Answer:
OPTION B IS THE CORRECT
Step-by-step explanation:
[tex](\sqrt{2}+\sqrt{3})(\sqrt{5}-\sqrt{7})[/tex]
[tex]\sqrt{2}(\sqrt{5}-\sqrt{7})+\sqrt{3}(\sqrt{5}-\sqrt{7})[/tex]
[tex]\sqrt{2*5}-\sqrt{2*7}+\sqrt{5*3}-\sqrt{3*7}[/tex]
[tex]\sqrt{10}+\sqrt{14}+\sqrt{15}-\sqrt{21}[/tex]
Answer:
√10 + √15 -√14 - √21Option B is the right option..
Solution,
[tex]( \sqrt{2} + \sqrt{3} )( \sqrt{5} - \sqrt{7} ) \\ [/tex]
Multiply each term in the first parantheses by each term in second paranthesis:
[tex] \sqrt{2} \times \sqrt{5} - \sqrt{2} \times \sqrt{7} + \sqrt{3} \times \sqrt{5} - \sqrt{3} \times \sqrt{7} \\ [/tex]
Calculate the product:
[tex] \sqrt{10} - \sqrt{14} + \sqrt{15} - \sqrt{21} \\ \sqrt{10} + \sqrt{15} - \sqrt{14} - \sqrt{21} [/tex]
Hope this helps....
Good luck on your assignment..
10/13 = 8 - 2z/52 Thats the question. Im dyin for help. :)
Answer:
z = 188
Step-by-step explanation:
1. 10/13 = 8 - 2z/52 (simplify - 2z/52)
10/13 = 8 (- 1/26)*z
2. 10/13 = (- 1/26)*z + 8 (flip for ease in solving)
(- 1/26)*z + 8 = 10/13
3. (- 1/26)*z + 8 = 10/13 (inverse: subtract 8 from each side to isolate variable z)
(- 1/26)*z = 10/13 - (8*13)/(1*13) (common denominator needed for add/subtract)
(- 1/26)*z = - 94/13 (simplify)
4. (- 1/26)*z = - 94/13 (inverse: multiply both sides by -26/1 to isolate variable z)
z = 188Answer:
188
Step-by-step explanation:
:> Thanks
Can someone please help me
Answer:
square 20 has 44 green squares
square 21 has 45 green squares
Step-by-step explanation:
To solve the problem, we need to observe the cases, and determine/define a rule for each case (odd number of sides, or even number of sides).
For square one, we note that the centre square is shared by two diagonals, so we saved one square from the two diagonals.
The side length is 3 for square 1, 4 for square 2, and so on.
Let
n= square number (1, 2,3...)
L = side length (3,4,5...)
G1(n) = function that gives the number of green squares for square n, n=odd
G2(n) = function that gives the number of green squares for square n, n=even
side length, L=n+2 ................(1)
G1(n) = twice the side length less one, as discussed above
G1(n) = 2L-1 now substitute L=n+2
G1(n) = 2(n+2) -1 simplify
G1(n) = 2n + 3
Check:
for n=1, square 1 has 2*1+3 = 5 green squares ... checks
for n=3, square 3 has 2*3+3 = 9... checks
for n=5, square 5 has 2*5+3 = 13 ....checks
For even squares, it is even easier, because
G2(n) = 2L = 2(n+2)
check:
for n=2, square 2 has 2(2+2) = 8 green squares........checks
for n=4, square 4 has 2(4+2) = 12 green squares........checks.
Fincally, we apply our formula to n=20 and n=21
square 20 : G2(20) = 2(n+2) = 2(20+2) = 44 green quars
square 21 : G1(21) = 2n+3 = 2(21)+3 = 45 green squares
Find the mean, median, mode and range for the following set of numbers. answers with the corresponding numbers
5,6,6,11,12
Answer:
Mean: 8
Median: 6
Mode: 6
Range: 7
Step-by-step explanation:
Mean: 5+6+6+11+12=40 Then. 5 numbers, so 40 divided by 5=8.
Median: The middle number which is 6
Mode: The most occurring number which is 6.
Range: Highest number(12)-lowest number (5)=7
Answer: median= 1.05
Step-by-step explanation: mean: 8
mode: 6
Please Help Me!!!!! The displacement of a particle d (in km) as a function of time t (in hours) is given by: d(t) = 2t^3 + 5t^2 − 3. Find the displacement, velocity and acceleration at t = 4 hours. Indicate the correct units for each of these quantities.
