Answer:
√10+√15-√14-√21
Explanation:
(√2 * √5) = √10
(√2 * -√7) = -√14
(√3 * √5) = √15
(√3 * -√7) = -√21
Put it all together: √10 + √15 - √14 - √21
Hope this helped :)
The simplified form of the expression (√2+√3)(√5-√7) is √10-√14+√15-√21
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (√2+√3)(√5-√7)
√2(√5-√7) + √3(√5-√7)
We have to apply distributive property
√2.√5 - √2.√7 + √3.√5 -√3.√7
√2×5 -√2×7 +√3×5 -√3×7
√10-√14+√15-√21
Hence, the simplified form of the expression (√2+√3)(√5-√7) is √10-√14+√15-√21
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Find the volume of the following figure.
6 cm3
7 cm3
8 cm3
5 cm3
Answer:
7 cm³
Step-by-step explanation:
Assume each cube has an edge 1 cm in length.
Each cube has volume 1 cm³.
There are 7 cubes.
volume = 7 cm³
The mean mass of a squad of 19 rugby players is 87 kg
A player of mass 102 kg joins the squad.
Work out the mean mass of the squad now, in kilograms (kg).
19 players x 87kg = 1653 total kg
1653 kg + 102kg = 1755 kg
1755kg / 20 players = 87.75kg mean mass
Answer: 87.75 kg
What is the solution of 5sin2θ=3 for 0≤θ≤2π? Please help.
Answer:
C) [tex]\theta\approx\{0.3218,1.249,3.463,4.3908\}[/tex]
Step-by-step explanation:
[tex]5\sin2\theta=3;\: 0\leq\theta\leq 2\pi\\\\\sin2\theta=\frac{3}{5}\\ \\2\theta\approx\{0.6436,2.498,6.926,8.7816\}\\\\\theta\approx\{0.3218,1.249,3.463,4.3908\}[/tex]
A large bin of Peanut M&M's contains red, yellow, blue, and brown M&M's. Lexi
scoops out a bowl full of M&M's and counts how many of each type she has: 12 red,
7 yellow, 14 blue, and 9 brown.
Luke scoops out a bowl of 36 Peanut M&M's. About how many should he expect to
be blue?
Answer:
About 12 blue m&m’s
Step-by-step explanation:
For every 36 minutes of sprinting, Scarlett earned 12 dollars for charity. To find the unit rate of this, I would first need to structure the equation. In this case, I would use division, so my equation would be 36 ÷ 12 = 3. The final answer would be, for every 3 minutes, Scarlett earns $1. is this right? i will give 15 points:)
Answer:
$1 every 3 minutes
Step-by-step explanation:
Cause every 36 minutes Scarlett earns $12 and if you divide 36 by 12 it will give 3 minutes which means she earns $1 per 3 minutes. You're right.
The graph shows a probability distribution. What is P(X<3)?
The value of probability P(X<3) is 0.3 after calculating the area up to 3 option second is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a probability distribution shown in the picture.
To find the probability P(X<3) = area up to 3
From the probability distribution:
P(X<3) = (1/2)×3×(0.20)
P(X<3) = 1.5×0.20
P(X<3) = 0.3
Thus, the value of probability P(X<3) is 0.3 after calculating the area up to 3 option second is correct.
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Please help me with this!
Answer:
sin(4)
Step-by-step explanation:
sin(-184) is the equivalent to sin(4) (degree), positive and acute angle.
Write and simplify the expression equivalent to 2(7x + 3) + 9x.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression 2(7x+3)+9x.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
We need to multiply 2 times 7x and 3, and then add 9x.So, let's compute...
\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\//\\//\\\/
After performing multiplication we obtain
[tex]\star~\mathrm{14x+6+9x}[/tex]
Now add 9x:
[tex]\star~\mathrm{23x+6}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
A person borrows $50000 loan from bank at a rate of 10% for 5 years compounded yearly.
a) Calculate the total amount paid after 5 years.
b) Find the interest paid.
[tex]\large\boxed{Formula: A= P(1+ \frac{R}{100}{)}^{T}}[/tex]
Let's substitute according to the formula.
[tex]A= 50000(1+ \frac{10}{100}{)}^{5}[/tex]
A= $80525.5
Now, we can find the interest paid
[tex]\large\boxed{I= A-P}[/tex]
We'll have to deduct the total amount from the principal amount.
Let's substitute according to the formula.
[tex]I= 80525.5-50000[/tex]
I= $30525.5
Hence, the total amount paid after 5 years is $80525.5 and $30525.5 was paid as interest.
