Answer:
1. B= 6
2. B= 3.333333333
3. B= 12
Step-by-step explanation:
1. 14/ 2 1/3 (two and one third)=6
2. 14/ 4 1/5(four and one fifth)= 3.333333333
3. 14/ 7/6 (seven sixth)= 12
3.) Explain why we always get an integer when multiplying a radical expression by its conjugate? Provide your own appropriate example with supporting work that matches your explanation.
By answering the above question, we may state that by equation Once more, we can observe that the two conjugates' product is an integer.
What is equation?Using the equals notation (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of three mathematical expressions by a mathematical assertion.
The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are inscribed on opposite sides of a letter. Most of the time, the symbol and the particular software match. e.g., 2x - 4 = 2 is an example.
An integer is always obtained when a radical expression is multiplied by its conjugate since the product has the form[tex]a^2 -b^2[/tex], where a and b are rational numbers. This is so that we may obtain the difference of the squares of the two terms within the radical when we multiply the two conjugates.
Consider the radical expression [tex]\sqrt3 - \sqrt2[/tex] and its conjugate, [tex]\sqrt3 - \sqrt2[/tex] , to understand this. These two expressions can be multiplied as follows:
[tex]\sqrt{\sqrt3 - \sqrt2\\[/tex]
[tex]\sqrt{(\sqrt3 - \sqrt2) ((\sqrt(3 + \sqrt(2)))} = 3 - \sqrt(2 ) = 1$$[/tex]
As a result, we can observe that the two conjugates' product is an integer.
The radical phrase [tex]\sqrt5 - \sqrt3[/tex] and its conjugate, [tex]\sqrt5 +\sqrt3[/tex] , serve as another illustration.
[tex](\sqrt5 -\sqrt3)[/tex]
[tex](\sqrt(5) + \sqrt(3)) = \sqrt(5) \times \sqrt(5) + \sqrt(5) \times \sqrt(3) - \sqrt(3) \times \sqrt(3)[/tex]
[tex](\sqrt5 - \sqrt3)( \sqrt 5+ \sqrt3) = 5 - 3 = 2[/tex]
Once more, we can observe that the two conjugates' product is an integer.
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-3.75q -5q = 26.25 please give me a correct answer!
Answer:
q= -3
Step-by-step explanation:
Help!
Sarah was standing on a dock next to the ocean. She kicked a soccer ball off the dock to her friend in the water. 4 seconds after she kicked the ball it reached a height of 9 feet above the water. It hit the water 6 seconds later.
Write an equation for the path of the rock in y=a(x-h)^2+k and give the height of the dock that she kicked the ball from. Show your work!
Answer:
1) The equation for the of the ball in y = a·(x - h)² + k is;
y = -16·(x - 5)² + 25
2) The height of the dock, d = -375 feet below the water level
Step-by-step explanation:
1) The question is with regards to quadratic function representing projectile motion
The given parameters are;
The height the ball reaches 4 seconds after Sarah kicked the ball = 9 feet
The time the ball hits the water = 6 seconds after reaching the 9 feet height
The form of the quadratic equation representing the motion is given as follows;
y = a·(x - h)² + k = a·x² - 2·a·h·x + a·h² + k
Let 'x' represent the time of motion of the ball, and let 'a', represent the acceleration due to gravity, we have;
The equation for the ball, y = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
h = The horizontal component of the vertex coordinate = 0
Therefore, we have;
When x = 0, y = d
d = -16·(0 - h)² + k = -16·h² + k
d = -16·h² + k
When x = 4, y = 9 - d
9 - d = -16(4 - h)² + k = -16(4 - h)² + k
When x = 2, y = d
d = -16(2 - h)² + k
When x = 6, y = 9
9 = -16(6 - 5)² + k
When x = 8, y = d
d = -16(8 - h)² + k
-16(8 - h)² - (-16(2 - h)²) = 0
h = 5
From 9 - d = -16(4 - h)² + k = -16(4 - 4)² + k
d = 9 - k
9 = -16(6 - h)² + k
k = 9 + 16(6 - 5)² = 25
d = 9 - k = 9 - 25 = -16
Therefore, h = 5, k = 25
The equation for the of the ball in y = a·(x - h)² + k is therefore;
y = -16·(x - 5)² + 25
2) When x = 0, y = d, ∴ d = -16(0 - 5)² + 25 = -375 feet below the water
The height of the dock, d = -375 feet below the water level
5x - 1 - 2x = 20. Solve for x.
