Answer:
\( ( \frac{x}{6} + \frac{y}{2 \sqrt{a} } )( \frac{x}{6} - \frac{y}{2 \sqrt{a} }\)
Step-by-step explanation:
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⠀⠀Question :\( \sf \large\frac{ {x}^{2} }{36} - \frac{ {y}^{2} }{4a} \)
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⠀
⠀
⠀⠀Solution :⠀
Using (a² - b²) identity
(a² - b²) = (a + b)(a - b)
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⠀
\( \sf \large {( \frac{x}{6}) }^{2} - {( \frac{y}{2 \sqrt{a} }) }^{2} \\ \\ \boxed{ \large {\tt( \frac{x}{6} + \frac{y}{2 \sqrt{a} } )( \frac{x}{6} - \frac{y}{2 \sqrt{a} } )}}\)
44,518 ÷ 111 PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
401.063063063
Step-by-step explanation:
In the right trapezoid ABCD shown below, the dimensions of three sides, in inches, are shown. What is the perimeter of ABCD in inches?
The perimeter of ABCD in inches is 30 in.
What is perimeter?Perimeter is the measurement of the total distance around an object.
To calculate the perimeter of ABCD, we use the formula below
Formula:
P = /AD/+/AB/+/BC/+/CD/.......................... Equation 1Where:
P = Perimeter/AD/ = 4 in/AB/ = 9 in/CD/ = 12 inTo find /BC/ we use Pythagoras theorem
/BC/ = √(4²+3²)/BC/ = √25/BC/ = 5 inSubstitute these values into equation 1
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a stone is dropped from the top of a cliff. it is observed to hit the ground 5.78 s later how high is the cliff?
Using the formula;
H= ut + 1/2 gt²
The initial velocity = 0
Hence H= 1/2 gt²
g= 10m/s t= 5.78 s
H = 1/2 x 10 x 5.78²
H = 167.042 m
H = 167 m approximately
In the 21st century, Marco will celebrate his Nth birthday in the year N2. In what year did he celebrate his 13th birthday?
Marco celebrated his 13th birthday in the year 2021 - 13 = 2008.
In the 21st century, Marco will celebrate his Nth birthday in the year N2.
If Marco celebrates his Nth birthday in the year N2, we can say that Marco was born in N2 - N.
For example, if Marco is 30 years old in the year 2050 (N2 = 50), then he was born in 2020
N2 - N = 50 - 30
= 20
If Marco celebrated his 13th birthday in the year 20XX (let's say it is the year 2021), then he was born in
2021 - 13 = 2008.
Therefore, Marco celebrated his 13th birthday in the year 2021 - 13 = 2008.
Another way to approach this is to find the difference between N2 and N, which is the number of years between Marco's Nth and 1st birthdays.
Then, we can subtract that difference from the year of Marco's Nth birthday to get the year of his 13th birthday.
That is, N2 - N = number of years between Marco's Nth and 1st birthdays:
N2 - (N2 - N) = N, which is the year of Marco's Nth birthday
N - 13 = year of Marco's 13th birthday.
For example, if Marco is 25 years old in the year 2050 (N2 = 50), then N = 25 and his 13th birthday was in the year 2025 - 13 = 2012.
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Y=5x
A proportional relationship
Yes, the equation y = 5x represents a proportional relationship
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is y=5x.
In a proportional relationship, the ratio of y to x is constant.
In the given equation the variable x and y has a proportional relationship.
The equation is in the form of y=mx+b
the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.
Hence, Yes, the equation y = 5x represents a proportional relationship
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Find the surface area. Please help!! I need it quick
Answer:
This is a right trapezoidal prism.
To find the total surface area,
First we have to find the area of the 2 trapezoids.
Let us find now.
\(Area=2*\frac{1}{2} (a+b)*h\)
\(Area=2*\frac{1}{2} (1.4+2.3)*1.9\\\)
\(Area=3.7*1.9\)
\(Area = 7.03m^{2}\)
Now you have to find the areas of the 3 rectrangles.
Let us find now.
(4.8 × 2.1) + ( 4.8 × 2.3)+ ( 1.9 × 4.8)
10.08 m² + 11.04 m² + 9.12 m²
= 30.24 m²
Now let us find the total surface area of this solid.
7.03 m² + 30.24 m²
= 37.27 m²
If a train travels 420 miles in 24 hours, what is its unit rate of travel?
