The fraction of the distances of the points A(2·a + 3, 3·a + 4), and B(4 - a, 5 - a) from the x- and y-axis and the value of a > 5, indicates that the value of a is 16.[tex]\overline{4}[/tex]
What is a fraction in mathematics?A fraction is a representation of the amount a part of an item compared to the whole of the item.
The distance from the x-axis to the point A(2·a + 3, 3·a + 4) = 3·a + 4
The distance from the y-axis to the point B(4 - a, 5 - a) = 4 - a
Therefore; 1/5 of the distance from the x-axis to the point A(2·a + 3, 3·a + 4) is (1/5) × (3·a + 4)
6/7 of the distance from the y-axis to the point B(4 - a, 5 - a) is (6/7) × (4 - a)
The details in the question indicates; (1/5) × (3·a + 4) = (6/7) × (4 - a)
However, if a > 5, then 4 - a < 0, while (3·a + 4) > 0, from which we get;
If a > 5, then, (1/5) × (3·a + 4) = (6/7) × (a - 4)
[tex]\dfrac{1}{5} \times (3\cdot a + 4) = \dfrac{6}{7} \times (a -4)[/tex]
7 × (3·a + 4) = 5 × 6 × (a - 4)
21·a + 28 = 30·a - 120
30·a - 21·a = 9·a = 120 + 28 = 148
a = 148/9 = 16.[tex]\overline 4[/tex]
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Solve the area of the following shapes
Find the equation of a line that passes through (-7,2) and is parallel to the line 7x+2y=0
Answer:
write the given equation in a standard form of y = mx + c
7x + 2y = 0
2y = -7x
y = -7/2x
parallel lines have equal gradient
m = -7/2
y - y1 = m(x - x1)
y - 2 = -7/2(x - (-7) )
y - 2 = -7/2( x + 7 )
y - 2 = -7/2x - 49/2
y = -7/2x - 49/2 + 2
y = -7/2 - 45/2
Help pls any one pls fast
Answer:
p=106
Step-by-step explanation:
p and 106 are corresponding so they are =
y=-2x+4y=−2x+4y, equals, minus, 2, x, plus, 4 Complete the missing value in the solution to the equation. ((left parenthesis ,-2),−2)
After solving the equation for x, the resultant answer is (3, -2).
What are equations?The definition of an equation in algebra is a mathematical statement that shows the equivalence of two mathematical expressions.
For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, we have the equation:
y = -2x +4
Now, get value of x for y = -2 as follows:
Fill in the equation with the value of y and find x:
-2 = -2x +4 . . . . use -2 for y
-6 = -2x . . . . . . . subtract 4
3 = x . . . . . . . . . .divide by -2
Therefore, after solving the equation for x, the resultant answer is (3, -2).
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Complete question:
y=−2x+4y, equals, minus, 2, x, plus, 4
Complete the missing value in the solution to the equation.
1. Each month, Billy earns $2000 for working the night shift at Amazon, before taxes and
retirement are taken out. If 8% of his paycheck goes to income taxes, and 10%
automatically goes into retirement, what is Billy's net pay each month?
The net pay of Billy after 8% taxes and 10% retirement policy is $1600.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, From Billy's salary of $2000 8% of his paycheck goes to income taxes, and 10% automatically goes into retirement.
So, To obtain a net salary of Billy we'll subtract the percentage amount of 8% and 10% from the base of $2000.
Therefore, Net pay of Billy is {2000 - (8/100)×2000 - (10/100)×2000}.
= {2000 - 160 - 200}.
= (2000 - 360).
= $1640
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Shelby wants to buy a car and wants the best deal. Dealer #1 wants $100 down, and payments of $100 per month. Dealer #2 wants $10 down, and payments of $250 per month.
can someone help me with this
The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.
The given functions are c(x)=2x, b(x)=x+5 and r(x)=0.75x.
What is the composite function?When the result of one function is used as the input for another, this is known as a composite function.
The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage).
