Answer:
1 ⅓
Step-by-step explanation:
there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓
Given the polynomial 9x2y6 − 25x4y8, rewrite as a product of polynomials.
(9xy3 − 25x2y4)(xy3 + x2y4)
(9xy3 − 25x2y4)(xy3 − x2y4)
(3xy3 − 5x2y4)(3xy3 + 5x2y4)
(3xy3 − 5x2y4)(3xy3 − 5x2y4)
Answer:
Option 3
(3xy³ + 5x²y⁴) (3xy³ - 5x²y⁴)
Step-by-step explanation:
Factorize polynomials:
Use exponent law:
\(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)
9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²
25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²
Now use the identity: a² - b² = (a +b) (a -b)
Here, a = 3xy³ & b = 5x²y⁴
9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²
= (3xy³)² - (5x²y⁴)²
= (3xy³ + 5x²y⁴) (3xy³ - 5x²y⁴)
a A factory worker packs 2 ^ 5 mugs into the bottom layer of a box for shipping . If each box can hold 6 layers of mugs , how many mugs can be packed into each box ?
for questions that require a numerical answer, you may be told to round your answer to a specified number of decimal places or you may be asked to provide an exact answer. when asked to provide an exact answer, you should enter repeating decimals in their fraction form and irrational numbers such as e^5, ln(4), or V2 in their symbolic form. consider the function f(x)= e^x +1/3x a. Find f(5), Give an exact answer b. Find f(11), Give your answer rounded to 3 decimal places
The value of f(5) is e^5 + 5/3, which is exactly 150.0798257693, and the value of f(11) is e^11 + 11/3, which is approximately 59877.808.
The function is f(x)= e^x + 1/3x
To find the value of f(5), put the value of x = 5 in the function f(x)= e^x + 1/3x. Which is equal to f(5) = e^5 + 5/3.
Similarly, to find the value of f(11), put the value of x = 11 in the function f(x)= e^x + 1/3x.
Which is equal to f(11) = e^11 + 11/3
f(11) = 59874.141715198 + 3.6666666667
f(11) = 59877.808381865
f(11) ≈ 59877.808
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the running club has $1,328 to spend on new uniform. of each uniform cost $52 how many uniforms can they buy?
Answer: The running club can buy 25 uniforms
Step-by-step explanation: If the running club has $1,328 to spend on new uniforms and each uniform costs $52, we can find the number of uniforms they can buy by dividing the total amount of money by the cost of each uniform:
$1,328 ÷ $52 = 25.54
Therefore, the running club can buy 25 uniforms with $1,328.
I hope this helps, and have a great day!
Mathematics
Simplify the following equation: (5 + √ 3)²
If you know how to do it please provide a step by step explain ation.
Thank you.
Answer:
\(25 + 10 \sqrt{3} + 3\)
Step-by-step explanation:
\((5 + \sqrt{3} )^{2} \\ (5 + \sqrt{3} )(5 + \sqrt{3} ) \\ 5(5 + \sqrt{3} ) + \sqrt{3} (5 + \sqrt{3} ) \\ 25 + 5 \sqrt{3} + 5 \sqrt{3} + 3 \\ 25 + 10 \sqrt{3} + 3\)
WILL GIVE BRAINLIESTTT!!!! PLS HELP
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Create a proportion using the form %/100 = is/of to represent the following word problem.
Seven is what percent of 30?
PLEASE HELP ITS MATH THANK YOUUUU
Answer:
99000 millimeters kdknwjdhdiqkwpshd
What are the solutions of the equation x^2+6x-9=0
Answer:
Below
Step-by-step explanation:
x^2 + 6x + 9 = 0 can be factored to
(x+3)(x+3) = 0 showing that x = -3 is a double root solution
Find the dicontinuities of the function.
f(x) =
x2 + 12x + 27
x2 + 4x + 3
.
There is a removable discontinuity at
(
,
).
