Answer: 34
Step-by-step explanation:
[tex]a=3+2\sqrt{2} \\\\\dfrac{1}{a} =\dfrac{1}{3+2\sqrt{2}} =\dfrac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})} =\dfrac{3-2\sqrt{2}}{3^2-2^2*2} =3-2\sqrt{2}\\\\\\a+\dfrac{1}{a} =3+2\sqrt{2}+3-2\sqrt{2}=6\\\\(a+\dfrac{1}{a})^2=6^2=36=a^2+\dfrac{1}{a^2}+2\\\\\\a^2+\dfrac{1}{a^2}=36-2=34\\[/tex]
Please answer maths question! Photo is easier to read
Answer:
Step-by-step explanation:
152
R varies directly as S and inversely as T. if R = 8 when S = 4 and T = 3, then R is equal to
Answer:
R = 6S/T
Step-by-step explanation:
R ∝ S/ T
》R = kS/ T
》k = RT/ S
If R = 8 when S = 4 and T = 3
then, k = (8 × 3)/ 4
k = 6
∴ R = (6 × S)/ T
In the figure below, which answer choice correctly identifies the name of two rays?
Answer:
plz mark me as brainlist
Step-by-step explanation:
b)JK and KL
Answer:
JK AND KL
Step-by-step explanation:
"Write two equations: one parallel, one perpendicular to (5,-2) y= 1/5x-3
Write in the form y=mx±b,y=mx±b (first the parallel, then the perpendicular)"
Answer:
For parallel:
gradient is 1/5
[tex]y = mx + c[/tex]
consider (5, -2):
[tex] - 2 = ( \frac{1}{5} \times 5) + c \\ - 2 = 1 + c \\ c = - 3[/tex]
[tex]{ \boxed{ \bf{equation : y = \frac{1}{5}x - 3 }}}[/tex]
For perpendicular:
gradient, m1:
[tex]m _{1} \times m_{2} = - 1 \\ m _{1} \times \frac{1}{5} = - 1 \\ \\ m _{1} = - 5[/tex]
gradient = -5
[tex]y = mx + c \\ - 2 = (5 \times - 5) + c \\ - 2 = - 25 + c \\ c = 23[/tex]
[tex]{ \boxed{ \bf{equation :y = - 5x + 23 }}}[/tex]
Answer:
Parallel: [tex]y=\displaystyle \frac{1}{5}x-3[/tex]
Perpendicular: [tex]y=-5x+23[/tex]
Step-by-step explanation:
Hi there!
What we must know:
Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slopePerpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, -6/7 and 7/6)Finding the Parallel Line
[tex]y=\displaystyle \frac{1}{5} x-3[/tex]
Given this equation, we can identify that its slope (m) is [tex]\displaystyle \frac{1}{5}[/tex]. Because parallel lines always have the same slope, the slope of the line we're currently solving for would be [tex]\displaystyle \frac{1}{5}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle \frac{1}{5}x+b[/tex]
Now, to find the y-intercept, plug in the given point (5,-2) and solve for b:
[tex]-2=\displaystyle \frac{1}{5}(5)+b\\\\-2=1+b\\-2-1=b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=\displaystyle \frac{1}{5}x+b[/tex]:
[tex]y=\displaystyle \frac{1}{5}x+(-3)\\\\y=\displaystyle \frac{1}{5}x-3[/tex]
Our final equation is [tex]y=\displaystyle \frac{1}{5}x-3[/tex].
Finding the Perpendicular Line
[tex]y=\displaystyle \frac{1}{5} x-3[/tex]
Again, the slope of this line is [tex]\displaystyle \frac{1}{5}[/tex]. The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
To find the y-intercept, plug in the point (5,-2) and solve for b:
[tex]-2=-5(5)+b\\-2=-25+b\\-2+25=b\\23=b[/tex]
Therefore, the y-intercept is 23. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+23[/tex]
Our final equation is [tex]y=-5x+23[/tex].
I hope this helps!
A survey was conducted to see which of four major sports American college students prefer to watch: baseball, basketball, football, or soccer. Of those surveyed, 53% said they prefer football, 26% chose basketball, and 15% preferred baseball. If there were 1,000 American college students in a room, how many would you expect to prefer soccer?
Answer:
Step-by-step explanation:
53+26+15=94
94-100=6
So I'm just gonna assume that 6% of people prefer to watch soccer.
Now to solve how many people out of 1000 would watch soccer we'd have to multiply 1000 by 0.09 which gives us 90.
So 90 people out of 1000 would prefer to watch soccer.