Answer:
Step-by-step explanation:
Displacement: d(t) = 2t^3 + 5t^2 - 3
Velocity: (d/dt)(2t^3 + 5t^2 - 3) = v(t) = 6t^2 + 10t
Acceleration: (d/dt)(d/dt)(6t^2 + 10t) = a(t) = 12t + 10
At time t = 4hr,
d(4) = [128 + 80 - 3] km = 205 km
v(4) = [96 + 40] km/hr = 136 km/hr
a(4) = [48 + 10] km per hour squared = 58 km over hours squared
Answer:
Step-by-step explanation:
hello,
for t = 4 hours
[tex]d(4)=24^3+54^2-3=2*64+5*80-3=128+80-3=205[/tex]
this is 205 km
d is differentiable and
[tex]d'(t)=6t^2+10t[/tex]
and
[tex]d'(4)=6*4^2+10*4=6*16+40=96+40=136[/tex]
this is 136 km/h
d' is differentiable and
[tex]d''(t)=12t+10[/tex]
and
[tex]d''(4)=12*4+10=48+10=58[/tex]
this is [tex]58 \ km/h^2[/tex]
What is the center and radius of the circle that has the equation x+72+y-42=49? Explain.
Answer: The center is (-7, 4) and the radius is 7.
Step-by-step explanation:
The equation for a circle usually is:
(x - a)^2 + (y - b)^2 = R^2
where R is the radius, and (a, b) is the center of the circle.
I guess that the equation in this case is:
(x + 7)^2 + (y - 4)^2 = 49
then, in this case we have:
a = -7 and b = 4, then (a, b) = (-7, 4)
this means that the center of our circle is in the point (-7, 4)
and we know that:
R^2 = 49
R = √49 = 7
Then the radius is equal to 7.
A finance blogger is writing an article about credit card use. As they write their article, the finance blogger is interested in the average number of credit cards per adult. Based on previous research, an adult has 4 credit cards, on average. The finance blogger believes this average is different. If the finance blogger chooses a p-value approach, what does the p-value need to be compared to in order to determine if there’s enough evidence to support their claim?
Answer:
significance level
Step-by-step explanation:
Rohit visited a pumpkin patch with his family. The table shows the relationship between the weight and price of a pumpkin.
A table titled Pumpkin Patch Sales with two columns and six rows. The first column, Weight in pounds, has the entries, 4, 8, 12, 16, 20. The second column, Price in dollars, has the entries, 6, 12, 18, 24, 30.
Which statement describes the slope of a graph of the data?
For each additional pound, the price increases $0.50.
For each additional pound, the price increases $1.50.
For every additional dollar, the pumpkin can increase by 1.5 pounds.
For every additional dollar, the pumpkin can increase by 0.5 pounds.
Answer:
For each additional pound, the price increases $1.50.
Step-by-step explanation:
Lets find the slope of the graph of othe given data.
Let x be the weight of pumpkin in pounds
Let y be the price of the pumpkin in dollars.
For 4 pound pumpkin the price is 6 dollars, so first point is (4,6)
For 8 pound pumpkin the price is 12 dollars, so first point is (8,12)
Find the slope between these points
m = y₂ - y₁ / x₂ - x₁
m = 12 - 6 / 8 -4
m = 6/4
m = 1.5
Which means that for every pound increase in weight, the price of pumpkin increases by 1.5 dollars
Answer:
B
Step-by-step explanation:
if the domain of a coordinate transformation that is reflected over the y-axis is (-1,3),(2,1),(5,-1)and(-1,-2) what is the range
Answer:
Range remains the same.
Step-by-step explanation:
(1,3),(-2,1),(-5,-1) and (1,-2)
The range is { -2 ≤ y≤ 3 } .
What is Transformation?Transformation is changing the graph to a new one by Rotation, Reflection, Translation, and Dilation.
Reflection is to create a mirror image of the coordinate or the figure.
After reflection along any axis, the coordinate of the other axis changes to its additive inverse.
(x,y) ----> when reflected along y axis ----> ( -x , y)
The domain is all the values a function can have as input and the range is all the values that a function can have.
The original coordinate changes to (-1,3),(2,1),(5,-1)and(-1,-2).
When reflected along the y-axis, the coordinates of the x-axis change and there is no change in the y-axis.
So the value of the domain changes while the range remains the same.
