Answer:
95/4
Step-by-step explanation:
Given,
a/b =2/3
Therefore, 2a²+3b²/a²+b² = ?
We get,
a/b = 2/3
So, we can write
a = 2 and b = 3
Now,
2×(2)² + 3×(3)²/(2)² + (3)² [Putting the values of a and b]
= 2×4 + 3×9/4 + 9
= 8 +27/4 + 9
= (32+27+36)/4 [ Taking L.C.M, we get 4]
= 95/4
Find all values of x for which the series converges. (Enter your answer using interval notation.) [infinity] 9 x − 7 9 n n = 0 For these values of x, write the sum of the series as a function of x.
Answer:
The series converges to [tex]$ \frac{1}{1-9x} $[/tex] for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]
Step-by-step explanation:
Given the series is [tex]$ \sum_{n=0}^{\infty} 9^n x^n $[/tex]
We have to find the values of x for which the series converges.
We know,
[tex]$ \sum_{n=0}^{\infty} ar^{n-1} $[/tex] converges to (a) / (1-r) if r < 1
Otherwise the series will diverge.
Here, [tex]$ \sum_{n=0}^{\infty} 9^n x^n = \sum_{n=0}^{\infty} (9x)^{n} $[/tex] is a geometric series with |r| = | 9x |
And it converges for |9x| < 1
Hence, the given series gets converge for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]
And geometric series converges to [tex]$ \frac{a}{1-r} $[/tex]
Here, a = 1 and r = 9x
Therefore, [tex]$ \frac{a}{1-r} = \frac{1}{1-9x} $[/tex]
Hence, the given series converges to [tex]$ \frac{1}{1-9x} $[/tex] for [tex]$ \frac{-1}{9} < x < \frac{1}{9} $[/tex]
The diagonal of a rectangle is 10 units. The width is 6 units, What is the area of the rectangle in square
units?
Answer:
48 square units
Step-by-step explanation:
Let the length of the rectangle be x units.
By Pythagoras theorem:
[tex]x = \sqrt{ {10}^{2} - {6}^{2} } \\ x = \sqrt{ 100 - 36 } \\ x = \sqrt{64} \\ x = 8 \: units \\ [/tex]
Length of rectangle = 8 units
Area of rectangle
= Length * width
= 8 * 6
= 48 square units
You are a furniture restorer who is mixing a solution of olive oil and lemon juice. The solution is for polishing wooden furniture to give it a shine and a fresh scent. You fill 50% of a cup with lemon juice and 25% of a quart with olive oil. Afterwards, you mix the olive oil and the lemon juice in another container. How many cups of the solution do you have for polishing wooden furniture? 1.5 2.0 2.5 4.5 5.0
The correct answer is A. 1.5 cups
Explanation:
The total of polishing wooden furniture is equivalent to the total of olive oil plus the total of lemon juice. Additionally, in this case, the result should be given in cups. First, let's consider the values given.
50% of a cup of lemon juice + 25% of a quart with olive oil
The first quantity 50% of a cup of lemon indicates half cup of lemon was added, which is equivalent to 0.5 cups as 1 cup = 100% of a cup and 50% is the half.
Now, the second quantity is provided in quarts, which is not the same as a cup. Indeed 1 quart is equivalent to 4 cups, which represents 100%. This means 100% = 4 cups. Now, to calculate the 25% follow this procedure.
1. Write the values
4 = 100 (total percentage)
x = 25 (percentage to be calculated
2. Solve this by using cross multiplication
x100 = 4 × 25
x100 = 100
x = 100 ÷ 100
x = 1 (cups in 25%)
This means 1 cup of olive oil was added and this plus 0.5 cup of lemon juice is equivalent to 1.5 cups of solution.
Need help... Thank you
Answer:
3
because that's the definition of corresponding angles
-6= 2(w + 5) PLEASE ANSWER AND SHOW WORK!!!