Answer:
Step-by-step explanation:
I'm assuming you meant to type in
\(f(x)=\frac{x^2+12x+27}{x^2+4x+3}\) because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to
\(f(x)=\frac{(x+3)(x+9)}{(x+1)(x+3)}\) and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.
The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!
Using only 3,4&5 what equals 11
(5×3)-4 = 11
hope it helps...!!!
Answer:
(5*3)-4=11
Step-by-step explanation:
because when you multiply 5*3=15, then subtract 4 from it, it gives you 11. There are no other options becuase 5*4-3=17 and 4*3-5=16 and 5*4+3=23 and 4*3+5=17.
If P(2,4) and Q(-3,2),
then the slope of PQ is. Find
the slope of P'Q' under the
translation T(x, y) = (x + 3, y − 4).
Simplify completely
Step-by-step explanation:
The slope of the line passing through the points P(2, 4) and Q(-3, 2) can be found using the slope formula:
slope of PQ = (change in y) / (change in x) = (2 - 4) / (-3 - 2) = -2 / -5 = 2/5
To find the slope of the translated line P'Q', we need to first apply the translation T(x, y) = (x + 3, y − 4) to the original points P and Q to get their new coordinates:
P' = T(P) = (2 + 3, 4 − 4) = (5, 0)
Q' = T(Q) = (-3 + 3, 2 − 4) = (0, −2)
Now we can find the slope of P'Q' using the new coordinates:
slope of P'Q' = (change in y) / (change in x) = (-2 - 0) / (0 - 5) = 2/5
Therefore, the slope of P'Q' is also 2/5, which is the same as the slope of PQ. This means that the translation T(x, y) = (x + 3, y − 4) did not change the slope of the line PQ.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.
We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding
m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.
m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.
m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).
m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.
m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.
Based on the above analysis, the statements that are always true regarding the diagram are
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 = 180°
m∠2 + m∠3 + m∠5 = 180°
Therefore, the correct options are B, C, and E.
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If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=8/17and cos b=12/13
1) -220/221
2) -140/221
3) 140/221
4) 220/221
Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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If △EFG ≅ △NML, what are the congruent corresponding parts?
Answer:
c
Step-by-step explanation:
100% sure and correct :) ❤️
can someone help me solve this problem
Answer:
18 and 40
Step-by-step explanation:
Let x be the age of Claire and y the age of her mother
Claire's mother is 4 years more than twice Claire's age
y = 2x+4The sum of their ages are is 58
x+y = 58the system is:
\(\left \{ {{y=2x-4} \atop {y+x=58}} \right.\)
Multiply (y+x = 58) by -1 and then add it to (y = 2x+4) to eliminate y
-y-x = -58 -y-x+y = 2x+4-58 -x -2x = -54-3x = -54x = 54/3x = 18y= 58-18 = 40
so claire's mother is 40 years old and claire is 18
A section of a rectangle is shaded to form a trapezoid. The lengths of the 2 bases are 7 and x. The length of a side that forms a right angle with side x is 7. A section of a rectangle is shaded. The area of the shaded section is 63 square units. What is the value of x?
Given the shaded area of 63 square units, and the lengths of the bases and the right angle side, we can set up an equation using the formula for the area of a trapezoid. By solving this equation, we find that x is equal to 11.
Let's analyze the given information step by step to find the value of x.
We have a rectangle with two bases, one measuring 7 units and the other measuring x units. Additionally, there is a right angle formed with side x, which means that the height of the trapezoid is also 7 units. We are told that the area of the shaded section is 63 square units.
The formula to calculate the area of a trapezoid is (base1 + base2) * height / 2. Applying this formula to our situation, we can write the equation as (7 + x) * 7 / 2 = 63.
Simplifying the equation, we have (7 + x) * 7 = 126.
Expanding, we get 49 + 7x = 126.
Subtracting 49 from both sides, we have 7x = 77.
Dividing both sides by 7, we find x = 11.
Therefore, the value of x is 11.
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If two lines intersect and one of the angles formed has a measure of 67º, which of the following statements are true? Explain your answers
More than one answer may be correct, select all correct answers
A: Vertical angles are congruent, therefore another angle must equal 67º
B: The lines form linear pairs
C: The lines form complementary angles
D: One of the angles formed measures 23º
E: Two of the angles formed measure 113º
F: Two of the angles formed will have a sum of 180º
G: None of the above
The statements that are true are:
A : Vertical angles are congruent, therefore, another angle must equal 67°
F: Two of the angles formed will have a sum of 180°
What happens when two lines intersect?
When two lines intersect, their vertical angles are always the same and the sum of the two angles on a straight line is 180°
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PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.
Answer:
321.50 dollars.
Step-by-step explanation:
Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.
This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.
Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.
Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.
Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.
27. What is the reflection image of (5, –3) across the y-axis? (–5, 3) (–5, –3) (–3, 5) (5, 3)
The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).
Tiago has. 60 marbles
and his cousin has one fifth
of Tiagos marbles, how many
marbles does the two cousins have?
Answer:
12
Step-by-step explanation:
Sam has a deck that is shaped like a triangle with a base of 18 feet and a height of 7 feet. He plans to build a 2:5 scaled version of the deck next to his horse's water trough.
Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points)
Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points)
Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;
Part A; Base length of the new deck = 7.2 feet
Height of the new deck = 2.8 feet
Part B; The area of the original deck is 63 square feet
The area of the new deck is 10.08 square feet
Part C; The ratio of the areas is the square of the scale factor
What is a scale factor?A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.
The base length of the triangular deck = 18 feet
The height of the triangular deck = 7 feet
The scale factor for the scaled version Sam intends to build = 2 : 5
Part A; The dimensions of the new deck are;
Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet
The height of the new deck = (2/5) × 7 = 2.8 feet
Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet
Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet
Part C; The ratio of the areas is; 10.08/63
Ratio of the area = 10.08/63 = 4/25 = 4 : 25
The scale factor is; 2 : 5
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A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA = B + Ph, since the vase has a bottom but no top. Use 3.14 for π
and round to the nearest tenth of a square inch.
The surface area of the cylindrical pottery vase is 177.55 in².
Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,
SA of a cylinder = 2π×radius(h+r)
= 2×3.14×2.15(2.15+11)
= 177.55 in²
Hence, the surface area of the cylindrical pottery vase is 177.55 in².
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Put the following equation of a line into
slope-intercept form, simplifying all
fractions.
8y - 2x =-40?
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x)
\(\frac{1}{x}+\frac{2}{3x}\)
Answer:
5/3x
Step-by-step explanation:
1/x + 2/3x
LCM of ( x, 3x ) = 3x
1/x
= ( 1/x ) * ( 3/3 )
= ( 1 * 3 ) / ( x * 3 )
= 3/3x
1/x + 2/3x
= 3/3x + 2/3x
= ( 3 + 2 ) / 3x
= 5/3x
Estimate the distance you can travel in 6 hours 55 minutes if you drive on average 51 miles per hour. Round your answer to the nearest mile
- - - - - - - - - - - - - - - - - - - - - - - -
Heyo! Your explanation is below, if necessary.
- - - - - - - - - - - - - - - - - - - - - - - -
If it's 51 miles per hour, simply multiply the distance by the number of hours.
51 x 6 = 306
51 x 55/60 = 46.75
Now, add the products.
306 + 46.75 = 352.75
- - - - - - - - - - - - - - - - - - - - - - - -
Have a great day/night!
~pinetreee :)
Julio is playing a trivia game. On his first tum, he lost 120 points. On his second tum, he lost 75 points. On
his third tum, he lost 60 points. Enter a sum of three negative integers that models the change to Julio's
score after his first three turns. Enter the sum in the order of his turns.
Answer:
-120,-75,-60
(t)-120-75-60
Answer:
negative 255
Step-by-step explanation:
0-120=-120
-120-75=-195
-195-60=-255
hello there
I am looking for help here pls
Answer:
b
Step-by-step explanation:
I'm not sure how to explain this if it is correct plz mark as brainiest