Answer:
x = 7
Step-by-step explanation:
Given
5x - 1 - 2x = 20, that is
3x - 1 = 20 ( add 1 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Step-by-step explanation:
5x-1-2x=20
3x-1=20
3x=20+1
3x=21
3x/3=21/3
x=7
-------- hope it helped
A car is purchased for $16,000. After each year, the resale value decreases by 20%. What will the resale value be after 3 years?
Use the calculator provided and round your answer to the nearest dollar.
Pleaseeee answer correctly
Answer: (I REDID THIS ANSWER)
$128
Step-by-step explanation:
20% off of $16,000 = $3,200
20% off of $3,200 = $640
20% off of $640 = $128
Answer= $128
Determine the rate of change from the table below:
Answer:
Plus 4 miles every 2 hours
Hours= +2
Miles= +4
Help pls-
Bram invested $10,000 in an account that earns simple 5% interest annually.
Question 1: How much interest does the account earn in the first 10 years? (Round to the nearest dollar)
Question 2: How much more would the account earn in interest in the first 10 years if the interest compounded continuously? (Round to the nearest dollar)
Answer:
Answer 1: $6,289
Answer 2: $198
Step-by-step explanation:
1-
a(10)=10,000(1+.05)^10
=16,288.95 =16,288-10,000=$6,289
2-
A(t)=pe^rt=a(10)=10,000e^(.05)(10)=16,487-10,000=6487
6487-6289=$198
need help to solve please
Answer:
[tex]\displaystyle m\angle RTU=73^\circ[/tex]
Step-by-step explanation:
Interior Angle of a Circle
An interior angle of a circle is formed at the intersection of two lines that intersect inside a circle.
Lines AC and BD of the figure attached below intersect forming arcs p and q. The measure of the interior angle x is:
[tex]\displaystyle x=\frac{p+q}{2}[/tex]
The question includes the drawing of a circle with lines US and RV intersecting at point T. The measure of the interior angle RTU is:
[tex]\displaystyle m\angle RTU=\frac{68^\circ+78^\circ}{2}[/tex]
[tex]\displaystyle m\angle RTU=\frac{146^\circ}{2}[/tex]
[tex]\boxed{\displaystyle m\angle RTU=73^\circ}[/tex]
Indiana is hiking at a rate of 5 miles per hour. At this rate, how long will it take her to hike 22 miles?
[tex]v =\dfrac{d}{t}[/tex]
[tex]5 = \dfrac{22}{t}[/tex]
[tex]t = \dfrac{5}{22}[/tex]
She will take [tex]\dfrac{5}{22}[/tex] hours or 13 minutes and 38 secs.
Which of the sets of ordered pairs represents a function? (5 points)
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
Group of answer choices
Only A
Both A and B
Neither A nor B
Only B
Answer:
Both a and b
Step-by-step explanation:
PLEASE HELP FAST...WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER
3. What is the length of segment AB? Show or explain how you know.
Answers
I got answer 16.9
Step-by-step explanation:
1. Let's first look at triangle XYC. We know angle Y is 90 degrees because it has the symbol. and it is given that Angle X 45 degrees. Using the triangle interior angle theoreom, a triangle has 180 degrees so Angle C is 45 degrees. Know let find the sides, First we can deduce XY is 5 cm because of the triangle midsegment theorem XY is half of BC so since we know BC is 10 that means XY is 5. Then applying 45-45-90 triangle rules, XY=5, YC=5 and XC=[tex]5\sqrt{2}[/tex].