Answer:
[tex]w=-8[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-6=2(w+5)[/tex]
First, distribute the right side:
[tex]-6=2(w)+2(5)\\-6=2w+10[/tex]
Subtract 10 from both sides. The right cancels:
[tex](-6)-10=(2w+10)-10\\-16=2w[/tex]
Divide both sides by 2. The right cancels:
[tex](-16)/2=(2w)/2\\-8=w[/tex]
Flip:
[tex]w=-8[/tex]
Thus, the value of w is -8.
Answer:
-8 = w
Step-by-step explanation:
-6= 2(w + 5)
Divide each side by 2
-6/2= 2/2(w + 5)
-3 = w+5
Subtract 5 from each side
-3-5 = w+5-5
-8 = w
Evaluate the Expression
If x = -3, y = 6, and z = -5
-15 + x + y =
Answer:
-12
Step-by-step explanation:
-15+x+y=
-15+(-3)+6
-15-3+6
-15+3
-12
a car takes 8 hours to reach to its destination with a speed of 75km/hr. how much time will it take if the speed is 60km/hr?
Answer:
10 hours
Step-by-step explanation:
speed = distance/time
s = d/t
d = st
d = 75 km/h * 8 h = 600 km
t = d/s
t = 600 km/(60 km/h) = 10 h
Answer: 10 hours
Chen took 54 photos with his digital camera. He stored an equal number of photos in each of 6 folders on his computer. Which multiplication sentence could Chen use to find the number of photos in each folder? 0 6 X 54 = 324 0 54 + 6 = 9 O 6 X 9 = 54 O 5 X 9= 45 plz help me
Answer:
6x9=54
Step-by-step explanation:
6 folders with 9 photos in each = 54 photos all together.
The area of the indoor sports exhibition is shown below. What is its perimeter? m What is its area? m2
Answer:
Area = 3097.96[tex]m^{2}[/tex]
Perimeter = 270.96m
Step-by-step explanation:
Step 1: State the shapes making up the indoor sports exhibiti[tex]\pi[/tex]on
2 rectangles
1 semi circle
Step 2: Find the area and perimeter of the shapes
ARectangle1 = lw = (10)(40) = 400m^2
PRectangel1 = 2l + w = 2(10) + 40 = 60m
ARectangle2 = lw = (33)(68) = 2244m^2
PRectangel2 = l + w = 33 + 68 = 101m
ASemiCicle = [tex]\frac{\pi r^{2}}{2} =\frac{\pi 17^{2} }{2} =\frac{289\pi }{2}=144.5\pi=453.96m^{2}[/tex]
PSemiCircle = [tex]2\pi r=2\pi(17)=35\pi =109.96m[/tex]
Step 3: Add up the areas and perimeters
Area = 400 + 2244 + 453.96
Area = 3097.96[tex]m^{2}[/tex]
Perimeter = 60 + 101 + 109.96
Perimeter = 270.96m
Therefore the area of the indoor sports exhibition is 3097.96[tex]m^{2}[/tex] and the perimeter is 270.96 m
Assignment
Section (A) 5 Marks
Q.No. 1. Do as directed;
(1) Which one of the following is square of 4;
a) 2
b) 8
c) 16
d) 64
(II)Unit digit in the square of 3457 is;
a) 3
b) 7
c) 4
d) 9
(III) Cube root of 64 is;
a) 8
b) 4
c) 2
d) 10
(IV) Ratio of 2:4 is;
a) 4:1
b) 1:2
c) 1:3
d) None of these
(V) Discount =
a) Marked Price - Sale Price
B) Sale Price - Marked Price
......
I need help with the questions could someone answer them all?
Answer:
circumference= 40.82 cm
Step-by-step explanation:
formula circumference= 2 x pi x radius ( 2 x 3.14x 6.5)
3) shaded region = area circle - area rectangle = 132.665 cm - 60 cm^2= 72.665 cm^2
4) 1 foot = 30.48 cm, 6 feet = 182.88 cm = radius 182.88 cm area circle = pi x square radius = 3.14 x 182.88 ^2 ----------> 3.14 x 33445.0944 =105017.5964 cm^2
if 5.49 = 70% , 100% = x so 5.49 x 100 divided 70 = X so X = 7.844 then 5.49 is the 70 % of 7.844
if 6.99 is 36% of something, 6.99 = 36%
X = 100%
so 6.99 x 100 = X (equis) x 36%
6.99 x 100 / 36 = X, so X = 19.416 . 6.99 is the 36% of 19.416
M. Score: 0 of 1 pt
5 of 12
5.1.35
Find the prime factorization of the composite number.
