[tex]\huge{\colorbox{pink}{Hope It Helps You ! }}[/tex]
Answer:
[tex]\sqrt{30}-3[/tex]
Step-by-step explanation:
Write the given expression in a numerical format:
[tex]\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}[/tex]
A logical first step to take in this problem is to convert the denominator to a rational value. Currently, the denominator is an irrational value, meaning that it is a never-ending value. One wants it to be a rational value. This can be done by multiplying the denominator by its conjugate. The conjugate of this number is simply the denominator with the second addend times negative one. Remember to multiply both the numerator and denominator by this value, as a number over itself is the same as multiply by (1) Use this idea here:
[tex]\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}[/tex]
[tex]=\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}*\frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}-\sqrt{3}}[/tex]
Simplify,
[tex]=\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}*\frac{\sqrt{10}-\sqrt{3}}{\sqrt{10}-\sqrt{3}}[/tex]
[tex]=\frac{7\sqrt{3}(\sqrt{10}-\sqrt{3})}{(\sqrt{10}+\sqrt{3})(\sqrt{10}-\sqrt{3})}[/tex]
[tex]=\frac{7\sqrt{30}-7\sqrt{3*3}}{\sqrt{10*10}-\sqrt{3*3}+\sqrt{10*3}-\sqrt{10*3}}[/tex]
Note that any value times itself under the radical is equal to the number, meaning ([tex]\sqrt{a*a}=a[/tex]). Apply this to the problem,
[tex]=\frac{7\sqrt{30}-7\sqrt{3*3}}{\sqrt{10*10}-\sqrt{3*3}+\sqrt{10*3}-\sqrt{10*3}}[/tex]
[tex]=\frac{7\sqrt{30}-7*3}{10-3}[/tex]
[tex]=\frac{7\sqrt{30}-21}{7}[/tex]
[tex]=\sqrt{30}-3[/tex]
What is the remainder when (x^3 + 1) is divided by (x^2 – x + 1)?
O x +1
Ο x
O 2
Ο 0
Answer:
The answer is 0 .... solution is X+1 the REMAINDER IS 0
Step-by-step explanation:
The remainder when (x³ + 1) is divided by (x² - x + 1) is 0.
The correct option is D.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
We can use polynomial long division to find the remainder of (x³ + 1) divided by (x² - x + 1):
x + 1
-------------
x² - x + 1 | x³ + 0x² + 0x + 1
- (x³ - x² + x)
---------------
x² - x + 1
- (x² - x + 1)
-------------
0
Therefore, the remainder when (x³ + 1) is divided by (x² - x + 1) is 0.
To learn more about Polynomials;
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Tiana would like to buy ice cream cones for her birthday party, but since she
does not have very much ice cream, she wants cones with the smallest
volume. Which of the following brands of ice cream cones should she buy?
Brand A:
height of cone = 15 cm
radius of cone base = 4 cm
Brand B:
height of cone = 12 cm
radius of cone base = 5 cm
A. Brand A
B. Brand B
C. Either - the cones have equal volumes
The smallest volume of ice cream in Brand A.
How to estimate the volume of cone?
Given:
Brand A:
height of cone = 15 cm
radius of cone base = 4 cm
Brand B:
height of cone = 12 cm
radius of cone base = 5 cm
Volume of cone = 1/3πr² h
Volume of ice cream A = ( π [tex]4^2[/tex] (15) ) /3 = 240 π/3 = 80 π
Volume of ice cream B = ( π [tex]5^2[/tex] (12) ) /3 = 300 π/3 = 100 π
In comparison, you can figure out which one would give her more volume of ice cream in Brand A.
Therefore, the correct answer is option A. Brand A.
To learn more about the volume of cone
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Tom wants to borrow $16,578 for a car. The bank is going to charge him 12% interest annually, compounded monthly. If his car payment is $345.00 a month. How much will he owe at the end of 4 months? (Take this one month at a time. Determine the interest for the month; add it to the principal. Then subtract the payment, and that is your new principal for the next month.)