5² + 12² =
64a3³
Work out the value of a.
Your final line should say, a =
Answer:
a = 13/4Step-by-step explanation:
√(5²+12²) = ∛(64a³)
√(25+144)=√(64a)
√169 = √(64a)
13 = 4a
a = 13/4
What is the y intercept of this quadratic? (Picture)
Answer:
We know that the y intercept is -3 because that is where it intersects! The point for the y intercept is (0, -3)
Step-by-step explanation:
Figure FGHJ is shown below.
Figure F G H J has 4 sides. Sides F J and G H are congruent and parallel, and sides G F and H J are congruent and parallel. Angles G and J are 130 degrees.
Which names accurately describe figure FGHJ? Select two options.
parallelogram
quadrilateral
rectangle
rhombus
trapezoid
30 Use the method of completing the square to determine the vertex of f(x) = x² - 14x - 15.
State the coordinates of the vertex.
Answer:
x² - 14x - 15 = (x − 7)² − 64Then the coordinates of the vertex are (7 , -64)Step-by-step explanation:
x² - 14x - 15 = x² - 14x + (49 - 49) - 15
= (x² - 14x + 49) - 49 - 15
= (x² - 14x + 7²) - 49 - 15
= (x − 7)² − (49 + 15)
= (x − 7)² − 64
x² - 14x - 15 = (x − 7)² − 64
Then the coordinates of the vertex are (7 , -64)
What is the median pumpkin weight?
Answer:
17
Step-by-step explanation:
The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:
[tex]10, 12, 14, 16, 18, 20, 22, 24[/tex]
Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 16 and 18. The median is the average of these numbers. We have
[tex]{\frac{ 16 + 18 }{2}}[/tex]
Therefore, the median is
[tex]17[/tex]
PLS I NEED 100% TO GET A GOOD MATH GRADE THIS YEAR
The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:
At least how many schools have participated for 1 year or less? (5 points)
6 schools
8 schools
12 schools
14 schools
Answer:
6 schools
Step-by-step explanation:
I did the same assignment
Find the general solution of the given differential equation. Cos(x) dy dx (sin(x))y = 1
The general solution to the differential equation is y = sinx + c cosx.
What is differential equation?It is defined as the equation which contains functions, derivative of the functions to make an expression.
We have a differential equation:
[tex]\rm cosx\left(\dfrac{dy}{dx}\right)+\left(sinx\right)y\:=\:1[/tex]
Multiply by dx:
(cosx) dy + (sinx) y dx = dx
(cosx) dy = (1 - (sinx) y) dx
After simplification and integrating, we will get:
[tex]\rm y = \dfrac{tan x}{sec x}+ \dfrac{c}{secx}[/tex]
y = sinx + c cosx
Thus, the general solution to the differential equation is y = sinx + c cosx.
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Which is the correct answer for 62 + ∛125 ?
Answer: 67
Step-by-step explanation:
∛125 = 5
62 + 5 = 67
Cut-1 Cut-2 Number of rope cutting 1 2 3 Resulting pieces 3 5 7 1.2.1 The number of pieces of ropes for FIVE cuts. 4 S
The answer to the all parts given below.
What is sequence?A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.
For 5 cuts number of pieces will be 11 pieces.
General formula:
Tn= 2n+1
For 153 rope pieces number of rope cutting
2n+1=153
2n= 152
n= 76
For 11 cuttings rope pieces will be
2(11)+1
= 23
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The perimeter of an equilateral triangle is 96 cm. Find the length of the side of the triangle.
Answer:
Answer : Length(l) = 32 cm
Step-by-step explanation:
Given,
Perimeter(P)=96 cm
Length(l)=?
We know that,
P = 3l
96 = 3l
96÷3 = l
32 = l
Therefore, length(l) = 32 cm
What is the measure of major B 84° O 276° O252° O 84° O 168 arc AB? A
Answer:
A - 84°
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle that intersects it.
The central angle of this circle measures 84° and it intercepts arc AB, meaning arc AB measures 84°
Multiply the following
(a) 2.7x4
(b) 0.79x32.4
(c)1.07 x 0.02
(d) 2.3x4.35
(e) 2.5x100
(f) 0.0008x100
g) 0.25x 10000
h)3x0.55
i)0.08x5
j)351.06x4
k)0.3x0.03
l) 21.7x0.1
m) 200.02 x 2.2
Kindly look into this and try to answer all of them this contains 30 points
Please help me with this probability question; I’d really appreciate it!