1- Operations with Fractions
2 1/2 - 5/3
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{5}{6}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving the Problem...}}\\\\2\frac{1}{2} -\frac{5}{3}\\\\----------------\\\rightarrow \text{LCM} (2,3): 6\\\\\rightarrow 2\frac{1}{2}=\frac{5}{2}=\frac{5*3}{2*3}=\frac{15}{6}\\\\\rightarrow \frac{5}{3}=\frac{5*2}{3*2} =\frac{10}{6}\\\\\\\rightarrow \frac{15}{6} - \frac{10}{6}\\\\\rightarrow \boxed{\frac{5}{6}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Need help with solving please
Answer:
x=8
Step-by-step explanation:
4 ^(1/2x) = 256
Rewriting 256 as a power of 4
4 ^(1/2x) = 4^4
Since the bases are the same, the exponents are the same
1/2x = 4
Multiply each side by 2
1/2x *2 = 4*2
x=8
Miguel's coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $5.95 per pound, and Type B coffee costs $4.65 per pound. This month's blend used three times as many pounds of Type B coffee as Type A, for a total cost of $796.00. How many pounds of Type A coffee were used?
Answer: 40 lb of Type A
Step-by-step explanation:3 pounds of Type B and 1 pound of Type A will give 4 pounds of mix at a cost of ... 3($4.65) +($5.95) = $19.90Then $796 is the cost equivalent of 796/19.90 = 40 times that 4-lb mix. Since each instance of that 4-lb mix has 1 lb of Type A, $796 worth of blend has 40 lb of Type A coffee._____Additional commentIf you'd like to do this using a variable, you can let 'a' represent the amount of Type A coffee used. Then (3a) is the amount of Type B, and the total cost is ... 5.95a +4.65(3a) = 796 19.90a = 796 . . . . . . . . simplify a = 796/19.90 = 40 . . . as above___There will be 120 lb of Type B coffee in that amount of blend.
The amount of Type A coffee that were used is 40 pounds.
What are word problems in Algebra?Word problems in Algebra can be solved by correctly identifying the parameters given and the one(s) meant to be solved with the appropriate use of arithmetic operations.
From the given information;
Type A coffee costs Miguel $5.95 per poundType B coffee costs $4.65 per pound.For this month, the equation can be expressed as:
A + 3AThus;
5.95A + 3(4.65)A = 796.005.95A +13.95A = 796.0019.9A = 796.00A = 796.00/19.9A = 40Therefore, we can conclude that the amount of pounds of type A coffee that were used is 40 pounds.
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How would you write 5x5x5x5x5x5 in exponential form
Answer:
5^6
Step-by-step explanation:
This is because the exponent is how many numbers are in the multiplication equation, in this case, five. Because there are six five's being multiplied together, our exponent is six.
4. 2) 836
does anyone know this?
Answer:
418
Step-by-step explanation:
2) 836 = 836/2
=418
•°•2) 836=418
Answer:
836/2=418,Hope it helps.
PLZZ HELP ME (50 POINTS)
Answer:
x = w / 57r is the answer
Given that LMN and PQR are
complementary angles, find the measures
of the angles if the m LMN = 8x + 1 and
the m PQR = 2x + 9.
Answer:
∠ LMN = 65° , ∠ PQR = 25°
Step-by-step explanation:
Complementary angles sum to 90°
∠ LMN + ∠ PQR = 90° , that is
8x + 1 + 2x + 9 = 90
10x + 10 = 90 ( subtract 10 from both sides )
10x = 80 ( divide both sides by 10 )
x = 8
Then
∠ LMN = 8x + 1 = 8(8) + 1 = 64 + 1 = 65°
∠ PQR = 2x + 9 = 2(8) + 9 = 16 + 9 = 25°
In a survey of mobile and telephone, it was found that 200 people had telephone, 25
had both, 135 did not have telephone and 300 did not have mobile.
i. How many people participated in the survey?
ii. How many people had mobile only
Answer:
a)660
b)135
Step-by-step explanation:
a)200+25+135+300=660
b) 135 because since 135 do not have telephone, they will have mobile instead.
Hope this helps! Thanks.
If there are 2.54 centimeters in 1 inch, how long in inches is a meter stick? Hint: There are 100 centimeters in 1 meter. Round your answer to the nearest hundredth.
Answer:
i dont know that well but i do know 1 meter is roughly 2ft, so id say about 25.5 inches
0.01 inch is the length of a meter stick.
