[tex]\left(\sqrt x - \sqrt{3y} \right) \left(\sqrt x + \sqrt{3y} \right)\\\\=\left(\sqrt x\right)^2 - \left(\sqrt{3y} \right)^2\\\\=x -3y[/tex]
x - 3y
Solving Stepwise:
[tex]\hookrightarrow \sf \left(\sqrt{x}-\sqrt{3y}\right)\left(\sqrt{x}+\sqrt{3y}\right)[/tex]
[tex]\sf apply \ the \ rule : \bold{\left(a-b\right)\left(a+b\right)=a^2-b^2}[/tex][tex]\hookrightarrow \sf \left(\sqrt{x}\right)^2-\left(\sqrt{3y}\right)^2[/tex]
[tex]\hookrightarrow \sf x-3y[/tex]
For triangle xyz , the measures of angles x,y, and Z are known. Which method should be used to start solving triangle xyz?
law of sines
law of cosines
neither law can be used
both laws can be used
Answer:
neither law can be used
Step-by-step explanation:
to solve the given triangle the given measurements are not enough (one more value should be known).
In order for the data in the table to represent a linear function with a rate of change of 5, what must be the value of a? a = 3 a = 8 a = 18 a = 33
To represent the linear function in order for the data the value of a=18.
What is a linear function?
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
It is given that for a linear function the value is changing at the rate of 5 so we can see in the table as the function independent value is changing then the value of the dependent linear function increases by 5.
So the value of a will be equal to 18.To represent the linear function in order for the data the value of a=18.
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re for Question 1: of 5 points)
Sandy has a ladder that is 16.5 ft long. He wants to lean the ladder against a vertical wall so that the top
the ladder is 15.9 ft above the ground. For safety reasons, he wants the angle the ladder makes with th
ground to be no greater than 76°. Will the ladder be safe at this height? Show your work and draw a diagram
to support your answer.
The ladder will be safe at this height .
What is trigonometric ratios?There are six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
According to question
Sandy has a ladder whose length = 16.5 feet
He wants to lean the ladder against a vertical wall 15.9 feet above the ground.
And he wants the angle the ladder makes with the
ground to be < 76°.
As Perpendicular = 15.9 feet
and Hypotenuse = 16.5
Sin Ф = [tex]\frac{Perpendicular }{Hypotenuse}[/tex]
Sin Ф = [tex]\frac{15.9}{16.5}[/tex]
Sin Ф = 0.9636
Therefore, Ф ≈ 74.49 (approx.)
That means it is safe .
Hence, The ladder will be safe at this height as it is not greater than 76° .
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# SPJ2
Which expression represents a number that is 4 times as great as the quotient of 25 and 5?
A. (25 x 5) x 4
B. 4 ÷ ( 25 ÷ 5 )
C. 4 x ( 25 ÷ 5 )
D. (25 ÷ 5 ) ÷ 4
Answer:
(25 ÷ 5 ) ÷ 4
Step-by-step explanation:
solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.
Answer:
C
Step-by-step explanation:
the quotient of 25 and 5 is 25 ÷ 4 , then multiply this by 4 , so
4 × (25 ÷ 5 ) → C
In how many ways can 6 students be seated in a row of 6 seats if 2 of the students insist on sitting beside each other?
Using the arrangements formula, it is found that there are 240 ways for the students to sit.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex].
In this problem:
The 2 students can sit in 2! ways, in 5 positions(1 and 2, 2 and 3, 3 and 4, 4 and 5 or 5 and 6).The remaining 4 students can sit in 4! ways.Hence:
T = 5 x 2! x 4! = 240.
There are 240 ways for the students to sit.
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You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually. determine the amount needed in the account such that you can withdraw the needed amount at the end of each period for 15 years. round to the nearest cent. a. $239,364.66 b. $182,713.25 c. $184,311.99 d. $237,288.39
The amount needed in the account is 182,713.25 dollars then the correct option is B.
What is a monthly payment?The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.
Then the formula of monthly payment (MP) will be
[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]
The formula can be written as
[tex]\rm P = MP \times \dfrac{(1+r)^n-1}{r(1+r)^n}\\[/tex]
You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually.
