Micah's best long jump is 3 meters long.
In this question we have been given Avi and Micah are teammates on a track and field team.
We need to find the how long is Micah's best long jump.
Let Micah's best long jump is x meters and Avi's best long jump is y meters.
Avi's best long jump is 3 1/2 meters.
⇒ y = 3 1/2 meters
We write this improper fraction as proper fraction.
3 1/2 = 7/2
Also, Avi's best long jump is 1 1/6 times as long as Micah's.
So, we get an equation
y = (1 1/6) * x
We write improper fraction 1 1/6 as 7/6
So equation becomes,
y = 7/6 * x
Subatitute the value of y
7/2 = 7/6 * x
x = (7/2)/(7/6)
x = 6/2
x = 3 meters
Therefore, Micah's jump is 3 meters long.
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WHAT IS a^4 + b^4
Urgent!
The solution to the expression a⁴ + b⁴ is 641 when a = 2 and b = 5
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
a = 2
b = 5
Also, from the question, we have
a^4 + b^4
Express the exponents in the above expression properly
So, we have the following representation
a⁴ + b⁴
Substitute the known values in the above equation, so, we have the following representation
a⁴ + b⁴ = 2⁴ + 5⁴
Evaluate the exponents
'This gives
a⁴ + b⁴ = 16 +625
Evaluate the sum
'This gives
a⁴ + b⁴ = 641
Hence, the solution is 641
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Complete question
Given that a = 2 and b = 5
WHAT IS a^4 + b^4
In the figure, △EBA ≅ △EDC.
Triangles E B A and E D C are connected at point E. Angles A B E and E C D are right angles. Angle A E B and D E C are congruent. Sides B E and E D are congruent.
Because CPCTC, which relationships are true?
Check all that apply.
AE ≅ CE
∠BAE ≅ ∠DCE
∠CDE ≅ ∠BAE
AB ≅ BE
AC ≅ BD
Answer:
1. works
2. works
3. does not work
4. does not work
5. does not work because it does not exist
Step-by-step explanation:
if you have room on your paper, drawing a diagram would be super helpful.
I don't know if I'm 100% right so check with other people before submitting
Answer:The answers are A and B (AE =CE, BAE=CDE)
Step-by-step explanation:
Solve for x. Round to the nearest tenth.
X
21 27
The value of x for the given figure will be equal to √212.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Apply the Pythagorean theorem for the first triangle,
H² = x² - 6²
Apply the Pythagorean theorem for the second triangle,
B² = 27² - x²
Apply the Pythagorean theorem to the third triangle,
H² = 27² - x² - 21²
H² = -x² + 288
x² - 6² = -x² + 288
2x² = 424
x² = 212
x=√212
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3x+8 = 3x+ does it have one solution no solution or infinite solutions? help needed extremely
Answer:
No solution
Step-by-step explanation:
There is no real value of [tex]x[/tex] you can substitute into this equation to make it true.
Two whole number A and B atify the following condition. Find A and B. A and B =44
After solving the equation, the value of A will be equal to 16 and the value of B will be equal to 28.
What is an arithmetic operation?
The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
As per the provided data in the question,
The given equation is,
A + B = 44
Given ratio A:B = 4:7
Let the value of A = 4x and value of B = 7x
4x + 7x = 44
11x = 44
x = 4
A = 4x
A = 4(4) = 16
B = 7x
B = 7(4) = 28.
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Are the following compound statements are logically equivalent P ∧ Q ∨ Q and P ∨ Q?
Answer:
Step-by-step explanation:
This has some significance in logic because if two propositions have the same truth table they are in a logical sense equal to each other – and we say that they are logically equivalent. So: ¬p∨(p∧q)≡p→q, or "Not p or (p and q) is equivalent to if p then q."
...
Logically Equivalent Statements.
p q p→q
F F T
V-(j+y)=61y+82
solve for y
The value of expression in terms of y is y = (v-j-82)/62
What is expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given that an expression v-(j+y)=61y+82
Solving for y,
v-(j+y)=61y+82
v-j-y = 61y+82
v-j-82 = 61y+y
v-j=92 = 62y
y = (v-j-82)/62
Hence, The value of expression in terms of y is y = (v-j-82)/62
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Write an equation to represent this scenerio
You are about to take a major assessment, and each question is one two types. Multiple-choice questions are worth 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points. Let x represent the number of multiple-choice questions, and let y represent the number of short-response questions.
The equation to represent this scenario is 2x+4y = 100
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
The worth of x number of multiple-choice questions = 2x
The worth of y number of short-response questions = 4y
Assessment is worth 100 total points.