A critical hit has the base damage x multiplied, next the damage reduction is applied to the critical hit. Bonus damage is not subject to damage reduction or critical hits, so this is applied last.
Here, Critical hit × Bonus × Damage reduction
That is, (c·r·b)(x) or (r·c·b)(x)
The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.
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Complete the chart for the given proof. GIVEN: the midpoint of AB <AX = <NY NX = BY PROVE: <X = <Y
Two-column proof
See missing statements and reasons below.
Statement Reason
N is the midpoint of AB GivenAN ≅ NB Definition of a midpointAX ≅ NY GivenBX ≅ BY GivenΔAXN ≅ ΔNYB Side-side-side congruency∠X ≅ ∠Y CPCTCProvedSolve the following rational equation. Be sure to list the NPV’s and verify your solution(s).
[tex]\frac{2}{2x-6}-\frac{x}{x^2-9} =\frac{3}{x-3}[/tex]
Answer:
NPV: ±3x = -2Step-by-step explanation:
You want the solutions to the rational equation ...
[tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}=\dfrac{3}{x-3}[/tex]
RewriteWe choose to rewrite the equation in the form f(x) = 0. We can start by subtracting the term on the right side (from both sides).
[tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}-\dfrac{3}{x-3}=0\\\\\dfrac{2}{2(x-3)}-\dfrac{x}{(x-3)(x+3)}-\dfrac{3}{x-3}=0\\\\\\\dfrac{(x+3)-x-3(x+3)}{(x-3)(x+3)}=0\qquad\text{cancel 2 in first term; common denominator}\\\\\\\dfrac{-3x-6}{(x-3)(x+3)}=0\qquad\text{collect terms}[/tex]
SolutionThe "not-possible values" will be values of x that make the denominator zero: x = ±3. The solution is ...
[tex]-3(x+2)=0\qquad\text{numerator must be zero}\\\\\boxed{x=-2}\qquad\text{divide by -3, subtract 2}[/tex]
CheckIn the original equation, we have ...
[tex]\dfrac{2}{2(-2)-6}-\dfrac{-2}{(-2)^2-9}=\dfrac{3}{(-2)-3}\\\\\dfrac{2}{-10}-\dfrac{-2}{-5}=\dfrac{3}{-5}\\\\-\dfrac{1}{5}-\dfrac{2}{5}=-\dfrac{3}{5}\qquad\text{TRUE}[/tex]
__
Additional comment
We like to write the equation as a single fraction compared to zero so that any common factors can be cancelled from numerator and denominator. This helps prevent extraneous solutions. Here, there are none.
I need help with this fast someone pls I’ll give tons of points
Answer:
look it up
Step-by-step explanation:
What value of P makes this equation true
2p=-3p-6/4
Answer:
The answer is p = -6/3. This is the value of p that makes the original equation true.
Step-by-step explanation:
To solve this equation, we must first isolate the variable p on one side of the equation. To do this, we can use the properties of equality to add or subtract the same value from both sides of the equation.
First, we can subtract 2p from both sides of the equation to get rid of the 2p term on the left side. This gives us 0 = -3p - 6/4.
Next, we can add 6/4 to both sides of the equation to get rid of the constant term on the right side. This gives us 6/4 = -3p.
Finally, we can multiply both sides of the equation by -4/3 to get rid of the coefficient -3 on the right side. This gives us -6/3 = p.
Therefore, the value of p that makes the equation true is p = -6/3.
13. Identify the table that does not represent a function.
The four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e : ( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).
What is Function?
Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.
There are many types of functions in mathematics such as :
Linear Function → f(x) = ax + b
Quadratic Function → f(x) = ax² + bx + c
Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
Logarithmic function → f(x) = ln x
Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...
If function f : x → y , then inverse function f⁻¹ : y → x
Let us now tackle the problem!
According to the definition above, it can be concluded that a function cannot have the same x value.
Of the four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e :
( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).
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3. Lucas and Tucker each have a baseball card collection.
The number of cards in Lucas's collection can be represented by c.
The number of cards in Tucker's collection is 4 times the number in Lucas's collection.