Answer:
Step-by-step explanation:
Principal, P = $16,578
Interest rate, r = 12% = 0.12
Monthly interest rate = annual interest rate / 12
= 12%/12
= 1%
= 0.01
Time, t = 1 year
Number of period, n = 12
Car payment per month = $345.00
Month 1:
A = P(1 + r/n)^nt
A = 16,578(1 + 0.01/12)^(12)(1)
A = 16,578(1 + 0.000833333)^(12)
= 16578(1.000833333)^12
= 16578(1.0100459608871)
A = $16,744.54
Principal after month 1 repayment = $16,744.54 - $345
= $16,399.54
Month 2:
A = P(1 + r/n)^nt
= $16,399.54(1 + 0.01/12)^(12)(1)
= 16,399.54(1 + 0.000833333)^(12)
= 16,399.54(1.000833333)^12
= 16399.54(1.0100459608871)
= 16,564.289137406431934
= $16,564.29
Principal after month 2 repayment = $16,564.29 - $345
= $16,219.29
Month 3:
A = P(1 + r/n)^nt
= $16,219.29(1 + 0.01/12)^(12)(1)
= 16,219.29(1 + 0.000833333)^(12)
= 16,219.29(1.000833333)^12
= 16219.29(1.0100459608871)
= 16382.228352956532159
= $16,382.23
Principal after month 3 repayment = $16,382.23 - $345
= $16,037.23
Month 4:
A = P(1 + r/n)^nt
= $16,037.23(1 + 0.01/12)^(12)(1)
= 16,037.23(1 + 0.000833333)^(12)
= 16,037.23(1.000833333)^12
= 16037.23(1.0100459608871)
= 16198.339385317426733
= $16,198.34
Principal after month 4 repayment = $16,198.34 - $345
= $15,853.34
HELP ASAP 2 and 3!! please :)
Answer:
2. D. division property of equality
3. B. transitive
Step-by-step explanation:
2. well, we divide both sides by the same factor 3.
3. the same reason as for 4. we are using that if A = B, and B = 30, then A =30 in both lines.
The graph of a quadratic function
displays output values that approach
negative infinity. What do you know
about the leading coefficient of this
function?
A
The leading coefficient is negative.
B
The leading coefficient is positive.
Answer:
A
The leading coefficient is negative.
Step-by-step explanation:
Quadratic equation:
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
The leading coefficient is a.
a negative:
The graph of the function is concave down, that is, it displays values that approach negative infinity.
a positive:
The graph of the function is concave up, that is, it displays values that approach up infinity.
In this question:
Displays values that approach negative infinity, so the leading coefficient is negative, and the correct answer is given by option A.
Answer:
B it's positive.. I went with negative because that's what it said, but it was wrong!
Step-by-step explanation:
C. f(x) = x2 +7; Find f(7)
Answer:
f(7) = 21
Step-by-step explanation:
f(7)=(7)2+7
= 14+7
= 21
Given JIH~ LMN. what is the value of LN?
Answer:
7 units
Step-by-step explanation:
In similar triangles, corresponding sides are same ratio.
[tex]\frac{LN}{JH}=\frac{LM}{JI}\\\\\frac{LN}{14}=\frac{5}{10}\\\\LN=\frac{5}{10}*14\\\\LN=7[/tex]
plzzz helppp will mark brainlest stpps plzz if possible
Answer:
c.
Step-by-step explanation:
Law of sines
[tex]\frac{Sin A}{a}[/tex] = [tex]\frac{Sin B}{b}[/tex]
A and B are angles.
a and b are sides opposite corresponding angles.
1) solve the following system of Equations by graphing. Label the solution and all intercepts.
Please show me how u did it and graphed it ;-;
Answer:
Um. There is no equation?
Step-by-step explanation:
Help me pls‼️‼️‼️❤️❤️
Answer:
= 50%
Step-by-step explanation:
There is one point, random number = 1
There are two circles, sample space = 2
[tex]{ \tt{probability = \frac{1}{2} }} \\ { \tt{percentage = \frac{1}{2} \times 100\% }} \\ = 50\%[/tex]
Answer:
25%
Step-by-step explanation:
1. Find the area of both Circles: [tex]A = \pi r^{2}[/tex] [tex]A = \pi 2^{2}[/tex] = [tex]4\pi[/tex] [tex]A = \pi 1^{2} = \pi[/tex]
2. [tex]\frac{\pi }{4\pi }[/tex] to find the percentage
3. 0.25 = 25%
Lusia tiene $500, decide gastar el 15% de esta cantidad en la compra de un postre para despues de la comida
¿ A cuánto asciende la cantidad en pesos que dispone lusia para comprar el postre
Answer:
Gasto en postre= $75
Step-by-step explanation:
Dada la siguiente información:
Lusia tiene $500, decide gastar el 15% de esta cantidad en la compra de un postre para despues de la comida.