So, the equation to represent this scenario is 2x+4y = 100
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Can someone please help me with this assignment? I will mark your answer brainliest! :)
Multiply. Write your answer as a fraction in simplest form.6x5/9
Answer:
10/3
Step-by-step explanation:
6 × 5 ÷ 9 = 30/9
However, you will realize that the numerator (30) and denominator (9) both are multiples of 3. That means we can divide the numerator and denominator by 3 to get an equivalent fraction:
(30 ÷ 3)/(9 ÷ 3) = 10/3
Therefore, the answer is 10/3
What is the length of the mid-segment of a trapezoid whose vertices are I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)?
The length of the mid-segment of the given trapezoid will be 8.5.
What is quadrilateral?A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.
In other meaning, a quadrilateral is a kind of polygon in which four sides for example rectangle, square, and parallelogram are quadrilateral.
As per the given vertices,
I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)
The trapezoid has been plotted below.
The length of LK = 3 - (-3) = 6 units.
Length IJ = 8 - (-3) = 11 units
The length of midsegment x = (11 + 6)/2 = 17/2 = 8.5
Hence "The supplied trapezoid's mid-segment will be 8.5 inches long.".
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Rationalise the denominator 1/5-root 2
Answer:
the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).
Step-by-step explanation:
Correctly me if im wrong. To rationalize the denominator of the fraction 1/(5^(1/2)-2), we can use the conjugate of the denominator. The conjugate of a+b is a-b, so the conjugate of 5^(1/2)-2 is 5^(1/2)+2. We can then multiply the numerator and denominator of the fraction by the conjugate to obtain:
1/(5^(1/2)-2) * (5^(1/2)+2)/(5^(1/2)+2)
= (1*(5^(1/2)+2)) / ((5^(1/2)-2)*(5^(1/2)+2))
= (5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)
Notice that we can further simplify this expression by substituting 5^(1/2) with x and expanding the denominator:
(5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)
= (x+2) / (x^2 - 2x - 4)
= (x+2) / (x-2)(x+2)
The denominator of this expression can be further simplified by factoring out x-2, which gives us:
(x+2) / (x-2)(x+2)
= (x+2) / (x-2)(x-2 + 4)
= (x+2) / (x-2)(x^2 - 2x + 4 - 4)
= (x+2) / (x-2)(x^2 - 2x)
= (x+2) / (x-2)((x-1)(x+1))
Finally, we can use the fact that x-1 and x+1 are factors of x^2-2x, which means that we can factor out x-1 and x+1 from the denominator to obtain the fully simplified expression:
(x+2) / (x-2)(x^2 - 2x)
= (x+2) / (x-2)(x-1)(x+1)
= (x+2) / ((x-2)(x-1)(x+1))
Therefore, the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).
solve the given initial-value problem. the de is homogeneous. xy2 dy dx = y3 − x3, y(1) = 2
Answer: The differential equations is
y3 3x3logx = 8x3.
Step-by-step explanation:
break the given original- value problem. The DE is homogeneous. xy2dy/ dx = y3- x3; y( 1) = 2.
result
Given a homogenous discriminational equation, xy2 dy/ dx = y3- x3
xy2dy/ dx = y3- x3
dy/ dx = ( y3- x3)/ xy2
dy/ dx = (( y/ x) 3- 1)/( y2/ x2)---( 1)
Put y/ x = v ⇒ y = xv
separatew.r.t x
dy/ dx = x.dv/ dx v
Equation( 1) becomes,
⇒ dv/ dx v = ( v3- 1)/ v2
⇒ dv/ dx = (( v3- 1)/ v2)- v
⇒ dv/ dx = ( v3- 1- v3)/ v2
v2. dv = -1/x.dx
Integrate on both sides, we get
∫ v2. dv = ∫- 1/x.dx
v3/ 3 = - logx C
1/3( y3/ x3)) log x = C( 2)
Now, given that y( 1) = 2
Substituting y = 2 and x = 1 in equation( 2)
(1/3) ×(23/13)) log 1 = C
C = 8/3
From equation( 2), we get
⇒( y3/ 3x3) logx = 8/3
thus, the needed differential equation is y3 3x3logx = 8x3.
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Which of these points is closest to the point (7,1)?
A
(4,1)
B
(7,-1)
C.
(7,4)
D
(11,1)
Answer:
B (7,-1)
Step-by-step explanation:
(7,-1) is 2 points away from (7,1).
(4,1) and (7,4) are both 3 points away. (11,1) is 4 points away.
That makes B (7,-1) the closest to (7,1)
34×3333333 and then the answer n×454 = x
[tex]34\times3333333=n[/tex]
[tex]34\times3333333=113333322(n)[/tex]
[tex]n\times454=x[/tex]
[tex]113333322(n)\times454=x[/tex]
[tex]113333322(n)\times454=51453328188(x)[/tex]
[tex]\fbox{x = 51453328188}[/tex]
Which of the following are equivalent fractions?
