Decide which of the following is a reasonable answer for
Answer:
[tex]9 \frac{4}{5} [/tex]
Step-by-step explanation:
[tex] \frac{7}{5} \times 7 = \frac{7}{5} \times \frac{7}{1} [/tex]
[tex] \frac{7}{5} \times \frac{7}{1} = \frac{49}{5} = 9 \frac{4}{5} [/tex]
Factorisation of 3p^3 + 9p^2- 15pq
Answer:
STEP 1:Equation at the end of step 1 ((3 • (p3)) + 32p2) - 210p
STEP 2 :Equation at the end of step 2: (3p3 + 32p2) - 210p
STEP 3:STEP 4:
Pulling out like terms 4.1 Pull out like factors : 3p3 + 9p2 - 210p = 3p • (p2 + 3p - 70)
Trying to factor by splitting the middle term 4.2 Factoring p2 + 3p - 70 The first term is, p2 its coefficient is 1 .The middle term is, +3p its coefficient is 3 .The last term, "the constant", is -70 Step-1 : Multiply the coefficient of the first term by the constant 1 • -70 = -70 Step-2 : Find two factors of -70 whose sum equals the coefficient of the middle term,
which is 3 . -70 + 1 = -69 -35 + 2 = -33 -14 + 5 = -9 -10 + 7 = -3 -7 + 10 = 3 That's itStep-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 10 p2 - 7p + 10p - 70
Step-4 : Add up the first 2 terms, pulling out like factors : p • (p-7) Add up the last 2 terms, pulling out common factors : 10 • (p-7)Step-5 : Add up the four terms of step 4 : (p+10) • (p-7) Which is the desired factorization
Final result : 3p • (p + 10) • (p - 7)
Step-by-step explanation:
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The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of x such that the sum of numbers of houses preceding the house numbered x is equal to sum of the number of houses following x.
Don't Spam
Answer:
Number of the houses as x =35
Step-by-step explanation:
The number of houses is 1, 2, 3, ..., 49
By observation, the numbers of houses are in an A.P.
Hence
First-term, a = 1
Common difference, d = 1
Let us assume that the number of xth house can be expressed as below:
We know that sum of n terms in an A.P. is given by the formula Sₙ = n/2 [2a + (n - 1) d]
Sum of number of houses preceding xth house = Sₓ ₋ ₁
Sₓ ₋ ₁ = (x - 1) / 2 [2a + ((x - 1) - 1)d]
= (x - 1) / 2 [2 × 1 + ( x - 2) × 1]
= (x - 1) / 2 [2 + x - 2]
= [x (x - 1)] / 2 ---------- (1)
By the given information we know that, sum of number of houses following xth house = S₄₉ - Sₓ
S₄₉ - Sₓ = 49 / 2 [2 × 1 + (49 - 1) × 1] - x / 2 [2 × 1 + (x - 1) × 1]
= 49 / 2 [2 + 48] - x / 2 (2 + x - 1)
= (49 / 2) × 50 - (x / 2) (x + 1)
= 1225 - [x (x + 1)] / 2 ---------- (2)
It is given that these sums are equal, that is equation (1) = equation(2)
x (x - 1) / 2 = 1225 - x (x + 1) / 2
x² / 2 - x / 2 = 1225 - x² / 2 - x / 2
On solving further we get,
x² = 1225
x = ± 35
As the number of houses cannot be a negative number, we consider the number of houses as x = 35
35 is the correct answer
Step-by-step explanation:
Given that the houses in a row are numbered consecutively from 1 to 49. We need to show that there exists a value of x such that the sum of numbers of houses preceding the house numbered x is equal to sum of the number of houses following x. Making it more simple for you; sum of (1, 2, 3, 4.... upto x - 1) is equal to sum of (x + 1), (x + 2), (x + 3).... upto 49.
→ Sum of (x - 1) terms = Sum of (49 - x) terms
"x" is the number of houses required. The sum of houses are in AP where the value of a is 1 and d is also 1; where 'a' is first term and 'd' is common difference. We know that sum of nth term of an AP is given by: T(n) = a + (n - 1)d and upto nth term by S(n) = n/2 (2a + (n - 1)d). And also by T(n) = S(n) - S(n - 1).