Para calcular la cantidad a gastar en el postre, debemos usar la siguiente formula:
Gasto en postre= presupuesto total*porcentaje para postre
Gasto en postre= 500*0.15
Gasto en postre= $75
Which graphs show functions with direct variation? select three options.
Answer:
the daily graphs
Step-by-step explanation:
the news paper
Answer:
B C E
Step-by-step explanation:
Someone plz help me and show the work 10 points!
Answer:
78°
Step-by-step explanation:
you have to add it up and then divide after multiply
Write the y-intercept of the line
Answer: -2. Bc if you look on the graph of the y axis you'll see its located at -2.
Hope this helps :)
Step-by-step explanation:
Which of the following situations could be represented by the expression, 25x+100?
You make 25 dollars per day, where x is the number of days you work. Then, you get 100$ from your end-of-the-year bonus.
Y= 3x+6; (4,7) in slop intercept form
What we are given:
*equation
* intercepts (4,7)
All we have to do is plug in what we know:
Y= 3x + 6
x=4 and y= 7
NEW EQUATION:
7= 3(4) + 6
7= 12+6
7= 18
then divide 18 by 7
18/7= 2.5
Kristen and Stephen share some money on the ratio 3:2 Kristen receives $72. How much will Stephen receive
Answer:
$48
Step-by-step explanation:
A ratio of 3:2 could be $3 and $2, or any multiple of 3 and 2 such as $6 and $4. Kristen corresponds to $3 and receives $72.
$72/$3 = x/$2
3x = 2 * $72
3x = $144
x = $48
Answer: $48
Answer:
$48
Step-by-step explanation:
Since we are given the ratio 3:2 we can use that with the given number to find our missing amount
first, we divide 72 by 3 to find what 1/3 will be 72/3 = 24
Then, we multiply by 2 to find our missing amount 24 * 2 = 48
Which of the following expressions can be used to find x? Solve for x. Round to the nearest hundredth. A tan 28 = x32 ; x=17.01∘ B sin 28 = x32 ; x=15.02∘ C tan 28 = 32x ; x=60.18∘ D tan x= 2832; x=41.19∘
Answer:
B
Step-by-step explanation:
Add. State the sum in simplest form.
6/5x + 7/3y
Answer:
6x/5 + 7y/3
Step-by-step explanation:
Answer:
3.53xy
Step-by-step explanation:
I’m probably wrong but give it a try I think
HELP! (25 points) i think i might know the answer
Answer:
[tex]\sqrt{7}[/tex]
Step-by-step explanation:
At a homecoming pep rally, one student will win free tickets to the homecoming dance. There are 2,400 students attending the pep rally. The student council wants to pull the winning student’s name from a container with the school’s mascot on it. Unfortunately, the container only holds 600 names.
Which method can the student council use to ensure each student has a fair chance of winning?
A.
Randomly assign the 2,400 students to four equal groups. Select a group at random and put all the names from that group in the container. Randomly select the winner from the container.
B.
Put the names of the first 600 students who arrive at the pep rally in the bag. Randomly select the winner from the container.
C.
Select a section of the bleachers and only put the names of students sitting in that section in the container. Randomly select the winner from the container.
D.
Select a grade and only put the names of students from that grade in the container. Randomly select the winner from the container.
Answer:
A
Step-by-step explanation:
Answer A. Logically speaking there is no fair chance unless they use all the names but we can rule out C by the higher chance of students crowding, B is less likely as selecting winners from students who arrive first would be nearly the same as who bought their tickets first. D, selecting a grade excludes (estimating) around 1500 students or more from being included. A is the only logical answer left and by dividing them randomly you give everyone a full chance.