795
795 =
(Type your answer using exponential notation.)
Answer:
3×5×53
Step-by-step explanation:
You can use divisibility rules to find the small prime factors.
The number ends in 5, so is divisible by 5.
795/5 = 159
The sum of digits is 1+5+9 = 15; 1+5 = 6, a number divisible by 3, so 3 is a factor.
159/3 = 53 . . . . . a prime number,* so we're done.
795 = 3×5×53
_____
* If this were not prime, it would be divisible by a prime less than its square root. √53 ≈ 7.3. We know it is not divisible by 2, 3, or 5. We also know the closest multiples of 7 are 49 and 56, so it is not divisible by 7. Hence 53 is prime.
Help!!! PLEASE Math Hurry I have 10mins to finish
Answer:
x0 is the answer I just did that question and got it right
Answer: Answer is in the steps
Step-by-step explanation:
If we given the angle measure in variables then we will sum them up equal 180 and solve for x to determine the angle measure.
9x + x +x+4 = 180
11x + 4 = 180
-4 -4
11x = 176
x=16
In this case we can find the angle measures by using the expressions.
x = 16 degrees
x+4 = 20 degrees
9x = 144 degrees
Paul purchased 8 computers which cost him a total of $6,016, and Mary purchased 8 printers which cost her $1,080.
Steve purchased 25 DVD movies which cost $350, and Sally purchased 34 CD’s which cost $306. How much would 7 computers, 9 printers, 23 DVD’s, and 30 CD’s cost?
triangle town wants to build a school that is equidistant from its three cities L,M, and N. Which construction correctly finds the best location of the school? A. Construction Y because point E is the incenter of triangleLMN B. Construction Y because point E is the circumcenter of triangleLMN C. Construction X because point C is the incenter of triangleLMN D. Construction X because point C is the circumcenter of triangleLMN
Answer:
C. Construction X because point C is the incenter of triangle LMN.
Step-by-step explanation:
The construction requires that the school must be at equal distance to cities of the triangle town. Thus, it must be located at the point of intersection of the straight path from the three cities L, M, and N.
To be able to construct the school with the specification, option C is the most suitable. Construction X describe the appropriate method because point C is the incenter of triangle town of cities L, M, and N.
Answer:
A
Step-by-step explanation:
Construction Y because point E is the circumcenter of Triangle LMN
A manufacturer buys large quantities of certain fuel pumps. He finds that his cost depends on the number of cases, q, bought at the same time according to the table below, where cost(q), measured in dollars, is the total cost of purchasing q cases. Find the marginal cost at q = 108.
9 96 100 104 108 112 116 cost(q)
1780 1850 1920 1990 2060 2120
a) $15.80/case
b) $10.50/case
c) $17.50/case
d) $14.00/case
Answer:
The correct option is c) $17.50/case.
Step-by-step explanation:
Note: The data in the question are merged. The data are therefore sorted and the whole question is represented before answering the question. Please, see the attached pdf file for the sorted data and the represented question.
The explanation of the answer is now given as follows:
Marginal cost refers to the cost incurred in order to produce one more unit of a product.
Therefore, marginal cost is the change in the total cost that is caused by a one-unit increase in the quantity of a commodity that is produced.
From the table in the question, the marginal cost at q = 108 can be calculated as follows:
Change in total quantity at 180 cases = 108 - Number of cases immediately before 108 = 180 - 104 = 4
Change in total cost at 180 cases = Total cost at 108 cases - Total cost immediately before 108 cases = 1990 - 1920 = 70
Marginal cost at 108 cases = Change in total cost at 180 cases / Change in total quantity at 180 cases = 70 / 4 = 17.50 per case
Therefore, the correct option is c) $17.50/case.