16 mph
19.5 mph
17.5 mph
15.2 mph
17.5mph
420÷24= 175
Hope this helped you- have a good day bro cya)
Answer:
17.5mph
Step-by-step explanation:
Help me and show your work.
Answer:
Infinite solutions
Step-by-step explanation:
Equation 1:
4x-6y=4
3(4x-6y=4)
12x-18y=12
Equation 2
(12x-18y=12)/3
4x-6y=4
They are the same equation, therefore, there are infinite solutions
rights answers only:)
The measure of angle 6 is 38°.
What are vertically opposite angles?
Vertically opposite angles are pairs of angles formed by two intersecting lines that are opposite to each other and share the same vertex but are not adjacent angles.
When two lines intersect, they form four angles at the intersection point. The vertical opposite angles are the pairs of angles that are opposite to each other and are not adjacent angles.
We know that, if two lies are parallel and a transversal cuts the lines.
then, the angle formed are corresponding angles ad the vertically opposite angles formed will be equal.
similarly, In the give figure,
we ca see that angle 6 ad angle 38 are vertically opposites angle.
so, angle 6 = 38°
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X-intercept (3,0) and y-intercept (0, -6).
Find the distance between 5,3 and -7,7 express as a radical or a number rounded to the nearest hundreth
Answer:
The distance between the given points is:
\(distance=\sqrt{160} =4\,\sqrt{10} \approx 12.65\)
Step-by-step explanation:
We use the distance formula on the coordinate plane:
\(distance=\sqrt{(x_2-x_1)^2+(y_2-y_i)^2} \\distance=\sqrt{(-7-5)^2+(7-3)^2}\\distance=\sqrt{(-12)^2+(4)^2}\\distance=\sqrt{144+16} \\distance=\sqrt{160} \\distance=4\,\sqrt{10} \\distance\approx 12.65\)
In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184 Please select the best answer from the choices provided A B C D
The value of CPI will be 178.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Now,
Since, In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Hence, The value of CPI will be;
CPI = 118.10 × 100 / 66.35
= 11810 / 66.35
= 178
Thus, The value of CPI will be 178.
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10 POINTS!!!!!!!!!!! PLEASE HELP QUICKLY!!!!!! SCREENSHOT ATTACHED
Answer:
18
Step-by-step explanation:
∠BCD=2x (alternate interior angles)
∠BCD+∠CDE=180° (same side interior angles)
Thus, 10x=180, meaning x=18.
Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
K = 1/3
The coordinates of the points after dilation is D'(-5/3,1), E'(1,-2/3), F'(5/3,-1), and C'(-1,-4/3)
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given that the scale factor is 1/3. The coordinates of the points after dilation is,
D(-5,3) = D'(-5/3,1)
E(3,-2) = E'(1,-2/3)
F(5,-3) = F'(5/3,-1)
C(-3,-4) = C'(-1,-4/3)
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A rectangle is shown. The length of the rectangle is labeled 10 feet. The width of the rectangle is labeled 4 feet.
What are the dimensions if the poster is enlarged by a factor of three over two?
A. 12ft by 30ft
B. 2ft by 5ft
C.6ft by 15ft
D.5ft by 12ft
Answer:
C, 6 by 15 ft.
Step-by-step explanation:
10*3/2=15, and 4*3/2=6, so we get 6 by 15ft
Pls brainliest for leveling up
find the standard form of the equation for the circle with the following properites. center (9,-1/3) and tangent to the x-axis
To find the standard form of the equation for the circle, we need to determine the radius and use the formula (x - h)^2 + (y - k)^2 = r^2, The standard form of the equation for the circle with center (9, -1/3) and tangent to the x-axis is (x - 9)^2 + (y + 1/3)^2 = (1/3)^2.
To find the standard form of the equation for the circle, we need to determine the radius and use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
Given that the circle is tangent to the x-axis, we know that the distance between the center and the x-axis is equal to the radius. Since the y-coordinate of the center is -1/3, the distance between the center and the x-axis is also 1/3.
Therefore, the radius of the circle is 1/3.
Plugging the values of the center (9, -1/3) and the radius 1/3 into the formula, we get:
(x - 9)^2 + (y + 1/3)^2 = (1/3)^2.
This is the standard form of the equation for the circle with center (9, -1/3) and tangent to the x-axis.
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Find the area of the figure.