As per given problem:
→ (x - 1)/2 (Sum of first and last term) = (49 - x)/2 (Sum of first and last term)
→ (x - 1)(Sum of first and last term) = (49 - x) (Sum of first and last term)
Where first term and last term in LHS is 1 and (x - 1) & in RHS is (x + 1) and 49. Substitute them.
→ (x - 1) (1 + (x - 1)) = (49 - x) ((x + 1) + 49)
→ (x - 1) (1 + x - 1) = (49 - x) (x + 1 + 49)
→ (x - 1) (x) = (49 - x) (x + 50)
→ x² - x = 49x + 2450 - x² - 50x
On solving we get,
→ 2x² - 2450 = 0
→ 2x² = 2450
→ x² = 1225
→ x = ± 35
The number of houses is a positive integer. So negative value neglected. We left with x = 35. Therefore, the value of x is 35.
The circumference of the Earth model at the Globe Arena is 56.52 centimeters. What is
the volume of the Earth model?
A. 9156.24 cubic cm
B. 339.12 cubic cm
C. 3052.08 cubic cm
D. 1017.36 cubic cm
Answer:
3052 cm^3 (Answer C)
Step-by-step explanation:
The formula for the circumference of a circle of radius r is C = 2(pi)(r). We know that C = 56.52 cm and want to find the model's radius:
C 56.52 cm
Solving for r, we get ---------- so that in this case r = ------------------ or
2(pi) 6.28
r = 9 cm.
The formula for the volume of a sphere of radius r is V = (4/3)(pi)(r^3), which here comes out to:
V = (4/3)(3.14)(9 cm)^3 = 3052 cm^3 (Answer C)
Elise paid 2/3 as much for a sweater as she did for a pair of shoes. How much did elise pay for the sweater if the shoes cost each given amount?Shoes Cost $60: Sweater cost $20,$40,$90
Work Shown:
(2/3)*60 = (2*60)/3 = 120/3 = 40
Notice how 40/60 = 2/3
William has scored a total of 235 points on the first three math tests taken in his mathematics class. If his mathematics test are always worth 100 points, how many points must he earn on his next test in order to have an average of 80%
Answer:
85 points
Step-by-step explanation:
His total points will be 235+x
Number of tests will be 4
(235+x)/4 = 80
multiply by 4
235+x= 4*80
235+x= 320
x=320-235
x= 85
He has to get 85 points to average 80
The total length of a road trip was 13.2 hours. If highway signs are posted every 0.6 hours, including one at the end of the road trip, how many highway signs will there be on the road trip? HELP
Answer:
22
Step-by-step explanation:
Formula : total divide by every hour
13.2/0.6 = 22
Thus, There will be 22 highways sign on the road trip.
[RevyBreeze]
21 – 3x = 6
3
21 – 3(
x
) = 6?
-3x
= 6?
Answer:
x = 5
Step-by-step explanation:
21 - 3x = 6
21 - 6 = 3x
15 = 3x
5 = x
therefore x=5
Mrs. Feiner gets 80% right on a quiz with 20 questions.
How many questions does she get right?
A. 15
B. 16
c. 18
D.19
16 answer correct
80×20
_______. =16
100
Brainliest
y^2-4xy-7y+28x please send the answer asap
Answer:
= (y - 4x) (y - 7)
Step-by-step explanation:
y^2-4xy-7y+28x
--
factor out y from y^2 - 4x : y(y - 4x)
factor out 7 from 28x - 7y : 7(4x - y)
= y (y - 4x) + 7(4x - y)
7 (4x - y) + 7(y - 4x)
= y (y - 4x) - 7(y - 4x)
= (y - 4x) (y - 7)
im back fellow humans..pls help
Answer:
-2, -10, and -3
Step-by-step explanation:
-2, -10, and -3 are all colder than -1.
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!!!
Answer:
a , d , e
Step-by-step explanation:
Tommy has 5 jars of marble. Each Jar is filled 2/3 with marbles. How many full Jars does tommy have? Make a model and shade in the model and complete the calculation.