Evaluate -x+(-8) for x= 7.1
Answer:
-15.1
Step-by-step explanation:
Answer:
-15.1Step-by-step explanation:
[tex]-x+(-8) \\\\x = 7.1[/tex]
Substitute 7.1 for x in the given equation
[tex]-(7.1 )+(-8)[/tex]
Remove parentheses (a)=a
[tex]=-7.1-8[/tex]
Subtract the numbers: -7.1-8=-15.1
[tex]-15.1[/tex]
After using a 15% off coupon, the price of a sheet cake is $30.94. What was the original price?
Answer:
The original price was 36.40
Step-by-step explanation:
p = original price of cake
using the coupon
p - 15% off = 30.94
p - .15 p = 30.94
Combine like terms
.85p = 30.94
divide each side by .85
p = 30.94/.85
p =36.40
The original price was 36.40
2x-(x-(2x+3)-3x-11 help plssss
Answer:
I'll say x = 8
Step-by-step explanation:
because Simplifying
2x + -3 = 3x + -11
Reorder the terms:
-3 + 2x = 3x + -11
Reorder the terms:
-3 + 2x = -11 + 3x
Solving
-3 + 2x = -11 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-3 + 2x + -3x = -11 + 3x + -3x
Combine like terms: 2x + -3x = -1x
-3 + -1x = -11 + 3x + -3x
Combine like terms: 3x + -3x = 0
-3 + -1x = -11 + 0
-3 + -1x = -11
Add '3' to each side of the equation.
-3 + 3 + -1x = -11 + 3
Combine like terms: -3 + 3 = 0
0 + -1x = -11 + 3
-1x = -11 + 3
Combine like terms: -11 + 3 = -8
-1x = -8
Divide each side by '-1'.
x = 8
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 4x - 14}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2x - x - (2x + 3) - 3x - 11}[/tex]
When there is a ( - ) in front of parentheses in an expression, change the sign of each term
⇒[tex] \sf{2x - x - 2x - 3 - 3x - 11}[/tex]
Collect like terms
⇒[tex] \sf{2x - x - 2x - 3x - 3 - 11}[/tex]
Since the terms having opposite signs adds up to zero, remove them from the expression
⇒[tex] \sf{ - x - 3x - 3 - 11}[/tex]
⇒[tex] \sf {- 4x - 14}[/tex]
Hope I helped!
Best regards!!
PLEAAASE ANSWER TIMER IS RUNNING OUT
Answer:
the correct answer is 1/2.
How i came to this answer was adding all of the number of medals together for all of the years, coming up to a total of 22. When asking about probability of any given set or amount of things, you always take the selected values and take them out of the whole amount. Years 2009 and 2012 have a whole selected value of 11 (4+7). Therefore you're "taking" 11 from 22, coming up with the fraction 11/22 seeing as that is not a answer choice the next step is to simply the fraction to 1/2.
Answer:
C Mark me as brainliest!!!
Step-by-step explanation:
Determine whether the situation involves permutations or combinations. Then solve. How many ways are there to place an algebra book, a geometry book, a chemistry book, an English book, and a health book on a shelf?
Answer:
The situation involves permutationThe number of arrangement is 120Step-by-step explanation:
Given that
Algebra book=1
Geometry book=1
Chemistry book= 1
English book= 1
Health book= 1
Total number of books N = (1+1+1+1+1)= 5
Permutation is used to determines the number of possible arrangements in a set when the order of the arrangements is crucial.
Number of arrangements = N!