Sue has 20 biscuits in a tin there are : 12 plain 5 chocolate 3 currant sue takes out two biscuits out the tin what is the probability that the two biscuits are not the same
Answer:
P(2 different) ≈ 58.42%
Step-by-step explanation:
To find the probability that the 2 selected are different, we have to first find the probability that the 2 selected are the same.
probability that they are the same;
P(2 plain biscuits) = (12/20) × (11/19) = 132/380
P(2 chocolates) = (5/20) × (4/19) = 20/380
P(2 currant chocolates) = (3/20) × (2/19) = 6/380
Thus, generally;
P(2 same biscuits of either 3 types) = (132/380) + (20/380) + (6/380)
P(same) = 158/380
P(same) = 79/190
Thus, the probability that they are different will be;
P(2 different) = 1 - P(two same)
Thus;
P(2 different) = 1 − (79/190)
P(2 different) = 111/190
P(2 different) ≈ 58.42%
Answer:
0.5842
this is what I got and it was right
Factor x4 – 81. Question 20 options: A) (x2 + 3)(x2 – 3) B) (x2 – 9)(x + 3)(x – 3) C) (x2 + 9)(x + 3)(x – 3) D) (x + 3)2(x – 3)2
Answer:
C is correct
Step-by-step explanation:
A square minus a square can always be factored into the square root of the 1st term plus and minus the square root of the 2nd term. So
x**4 - 81 = (x**2 + 9)(x**2 -9) = (x**2 + 9) (x + 3)(x - 3)
DIVISON METHOD OF 527,646,1105
Answer:
17 is the answer
Step-by-step explanation:
A cone has a volume of 150 cm cubed and a base with an area of 12 cm square. What is the height of the cone?
(I'm asking this again :') No one answered it.)
P.S Its 30 Points now
SO PLEASE HELPPP tyyyy :)
Answer:
37.5cm
Step-by-step explanation:
V=1/3Bh
150=1/3 12h
150=4h
37.5=h
Which system is equivalent to y=-2x^2 y=x-2
a) y=-2y^2 x=y-2
b) y=-2y^2+2 x=y+2
c) y=-2y^2-8y-8 x=y+2
d) y=-2y^2+8y-8 x=y-2
Answer:
answer C
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&-2x^2\\y&=&x-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2(y-2)^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2y^2-8y-8\\\end{array}\right.\\\\[/tex]
help help help it is simple one
Answer:
[tex] 3^{ -x+3}[/tex]
Step-by-step explanation:
We need to simplify out the given exponential expression . The given expression to us is ,
[tex]\rm\implies \dfrac{\dfrac{1}{3}}{3^{x-4}} [/tex]
We can use the Law of Exponents to simplify the given expression . Recall that ,
[tex]\rm\implies \red{\dfrac{a^m}{a^n}= a^{m-n}}[/tex]
Note that , we can write ,
[tex]\rm\implies \dfrac{1}{3}= 3^{-1}[/tex]
Therefore our expression becomes ,
[tex]\rm\implies \dfrac{ 3^{-1}}{3^{x-4}}[/tex]
Simpify using the Law of Exponents ,
[tex]\rm\implies 3^{ -1 - ( x - 4 )}[/tex]
Open the brackets in exponent ,
[tex]\rm\implies 3^{ -1 - x +4 }[/tex]
Simplify to get final expression ,
[tex]\rm\implies \boxed{\quad \blue{ 3^{-x+3} \quad}}[/tex]
Grant is a member of a book club. He pays a $10 yearly membership fee and can purchase books through the club for $2.75 each. His total annual cost is a function of the number of books that he purchases in a year. Let b represent the number of books he purchases in a year. Which function, C(b), represents his yearly cost
Does the function ƒ(x) = 5e0.25x represent exponential growth, decay, or neither?
Step-by-step explanation:
it is exponential growth because the coefficient of x is not negative
the evidence is in the image above
the gradient increases
Please help out will give brainliest to the first person
Answer:
b = 74
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles in a triangle
b-44 + b+18 = b+48
2b-26 = b+48
Subtract b from each side
2b-b-26 =b+48-b
b-26 = 48
Add 26 to each side
b-26+26 = 48+26
b =74