To find the length of a meter stick in inches, we can use the conversion factor:
1 meter = 100 centimeters
1 inch = 2.54 centimeters
We can set up the proportion:
1 meter / 100 centimeters = x inches / 1 inch
Cross-multiplying:
1 meter × 1 inch = 100 centimeters × x inches
x = (1 meter × 1 inch) / (100 centimeters)
x = 1 inch / 100
x = 0.01 inch
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Tom and Larry are food inspectors at a cookie making company. Tom tests every 8th batch of dough for fat percentage. Larry tests every 28th batch of dough for carbohydrate percentage. If they both start working at the same time, which batch will be the first that they both test?
9514 1404 393
Answer:
56th batch
Step-by-step explanation:
The least common multiple of 8 and 28 is 8·7 = 56. Tom and Larry will both test the 56th batch.
__
There are a couple of ways to find the least common multiple (LCM) of a pair of numbers.
1. Factor them and use the highest power of the unique factors.
8 = 2³
28 = 2²×7
Unique factors are 2 and 7. Their highest powers are 3 and 1, so the LCM is ...
(2³)(7) = 56
__
2. Divide the product by the greatest common divisor (GCD). Here, both numbers are divisible by 4:
8 = 4·2
28 = 4·7
So, the LCM is 8×28/4 = 56.
Answer:
Step-by-step explanation:
8=2x2x2
28=2x2x7
lcm of 8,28= 56
Is [tex] \frac{1}{ \sqrt{5} } [/tex] a rational or a non-rational number
Answer:
yes it is a rational number..
brainiest to whoever right
Answer:
The area is 7.5 square units
what is the 30th square number
plz tell the answer
Answer:
900
.........................
Answer:
900
Step-by-step explanation:
30 square is like 30×30=900
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) to the left or shift it up
Part B
f(x+k) for a shift to the left
f(x) + k for a shift up
Part C
Looking at shifting f(x) to g(x) by going left, we are shifting 6 units to the left
f(x+6) will shift f(x) 6 units to the left
g(x) = f(x+6)
We can all shift f(x) up, we can shift up 18 units
f(x) +18 will shift the function up 18 units
g(x) = f(x) +18
please solve this question i need help
Answer:
a=50
b=130
c=130
Step-by-step explanation:
2a-50=a(vertically opposite angles)
a=50
a+c=180(angles on straight line)
50+c=180
c=180-50=130
b=c(vertically opposite angles)
b=130
ans all these questions please
Answer:
the answer is in picture
a cylindrical barrel contains 42 gallons of oil the diameter is 18 inches. determine the radius of a barrel in centimetres
Help me please! What shape is it?
You're a square !!!1!!!!!!!!11
from 8 abc subtract abc. from 8 abc subtract 8
after a 20% reduction, you purchase a television for $336. What was the television's price before the reduction?
What’s the answer for 5g=20
simplify the expression 44=5g-8-g
Answer:13
Step-by-step explanation:
Choose the correct option
Answer:
(c)
Step-by-step explanation:
for the volume of a box all three dimensions must be multiplied with each other to create a cubic result.
3x²y × 4y²z × 5z²x
we need to combine the elements belonging to each other = that can be combined for simplification :
the constants, the x, the y and the z.
3×4×5 = 60
x²×x = x³
y×y² = y³
z×z² = z³
so, in total, that multiplication result is
60x³y³z³
therefore, (c) is the right answer
Answer:
volume of a retagular box whose adjacent egged 3x²y , 4y²z and 5z²x respectively is
( C ) 60x³y³z³
Step-by-step explanation:
hope it's help
#MASTER GROUP
# FIRST MASTER
# PHILIPPINES
Matrix addition is shown here.
([3,-2,3],[-5,2,11])=([-5,-4,4],[-4,2,-1])=([m,-6,-2],[-9,7,5])
Enter the value of s
Answer:
The value of s=10
Step-by-step explanation:
11+(-1)=10
In a charity triathlon, Mark ran half the distance and swam a quarter of the distance. When he took a quick break to get a drink of Gatorade, he was just starting to bike the remaining 24 miles. What was the total distance of the race?
The total distance of the race is D = 96 miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let's denote the total distance of the race as "d" miles.
According to the given information, Mark ran half the distance and swam a quarter of the distance. This can be expressed as:
Distance Mark ran = d/2 miles
Distance Mark swam = d/4 miles
After Mark's quick break, he was just starting to bike the remaining 24 miles. Since he has already completed running and swimming, the total distance he has covered at that point is:
And this distance is equal to 24 miles, as given in the problem:
d/2 + d/4 + 24 = d
On simplifying the equation , we get
( 3/4 )d + 24 = d
Subtracting ( 3/4 )d on both sides , we get
( 1/4 )d = 24
Multiply by 4 on both sides , we get
d = 96 miles
Hence , the total distance of the race, denoted by "d", is 96 miles
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