Answer:
Arav is 30 and Pawan is 40
Step-by-step explanation:
We can call Arav's age x and Pawan's age x + 10, therefore we can write the following equation:
1/7((x + 10) - 5) = 1/5(x - 5)
1/7(x + 5) = 1/5(x - 5)
5(x + 5) = 7(x - 5)
5x + 25 = 7x - 35
-2x = -60
x = 30 so x + 10 = 40
The slope of the line below is -3 which is the following is the point - slope from the line ?
Answer:
D. y + 6 = -3(x - 2)
Step-by-step explanation:
To find the equation in point-slope form, you need to use the slope and a point from that line. The slope is -3 and the point given is (2, -6).
Point-slope form is y - y₁ = m(x - x₁). Plug in the slope and point.
y - (-6) = -3(x - 2)
y + 6 = -3(x - 2)
Answer:
D. [tex]y - 2 = -3(x+6 )[/tex]
Step-by-step explanation:
Well point slope form is,
[tex]y - y_{1} = m(x-x_{1} )[/tex]
So we already have slope meaning we can plug that in for m.
[tex]y - y_{1} = -3(x-x_{1} )[/tex]
And with the given point (2,-6),
we can create point slope form.
[tex]y - 2 = -3(x+6 )[/tex]
Therefore,
the answer is d. [tex]y - 2 = -3(x+6 )[/tex].
Hope this helps :)
HELP ME PLEASEEEE! Thank you
Answer:
A. Yes
B. Yes
C. No
Step-by-step explanation:
We can substitute each value in to the equation and see if the sides match up. Let's start with a.
[tex]4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5[/tex]
So, n = 2 works for equation a. Let's try B.
[tex]9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11[/tex]
So, m = [tex]\frac{10}{3}[/tex] works for B. Now let's try C.
[tex]3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54[/tex]
So y = 30 doesn't work for C.
Hope this helped!
Ava is buying paint from Amazon. Ava
needs 3/4 cup of blue paint for every 1
cup of white paint. Ava has 28 ounces
of white paint. How much blue paint
does he need?
Answer:
2.625 cups or 21 ounces
Step-by-step explanation:
Ava needs 3/4 cup of blue paint for every 1 cup of white paint. So, the ratio is 0.75 : 1.
She has 28 ounces of white paint. But, you have to convert ounces to cups.
1 cup = 8 ounces
28 ounces ÷ 8 ounces/cup = 3.5 cups
Now set up a ratio.
[tex]\frac{0.75}{1} = \frac{x}{3.5}[/tex]
X (how much blue paint is needed) is over 3.5 cups (the amount of white paint she has)
Cross multiply and divide.
[tex]\frac{0.75}{1} = \frac{x}{3.5}[/tex]
x = 0.75 × 3.5
x = 2.625 cups
To convert to ounces, multiply by 8.
2.625 cups × 8 ounces = 21 ounces
Therefore, Ava needs 2.625 cups or 21 ounces of blue paint.
Hope that helps.
Hi ... i appreciate you to answer this questuion...
[tex] \frac{ {x}^{2} }{ {x}^{4} + 1 } [/tex]
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{x^2}{x^4+1}=\dfrac{1}{7} \ \ }[/tex]
Step-by-step explanation:
Hello,
We know that (let's assume that x is different from 0 as we cannot divide by 0)
[tex]x+\dfrac{1}{x}=3[/tex]
and we want to estimate
[tex]\dfrac{x^2}{x^4+1}[/tex]
Let's take the square.
[tex]9=3^2=(x+\dfrac{1}{x})^2=x^2+2\cdot x \cdot \dfrac{1}{x}+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}=\dfrac{x^4+1}{x^2}+2[/tex]
So, we can write
[tex]\dfrac{x^4+1}{x^2}=9-2=7 \\ \\\\\text{*** let's take the inverse ***} \\ \\\dfrac{x^2}{x^4+1}=\dfrac{1}{7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
How many more unit tiles must be added to the function
f(x)=x2-6x+1 in order to complete the square?
-X
--X
0 0
Answer:
8 more unit of tiles
Step-by-step explanation:
The function is given as;
f(x) = x² - 6x + 1
Now, we want to add more unit tiles to complete the square.
The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.
Now, Let's make a general order 1 expression ax + b to be the side of the square.
