Answer:
a = -3
b = 5
Step-by-step explanation:
[tex]\frac{10-\sqrt{18}}{\sqrt{2}}[/tex]
Simplify the square root of 18.
[tex]\frac{10-3\sqrt{2}}{\sqrt{2}}[/tex]
Rationalize the fraction.
[tex]\frac{\left(10-3\sqrt{2}\right)\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]
[tex]\frac{2\left(5\sqrt{2}-3\right)}{2}[/tex]
[tex]5\sqrt{2}-3[/tex]
Rewrite the answer in the form a+b√2.
[tex]-3 + 5\sqrt{2}[/tex]
The given form of expression a + b √2 where a and b are integers then the values of a and b are -3 and 5.
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
[tex]\frac{10 -\sqrt18} {\sqrt 2}= a + b \sqrt 2[/tex]
Simplify the square root of 18 then Rationalize the fraction,
[tex]\\\frac{10 -3\sqrt2} {\sqrt 2}\\\\\frac{(10 -3\sqrt2) \times \sqrt{2} } {\sqrt 2 \sqrt 2}\\\\\frac{ 2(5\sqrt2 -3) } { 2}\\\\(5\sqrt2 -3)[/tex]
Thus, the values of a and b are -3 and 5.
Learn more about factors;
https://brainly.com/question/24182713
Ok so I’m in high school and I forgot everything I learned in 6-7th grade so what is 14/2 + 12/6 I got 54/6 but I don’t know what to do to get it into simplest form btw I’m very dumb so please explain it like you would to a 4yr old
Answer:9
Step-by-step explanation:
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator. Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1. (14/2 x 3/3)+(12/6 x 1/1). Complete the multiplication and the equation becomes 42/6+12/6. The two fractions now have like denominators so you can add the numerators. 42+12/6=54/6. Divide 54 by 6 and get 9. hope this helps :)
Put the following numbers in order from least to greatest.
3)-1.7, 2, 0,-5
4) 4.5, -3,1/2,-2.3
5) -2.8, -2/3, -209
Venla is 5 years older than her cousin Kora.
Write an equation for the age of Venla, v, when Kora is k years old.
How old is Kora when Venla is 18 years old?
years
Answer:
13
Step-by-step explanation:
v=k+5
k=Kora's age
if v=18
k=v-5
k=18-5
j=13
P(t)P(t)P, left parenthesis, t, right parenthesis models the distance of a swinging pendulum (in \text{cm}cmstart text, c, m, end text) from the place it was released ttt seconds after it starts to swing. Here, ttt is entered in radians. P(t) = -5\cos\left(2\pi t\right) + 5P(t)=−5cos(2πt)+5P, left parenthesis, t, right parenthesis, equals, minus, 5, cosine, left parenthesis, 2, pi, t, right parenthesis, plus, 5 What is the first time the pendulum reaches 3.5\text{ cm}3.5 cm3, point, 5, start text, space, c, m, end text from the place it was released? Round your final answer to the nearest hundredth of a second.
Answer:
0.20secondStep-by-step explanation:
Given the distance of a swinging pendulum modeled by the equation P(t)=−5cos(2πt)+5, to get the first time the pendulum reaches 3.5cm, we will have to substitute P(t)= 3.5cm into the given equation and calculate the value of 't' as shown;
3.5 = −5cos(2πt)+5
Subtracting 5 from both sides;
3.5-5 = −5cos(2πt)+5-5
-1.5 = −5cos(2πt)
Dividing both sides by -5 will give;
[tex]\frac{-1.5}{-5} = cos2\pi t\\0.3 = cos2\pi t\\2\pi t=cos^{-1} 0.3\\2\pi t = 72.54^{0} \\360t = 72.54^{0} \\t = \frac{72.54}{360} \\t = 0.20secs[/tex]
The first time the pendulum reaches 3.5cm is after 0.20secs
FIND X FOR 10 POINTS
Answer: 30.
Step-by-step explanation: This is a triangle with a 90 degree angle and a 60 degree angle. So, a 180 degree angle - a 90 degree angle - 60 degree angle = 30.
how to do area and perimeter
Answer:
Step-by-step explanation:
area and perimeter of WHAT? specify plz.
Answer this, pic below
Answer:
The answer is, A. it is constant
Step-by-step explanation:
Between the x values 4 and 8 the line does not decrease or increase. It stays in a straight line causing it to be constant.
Answer: Its constant ( constant means it isnt moving like its just stable)
The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks? A. –270 cents per week B. –90 cents per week C. –87 cents per week D. –30 cents per week
Answer:
D
Step-by-step explanation:
In 3 weeks the stock decreased 60 + 10 + 20 = 90 cents so it decreased about 90 / 3 = 30 cents per week so it is D.