8 ft
10 ft
O a
Ob
80.0.42
105.1.12
50.3.12
25.3.12
С
8 .
d
Answer:
b because you add the 8 by 2 because 10 is too long and 8 is perfect size
Someone please help....
What is the value of the”?” Next to the blue arrow.
Answer: the number is 20, as the denominator 9 multiplied by 4 is 36. simply multiply the numerator by 4.
Subtract the rational expressions: Options are in picture
(The first picture from the left is the question. The rest are options.)
The expression is subtracted to give (a-2)(a+3)/2a². Option A
How to simply the expression
We need to know that algebraic expressions are defined as expressions that are made up of terms, variables, constants, factors and coefficients.
These expressions are made up of arithmetic operations, such as;
Addition BracketSubtractionMultiplicationParenthesesFrom the information given, we have;
a+ 1/2a - 3/a²
Find the lowest common factor
a( a + 1) - 2(3)/2a²
expand the bracket, we have;
a² + a - 6/2a²
factorize the numerator
a² + 3a - 2a - 6/2a²
a(a + 3) - 2(a +3)/2a²
(a-2)(a+3)/2a²
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Finding a final amount in a word problem on expA certain forest covers an area of 2600 km². Suppose thaUse the calculator provided and round your answer to the2.kmХ?
Since the area decreases the same percent each year, we will use the exponential function of decay to solve the question
\(f(x)=ab^x^{}\)Where:
a is the initial value
b is the factor of decay
y is the new value
x is the time
\(\because a=2600km^2\)\(\because b=1-\frac{7}{100}=0.93\)\(\because x=7years\)\(y=2600(0.93)^7\)Let us find the answer using the calculator
\(y=1564.422264km^2\)Round it to the nearest square km means a nearest whole number
y = 1564 km^2
The final amount is 1564 square kilometers
1. Determine the values of a and k when 299,790,000 is written in scientific notation.2. Determine the values of a and k when 0.51 is written in scientific notation.
(a) On writing 299790000 in scientific notation , the value of a is 2.9979 and value of k is 8 .
(b) On writing 0.51 in scientific notation , the value of a is 5.1 and value of k is -1 .
What is Scientific Notation ?
The general form of writing a number in scientific notation is ⇒ \(a\times 10^{k}\) ;
Part (a) ;
the number is given to be : 299790000 ;
For writing it in scientific notation, decimal point will be placed after 2 ;
So , the scientific notation of the number is ⇒ \(2.9979 \times 10^{8}\) ,
On comparing it with the general form of scientific notation,
we get , a = 2.9979 and k = 8 .
Part (b) ;
the number is given to be : 0.51 ;
For writing it in scientific notation, decimal point will be placed after 5 ;
So , the scientific notation of the number is ⇒ \(5.1 \times 10^{-1}\) ,
On comparing it with general form of scientific notation,
we get , a = 5.1 and k = -1 .
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Math/Geometry
HELP ASAP PLS GEOMETRY
Answer:ANSWER IS CBD by ?
Step-by-step explanation:
ok so ABC is equal to 180 degreess so /_\ would a right angle which is 90
In clinical trials for the drug Adderall (which treats attention deficit hyperactivity disorder (ADHD)), researchers were concerned about a possible vomiting side effect.
In an experiment, 26 of 374 subjects assigned randomly to take Adderall experienced vomiting as a side effect, and 8 of 210 subjects randomly assigned to take a placebo (fake pill) experienced vomiting as a side effect.
Is there evidence that taking Adderall increases the probability of vomiting? Carry test of hypotheses, but you don’t need to state assumptions or check conditions. You should include proper hypotheses, a computed p-value, and a conclusion in context of the problem.
There is evidence to suggest that taking Adderall increases the probability of vomiting compared to taking a placebo in this clinical trial.
Null hypothesis (H₀): The probability of vomiting is the same for subjects taking Adderall and those taking a placebo.
Alternative hypothesis (H₁): The probability of vomiting is higher for subjects taking Adderall compared to those taking a placebo.
We can perform a one-sided proportion test to compare the proportions of vomiting between the Adderall group and the placebo group.