From the function forming the square after adding some p unit tiles, we have;
f(x) + p = (side of square)²
Thus;
x² - 6x + 1 + p = (ax + b)²
x² - 6x + 1 + p = a²x² + 2abx + b²
Comparing both sides of the equation, we have;
a² = 1
2ab = 6
b² = 1 + p
From a² = 1, a = 1
From 2ab = 6,putting 1 for a, we have;
2(1)b = 6
b = 6/2
b = 3
From b² = 1 + p
Putting 3 for b, we have;
3² = 1 + p
9 = 1 + p
9 - 1 = p
p = 8
Thus, 8 more unit of tiles are required to complete the square.
If Geo had 3/8 of a pizza and his sister had 7/9 of another pizza, how much pizza do they have in all?
Answer:
[see below]
Step-by-step explanation:
Geo has 3/8 of a pizza. His sister has 7/9 of another pizza.
Add the values:
[tex]\frac{3}{8}+\frac{7}{9}\\\\ \text{The LCM of the denominators is 72.}\\\\\frac{3*9}{8*9}=\frac{27}{72}\\\\\frac{7*8}{8*9}=\frac{56}{72}\\\\\frac{27+56}{72}=\frac{83}{72}\\\\\frac{83}{72}=1\frac{11}{72}\\\\\boxed{\frac{3}{8}+\frac{7}{9} = 1\frac{11}{72}}[/tex]
Choose two values, a and b, each between 8 and 15. Show how to use the identity a^3+b^3=(a+b)(a^2-ab+b^2) to calculate the sum of the cubes of your numbers without using a calculator
I really need help with this
Answer:
Step-by-step explanation:
a = 8
b = 10
a^3 =8^3 = 512
b^3= 10^3 =1000
a^3 + b^3 = 1512
a^2 = 64
-ab = - 80
b^2 = 100
a + b=18
(a + b) (64 - 80+ 100)
18 * (84)
1512'
Choose the best estimate for the multiplication problem below.
82.17
7.32
X
A. 560
B. 860
C. 420
Hey there!
We see that the first factor is 82.17, which is about 80. Then, we have 7.32, which is about 7.
80 times 7 is just doing 8 times 7 but putting a zero on the end!
So, 80 times 7 is 560, so our best estimate is A.560
Have a wonderful day!
a firefighter dives at 7.5 m/sec from window to net. If window is 34 m above net, what speed does firefighter hit net. ACCELRATION IS 9.8 m/sec^2
Answer:
Step-by-step explanation:
This is more physics than math, but since "The book of nature is written in the language of mathematics"...
Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is
[tex]v^2=v_0^2+2a[/tex]Δx
where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:
[tex]v^2=(7.5)^2+2(-9.8)(-34)[/tex]
Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)
What we have here is
[tex]v^2=56+670[/tex] and
[tex]v=\sqrt{56+670}[/tex]
That leaves us with
v = 26.94438j
But don't forget we round that to the tens place which comes out in the end, finally, to
v = 30 m/s
Solve . -9 2/7(-10 3/7).
Answer:
315943/12683
Step-by-step explanation:
Well -9 2/7 * -10 3/7 is 315943/12683
Answer:
540/49
Step-by-step explanation:
Work on the brackets first: (-10✖️3/7)=-30/7
-30/7✖️2/27=-60/49
-60/49✖️-9=540/49
The formula for the distance travelled over time t and at an average speed v is v⋅t. Amit ran for 40 minutes at a speed of about 5 kilometres per hour. What calculation will give us the estimated distance Amit ran in kilometres?
Answer:
3 1/3 km or 3.33 km (to the hundredth)
Step-by-step explanation:
Using the given formula,
estimated distance = v.t = velocity * time,
velocity = 5 km/h
time = 40 minutes = [tex]\frac{40}{60}[/tex] hours = [tex]\frac{2}{3}[/tex] hours
Therefore
distance = 5 km/h * [tex] \frac{2}{3} [/tex] hours = 10/3 km
= 3.33 km approximately
Answer:
[tex]\boxed{Distance = 3.33\ km}[/tex]
Step-by-step explanation:
Given:
Time = t = 40 min = 40/60 = 0.67 hours
Speed = v = 5 km/hr
Required:
Distance = S = ?
Formula:
Distance = Speed × Time
Solution:
Distance = 5 × 0.67
Distance = 3.33 km
Which equation is parallel to y= 3/4x + 4 and passes through the point (0,2)
A. Y=4/3x - 2
B. Y=3/4x - 2
C. Y=3/4x + 2
D. Y= 4/3x + 2
Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{4}[/tex] x + 4 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
Parallel lines have equal slopes, thus this is slope of parallel line.