2.Now let look at the triangle XBC. Let find one missing angles. In the triangle . A angle bisector XC bisects XY and BC . Using that information Angle C of XYC = Angle C of XBC. So angle C=45 degrees. Knowing looking at the main triangle ABC Angle A=30, Angle C= 45+45=90 and Angle B=60 by interior triangle theorem. So going back to Angle X so angle x is 75 degrees due to interior triangle theorm. Also since Y=90 degrees it forms a linear pair to triangle AXY so Y=90 for AXY
Now let apply 30-60-90 triangle rules to AXY. XY =5, AY=[tex]5\sqrt{3}[/tex] and AX=10.
Finally. Apply 30-60-90 triangle rules to ABC. AC=[tex]5\sqrt{3}[/tex] +5 BC=10 and AB should turrn out to be 16.9.
This may not be right,but good luck:)
the volume of a cylinder is 72 pi cm^3. if the radius is 3cm, what is it the height of the cylinder?
The height of the cylinder is 8cm
The formula for calculating the volume of the cylinder is expressed as;
[tex]V = \pi r^2 h[/tex]
r is the radius
h is the height
Substitute the given parameters into the formula:
[tex]V = \pi r^2 h\\72 \pi = \pi \times 3^2h\\72 = 9h\\h=\frac{72}{9}\\h = 8cm[/tex]
Hence the height of the cylinder is 8cm
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A line has a slope of -
and a y-intercept (vertical intercept) of 9.
The first one is correct you take the slope and multiple it by x and then add or subtract your y intercept depending on whether it is positive or negative. In this case it's positive so it would by -3/7x+9
Nancy divided her marbles into 7 equal piles. What
fraction of the total marbles would 2 piles be?
Mark borrowed $125 from his dad to pay some bills. If he has already paid back $30, how much does he still owe?
*inequalities*
Answer:
Mark borrowed> (Subtracting) 125 dollars, so he will have negative 125 because he took it away. He gives back> (Addition) 30 dollars.
-125+30= -95. So, he owes 95 dollars.
(Easy way)
125-30= 95 dollars.I hope this helped :))
Solve the system for a and b:
9 = ab^2
-72=ab^5
Answer:
a = [tex]\frac{9}{4}[/tex] , b = - 2
Step-by-step explanation:
Given the 2 equations
9 = ab² → (1)
- 72 = a[tex]b^{5}[/tex] → (2)
Divide (2) by (1)
[tex]\frac{-72}{9}[/tex] = [tex]\frac{ab^5}{ab^2}[/tex]
- 8 = b³ ( take the cube root of both sides )
[tex]\sqrt[3]{-8}[/tex] = b , that is
b = - 2
Substitute b = - 2 into (1) and solve for a
9 = a(- 2)² = 4a ( divide both sides by 4 )
[tex]\frac{9}{4}[/tex] = a
A recipe for 2 dozen of Mr.M’s cookies calls for 2 1/2 cups of chocolate chips. He is making 6 dozen cookies. How many cups of chocolate chips does he require? Simplify you answer
Roger restores vintage automobiles. The number of automobiles Roger has restored, f, after n number of years can be described by the equation f(n)=2+5n. What is the rate of change in this situation?
Answer:
The change of rate of the situation is 5.
Step-by-step explanation:
Given f(n) = 2 + 5n. The rate of change is still the same as the slope of the equation. We know that the equation of a line is given as:
f(x) = y = mx + c where m is the slope. In our given equation, f(n) = 2 + 5n = 5n + 2, we see that m = 5 which is our slope.
Therefore, the change of rate of the situation is 5.