The range is { -2 ≤y≤3}
To know more about Transformation
brainly.com/question/11709244
#SPJ5
Olivia is thinking of a number. She says “my number is odd is is a factor of 30 and a multiple of 3” there are two possible numbers Olivia can be thinking of. What are they?
Answer:
3 and 15
Step-by-step explanation:
Let's list the factors of 30:
1, 2, 3, 5, 10, 15, 30
Of these, the odd ones are:
1, 3, 5, 15
Of these, the only numbers that are multiples of 3 are 3 and 15.
The two numbers which Olivia can be thinking about that are odd numbers and multiple of 3 are 3 and 15.
Olivia is thinking of a number which is a factor of 30.
The first thing to do is to write out all the factors of 30. So, we have:
1, 2, 3, 5, 6, 10, 15, 30Now, Olivia made it clear that the number she was thinking about is an odd number and also a multiple of 3.
From the above factors of 30, the two numbers which Olivia can be thinking about that are odd numbers and multiple of 3 are 3 and 15.
Learn more about factors of a number here:
https://brainly.com/question/14801938?referrer=searchResults
Which of the following equations demonstrate that the set of polynomials is not closed under the certain operations?
A. Subtraction: (3x4 + x) - (-2x4 + x) = 5x4
B. Multiplication: (x2 - 5x+3)(x - 5) = x3 - 10x2 +28x - 15
C. Division: (x2+x)=(x + 1) =X
D. Division: (x2 - 5x + 3) + (x-5) = x + -3/X-5
Answer:
D. Division: (x² - 5x + 3) ÷ (x-5) = x + 3/(x - 5)
Step-by-step explanation:
Polynomials are closed under subtraction and multiplication because any subtraction or multiplication of polynomials gives as result another polynomial.
As can be seen in option D, polynomials aren't closed under division because not every division between polynomials gives as result another polynomial.
A boat has an angle of depression of 38° looking down to a submarine. The distance from the
boat to the submarine is 500 yards. How far below sea level is the submarine?
Answer: 307.8 yards
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle of depression of the boat looking down to a submarine, the hypotenuse is the distance from the boat to the submarine, and the opposite side (x) is the distance between the submarine and the sea level:
Replacing with the values given:
Sin 38 = x/ 500
Solving for x
Sin 38 (500) =x
x= 307.8 yards
Feel free to ask for more if needed or if you did not understand something.
what is pi rounded to the nearest 15th
Answer:
3.1415926535 8979
Step-by-step explanation:
bruh just search it in google
A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse? Question 2 options: A) Obtuse B) Right C) Can't be determined D) Acute
Answer:
D: Acute triangle
Step-by-step explanation:
First check whether this could be a right triangle. Using the Pythagorean Theorem, we get:
5^2 + 6^2 = ? = 7^2 This equation is not true, and therefore the triangle is not a right triangle.
The side lengths 5, 6 and 7 are very close to one another, and so the triangle must have essentially similar interior angles, which means that all three angles are acute. Answer D is correct: This is an acute triangle.
Answer: D) Acute
Step-by-step explanation:
Max collected data on height of each of his 20 classmates. The box plot shown represents his data. Pic of data is shown plz help thx
Answer: Though I don't know your question, the median height is 65 inches. The range is 17 and the intequartile range is 8.
Step-by-step explanation:
Median- Center of Data
Range- Highest Value minus Lowest Value
Interquartile Range- Quartile 3 minus Quartile 1
Answer:
Here you go
Step-by-step explanation:
A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population? A.Testing all of the people in my city would be expensive and take too much time B.Testing all of the people in the hospital wouldn't tell them about my specific condition C.Testing all the blood in my body isn't really possible while keeping me alive
Answer:
B. Testing all of the people in the hospital wouldn't tell them about my specific condition
Step-by-step explanation: As explained in the answer, the doctor suspects that you have a specific strain of flu, so it is not useful to test others because the suspected patient is already near. Also, you may be the first carrier of this strain of flu so the doctor would maybe want to focus on any changes found daily.
Please help me out i need it ASAP
Answer: C
Step-by-step explanation:
5 squareroot 2 = 7.07 which if you look up a 45 45 90 triangle calculator it is also eqivelant :)
Solve the inequality - 9x/11 - 7 < -5.
Answer:
x > -22/9
Step-by-step explanation:
-9x/11 < 2 (add 7 to both sides)
-9x < 22 (multiply both sides by 11)
x > 22/-9 (Switch the sign because you are dividing by a negative number)
Answer:
x > -22/9
Step-by-step explanation:
- 9x/11 - 7 < -5
Add 7 to both sides.