The line crosses the y- axis at (0, 2) ⇒ c = 2
y = [tex]\frac{3}{4}[/tex] x + 2 → C
can anyone plz help me?
Answer:
SAS Postulate
Step-by-step explanation:
In EDG & ADC ,
1) AD = ED ( given )
2)angle( EDG ) = angle ( ADC )................ [ Vertical Opposite Angles are equal ]
3) GD = CD ( D is the mid - point of CG )
So triangles EDG & ADC are congruent by SAS postulate....
X*2+1=10 then x=? Tell me the value of x
Answer:
4.5Step-by-step explanation:
[tex]x \times 2 + 1 = 10[/tex]
[tex]2x + 1 = 10[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 10 - 1[/tex]
Subtract the numbers
[tex]2x = 9[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Calculate
[tex]x = 4.5[/tex]
Hope this helps..
Best regards!!
Which expression is equivalent to
-21/4over -2/3
Answer:
[tex]\frac{9}{4}/\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].
[tex]-\frac{2}{3}[/tex] can stay put.
The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.
In addition, when two negatives are put together the answer must always be positive.
Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square. Need help quick Plz!!!
Answer:
The answer is below
Step-by-step explanation:
The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).
From the sector, AB = AC = radius of the sector (r) = 12. Therefore:
[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]
From the triangle: AC² = AB² + BC²
AC² = 12² + 12² = 144 + 144
AC² = 288
AC=√288 = 12√2
[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]
Nicole has x marbles. Together we have 44 marbles. How many marbles will I have if I lose 1/4 of my marbles ?
Answer:
I have:
33 - 3N/44 marbles
N = marbles of Nicole
Step-by-step explanation:
Nicole + me = 44 marbles
m = 44 - N
m = me
N = Nicole
if i lose 1/4 of my marbles
4/4 - 1/4 = 3/4
i have left:
3/4 of my marbles
then:
m = 3(44-N)/4
m = 3*44/4 + 3*-N/44
m = 33 - 3N/44
I have finally:
33 - 3N/44
A card is drawn from the deck. What is the probability it is either black face card or a
spade?
Answer:
about 37% chance or, rounding to the nearest tenth, 36.5% chance
Step-by-step explanation:
since there are only 6 black face cards out of 52 cards, so the fraction is 6/52
there are also 13 spade cards out of 52 cards, so the fraction is 13/52
to find the percent you have to add the two fractions becuase all you want to do is draw a black face card or a spade card. when you add them you get 19/52
then dividing the fraction gives you .3653846154 on my calculator :)
LeBron buys 500 shares of Tiger Corporation for $10 a share. The corporation’s president is caught committing fraud and the stock drops to $3 a share. LeBron sells all his shares. How much can he take off his income as a capital loss this year?
Answer:
$3,500
Step-by-step explanation:
First, Lets analyze the problem.
LeBron buys 500 shares for $10 a share. So he buys 500 shares for $5,000.
Now the price drops to $3, he had 500 stocks, the stocks are now only worth $1500.
5000-1500=3,500
He has lost $3,500 in the Tiger Corporation shares.
Which line will have no solution with the parabola y - x + 2 = x2?
5
3+
N
-5 -4 -3 -4
2 3 4 5 X
th
-3
44+
-5
Answer:
yes
Step-by-step explanation: i agree its 3
Which of the following best classifies a quadrilateral with coordinates A(8, 4), B(6, 0), C(3, 2), and D(7, 10)? Trapezoid Parallelogram Kite Rectangle
Answer:
Trapezoid
Step-by-step explanation:
Got it right on quiz
The following that best classifies a quadrilateral with coordinates is :
A) Trapezoid
The following that best classifies a quadrilateral with coordinates is Trapezoid.A trapezoid could be a quadrilateral with one match of inverse sides parallel. In some cases individuals characterize trapezoids to have at slightest one match of opposite sides parallel, and some of the time say there's one and as it were one combine of inverse sides parallel.Thus, the correct answer is A.
Find out more information:
https://brainly.com/question/24200218referrer=searchResults
What transformation maps rectangle QRST to rectangle Q’R’S’T’?
reflection
rotation
stretch
translation
Answer:
Reflection
Step-by-step explanation:
Just took the test got a 100%
edg 2021
Answer:
A: Reflection
Step-by-step explanation:
Let's be honest, no one hardly ever pays attiontion to the explanation.