Write an equation for the locus of points equal distant from the focus
(-4,2) and the directrix y = 4
Identifying factors
What is 0.00000078 is sceintific notaion
[tex]7.8 \times {10}^{ - 7} [/tex]
Does anyone know the answer to this??
Emily and Mike are sister and brother. Emily has twice as many brothers as sisters, and Mike has as many brothers as sisters. How many girls and boys are there in this family?
Step-by-step explanation:
3x is answer because emily = 2X , mike = x
X + 2x
= 3x
Help me pleasee. Solve the system by substitution
Answer:
(3, - 2 )
Step-by-step explanation:
Given the 2 equations
4x - 2y = 16 → (1)
y = - 5x + 13 → (2)
Substitute y = - 5x + 13 into (1)
4x - 2(- 5x + 13) = 16 ← distribute and simplify left side
4x + 10x - 26 = 16
14x - 26 = 16 ( add 26 to both sides )
14x = 42 ( divide both sides by 14 )
x = 3
Substitute x = 3 into (2) for corresponding value of y
y = - 5(3) + 13 = - 15 + 13 = - 2
solution is (3, - 2 )
Choose the graph of this equation.
y=−32x−2
__________________________________________________________
Answer:
CStep-by-step explanation:
__________________________________________________________
The answer is C because it matches the other graph from Desmos.
( -1.333,0 ) ( 0,-2 )
( Picture Below )
__________________________________________________________
Hope this helps! <3
__________________________________________________________
The graph of the equation y = -(3/2)x -2 is C.
What is Slope?Slope of a line is defined as the change in the value of y-coordinate with respect to the value of the x-coordinate. It is usually denoted by 'm'.
Slope can also be defined as the tangent of the angle that the line is making with the X-axis.
The equation of a line in slope-intercept form is y = mx + c, where m is the slope and c is the y-intercept.
For y = -(3/2)x -2, m = -3/2 and c = -2
Here slope is negative, so the line will be directing downwards from left to right.
So we eliminate graph B.
y-intercept is the y-coordinate of the point where the line touches with the X-axis. The x-coordinate at that point will be zero.
So we got the a point on the line ( 0, -2 )
Since graph A does not pass through this point, it is also eliminated.
Now we find x-intercept which is the x-coordinate of the point where the line touches with the X-axis. The y-coordinate will be zero there.
So, 0 = -(3/2)x -2
⇒ 2 = -(3/2)x
⇒ x = -4/3
⇒ x = -1.333
So the line touches ( -1.333, 0).
Hence, graph C is the one which satisfies the equation y = -(3/2)x -2.
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Write the equation in the point-slope form given the points (-5,-4) (3,4)
I need help with this question
Answer:
34cm
Step-by-step explanation:
bc i konow
Answer:
no, a right angle is 90 degrees. it isn't.
Step-by-step explanation:
the bottom left angle should look like this: L, which it doesn't.
I NEED HELP PLZ I just have a little trouble on it
Answer: In fraction form it will be 1/160
Step-by-step explanation: Hope this helps :)
What is 2.25% of 3,200 ?
Answer:
72
Step-by-step explanation:
(pls mark me brainliest if u can)
Ur amazing if u understand bearings
Sam's "bearing" is simply the direction in which he's moving, which is the angle made with due East.
From point A to point B, his bearing is 335°, and from point B to C, his bearing is 45°. In both cases, the angle is made with due East from the second point. See the sketch for a rough approximation of this. Note that it is not to scale.
To get it into scale, you have to compute the distances traveled along each bearing.
• Moving at 6 km/h for 20 min = 1/3 h would cover a distance of
(6 km/h) • (1/3 h) = 2 km
• Moving at 10 km/h for 15 min = 1/4 h would mean a distance of
(10 km/h) • (1/4 h) = 2.5 km
In your sketch, 1 cm should represent 500 m = 0.5 km, so the arrow from A to B should have a length of 4 cm, while the arrow from B to C should have a length of 5 cm.