Calculation: 5x 2/3= Blank/3 =______
5 / ( 2 / 3 ) = 7.5
7 full jars
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x=45
Step-by-step explanation:
A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles. Four marbles are chosen
without replacement. What is the probability that they are all white?
Answer:
10.6 all white marbles
Step-by-step explanation:
Submitted to you
At a shelter 15% of the dogs are puppies there are 60 dogs at the shelter. How many are puppies?
Explanation:
One method is to do the steps like this
15% of 60 = 0.15*60 = 9
Or you can solve like this
part/whole = percent/100
x/60 = 15/100
100x = 60*15
100x = 900
x = 900/100
x = 9
The radius of a circle is 16 millimeters. What is the circle's area?
Use 3.14 for .
please answer windowesssssssssssssss
Answer:
803.84 millimeters²
Step-by-step explanation:
How do we find the area of a circle?
The area of a circle is πr², where r = radius. In this case, we have to approximate pi to 3.14.Solving
[tex]3.14 *16^2[/tex] [tex]3.14*256[/tex] [tex]803.84[/tex]Therefore, the area is 803.84 square millimeters.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Solution:
We know that:
Radius = r = 16 mmArea of circle = (π)(r²)Finding the area of the circle:
Area of circle = (3.14)(16²)=> Area of circle = 3.14 x 16²=> Area of circle = 3.14 x 256=> Area of circle = 803.84 mm²Find the measure of the missing angles .
Answer:
x = 29°, y = 61°
Step-by-step explanation:
x + 61 = 90
Because of the right angle symbol
x = 90 - 61
x = 29°
x + y = 90
Because vertically opposite angles are equal
29 + y = 90
y = 90 - 29
y = 61°
the equation y = x + 8 represents the length, y, in inches of a sleeping bag for a person who is x inches tall. which ordered pair does not belong on the graph?
Answer:
i dont know can u help me
Step-by-step explanation:
An 8 inch by 12 inch sheet of cardboard has squares
cut out of the corners. What should the side length of
the squares be to maximize the volume?
Answer:
96
Step-by-step explanation:
Daina gives 2/3 of his money to Carol. Carol gives 6/7 of this money to Zak.
What fraction of Daina's money does Zak get?
what is the answer to 3 divided by 4/5
Answer:
3/ 4/5=3.75
Step-by-step explanation:
3/ 4/5
3/ 0.80
= 3.75
I TRIED TO MAKE IT AS EASY AS POSSIBLE!
PLS MARK AS BRAINLIEST!
Rewrite each algebraic expression with as few terms as possible using the Commutative and Associative Properties. (2x - 2y) + (5x + 7y)
Answer:
probably 7x + 5y
Step-by-step explanation:
Answer: 7x + 5y
Step-by-step explanation: You combine the like terms so you would add 2x and 5x to get 7x-2+7y. Then you combine the other like terms so subtract -2y and 7y (You are subtracting because a negative and a positive is a negative).
I hope this helps :)
Please help me I need help
Will mark BRAINLIEST
2. Given A=15°, b=8, and a=6, use the Law of Sines to solve the triangle (if possible)
for the value of c. If two solutions exist, find both. Round answer to two decimal places.
A) c=11.01
B) c=2.10 and 13.36
C) c=12.14
D= c=1.12 and 10.24
E) not possible
Answer:
B
Step-by-step explanation:
The Law of Sines states that
sinA/a = sinB/b = sinC/c
We know A, a, and b. Given this, we can solve for B, and given that, we can solve for C and then c.
First, we solve for B.
sinA/a = sinB/b
sin(15°)/6 = sinB/8
sin(15°)/6 * 8 = sinB
arcsin(sin(15°)/6 * 8) = B ≈ 20.187
Note that there can be a second B value. We can check if there is a second B value by first subtracting the B value we got from 180.
180 - 20.187 = 159.813
Next, we can add that to our existing angle, A = 15°. If that is less than 180, then we do have a second solution. 159.813 + 15 = 174.813 < 180 so there does exist a second solution where B = 159.813
Next, we can solve for C.
