Answers
9514 1404 393
Answer:
a=2√2+4b = 3Step-by-step explanation:
√24 = 2√6
√48 = 4√3
Then the sum is ...
√24 +√48 = 2√6 +4√3
Factoring out √3, we have ...
= (2√2 +4)√3
Matching this to the form a√b, we have
(2√2+4)√3 ⇒ a=2√2+4, b = 3
Related Questions
Simplify the expression: y9 * y-2
Answers
Answer:
[tex]y^7[/tex]
Step-by-step explanation:
If we want to simplify the expression [tex]y^9 \cdot y^{-2}[/tex], we have to note that exponent rules state that [tex]x^a \cdot x^b = x^{a+b}[/tex].
This means that if we add the exponents, that will be what we raise y to the power of.
[tex]9 + -2 = 9-2 = 7[/tex]
So [tex]y^7[/tex].
Hope this helped!
A sports stadium has 10000 seats, divided into box seats, lower-deck seats, and upper-devk seats. Box seats sell for 10 dollars, lower-deck seats sell for 8 dollars, and upper-deck seats sell for 5 dollars.If all the seats are sold, the total revenue for a game is 70000 dollars.The stadium has 4 times as many upper* deckseats as box seats.How many lower-deck seats are in the stadium?
Answers
Answer:
Number of box seats = 1000
Number of lower deck seats = 5000
Number of upper deck seats = 4000
Step-by-step explanation:
Let number of box seats = [tex]x[/tex]
Let number of lower deck seats = [tex]y[/tex]
Let number of upper deck seats = [tex]z[/tex]
As per question statement:
[tex]x+y+z=10000[/tex] ...... (1)
Cost for box seat = $10
Cost for [tex]x[/tex] box seats = 10[tex]x[/tex]
Cost for lower deck seat = $8
Cost for [tex]y[/tex] lower deck seats = 8[tex]y[/tex]
Cost for lower deck seat = $5
Cost for [tex]z[/tex] lower deck seats = 5[tex]z[/tex]
As per question statement:
[tex]10x+8y+5z=70000[/tex] ..... (2)
[tex]z = 4x[/tex] ..... (3)
Putting value of [tex]y[/tex] in (1) and (2):
[tex]x+y+4x=10000\\\Rightarrow 5x+y=10000[/tex] ....... (4)
[tex]10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)[/tex]
8 [tex]\times[/tex] (4) - (5):
[tex]10x =[/tex]10000
[tex]\Rightarrow x = 1000[/tex]
By (3):
[tex]z = 4000[/tex]
Now, by equation (1):
[tex]y[/tex] = 5000
Number of box seats = 1000
Number of lower deck seats = 5000
Number of upper deck seats = 4000
11. Through (-3,-5), perpendicular to -2x - 5y = -19
A. y=2/5x+2/5 B. y=3/5x-19/5 C. y=-5/2x+5/2 D. y=5/2x+5/2
12. Through (-8,1), parallel to -8x + 5y = 89
A. y=-8/5x-69/5 B. y=8/5x+69/5 C. y=8/5x-89/5 B. 5/8x-1/8
14. Through (-8,1), perpendicular to -5x + 9y = 49
A. y=-9/5x-67/5 B. y=-9/5x C. y=-5/9x-67 D.y=9/5x+67/5
Answers
Answer:
11) D. y=5/2x+5/2 , 12) B. y=8/5x+69/5, 14) A. y=-9/5x-67/5
Step-by-step explanation:
11) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:
[tex]y-y_{o} = m_{\perp}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of the given point, dimensionless.
[tex]m_{\perp}[/tex] - Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:
[tex]m_{\perp} = -\frac{1}{m}[/tex]
Where [tex]m[/tex] is the slope of the original line, dimensionless.
The original slope is determined from the explicitive form of the given line:
[tex]-2\cdot x - 5\cdot y = -19[/tex]
[tex]2\cdot x +5\cdot y = 19[/tex]
[tex]5\cdot y = 19 - 2\cdot x[/tex]
[tex]y = \frac{19}{5} -\frac{2}{5}\cdot x[/tex]
The original slope is [tex]-\frac{2}{5}[/tex], and the slope of the perpendicular line is:
[tex]m_{\perp} = -\frac{1}{\left(-\frac{2}{5}\right) }[/tex]
[tex]m_{\perp} = \frac{5}{2}[/tex]
If [tex]x_{o} = -3[/tex], [tex]y_{o} = -5[/tex] and [tex]m_{\perp} = \frac{5}{2}[/tex], then:
[tex]y-(-5) = \frac{5}{2}\cdot [x-(-3)][/tex]
[tex]y + 5 = \frac{5}{2}\cdot x +\frac{15}{2}[/tex]
[tex]y = \frac{5}{2}\cdot x +\frac{5}{2}[/tex]
The right answer is D.