Answer:
The answer is D
Step-by-step explanation:
I took the test.
how many years will it take for the area of the glacier to decrease to 15 square kilometers
Answer:
aprox: 9 years?
Step-by-step explanation:
im sorry if this is wrong!
Determine whether the system of linear equations has one solution infinitely many solutions or no solution explain your reasoning. y=3x+5 and y=3x-5
Answer: The equations have no solution because no solution graphs have the same slopes but difference y- intercepts.And by looking at the equations they both have same slope as 3 but different y-intercepts 5 and -5.
Step-by-step explanation:
y= 3x + 5
y = 3x- 5
3x + 5 = 3x -5
-3x -3x
5 ≠ 5
What is the solution to the equation -4(2x+3) =2x+6-(8x+2)?
x = -10
x = -8
X=-5/2
x=-4/7
Answer:
x = -8
Step-by-step explanation:
solve:
-4(2x+3) =2x+6-(8x+2)
-8x-12 = 2x+6-8x-2
-8x-12 = -6x + 4
-2x = 16
x = -8
Hope this helps.
Good Luck
Answer:
[tex]x = - 8[/tex]
Second answer is correct
Step-by-step explanation:
[tex] - 4(2x + 3) = 2x + 6 - (8x + 2) \\ - 8x - 12 = 2x + 6 - 8x - 2 \\ - 8x - 12 = - 6x + 4 \\ - 8x + 6x = 12 + 4 \\ - 2x = 16 \\ \frac{ - 2x}{ - 2} = \frac{16}{ - 2} \\ x = - 8[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Select the correct answer.
What is the missing value in the table of equivalent ratios?
1 | 12
2 24
336
448
5 ?
Ο Α.
54
OB
58
Ос.
60
OD
64
O E 68
Answer:I think 60
Step-by-step explanation:
Answer:
60 i am positive
Step-by-step explanation:
jordan has some music books. he will buy 9 new music books each year. he will have 52 music books in 5 years.
Rate of change per year= ___
Initial value = _____
Answer:
760 music books per each 5 years
Step-by-step explanation:
amanda has a board that is 7 feet long. how many 1/4 foot sections can she cut from this board
Answer:
28
Step-by-step explanation: You need to divide 7 by 1/4. Whenever you divide fractions you keep the first number as it is, change the sign to multiplication and write the reciprocal of the second fraction which is you have to flip the fraction. It is going to be 7 times 4/1. Which is 28/1 which is 28.
PLEASE SOMEONE HELP ME I NEED SOMEONES HELP ASAP!!!!!!!!PLEASE IM BEGGING YOU SO MUCH PLEASE!!!!!
Suppose a family pays $29.99 for dinner . They leave a 15% tip. Find both the tip and the total price of the meal. Round your answers to the nearest cent.
Show your work below:
Tip = $15.20
Total = $45.20
Tip = $9.40
Total = $24.56
Tip = $1.10
Total = $31.10
Tip = $4.50
Total = $34.50
Answer:
Tip = $4.50
Total = $34.50
Step-by-step explanation:
Multiply 29.99 by .15 to find the tip.
Then add the tip to the original number.
Which statement is true about this right triangle?
y²+ z² = x²
Z + y = x
X
x² + y2 = z?
у
x²+ z² = y²
Answer:
Step-by-step explanation:
the Pythagorean theorem is :
a^2+b^2=c^2
c is the hypotenuse
if y is the hypotenuse then x^2+z^2=y^2
if x is the hypotenuse then y^2+z^2=x^2
My mom built a new sandbox that is 3 \text { m}3 m3, start text, space, m, end text long, 2 \text { m}2 m2, start text, space, m, end text wide, and 1 \text { m}1 m1, start text, space, m, end text high for my sister and me. Sand for the sandbox costs \$4.50$4.50dollar sign, 4, point, 50 per cubic meter. How much will it cost to completely fill the sandbox with sand? \$$dollar sign
Answer:
$27
Step-by-step explanation:
The dimensions of the sandbox (that is a rectangular prism) are 3m x 2m x 1m.
We need to first find the volume of the sandbox.
The volume of a rectangular prism is:
V = L * W * H
where L = length
W = Width
H = height
The volume of the sandbox is:
V = 3 * 2 * 1 = [tex]6 m^3[/tex]
Sand for the sandbox costs $4.50 per cubic meter.
The cost to completely fill the sandbox is:
4.50 * 6 = $27
what is the value of the expression 1/2 (m÷3) +n A. 13/5 B. 13/10 C. 15/11 D. 15/17
Answer:
So far I have gotten 3m + n, there is not equal sign so I am unable to finish this question further.