We know that the angles in a triangle add to 180°, so A + B + C = 180. Therefore, for the first solution:
15 + 20.187 + C = 180
C = 180 - 15 - 20.187 = 144.813°
and for the second:
15 + 159.813 + C = 180
C = 180 - 15 - 159.813 = 5.187
Finally,
sinA/a = sinC/c
multiply both sides by c to no longer have it as a denominator
sinA * c / a = sinC
divide both sides by (sinA/a) to isolate c
for the first solution:
c = sinC*a/sinA = 13.35868 ≈ 13.36
and for the second:
c = sinC*a/sinA ≈ 2.10
Bill is filling a box up with bottle caps. The box is 1 1/2 feet long, 15 inches wide, and 9 inches high. What is the volume of the box in cubic inches
11/2 so 15 inches high cubic box will get more high I guess
The shaded part of the circle below represents the portion of a garden where a landscaper planted rose bushes. What is the approximate area of the part of the garden used for rose bushes?
Answer:
942ft^2
Step-by-step explanation:
Use the equation (θ/360)*[tex]\pi[/tex][tex]r^{2}[/tex] to get the area of the shaded sector.
(120/360)*[tex]\pi[/tex]*[tex]30^{2}[/tex]
(1/3)*[tex]\pi[/tex]*900
≈942[tex]ft^{2}[/tex]
The area of the shaded region is 942 square ft if the radius of the circle is 30 ft option (G) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a circle shown in the picture.
The area of the shaded region:
[tex]\rm A = \dfrac{120}{360}\pi (30)^2[/tex]
A = 942.47 ≈ 942 square ft
Thus, the area of the shaded region is 942 square ft if the radius of the circle is 30 ft option (G) is correct.
Learn more about circle here:
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NEED HELP ASAP EASY 10 POINTS
Answer:
2x+3
Step-by-step explanation:
factor into [tex](2x+3)^{2}[/tex]
then square root it [tex]\sqrt{(2x+3)^{2} }[/tex]
We know that,
[tex]{ \longrightarrow \bf \qquad \: {(a + b)}^{2} = {a}^{2} + 2.a.b + {b}^{2} }[/tex]
Solution :
[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + 9 }[/tex]
We can also write it as,
[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + {3}^{2} }[/tex]
Now, using the formula, we'll solve the expression.
[tex]{ \longrightarrow \sf \qquad \: {2x}^{2} + 2.2x.3 + {3}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad \: (2x + 3)^{2} }[/tex]
Since,
Area = (side)²Therefore,
The Length of one side is (2x + 3) .100 POINTS!!!!! AND BRAINLIEST!!!!!!
Instructions: Find the equation of the line through point (1,5) and perpendicular to x+3y=6. Use a slash ("/") for fractions (e.g. 1/2 for 12). DO not include spaces in your answers.
Y=_______
1. Turn x+3y=6 into slope intercept form:
3y = 6 - x
y = 2 - 1/3x
2. The perpendicular slope is always the negative reciprocal.
-1/3 becomes 3/1
3. Find the intercept
5 = (3/1)1 +b
b = 2
Answer: y = 3x + 2, or y = 3/1x + 2
What is the product? startfraction 4 n over 4 n minus 4 endfraction times startfraction n minus 1 over n 1 endfraction startfraction 4 n over n 1 endfraction startfraction n over n 1 endfraction startfraction 1 over n 1 endfraction startfraction 4 over n 1 endfraction
The product of the two terms [tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex] is [tex]\dfrac{n}{(n+1)}[/tex].
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.
The product of the two fractions can be written as,
[tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex]
Taking 4 as the common term from both numerator and denominator of the first fraction, therefore,
[tex]\dfrac{4n}{4(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\=\dfrac{n}{(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\[/tex]
Now, cancelling the common factor from the numerator and the denominator, we will get,
[tex]=\dfrac{n}{(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\\\=\dfrac{n}{(n+1)}[/tex]
Hence, the product of the two terms [tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex] is [tex]\dfrac{n}{(n+1)}[/tex].
Learn more about Fraction:
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Find the error in this and then solve it correctly
Answer: m<D = 30
Step-by-step explanation: In the third step of the problem, it says that E is next to itself and equals 90. However, this is not true. Angle BEA and angle CED are vertical angles and are both equal to 65°. This means that to find the measurement of angle D, subtract 65 and 85 from 180, which equals 30.