12) The function of the parallel line can be found in terms of its slope and a given point by this formula:
[tex]y-y_{o} = m_{\parallel}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of the given point, dimensionless.
[tex]m_{\parallel}[/tex] - Slope, dimensionless.
Its slope is the slope of the given, which must be transformed into its explicitive form:
[tex]-8\cdot x + 5\cdot y = 89[/tex]
[tex]5\cdot y = 89 +8\cdot x[/tex]
[tex]y = \frac{89}{5}+\frac{8}{5} \cdot x[/tex]
The slope of the parallel line is [tex]\frac{8}{5}[/tex].
If [tex]x_{o} = -8[/tex], [tex]y_{o} = 1[/tex] and [tex]m_{\parallel} = \frac{8}{5}[/tex], then:
[tex]y-1 = \frac{8}{5}\cdot [x-(-8)][/tex]
[tex]y-1 = \frac{8}{5}\cdot x +\frac{64}{5}[/tex]
[tex]y = \frac{8}{5}\cdot x +\frac{69}{5}[/tex]
The correct answer is B.
14) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:
[tex]y-y_{o} = m_{\perp}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of the given point, dimensionless.
[tex]m_{\perp}[/tex] - Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:
[tex]m_{\perp} = -\frac{1}{m}[/tex]
Where [tex]m[/tex] is the slope of the original line, dimensionless.
The original slope is determined from the explicitive form of the given line:
[tex]-5\cdot x +9\cdot y = 49[/tex]
[tex]9\cdot y = 49+5\cdot x[/tex]
[tex]y = \frac{49}{9} +\frac{5}{9}\cdot x[/tex]
The original slope is [tex]\frac{5}{9}[/tex], and the slope of the perpendicular line is:
[tex]m_{\perp} = -\frac{1}{m}[/tex]
[tex]m_{\perp} = -\frac{1}{\frac{5}{9} }[/tex]
[tex]m_{\perp} = -\frac{9}{5}[/tex]
If [tex]x_{o} = -8[/tex], [tex]y_{o} = 1[/tex] and [tex]m_{\perp} = -\frac{9}{5}[/tex], then:
[tex]y-1 = -\frac{9}{5}\cdot [x-(-8)][/tex]
[tex]y-1 = -\frac{9}{5}\cdot x-\frac{72}{5}[/tex]
[tex]y = -\frac{9}{5}\cdot x -\frac{67}{5}[/tex]
The correct answer is A.
this is the second question I don't undrstand
Answers
Answer:
[tex]d=\sqrt{58}[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in your coordinates into the distance formula to find the length of AB:
[tex]d=\sqrt{(9-2)^2+(4-1)^2}[/tex]
[tex]d=\sqrt{(7)^2+(3)^2}[/tex]
[tex]d=\sqrt{49+9}[/tex]
[tex]d=\sqrt{58}[/tex]
/58
I’m not sure I’m just a high schooler sooo I hope it helps
whats bigger 0.32 or 1/4??
Answers
Answer:
0.32 is bigger
Step-by-step explanation:
change 1/4 to decimal
can I get brainliest
Answer:
0.32
Step-by-step explanation:
Its bigger because if you turn 1/4 into a fraction it's 0.25
what 5 times a number b is
Answers
Answer:
2.5 x 2 = 5 Hope That Is What Your Looking For
Answer:
5b
Step-by-step explanation:
5 times number b is 5 * b.
In math, we can shorten the writing of a multiplication by a variable by not writing the multiplication sign.
5b means 5 * b
Answer: 5b
Write an equation to represent each situation. a) Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95. b) Blueberries are $4.99 a pound. Jada buys p pounds of blueberries and pays c dollars. c) Blueberries are d dollars a pound. Lin buys q pounds of blueberries and pays t dollars.
Answers
Answer:
A) $4.99b = $14.95
B) $4.99p = $c
C) $qd = $t
Step-by-step explanation:
A) We are told that cost of blueberries is $4.99 a pound.
Now, Diego buys b pounds of blueberries and pays $14.95.
Since 1 pound costs $4.99, then b pounds will cost $4.99b
Since he paid $14.95, then the equation is;
$4.99b = $14.95
B) We are told that cost of blueberries is $4.99 a pound.
Now, Jada buys p pounds of blueberries and pays $c.