2 / 3 , 4/6
Answer: 1/2
Step-by-step explanation:
:D
WILL GIVE BRAINLIST AND EXTRA POINTS TO BEST ANSWER PLEASE HLEP
7. Melanie bought some pizza for $2.50 per pound and hot dogs for $1.50 per pound. She spent a total of $30. Use the graph below to sketch all the possible combinations of pizza, p, and hot dogs, h, Melanie could have bought?
The solutions for the number of pizzas p and hot dogs h is
a) A ( p , h ) = A ( 0 , 20 )
b) B ( p , h ) = B ( 3 , 15 )
c) C ( p , h ) = C ( 6 , 10 )
d) D ( p , h ) = D ( 9 , 5 )
e) E ( p, h ) = E ( 12 , 0 )
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of pizza be = p
Let the number of hot dog = h
The cost of one pizza be = $ 2.50
The cost of one hot dog = $ 1.50
Now , the total amount with Melanie = $ 30
So , the equation will be
2.50p + 1.50h = 30
On simplifying the equation , we get
2.5p + 1.5h = 30 be equation (1)
Multiply equation (1) by 10 , we get
25p + 15h = 300
Now , the values of p and h which will satisfy the equation is
a)
Let p = 0 , h = 20
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 0 ) + 15 ( 20 ) = 300
300 = 300
So , the point A ( 0 , 20 ) satisfies the equation
b)
Let p = 3 , h = 15
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 3 ) + 15 ( 15 ) = 300
75 + 225 = 300
300 = 300
So , the point B ( 3 , 15 ) satisfies the equation
c)
Let p = 6 , h = 10
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 6 ) + 15 ( 10 ) = 300
150 + 150 = 300
300 = 300
So , the point C ( 6 , 15 ) satisfies the equation
d)
Let p = 9 , h = 5
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 9 ) + 15 ( 5 ) = 300
225 + 75 = 300
300 = 300
So , the point D ( 9 , 5 ) satisfies the equation
e)
Let p = 12 , h = 0
The equation is 25p + 15h = 300
Substitute the value of p and h , we get
25 ( 12 ) + 15 ( 0 ) = 300
300 = 300
So , the point E ( 12 , 0 ) satisfies the equation
Hence , The solutions for the number of pizzas p and hot dogs h is
a) A ( p , h ) = A ( 0 , 20 )
b) B ( p , h ) = B ( 3 , 15 )
c) C ( p , h ) = C ( 6 , 10 )
d) D ( p , h ) = D ( 9 , 5 )
e) E ( p, h ) = E ( 12 , 0 )
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I'LL GIVE BRAINLIEST!!
Jessica is building a fence around her garden. For every 3 feet of fencing, the cost is $27. Complete the table below showing the length of the fence and the cost.
Answer:
1, 54, 9, 90
Step-by-step explanation:
3ft=27$, so 1ft=9$. The constant of proportionality is 9 from feet to money so multiply the rest by 9 to get 54, divide backwards to get 9, and then multiply 10 by 9 to get 90.
Answer:
Length : 6 9 10
Cost ($) :54 81 90
Step-by-step explanation:
First, divide 27 by 3 to find the cost of 1 feet fence.
We get the answer 9
Then, to find the length, divide the cost by 9
And to find the cost, multiply the length of fence with 9.
Simple!
(btw I came here for the brainliest especially, so I hope you keep your word:) And hope this helped!)
Parallel and perpendicular through points
The equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5 is 5y + x = -14.
What is a line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
Point (6,-4),
2x - y = 5,
Calculate the slope as the line is perpendicular to line 2x - y = 5
m = 2
The slope of the line perpendicular, m = - 1 / 5
Calculate the equation of the line as shown below,
[tex]y - (-4) = - 1 / 5 (x - 6)[/tex]
5 (y + 4) = -x + 6
5y + 20 = -x + 6
5y + x = -14
Therefore, the equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5 is 5y + x = -14.
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The complete question is:
What is an equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5?
How to figure out the unit rate of 4/5 cup of lime juice for every 2 cups of yogurt what is the rate in cups of lime juice per cup of yogurt
Answer:
i think the answer is 2/5
Step-by-step explanation:
Find the measure of <1
A. 30 degree
B. 122 degree
C. 92 degree
D. 58 degree
Help!!!
(Picture is provided)
Answer: D. 58 degree
Step-by-step explanation:
A triangle has a total of 180 degrees
92 + 30 = 122 degree
180 - 122 = 58 degree
So, the answer is D. 58 degree
An airplane can level 1,500 miles in 4.5 hours at a constant speed how long will it take the airplane to travel 200 miles
Answer: 0.6 hours
Step-by-step explanation:
We will set up a proportion to help us solve.