The total number of cards in both collections is 205.
What is c, the number of baseball cards in Lucas's collection?
41 cards
51 cards
820 cards
164 cards
.
●
In ADEF, FDFE. Name two congruent angles.
E
D
F
D-0
Step-by-step explanation:
It is not possible to determine the congruent angles in the given statement, as it is incomplete and does not provide enough information. In order to determine congruent angles, we need to know the shape and the specific angles being compared. For example, if the statement was "In a triangle ABC, angles A and C are congruent," then we would know that angles A and C are congruent.
Which is an equation of the line with a slope of 1/4 and a y intercept of -2
use y = mx + b
this is slope and y intercept
m is slope b is y intercept
y = 1/4x -2
A conductor is mapping a trip and records the distance the train travels over certain time intervals?
The speed that the train travels is given as follows:
45 miles per hour.
How to obtain the train's velocity?The train travels at a constant speed, hence the distance traveled by the train over time is modeled by the proportional relationship defined as follows:
d = vt.
In which the variables of the equation are defined as follows:
v is the train's velocity.t is the time.Since the velocity is constant, it's equation is defined as follows:
v = d/t.
One point on the table is given as follows:
(1,45).
Hence the constant velocity of the train is calculated as follows:
v = 45/1 = 45 miles per hour.
Missing InformationThe problem is given by the image shown at the end of the answer.
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There are 121 males and 104 females participating in a marathon. To the nearest percent, what percent of the participants are female?
Answer:
54% are females
Step-by-step explanation:
In total there would be 225 participants -
104 + 121 = 225
Next, Divide 121 and 225. After, multiply by 100.
225/121(100)=53.78
53.78 rounded to the nearest percent is 54.
I hope this helped your question!
Find the inverse of the following function pairs
Answer:
B
Step-by-step explanation:
This is the only pair of functions where [tex]f(g(x))=g(f(x))=x[/tex].
Which ordered pairs lie on the graph of the exponential function f(x) = 3(2)2x ?
Select each correct answer.
Responses
(0,1)
, , begin ordered pair 0 comma 1 end ordered pair, ,
(3,192)
, (3,192) ,
(1,12)
The ordered pair (1, 12) lies on the graph of the exponential function f(x) = 3(2)2x. which is the correct answer would be option (A).
The graph of an exponential function of the form f(x) = abˣ is a curve that passes through the point (0, a), where a is the initial value of the function.
In the given equation, the initial value is 3, so the graph of f(x) passes through the point (0, 3).
To find other points on the graph of f(x), we can plug different values of x into the equation and solve for the corresponding value of y.
For example, if we plug x = 3 into the equation, we get:
f(3) = 3(2)² × 3
= 3(16)
= 48
Therefore, point (3, 48) does not lie on the graph of f(x).
Similarly, if we plug x = 1 into the equation, we get:
f(1) = 3(2)² × 1
= 3(4)
= 12
Thus, point (1, 12) lies on the graph of f(x).
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The theater was full when the movie began. Seventy-six people left
before the movie ended. One hundred twenty-four people remained.
How many people were in the theater when it was full?
The number of people were 200 in the theater when it was full.
What is a theater?
In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.
Given that, the theater was full when the movie began.
76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.
Apply algebraical operation that is addition to find the required answer.
Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.
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I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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Find the Missing Side Lengths
Instructions: Use the ratio of a 45-45-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
x=____
y=_____
The value of x is 13 units and the value of y is 13 units
The given triangle is right triangle
The ratio of the given triangle angles = 45-45-90 degrees
To find the length of the sides we have to use the trigonometric functions
sin θ = Opposite side / hypotenuse
cos θ = Adjacent side / hypotenuse
tan θ = Opposite side / adjacent side
Find the value of x
sin 45 = Opposite side / 13[tex]\sqrt{2}[/tex]
Opposite side = 13[tex]\sqrt{2}[/tex] × sin 45
= 13 units
Similarly
cos 45 = Adjacent side / 13[tex]\sqrt{2}[/tex]
Adjacent side = 13[tex]\sqrt{2}[/tex] × cos 45
= 13 units
Therefore, the length of the side x and y is 13 units
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28+16x^4 i need it factored completely
Answer:
[tex]4(x^4+7)[/tex]
Step-by-step explanation:
Taking out the greatest common factor,[tex]16x^4+28=4(x^4+7)[/tex].
A plane took off from the runway. When the plane had flown 1000 m, it had covered a horizontal distance
of 800 m. Find the measure of the angle to the nearest degree at which the plane rose from the ground.
1000
Answer:
36.9 degrees
Step-by-step explanation:
distance that the plane travels (hypotenuse) = 1000m
horizontal distance (adjacent) = 800m
cos(angle) = adjacent/hypotenuse
cos(angle) = 800/1000
angle = cos-1(800/1000)
angle = 36.9 degrees
What is the sum when you add seven-and-five-twelfths and three-and-seven-twelfths together? Make sure to show the answer in simplest terms
Answer:
11
Step-by-step explanation:
A candy distributor needs to mix a 20% fat-content chocolate with a 60% fat-content chocolate to create 200 kilograms of a 22% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Answer: They must mix __ Kilograms of the 20% chocolate and __ Kilograms of the 60% chocolate.
Using a system of equations to solve the problem, the candy distributor must mix 190 Kilograms of the 20% chocolate and 10 Kilograms of the 60% chocolate to create 200 Kilograms of a 22% fat-content chocolate.
What is a system of equations?A system of equations means two or more equations solved simultaneously.
They are known as simultaneous equations and can be solved graphically, by elimination, by substitution, or matrix.
The fat-content of one of the chocolate blend = 20%
The fat-content of the second chocolate blend = 60%
The expected mixture will have a fat-content = 22%
The total kilograms of the end mixture = 200 kilograms
Let the 20% fat-content chocolate = x
Let the 60% fat-content chocolate = y
x + y = 200 ... Equation 1
Solving for x, x = 200 - y
0.2x + 0.6y = 0.22(200) ... Equation 2
By substitution in Equation 2:
0.2(200 - y) + 0.6y = 44
40 - 0.2y + 0.6y = 44
40 + 0.4y = 44
0.4y = 4
y = 10
x = 200 - y
x = 190 (200 - 10)
Based on the system of equations, 190 kilograms of the 20%-fat-content chocolate must be mixed with 10 kilograms of the 60% fat-content chocolate.
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What fraction is equal to 100%
Any fraction whose numerator is the same number as its denominator will equal 1, which is 100%. Hence, fraction [tex]\frac{5}{5}[/tex] is a fraction that equals 100%.
Answer:
[tex]\frac{5}{5}[/tex]
Step-by-step explanation:
To get a percentage out of a fraction, you divide the fraction and then move the decimal point two places to the right. [tex]\frac{5}{5} =1[/tex] is also equal to 1.0
Move the decimal two places to the right and you get 100%
f(x) = 5x-10 and g(x) = -x+4
Calculate f(-3)
The value of f(-3) if f(x) = 5x - 10 and g(x) = -x + 4 is -25.
What is the equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Given:
f(x) = 5x - 10 and g(x) = -x+4
Calculate the f(-3) by putting the value of x = -3 as shown below,
f(x) = 5(-3) - 10
f(x) = - 15 - 10
f(x) = -25
Therefore, the value of f(-3) if f(x) = 5x-10 and g(x) = -x+4 is -25.
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Helppppp!!!!!!! Please
Then translons the resulting image units to the right is y=0 5 units.
What is line?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that are inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Reflect [tex]$\triangle P Q R$[/tex] across the line [tex]$y=0$[/tex]. we can get [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex]. then translate [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex] 5 units to the right. we can get s STU. So the answer is A. y=0 5 units.
A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
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Given NEB NE is 7.5cm and TAN of B is 4 Fill in the rest of the triangle.
Answer:
Hope the picture will help you........