Since 1 pound costs $4.99, then p pounds will cost $4.99p
Since he paid $c, then the equation is;
$4.99p = $c
C) We are told that cost of blueberries is $d a pound.
Now, Lin buys q pounds of blueberries and pays $t.
Since 1 pound costs $d, then q pounds will cost $qd
Since he paid $t, then the equation is;
$qd = $t
Someone help please! I really need to finish this today.
Answers
Answer:
m∠E = 43°Step-by-step explanation:
AB║CD ⇒ m∠AGH = m∠CHF = 119° {corresponding angles}
m∠BGE = m∠AGH = 119° {vertical angles}
m∠BGE + m∠B + m∠E = 180° {sum of angles in triangle}
119° + 18° + m∠E = 180°
m∠E = 180° - 137° = 43°
Connor bought a baseball card eight years ago that has depreciated by $120 since he purchased it. Find the average yearly change in value of the card.
Answers
Answer:
The average yearly change in the value of the card is $15/year
Step-by-step explanation:
Here in this question, we are interested in calculating the average yearly change in the value of the card.
From the question, we can see that the value of the baseball card has depreciated by $120, thus we simply want to calculate the average yearly charge in the card value.
Mathematically, that would be ;
the total depreciation value/ number of years
From the question, the total depreciation value is $120 while the number of years is 8
Thus; the average yearly change in value of the card = 120/8 = $15/year
find the light of the third side
Answers
Answer:
I'm not sure if this is what your looking for but the answer should be √11
Step-by-step explanation:
its in the picture....
please do give me brainliest if i was able to help you.
thank you and have a good day
Which expressions are equivalent to 4(4a + 5) ? 3 answers
Answers
Answer:
16a+20
Step-by-step explanation:
4(4a+5) -----Distributive property
16a+20
Hope this helps ;) ❤❤❤
Use inductive reasoning to determine the next three terms in the sequence. 3, -6, 12, -24, 48,
Answers
Answer:
The next three terms in this sequence will be, -96, 192, and -384.
Hope this helped have a blessed day
Step-by-step explanation:
A farmland is 30cm long and 15cm wild what is the area of the farmland
Answers
Step-by-step explanation:
length(l)= 30cm
Breadth(b)=15cm
Area=l×b
=30×15
=450cm^2
it is 30 then 15 cm long its mean 45 answer
How do I solve equations bt extracting square roots?
Ex.
[tex]3(x + {4)}^{2} = 8[/tex]
Answers
Answer:
[tex]x=\frac{2\sqrt{6}}{3}-4,\:x=-\frac{2\sqrt{6}}{3}-4[/tex]
Step-by-step explanation:
[tex]3(x+4)^2 =8\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3\left(x+4\right)^2}{3}=\frac{8}{3}\\\\Simplify\\\left(x+4\right)^2=\frac{8}{3}\\\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}\\g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\mathrm{Solve\:}\:x+4=\sqrt{\frac{8}{3}}:\\\quad x=\frac{2\sqrt{6}}{3}-4\\\\\\\mathrm{Solve\:}\:x+4=-\sqrt{\frac{8}{3}}:\\\quad x=-\frac{2\sqrt{6}}{3}-4\\[/tex]
[tex]x=\frac{2\sqrt{6}}{3}-4,\:x=-\frac{2\sqrt{6}}{3}-4[/tex]
In 3x² - x + 5 = 0, what is the quadratic term
Answers
Step-by-step explanation:
Quadratic term = Coefficient of x^2 term = 3.
Find all possible values of the expression 1/y if: .125
Answers
Answer:
The possible values for 1/y of the expression 0.125 < y < 0.25 are in the range
4 < 1/y < 8
Step-by-step explanation:
The given information are;
The range of values of y are 0.125 < y < 0.25, therefore, we have;
The boundaries of the function, y are 0.125 and 0.25
The inverse of the boundaries of the function, y are 1/0.125 = 8 and 1/0.24 = 4
Therefore;
The limits of the inverse of the function y are ;
The inequality that represents 1/y is therefore;
1/0.25 < 1/y < 1/0.125 or 4 < 1/y < 8
The possible values of 1/y for the expression 0.125 < y < 0.25 are therefore;
4 < 1/y < 8.
What’s the 10th term in 1,4,6,10
Answers
Answer:
Step-by-step explanation:
Feb 8, 2017 - an=12n(n+1). Explanation: These are recognisable as triangular numbers, but let's use a general method for finding matching polynomial ...
1 answer
Changes to the cities and the environment:
1) List some ways in which the Tokugawa Shogunate strengthened Japan's economy.
2) How did rice production change?
3) Why were more roads required around Edo as the city grew?