The amount needed in the account is such that you can withdraw the needed amount at the end of each period for 15 years will be
MP = $6951.20
r = 0.00875
n = 30
Then we have
[tex]\rm P = 6951.20 \times \dfrac{(1+0.00875)^{30}-1}{0.00875(1+0.00875)^{30}}\\\\P = \$182713.25[/tex]
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Find the perimeter of the rectangle
Answer:
Step-by-step explanation:
perimeter = 2 (l + b)
= 2 {(2/3x+ 10) + (1/3x + 5)}
= (4/3x + 10) + (2/3 + 10)
= 4/3x + 20 +2/3 + 10
= 6/3x + 30
= 3x + 30
Which system of equations can be used to find the roots of the equation 4 x squared = x cubed 2 x? startlayout enlarged left-brace 1st row y = negative 4 x squared 2nd row y = x cubed 2 x endlayout startlayout enlarged left-brace 1st row y = x cubed 4 x squared 2 x 2nd row y = 0 endlayout startlayout enlarged left-brace 1st row y = 4 x squared 2nd row y = negative x cubed minus 2 x endlayout startlayout enlarged left-brace 1st row 4 x squared 2nd row y = x cubed 2 x endlayout
The system of equations can be used to find the roots of the considered equation is y = 4+x^2 and y= x^3 + 2 + x
How can we find the solution to an equation?We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.
For the given case, we are given with the equation [tex]4+x^2 = x^3 + 2 + x[/tex]
We can take two equations as:
[tex]y = 4+x^2 \\y= x^3 + 2 + x[/tex]
And when we will try to solve this system of equation, we will end up substituting the value of y in terms of x, and therefore, ending up on the same equation [tex]4+x^2 = x^3 + 2 + x[/tex]
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Answer:
D
y=4x^2
y=x^3+2x
Step-by-step explanation:
im trying to pass just like yall, Good luck to all
The scientist had a 35% saline solution that he mixed with 10 milliliters of a 75% saline solution to get a 40% saline solution. How many milliliters of the 35% solution were used?
x mL of the 35% saline solution contains 0.35x mL of salt.
10 mL of the 75% solution contains 0.75 • 10 mL = 7.5 mL of salt.
After mixing, the scientist would have a total volume of (x + 10) mL. We know its concentration is 40%, so it contains 0.40 (x + 10) mL of salt.
The total amount of salt before and after mixing must be the same, so
0.35x + 7.5 = 0.40 (x + 10)
Solve for x :
0.35x + 7.5 = 0.40x + 4.0
0.10x = 3.5
x = 35
The scientist used 35 mL of the 35% solution.
can anyone help me answer this
Answer:
Step-by-step explanation:
4(4/3) DIVIDED INTO 2(2/3) (mixed numbers)
16/3 DIVIDED INTO 8/3
16/8=2
16/3 divided into 8/3
is the same as
16/3 multiplied be 3/8
48/24 =2
Graph the points K(-2, -1), L(-1, 2), M(2, 4), and N(1,1) in desmos geometry. What is the distance from point M to point N?
options:
4
√10
3
√8
Quadrilateral KLMN has vertices K(-2,-2), L(1,1), M(0,4), and N(-3,5)
It is first translated by (x + 2,y - 1)
then
K(-2,-2) ---> K'(-2 + 2,-2 - 1) = (0,-3)
L(1,1), ---> L'(1 + 2,1 - 1) = (3,0)
M(0,4), ---> M' (0 + 2,4 - 1) = (2,3)
and
N(-3,5) ---> N' (-3 + 2,5 - 1) = (-1,4)
and then translated by (x - 3,y + 4)
K'(0,-3) ---> K''(0 - 3,-3 + 4) = (-3,1)
L'(3,0) ---> L''(3 - 3,0 + 4)= (0,4)
M'(2,3) ---> M'' (2 - 3, 3 + 4)= (-1,7)
and
N'(-1,4) ---> N'' (-1 - 3,4 + 4) = (-4,8)
the coordinates of K" L" M" N" after both translations are
K''= (-3,1)
L''= (0,4)
M''= (-1,7)
and
N'' = (-4,8)
hope im right if not im sorry but it going to be right cuz im good at this stuff for you
which expression is equivalent to (7x^3)^2(x^8)1/2
Answer: 49x^14
Step-by-step explanation:
PLS HELP
No links pls and Ty<333!!!
A circle's diameter is 8 centimeters.
What is the circle's area (use 3.14 for pi and round to the nearest
tenth)?
Answer:
16 pi cm^2
Step-by-step explanation:
Area = pi r^2 r = 1/2 d
= pi (4^2) = 16 pi cm^2
ASAP
Which statement is an example of causation?
o When it rains, the playground gets wet.
The height of children increases as their running speed increases.
O The increase in the number of ice-cream cones a vendor sells causes an increase in temperature.
O Students who eat a good breakfast each day are more physically active than those who skip breakfast.
Answer:
I beleive the fist one is.
Step-by-step explanation:
The first one is a possibility, the second has a correlaition, and the third, I believe is a correlation.
what is the cost of each shirt using the equation 10x+40?
1 shirt=
5 shirts=
10 shirts=
50 shirts=
The cost of 1 shirt would be 10
you would need to multiply the cost of one shirt by the number of shirts bought (x)
I can't seem to figure this one out, can someone help me?