<3
Can someone help me ASAP???!!
Answer:
25x ²−49y ²
Step-by-step explanation:
We need to find product of (5x+7)(5x−7y)
By using identity (a+b)(a−b)=a −b ²
We have a=5x,b=7y
Thus (5x+7y)(5x−7y)=(5x) ²−(7y)
let me know if it was helpful
25x² - 49y²
Step-by-step explanation:
To Find:
The product of (5x - 7y)(5 x + 7)
How to solve:
Just need to use the formula of a² - b² = (a+b)(a-b)
let's assume a = 5x and b = 7x
Solution:
(5x - 7y)(5 x + 7) = (5x)² - (7y)²
= 25x² - 49y²
Hence required answer is 25x² - 49y².
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
Answer:
x = 5 is the solution
Step-by-step explanation:
See the attachment for table values.
f(x) = g(x) for x = 5
The solution to the equation ...
2.5x -10.5 = 64(0.5^x)
is x = 5.
Pleas answer this question now
Answer:
[tex]x = 17[/tex]
Step-by-step explanation:
According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.
That is, [tex]x + 4 = 21[/tex]
Solve for x
[tex]x + 4 = 21[/tex]
Subtract 4 from both sides
[tex]x + 4 - 4 = 21 - 4[/tex]
[tex]x = 17[/tex]
PLEASE help me! The question is attached.
Answer:
The third option is correct
Step-by-step explanation:
We can rule out the first option because systems of equations CAN have decimal answers (this certain question cannot because of the domain) Same for the second option.
The last option says that all the numbers of forks knives and spoons must be equal but the question never specified that, in fact it looks like that is impossible since the variables have different coefficients.
The only logical answer is number 3
PLEASE ANSWER ASPAA The x-intercept of the equation 2y – x = -6 is: 3. -3. 6. None of these choices are correct.
Answer:
x = 6
Step-by-step explanation:
The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:
2(0) - x = -6
0 - x = -6
-x = -6
x = 6
Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find x
Answer:
x = 1
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, thus
AE = CE , substitute values
11x - 3 = 12 - 4x ( add 4x to both sides )
15x - 3 = 12 ( add 3 to both sides )
15x = 15 ( divide both sides by 15 )
x = 1
A university offers a Calculus class, a Sociology class, and a Spanish class. Youare given data below about a group of students who have all taken at least one ofthe three classes.(iv)(i) Group 1 contains 187 students. Of these, 61 students have taken Calculus,78 have taken Sociology, and 72 have taken Spanish. 15 have taken bothCalculus and Sociology, 20 have taken both Calculus and Spanish, and 13have taken both Sociology and Spanish. How many students in Calculushave taken all three classes?\
Let A, B, and C denote the sets of students that have taken calculus, sociology, and Spanish, respectively.
We're given that [tex]A\cup B\cup C[/tex] consists of 187 students.
We want to find the size of [tex]A\cap B\cap C[/tex], given that
• A has 61 students;
• B has 78;
• C has 72;
• [tex]A\cap B[/tex] has 15;
• [tex]A\cap C[/tex] has 20; and
• [tex]B\cap C[/tex] has 13.
Using the inclusion/exclusion principle, we have
[tex]|A\cup B\cup C|=|A|+|B|+|C|-(|A\cap B|+|A\cap C|+|B\cap C|)+|A\cap B\cap C|[/tex]
where |X| denotes the size of the set X. Plug in all the known sizes:
[tex]187=61+78+72-(15+20+13)+|A\cap B\cap C|[/tex]
[tex]\implies|A\cap B\cap C|=24[/tex]
so 24 students have taken all three classes.
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average of 72 litres of shower water (over the entire month). Water costs 0.20$ per litre. How much money did Trevor's family spend, in total, on shower water in the past month?
Answer:
The amount spent on shower water by Trevor's family in the past month is $86.4
Step-by-step explanation:
The given information are;
The number of people in Trevor's family house are 6
The volume of water each person showered with during the month = 72 litres
The water costs = $0.20 per litre
The total volume of water used for shower by the 6 people = 72 × 6 = 432 litres
The amount spent on shower water by Trevor's family in the past month = The total volume of water used for shower × The cost per litre of water
The amount spent on shower water by Trevor's family in the past month = 432 × 0.2 = $86.4.
Answer:
$86.4
Step-by-step explanation: