Hi!
in a probability table, the x represents a given event, and p is the probability of such event.
There are two rules if you have n events; then p₁ + p₂ + ... + pₙ = 1, this is because the probability is normalized.
whit this info you can discard the third option, because there is a probability bigger than 1, and then the addition of al the probabilities is bigger than 1.
The second rule is that there do not exist negative probabilities (because they don't have sense) then you can also discard the second option.
Now we need to check the first and the fourth options, we need to add the 4 probabilites in each and see if the result is 1.
for the first options we have :
0.2 + 0.35 + 0.15 + 0.25 = 0.95
this is not normalized, this is not a probability distribution table.
for the fourth option we have:
0.4 + 0.15 + 0.25 + 0.2 = 1
this is normalized, then this is a probability distribution table.
Then the only right answer is option 4.
What assumption must be made about the sun rays if you use this method of determining the circumference of a large sphere?
How old will Bill be in 10 years if he is x + 2 years old now?
Which expression represents this?
(x + 2) - 10
(x + 2) + 10
10(x + 2)
The probability that it will rain today is 0.4, and the
probability that it will rain tomorrow is 0.3. The
probability that it will rain both days is 0.2.
Determine the probability that it will rain today or
tomorrow
Final answer:
The probability that it will rain today or tomorrow, given the individual probabilities and the joint probability for both days, is calculated using the addition rule of probability, resulting in a probability of 0.5 or 50%.
Explanation:
The student is asking how to calculate the probability that it will rain today or tomorrow given the individual probabilities for rain on each day and the joint probability that it will rain on both days. This is a typical question involving the addition rule of probability.
To find the probability of either event A (rain today) or event B (rain tomorrow) occurring, we use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Where:
P(A) is the probability that it will rain today, which is 0.4,
P(B) is the probability that it will rain tomorrow, which is 0.3, and
P(A and B) is the probability that it will rain on both days, which is 0.2.
Substituting the given values, we get:
P(A or B) = 0.4 + 0.3 - 0.2
P(A or B) = 0.5
Therefore, the probability that it will rain today or tomorrow is 0.5, or 50%.
Simplify √24
A 3√8
B 2√12
C 2√6
D 4√6
Which ordered pairs are solutions to the inequality 2x + y > −4?
Select each correct answer.
A. (−3, 0)
B. (0, 1)
C. (−1, −1)
D. (5, −12)
E. (4, −12)
4. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What angle does each side form with the ground? (1 point)
156°
146°
73°
78°
True or False
5. All right triangles are isosceles. (1 point)
true
false
14. What does CPCTC represent and when would you use it? (4 points)
1) 2x + 35 = 180° so x= 180 - 35 / 2 =73°
the answer is 73°
2)
3) In geometry, "Corresponding parts of congruent triangles are congruent" (CPCTC) is a succinct statement of a theorem regarding congruent trigonometry, defined as triangles either of which is an isometry of the other. CPCTC states that if two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well. CPCTC is useful in proving various theorems about triangles and other polygons.
If triangles ABC and DEF are congruent, denoted as
Final answer:
Each congruent side of the A-frame house forms a 73° angle with the ground, and the statement that all right triangles are isosceles is false. CPCTC is a geometric theorem that states corresponding parts of congruent triangles are congruent.
Explanation:
Angles in an A-frame house
The given A-frame house forms an isosceles triangle with a peak angle of 34°. Using the theorem that the sum of angles in a triangle is 180°, we can calculate the angles each side forms with the ground. Since the two congruent sides are equal, the angles they form with the ground are also equal. There are two steps to solve this:
Subtract the peak angle from 180° to find the sum of the two base angles: 180° - 34° = 146°.
Divide the sum of the base angles by 2 (since they are equal in an isosceles triangle): 146° / 2 = 73°.
Therefore, each side forms a 73° angle with the ground.
All right triangles are isosceles - True or False?
This statement is false. Not all right triangles are isosceles. A right triangle is defined as having one 90° angle, but it doesn't necessarily have two sides of equal length, which would make it isosceles.
What does CPCTC represent?
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is a theorem used in geometry to conclude that the corresponding parts (angles or sides) of two triangles are congruent, given that the triangles themselves are proven to be congruent based on certain criteria like side-angle-side (SAS) or angle-side-angle (ASA).
Rewrite the expression below.
