Note: Consider the expression is [tex](4+\sqrt{2})(6-\sqrt{2})[/tex].
Given:
[tex](4+\sqrt{2})(6-\sqrt{2})[/tex]
To find:
The value of given expression in the form of [tex]b+c\sqrt{2}[/tex].
Solution:
We have,
[tex](4+\sqrt{2})(6-\sqrt{2})[/tex]
Using distributive property, we get
[tex]=4(6-\sqrt{2})+\sqrt{2}(6-\sqrt{2})[/tex]
[tex]=4(6)+4(-\sqrt{2})+\sqrt{2}(6)+\sqrt{2}(-\sqrt{2})[/tex]
[tex]=24-4\sqrt{2}+6\sqrt{2}-2[/tex]
On combining like terms, we get
[tex]=(24-2)+(6\sqrt{2}-4\sqrt{2})[/tex]
[tex]=22+2\sqrt{2}[/tex]
On comparing with [tex]b+c\sqrt{2}[/tex], we get
[tex]a=22,b=2[/tex]
Therefore, the required form is [tex]22+2\sqrt{2}[/tex].
What number is 25% of 160? (worth lots of points because why not lol) help me-
Answer:
40
Step-by-step explanation:
This can be solved by changing the percentage to a decimal number, then multiplying by 160.
0.25×160=40
Please help me will be much appreciated <3
Answer:
She earned 300 dollars by selling 100 headbands.
uhh.i dumb the screenshot is here
Answer:
40
Step-by-step explanation:
Just use a calculator. I didn´t need to. My brother helped me a little
parallel lines, transversal, and algebra really need help
Answer:
1. 58 = 5x-2, 60 = 5x, x = 12
2. 134 = 16x+22, 112 = 16x, x = 7
3. 125 = 7x-1, 126 = 7x, x = 18
4. 133+9x+2 = 180, 9x=45, x=6
5. 8x-77 = 3x+38, 5x = 115, x=23
6. 11x-47 = 6x-2, 5x = 45, x=9
7. 13x-21 = 5x+75, 8x = 96, x=12
8. 5x+3+9x-33 = 180, 14x = 210, x=15
9. 8x-31 = 6x+3, 2x = 34, x=17
5y+35+6(17)+3 = 180, 5y = 40, y = 8
10. 29x-3+15x+7 = 180, 44x = 176, x=4
13y-17+15(4)+7 = 180, 13y = 130, y=10
1. x = 12
2. x = 7
3. x = 18
4. x = 5
5. x = 23
6. x = 9
7. x = 12
8. x = 15
9. x = 17; y = 8
10. x = 4; y = 10
To find the value of each missing variable(s), we would need to apply our knowledge of algebra. However, recall the following rules of angles in parallel lines:
corresponding angles are congruent (i.e. equal to each other)vertically opposite angles are congruent alternate angles are congruent same-side interior angles are supplementary (i.e. sum up to give 180°alternate exterior angles are congruent.Let's solve the given problems as shown below given that line l is parallel to line m:
1. [tex]58 = (5x - 2)[/tex] (corresponding angles)
solve for x
[tex]58 = 5x - 2\\58 + 2 = 5x - 2 +2[/tex] (addition property of equality)
[tex]60 = 5x \\\frac{60}{5} = \frac{5x}{5}[/tex](division property of equality)
[tex]12 = x\\x = 12[/tex]
2. [tex]134 = 16x+22[/tex] (alternate exterior angles)
[tex]\\134 - 22 = 16x +22-22[/tex] (subtraction property of equality)
[tex]134 - 22 = 16x +22-22\\112 = 16x\\\frac{112}{16} = \frac{16x}{16}[/tex](division property of equality)
[tex]7 = x\\x = 7[/tex]
3. [tex]7x - 1 = 125[/tex] (alternate angles)
[tex]7x - 1 + 1 = 125 + 1\\7x = 126\\\frac{7x}{7} = \frac{126}{7} \\x = 18[/tex]
4. [tex](9x+2) + 133 = 180[/tex] (same-side interior angles)
[tex]9x+2 + 133 = 180\\9x + 135 = 180\\9x + 135 - 135 = 180 - 135\\9x = 45\\\frac{9x}{9} = \frac{45}{9} \\x = 5[/tex]
5. [tex]3x+38 = 8x-77[/tex] (alternate exterior angles)
[tex]77 + 38 = 8x - 3x\\115 = 5x\\\frac{115}{5} = \frac{5x}{5} \\23 = x\\x = 23[/tex]
6. [tex]6x-2 = 11x-47[/tex] (corresponding angles)
[tex]6x-2 = 11x-47\\47 - 2 = 11x - 6x\\45 = 5x\\x = 9[/tex]
7. [tex]5x+75 = 13x - 21[/tex] (alternate angles)
[tex]5x+75 = 13x - 21\\21 + 75 = 13x - 5x\\96 = 8x\\12 = x\\x = 12[/tex]
8. [tex](5x+3)+(9x-33)= 180[/tex] (same-side interior angles)
[tex]5x+3+9x-33= 180\\14x - 30 = 180\\14x - 30 + 30 = 180 + 30\\14x = 210\\x = 15[/tex]