- 9x/11 - 7 + 7 < -5 + 7
- 9x/11 < 2
Multiply both sides by 11.
-9x/11 × 11 < 2 × 11
-9x < 22
Divide both sides by -9, reverse sign.
-9x/-9 < 22/-9
x > -22/9
Judy spent 1/3 of her money on clothes and 1/4 of her money on books. What part of her money was spent?
Answer:
Step-by-step explanation:
Part of the money spent = Part of money spent on clothes + part of money spent on books
[tex]=\frac{1}{3}+\frac{1}{4}\\\\=\frac{1*4}{3*4}+\frac{1*3}{4*3}\\\\=\frac{4}{12}+\frac{3}{12}\\\\=\frac{4+3}{12}\\\\=\frac{7}{12}[/tex]
7/12 part of her money was spent
Answer:
7/12 of her money was spent.
Step-by-step explanation:
That is the sum of the 2 fractions:
1/3 + 1/4 LCM of 3 and 4 is 12 so we have:
4/12 + 3/12
= 7/12.
Expand the logarithm.
log4 (3xyz)2
Answer:
A. 2 log4 (3xyz).
Step-by-step explanation:
Since the logarithm is squared, it can be rewritten as 2 log4 (3xyz).
Hope this [somewhat] helps!
in which number does the digit 5 have a value that is 10 times as great as the digit 5 in the number 4.59?
Answer:
2775.9
Step-by-step explanation:
options are
A) 578
B) 2775.9
C) 134.591
D) 31.757
Value of digit 5 in 4.59 is 0.5 as is is at tenth place after decimal
0.5 = 5/10
ten times of this value = 5/10*10 = 5
Thus, 5 is the value, and hence the number which we require should be at unit place of the required number.
In the given question
A) 578
here 5 is at hundredth place
other way to represent is is 500+70+8
B) 2775.9
here 5 is unit place and is correct option
it can be represented as
2000+ 700+ 70+ 7 + 9/10
c)C) 134.591
here 5 is tenth place after decimal
it can be represented as
100+ 30+ 5 + 5/10+9/100 + 1/1000
d)31.757
here 5 is hundredth place after decimal
it can be represented as
30+ 1 + 7/10+5/100 + 7/1000\
Hence, 2775.9 is correct choice.
Which statement about this figure is true?
A. It has point symmetry
B. It has reflectional-symmetry
C. It has no reflectional symmetry
D. It has rotational symmetry with an angel of rotation if 120*
Answer:
I think its B
Step-by-step explanation:
both sides look the exact same and the body its to line of reflection
You are playing a board game. All even numbers are positive, and all odd numbers are negative. A positive number indicates forward movement, and a negative indicates backward movement. During your last 10 turns, you have gone back 90 spaces. if you spun the same number each time which number did you spin?
Answer:
Step-by-step explanation:
We khow that a positive number means going forward whereas a negative one means going bachward positive ⇒even negative⇒oddwe moved 90 spaces back so we are dealing with a an odd number we played ten timesLet o be the number we spinned ten times :
90= 10 o0= 90/10 o=9We spinned 9 ten times
Solve 6x^2 +5x - 4 = 0 by factoring. Enter each step. please help me.
Answer:
x = -4/3 x =1/2
Step-by-step explanation:
6x^2 +5x - 4 = 0
6 has factors of 3 and 2 and 6 and 1
4 has factors of -4 and 1 and -2 and 2, and -1 and 4
We want +5 in the middle
3* -1 + 4*2 = 5
( 3x+4) ( 2x -1) =0
Using the zero product property
3x+4 =0 2x-1 =0
3x = -4 2x =1
x = -4/3 x =1/2
Answer:
[tex]\frac{1}{2}[/tex] and [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
We can solve this equation using the quadratic formula, which is
[tex]\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}[/tex]
Assuming that with your equation, 6x² + 5x - 4 = 0, a is 6, b is 5, and c is -4.
We can substitute inside the equation.
[tex]\frac{{ - 5 \pm \sqrt {5^2 - 4 \cdot 6\cdot\-4} }}{{2 \cdot6}}}[/tex]
[tex]\frac{{ - 5 \pm \sqrt {25 + 96} }}{{12}}}[/tex]
[tex]\frac{{ - 5 \pm \sqrt {121} }}{{12}}}[/tex]
[tex]\frac{{ - 5 \pm 11 }}{{12}}}[/tex]
Now, we can find our two values by using subtraction/addition and division.