Answer:
I think the volume is 18
Step-by-step explanation:
6×3 = 18
PLEASE HELP URGENT
Given \tan \theta =0.6, find the value of b.
Answer:
b=8.5cm
Step-by-step explanation:
tanx (this represents tan theta, it's just easier to type) is equal to 0.6 and since the tanx ratio is opp/adj, we know that opp/adj = 0.6
To find what b is (adjacent as it is adjacent to the angle being used and it is not the hypotenuse), we just have to rearrange.
0.6=5.1/adj
to solve for adj, we can switch 0.6 and adj. (This works because to get adj by itself on one side you would multiply it to the other side and then divide 0.6 from both sides --> simple algebra)
so then you have
adj=5.1/0.6
adj=8.5cm
(if you want to check your solution you can use pythagoeran theorem, a^2+b^2=c^2) and sub everything in and make sure all the numbers equal the right thing!
The volume V of a given mass of gas varies
directly as the temperature T and inversely as the
pressure P. If V = 341.0 in 3 when T = 310° and
P=10 lb/in.2, what is the volume when T= 120°
and P= 15 lb/in.2?
Apply combine gas law
[tex]\\ \rm\dashrightarrow \dfrac{P1V1}{T1}=\dfrac{P2V2}{T2}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{10(341)}{310}=\dfrac{15V2}{120}[/tex]
[tex]\\ \rm\dashrightarrow 11=\dfrac{V2}{8}[/tex]
[tex]\\ \rm\dashrightarrow V2=88in^3[/tex]
Answer:
88 in³
Step-by-step explanation:
we are given that the volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P.
Condition-1:
The volume V of a given mass of gas varies directly as the temperature T , thus
[tex]V\propto T\\\implies V=kT[/tex]
Condition-1:
The volume V of a given mass of gas varies inversely as the pressure P, therefore,
[tex]V\propto 1/P\\\implies V=k\cdot 1/P[/tex]
combining 1 and 2 yields
[tex]V\propto k\cdot T/P[/tex]
Case-1:
V = 341.0 in³T = 310°P=10 lb/in²To find:
kFinding the constant of proportionality
[tex]341= k\cdot 310/10\\\implies k=341\times 10/310 \\ \implies \boxed{k=11}[/tex]
Case-1:
To find:
Vwhen:
T = 120°P=15 lb/in²k=11Finding the volume:
[tex]V= 11\times 120/15\\\implies V=11\times 8 \\ \implies \boxed{V=88}[/tex]
A man gave 35% of his money to his elder on and 40% of the remainder to the younger son.Now, he is left with 11700 rupees.How much money had he?
HELP NOwwwwWWWW ILL GIVE BRAINLIEST
line A is a perpendicular to line B. if the slope of line A is 3/7 what is the slope of line b?
Answer: -7/3
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other.
If 3K is x% of 3000, then an expression for x is..?
well, let's see it this way, we know that 3000 is the 100%, and we also know that 3K is x% of 3000, so then
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3000 & 100\\ 3K& x \end{array} \implies \cfrac{3000}{3K}=\cfrac{100}{x} \\\\\\ 3000x=300K\implies x=\cfrac{300K}{3000}\implies x=\cfrac{K}{10}[/tex]
Charlie buys a bag of 15 tangerines for 2.85
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
is each shape a parallelagram or not
Answer:
You can have almost all of these qualities and still not have a parallelogram.
Explanation:
The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.
Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
Answer: x > 38
Step-by-step explanation:
The amount of $300 was deposited into a continuously compounded interest account that paid 0.5% interest per year. Which of the following expressions would be used to
determine the number of years it would take for the account to have a balance of $600?
The expression that can be used to determine the number of years that it would take to have a balance of $600 is In2 ÷ In[tex]e^{0.005}[/tex].
How long would it take to have a balance of $600?When an amount is compounded continously, it means that both the amount deposited and the interest already accrued increases in value continously over a period of time.
Time = In(FV/PV) ÷ In([tex]e^{0.005}[/tex]
In2 ÷ In[tex]e^{0.005}[/tex]
H(x)=-(x+11)^2+1. What are the zeros of the function? What is the vertex of the parabola?
Answer:
x=-14
Step-by-step explanation:
-x-11^2+1
-x-11^3
-x^14
x=-14
(7x-3) (3x-17) y find value of x and y
Answer:
[tex]21yx^{2}-128xy+51y[/tex]
Step-by-step explanation:
what is -4(x+3) - 12x + 5 distributed
4. Name three different rays.
Answer:
Spotted eagle rayManta ray (oceanic)Manta ray (reef)Let me know if this is not what you meant by rays, I can change it if needed.
In a candy box, there are 5 times as many candies with nuts as candies without nuts. There are 24 candies in the box: How many candies with nuts are in the box?
Answer:im pretty sure its 20
Step-by-step explanation: because 4x5=20 and theres 24