-2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8)
Final answer:
The simplified expression is [tex]-2a^2 + 4ab - 5a - 2b + b^2[/tex]
Explanation:
The expression -2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8) needs to be rewritten by expanding and combining like terms using the distributive property. To expand the expression, multiply each term inside the parentheses by the term outside the parentheses. Then, combine the like terms to simplify the expression.
Let's expand each term as follows:
-2a * a = -2a²
-2a * b = -2ab
-2a * (-5) = +10a
3 * (-5a) = -15a
3 * 2b = +6b
b * 6a = +6ab
b * b = b²
b * (-8) = -8b
Now, combine the like terms:
[tex]-2a^2 - 2ab + 10a - 15a + 6b + 6ab + b^2 - 8b[/tex]
The simplified expression is -
[tex]-2a^2 + 4ab - 5a - 2b + b^2[/tex]
Mike’s weekly wages are $685.20. What is the amount after a 4.2% Social Security tax and a 15% Federal Withholding income tax are deducted? Round to the nearest cent.
Answer:
553.64 rounded to the nearest cent
or
553.65
Step-by-step explanation:
What is √6/√5 in simplest radical form?
Hi i know this is late like by 2 years but for future people the answer is
[tex]\frac{\sqrt{30} }{\sqrt{5} }[/tex]
hope this helps other ppl
Identify the explanatory and response variables in the following situation:
There is a strong positive correlation between latitude above the equator and number of hours of daylight on June 21.
A. Explanatory: Latitude
Response: Average temperature
B. Explanatory: Daylight hours
Response: Latitude
C. Explanatory: Time of year
Response: Daylight hours
D. Explanatory: Latitude
Response: Daylight hours
What is the solution to the equation? 3q 5 = -2q 20
a. q = 3
b. q = 5
c. q = 15
d. q = 25
turn 4√5 into an entire radical (unsimplify), the process
To turn 4√5 into an entire radical, the expression is rewritten as a single radical expression, √80, by identifying that 4 is a perfect square (4²), and multiplying it by the number inside the original radical (5) to get the product under one radical sign.
To turn 4√5 into an entire radical, we need to rewrite it as a single radical expression, effectively reversing the process of simplifying radicals. Let's start by recognizing that 4 is a perfect square and can be written as 4². So, we have 4 (the square root of 5), which can be expressed as √(4² × 5).
Here are the steps to convert 4√5 into an entire radical:
Identify the square of the number outside the radical: 4² = 16.
Multiply the square by the number inside the radical: 16 × 5 = 80.
Write the product under a single radical sign: √80.
Now, the expression 4√5 has been turned into an entire radical, √80.
p=3h+3u solve for h
...?
p=3h + 3u subtract 3u from both sides
p-3u=3h now divide both sides by 3
h = p/3 - u
Katie cut out a rectangular piece of wrapping paper that was 2 times as long and 3 times as wide as the box that she was wrapping. the box was 5 inches long and 4 inch's wide. what is the perimeter of the wrapping paper that katie cut?
Solve –2x2 – 16x – 44 = 0
answer please using quadtratic equation ...?
Answer: x=-4 + or - i square root of 6
look for the horizontal asymptote of
(sin x)/(1 + cos x).
How many faces, edges, and vertices does a triangular pyramid have?
A. 3 faces, 4 edges, 4 vertices
B. 3 faces, 3 edges, 3 vertices
C. 4 faces, 6 edges, 3 vertices
D. 4 faces, 6 edges, 4 vertices
Complete these ordered pairs for this equation.
Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
What is the greatest number of bracelets she could buy?
Answer:
The answer is 63.
Step-by-step explanation:
50-12=38 38/.6 is equal to 63.333 you can't buy .333 of a bracelet so she will be able to buy 63 and have little money left.
The greatest number of bracelets she could buy will be 63.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given data;
The total amount of money in my wallet = $50.00
Cost of shirt = $12.00
Price of bracelet per piece = $0.60
Let x is the no of the bracelet;
The equation obtained as;
⇒The total amount of money in my wallet = Cost of the shirt + Price of the bracelet per piece × No of the bracelet
⇒50 = 12 + 0.60 x
⇒0.60 x = 50-12
⇒x = 38/0.60
⇒x= 63.333 ≈ 63 bracelet
Hence the greatest number of bracelets she could buy will be 63.
To learn more about inequility, refer to https://brainly.com/question/20383699.
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