[tex]-5 + 11 = 6\\-5 - 11 = -16[/tex]
[tex]\frac{6}{12} =\frac{1}{2} \\-\frac{6}{12} =-\frac{4}{3}[/tex]
I hope this helped!
There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can we choose a Senator from a chosen state?
Answer:
2
Step-by-step explanation:
A state has 2 senators, so once you choose the state, there are 2 ways you can choose a senator from that state.
A sequence of transformations is described below.
A dilation about a point P
A rotation about another point Q
A vertical stretch about the horizontal line PQ
A reflection over a line PQ
Answer: Neither angle measures nor segment lengths
How many terms are in the following expression 55+ 14n -2m +3p
Answer:
4 terms
Step-by-step explanation:
There are 4 terms in the given expression:
=> 55
=> 14n
=> -2m
=> 3p
PLSSSSSSSS HELP (2 + 7i) - (6 + 8i) + (10 - 10i)
Answer:
6-11i
Step-by-step explanation:
(2 + 7i) - (6 + 8i) + (10 - 10i)
Distribute the minus sign
(2 + 7i) - 6 - 8i + (10 - 10i)
Combine like terms
2-6 +10 +7i-8i-10i
6 -11i
I need help on algebra
Answer:
1) 5x³ + 3x²
2) 25 - 3x⁵
3) -4ab + 2a² + 26
4) p²q³ + pq
Step-by-step explanation:
Like terms are expressions like 3x and 2x or 5x² and 8x².
1) x² + 5x³ + 2x²
5x³ + 3x²
2) -2x⁴ + 16 + 2x⁴ + 9 - 3x⁵
-2x⁴ + 2x⁴ + 25 - 3x⁵
25 - 3x⁵
3) ab - a² + 4² - 5ab + 3a² + 10
ab - a² + 16 - 5ab + 3a² + 10
ab - a² - 5ab + 3a² + 26
ab - 5ab + 2a² + 26
-4ab + 2a² + 26
4) 3p²q² - 3p²q³ + 4p²q³ - 3p²q² + pq
3p²q² + p²q³ - 3p²q² + pq
p²q³ + pq
Square ABCD has vertices at A(-1,3) B(0,7) C(4,6) and D(3,2). How many units is the perimeter of square ABCD
Answer:
16.492422502 units or 4√17 units
Step-by-step explanation:
The Perimeter of a Square can be defined as the Addition of it's 4 sides or the Multiplication of 4 and one of its sides.
This means,
The perimeter of square = a + b + c + d
or
4 × any of the sides because the sides of a square are equal to one another.
In the above question, we are given vertices at A(-1,3) B(0,7) C(4,6) and D(3,2)
The formula to solve for this is
√(x2 - x1)² + (y2 - y1)² when you have vertices: (x1 , y1 ) and (x2 , y2)
For Side AB: A(-1,3), B(0,7)
= √(x2 - x1)² + (y2 - y1)²
= √(0- (-1))² + (7 - 3)² = √1² + 4² = √1 + 16 = √17
For Side BC: B(0,7), C(4,6)
√(x2 - x1)² + (y2 - y1)²
= √(4 - 0)² + (6 - 7)² = √4² + 1² = √16 + 1 = √17
For Side AD : A(-1,3), D(3,2)
= √(x2 - x1)² + (y2 - y1)²
= √(3- (-1))² + (2 - 3)² = √4² + (-1)² = √16 + 1= √17
For Side CD: C(4,6), D(3,2)
= √(x2 - x1)² + (y2 - y1)²
= √(3 - 4)² + (6 - 2)² = √-1² + 4² = √1 + 16 = √17
From the above calculations we can side that sides AB = BC = AC = CD
Hence the perimeter of square ABCD can be calculated as 4 × √17 or √17 + √17 + √17 + √17
= 16.492422502 units or 4√17 units
To fill up a car with 16 gallons cost $30.24. Which of the following is an equation that determines the
cost c for g gallons of gas?
Answer:
30.24/16= $1.89 per gallon = c/g
Step-by-step explanation:
c = $30.24
g = 16
Divide c/g
Answer:
g gallon = $1.89 g
Step-by-step explanation:
Gallon = g
16 gallons = 16 g
Cost = $30.24
So,
16 gallons = $30.24
1 gallon = $30.24/16
1 gallon = $1.89
g gallon = $1.89 g