Step-by-step explanation:
Consider the equation y=-x^2-7x+12
Answer:
y = (x + 4)(x + 3)
Step-by-step explanation:
y = x ^2 + 7x + 12
The two numbers must add up to 7 and has a product of 12, and since the equation is all positive, then the two numbers are positive too.
So y = (x + 4)(x + 3) is the answer.
Check:
y = (x + 4)(x + 3)
y = x(x + 3) + 4(x + 3) distributive property
y = x^2 + 3x + 4x + 12
y = x^2 + 7x + 12
If f(x) = 2(x)2 + 5v(x+2), complete the following statement (round your answer to the nearest hundredth
Answer:
2
Step-by-step explanation:
1+1
If X = (8,4) and Y = (-8, 0), what is XY?
А. 16.49
В.2
С.272
D.8.94
Answer:
16.49
Step-by-step explanation:
The student council at Clarksville High School is making T-shirts to sell for a fundraiser, at a price of $10 apiece. The costs, meanwhile, are $8 per shirt, plus a setup fee of $98. Selling a certain number of shirts will allow the student council to cover their costs. What will the costs be? How many shirts must be sold?
Answer:
Costs are $490
49 shirts are sold
Step-by-step explanation:
98 + 8x = 10x
98 = 2x
49 = x
98 + 8(49) = $490 in costs
49 shirts sold
This is super confusing! Can someone plz explain? I'm giving more points!
Answer:
a ) Increased by 100 %, b ) Increased by 50 %, c ) Decreased by 33 and 1/3 %, d ) Decrease by 50 %, e ) Increased by 200 %, f ) 66 and 2 / 3 %
Step-by-step explanation:
See steps below;
[tex]a ) Percent Increase from 1 - 2 ;\\starting value - 1, end value - 2 ;\\2 - 1 = Increase by 1,\\1 / 1 - Solution; Increase by 100 percent[/tex]
[tex]b ) Percent Increase from 2 - 3 ;\\starting value - 2, end value - 3,\\3 - 2 = Increase by 1,\\1 / 2 - Solution; Increase by 50 percent[/tex]
[tex]c ) Percent Decrease from 3 - 2 ;\\starting value - 3, end value - 2,\\3 - 2 = Increase by 1,\\1 / 3 - Solution; Decrease by 33 and 1 / 3 percent[/tex]
[tex]d ) Percent Decrease from 2 - 1 ;\\starting value - 2, end value - 1,\\2 - 1 = Decrease by 1,\\1 / 2 - Solution ; Decrease by 50 percent[/tex]
[tex]e ) Percent Increase from 1 - 3 ;\\starting value - 1 , end value - 3,\\3 - 1 = Increase by 2,\\2 / 1 - Solution ; Increase by 200 percent[/tex]
[tex]f ) Percent Decrease from 3 - 1;\\starting value - 3, end value - 1,\\3 - 1 = Decrease by 2,\\2 / 3 - Solution ; Decrease by 66 and 2 / 3 percent[/tex]
Solution; a ) Increased by 100 %, b ) Increased by 50 %, c ) Decreased by 33 and 1/3 %, d ) Decrease by 50 %, e ) Increased by 200 %, f ) Decrease by 66 and 2 / 3 %
Solve the system by substitution.
y = 5x
y = -3x + 24
pls help :(
Answer:
x=3, y=15
Step-by-step explanation:
We substitute 5x for y, getting 5x = -3x + 24. We add 3 x to both sides, and have a equation like this: 8x = 24. Divide by 8 on both sides, and we know that x = 3. Since y is 5x, y is 5*3, which is 15.
find the nth term of this sequences
20,18,16,14
Answer:
12
Step-by-step explanation:
This would be the 5th term in the sequence.
Numbers are decreasing by two
Hope this helps!
Answer:
12 would be the 5th term
Some large boxes of small oranges contained 344 oranges each.how many oranges were in 4 boxes?
Answer:
1376
Step-by-step explanation: You have to multiply 344 and 4 which is 1376.
Answer:
Step-by-step explanation:
300x4=1200
4x44=176
1200+176=1376
If functions f and g are inverses of each other, then what is their composition, f(g(x))? (only have 2 hours to answer!) a. f(x) b. 0 c. 1 d. x
Answer: (d) x
Step-by-step explanation:
Inverses cancel each other leaving you with whatever is in the parenthesis.
Examples:
f(g(x)) = x
f(g(1)) = 1
f(g(2bc) = 2bc
Which expression has a value of
8
- ?
15
Answer:
15
Step-by-step explanation:
The sum of two numbers is no more than 28. Let x represent the first number, and let y represent the second number. Which
inequality represents this situation?
0 V3X+ 28/
y
x+y <28
X+ y = 28
What is the leading coefficient of the polynomial?
5x3 + 17 − 8x5 − 9x4