9. [tex]8x-31 = 6x+3[/tex] (alternate angles)
[tex]8x - 6x = 31 + 3\\2x = 34\\x = 17[/tex]
Solve for y
[tex](5y + 35) + (6x + 3) = 180[/tex] (same-side interior angles)
[tex]5y + 35 + 6x + 3 = 180\\[/tex]
Plug in the value of x
[tex]5y + 35 + 6(17) + 3 = 180\\5y + 35 + 102 + 3 = 180\\5y + 140 = 180\\5y = 180 - 140\\5y = 40\\y = 8[/tex]
10. [tex](29x-3)+(15x+7) = 180[/tex](supplementary angles)
Solve for y
[tex]13y - 17 = 29x - 3[/tex] (alternate exterior angles)
Plug in the value of x
[tex]13y - 17 = 29(4) - 3\\13y - 17 = 116 - 3\\13y - 17 = 113\\13y = 113 + 17\\13y = 130\\y = 10\\[/tex]
Learn more about parallel lines here:
https://brainly.com/question/16227989
Please help me solve this.
Answer:
9
Step-by-step explanation:
13*3=39
48-39=9
Answer:
48-39=9
^
(13 x 3=39)
what isvequivalent to y=23x−6?
Answer:
Slope = 46.000/2.000 = 23.000
x-intercept = 6/23 = 0.26087
y-intercept = -6/1 = -6.00000
The equation f = V + at represents the final velocity of an object, f, with an initial velocity, w, and an acceleration rate,
a, over time, t. Which is an equivalent equation solved for a?
Of-v=a
Of-vra
1
Of+V = a
o+v=a
Answer:
hey
Step-by-step explanation:
the answer is 5
help please i’ll give brainlest and lots of points
Answer:
1+1=2 so that's the answer
81/11 as a mixed number
Answer:
7 4/11
Step-by-step explanation:
this is the answer
Answer:
7 4/11
Step-by-step explanation:
81/11= 7 4/11
can someone help me. Arithmetic Sequences
Your bucket of Halloween candy has 125 pieces of candy in it. You decide that to ration yourself, you’re going to only eat 5 pieces per day.
What is the common difference?
Answer:
-5
Step-by-step explanation:
when you eat 5 pieces of candy per day then the sequence will be
125, 120, 115, 110, 105......
And Then, the common difference will be -5
What is it will mark Brainliest
The graph of f (x) = x + 5 is a vertical translation 5 units
up of the graph of f(x) = x. How can you obtain the graph of
f(x) = x + 5 from the graph of f (x) = x using a horizontal
translation?
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
[tex]\displaystyle f(x)=x[/tex]
To shift vertically n units, we can simply add n to our function. Hence:
[tex]f(x)=x+n[/tex]
So, a vertical shift of 5 units up implies that n=5. So:
[tex]f(x)=x+5[/tex]
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
[tex]f(x-n)=(x-n)[/tex]
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
[tex]f(x-1)=(x-1)[/tex]
Or:
[tex]f(x)=x-1[/tex]
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
A line passes through the points (-8,-4) and has a slope of 5/4.
hello can anyone help me ? here the question
Answer:
A. 1/5k - 2/3j and -2/3j +1/5k
Step-by-step explanation:
A. 1/5k - 2/3j and -2/3j +1/5k
B. 1/5k - 2/3j and -1/5k +2/3j
There is a change in the signs of each term
1/5k changed to -1/5k
-2/3j changed to +2/3j
Not equivalent
C. 1/5k - 2/3j and 1/5j - 2/3k
There is a change in the variables
1/5k changed to 1/5j
-2/3j changed to -2/3k
D. 1/5k - 2/3j and 2/3j - 1/5k
The is a change in the signs of each term
1/5k changed to -1/5k
-2/3j changed to +2/3j
The only equivalent expression is
A. 1/5k - 2/3j and -2/3j +1/5k
The amount of tax is $3.40, which is 5% of the food bill. How much was the food bill not including the tax?
If Simon wants to leave a 20% tip on the amount of the food bill before tax, how much should he leave for a tip?
What is Simon’s total bill including tax and tip? What percent of the food bill is this?