Number of arrangements= 5*4*3*2*1= 120
Can someone help my solve this?
you can write yd^2 or [tex]yd^{ \ 2}[/tex] to indicate "square yards"
=========================================================
Work Shown:
The triangle has a base of 3+3+2 = 8, and a height of 7
A = area of triangle
A = 0.5*base*height
A = 0.5*8*7
A = 28
The rectangle has a length and width of 3 and 2
B = area of rectangle
B = length*width
B = 3*2
B = 6
The shaded area is the difference of the two areas
C = area of shaded region
C = A - B
C = 28 - 6
C = 22
The expression 6n-3006n−3006, n, minus, 300 describes the amount of profit the school makes from the dance if nnn students buy tickets. What does 6n6n6, n represent in this context? Choose 1 answer: Choose 1 answer: (Choice A) A The amount of money the school charges for all nnn tickets (Choice B) B The amount of money the school spends on the dance (Choice C) C The number of students who buy tickets (Choice D) D The profit the school earns per ticket
Answer:
A The amount of money the school charges for all n tickets
Step-by-step explanation:
The number 6 in the term 6n is the "marginal" profit, the additional profit earned from the sale of 1 more ticket. Then 6n represents the revenue from the sale of all n tickets.
What are axioms in algebra called in geometry?
What are axioms in algebra called in geometry
Answer:
Axioms are generally statements made about real numbers. ... Sometimes they are called algebraic postulates. Often what they say about real numbers holds true for geometric figures, and since real numbers are an important part of geometry when it comes to measuring figures, axioms are very useful
please helppppppppppppppppppppppppppppp
Answer:
54
Step-by-step explanation:
angle A+angle B+Angle C =180 degree [ angle sum property of a triangle]
36 +90 + angle B =180 degree
126 +angle B =180 degree
angle B= 180-126
54 degree
Ans
What is 3+(−4)−8−(−1)?
Answer:
-8
Step-by-step explanation:
3+(−4)−8−(−1)=-8
x?(y + 1)) if x = -3 and y = 2
Answer:
-9
Step-by-step explanation:
add x and y to the equation.
so now its -3(2+1)
add 2 and 1
now its -3(3)
multiply.
now its -9
Answer:
-9
Step-by-step explanation:
Hello!
It is asking us for the answer when x = -3 and y = 2 so we put in those values for x and y
-3(2 + 1)
Now follow PEMDAS
-3(3) = -9
The answer is -9
Hope this helps!
Rosie did the following problem. (7-1) 2 ÷ 6 + 4 · 3 6 2 ÷ 6 + 4 · 3 36 ÷ 6 + 4 · 3 6 + 4 · 3 10 · 3 30 Which statement best describes her answer?
Rosie is incorrect because she needs to do the exponent before subtracting. Rosie is incorrect because she needs to multiply before she divides. Rosie is incorrect because she needs to multiply before she adds. Rosie is correct.
Solve for the variables in each triangle below.
Answer:
A) 41 degrees
Step-by-step explanation:
A) SohCahToa
20 = hyp.
15 = adj.
therefore, use Cos (Cah).
cos x = 15/20
x= cos^-1 (15/20)
x= 41 degrees
The required values are shown below.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.
Since, All the triangle are right angle triangle.
Use right angle properties,
(a)
To find the value of θ,
Use cos θ = base/hypotenuse = 15 / 20 = 3/4
cos θ = 3/4
θ = cos⁻¹ (3/4)
θ = 41.41
The value of θ is 41.41°.
(b)
Use sin θ = 3/10 =
θ = 17.45
The value of θ is 17.45.
(c)
Use Pythagorean theorem,
x² + x² = 5²
2x² = 25
x² = 25/2
x = 5/√2
(d)
sin30 = x / 8
1/2 = x/8
x = 4
cos 30 = y / 8
√3 / 2 = y/8
y = 4√3
The values of x and y are 4 and 4√3 respectively.
To know more about Triangle on :
https://brainly.com/question/2773823
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The ratio of adults to children on a field trip is 2:7. If there are 14 adults on the trip, how many children are there?
Answer:
49 children
Step-by-step explanation:
Adult : Child = 2 : 7
Adult = 14
2 = 14
So, 1 = 14/2 = 1 = 7 in the ratio.
So, 7 x 7 = 49 children are there.
Answer:
49
Step-by-step explanation:
Let's set up a proportion!
2 14
-- --
7 x
Now, we cross multiply
14 times 7 = 98
2 times x = 2x
98 = 2x
98 divided by 2 equals 49