[tex]\displaystyle \frac{1,500\; \;miles}{4.5\;\;hours} =\frac{200\;\;miles}{x\;\;hours}[/tex]
Next, we will cross-multiply and solve by multiplying and using inverse operations.
1,500 * x = 200 * 4.5
1,500x = 900
x = 0.6 hours
need help asap! 100 points
also the option for "This interpretation ___ in the context of the problem."
is "Makes sense" and "Does Not Make sense"
and for "Based on the observations above, it is clear that an appropriate domain for the function is ______"
is: all real numbers
non negative real numbers
real numbers in a a
whole numbers (0,1,2,....)
positive integers (0,1,2,3,....)
integers in a
What is the function?
The function in this problem is defined as follows:
f(x) = 6x - 1.
Giving how many points a player is awarded when a dice of x is rolled.
The possible values at which the dice can land is up:
1,2,3,4,5,6.
Then the numeric values of the function are calculated replacing x by their values.
The only inputs that make sense are 1,2,3,4,5,6, as they are the values at which the dice can land. For example, a dice cannot land on neither 5.5 nor 10.
Missing Information
The function in this problem is defined as follows:
f(x) = 6x - 1.
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What is the absolute value of the integer -(-22)?(It is -(-22), not -22).
Answer:
22
Step-by-step explanation:
Knowledge Needed
| | (absolute value) = Makes anything inside positive after solving.
A negative number multiplied or divided by another negative number is positive.
Question
Set up the equation
| -(-22) |
| 22 |
Stays positive.
22
Reggie picked 32 apples in 4 minutes. What is the unit rate?
Answer:
8
Step-by-step explanation:
Based on the given conditions, formulate: 32 / 4 Cross out the common factor
Here is a scale drawing.
The tree has a height of 22 m
Work out the height of the building.
The height of the building is 44 meters
How to determine the height of the building?From the question, we have the following parameters that can be used in our computation:
Height of the tree = 22 m
From the question, we understand that
Scale of the diagram = 2
This means that
Height of the building = Height of the tree * Scale of the diagram
Substitute the known values in the above equation, so, we have the following representation
Height of the building = 22 m * 2
Evaluate
Height of the building = 44 m
Hence, the height is 44 m
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Two stores have the same item for the same price. • Store A offers successive discounts of 5% one week, 10% the next week, and 10% the third week. • Store B offers one discount of 25% the third week. Which offer results in the greater discount? Justify your answer. Show your work.
Answer:
Below
Step-by-step explanation:
10 % OFF means you pay 90% of price
x = original price
Store A : 5% off means price is .95x
then another 10% off would mean .9 * (.95x)
then another 10% off would mean .9 * ( .9 *(.95x)
this equals .7695 x
Store B 25% off means you pay 75%
price is then .75x
price of .75x at store B is < than .7695 x at store A
so B has greater discount
Answer:
Step-by-step explanation: To compare the discounts offered by Store A and Store B, we need to calculate the final price of the item after all discounts have been applied.
For Store A, the successive discounts of 5%, 10%, and 10% can be applied as follows:
The initial price of the item is reduced by 5%, resulting in a price of 0.95 * Price.
The price from step 1 is reduced by an additional 10%, resulting in a price of 0.9 * (0.95 * Price) = 0.855 * Price.
The price from step 2 is reduced by an additional 10%, resulting in a price of 0.9 * (0.855 * Price) = 0.7695 * Price.
For Store B, the single discount of 25% can be applied as follows:
The initial price of the item is reduced by 25%, resulting in a price of 0.75 * Price.
Comparing the final prices of the item at Store A and Store B, we can see that Store B offers a greater discount. The final price of the item at Store A is 0.7695 * Price, while the final price at Store B is 0.75 * Price. Since 0.75 is less than 0.7695, the final price at Store B is lower.
Therefore, Store B offers a greater discount on the item.
1/2(40x-16)=32
What is the solution for x
Answer: x=2
Step-by-step explanation:
1/2(40x-16)=32
20x - 8 = 32
Add 8 on both sides
20x = 40
Divided both sides by 20
x = 2
what is 2+(-8) reinforce
Answer:
-6
Step-by-step explanation:
2+(-8)=-6
The coordinates of points a and b are a(2, 16) and b(22, 4). what are the coordinates of the point that is 34 of the way from a to b?
The coordinates of the point is (17, 7)
How to determine the coordinates of the point?From the question, we have the following parameters that can be used in our computation:
Point A = (2, 16)
Point B = (22, 4)
Ratio = 3/4
The ratio can be expressed as
m : n = 3 : 1
The coordinates of the point can be calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
Substitute the known values in the above equation, so, we have the following representation
Point = 1/(3 + 1) * (3 * 22 + 1 * 2, 3 * 4 + 1 * 16)
So, we have
Point = 1/4* (68, 28)
So, we have
Point = (17, 7)
Hence, the point is (17, 7)
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