The attendance at a village fair depends on the weather.
The probability of a high attendance at the fair is 0.9.
This is reduced to 0.4 if it is raining.
The probability of it raining is 0.2.
What is the probability of its raining and there being a high attendance?
0.6
0.08
0.36
0.18
Answer:
B. 0.08
Step-by-step explanation:
In order to solve this problem, we must account for all possibilities. The sum of all posssiblities must sum up to 1.
1 - High Attendance/No Rain
0.9*0.8 = 0.72
2- High Attendance/ Rain
0.4*0.2 = 0.08
3 - Low Attendance/No Rain
0.1*0.8 = 0.08
4 - High Attendance/No Rain
0.6*0.2 = 0.12
Now we answer the question of rain and high attendance.
0.08/1 = 0.08
help i will give 20 thax
Ty's brother will get 3/4th part of the pizza.
What is Division ?The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.
Here, Total number of Pizza = 1
Number of parts required = 4
Now, each member will get the part of pizza = 1/4
Total number of brothers = 3
Ty's brother will get pizza = 3 X 1/4
= 3/4
Thus, Ty's brother will get 3/4th part of the pizza.
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Answer:
3/4
Step-by-step explanation:
because there are 4 people so ty get 1/4 and his brothers get the rest.
PLS HELP
Which shows the following expression after the negative exponents have been eliminated?
Answer:
Option 2
Step-by-step explanation:
Given :
[tex]\frac{xy^{-6} }{x^{-4}y^{2} }[/tex]
=============================================================
Applied Rule :
[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]
============================================================
Solving :
⇒ To remove negative exponents, bring to the opposite side (e.g. if in the denominator, bring to the numerator)
⇒ [tex]\frac{x(x^{4}) }{y^{2}(y^{6}) }[/tex]
Please help me fast and thank you if you do
Answer:
8 > u > 6
Step-by-step explanation:
We have to solve this inequality as 2 separate inequalities.
==============================================================
Inequality 1 :
⇒ 10 > 5u/4
⇒ 5u < 10 × 4
⇒ 5u < 40
⇒ u < 8 [Box 1]
============================================================
Inequality 2 :
⇒ 5u/4 > 15/2
⇒ 5u/2 > 15
⇒ u/2 > 3
⇒ u > 3 × 2
⇒ u > 6 [Box 2]
============================================================
Solution :
⇒ 8 > u > 6
What is the value of x log3x equals 4
[tex]~~~~\log_3 (x) = 4\\\\\implies x= 3^4 \\\\\implies x= 81[/tex]
6x1 + 9 x 1/10 + 8 x 1/100 + 3 x 1/1000=?
Answer:
6983/1000 OR 6.983
Step-by-step explanation:
6*1=6
9*1/10=9/10
8*1/100=8/100
3*1/1000=3/1000
6+9/10+8/100+3/1000=6983/1000
OR
6.983
Mrs. Nygaard needs 12 hours to grade all of her students’ projects. She made a chart to show how much time she could spend grading the projects during the week.
Project Grading
Day
Hours Grading
Monday
1 and three-fourths
Tuesday
1 and one-half
Wednesday
1 and one-fifth
Thursday
2
Friday
1 and one-fourth
How many hours will Mrs. Nygaard need to work over the weekend to finish grading the projects?
Answer:
2
Step-by-step explanation:
I think Mrs. Nygaard would need 2 hours to work over the weekend to finish grading the projects .
I need help! 50 points!
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
Rotate the point (7, 8) around the origin 90 degrees counter clockwise. State the image of the point .
By applying the equation for the rotation around the origin we conclude that the image of the point (7, 8) after rotating 90° counterclockwise is (-8, 7).
How to rotate a point around the origin
In this question we must apply a rigid transformation on a point to find its image, rigid transformations are transformations applied on geometric loci such that Euclidean distances are observed in every point of the loci. A rotation about the origin is a kind of rigid transformation and is defined by the following expression:
(x', y') = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
(x, y) - Original point(x', y') - Resulting pointθ - Angle of rotation, in degrees.Please notice that positive values of θ represents a counterclockwise rotation. If we know that (x, y) = (7, 8) and θ = 90°, then the resulting point is:
(x', y') = (7 · cos 90° - 8 · sin 90°, 7 · sin 90° + 8 · cos 90°)
(x', y') = (-8, 7)
By applying the equation for the rotation around the origin we conclude that the image of the point (7, 8) after rotating 90° counterclockwise is (-8, 7).
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