Let's calculate the test statistic and p-value:
Adderall group:
Number of subjects (n₁) = 374
Number of subjects experiencing vomiting (x₁) = 26
Proportion of vomiting in Adderall group (p₁) = x₁ / n₁ = 26 / 374 ≈ 0.0695
Placebo group:
Number of subjects (n₂) = 210
Number of subjects experiencing vomiting (x₂) = 8
Proportion of vomiting in placebo group (p₂) = x₂ / n₂ = 8 / 210 ≈ 0.0381
Under the null hypothesis, assuming the proportions are equal, we can calculate the pooled proportion (p):
p = (x₁ + x₂) / (n₁ + n₂)
= (26 + 8) / (374 + 210)
= 34 / 584
=0.0582
We calculate the test statistic, which follows an approximately normal distribution under the null hypothesis:
z = (p₁ - p₂) / √(p (1 - p)× (1/n₁ + 1/n₂))
= (0.0695 - 0.0381) / √(0.0582 × (1 - 0.0582) × (1/374 + 1/210))
= 2.048
Using the z-test, we can calculate the p-value associated with the test statistic.
Since we are testing if the probability of vomiting is higher for the Adderall group, it is a one-sided test.
We find the p-value corresponding to the observed z-value:
p-value = P(Z > 2.048)
Using a standard normal distribution table, we find that the p-value is 0.0209.
The computed p-value of 0.0209 is less than the conventional significance level of 0.05.
Therefore, we have evidence to reject the null hypothesis.
We can conclude that there is evidence to suggest that taking Adderall increases the probability of vomiting compared to taking a placebo in this clinical trial.
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for each relation, decide whether or not it is a function
Answer:
Relation 1,2,and 4 are functions, but relation 3 not is a function.
Step-by-step explanation:
function 1 input, no function with the same input like m in relation 3.
Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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the region enclosed by the curve of f and the x axis rotated 360 about the x axis find the volume of the solid
The volume of the solid generated by rotating the region enclosed by the curve of $f(x) = x^2 - 1$ and the x-axis around the x-axis is $\frac{16\pi}{15}$.
To find the volume of the solid generated by rotating the region enclosed by the curve of a function $f(x)$ and the x-axis around the x-axis, we use the formula:
$V = \int_{a}^{b} \pi [f(x)]^2 dx$
where $a$ and $b$ are the limits of integration.
Let's assume the function $f(x) = x^2 - 1$, then we have:
$V = \int_{-1}^{1} \pi [(x^2 - 1)]^2 dx$
$V = \int_{-1}^{1} \pi (x^4 - 2x^2 + 1) dx$
$V = \pi \left[\frac{x^5}{5} - \frac{2x^3}{3} + x\right]_{-1}^{1}$
$V = \pi \left[\left(\frac{1}{5} - \frac{2}{3} + 1\right) - \left(-\frac{1}{5} + \frac{2}{3} - 1\right)\right]$
$V = \pi \left[\frac{16}{15}\right]$
$V = \frac{16\pi}{15}$
Therefore, the volume of the solid generated by rotating the region enclosed by the curve of $f(x) = x^2 - 1$ and the x-axis around the x-axis is $\frac{16\pi}{15}$.
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complete the solution of the equation. find the value of y when x equals 7. 2x + y=24
Answer:
y = 10
Step-by-step explanation:
x = 7
2x + y = 24
y = -2x + 24
y = -2 * 7 + 24
y = -14 + 24
y = 10
Hope this helps!
Answer:
y = 10
Step-by-step explanation:
2(7) + y = 24
14 + y =24
y + 14 = 24
14 - 14 = y
24 - 14 = 10
y = 10
Hope this helped! :)
A factory makes 1,200 shirts every 6 hours. The factory makes shirts for 9 hours each workday. How many shirts does the factory make per hour? shirts per hour How many shirts does the factory make per workday (9 hours) ? shirts per workday How many workdays will it take to make 12,600 shirts? workdays
Answer:
they make 200 per hour and 1800 every 9 hours and it would take 7 workdays to make 12,600
Step-by-step explanation:
yep I'm smart
Bananas are sold at four different grocery stores.Which store has the lowest price per pound?
Answer:
There is not enough information to answer, input more information the re-ask the question
Step-by-step explanation:
Which of the following values is not an irrational number?
80, 7, 2.87, √59
80, 7, and 2.87 are not irrational numbers.
What is an irrational number?
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, etc all are irrational.
Given numbers: 80, 7, 2.87, √59
80 = It is a rational number
7 = It is a rational number
2.87 = It is a rational number
√59 = It is an irrational number.
Hence, 80, 7, and 2.87 are not irrational numbers.
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