4) Why was timber such an important resource in medieval Japan?
5) Describe the environmental policies introduced to protect forests and change the way timber was harvested.
6) Write a paragraph to explain, in broad terms, the impact that the Tokugawa shogunate had on Japan.
Answers
Answer:
Sorry i don't really know all of the question but I hope the ones I know help.
Step-by-step explanation:
The second questions answers is:
The most significant change in rice production technologies started from 2000 to 2013 and it was the introduction and adoption of new rice seed varieties. Southern rice producers increased it by planting Hybrid and non-genetically modified herbicide.
The third questions answer;
more roads were required cause Edo grew into a huge city with a lot of buildings and they needed road.
The fourth question answer; timber was important cause it was used to supply construction needed for the growing of population in the peaceful time. some places like the Shogun Leyasu and many of the Daimyo started building huge castles and templates to show their power to each other.
what is 36-(-30)-60+6
Answers
Answer
The answer is 0
What is the length of NO?
N= (7,-4)
O=(-7,-4)
Answers
Answer:
I believe it would be 14.
Step-by-step explanation:
The distance between 7 and -7 should be 14.
The length of NO is 14 units
What is the length of NO?Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the length is given by:
d =√((x2 – x1)² + (y2 – y1)²)
We:
N= (7,-4) : x1 = 7 , y1 = -4
O = (-7,-4): x2 = -7 , y2 = -4
Using the formula with the given values:
d=√((-7 – 7)² + (-4 – (-4))²)
d=√((-14 )² + (0)²)
d=√196
d= 14
Therefore, the length of NO is 14 units
Learn more about the distance between two points on:
brainly.com/question/17704491
#SPJ6
solve a/3 + 4 = 6
a=
Answers
Answer:
a = 6
Step-by-step explanation:
Given
[tex]\frac{a}{3}[/tex] + 4 = 6 ( subtract 4 from both sides )
[tex]\frac{a}{3}[/tex] = 2 ( multiply both sides by 3 to clear the fraction )
a = 6
Answer:
a=6
Step-by-step explanation:
a/3=6-4
a/3=2
a=6
Find the measures of the angles of a triangle if the measure of one angle is three times the measure of a second angle and the third angle measures 3 times the second angle decreased by 30.
Answers
Answer:
90°,30°,60°
Step-by-step explanation:
hope it helps
A number is five less than one fourth of itself
Answers
Answer:
x = 1/4x - 5
Step-by-step explanation:
Step 1: Translate from word to math
A number = x
five less = -5
one-fourth = 1/4
of itself = x
Step 2: Combine
x = 1/4x - 5
Solve for x
x to the power of 2 = 1/4
Answers
Please explain also
Answers
Answer:
300 m^2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask =)
what is 1/8 plus 4/5
Answers
=1/8+4/5= 5+32/40
=37/40
help to! this is also due today !
Answers
Answer:
9.
Step-by-step explanation:
The square root of 81 is 9 so therefore the answer is 9.
k (n) = 4n – 4; Find k (8)
28
4
-32
-24
The answer
Answers
Answer:
Step-by-step explanation:
k(8) = 4(8) - 4
= 32 - 4
= 28
answer is A
A triangle has side lengths of (6.4c-2.5)(6.4c−2.5) centimeters, (8.7c-7.8)(8.7c−7.8) centimeters, and (6.4d-1.2)(6.4d−1.2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answers
Answer:
15.1c + 6.4d - 11.5
Step-by-step explanation:
Given the following :
Lengths of the side of a triangle :
(6.4c-2.5) centimeters
(8.7c-7.8) centimeters
(6.4d-1.2) centimeters
Assume the sides Given are labeled A, B and C respectively,
The perimeter of a triangle is related vyvtge formula :
Perimeter = (A + B + C)
Perimeter = (6.4c - 2.5) + (8.7c - 7.8) + (6.4d - 1.2)
= (6.4c - 2.5) + (8.7c - 7.8) + (6.4d - 1.2)
= 6.4c - 2.5 + 8.7c - 7.8 + 6.4d - 1.2
= 6.4c + 8.7c + 6.4d - 2.5 - 7.8 - 1.2
= 15.1c + 6.4d - 11.5
The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d?
Answers
Answer:
9km
Step-by-step explanation:
If the distance on the map of 8cm between her house and school is equal to 12km actual distance. This means that each cm on the map represent 1.5km in actual distance (12/8=1.5).
This means that D is equal to 9km actual distance, because if each cm represents 1.5km, then 6 cm represents 9km (6x1.5=9).
Hope this helped!
Answer:
B
Step-by-step explanation:
9 km