Answer:
You are told tax is $3.40 which is 5% of the total priceWe want to find the original food bill not including the tax of $3.40We also want to find the tip quantity based on the original food billSo X * 0.05= 3.40 Gives us X= 68 Hence the original bill was $68Now $68* .20 = $13.6I'm confident you can answer the rest with the information I've provided.Mr. M has a recipe for sourdough bread. He uses 8/3 cups of flour to make 2 loaves of sourdough bread. If you were to follow the same recipe, which equation would work for making y loaves of bread with x cups of flour?
Answer:
2y=8/3x
Step-by-step explanation:
someone answer please:)
I think its saying to find out what a means
The Science Club went on a two-day field trip. The first day the members paid $70 for transportation plus $19 per ticket to the planetarium. The second day they paid $100 for transportation plus $16 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Answer:
$170 + $35n
Step-by-step explanation:
Given that:
First day:
Transport fare = $70
Fee per ticket = $19
2nd day:
Transport fare = $100
Fee per ticket = $16
Total cost in dollars for the two days for n members
Number of members = n
First day:
70 + 19n
Second day :
100 + 16n
Totak cost :
(70 + 19n) + (100 + 16n)
70 + 100 + 19n + 16n
170 + 35n
$170 + $35n
ANSWER PLEASE 40 POINTS!
Answer: |10 - (-8)|
The absolute value is 18
Step-by-step explanation:
The distance between two numbers is a subtraction equation.
10 - (-8) Subtracting a negative is like adding a positive
10 + 8 = 18
If you look at it as the first negative sign means -1 multiplied by the next negative number, "Remember that a negative times a negative is a positive!"
Answer:
|-10 - (-8)|
Step-by-step explanation:
Distance from 10 to 0: 10Distance from 0 to -8: 8Put them together (with absolute value): |-10 - (-8)|I hope this helps!
Is it scaling isosceles or equilateral and what is the answer
Answer:
[tex]scalene[/tex]
Step-by-step explanation:
[tex]\textsf{Sum of internal angles;}[/tex]
[tex]71+50+6x-1=180[/tex]
[tex]6x-1=180-71-50[/tex]
[tex]6x-1=59[/tex]
1/5(x-2)=1/10(x+6) and
0.35(x+4)=0.25(x-6) please
Answer:
1) x=10 2) x= -7.25
Step-by-step explanation:
Im not sure
A rectangle has an area of 135 ft 2 . What is the length, if the width is 9 ft?
Answer:
15 ft
Step-by-step explanation:
A=LxW
135 ft2 =m X 9ft
Divide 135 by 9
& that equals 15ft.
To check your answer, you multiply 15X9 and that equals 135. So the length of the rectangle is 15ft.
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
(3x-9)°
(x+15)
Answer:
318.6
Step-by-step explanation:
(3x-9) + (x+15) = 180
3x (x+15) -9 (x+15)
4x + 45x - 9x + 6 = 180
40x + 6 = 180
40x = 180 - 6
40x = 174
x = 4.34
(3x-9) = 4.34 * 3x-9 = 4.02
(x+15) = 4.34 + 15 = 19.34
180 - (4.02 + 19.34)
= 180 - 23.36
= 156.64
hope this answer helps!!
what does x equal and what are the angle measures?? help Asap
all triangles are 180 always. make a equation 2x+x+x+8 then combine like terms so it will be 4x+8 then divide by 4 on bith sides x=2
I need help with this geometry problem please
Answer:
A. 29
Step-by-step explanation:
Set 5x - 11 = to 3x + 5, and then solve for X, and substitute the x value (8) back into the equation to get 29.
~theLocoCoco
4. What is the value of -24 + 6?
Answer:-18
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
Please give brainliest!
please help me answer this!! geometry
Answer:
-2x+7(10+18)
Step-by-step explanation:
Hope this helps
what is 53829-(-538)7902(6)=?
Answer:
25561485
Step-by-step explanation:
What is the quotation (-3)^0/(-3)^2
Hey there!
(-3)^0 / (-3)^2
(-3)^0 = 1 ⬅️ Numerator
(-3)^2 = (-3)(-3) = 9 ⬅️ Denominator
Answer: 1/9 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
PLEASE HELP FAST I WILL GVIE BRAINLIST AND EXTRA MARKS FOR CORRECT ANSWER! THANKS
Answer:
f(-2) = 2
Step-by-step explanation:
Look at the graph and find -2 on the x-axis and see what the y-coordinate is on the line where x is -2. When you do this, you can see that where x is -2, y is 2.
So basically it wants the y-value :)
Answer:
1.25
Step-by-step explanation:
the answer is 1.25. To get that, I found the slope, wrote the equation in point slope form, and then I calculated when the f(x) function hits the line